Thermodynamic foundations of applications of ab initio methods for determination of the adsorbate equilibria: hydrogen at the GaN(0001) surface.

Thermodynamic foundations of ab initio modeling of vapor-solid and vapor-surface equilibria are introduced. The chemical potential change is divided into enthalpy and entropy terms. The enthalpy path passes through vapor-solid transition at zero temperature. The entropy path avoids the singular point at zero temperature passing a solid-vapor transition under normal conditions, where evaporation entropy is employed. In addition, the thermal changes are calculated. The chemical potential difference contribution of the following terms: vaporization enthalpy, vaporization entropy, the temperature-entropy related change, the thermal enthalpy change and mechanical pressure is obtained. The latter term is negligibly small for the pressure typical for epitaxy. The thermal enthalpy change is two orders smaller than the first three terms which have to be taken into account explicitly. The configurational vaporization entropy change is derived for adsorption processes. The same formulation is derived for vapor-surface equilibria using hydrogen at the GaN(0001) surface as an example. The critical factor is the dependence of the enthalpy of evaporation (desorption energy) on the pinning of the Fermi level bringing a drastic change of the value from 2.24 eV to -2.38 eV. In addition it is shown that entropic contributions considerable change the hydrogen equilibrium pressure over the GaN(0001) surface by several orders of magnitude. Thus a complete and exact formulation of vapor-solid and vapor-surface equilibria is presented.

Polar GaN Surfaces under Gallium Rich Conditions: Revised Thermodynamic Insights from Ab Initio Calculations.

This paper presents an improved theoretical view of ab initio thermodynamics for polar GaN surfaces under gallium-rich conditions. The study uses density functional theory (DFT) calculations to systematically investigate the adsorption of gallium atoms on GaN polar surfaces, starting from the clean surface and progressing to the metallic multilayer. First principles phonon calculations are performed to determine vibrational free energies. Changes in the chemical potential of gallium adatoms are determined as a function of temperature and surface coverage. Three distinct ranges of Ga coverage with very low, medium, and high chemical potential are observed on the GaN(000-1) surface, while only two ranges with medium and high chemical potential are observed on the GaN(000-1) surface. The analysis confirms that a monolayer of Ga adatoms on the GaN(000-1) surface is highly stable over a wide range of temperatures. For a second adlayer at higher temperatures, it is energetically more favorable to form liquid droplets than a uniform crystalline adlayer. The second Ga layer on the GaN(0001) surface shows pseudo-crystalline properties even at a relatively high temperature. These results provide a better thermodynamic description of the surface state under conditions typical for molecular beam epitaxy and offer an interpretation of the observed growth window.

Polarization Doping in a GaN-InN System-Ab Initio Simulation.

Polarization doping in a GaN-InN system with a graded composition layer was studied using ab initio simulations. The electric charge volume density in the graded concentration part was determined by spatial potential dependence. The emerging graded polarization charge was determined to show that it could be obtained from a polarization difference and the concentration slope. It was shown that the GaN-InN polarization difference is changed by piezoelectric effects. The polarization difference is in agreement with the earlier obtained data despite the relatively narrow bandgap for the simulated system. The hole generation may be applied in the design of blue and green laser and light-emitting diodes.

Self-formed compositional superlattices triggered by cation orderings in m-plane Al1-xInxN on GaN.

