v.n. shastin 1, r.kh. zhukavin 1, k.a. kovalevsky 1, v.v. tsyplenkov 1, s.g. pavlov 2, h.-w. hübers...

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V.N. Shastin 1 , R.Kh. Zhukavin 1 , K.A. Kovalevsky 1 , V.V. Tsyplenkov 1 , S.G. Pavlov 2 , H.-W. Hübers 2 . N.V. Abrosimov 3 , H. Riemann 3 1 Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod, Russian Federation 2 Institute of Planetary Research, Germany Aerospace Center, Berlin, Germany 3 Institute of Crystal Growth, Berlin, Germany Supported by RAS, RFBR (Russia), DFG (Germany) IPM RAS IKZ Кремниевые лазеры для терагерцового диапазона (Silicon lasers for terahertz domain)

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VN Shastin1

RKh Zhukavin1 KA Kovalevsky1 VV Tsyplenkov1 SG Pavlov2 H-W Huumlbers2

NV Abrosimov3 H Riemann 3

1Institute for Physics of Microstructures Russian Academy of Sciences Nizhny Novgorod Russian Federation

2Institute of Planetary Research Germany Aerospace Center Berlin Germany

3Institute of Crystal Growth Berlin Germany

Supported by RAS RFBR (Russia) DFG (Germany)

IPM RAS

IKZ

Кремниевые лазеры для терагерцового диапазона

(Silicon lasers for terahertz domain)

Contents

Unstressed silicon Experimental results Donor state relaxation rates

Stressed silicon Experimental results Donor state relaxation rates

1s(A1)

1s(T2)

1s(E)

-

P As Sb Bi

2p0

2s2pplusmn

10 m

eV

1s(T28)

1s(T27)

Conduction Band

Group V Donors in Silicon

+~1r ~(r)

Состояния мелких доноров в кремнии

1AE

0 0 0 0 1-1=

0 0 1-1 0 0=

1-1 0 0 0 0=

T2

1 1-1-1 0 0

=

1 1 1 1-2-2=

E

1 1 1 1 1 1=

A1 6

1

12

1

2

1

2

1

2

1

2

1

Principle state lifetimes

P As

Pump-probe ~30 ps ~20 ps

FWHM SiN ~26 ps NTD 12х1014 cm-3

FWHM Si28 ~80 ps

2pplusmn state (A1 E)

Exp P As

Pump-probe ~30 ps ~50 ps

FWHM SiN

~32 ps NTD 12х1014 cm-3

~30 ps7х1014 cm-3

FWHM Si28

~160 ps

2p0 state (A1 E)

Theory P As Sb

2р0 (ps)

А1 40 50 50

Е 32 56 50

T2 37 62 54

2рplusmn (ps)

52 47 52

Layout of the experiment

TEA CO2 laser excitation unstressed silicon (Family of experimental data)

Operating temperature

5 10 15 20 25 30 35

SiP SiSb SiBiSiAs

Si l

aser

s em

issi

on a

u

temperature K

Donors concentration 11015 - 5 1015 cm-3

Threshold intensity 10-100 kWcm2

Small signal gain 01-02 cm-1

120 140 160 180 200 220 240

36 42 48 54 60 66 72

Si l

aser

em

issi

on (

au

)

frequency (THz)

wavenumber (cm-1)

SiAs SiBiSiPSiSb

Emission spectra

2times3times7 mm3

THz

Quantum efficiency Exp Theory up to 10

SiP experiment(106 microm TEA CO2 laser excitation)

P donor THz output vs pump intensity under different stress

50 100 150 2000

10

10

0

em

issi

on a

u

frequency cm-1

SiP [100] 023 kbar 065 12

0

00 05 10 15 20 250

100

200

300

400

500

600 180 75 50 25 17 9 5 3 2

stress kbar

emis

sion

mV

SiP [100]

S=493x255 mm2

pump

kWcm2(a)

2 20 2000

100

200

300

400

500

600059

0

043

029118

147

177

221

266

SiP [100]

S=493x255 mm2

em

issi

on

mV

pump CO2 kWcm2

stress kbar

Sb donor THz output vs pump intensity and compressive stress

00 02 04 06 08 10 12 14 160

5

10

15

20

25

30

35

40

45

pump (kWcm2)

200 85 50 30 10 16 023 015

em

issi

on m

V

stress kbar

SiSb [100]

65x49x32 mm3

Nd= 1015cm-3

02 2 20 2000

5

10

15

20

25

30

35

40

45

65x49x32 mm3

SiSb[100]

emis

sion

mV

pump kWcm2

046023

0

081

105117128

stress kbar

SiSb experiment(106 microm TEA CO2 laser

excitation)

150 160 170 180 190 200

00 10 201720

1725

1730

10

0

0

emis

sion

au

frequency cm-1

SiSb [110] 624 bar 936 bar 1872 bar

0

sress kbar

cm-1

2p0 - 1s(B

2)

200kWcm2 correspond 1025quantcm2s

0 1 2 3 400

01

02

03

04 04 06 08

SiSb em

issi

on V

pump intensity 106 m kWcm2

stress [100] kbar 005 01 02 03

00 05 10 15 2(a) photon flux density 1023 quantcm2

SiSb Under Q-switch CO2 laser pump

Least value of threshold intensity ~150Wcm2

0 1 2 3 40

10

20

30

40

50

60

SiAs

[100] 617x(47x275) mm3

emis

sion

mV

stress kbar

200 150 85 50 30 10 16 1

pump (kWcm2)

2 20 2000

10

20

30

40

50

60 3831

283254

196

17

110810530250

SiAs[100]

617x(47x275) mm3

em

issi

on m

V

pump kWcm2

stress kbar

SiAs experiment(106 microm TEA CO2 laser

excitation)

As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

As donor THz output vs pump intensity under different stress

160 180 200 220

10

0

0

00 05 10 15 20 25

170

175

180

185

190

195

200

205

210

215

220

2p+-

1s(T2)

2p0 1s(B

2)

