🔬 materials science

No band gap, no problem: Defects in InAs using a band-avoiding occupation-constrained density functional theory

This paper introduces a band-avoiding occupation-constrained density functional theory (ba-occ-DFT) method that overcomes the zero band gap problem in narrow-gap semiconductors like indium arsenide (InAs), enabling accurate predictions of atomic defect levels despite the failure of standard DFT to reproduce the experimental band gap.

Original authors: Peter A. Schultz, Arthur H. Edwards, Evan M. Anderson, Anthony C. Knighton, Leopoldo Diaz

Published 2026-07-30

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CC BY 4.0

Original authors: Peter A. Schultz, Arthur H. Edwards, Evan M. Anderson, Anthony C. Knighton, Leopoldo Diaz

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to build a perfect digital city inside a computer. To make this city work, you need to understand the "rules of the road" for electrons, the tiny particles that carry electricity. Scientists use a powerful set of mathematical rules called Density Functional Theory (DFT) to predict how these electrons behave in materials like silicon or gallium arsenide. Think of DFT as a super-accurate mapmaker. Usually, this mapmaker is great at drawing the streets and buildings (the structure of the material), but it has a famous blind spot: it often gets the height of the "energy cliffs" wrong. In the world of semiconductors, there is a gap between the low-energy valley where electrons hang out and the high-energy hill they need to climb to conduct electricity. This is called the "band gap." For most materials, the mapmaker underestimates how wide this gap is. But for a specific material called Indium Arsenide (InAs), the mapmaker gets so confused that it draws the gap as having zero width, making the valley and the hill touch. This is a disaster for engineers because if they can't see the gap, they can't predict where "traffic jams" (defects) will happen when the material gets damaged by radiation in space. Without knowing where these jams are, we can't build better detectors for satellites or faster, low-power electronics.

This paper tackles that specific disaster in Indium Arsenide. The authors, working at Sandia National Laboratories and the Air Force Research Laboratory, realized that the standard way of using the mapmaker (DFT) was failing because it was forcing electrons to sit in the wrong places when the gap disappeared. They developed a clever new trick called "band-avoiding occupation-constrained DFT" (or ba-occ-DFT). Imagine a classroom where the teacher (the computer) usually tells students (electrons) to sit in the lowest, most comfortable seats first. But in this specific classroom, the "lowest seats" are actually broken chairs that make the whole room wobble. The new trick is to tell the teacher: "Ignore the broken chairs at the front of the room. Instead, force the students to sit in the specific, sturdy chairs in the middle that represent the actual defect." By manually rearranging the seating chart to avoid the broken spots, the authors were able to calculate the true energy of the defects without the computer getting confused by the zero-width gap.

The results of this simulation are quite revealing. When they applied this new seating rule to Indium Arsenide, they found that the material behaves very differently than previous theories suggested. They discovered that while some defects act like simple holes in the material, others are actually "shapeshifters." For instance, a missing atom (a vacancy) doesn't just sit there; it causes a neighboring atom to hop over and take its place, creating a new, more stable structure. The simulations showed that most of the simple defects in this material act as "shallow donors," meaning they trap electrons very loosely, creating a broad range of energy levels just above the bottom of the gap. This finding offers a potential explanation for a mysterious "broad shoulder" seen in recent experiments on irradiated Indium Arsenide, which other theories couldn't explain. The authors are careful to note that while their simulations are consistent with the limited experimental data available, they are not a final proof; they suggest that these shallow defects are likely the cause of the experimental observations, but more specific experiments are needed to confirm the identity of every defect.

Crucially, the paper argues against the idea that the problem was that the computer was making the defects too "spread out" or fuzzy. In fact, their simulations show the defects are quite localized and tight. The real issue was simply that the computer was too eager to fill up the wrong energy levels because the gap had collapsed. By using their new "band-avoiding" method, they successfully separated the problem of the broken map (the band gap) from the problem of finding the defects. They demonstrated that even with a zero-width gap in the simulation, you can still get reliable predictions about where defects sit and how they behave, provided you strictly control where the electrons are allowed to sit. This approach allows scientists to study these tricky materials without needing to use much more expensive and complex calculation methods that have previously failed to provide accurate results for Indium Arsenide.

Technical Summary: Band-Avoiding Occupation-Constrained DFT for Defects in InAs

Problem Statement
Density Functional Theory (DFT), particularly within the Local Density Approximation (LDA) or Generalized Gradient Approximation (GGA), is highly successful for structural energetics but suffers from the "band gap problem," significantly underestimating the fundamental band gap of semiconductors and insulators. This issue is acute in narrow-gap semiconductors like indium arsenide (InAs), where the DFT conduction band edge (CBE) collapses to the valence band edge (VBE) at the $\Gamma$ -point, resulting in a zero DFT band gap. This collapse seemingly precludes the quantitative prediction of defect charge transition levels, as spurious occupation of the CBE state contaminates the calculation of localized defect states. Furthermore, standard hybrid functional approaches (e.g., HSE06), while correcting the bulk band gap, have failed to provide reliable defect predictions in InAs due to issues with defect state dispersion and hybridization in finite supercells.

