arXiv subjects

Karol Kawka

Publications and source records attributed to Karol Kawka.

5 recordsLinked to original sources

arXiv2026

Tiling decomposition multiplicity predicts stability of GaN(0001) surface reconstructions

The stable adatom configurations of a semiconductor surface have traditionally been sought by sampling: density functional theory (DFT) energies steer a heuristic or Bayesian search through a configuration space far too large to cover. Here we show that, for the GaN(0001)-$(6\times6)$ surface under the electron counting (EC) rule, the search can instead be posed as a discrete tiling problem and solved exhaustively. Enumerating all rhombus tilings of the surface lattice, together with all EC-compatible adatom arrangements built on them, yields the complete catalog of 416,683 configurations at fixed stoichiometry (3 Ga adatoms and 18 H atoms), organized by symmetry into 14 Ga placement classes. The number of tilings compatible with a given configuration, its tiling decomposition multiplicity $n_\mathrm{til}$, predicts stability. Within each class, the configuration maximizing $n_\mathrm{til}$ is the most stable. The rule holds strictly in 13 of the 14 classes; in the remaining class the minimum is itself among the highest-multiplicity configurations, with the $n_\mathrm{til}$-max configuration only 8.5 meV above it; this ordering is reproduced by independent DFT calculations, and the difference is negligible at growth temperature. Stability screening uses a machine-learning interatomic potential validated against 710 DFT-computed structures. The rule reduces the candidate set for first-principles evaluation from 416,683 to 24 configurations, all of which have been evaluated with DFT. Analysis of the rule identifies the local mechanism, the avoidance of adjacent bare surface sites, while the existence of a compatible tiling remains a separate requirement with an energy cost of its own. Enumeration thus provides what sampling cannot: a coverage guarantee, and a route to stable-structure prediction in which first-principles input enters only at the final ranking step.

cond-mat.mtrl-sci↗

arXiv2026

PyAPX: Python toolkit for atomic configuration pattern exploration

In materials discovery, the integration of first-principles calculations with machine learning techniques has been actively studied for two key tasks: crystal structure prediction, which searches for stable structures given a chemical composition, and elemental substitution, which explores chemical compositions that yield desirable properties in a given crystal structure. However, even when both the crystal structure and chemical composition are fixed, material properties can still vary depending on the atomic arrangements (configurations) at crystallographic sites. To support detailed material design, we present PyAPX, a Python toolkit that performs Bayesian searches of stable atomic configurations. A distinctive feature of this initial release is the introduction of encoding methods suitable for configuration search, and we evaluate their performance using the h-BCN system. As a result, they were confirmed to yield superior convergence compared to commonly used one-hot encoding. PyAPX is broadly applicable to crystalline materials and is expected to further advance materials discovery.

cond-mat.mtrl-sci↗

arXiv2025

Exploration of stable atomic configurations in graphene-like BCN systems by Bayesian optimization

h-BCN is an intriguing material system where the bandgap varies considerably depending on the atomic configuration, even at a fixed composition. Exploring stable atomic configurations in this system is crucial for discussing the energetic formability and controllability of desirable configurations. In this study, this challenge is tackled by combining first-principles calculations with Bayesian optimization. An encoding method that represents the configurations as vectors, while incorporating information about the local atomic environments and domain knowledge, is proposed for the search. The proposed encoding method proved effective in the search, resulting in the discovery of two interesting and stable semiconductor configurations. Furthermore, the optimization behavior is discussed through principal component analysis, confirming that the ordered BN network and the C configuration features are well embedded in the search space. While our approach provided a tailored encoding for the h-BCN system in this study, it holds promise for broader application to other materials by adapting the domain knowledge matrix to each target system.

cond-mat.mtrl-sci↗

arXiv2025

Limited Diffusion of Silicon in GaN: A DFT Study Supported by Experimental Evidence

Silicon (Si) is the primary donor dopant in gallium nitride (GaN), introduced through epitaxial growth or ion implantation. However, precise control over Si diffusion remains a critical challenge for high-performance device applications. This study investigates Si diffusion mechanisms in bulk GaN using first-principles density functional theory (DFT) calculations, supported by ultra-high-pressure annealing (UHPA) experiments. Vacancy-mediated diffusion pathways were analyzed using the SIESTA code, with minimum energy paths (MEPs) and activation barriers determined via the nudged elastic band (NEB) method. The results indicate that Si diffusion barriers vary with crystallographic direction, with the lowest barrier of 3.2 eV along [11-20] and the highest barrier of ~9.9 eV along [1-100], rendering diffusion in this direction highly improbable. Alternative diffusion mechanisms, including direct exchange and ring-like migration, exhibit prohibitively high barriers ($>$12 eV). Phonon calculations confirm that temperature-induced reductions in effective diffusion barriers are minimal. Experimental validation using SIMS analysis on Si-implanted GaN samples subjected to UHPA (1450°C, 1 GPa) confirms negligible Si diffusion under these extreme conditions. These findings resolve inconsistencies in prior reports and establish that Si-doped GaN remains highly stable, ensuring reliable doping profiles for advanced electronic and optoelectronic applications.

cond-mat.mtrl-sci↗

arXiv2024

Augmentation of the Electron Counting Rule with Ising Model

On semiconductor growth surfaces, surface reconstructions appear. Estimation of the reconstructed structures is essential for understanding and controlling growth phenomena. In this study, the stability of a mixture of two different surface reconstructions is investigated. Since the number of candidate structures is enormous, the structures sampled by Bayesian optimization are analyzed. As a result, the local electron counting (EC) rule alone was found to be insufficient to explain such stability. Then, augmenting the EC rule, a data-driven Ising model is proposed. The model allows the evaluation of the whole enormous number of candidate structures. The approach is expected to be useful for theoretical studies of such mixtures on various semiconductor surfaces.

cond-mat.mtrl-sci↗