давление кбар

част

ота

см

-1SiAs [100]

em

issi

on a

u

frequency cm-1

240 bar 360 600

frequency

cm

-1

stress kbar

0

0 1 2170

220

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

Contents

Unstressed silicon Experimental results Donor state relaxation rates

Stressed silicon Experimental results Donor state relaxation rates

1s(A1)

1s(T2)

1s(E)

-

P As Sb Bi

2p0

2s2pplusmn

10 m

eV

1s(T28)

1s(T27)

Conduction Band

Group V Donors in Silicon

+~1r ~(r)

Состояния мелких доноров в кремнии

1AE

0 0 0 0 1-1=

0 0 1-1 0 0=

1-1 0 0 0 0=

T2

1 1-1-1 0 0

=

1 1 1 1-2-2=

E

1 1 1 1 1 1=

A1 6

1

12

1

2

1

2

1

2

1

2

1

Principle state lifetimes

P As

Pump-probe ~30 ps ~20 ps

FWHM SiN ~26 ps NTD 12х1014 cm-3

FWHM Si28 ~80 ps

2pplusmn state (A1 E)

Exp P As

Pump-probe ~30 ps ~50 ps

FWHM SiN

~32 ps NTD 12х1014 cm-3

~30 ps7х1014 cm-3

FWHM Si28

~160 ps

2p0 state (A1 E)

Theory P As Sb

2р0 (ps)

А1 40 50 50

Е 32 56 50

T2 37 62 54

2рplusmn (ps)

52 47 52

Layout of the experiment

TEA CO2 laser excitation unstressed silicon (Family of experimental data)

Operating temperature

5 10 15 20 25 30 35

SiP SiSb SiBiSiAs

Si l

aser

s em

issi

on a

u

temperature K

Donors concentration 11015 - 5 1015 cm-3

Threshold intensity 10-100 kWcm2

Small signal gain 01-02 cm-1

120 140 160 180 200 220 240

36 42 48 54 60 66 72

Si l

aser

em

issi

on (

au

)

frequency (THz)

wavenumber (cm-1)

SiAs SiBiSiPSiSb

Emission spectra

2times3times7 mm3

THz

Quantum efficiency Exp Theory up to 10

SiP experiment(106 microm TEA CO2 laser excitation)

P donor THz output vs pump intensity under different stress

50 100 150 2000

10

10

0

em

issi

on a

u

frequency cm-1

SiP [100] 023 kbar 065 12

0

00 05 10 15 20 250

100

200

300

400

500

600 180 75 50 25 17 9 5 3 2

stress kbar

emis

sion

mV

SiP [100]

S=493x255 mm2

pump

kWcm2(a)

2 20 2000

100

200

300

400

500

600059

0

043

029118

147

177

221

266

SiP [100]

S=493x255 mm2

em

issi

on

mV

pump CO2 kWcm2

stress kbar

Sb donor THz output vs pump intensity and compressive stress

00 02 04 06 08 10 12 14 160

5

10

15

20

25

30

35

40

45

pump (kWcm2)

200 85 50 30 10 16 023 015

em

issi

on m

V

stress kbar

SiSb [100]

65x49x32 mm3

Nd= 1015cm-3

02 2 20 2000

5

10

15

20

25

30

35

40

45

65x49x32 mm3

SiSb[100]

emis

sion

mV

pump kWcm2

046023

0

081

105117128

stress kbar

SiSb experiment(106 microm TEA CO2 laser

excitation)

150 160 170 180 190 200

00 10 201720

1725

1730

10

0

0

emis

sion

au

frequency cm-1

SiSb [110] 624 bar 936 bar 1872 bar

0

sress kbar

cm-1

2p0 - 1s(B

2)

200kWcm2 correspond 1025quantcm2s

0 1 2 3 400

01

02

03

04 04 06 08

SiSb em

issi

on V

pump intensity 106 m kWcm2

stress [100] kbar 005 01 02 03

00 05 10 15 2(a) photon flux density 1023 quantcm2

SiSb Under Q-switch CO2 laser pump

Least value of threshold intensity ~150Wcm2

0 1 2 3 40

10

20

30

40

50

60

SiAs

[100] 617x(47x275) mm3

emis

sion

mV

stress kbar

200 150 85 50 30 10 16 1

pump (kWcm2)

2 20 2000

10

20

30

40

50

60 3831

283254

196

17

110810530250

SiAs[100]

617x(47x275) mm3

em

issi

on m

V

pump kWcm2

stress kbar

SiAs experiment(106 microm TEA CO2 laser

excitation)

As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

As donor THz output vs pump intensity under different stress

160 180 200 220

10

0

0

00 05 10 15 20 25

170

175

180

185

190

195

200

205

210

215

220

2p+-

1s(T2)

2p0 1s(B

2)

давление кбар

част

ота

см

-1SiAs [100]

em

issi

on a

u

frequency cm-1

240 bar 360 600

frequency

cm

-1

stress kbar

0

0 1 2170

220

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

1s(A1)

1s(T2)

1s(E)

-

P As Sb Bi

2p0

2s2pplusmn

10 m

eV

1s(T28)

1s(T27)

Conduction Band

Group V Donors in Silicon

+~1r ~(r)

Состояния мелких доноров в кремнии

1AE

0 0 0 0 1-1=

0 0 1-1 0 0=

1-1 0 0 0 0=

T2

1 1-1-1 0 0

=

1 1 1 1-2-2=

E

1 1 1 1 1 1=

A1 6

1

12

1

2

1

2

1

2

1

2

1

Principle state lifetimes

P As

Pump-probe ~30 ps ~20 ps

FWHM SiN ~26 ps NTD 12х1014 cm-3

FWHM Si28 ~80 ps

2pplusmn state (A1 E)

Exp P As

Pump-probe ~30 ps ~50 ps

FWHM SiN

~32 ps NTD 12х1014 cm-3

~30 ps7х1014 cm-3

FWHM Si28

~160 ps

2p0 state (A1 E)

Theory P As Sb

2р0 (ps)

А1 40 50 50

Е 32 56 50

T2 37 62 54

2рplusmn (ps)

52 47 52

Layout of the experiment

TEA CO2 laser excitation unstressed silicon (Family of experimental data)

