PISCES-2ET and Its Application Subsystems - Stanford Technology ...

Material Properties for Heterostructures
4.4 Band Structure Parameters
4.4.1 Bandgap
We will discuss first those compound semiconductors which need only one mole fraction to determine
the composition, that is, either Ge x Si 1-x or ternaries. For Ge x Si 1-x , currently only the data for the
strained layer [30] is accessible in the program. The formulation is as follows (in units of eV):
E g ( x) =
1.16 – 0.945
E gSi , – -----------------------------x
0.245
x ≤ 0.245
=
0.945 – 0.87
0.945 – ----------------------------- ( x – 0.245)
0.35 – 0.245
0.245 < x ≤ 0.35
=
0.87 – 0.78
0.87 – -------------------------- (
0.5 – 0.35
– 0.35 ) 0.35 < x ≤ 0.5
0.78 – 0.72
= 0.78 – -------------------------- (
0.6 – 0.5
– 0.5 )
0.5 < x ≤ 0.6
=
0.72 – 0.69
0.72 – -------------------------- ( x – 0.6)
0.675 – 0.6
0.6 < x ≤ 0.675
=
0.69 – 0.66
0.69 – -------------------------------- ( x – 0.675)
0.735 – 0.675
0.675 < x ≤ 0.735
= 0.66
x > 0.735
(4.4)
For Al x Ga 1-x As, simply use
E g ( x) = 1.424 + 1.247x
x ≤ 0.45 (direct band)
= 1.900 + 0.125x + 0.143x 2 x > 0.45 (indirect band)
(4.5)
For bandgap of Al x In 1-x As, as x is increased from 0 to 1 the band structure also undergoes a
transition from the direct to indirect bandgap and the critical composition is x = 0.56 . The expression
for E g at room temperature is as follows [31]:
E g = 2.95x + 0.36( 1 – x) – 0.7x( 1 – x)
x ≤ 0.56 (direct)
= 2.16x + 1.37( 1 – x) – 0.7x( 1 – x)
x > 0.56 (indirect)
(4.6)
PISCES-2ET – 2D Device Simulation for Si and Heterostructures 37