Methodology: Band-Avoiding Occupation-Constrained DFT (ba-occ-DFT)
The authors propose a band-avoiding occupation-constrained DFT (ba-occ-DFT) approach to decouple the band gap problem from the calculation of localized defect levels. The core hypothesis is that while the spurious CBE state descends to the VBE at the $\Gamma$ -point, the localized defect state remains distinct and energetically higher.

Key methodological features include:

Occupation Constraints: The method modifies the standard Aufbau principle by imposing non-Aufbau occupations specifically at the $\Gamma$ -point. It enforces the "excitation" of an electron from the spurious CBE state to the localized defect state, thereby avoiding the occupation of the band-edge state.
k-point Sampling: Calculations utilize supercells (64 to 1000 atoms) with regular k-point grids (e.g., $2\times2\times2$ ). The method acknowledges that defect states in narrow-gap systems exhibit significant dispersion in small supercells; therefore, a converged k-grid is essential to sample this dispersion, rather than relying solely on $\Gamma$ -point calculations.
Boundary Conditions: The calculations employ the Local Moment Countercharge (LMCC) approach to enforce rigorous Coulomb boundary conditions for charged supercells, removing finite-size errors.
Functionals: The primary calculations utilize the PBE functional with SeqQuest, supplemented by HSE06 hybrid functional calculations (using VASP) for validation on smaller supercells.

Key Results
The ba-occ-DFT approach was applied to intrinsic point defects in InAs, including antisites ( $As_{In}$ , $In_{As}$ ), vacancies ( $v_{In}$ , $v_{As}$ ), divacancies ($vv$), and interstitials ( $As_i$ , $In_i$ ).

Validation of the Approach: In the case of the arsenic antisite ( $As_{In}$ ), standard PBE calculations in small supercells showed large defect state dispersion ( $\sim0.5$ eV) and hybridization with the CBE. However, as supercell size increased (up to 1000 atoms), the defect state flattened, and the ba-occ-DFT successfully isolated the localized state from the descending CBE. The method yielded stable self-consistent calculations where the defect character was preserved.
Defect Level Predictions:
- Arsenic Antisite ( $As_{In}$ ): Identified as a low-energy defect with donor states at 0.35 eV ( $0/1+$ ) and 0.12 eV ( $1+/2+$ ) relative to the VBE. The formation energy is low (1.09 eV for neutral), suggesting appreciable population in as-grown material.
- Indium Vacancy ( $v_{In}$ ): Contrary to previous theories, the simple $v_{In}$ is not thermodynamically stable in the gap. A site-shifted configuration ( $v^*_{In}$ , where a neighboring As hops into the In site) is more stable. This configuration exhibits a negative- $U$ transition ( $3-/1+$ ) at 0.45 eV, above the experimental band gap.
- Arsenic Vacancy ( $v_{As}$ ): Stable only as a simple vacancy in positive charge states, with a negative- $U$ transition ( $1+/3+$ ) at 0.04 eV.
- Interstitials: Both $As_i$ and $In_i$ adopt positive charge states ( $1+$ to $3+$ ).
Effective Defect Band Gap (EDBG): The calculations define an EDBG bounded by the $In_{As}(2+/1+)$ transition (VBE bound) and the $As_i(1-)$ state at 0.41 eV (CBE bound), showing reasonable agreement with experimental observations.
Comparison with Hybrid Functionals: HSE06 calculations on small supercells failed to improve upon PBE; the defect bands still showed significant dispersion and untrustworthy $\Gamma$ -point levels. This highlights that opening the band gap alone does not guarantee clean localized defect states in finite supercells without proper occupation constraints.

Significance and Claims
The paper claims that the ba-occ-DFT approach successfully circumvents the band gap problem in narrow-gap semiconductors like InAs, enabling rigorous defect level predictions even when the DFT band gap is zero. The authors emphasize that the primary issue is not the over-delocalization of defect states (as defect states in PBE are well-localized) but the over-stabilization of delocalized band states (the CBE collapse). By strictly enforcing the occupation of local defect states and avoiding spurious band occupations, the method separates band-edge errors from defect level calculations.

The results are consistent with limited experimental data for InAs, such as the observation of shallow donor states and the "EL2-like" behavior of the arsenic antisite. The authors note that the method explains recent experimental observations of broad shallow-emission shoulders in DLTS for irradiated InAs, attributing them to the shallow donor nature of primary displacement defects. The approach is presented as a straightforward implementation into existing DFT supercell codes, extending the accuracy of DFT+LMCC to systems where conventional hybrid functional approaches are computationally impractical or have failed.

Technical Summary: Band-Avoiding Occupation-Constrained DFT for Defects in InAs

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