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Band gap of strained AlGaInP on GaAs substrate

Note: This tutorial's copyright is owned by Stefan Birner, www.nextnano.de.

Author: Stefan Birner

If you want to obtain the input files that are used within this tutorial, please contact stefan.birner@nextnano.de.
-> 1DAlGaInP_onGaAs.in
-> 1DAlGaInP_onGaAs_no_bowing.in
-> 1DAlGaInP_onGaAs.xls
 

Band gap of strained AlGaInP on GaAs substrate

In this tutorial we want to study the band gaps of strained Al_xGa_yIn_1-x-yP on a GaAs substrate.

The material parameters are taken from
Band parameters for III-V compound semiconductors and their alloys
I. Vurgaftman, J.R. Meyer, L.R. Ram-Mohan
J. Appl. Phys. 89 (11), 5815 (2001)

To understand the effect of strain on the band gap on the individual components of this quaternary, we first examine the effects on
 1) AlP            strained tensilely          with respect to GaAs
 2) GaP           strained tensilely          with respect to GaAs
 3) InP             strained compressively with respect to GaAs
 4) Al_xGa_1-xP   strained tensilely          with respect to GaAs
 5) Ga_xIn_1-xP    strained                       with respect to GaAs
 6) Al_xIn_1-xP     strained                       with respect to GaAs
 7) Al_0.4Ga_0.6P strained tensilely         with respect to GaAs
 8) Ga_0.4In_0.6P strained compressively with respect to GaAs
 9) Al_0.4In_0.6P  strained compressively with respect to GaAs

Each material layer has a length of 10 nm in the simulation.

The material layers 4), 5) and 6) vary its alloy contents linearly:
 4) Al_xGa_1-xP   from 10 nm to 20 nm from x=0.0 to x=1.0
 5) Ga_xIn_1-xP    from 30 nm to 40 nm from x=0.0 to x=1.0
 6) Al_xIn_1-xP     from 50 nm to 60 nm from x=1.0 to x=0.0

Strain

-> 1DAlGaInP_onGaAs.in

There is no external stress applied to the structure, so Poisson's ratio holds.
All layers are strained pseudomorphically with respect to a GaAs substrate (i.e. the layers are biaxially strained in the plane perpendicular to the growth direction to match the lattice constant of GaAs).

The biaxial strain in the layers can be calculated with this formula:
e_xx = e_yy = (a_substrate - a) / a
where a is the lattice constant.

The output of the strain tensor can be found in this file:
=> strain1/strain_cr1D.dat

The hydrostatic strain is the trace of the strain tensor and corresponds to the volume deformation:
e_hydro = Tr(e_ij) = e_xx + e_yy + e_zz

Band gaps

The following figure shows the conduction band edges at the Gamma, L and X points and the heavy hole, light hole and split-off hole valence bands.
The red line shows that band gap, i.e. the difference between the lowest conduction band minimum and the valence band maximum.
The band gap maximum occurs at Al_0.55In_0.45P (2.355 eV).

The conduction and valence band edges have been obtained taking into account the shifts and splittings of the bands due to strain and deformation potentials.

Note that conduction and valence band offsets are not taken into account in this plot.
The zero of energy was taken to be the unstrained heavy hole / light hole band edge.

Due to strain, the degeneracy of the heavy and light hole is lifted. Also, the X band splits into two X bands (2 fold and 4 fold degeneracy).

In the case of tensile (compressive) strain, the light (heavy) hole band is the valence band maximum.

Note that the material parameters include band gap bowing.

-> 1DAlGaInP_onGaAs_no_bowing.in

The following figure compares the overall band gap to the case where band gap bowing has been neglected.

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