low temperature optical and electronic properties of cvd
TRANSCRIPT
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
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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Outline:
I) Optical properties
II) Electronic Properties:
ConductivityMobilityDrift Velocity in Diamond: HolesDefects (H1 center)Deep trapping of carriers
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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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Schematic Absorption
Several types of phonons involver:
• one longitudinal acoustic phonon
• Two transversal acoustic phonons
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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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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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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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Typical absorption spectra
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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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Mobility
Textbook example: Temperature dependentmobility in n-type Si (S.M. Sze:SemiconductorDevices)
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The band structure and the phonon bands in diamond
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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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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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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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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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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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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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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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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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Carbon hyperfine interaction with HydrogenDistance: 1.9 to 2.3 A
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Defect Model: X. Zhou, G.D. Watkins et al. PRB 54 (1996) p. 7881
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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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Temperature dependent capture cross sectionsfor 7 deep levels in GaAs and two in GaP (D.V. Lang)
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Time-of-flight setup
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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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Model:
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After laser exposure the internal field is reversed, giving rise to a current in oposit direction
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The same features for electrons and holes: Traps or defect, whichcan be occupied by electrons and holes!