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

Akira Kusaba; Karol Kawka; Karol Pozyczka; Krzysztof Golyga; Michal Bockowski; Michal Fijalkowski; Pawel Kempisty

arxiv: 2503.21382 · v1 · pith:MCLALXDHnew · submitted 2025-03-27 · ❄️ cond-mat.mtrl-sci · physics.comp-ph

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

Karol Kawka , Pawel Kempisty , Akira Kusaba , Krzysztof Golyga , Karol Pozyczka , Michal Fijalkowski , Michal Bockowski This is my paper

Pith reviewed 2026-05-22 22:54 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.comp-ph

keywords silicon diffusiongallium nitrideDFT calculationsvacancy-mediated diffusiondiffusion barriersultra-high pressure annealingSIMS analysisdopant stability

0 comments

The pith

Silicon diffusion in GaN varies sharply by crystal direction, with barriers reaching 9.9 eV and making some paths effectively impossible.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses density functional theory to map how silicon atoms move through gallium nitride by jumping into nearby vacancies. It calculates the energy barriers for these jumps along different crystal axes and finds the lowest at 3.2 eV while the highest reaches 9.9 eV. Other possible movement routes, such as direct swaps or ring shifts, require more than 12 eV. Temperature effects from lattice vibrations do little to lower these barriers, and high-pressure annealing tests at 1450°C show almost no silicon movement in implanted samples. This matters because silicon serves as the main donor dopant for making GaN conductive, so uncontrolled spreading would blur the sharp doping profiles needed in transistors and light-emitting devices.

Core claim

Vacancy-mediated diffusion pathways were analyzed using the SIESTA code and nudged elastic band method, yielding direction-dependent activation barriers of 3.2 eV along [11-20] and approximately 9.9 eV along [1-100]. Direct exchange and ring-like mechanisms exceed 12 eV. Phonon calculations indicate minimal temperature-induced barrier reduction. Secondary ion mass spectrometry on Si-implanted GaN after ultra-high-pressure annealing at 1450°C and 1 GPa confirms negligible diffusion, establishing that Si-doped GaN remains stable under extreme conditions.

What carries the argument

Vacancy-mediated minimum energy paths calculated with the nudged elastic band method in DFT, which determine the direction-specific activation barriers for silicon jumps.

If this is right

Diffusion along the [1-100] direction is highly improbable under any practical conditions.
Alternative mechanisms such as direct exchange remain unavailable due to barriers above 12 eV.
Silicon dopant profiles in GaN stay fixed even during ultra-high-pressure annealing at 1450°C.
Doping stability supports reliable device fabrication without post-growth diffusion concerns.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Device layouts could exploit the anisotropic barriers by aligning current flow with low-barrier directions to allow controlled local redistribution if needed.
The same computational approach could be applied to other common dopants such as magnesium or oxygen to map their stability limits.
Lower-temperature processing steps might suffice for GaN devices if diffusion is already ruled out at the highest practical temperatures.

Load-bearing premise

That vacancy-mediated diffusion is the dominant mechanism for silicon movement inside bulk GaN crystals.

What would settle it

Secondary ion mass spectrometry profiles that show clear broadening or redistribution of implanted silicon after annealing at 1450°C and 1 GPa would contradict the claim of negligible diffusion.

Figures

Figures reproduced from arXiv: 2503.21382 by Akira Kusaba, Karol Kawka, Karol Pozyczka, Krzysztof Golyga, Michal Bockowski, Michal Fijalkowski, Pawel Kempisty.

**Figure 2.** Figure 2: Energy barriers for the diffusion of a Si atom in GaN via the vacancy-mediated [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Energy barriers for various diffusion mechanisms. The left graph presents the mini [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Change of the effective energy barrier to vacancy-mediated migration of Si atom in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Diffusion coefficient of Si in GaN along the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Results of characterization of the MOVPE-GaN/Ammono-GaN sample (10- [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

**Figure 7.** Figure 7: SIMS-measured Si concentration profiles in HVPE-GaN after UHPA processing (3 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗

read the original abstract

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{\deg}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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Si diffusion in GaN is limited by direction-dependent barriers around 3.2 eV minimum, with DFT and UHPA-SIMS experiments lining up.

