First-Principles Electronic Structure and Computational Semiconductor Physics
Why Computation Is Central
Predictive materials science
Modern semiconductor research depends on first-principles methods to predict band structures, defect energetics, interfaces, and phase stability. Computation is indispensable because experimental screening across chemical space is too slow and too expensive.
Important limitation
Standard density-functional theory often underestimates band gaps and may misplace defect levels, so interpretation requires care.
Density Functional Theory and Beyond
Exchange-correlation and quasiparticles
Kohn-Sham DFT provides a powerful ground-state framework, but band gaps and excited states usually require corrections such as hybrid functionals, , and Bethe-Salpeter calculations. These methods better capture quasiparticle energies and excitons.
Common theoretical levels
| Method | Strengths | Weaknesses |
|---|---|---|
| DFT | Efficient, structural trends | Band-gap errors, excited-state limits |
| Hybrid DFT | Improved gaps | Costly for large systems |
| Quasiparticle accuracy | Computationally expensive | |
| BSE | Excitonic optical spectra | Requires accurate quasiparticle input |
Why is plain DFT often insufficient for optical gaps in semiconductors?
The Kohn-Sham spectrum is not, in general, equal to the true excited-state spectrum.
Correct answer: Because Kohn-Sham eigenvalues are not generally true quasiparticle excitation energies
What physical quantity does primarily improve?
The self-energy correction goes beyond semilocal DFT.
Correct answer: Quasiparticle energies, especially band gaps and band-edge positions.
Machine Learning and High-Throughput Discovery
Data-driven screening
Machine learning now accelerates the search for semiconductors with desired band gaps, mobilities, defect tolerance, and stability. Graph neural networks, active learning, and surrogate models are increasingly used to explore large chemical and structural spaces.
Computational discovery workflow
High-throughput DFT
- Enumerate candidates
- Generate labeled data
ML surrogate modeling
- Rank materials cheaply
- Explore large design spaces
What is one major advantage of active learning in materials discovery?
Active learning focuses resources on the most informative candidates, improving efficiency.
Correct answer: It selects the most informative new samples to compute or measure
Why are graph neural networks attractive for crystalline semiconductors?
This makes them effective for property prediction across diverse materials.
Correct answer: They can encode atomic connectivity and local environments in a way that respects structure and chemistry.