99
Electronic Properties of Strain-Engineered Semiconductors
our simulations. In the following, we present the parameters defined during
simulation in the parameter file:
LatticeParameters
{
* DC2 (l) defines Bir & Pikus deformation potentials for
conduction subband = l
* DV2 (l) defines Bir & Pikus deformation potentials for
valence subband = l
* The subband energy shift due to strain (E) is equal to the
following sum:
* (Bir & Pikus expression)
* D2 [1]*E11 + D2 [2]*E22 + D2 [3]*E33 +
* D2[4]*(0.5*D2[5]^2*((E11-E22)^2+(E22-E33)^2+(E33-E11)^2)+D2[
6]*(E23^2+E13^2+E12^2))
*
* Egley’s data for Bir & Pikus expressions:
*
* DC2 (1) = 9.5,0,0,0,0,0
* DC2 (2) = 0, 9.5,0,0,0,0
* DC2 (3) = 0, 0, 9.5,0,0,0
* DV2 (1) = 0, 0, 0,-1, 0.5,4
* DV2 (2) = 0, 0,0,1,0.5,4
*
D C2 (1) = 9.5, 0.0000e+00, 0.0000e+00, 0.0000e+00,
0.0000e+00, 0.0000e+00 # [eV]
D C2 (2) = 0.0000e+00, 9.5, 0.0000e+00, 0.0000e+00,
0.0000e+00, 0.0000e+00 # [eV]
D C2 (3) = 0.0000e+00, 0.0000e+00, 9.5, 0.0000e+00,
0.0000e+00, 0.0000e+00 # [eV]
D V2 (1) = 0.0000e+00, 0.0000e+00, 0.0000e+00, -1.0000e+00,
0.5, 4
# [eV]
D V2 (2) = 0.0000e+00, 0.0000e+00, 0.0000e+00, 1, 0.5, 4
# [eV]
}
Equations (4.16) and (4.17) have a common part (
)
11
22
33
′
ε + ′
ε + ′
ε , and therefore these expressions are combined in one general expression that gives a
flexibility of its definition in the parameter file:
,
1
2
3
B i
Ε = δΕ + δΕ + δΕ
(4.18)
where
(
)
(
)
(
)
1
1 11
22
33
2 11
3 3
3 22
33
4 23
5 13
6 12
i
B
i
B
i
B
i
B
i
i
δΕ = ξ ′
ε + ′
ε + ′
ε +ξ
′
ε − ′
ε +ξ ′
ε − ′
ε +ξ ′
ε + ′
ξ ′
ε + ′
ξ ′
ε
2
1
2
11
2
2
22
3
2
33
i
B
i
B
i
B
δΕ = ξ ′
ε + ξ ′
ε + ξ ′
ε
2
((
) (
) (
)
3
4
2
5
2 2
11
22
2
22
33
2
11
33
2
6
2 2
11
2
22
2
33
2
i
B
i
B
i
B
( )
( ) (
)
δΕ = ξ
ξ
′
ε − ′
ε
+ ′
ε − ′
ε
+ ′
ε − ′
ε
+ ξ
′
ε + ′
ε + ′
ε