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

Material Properties for Heterostructures
usually assumed in this case that the amount of the edge shift for both the conduction and valence
bands are the same. For the current implementation, except of Al x Ga 1-x As, Al x In 1-x As, and Ga x In 1-
x As y P 1-y , it is assumed that all bandgap change due to the composition change occurs only at the
valence edge due to the lack of sufficient experimental data. However, the bandgap narrowing due to
the heavy doping effect, is accounted for in the aforementioned manner for all materials, i.e., evenly
split. For Al x Ga 1-x As / GaAs, ∆E C : ∆E V is taken as 0.6 : 0.4 and for Al x In 1-x As / InAs, 0.706 : 0.294,
where ∆E is considered positive when the band edge is expanding, that is the bandgap becomes larger.
For Ga x In 1-x As y P 1-y / InP the bandgap change is simply assumed evenly split among the conduction
and valence bands edges 1 . By designating the percentage of the shift of conduction band edge with
respect to the bandgap change as γ, we have the following relationship for the electron affinity as
function of the mole fractions:
χ( x,
y) = χ( 00 , )–
γ[ E g ( x,
y) – E g ( 00 , )]
(4.13)
For ternaries, y does not appear in the formula. And
∆E C
=
– ∆χ
(4.14)
∆E V = ∆χ + ∆E g
(4.15)
4.4.3 Effective Mass and Density of States
The calculation of the effective density of states is based on the density-of-state effective mass, which
in turn depends on the mole fraction. Moreover, one needs to consider for electrons the effective
masses at different valleys in the conduction band and for holes the light and heavy masses in order to
construct the overall effective masses used in computing the densities of states. We use a different
formulation to compute effective masses for each different material system based on our best
knowledge. For Al x Ga 1-x As / GaAs material system, since we know composition dependence of
electron effective mass and band gap at each valley (Γ, L, and X), we can use weighted scheme to
compute the electron effective mass (for details, see [33]). And for holes, the following linear formula
is used:
1. ∆E C = ( 71±
7)%∆E g is measured for Al 0.48 In 0.52 As / Ga 0.47 In 0.53 As in [34].
PISCES-2ET – 2D Device Simulation for Si and Heterostructures 39