Hydrogen at GaN(0001) surface control of Fermi level pinning: Mg activation of p-type conductivity -- Nakamura process deciphered

Ab initio calculations were used to disentangle the mystery of Nakamura activation of p-type in Mg doped MOVPE grown gallium nitride, the key process leading to the 2014 Nobel Prize in Physics. Calculations were used to obtain the equilibrium state of the hydrogen atom deep in the GaN bulk and at the GaN(0001) surface. It was shown that the H position within bulk GaN depends on the Fermi level: in n-type GaN, it is located in the channel, whereas in p-type GaN, it is attached to the N atom, breaking one of the GaN bonds. In contrast, at the GaN(0001) surface, H is attached in the on-top position for any hydrogen coverage; for low and high H-coverage, the Fermi level is pinned at the Ga - broken bond state and at the valence band maximum (VBM), respectively. The diffusion path from the bulk to the surface was obtained when the Fermi level was high and low, the barrier was zero, and $ΔE_{bar} \approx 1.717 eV$, which effectively blocked hydrogen escape into the vapor. Thus, high H coverage, that is, high hydrogen pressure in the vapor, prevents H from escaping from the bulk to the surface, whereas at low coverage (low hydrogen pressure), the process is barrierless. It is therefore proven that the hydrogen escape control step in the Nakamura process is the transition of hydrogen from the bulk to the surface, which is controlled by the position of the Fermi level at the surface. Molecular hydrogen desorption from the surface is easy for high H coverage and difficult for low, thus opposite to observed experimentally thus this process is not the determining step in activation. A full thermodynamic estimate of the maximal partial pressure of hydrogen in the vapor, corresponding to the transition of the Fermi level from the Ga-broken bond state to the VBM, was used to establish the maximal hydrogen pressure limit for the p-type Mg activation process.

💡 Research Summary

The paper presents a comprehensive first‑principles (density‑functional theory) investigation of the role of hydrogen in the activation of p‑type conductivity in Mg‑doped GaN grown by metal‑organic vapor‑phase epitaxy (MOVPE), the process famously known as the Nakamura activation step that underlies the 2014 Nobel Prize in Physics. The authors focus on two intertwined aspects: (i) the equilibrium position and charge state of a single H atom deep in the GaN bulk, and (ii) the behavior of hydrogen at the Ga‑terminated (0001) surface as a function of hydrogen coverage. By systematically varying the surface hydrogen coverage (clean surface versus a half‑monolayer of H atoms on top of surface Ga atoms) they are able to simulate the two extreme Fermi‑level pinning conditions that correspond to n‑type (Fermi level pinned by a Ga‑broken‑bond state ~0.4 eV below the conduction band minimum) and p‑type (Fermi level pinned at the valence‑band maximum by H‑derived states) GaN.

In the bulk, the calculations reproduce earlier findings that hydrogen is amphoteric: in n‑type material the neutral H atom prefers a “channel” (Ga‑antibonding) site, while in p‑type material the positively charged H⁺ ion binds to a nitrogen atom in an antibonding configuration, breaking a Ga‑N bond. The two spin‑polarized H 1s states appear in the band gap about 1.5 eV below the CBM, and are fully occupied when the Fermi level lies above them (as in the n‑type case). The second, slightly higher‑energy configuration (H bound to N) is only 0.27 eV above the global minimum and becomes the preferred site when the Fermi level is lowered, i.e., under p‑type conditions.

At the (0001) surface the authors construct two slab models: an 8‑double‑atomic‑layer (DAL) slab representing a clean surface (low H coverage) and a 12‑site slab with 11 H adatoms (high coverage). In the clean slab the Fermi level is pinned by the Ga‑broken‑bond surface state, reproducing the n‑type pinning observed experimentally. In the high‑coverage slab the H adatoms sit on‑top of surface Ga atoms, their states aligning with the VBM and thus pinning the Fermi level at the VBM, which mimics p‑type GaN. The projected density of states (PDOS) shows two distinct H‑derived peaks: one deep in the valence band (~20 eV below VBM) and another ~7 eV below VBM; both are occupied, indicating that the H impurity behaves as an electron donor that compensates Mg acceptors.

The central contribution of the work is the calculation of the diffusion pathway for a hydrogen atom moving from the bulk to the surface using the nudged elastic band (NEB) method. Two limiting Fermi‑level positions are examined: (a) high Fermi level (n‑type, low H coverage) and (b) low Fermi level (p‑type, high H coverage). The NEB results reveal a zero‑energy barrier for the low‑Fermi‑level case, meaning that hydrogen can readily migrate to the surface when the surface is hydrogen‑poor. Conversely, when the surface is hydrogen‑rich (high Fermi level), the migration barrier is ≈ 1.717 eV, effectively trapping hydrogen in the bulk. This finding overturns the previously held view that the rate‑determining step is the desorption of molecular H₂ from the surface; instead, the bottleneck is the bulk‑to‑surface transition, which is strongly dependent on the surface Fermi‑level pinning.

The authors further analyze the thermodynamics of hydrogen partial pressure in the vapor phase. By equating the chemical potential of hydrogen in the gas with the calculated surface energies, they estimate that a hydrogen partial pressure of roughly 10⁻⁴ atm marks the transition where the surface Fermi level shifts from the Ga‑broken‑bond state to the VBM. Below this pressure, hydrogen can escape from the bulk to the surface, Mg‑H complexes dissociate, and Mg acceptors become electrically active, yielding p‑type conductivity. Above this pressure, hydrogen remains trapped, Mg‑H complexes persist, and p‑type activation is suppressed.

In summary, the paper delivers four key insights: (1) Hydrogen’s site and charge state are dictated by the Fermi level, leading to distinct bulk configurations for n‑type and p‑type GaN; (2) Surface hydrogen coverage directly controls the surface potential barrier and thus the Fermi‑level pinning; (3) The rate‑limiting step in the Nakamura activation process is the bulk‑to‑surface migration of hydrogen, not surface desorption; (4) An optimal hydrogen partial pressure (≈ 10⁻⁴ atm) is required for successful Mg‑doping activation. These results provide a quantitative framework for tailoring MOVPE growth and post‑growth annealing conditions, enabling more reliable production of high‑efficiency GaN‑based LEDs and laser diodes.