Operating temperature

5 10 15 20 25 30 35

SiP SiSb SiBiSiAs

Si l

aser

s em

issi

on a

u

temperature K

Donors concentration 11015 - 5 1015 cm-3

Threshold intensity 10-100 kWcm2

Small signal gain 01-02 cm-1

120 140 160 180 200 220 240

36 42 48 54 60 66 72

Si l

aser

em

issi

on (

au

)

frequency (THz)

wavenumber (cm-1)

SiAs SiBiSiPSiSb

Emission spectra

2times3times7 mm3

THz

Quantum efficiency Exp Theory up to 10

SiP experiment(106 microm TEA CO2 laser excitation)

P donor THz output vs pump intensity under different stress

50 100 150 2000

10

10

0

em

issi

on a

u

frequency cm-1

SiP [100] 023 kbar 065 12

0

00 05 10 15 20 250

100

200

300

400

500

600 180 75 50 25 17 9 5 3 2

stress kbar

emis

sion

mV

SiP [100]

S=493x255 mm2

pump

kWcm2(a)

2 20 2000

100

200

300

400

500

600059

0

043

029118

147

177

221

266

SiP [100]

S=493x255 mm2

em

issi

on

mV

pump CO2 kWcm2

stress kbar

Sb donor THz output vs pump intensity and compressive stress

00 02 04 06 08 10 12 14 160

5

10

15

20

25

30

35

40

45

pump (kWcm2)

200 85 50 30 10 16 023 015

em

issi

on m

V

stress kbar

SiSb [100]

65x49x32 mm3

Nd= 1015cm-3

02 2 20 2000

5

10

15

20

25

30

35

40

45

65x49x32 mm3

SiSb[100]

emis

sion

mV

pump kWcm2

046023

0

081

105117128

stress kbar

SiSb experiment(106 microm TEA CO2 laser

excitation)

150 160 170 180 190 200

00 10 201720

1725

1730

10

0

0

emis

sion

au

frequency cm-1

SiSb [110] 624 bar 936 bar 1872 bar

0

sress kbar

cm-1

2p0 - 1s(B

2)

200kWcm2 correspond 1025quantcm2s

0 1 2 3 400

01

02

03

04 04 06 08

SiSb em

issi

on V

pump intensity 106 m kWcm2

stress [100] kbar 005 01 02 03

00 05 10 15 2(a) photon flux density 1023 quantcm2

SiSb Under Q-switch CO2 laser pump

Least value of threshold intensity ~150Wcm2

0 1 2 3 40

10

20

30

40

50

60

SiAs

[100] 617x(47x275) mm3

emis

sion

mV

stress kbar

200 150 85 50 30 10 16 1

pump (kWcm2)

2 20 2000

10

20

30

40

50

60 3831

283254

196

17

110810530250

SiAs[100]

617x(47x275) mm3

em

issi

on m

V

pump kWcm2

stress kbar

SiAs experiment(106 microm TEA CO2 laser

excitation)

As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

As donor THz output vs pump intensity under different stress

160 180 200 220

10

0

0

00 05 10 15 20 25

170

175

180

185

190

195

200

205

210

215

220

2p+-

1s(T2)

2p0 1s(B

2)

давление кбар

част

ота

см

-1SiAs [100]

em

issi

on a

u

frequency cm-1

240 bar 360 600

frequency

cm

-1

stress kbar

0

0 1 2170

220

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
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  • Slide 11
  • Slide 12
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  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

+~1r ~(r)

Состояния мелких доноров в кремнии

1AE

0 0 0 0 1-1=

0 0 1-1 0 0=

1-1 0 0 0 0=

T2

1 1-1-1 0 0

=

1 1 1 1-2-2=

E

1 1 1 1 1 1=

A1 6

1

12

1

2

1

2

1

2

1

2

1

Principle state lifetimes

P As

Pump-probe ~30 ps ~20 ps

FWHM SiN ~26 ps NTD 12х1014 cm-3

FWHM Si28 ~80 ps

2pplusmn state (A1 E)

Exp P As

Pump-probe ~30 ps ~50 ps

FWHM SiN

~32 ps NTD 12х1014 cm-3

~30 ps7х1014 cm-3

FWHM Si28

~160 ps

2p0 state (A1 E)

Theory P As Sb

2р0 (ps)

А1 40 50 50

Е 32 56 50

T2 37 62 54

2рplusmn (ps)

52 47 52

Layout of the experiment

TEA CO2 laser excitation unstressed silicon (Family of experimental data)

Operating temperature

5 10 15 20 25 30 35

SiP SiSb SiBiSiAs

Si l

aser

s em

issi

on a

u

temperature K

Donors concentration 11015 - 5 1015 cm-3

Threshold intensity 10-100 kWcm2

Small signal gain 01-02 cm-1

120 140 160 180 200 220 240

36 42 48 54 60 66 72

Si l

aser

em

issi

on (

au

)

frequency (THz)

wavenumber (cm-1)

SiAs SiBiSiPSiSb

Emission spectra

2times3times7 mm3

THz

Quantum efficiency Exp Theory up to 10

SiP experiment(106 microm TEA CO2 laser excitation)

P donor THz output vs pump intensity under different stress

50 100 150 2000

10

10

0

em

issi

on a

u

frequency cm-1

SiP [100] 023 kbar 065 12

0

00 05 10 15 20 250

100

200

300

400

500

600 180 75 50 25 17 9 5 3 2

stress kbar

emis

sion

mV

SiP [100]

S=493x255 mm2

pump

kWcm2(a)

2 20 2000

100

200

300

400

500

600059

0

043

029118

147

177

221

266

SiP [100]

S=493x255 mm2

em

issi

on

mV

pump CO2 kWcm2

stress kbar

Sb donor THz output vs pump intensity and compressive stress

00 02 04 06 08 10 12 14 160

5

10

15

20

25

30

35

40

45

pump (kWcm2)

200 85 50 30 10 16 023 015

em

issi

on m

V

stress kbar

SiSb [100]

