Download A Program for Calculating Mobility and Carrier Density

Table 1: Momentum Relaxation Times and reduced Energy dependence for
Materials with Isotropic Parabolic Bands [1]
Scattering mechanism
τi
ri
Ionized
0.414ǫ2r (0)T 3/2
m∗ 1/2
Z 2 NI (cm− 3)g(n∗,T,x) m
3/2
Neutral
m∗ 2
8.16x106
ǫr (0)Nn (cm− 3) m
0
Deformation Potential
2.4x10−20 Cl (dyn/cm2 ) m 1/2
2 (eV )T 3/2
m∗
ξa
−1/2
Piezoelectric
9.54x10− 8
m 1/2
h214 (V /cm)(3/Cl +4/Ct )T 1/2 m∗
1/2
Deformation Potential
4.83x10−20 Cl (dyn/cm2 )[exp(θ/T )−1] m 3/2
2 (eV )T 1/2 θ
m∗
ξA
−1/2
Polar
9.61x10−15 ǫr (0)ǫr (∞)[exp(θ/T )−1] m
m∗
ǫr (0)−ǫr (∞)θ 1/2 (θ/T )r
r(θ/T )
Impurities
Acoustic Phonons
Optical Phonons
The Fermi Energy Ef is found by solving the charge neutrality equation.
N d− − N a+ = n − p
(7)
R∞
R∞
Na
x1/2 dx
x1/2 dx
−
1+exp(x−ηn ) , p = Nv 0 1+exp(x−ηp ) , N a = 1+ga exp[(Ea −Ef )/kT ] ,and
f
E −E
Nd
−Ec
and where ηn = E kT
and ηp = vkT f , N c =
N d+ = 1+gd exp([(E
f −Ed )/kT ]
∗Mh 3/2
∗Me 3/2
2( 2∗π∗k∗T
) , Nv = 2( 2∗π∗k∗T
) ,
h2
h2
where n = Nc
0
Scattering from dislocations also occurs. The momentum relaxation time τdis
2 3/2
3 2 2
(1+4λ2 K⊥
)
2
b T 1/2
where λ = ( ǫk
and k⊥
=
follows the equation τdis = N~disǫmc∗ e4
λ4
e2 n∗ )
∗
2Em
~2 [2]
Note that this program does not take the effect of dislocations on the charge
balance equation into account. This is a valid assumption when the dislocation
concentration is low.
In Table 1, NI = concentration of ionized impurities; g(n∗, T, x) = ln(1 + b) −
b/(1 + b); b = 4.31x1013 [ǫr (0)T 2 /n∗](m ∗ /m)x; Nn = concentration of neutral
impurities; Cl = 1/5(3C11 + 2C12 + 4C44 );Ct = 1/5(C11 − C12 + 3C44 );θ =
hωLO /k.
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