Calculate Electronic Band Gap¶
This tutorial page explains how to calculate an electronic band gap based on Density Functional Theory. We consider crystalline silicon in its standard equilibrium cubic-diamond crystal structure, and use VASP as our main simulation engine during this tutorial.
!!!note simulation engines considered in this tutorial" The present tutorial is originally designed for VASP (ver. 5.3.5 or 5.4.4), however, the steps demonstrated below are identical for other similar software, such as Quantum ESPRESSO (ver. 5.4 to 6.3), for example.
The electronic band gap defines the energy difference between the highest occupied electronic state and the lowest unoccupied state within the electronic band-structure of the material under investigation.
Direct vs Indirect Gaps
We support the extraction of both the direct and indirect band gaps. The difference between the two types is explained in this page.
Silicon in its cubic-diamond crystal structure is the default material that is shown on new job creation, unless this default was changed by the user following account creation. If silicon is still the default choice, it will as such be automatically loaded at the moment of the opening of Job Designer.
Set Sampling in Reciprocal Space¶
It is critical to have a high k-point density in order to calculate the band gap with sufficient accuracy.
For the case of VASP, the band gap workflow is composed of two units. The first unit specifies the settings for the self-consistent calculation of the energy eigenvalues and wave functions. The second unit calculation is a non self-consistent calculation using the wave functions and charge density of the previous calculation.
We set the size of the grid of k-points to 18 x 18 x 18 in the first workflow unit. The validity of this choice of k-grid size for yielding accurate results of order meV in the final energy can be verified by performing the relevant convergence study.
Before submitting the job, the user should click on the "Compute" tab of Job Designer and inspect the compute parameters included therein. Silicon is a small structure, so four CPUs and one minute of calculation runtime should be sufficient.
When both unit computations are complete at the end of Job execution, switching to the Results tab of Job Viewer will show the results of the simulation, including the indirect band gap found for Si (~0.6 eV).
Silicon as Indirect Gap Semiconductor
The user will notice that we identify both the direct band gap and the indirect band gap. This calculation is done during the first, self-consistent step of the calculation on the dense k-point mesh. It can be deduced that the indirect band gap is significantly smaller than the smallest direct band gap, which is the reason why silicon is classed as an indirect gap semiconductor.
Comparison with Experimental Value¶
The calculated value of ~0.6 eV for the indirect band gap is significantly below the tabulated experimental value for the band gap of Silicon of ~1.1 eV, however as discussed elsewhere this underestimation is expected given our adoption of the Generalized Gradient Approximation. The use of more accurate techniques, such as Hybrid Screened Exchange (HSE), for example, allows to significantly improve the comparison. See the corresponding tutorial for more details.
We demonstrate the above-mentioned steps involved in the creation and execution of a Band Gap computation workflow on silicon using the simulation engine in the following animation.