65x49x32 mm3

Nd= 1015cm-3

02 2 20 2000

5

10

15

20

25

30

35

40

45

65x49x32 mm3

SiSb[100]

emis

sion

mV

pump kWcm2

046023

0

081

105117128

stress kbar

SiSb experiment(106 microm TEA CO2 laser

excitation)

150 160 170 180 190 200

00 10 201720

1725

1730

10

0

0

emis

sion

au

frequency cm-1

SiSb [110] 624 bar 936 bar 1872 bar

0

sress kbar

cm-1

2p0 - 1s(B

2)

200kWcm2 correspond 1025quantcm2s

0 1 2 3 400

01

02

03

04 04 06 08

SiSb em

issi

on V

pump intensity 106 m kWcm2

stress [100] kbar 005 01 02 03

00 05 10 15 2(a) photon flux density 1023 quantcm2

SiSb Under Q-switch CO2 laser pump

Least value of threshold intensity ~150Wcm2

0 1 2 3 40

10

20

30

40

50

60

SiAs

[100] 617x(47x275) mm3

emis

sion

mV

stress kbar

200 150 85 50 30 10 16 1

pump (kWcm2)

2 20 2000

10

20

30

40

50

60 3831

283254

196

17

110810530250

SiAs[100]

617x(47x275) mm3

em

issi

on m

V

pump kWcm2

stress kbar

SiAs experiment(106 microm TEA CO2 laser

excitation)

As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

As donor THz output vs pump intensity under different stress

160 180 200 220

10

0

0

00 05 10 15 20 25

170

175

180

185

190

195

200

205

210

215

220

2p+-

1s(T2)

2p0 1s(B

2)

давление кбар

част

ота

см

-1SiAs [100]

em

issi

on a

u

frequency cm-1

240 bar 360 600

frequency

cm

-1

stress kbar

0

0 1 2170

220

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

Principle state lifetimes

P As

Pump-probe ~30 ps ~20 ps

FWHM SiN ~26 ps NTD 12х1014 cm-3

FWHM Si28 ~80 ps

2pplusmn state (A1 E)

Exp P As

Pump-probe ~30 ps ~50 ps

FWHM SiN

~32 ps NTD 12х1014 cm-3

~30 ps7х1014 cm-3

FWHM Si28

~160 ps

2p0 state (A1 E)

Theory P As Sb

2р0 (ps)

А1 40 50 50

Е 32 56 50

T2 37 62 54

2рplusmn (ps)

52 47 52

Layout of the experiment

TEA CO2 laser excitation unstressed silicon (Family of experimental data)

Operating temperature

5 10 15 20 25 30 35

SiP SiSb SiBiSiAs

Si l

aser

s em

issi

on a

u

temperature K

Donors concentration 11015 - 5 1015 cm-3

Threshold intensity 10-100 kWcm2

Small signal gain 01-02 cm-1

120 140 160 180 200 220 240

36 42 48 54 60 66 72

Si l

aser

em

issi

on (

au

)

frequency (THz)

wavenumber (cm-1)

SiAs SiBiSiPSiSb

Emission spectra

2times3times7 mm3

THz

Quantum efficiency Exp Theory up to 10

SiP experiment(106 microm TEA CO2 laser excitation)

P donor THz output vs pump intensity under different stress

50 100 150 2000

10

10

0

em

issi

on a

u

frequency cm-1

SiP [100] 023 kbar 065 12

0

00 05 10 15 20 250

100

200

300

400

500

600 180 75 50 25 17 9 5 3 2

stress kbar

emis

sion

mV

SiP [100]

S=493x255 mm2

pump

kWcm2(a)

2 20 2000

100

200

300

400

500

600059

0

043

029118

147

177

221

266

SiP [100]

S=493x255 mm2

em

issi

on

mV

pump CO2 kWcm2

stress kbar

Sb donor THz output vs pump intensity and compressive stress

00 02 04 06 08 10 12 14 160

5

10

15

20

25

30

35

40

45

pump (kWcm2)

200 85 50 30 10 16 023 015

em

issi

on m

V

stress kbar

SiSb [100]

65x49x32 mm3

Nd= 1015cm-3

02 2 20 2000

5

10

15

20

25

30

35

40

45

65x49x32 mm3

SiSb[100]

emis

sion

mV

pump kWcm2

046023

0

081

105117128

stress kbar

SiSb experiment(106 microm TEA CO2 laser

excitation)

150 160 170 180 190 200

00 10 201720

1725

1730

10

0

0

emis

sion

au

frequency cm-1

SiSb [110] 624 bar 936 bar 1872 bar

0

sress kbar

cm-1

2p0 - 1s(B

2)

200kWcm2 correspond 1025quantcm2s

0 1 2 3 400

01

02

03

04 04 06 08

SiSb em

issi

on V

pump intensity 106 m kWcm2

stress [100] kbar 005 01 02 03

00 05 10 15 2(a) photon flux density 1023 quantcm2

SiSb Under Q-switch CO2 laser pump

Least value of threshold intensity ~150Wcm2

0 1 2 3 40

10

20

30

40

50

60

SiAs

[100] 617x(47x275) mm3

emis

sion

mV

stress kbar

200 150 85 50 30 10 16 1

pump (kWcm2)

2 20 2000

10

20

30

40

50

60 3831

283254

196

17

110810530250

SiAs[100]

617x(47x275) mm3

em

issi

on m

V

pump kWcm2

stress kbar

SiAs experiment(106 microm TEA CO2 laser

excitation)

As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

As donor THz output vs pump intensity under different stress

160 180 200 220

10

0

0

00 05 10 15 20 25

170

175

180

185

190

195

200

205

210

215

220

2p+-

1s(T2)

2p0 1s(B

2)

давление кбар

част

ота

см

-1SiAs [100]

em

issi

on a

u

frequency cm-1

240 bar 360 600

frequency

cm

-1

stress kbar

0

0 1 2170

220

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

Layout of the experiment

TEA CO2 laser excitation unstressed silicon (Family of experimental data)