read the letter

The main point here is that Si stays put in GaN under high-temperature processing because vacancy-mediated jumps face barriers of at least 3.2 eV along the easiest direction and much higher along others, and the experiments match that prediction. The directional values and the specific UHPA conditions with SIMS checks are the concrete new pieces. They also rule out direct exchange and ring mechanisms at over 12 eV and show phonons do not lower the barriers much with temperature. That combination gives the work some weight for people who need stable doping profiles in power devices. The calculations use standard NEB in SIESTA and the experiment is straightforward implantation plus annealing at 1450 °C and 1 GPa. The soft spots are the usual ones for this kind of study: we do not see the full convergence data or the exact exchange-correlation functional here, so the precise 3.2 eV number could shift a bit, but the gap to the other directions and the experimental null result make the overall claim less sensitive to small errors. The vacancy assumption is not hidden; they checked the alternatives and found them prohibitive. This is useful reading for anyone working on GaN doping control or implantation activation. It is not revolutionary but it is a clean, self-consistent piece that resolves some earlier contradictions in the literature. I would send it to peer review because the central claim is testable, the methods are standard, and the experimental tie-in is real rather than decorative.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates vacancy-mediated Si diffusion in bulk GaN using DFT (SIESTA code, NEB method) and reports direction-dependent activation barriers, with a minimum of 3.2 eV along [11-20] and ~9.9 eV along [1-100]; alternative mechanisms exceed 12 eV. Phonon analysis indicates minimal temperature-induced barrier reduction. UHPA experiments (1450°C, 1 GPa) with SIMS on Si-implanted samples show negligible diffusion, concluding that Si-doped GaN remains stable with reliable doping profiles.

Significance. If the computed barriers and experimental null result hold, the work would resolve prior inconsistencies on Si diffusion in GaN and support stable doping for high-power devices. The explicit evaluation of multiple mechanisms and the computational-experimental pairing are strengths.

major comments (2)

[Methods (DFT/NEB)] Computational methods section: explicit convergence tests (k-point sampling, basis-set size, supercell dimensions, and NEB spring constants) for the reported barriers of 3.2 eV and 9.9 eV are absent; without them the direction dependence and absolute values cannot be verified at the claimed precision.
[Experimental validation] Experimental section: SIMS depth profiles, implantation fluence, annealing time, and quantitative upper limits on diffusion length or diffusivity are not reported, so the claim of 'negligible' diffusion at 1450 °C cannot be assessed for sensitivity or consistency with the 3.2 eV barrier.

minor comments (1)

[Phonon analysis] The abstract states phonon calculations confirm minimal barrier reduction, but the main text should specify the phonon method (finite-displacement vs. DFPT) and the quantitative procedure used to obtain the effective temperature-dependent barrier.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address each of the major comments below and have revised the manuscript to incorporate additional details as requested.

read point-by-point responses

Referee: [Methods (DFT/NEB)] Computational methods section: explicit convergence tests (k-point sampling, basis-set size, supercell dimensions, and NEB spring constants) for the reported barriers of 3.2 eV and 9.9 eV are absent; without them the direction dependence and absolute values cannot be verified at the claimed precision.

Authors: We agree that the manuscript would benefit from explicit documentation of the convergence tests. In the revised version, we will include a new subsection in the Computational Methods detailing the convergence with respect to k-point sampling, basis set size, supercell size, and NEB parameters. These tests were performed during the study and confirm the stability of the reported barriers to within 0.05 eV. revision: yes
Referee: [Experimental validation] Experimental section: SIMS depth profiles, implantation fluence, annealing time, and quantitative upper limits on diffusion length or diffusivity are not reported, so the claim of 'negligible' diffusion at 1450 °C cannot be assessed for sensitivity or consistency with the 3.2 eV barrier.

Authors: We acknowledge the need for more detailed experimental reporting to allow quantitative assessment. The revised manuscript will include the SIMS depth profiles, the implantation fluence and annealing conditions used, as well as an estimate of the upper limit on the diffusion length derived from the SIMS detection limits. This will enable direct comparison with the calculated barriers. revision: yes

Circularity Check

0 steps flagged

No significant circularity; DFT barriers and SIMS validation are independent

full rationale

The derivation chain consists of first-principles DFT (SIESTA + NEB) to compute direction-dependent activation barriers for vacancy-mediated Si diffusion, followed by separate experimental SIMS validation under UHPA conditions. No equations reduce the reported barriers (3.2 eV minimum) to fitted parameters or self-citations; alternative mechanisms are explicitly computed and shown to exceed 12 eV. The vacancy-mediated focus is justified within the paper by prohibitive barriers for other paths rather than assumed by definition. The central claim is self-contained against external benchmarks and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review limits visibility into parameters; standard DFT assumptions are invoked without detail.

axioms (2)

domain assumption Vacancy-mediated diffusion is the primary mechanism analyzed
Pathways analyzed using SIESTA and NEB as stated in abstract
standard math Nudged elastic band method locates true minimum energy paths
Used to obtain activation barriers

pith-pipeline@v0.9.0 · 5806 in / 1285 out tokens · 118965 ms · 2026-05-22T22:54:59.783063+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

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Koleske, A

D. Koleske, A. Wickenden, R. Henry, M. Twigg, Influence of MOVPE growth conditions on carbon and silicon concentrations in GaN, Journal of Crystal Growth 242 (1) (2002) 55–69. doi:10.1016/S0022-0248(02)01348-9

work page doi:10.1016/s0022-0248(02)01348-9 2002

[2] [2]

Deatcher, C

C. Deatcher, C. Liu, M.-G. Cheong, L. Smith, S. Rushworth, A. Widdowson, I. Watson, Silicon doping of gallium nitride using ditertiarybutylsilane, Chemical Vapor Deposition 10 (4) (2004) 187–190. doi:10.1002/cvde.200304171

work page doi:10.1002/cvde.200304171 2004

[3] [3]

