First-Principles Surface Phase Diagram for Hydrogen on GaN Surfaces

Abstract

We discuss the derivation and interpretation of a generalized surface phase diagram, based on firstprinciples density-functional calculations. Applying the approach to hydrogenated GaN surfaces, we find that the Gibbs free energies of relevant reconstructions strongly depend on temperature and pressure. Choosing chemical potentials as variables results in a phase diagram that provides immediate insight into the relative stability of different structures. A comparison with recent experiments illustrates the power of the approach for interpreting and predicting energetic and structural properties of surfaces under realistic growth conditions. DOI: 10.1103/PhysRevLett.88.066103 PACS numbers: 68.35. -p, 68.43. -h, 81.10. -h A detailed understanding of semiconductor surface reconstructions is essential for controlling growth and materials properties. In the case of GaN, where materials quality is still limiting device progress, the investigations until now have focused on reconstructions of bare GaN surfaces [1]. The present study focuses on the role of hydrogen (H), which is important because H is abundantly present in the most commonly used growth techniques for nitride semiconductors, including metal-organic chemical vapor deposition (MOCVD), hydride vapor-phase epitaxy (HVPE), and molecular-beam epitaxy (MBE) when NH 3 is used as the nitrogen source.We have therefore performed detailed investigations of H interactions with GaN surfaces based on state-of-the-art pseudopotential-density-functional calculations. We focus on the technologically most relevant GaN(0001) surface, which is the polarity observed during MOCVD of GaN on sapphire as well as MBE on Si-face SiC. Since we are particularly interested in consequences for growth, it is essential to take finite temperature effects into account, requiring the calculation of free energies. This distinguishes our approach from previous work in which only zerotemperature energies were calculated, and then only for a small number of structures [2][3][4]. We will show that the energetic and structural features of the surface reconstructions dramatically depend on temperature (T) and pressure (p).In thermochemistry, the Gibbs free energy G is usually expressed as a function of T and partial pressures. An alternative approach is to use chemical potentials m as variables and to express G as a function of p, T, and all independent m's. For the system at hand, the Gibbs' Phase Rule produces four degrees of freedom, resulting in a four-dimensional phase space that is difficult to analyze or visualize. Our detailed analysis will show that the explicit dependence on p and T is small and can be neglected. The surface energy can then be expressed solely as a function of the chemical potentials m Ga and m H , while the p and T dependence is implicit. The advantage of this methodology is its physically intuitive character. Comparison with experiment requires only that the chemical potentials be evaluated as a function of T and partial pressures. The power of this approach will b...

Effects of hydrogen during molecular beam epitaxy of GaN

“…In this scenario, H does not form bonds directly with GaN surface, but instead it affects the gas species near the growth interface and/or the surface adsorbed species. In contrast, when there is enough hydrogen (µ H approaching -1.6 eV), it begins to bond with surface directly, consistent with the theoretical predictions of Van de Walle et al [7]. Since hydrogen now can bond with surface, the amount of hydrogen in the gas vapor is correspondingly reduced.…”

“…Comparing to the Ref. [7], we tentatively associate this surface with the N ad -H + Ga-H structure. Since hydrogen atoms do not have significant effects on Auger spectroscopy, it is expected that this N ad -H + Ga-H surface will have same Ga/N Auger ratio as a N-adatom surface.…”

“…[7], in which µ H is determined using results for an ideal gas of H 2 molecules at specified temperature and pressure. This method does not consider the effect of plasma and non-equilibrium nature of MBE on µ H , so there may be some uncertainty in comparing our µ H values with the theoretical ones [7]. On the Ga-rich side of Fig.…”

“…For larger H pressures and under Ga-poor conditions we observe a new surface structure, appearing as a sharp 2 × 2 pattern in reflection high-energy electron diffraction (RHEED). We tentatively associate this surface with the N ad -H + Ga-H structure predicted by Van de Walle et al [7]. Under Ga-rich conditions with the "1×1" present, the effect of hydrogen is to modify the surface morphology:…”

“…Surface studies for MOCVD films also exist [4]. Studies [5,6] have been carried out focusing on the dependence of growth rate of GaN films (of both polarities) in the presence of H. Theoretical work has also been performed to investigate the effect of H on GaN growth [7,8]. In this work, we study the GaN(0001) surface structure in the presence of H, in an effort to improve understanding of the link between MOCVD/RMBE and PAMBE growth.…”