Operating temperature

5 10 15 20 25 30 35

SiP SiSb SiBiSiAs

Si l

aser

s em

issi

on a

u

temperature K

Donors concentration 11015 - 5 1015 cm-3

Threshold intensity 10-100 kWcm2

Small signal gain 01-02 cm-1

120 140 160 180 200 220 240

36 42 48 54 60 66 72

Si l

aser

em

issi

on (

au

)

frequency (THz)

wavenumber (cm-1)

SiAs SiBiSiPSiSb

Emission spectra

2times3times7 mm3

THz

Quantum efficiency Exp Theory up to 10

SiP experiment(106 microm TEA CO2 laser excitation)

P donor THz output vs pump intensity under different stress

50 100 150 2000

10

10

0

em

issi

on a

u

frequency cm-1

SiP [100] 023 kbar 065 12

0

00 05 10 15 20 250

100

200

300

400

500

600 180 75 50 25 17 9 5 3 2

stress kbar

emis

sion

mV

SiP [100]

S=493x255 mm2

pump

kWcm2(a)

2 20 2000

100

200

300

400

500

600059

0

043

029118

147

177

221

266

SiP [100]

S=493x255 mm2

em

issi

on

mV

pump CO2 kWcm2

stress kbar

Sb donor THz output vs pump intensity and compressive stress

00 02 04 06 08 10 12 14 160

5

10

15

20

25

30

35

40

45

pump (kWcm2)

200 85 50 30 10 16 023 015

em

issi

on m

V

stress kbar

SiSb [100]

65x49x32 mm3

Nd= 1015cm-3

02 2 20 2000

5

10

15

20

25

30

35

40

45

65x49x32 mm3

SiSb[100]

emis

sion

mV

pump kWcm2

046023

0

081

105117128

stress kbar

SiSb experiment(106 microm TEA CO2 laser

excitation)

150 160 170 180 190 200

00 10 201720

1725

1730

10

0

0

emis

sion

au

frequency cm-1

SiSb [110] 624 bar 936 bar 1872 bar

0

sress kbar

cm-1

2p0 - 1s(B

2)

200kWcm2 correspond 1025quantcm2s

0 1 2 3 400

01

02

03

04 04 06 08

SiSb em

issi

on V

pump intensity 106 m kWcm2

stress [100] kbar 005 01 02 03

00 05 10 15 2(a) photon flux density 1023 quantcm2

SiSb Under Q-switch CO2 laser pump

Least value of threshold intensity ~150Wcm2

0 1 2 3 40

10

20

30

40

50

60

SiAs

[100] 617x(47x275) mm3

emis

sion

mV

stress kbar

200 150 85 50 30 10 16 1

pump (kWcm2)

2 20 2000

10

20

30

40

50

60 3831

283254

196

17

110810530250

SiAs[100]

617x(47x275) mm3

em

issi

on m

V

pump kWcm2

stress kbar

SiAs experiment(106 microm TEA CO2 laser

excitation)

As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

As donor THz output vs pump intensity under different stress

160 180 200 220

10

0

0

00 05 10 15 20 25

170

175

180

185

190

195

200

205

210

215

220

2p+-

1s(T2)

2p0 1s(B

2)

давление кбар

част

ота

см

-1SiAs [100]

em

issi

on a

u

frequency cm-1

240 bar 360 600

frequency

cm

-1

stress kbar

0

0 1 2170

220

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

TEA CO2 laser excitation unstressed silicon (Family of experimental data)

Operating temperature

5 10 15 20 25 30 35

SiP SiSb SiBiSiAs

Si l

aser

s em

issi

on a

u

temperature K

Donors concentration 11015 - 5 1015 cm-3

Threshold intensity 10-100 kWcm2

Small signal gain 01-02 cm-1

120 140 160 180 200 220 240

36 42 48 54 60 66 72

Si l

aser

em

issi

on (

au

)

frequency (THz)

wavenumber (cm-1)

SiAs SiBiSiPSiSb

Emission spectra

2times3times7 mm3

THz

Quantum efficiency Exp Theory up to 10

SiP experiment(106 microm TEA CO2 laser excitation)

P donor THz output vs pump intensity under different stress

50 100 150 2000

10

10

0

em

issi

on a

u

frequency cm-1

SiP [100] 023 kbar 065 12

0

00 05 10 15 20 250

100

200

300

400

500

600 180 75 50 25 17 9 5 3 2

stress kbar

emis

sion

mV

SiP [100]

S=493x255 mm2

pump

kWcm2(a)

2 20 2000

100

200

300

400

500

600059

0

043

029118

147

177

221

266

SiP [100]

S=493x255 mm2

em

issi

on

mV

pump CO2 kWcm2

stress kbar

Sb donor THz output vs pump intensity and compressive stress

00 02 04 06 08 10 12 14 160

5

10

15

20

25

30

35

40

45

pump (kWcm2)

200 85 50 30 10 16 023 015

em

issi

on m

V

stress kbar

SiSb [100]

65x49x32 mm3

Nd= 1015cm-3

02 2 20 2000

5

10

15

20

25

30

35

40

45

65x49x32 mm3

SiSb[100]

emis

sion

mV

pump kWcm2

046023

0

081

105117128

stress kbar

SiSb experiment(106 microm TEA CO2 laser

excitation)

150 160 170 180 190 200

00 10 201720

1725

1730

10

0

0

emis

sion

au

frequency cm-1

SiSb [110] 624 bar 936 bar 1872 bar

0

sress kbar

cm-1

2p0 - 1s(B

2)

200kWcm2 correspond 1025quantcm2s

0 1 2 3 400

01

02

03

04 04 06 08

SiSb em

issi

on V

pump intensity 106 m kWcm2

stress [100] kbar 005 01 02 03

00 05 10 15 2(a) photon flux density 1023 quantcm2

SiSb Under Q-switch CO2 laser pump

Least value of threshold intensity ~150Wcm2

0 1 2 3 40

10

20

30

40

50

60

SiAs

[100] 617x(47x275) mm3

emis

sion

mV

stress kbar

200 150 85 50 30 10 16 1

pump (kWcm2)

2 20 2000

10

20

30

40

50

60 3831

283254

196

17

110810530250

SiAs[100]

