[Paper Review] Semiconductor Physics: A Density Functional Journey

Sujoy Datta, Debnarayan Jana|arXiv (Cornell University)|Oct 25, 2020

Surface and Thin Film Phenomena4 citations

TL;DR

This paper reviews the evolution of Density Functional Theory (DFT) in semiconductor physics, emphasizing the performance of various exchange-correlation functionals—from LDA to hybrid and meta-GGA functionals—in predicting structural and electronic properties. It demonstrates that semi-local functionals like PBEsol and TM-TPSS offer accurate lattice constants and bulk moduli, while potential-only corrections (e.g., vLB, TBmBJ) effectively address bandgap underestimation without excessive computational cost.

ABSTRACT

The journey of theoretical study on semiconductors is reviewed in a non-conventional way. We have started with the basic introduction of Hartree-Fock method and introduce the fundamentals of Density Functional Theory (DFT). From the oldest Local Density Approximations (LDA) to the most recent developments of semi-local corrections [Generalised Gradient Approximation (GGA), Meta-GGAs], hybrid functionals and orbital dependent methodologies are discussed in detail. To showcase the performance of DFT, results obtained via different approximations are compared. We indicate the success of semi-local approximations in structural properties prediction. We also show how less computationally costly but withstand architecture of some semi-local DFT methods can solve the long riddle of bandgap underestimation. In semiconductor physics, the importance of not only the band structure prediction, but also, the proper calculation of Fermi energy, and, exact finding of band alignment is argued. The comparison of Fermi energy dependent properties can channelize the theoretical studies on modern age environment-friendly researches on semiconductors, like artificial photocatalysis, energy efficient opto-electronic devices, etc. This prescription on proper choice of DFT method is potentially competent to complement the experimental findings as well as can open up a pathway of advanced semiconducting materials discoveries.

Motivation & Objective

• To evaluate the performance of various DFT approximations in predicting key semiconductor properties such as bandgap, lattice constant, and bulk modulus.
• To address the long-standing issue of bandgap underestimation in Kohn-Sham DFT and assess the physical validity of correction schemes.
• To identify computationally efficient yet accurate functionals that balance structural and electronic property predictions for materials discovery.
• To guide the selection of appropriate DFT functionals for modern applications in photocatalysis and optoelectronics based on Fermi energy and band alignment accuracy.

Proposed method

• Systematic comparison of DFT functionals across Jacob's ladder: LDA, GGA (PBE, PBEsol), meta-GGA (TPSS, revTPSS, SCAN, TM-TPSS), and hybrid functionals.
• Use of the Kohn-Sham formalism to map interacting electron systems to non-interacting effective potentials, enabling single-particle calculations.
• Employment of the Birch-Murnaghan equation of state (EOS) to extract bulk modulus from energy-volume data, with fitting to E(V) curves.
• Application of potential-only corrections (e.g., vLB, BJ, TBmBJ) that modify the xc potential without functional derivative dependence.
• Use of Fermi energy-dependent properties and band alignment calculations to assess functional suitability for advanced optoelectronic applications.
• Benchmarking against experimental data and high-level methods (e.g., RPA, EXX) for transition pressures and electronic structure.

Experimental results

Research questions

• RQ1 Which DFT functionals provide the most accurate predictions for lattice constants and bulk moduli in semiconductors?
• RQ2 How do semi-local functionals like PBEsol and TM-TPSS compare to hybrid and meta-GGA functionals in correcting the bandgap underestimation problem?
• RQ3 To what extent can potential-only corrections (e.g., vLB, TBmBJ) improve bandgap prediction without increasing computational cost?
• RQ4 Can Fermi energy and band alignment calculations serve as reliable indicators for selecting DFT functionals in materials design for photocatalysis?
• RQ5 What is the role of derivative discontinuity in the failure of standard DFT to predict accurate bandgaps, and how do modern functionals address it?

Key findings

• PBEsol consistently outperforms other GGA functionals in predicting both lattice constants and bulk moduli, showing superior accuracy for solids.
• The TM-TPSS functional, which mixes TM exchange with TPSS correlation, delivers the best performance among semi-local functionals for both structural and electronic properties.
• vLB-FP-NMTO, a potential-only correction to LDA, achieves excellent agreement with experiment for lattice constants and bulk moduli in C3N4 polymorphs and group IV/III-V semiconductors.
• Bandgap underestimation remains a persistent issue in standard Kohn-Sham DFT, but potential-only corrections (e.g., TBmBJ) significantly improve accuracy without relying on empirical fitting.
• Semi-local functionals such as PBEsol and TM-TPSS provide a computationally efficient and accurate alternative to hybrid functionals for predicting structural properties.
• Accurate Fermi energy and band alignment calculations are essential for guiding the design of next-generation optoelectronic and photocatalytic materials.