Calculate Electronic Band Gap¶
This tutorial explains how to calculate the electronic band gap of crystalline silicon in its standard equilibrium cubic-diamond crystal structure, based on Density Functional Theory (DFT). VASP is used as the main simulation engine.
Simulation engines considered in this tutorial
This tutorial is designed for VASP (ver. 5.3.5 or 5.4.4), however the steps are identical for other engines such as Quantum ESPRESSO (ver. 5.4 to 6.3 and later).
1. Understand the band gap¶
The electronic band gap is the energy difference between the highest occupied electronic state and the lowest unoccupied state within the electronic band structure of a material.
Direct vs indirect gaps
The platform extracts both direct and indirect band gaps. The difference between the two types is explained in the band gaps reference.
2. Create a job¶
Silicon in its cubic-diamond crystal structure is the default material loaded on new job creation, unless the default was changed after account creation. If silicon is still the default, it is automatically loaded when the Job Designer is opened.
3. Select the workflow¶
Workflows for calculating the band gap can be imported from the Workflows Bank into the account-owned collection. The workflow can then be selected and added to the job being created.
4. Set sampling in reciprocal space¶
A high k-point density is critical for calculating the band gap with sufficient accuracy.
For VASP, the band gap workflow is composed of two units. The first unit performs a self-consistent field (SCF) calculation of the energy eigenvalues and wave functions. The second unit performs a non-self-consistent calculation using the wave functions and charge density from the first step.
The k-point grid is set to 18 × 18 × 18 in the first workflow unit. The validity of this grid size for yielding meV-level accuracy can be verified by performing a convergence study.
5. Submit the job¶
Before submitting the job, the Compute tab of Job Designer should be reviewed to verify the compute parameters. Silicon is a small structure, so four CPUs and one minute of calculation runtime are sufficient.
6. Examine the results¶
Once both unit computations complete, the Results tab of Job Viewer displays the simulation results, including the indirect band gap of Si (~0.6 eV).
Silicon as indirect gap semiconductor
Both the direct and indirect band gaps are identified. The calculation is performed during the first, self-consistent step on the dense k-point mesh. The indirect band gap is significantly smaller than the smallest direct band gap, which is why silicon is classified as an indirect gap semiconductor.
6.1. Compare with experiment¶
The calculated value of ~0.6 eV for the indirect band gap is below the tabulated experimental value of ~1.1 eV. As discussed in the DFT accuracy notes, this underestimation is expected when using the Generalized Gradient Approximation. More accurate techniques, such as Hybrid Screened Exchange (HSE), significantly improve the comparison. See the HSE band gap tutorial for details.
7. Video walkthrough¶
The animation below demonstrates the steps involved in the creation and execution of a band gap computation on silicon.