617x(47x275) mm3

em

issi

on m

V

pump kWcm2

stress kbar

SiAs experiment(106 microm TEA CO2 laser

excitation)

As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

As donor THz output vs pump intensity under different stress

160 180 200 220

10

0

0

00 05 10 15 20 25

170

175

180

185

190

195

200

205

210

215

220

2p+-

1s(T2)

2p0 1s(B

2)

давление кбар

част

ота

см

-1SiAs [100]

em

issi

on a

u

frequency cm-1

240 bar 360 600

frequency

cm

-1

stress kbar

0

0 1 2170

220

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

SiP experiment(106 microm TEA CO2 laser excitation)

P donor THz output vs pump intensity under different stress

50 100 150 2000

10

10

0

em

issi

on a

u

frequency cm-1

SiP [100] 023 kbar 065 12

0

00 05 10 15 20 250

100

200

300

400

500

600 180 75 50 25 17 9 5 3 2

stress kbar

emis

sion

mV

SiP [100]

S=493x255 mm2

pump

kWcm2(a)

2 20 2000

100

200

300

400

500

600059

0

043

029118

147

177

221

266

SiP [100]

S=493x255 mm2

em

issi

on

mV

pump CO2 kWcm2

stress kbar

Sb donor THz output vs pump intensity and compressive stress

00 02 04 06 08 10 12 14 160

5

10

15

20

25

30

35

40

45

pump (kWcm2)

200 85 50 30 10 16 023 015

em

issi

on m

V

stress kbar

SiSb [100]

65x49x32 mm3

Nd= 1015cm-3

02 2 20 2000

5

10

15

20

25

30

35

40

45

65x49x32 mm3

SiSb[100]

emis

sion

mV

pump kWcm2

046023

0

081

105117128

stress kbar

SiSb experiment(106 microm TEA CO2 laser

excitation)

150 160 170 180 190 200

00 10 201720

1725

1730

10

0

0

emis

sion

au

frequency cm-1

SiSb [110] 624 bar 936 bar 1872 bar

0

sress kbar

cm-1

2p0 - 1s(B

2)

200kWcm2 correspond 1025quantcm2s

0 1 2 3 400

01

02

03

04 04 06 08

SiSb em

issi

on V

pump intensity 106 m kWcm2

stress [100] kbar 005 01 02 03

00 05 10 15 2(a) photon flux density 1023 quantcm2

SiSb Under Q-switch CO2 laser pump

Least value of threshold intensity ~150Wcm2

0 1 2 3 40

10

20

30

40

50

60

SiAs

[100] 617x(47x275) mm3

emis

sion

mV

stress kbar

200 150 85 50 30 10 16 1

pump (kWcm2)

2 20 2000

10

20

30

40

50

60 3831

283254

196

17

110810530250

SiAs[100]

617x(47x275) mm3

em

issi

on m

V

pump kWcm2

stress kbar

SiAs experiment(106 microm TEA CO2 laser

excitation)

As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

As donor THz output vs pump intensity under different stress

160 180 200 220

10

0

0

00 05 10 15 20 25

170

175

180

185

190

195

200

205

210

215

220

2p+-

1s(T2)

2p0 1s(B

2)

давление кбар

част

ота

см

-1SiAs [100]

em

issi

on a

u

frequency cm-1

240 bar 360 600

frequency

cm

-1

stress kbar

0

0 1 2170

220

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
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  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

Sb donor THz output vs pump intensity and compressive stress

00 02 04 06 08 10 12 14 160

5

10

15

20

25

30

35

40

45

pump (kWcm2)

200 85 50 30 10 16 023 015

em

issi

on m

V

stress kbar

SiSb [100]

65x49x32 mm3

Nd= 1015cm-3

02 2 20 2000

5

10

15

20

25

30

35

40

45

65x49x32 mm3

SiSb[100]

emis

sion

mV

pump kWcm2

046023

0

081

105117128

stress kbar

SiSb experiment(106 microm TEA CO2 laser

excitation)

150 160 170 180 190 200

00 10 201720

1725

1730

10

0

0

emis

sion

au

frequency cm-1

SiSb [110] 624 bar 936 bar 1872 bar

0

sress kbar

cm-1

2p0 - 1s(B

2)

200kWcm2 correspond 1025quantcm2s

0 1 2 3 400

01

02

03

04 04 06 08

SiSb em

issi

on V

pump intensity 106 m kWcm2

stress [100] kbar 005 01 02 03

00 05 10 15 2(a) photon flux density 1023 quantcm2

SiSb Under Q-switch CO2 laser pump

Least value of threshold intensity ~150Wcm2

0 1 2 3 40

10

20

30

40

50

60

SiAs

[100] 617x(47x275) mm3

emis

sion

mV

stress kbar

200 150 85 50 30 10 16 1

pump (kWcm2)

2 20 2000

10

20

30

40

50

60 3831

283254

196

17

110810530250

SiAs[100]

617x(47x275) mm3

em

issi

on m

V

pump kWcm2

stress kbar

SiAs experiment(106 microm TEA CO2 laser

excitation)

As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

As donor THz output vs pump intensity under different stress

160 180 200 220

10

0

0

00 05 10 15 20 25

170

175

180

185

190

195

200

205

210

215

220

2p+-

1s(T2)

2p0 1s(B

2)

давление кбар

част

ота

см

-1SiAs [100]

em

issi

on a

u

frequency cm-1

240 bar 360 600

frequency

cm

-1

stress kbar

0

0 1 2170

220

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
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  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

0 1 2 3 400

01

02

03

04 04 06 08

SiSb em

issi

on V

pump intensity 106 m kWcm2

stress [100] kbar 005 01 02 03

00 05 10 15 2(a) photon flux density 1023 quantcm2

SiSb Under Q-switch CO2 laser pump

Least value of threshold intensity ~150Wcm2

0 1 2 3 40

10

20

30

40

50

60

SiAs

[100] 617x(47x275) mm3

emis

sion

mV

stress kbar

200 150 85 50 30 10 16 1

pump (kWcm2)

