InAs / GaSb broken gap quantum well (BGQW) (type-II band alignment)
Author: Stefan Birner
Input files required:
1DInAs_GaSb_BGQW_k_zero_nnp.in
1DInAs_GaSb_BGQW_k_parallel_nnp.in
1DInAs_GaSb_BGQW_k_parallel_nnp_01.in
1DInAs_GaSb_BGQW_k_parallel__nnp_11.in
This tutorial aims to reproduce Figs. 1, 2(a), 2(b) and 3 of Hybridization of electron, light-hole, and heavy-hole states in InAs/GaSb quantum wells
Material parameters used are taken from Optical transitions in broken gap heterostructures.
The heterostructure is a broken gap quantum well (BGQW) with 15 nm InAs and 10 nm GaSb, sandwiched between two 10 nm AlSb layers. Note that this heterostructure is asymmetric.
To be consistent with the above cited papers, strain is not included into the calculations although this would be possible. The structure has a type-II band alignment, i.e. the electrons are confined in the InAs layer, whereas the holes are confined in the GaSb layer. Depending on the width of the InAs and/or GaSb layers, things can be even more complicated because the hole states can hybridize with the electron states, making it difficult to distinguish between electron-like and hole-like states. Another difficulty arises because the lowest electron states might be located below the highest hole states. This requires a new algorithm to occupy the states according to a suitable Fermi level.
The following figure shows the electron and hole band edges of the BGQW structure.
band_structure/cb1D_001.dat
(Gamma conduction band edge) in units of [eV]band_structure/vb1D_001.dat
(heavy hole valence band edge) in units of [eV]band_structure/vb1D_002.dat
(light hole valence band edge) in units of [eV]band_structure/vb1D_003.dat
(split-off hole valence band edge) in units of [eV]

The origin of the energy scale is set to the InAs conduction band edge energy. The heavy hole and light hole band edges are degenerate because we neglect the effects of strain to be consistent with the above cited papers.
Results
The input file used here is 1DInAs_GaSb_BGQW_k_zero_nnp.in. The following figure shows the conduction band edge and the heavy/light hole valence band edges in this BGQW structure together with the electron (e1, e2), heavy hole (hh1, hh2, hh3) and light hole (lh1) energies and wave functions (
One can clearly see that the electron state (e1, e2) are confined in the InAs layer (left part of the figure), whereas the heavy (hh1, hh2, hh3) and light hole (lh1) states are confined in the GaSb layer (right part of the figure). One can see a slight hybridization of the e1 and lh1 states, i.e. these states are mixed states whereas the heavy hole states (hh1, h2, hh3) are not mixed and thus confined in the GaSb layer.
We use the data files
Schroedinger_kp/kp_8x8psi_squared_qc001_el_kpar0001_1D_dir.dat
, which containsSchroedinger_kp/kp_8x8psi_squared_qc001_el_kpar0001_1D_dir_shift.dat
, which contains
The latter file contains the square of the wave functions (for par0001
, i.e

The energies of the eigenstates are in units of [eV] and are contained in the file Schroedinger_kp/kp_8x8eigenvalues_qc001_el_kpar0001_1D_dir.dat
The input file 1DInAs_GaSb_BGQW_k_parallel.in was used for the following results. The following figure shows the
In this input file, the energy levels and wave functions for 24
Schroedinger_kp/kpar1D_disp_01_00el_8x8kp_ev_min001_ev_max020.dat
contains the
dispersion{
path{
name = "kpar_01_00_10"
point{ k = [0.0, 0.0, 1.0] }
point{ k = [0.0, 0.0, 0.0] }
point{ k = [0.0, 1.0, 0.0] }
spacing = 1 / $number_k_parallel
}
path{
name = "kpar_10_00_11"
point{ k = [0.0, 1.0, 0.0] }
point{ k = [0.0, 0.0, 0.0] }
point{ k = [0.0, 1.0, 1.0] }
spacing = 1 / $number_k_parallel
}
output_dispersions{}
output_masses{}
}
The first column contains the
The black lines are the results of nextnano++, the red dots are the results of nextnano³.

At an in-plane wave vector of 0.014 1/Å, strong intermixing between the e1 and the lh1 states occurs. In contrast to the wave functions at
In asymmetric quantum wells, the double spin degeneracy is lifted at finite values of
The file Schroedinger_kp/kp_8x8k_parallel_qc001_el1D_dir.dat
tells us which number of
k_par_number k_x [1/nm] k_y [1/nm]
1 0.000000E+000 0.000000E+000 ==> k|| = (kx,ky) = (0,0) [1/nm]
...
29 0.000000E+000 1.400000E+000 ==> k|| = (kx,ky) = (0,0.14) [1/nm]
1326 1.00000E+000 1.000000E+000 ==> k|| = (kx,ky) = (1.0,1.0) [1/nm]
In the following figure, we plot the square of the wave functions for num-kp-parallel = 10000
The wave functions (Schroedinger_kp/kp_8x8psi_squared_qc001_hl_kpar00029_1D_dir_shift.dat

The electron states (e1) couple strongly with the light hole states (lh1). This is expected from the energy dispersion plot because at 0.14 nm-1 a strong anticrossing is present for these states. One can also clearly see that for spin up and spin down states, different energy levels and different probability densities exist.
This is in contrast to the states at
Last update: nn/nn/nnnn