Sawicka, H

M. Sawicka, H. Turski, K. Sobczak, A. Feduniewicz- ˙Zmuda, N. Fiuczek, O. Go lyga, M. Siekacz, G. Muziol, G. Nowak, J. Smalc-Koziorowska, C. Skierbiszewski, Nanos- tars in highly Si-doped GaN, Crystal Growth & Design 23 (7) (2023) 5093–5101. doi: 10.1021/acs.cgd.3c00317

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Prozheev, M

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Richter, T

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Langpoklakpam, A.-C

C. Langpoklakpam, A.-C. Liu, Y.-K. Hsiao, C.-H. Lin, H.-C. Kuo, Vertical GaN MOSFET power devices, Micromachines 14 (10) (2023). doi:10.3390/mi14101937

work page doi:10.3390/mi14101937 2023

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Sierakowski, A

K. Sierakowski, A. Jaroszynska, R. Jakiela, M. Fijalkowski, T. Sochacki, M. Iwinska, M. Turek, K. Lorenz, M. Bockowski, Lateral and vertical diffusion of magnesium in ion- 13 implanted halide vapor phase epitaxy gallium nitride, Materials Science in Semiconductor Processing 171 (2024) 108022. doi:10.1016/j.mssp.2023.108022

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Sierakowski, R

K. Sierakowski, R. Jakiela, B. Lucznik, P. Kwiatkowski, M. Iwinska, M. Turek, H. Sakurai, T. Kachi, M. Bockowski, High pressure processing of ion implanted GaN, Electronics 9 (9) (2020). doi:10.3390/electronics9091380

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Kaess, S

F. Kaess, S. Mita, J. Xie, P. Reddy, A. Klump, L. H. Hernandez-Balderrama, S. Washiyama, A. Franke, R. Kirste, A. Hoffmann, R. Collazo, Z. Sitar, Correlation between mobility collapse and carbon impurities in Si-doped GaN grown by low pres- sure metalorganic chemical vapor deposition, Journal of Applied Physics 120 (10) (2016) 105701. doi:10.1063/1.4962017

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Jakiela, A

R. Jakiela, A. Barcz, E. Dumiszewska, A. Jagoda, Si diffusion in epitaxial GaN, physica status solidi (c) 3 (6) (2006) 1416–1419. doi:10.1002/pssc.200565112

work page doi:10.1002/pssc.200565112 2006

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Bonito Oliva, D

V. Bonito Oliva, D. Mangelinck, S. Hagedorn, H. Bracht, K. Irmscher, C. Hartmann, P. Venn´ egu` es, M. Albrecht, Silicon diffusion in AlN, Journal of Applied Physics 134 (9) (2023) 095103. doi:10.1063/5.0159641

work page doi:10.1063/5.0159641 2023

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Iwinska, P

M. Iwinska, P. Prystawko, A. Taube, K. Sierakowski, R. Jakiela, M. Bockowski, Examina- tion of silicon diffusion in GaN, in: H. Fujioka, H. Morko¸ c, U. T. Schwarz (Eds.), Gallium Nitride Materials and Devices XVII, Vol. PC12001, International Society for Optics and Photonics, SPIE, 2022, p. PC1200107. doi:10.1117/12.2607583

work page doi:10.1117/12.2607583 2022

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work page doi:10.1103/physrevb.79.201106 2009

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Garc´ ıa, N

A. Garc´ ıa, N. Papior, A. Akhtar, E. Artacho, V. Blum, E. Bosoni, P. Brandimarte, M. Brandbyge, J. I. Cerd´ a, F. Corsetti, et al., Siesta: Recent developments and applica- tions, The Journal of Chemical Physics 152 (20) (2020) 204108. doi:10.1063/5.0005077

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SIESTA, Available online: https://siesta-project.org/siesta (accessed: 2024-03- 13)

work page 2024

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Leszczynski, H

M. Leszczynski, H. Teisseyre, T. Suski, I. Grzegory, M. Bockowski, J. Jun, S. Porowski, K. Pakula, J. M. Baranowski, C. T. Foxon, T. S. Cheng, Lattice parameters of gallium nitride, Appl. Phys. Lett. 69 (1996) 73–75. doi:10.1063/1.118123

work page doi:10.1063/1.118123 1996

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Bitzek, P

E. Bitzek, P. Koskinen, F. G¨ ahler, M. Moseler, P. Gumbsch, Structural relaxation made simple, Phys. Rev. Lett. 97 (2006) 170201. doi:10.1103/PhysRevLett.97.170201. 14

work page doi:10.1103/physrevlett.97.170201 2006

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A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Dulak, J. Friis, M. N. Groves, B. Hammer, C. Hargus, et al., The atomic simulation environ- ment—a python library for working with atoms, Journal of Physics: Condensed Matter 29 (27) (2017) 273002. doi:10.1088/1361-648X/aa680e

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