2 20 2000

10

20

30

40

50

60 3831

283254

196

17

110810530250

SiAs[100]

617x(47x275) mm3

em

issi

on m

V

pump kWcm2

stress kbar

SiAs experiment(106 microm TEA CO2 laser

excitation)

As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

As donor THz output vs pump intensity under different stress

160 180 200 220

10

0

0

00 05 10 15 20 25

170

175

180

185

190

195

200

205

210

215

220

2p+-

1s(T2)

2p0 1s(B

2)

давление кбар

част

ота

см

-1SiAs [100]

em

issi

on a

u

frequency cm-1

240 bar 360 600

frequency

cm

-1

stress kbar

0

0 1 2170

220

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

0 1 2 3 40

10

20

30

40

50

60

SiAs

[100] 617x(47x275) mm3

emis

sion

mV

stress kbar

200 150 85 50 30 10 16 1

pump (kWcm2)

2 20 2000

10

20

30

40

50

60 3831

283254

196

17

110810530250

SiAs[100]

617x(47x275) mm3

em

issi

on m

V

pump kWcm2

stress kbar

SiAs experiment(106 microm TEA CO2 laser

excitation)

As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

As donor THz output vs pump intensity under different stress

160 180 200 220

10

0

0

00 05 10 15 20 25

170

175

180

185

190

195

200

205

210

215

220

2p+-

1s(T2)

2p0 1s(B

2)

давление кбар

част

ота

см

-1SiAs [100]

em

issi

on a

u

frequency cm-1

240 bar 360 600

frequency

cm

-1

stress kbar

0

0 1 2170

220

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

1 2 3

00

02

04

06 35 38 4 43

11 117 16 22 29

SiAs

emis

sion

V

pump kWcm2

stress [100] kbar

00 05 10 15(b) pump photon density 1023 quantcm2

Least value of threshold intensity ~300Wcm2

SiAs Under Q-switch CO2 laser pump

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
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  • Slide 7
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  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
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  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

20 20000

02

04

06

08

10 27

2522

1917

16

15

13

0

05

06

Pump intensity kW cm2

Inte

nsi

ty (

au

)

SiBi [100]

07(052034) mm3

07

Stress kbar

SiBi experiment(106 microm TEA CO2 laser

excitation)

Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s

Sb donor THz output vs pump intensity under different stress

00 05 10 15 20 25 300

200

400

600

800 200 80 60 35 23 15 9

SiBi [100]

07(052034) mm3

em

issi

on

m

V

stress kbar

pump

kWcm2

02 04 06 080

100

200

300 130 100 80 60 53 41

In

tens

ity a

u

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
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  • Slide 26
  • Slide 27
  • Slide 28

0 1 2 3 4 5

-40

-20

0

60

80

TA-g

TA-f

2p0(A

1ET

2)

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2)

Ene

rgy

(meV

)

Stress (kbar)

THz 1s(B2)

LO-g

pum

p en

ergy

117

meV

2 cont

0 1 2 3 4 5-60

-40

-20

0

60

80

LO-g

THz

LA-f

2s2p

+-

LA-gTA-f

4 co

nt

1s(T2)

1s(A1)

1s(E)

1s(A1)

2p0(A

1+B

2) E

ne

rgy

(meV

)

Stress (kbar)

THz1s(B

2)

pum

p en

erg

y 1

17 m

eV

2 cont

Energy levels of donors in stressed Si

As Sb

1211]100[ ss

XE u

X-valley splitting under uniaxial stress X

The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys

Intervalley phonon scattering of electrons in Si

K111K010

qN

qf

qg

ee[100]

[010][001]

e

Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
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  • Slide 26
  • Slide 27
  • Slide 28

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

21∙109 c-1

46∙1010 c-121∙1010 c-1

68∙109 c-1

2p0(А1+В2)

SiSb

Stress (06 kbar)

Laser state relaxation rates

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

29∙109 c-1

7∙1010 c-144∙1010 c-1

92∙109 c-1

2p0(А1+В2)

SiP

Stress (06 kbar)

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
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  • Slide 14
  • Slide 15
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  • Slide 17
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  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

26∙101035∙1010

42∙109

2p0(А1+В2)

Stress (25 kbar)

2pplusmn2s

15∙109

14∙109

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

0

2p0

1s(E)1s(T2)

1s(A1)

1s(A1)

1s(B2)

1s(B1)1s(E)1s(A1)

55∙109 2∙109

85∙109

2p0(А1+В2)

Stress (18 kbar)

2pplusmn2s

3∙1011

E

E

SiAs

SiBi

Laser state relaxation rates s-1

intra2pplusmn = 215 ∙1010 c-1

intra2p0= 2 ∙109 c-1

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
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  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

Влияние деформации на эффективность накачки рабочих состояний

(Pump efficiency of the laser states depending on stress)

СО2

Релаксация на фононах

THg

СО2

Релаксация на фононах

THg emission

E

THg emissionE

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28

001 01 1 10 100

1010

1011

1012

1013

1014 Nd=31015 cm-3

popu

latio

n c

m-3

pump kWcm-2

D-centers 2p

0

D-centers under 2p

0 under

001 01 1 10 100

1E-4

1E-3

001

01

1Nd=31015 cm-3

gain

and

abs

orpt

ion

cm

-1

pump kWcm-2

Population gain absorption

SiSb

Donor gain amp D--center absorption

Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)

Blue lines correspond to valley shift 5 meV (06 kbar)

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

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  • Slide 27
  • Slide 28

Summary

The axial compressive stress of silicon crystal applied along [100] crystallographic orientation

From the experiment

- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors

- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors

- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress

From the theoretical treatment

- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys

- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states

- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

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  • Slide 28

Current study amp Further development

1) Spin-orbit interaction amp laser frequencies SiSb SiBi

2) Group-V donor lasing from isotope enriched silicon 28Si

3) Low T donor relaxation in stressed silicon (exp study)

4) Donoracceptor lasing from low dimensional SiSiGe structures

5) CW operation

D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

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D- binding energy vs compression

LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
  • Slide 2
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  • Slide 5
  • Slide 6
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  • Slide 26
  • Slide 27
  • Slide 28

