The tuning of the type and size of bandgaps of III-V semiconductors is a major goal for optoelectronic applications. Varying the relative composition of several III- or V-components in compound semiconductors is one of the major approaches here. Alternatively, straining the system can be used to modify the bandgaps. By combining these two approaches, bandgaps can be tuned over a wide range of values, and direct or indirect semiconductors can be designed. However, an optimal choice of composition and strain to a target bandgap requires complete material-specific composition, strain, and bandgap knowledge. Exploring the vast chemical space of all possible combinations of III- and V-elements with variation in composition and strain is experimentally not feasible. We thus developed a density-functional-theory-based predictive computational approach for such an exhaustive exploration. This enabled us to construct the bandgap phase diagram (BPD) by mapping the bandgap in terms of its magnitude and nature over the whole composition-strain space. Further, we have developed efficient machine-learning models to accelerate such mapping in multinary systems. We show the application and great benefit of this new predictive mapping on device design.
BPD jokes
""" Me: I want to grow this. Can you please grow this for me? CPD: Yeahhhhhhhhhh! Hmmmmmmmmmm! BPD: Hey! Why do you wanna grow this? Me: I need a device like .... And I thoght this probably will work if I can grow this. BPD: Are you sure this will work as you want? Me: Nah! (after 2 days: Nope! It doesn't work. But we are going close. Let's try next one.) BPD: Wait. Don't waste your time and money. It seems to me this is not the right choice. Use here .... This will be the best option.
.
.
. Me: Wow. Thanks to both of you.
"""
General Notes
Strain definition
The strains are calculated according to the following equation: \[Strain(\%) = {a_f - a_{eqm} \over a_{eqm}}\times 100.\]
Where, \(a_f\) is the final stretched/compressed lattice constant, and \(a_{eqm}\) is the equilibrium lattice constant. For biaxial strain, \(a_f\) corresponds to the in-plane (substrate) lattice constant.
Isotropic strain: Systematically increased (decreased) the lattice parameters isotropically for expansion (compression); and optimized the position of the atoms only, keeping the volume of the cell fixed.
Bi-axial strain: Relax the structures only in the out-of-plane lattice direction ([001]) keeping the two in-plane lattice parameters ([100] & [010]) fixed with values that mimic the substrate.
This is a general work flow that has been used to automatize the calculations and analyses as much as possible. There are a lot places still left for further improvement. Feel free to adapt to your own work flow strategies in your environment.
Plane wave basis set in conjuction with the projector augmented wave (PAW) method
Primitive zinc blende cell
Energy cut-off: 450 eV
Electronic convergence criteria: 10-6 eV
Force convergence criteria: 10-2 eV/Å
10×10×10 Γ-center Monkhorst-Pack kpoint mesh.
PBE-D3 functional for structure optimization
TB09 functional including spin-orbit coupling for bandgap and band structure calculations
\[Strain(\%) = {a_f - a_{eqm} \over a_{eqm}}\times 100.\]
\(a_f\) is the final stretched/compressed lattice constant and \(a_{eqm}\) is the equilibrium lattice constant. For biaxial strain \(a_f\) corresponds to the in-plane (substrate) lattice constant.
Isotropic strain: Systematically increased (decreased) the lattice parameters isotropically for expansion (compression); and optimized the position of the atoms only, keeping the volume of the cell fixed.
Bi-axial strain: Relax the structures only in the out-of-plane lattice direction ([001]) keeping the two in-plane lattice parameters ([100] & [010]) fixed with values that mimic the substrate.
\(\Delta E_{CB} (eV)\): Difference between conduction band energies at Gamma point and other k-points.
(\Gamma - L): Difference between conduction band energies at \Gamma point and L-point.
(\Gamma - X): Difference between conduction band energies at \Gamma point and X-point.
and so on...
Results TableBandstructure Movies The movies shows the evolution of bandstuctures under strain. The band structures were calculated along the high symmetry path of zincblende structures. In all cases, the band energies were rescaled with respect to their corresponding VBM.
III-V quaternaryMachine learning based
Note: As epitaxial growth is the most common approach to grow multinary III-V semiconductors, below we map the bandgap phase diagram for these compounds under biaxial strain only.
Warning: The project is work in progress. Complete data is not available yet. Please contact to the below address for further details.
Supervised learning with SVM(rbf)
SVR(rbf) and SVC(rbf) ML models were used for the bandgap magnitude and bandgap nature, respectively.
Scripts (note: 'MachineLearning_*.py' are the main script. 'MachineLearning_*.py' imports functions from rest of the scripts.)
System specific scripts (note: 'ML_Models_*.py' imports functions from ../SupervisedLeaning/scripts folder.)
This page is created (22.09.2021) and maintained by Badal Mondal. If the results in this page are useful to you we will consider our efforts successful. We will highly appreciate if you cite the above references and this page, if you use the results from this page.
. Link