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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
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
Diamond is ULTRA COLD
Experimental regime
Assumptions: T = 300 K, νo = 1013 1/s
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
Outline:
I) Optical properties
II) Electronic Properties:
ConductivityMobilityDrift Velocity in Diamond: HolesDefects (H1 center)Deep trapping of carriers
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
Schematic Absorption
Several types of phonons involver:
• one longitudinal acoustic phonon
• Two transversal acoustic phonons
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
Temperature dependent absorption
Diamond parameter
β+α
−==T
T)0T(E)T(E2
gg
Eg(T=0)=5.48α = -1.979β = -1437
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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)
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
Typical absorption spectra
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
Mobility
Textbook example: Temperature dependentmobility in n-type Si (S.M. Sze:SemiconductorDevices)
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
The band structure and the phonon bands in diamond
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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?
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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:
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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.
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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:
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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)
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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.
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
Carbon hyperfine interaction with HydrogenDistance: 1.9 to 2.3 A
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
Defect Model: X. Zhou, G.D. Watkins et al. PRB 54 (1996) p. 7881
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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:
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
Temperature dependent capture cross sectionsfor 7 deep levels in GaAs and two in GaP (D.V. Lang)
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
Time-of-flight setup
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
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)
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
Model:
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
After laser exposure the internal field is reversed, giving rise to a current in oposit direction
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National Institute of Advanced Industrial Science and TechnologyDiamond Research Center
The same features for electrons and holes: Traps or defect, whichcan be occupied by electrons and holes!