0 2 4 6 8 10 12 14 16 18 2000

05

10

15

20

25

109 c

-1

SiP

2p0(A

1+B

2) - 1s(A

1

u) LA-g TA-g

Междолинное расщепление мэВ

00 05 10 15 20 25 30 350

2

4

6

8

10

12

14

1

09 c-1

Междолинное расщепление meV

SiP (TA-f)

2p0-1s(E)

2p0-1s(B

1)

2p0-1s(A

1

u)

Сумма

0 10 20 30 400

1

2

3

4

5

6

7

10

10 c

-1

Междолинное расщепление мэВ

SiP 1s(B2) - 1s(A1) TA-g

1s(B2) - 1s(A1) LA-g

1кбар соответствует 85 мэВ

SiP SiP

1s(E)

1s(T2)

1s(A1)

TA-f84∙109 c-1

TA-f124∙109 c-1

LA-g03∙109 c-1

LA-g575109 c-1

TA-g7∙1010 c-1

TA-g36∙1010 c-1

2p0

SiP

Темп внутридолинных переходов

2р0 - 1s 21∙109 с-1

26∙1010 c-1

7∙1010 c-1

36∙1010 c-1

0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
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0 10 20 30 40

0

1

2

3

4

5

intervalley splitting meV

10

10 c

-1

1s(B2)-1s(A

1) TА-g

1s(B2)-1s(A

1) LA-g

SiSb

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

intervalley splitting meV

109 c

-1

SiSb 2p

0(A

1+B

2)-1s(Au

1) LA-g

2p0(A

1+B

2)-1s(E) TA-f

2p0(A

1+B

2)-1s(Au

1) TA-g

Переходы 2p0-1s(A

1

u) и 2p0-1s(B

1)

на ТА-f фононах пренебрежимо малы

1 kbar yields 85 meV valley shift for [100]

stress

1 kbar yields 85 meV valley shift for [100]

stress

SiSb SiSb

1s(E)

1s(T2)

1s(A1)

TA-f~108 c-1

TA-f142∙109 c-1

LA-g26∙109 c-1

LA-g175∙109 c-1

TA-g46∙1010 c-1

TA-g38∙1010 c-1

2p0

SiSb

Intra valley scattering rate

2р0 - 1s 21∙109 с-1

18∙1010 c-1

38∙1010 c-1

46∙1010 c-1

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

  • Slide 1
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  • Slide 28

SiAs SiAs

LA-f079∙1010 c-1

1s(E)

1s(T2)

1s(A1)

TA-f122∙109 c-1

LA-g063∙109 c-1

LA-g07∙109 c-1

TA-f27∙1010 c-1

TA-f16∙1010 c-1

2p0

2s

2pplusmn

LA-g5∙1010 c-1

LA-g33∙1010 c-1

TA-f146 ∙109 c-1

LA-f098∙109 c-1

LA-f27∙1010 c-1

LA-g6∙109 c-1

LA-g6∙109 c-1

Intra valley scattering rates

2р0 - 1s 21∙109 с-1

2s - 1s 52∙109 c-1

2pplusmn - 1s 01 ∙109 c-1

2pplusmn - 2p0 144 ∙109 c-1

2pplusmn - 2s 89 ∙109 c-1

27∙1010 c-1

16∙1010 c-1

77∙1010 c-1

5∙1010 c-1

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

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0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

rate

10

9 s-1

intervalley splitting meV

SiAs 2p(+-)-1s(Al

1) LA-f

2p(+-)-1s(Au

1) LA-g

Relaxation of the lower laser level

f- and g-phonon scattering rates in As donor under stress

0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

intervalley splitting meV

109 c

-1

SiAs 2p

0-1s(Au

1) LA-g

2p0-1s(EB

1) TA-f

2p0-1s(Al

1) LA-f

2p0-1s(Au

1) TA-g

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

intervalley splitting meV1

010c-1

SiAs 1s(B

2)-1s(A

1

l) LA-g

1s(B2)-1s(A

1

l) TA-f

Relaxation of 2р(+-) and 2р0 states

1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

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1s(T2Г7)

1s(T2Г8)

1s(A1)

TA-f52∙109 c-1

LA-g~ 108 c-1

LA-g2∙109 c-1

LA-f47∙109 c-1

TA-f6∙109 c-1

2p0

2s

2pplusmn

LA-g053∙109 c-1

LA-g04∙109 c-1

TA-f14∙1010 c-1

TO-f~32∙1011 c-1

1s(E)

LA-g37∙109 c-1

SiBi SiBi

00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

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00 05 10 15 20 25 30 35 400

5

10

15

20

0 59 118 176 235 294 353 412 471

Intervalley splitting meV

1011

c-1

bar

SiBi 2p0-1s(Al

1) TO-f (для верхней ТО ветки) D

15 20 25 30 35 400

1

2

3

4

5

6

7

8

Intervalley splitting meV

1010

c-1

SiBi 2p

0 - 1s(Al

1) LA-f

0000 0493 0986 1479 1972 2465 2958 3451 39440

2

4

6

8

10

12

14

16

18

0 58 116 174 232 290 348 406 464

SiBi LO-g

2p+- - 1s(Al1)

Intervalley splitting meV

1010

c-1

2p+- - 1s(Al1)

with shiftedphonon dispersion on 05 meV

bar

7 8 9 10 11 12 130

5

10

15

20

25

30

35

Intervalley splitting meV

15 kbar

109 c

-1

SiBi2p(+-)-1s(Al

1) TO-f

для верхней ТО-f ветки для нижней ТО-f ветки

1 kbar

f- and g-phonon scattering rates in Bi donor under stress

0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

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0 2 4 6 80

2

4

6

8

Intervalley splitting meV

109 c

-1

SiBi 1s(B

7)-1s(Al

1)

0 20 40 60 800

2

4

6

8

10

12

14

Intervalley splitting meV

1010

c-1

SiBi1s(B

2)-1s(A

1

l) LA-g

Relaxation 1s(B2) state in Bi donor under stressed silicon

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