low temperature optical and electronic properties of cvd

National Institute of Advanced Industrial Science and TechnologyDiamond Research Center

Low TemperatureOptical and Electronic Properties

of CVD Diamond

for Detector Applications

Christoph E. Nebel

Diamond Research Center, AIST, Tsukuba, Japan


Diamond is ULTRA COLD

Experimental regime

Assumptions: T = 300 K, νo = 1013 1/s


Outline:

I) Optical properties

II) Electronic Properties:

ConductivityMobilityDrift Velocity in Diamond: HolesDefects (H1 center)Deep trapping of carriers


I. Optical Properties

Transition with phonon absorption (hν >Eg-Ep)

( )1

kTE

exp

EEhA)h(

p

2pg

a

−⎟⎟⎠

⎞⎜⎜⎝

⎛

+−ν=να

For hν > Eg + Ep both absorptions take place: )h()h()h( ea να+να=να

Transition with phonon emission (hν > Eg+Ep)

( )

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−−ν=να

kTE

exp1

EEhA)h(

p

2pg

e


Schematic Absorption

Several types of phonons involver:

• one longitudinal acoustic phonon

• Two transversal acoustic phonons


Temperature dependent absorption

Diamond parameter

β+α

−==T

T)0T(E)T(E2

gg

Eg(T=0)=5.48α = -1.979β = -1437


Temperature dependent variation of the band gap of Diamond

∆E = 15 meV

From 0 K to 300 K:

0 50 100 150 200 250 300 3505,460

5,465

5,470

5,475

5,480

5,485

Band

gap

of D

iam

ond

Temperature (K)


Near band edge absorption

Phonon coupling with excitons:

LO = 163 meV

TA = 87 meV

TO = 141 meV

R. Sauer, in „Thin Film Diamond, Elsevier 2003

EGx = exciton threshold energies(5.406 eV)

Eg = 5.467 eV


Typical absorption spectra


II. Electronic Properties: Conductivity

1,0 1,5 2,0 2,5 3,0 3,5 4,0105

107

109

1011

1013

1015

1017

PCD

Single Crystal IIa

Single Crystal Ib

Resis

tivity

(Ωcm

)

1000/T (K-1)

All undoped diamond layers(Ib, IIa and CVD) are n-type:

Conductivity of CVD diamondis governed by nitrogendoping (P1-center):

Eact = 1.7 eV Slope is1.7 eV


Mobility

Textbook example: Temperature dependentmobility in n-type Si (S.M. Sze:SemiconductorDevices)


The band structure and the phonon bands in diamond


Hole Mobilities

T-3/2: acoustic phonon scattering

T-2.8: optical phonon scattering

Isberg et al. : time-of-flight on undoped CVD diamond

(Science 297, p. 1670 (2002): 3800 cm2/Vs)

Reggiani: Time-of-flight on undoped natural diamond

Dean and Konorova: Hall Mobilities

Dr. Okushi et al. AIST: Hall effect on boron doped CVD diamond102 103

102

103

104

~T-2.8

~T-3/2

Theory Reggiani et al. Dean et al. Konorova et al. Isberg (intrinsic) AIST Boron doping

Hol

e M

obilit

y (c

m2 /V

s)

Temperature (K)

Why different phononscattering?


CVD Hole Mobility Limitations: Scattering due to residual impurities like Fe and Mo

1011 1012 1013 1014 1015 1016 1017 1018100

101

102

103

HOD

Single Crystal CVD Diamond

PCD

T = 300 K

Hol

e M

obili

ty (c

m2 /V

s)

Hole Density (cm-3)

( )i

2/32/1*

NTm∝µ

Scattering at ionizedimpurities:


Phosphorusdoped diamond

Electron Mobilities in natural and P-doped Diamond:

Isberg et al.,: Time-of-flight in undoped CVD diamond

( Science 297, p. 1670 (2002): 4500 cm2/Vs)

Nava: Time-of-flight on natural undoped diamond

Konorova: Hall effect

Redfield: Hall effect

Koizumi et al.: Hall effect on Phosphorus doped diamond

T-3/2: acoustic phonon scattering

102 103

102

103

104

~T-3/2

Theory Nava et al. Redfield Konorova et al. Koizumi

Elec

tron

Mob

ility

(cm

2 /Vs)

Temperature (K)

Isberg et al.


The saturation velocity limitation:

e

phonons

EeFv

dtEd

τ−=

∆

m

ss mveFdt

)mv(dτ

−=

0dt

)mv(ddt

Ed s ==∆

me τ=τ

me τ=τ

2/1

*phonon

s mE

v ⎟⎟⎠

⎞⎜⎜⎝

⎛=

Energy relaxation

Impuls relaxation

For steady state conditions:

For only on scattering process(one phonon)

Saturation velocity:vs= 3.8x107 cm/s

for 165 meV and m = 0.2 mo

2/1

*nonopticalpho

sat m3E8

v ⎥⎦

⎤⎢⎣

⎡π

=Better:


Drift Velocity in Diamond: Holes

102 103 104106

107

T = 85 K

Field in <110>

Field in <100>

Diamond: Holes

Drif

t Vel

ocity

(cm

/s)

Electric Field (V/cm)

Saturation hole velocity: 1.1x107 cm/s

Reggiani et al, PRB 23 (1981) p. 3050


Drift Velocity in Diamond: Electrons

102 103 104 105

106

107

Diamond: ElectronsT = 85 K

<100>

<110>

Drif

t Vel

ocity

(cm

/s)

Electric Field (V/cm)

Saturated drift velocity: 1.5x107 cm/s

Anisotropy: multivalley band structure

F. Nava et al., Sol. Stat. Com. 33 (1980) p. 475


Drift velocity

τ=µ=meFFvD

r

o kT⎟⎠⎞

⎜⎝⎛ ε

τ=τ

Drift velocity:

Scattering time:

r = -0.5 acoustic deformation potential scattering

r = +3/2 ionized imurity scattering Reggiani et al, PRB 23 (1981) p. 3050

J.L. Moll, Physics of Semiconductors (Wiley, 1964)


Defects: H1 Center g = 2.0028

Homoepitaxial singlecrystalline diamond:

Typical Density: 5x1018 cm-3

Zhou et al. PRB 54 (1996) p. 7881

N. Mizuochi et al. DRM in print.


Carbon hyperfine interaction with HydrogenDistance: 1.9 to 2.3 A


Defect Model: X. Zhou, G.D. Watkins et al. PRB 54 (1996) p. 7881


Deep trapping of carriers

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

τ−−

µτ=

texp1LEQ)t(Q o

crossthD SvN1

=τ

Capture cross section Scross: 10-14 cm2 – 10-15 cm2

2ro r

14

1)r(Eεπε

=

Hecht equation:

Deep trapping lifetime

εr(Diamond) = 5.7

εr(Si) = 11.9εr in diamond much smaller!

Ionized Impurities:


Temperature dependent capture cross sectionsfor 7 deep levels in GaAs and two in GaP (D.V. Lang)


Time-of-flight setup


Deep trapping of carriers (electrons and holes) in undoped CVD diamond

0,0 5,0x10-9 1,0x10-8 1,5x10-8 2,0x10-8-2,0x10-3

0,0

2,0x10-3

4,0x10-3

6,0x10-3

B

A PD

F = 0 V/cm

F = 1.2x103 V/cm

Curr

ent (

A)

Time (s)


Model:


After laser exposure the internal field is reversed, giving rise to a current in oposit direction


The same features for electrons and holes: Traps or defect, whichcan be occupied by electrons and holes!

low temperature optical and electronic properties of cvd

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