Immiscible semiconductors are of premier importance since the source of lighting has been replaced by white light-emitting-diodes (LEDs) composed of thermodynamically immiscible InxGa1-xN blue LEDs and yellow phosphors. For realizing versatile deep-ultraviolet to near-infrared light-emitters, Al1-xInxN alloys are one of the desirable candidates. Here we exemplify the appearance and self-formation sequence of compositional superlattices in compressively strained m-plane Al1-xInxN films. On each terrace of atomically-flat m-plane GaN, In- and Al-species diffuse toward a monolayer (ML) step edge, and the first and second uppermost < [Formula: see text]> cation-rows are preferentially occupied by Al and In atoms, respectively, because the configuration of one In-N and two Al-N bonds is more stable than that of one Al-N and two In-N bonds. Subsequent coverage by next < [Formula: see text]> Al-row buries the < [Formula: see text]> In-row, producing nearly Al0.5In0.5N cation-stripe ordering along [0001]-axis on GaN. At the second Al0.72In0.28N layer, this ordinality suddenly lessens but In-rich and In-poor < [Formula: see text]>-rows are alternately formed, which grow into respective {0001}-planes. Simultaneously, approximately 5-nm-period Al0.70In0.30N/Al0.74In0.26N ordering is formed to mitigate the lattice mismatch along [0001], which grow into approximately 5-nm-period Al0.70In0.30N/Al0.74In0.26N {[Formula: see text]} superlattices as step-flow growth progresses. Spatially resolved cathodoluminescence spectra identify the emissions from particular structures.

CH4 Adsorption Probability on GaN(0001) and (000-1) during Metalorganic Vapor Phase Epitaxy and Its Relationship to Carbon Contamination in the Films.

Suppression of carbon contamination in GaN films grown using metalorganic vapor phase epitaxy (MOVPE) is a crucial issue in its application to high power and high frequency electronic devices. To know how to reduce the C concentration in the films, a sequential analysis based on first principles calculations is performed. Thus, surface reconstruction and the adsorption of the CH4 produced by the decomposition of the Ga source, Ga(CH3)3, and its incorporation into the GaN sub-surface layers are investigated. In this sequential analysis, the dataset of the adsorption probability of CH4 on reconstructed surfaces is indispensable, as is the energy of the C impurity in the GaN sub-surface layers. The C adsorption probability is obtained based on steepest-entropy-ascent quantum thermodynamics (SEAQT). SEAQT is a thermodynamic ensemble-based, non-phenomenological framework that can predict the behavior of non-equilibrium processes, even those far from equilibrium. This framework is suitable especially when one studies the adsorption behavior of an impurity molecule because the conventional approach, the chemical potential control method, cannot be applied to a quantitative analysis for such a system. The proposed sequential model successfully explains the influence of the growth orientation, GaN(0001) and (000-1), on the incorporation of C into the film. This model can contribute to the suppression of the C contamination in GaN MOVPE.

Modeling the Non-Equilibrium Process of the Chemical Adsorption of Ammonia on GaN(0001) Reconstructed Surfaces Based on Steepest-Entropy-Ascent Quantum Thermodynamics.

Clearly understanding elementary growth processes that depend on surface reconstruction is essential to controlling vapor-phase epitaxy more precisely. In this study, ammonia chemical adsorption on GaN(0001) reconstructed surfaces under metalorganic vapor phase epitaxy (MOVPE) conditions (3Ga-H and Nad-H + Ga-H on a 2 × 2 unit cell) is investigated using steepest-entropy-ascent quantum thermodynamics (SEAQT). SEAQT is a thermodynamic-ensemble based, first-principles framework that can predict the behavior of non-equilibrium processes, even those far from equilibrium where the state evolution is a combination of reversible and irreversible dynamics. SEAQT is an ideal choice to handle this problem on a first-principles basis since the chemical adsorption process starts from a highly non-equilibrium state. A result of the analysis shows that the probability of adsorption on 3Ga-H is significantly higher than that on Nad-H + Ga-H. Additionally, the growth temperature dependence of these adsorption probabilities and the temperature increase due to the heat of reaction is determined. The non-equilibrium thermodynamic modeling applied can lead to better control of the MOVPE process through the selection of preferable reconstructed surfaces. The modeling also demonstrates the efficacy of DFT-SEAQT coupling for determining detailed non-equilibrium process characteristics with a much smaller computational burden than would be entailed with mechanics-based, microscopic-mesoscopic approaches.

Surface Stability and Growth Kinetics of Compound Semiconductors: An Ab Initio-Based Approach.

We review the surface stability and growth kinetics of III-V and III-nitride semiconductors. The theoretical approach used in these studies is based on ab initio calculations and includes gas-phase free energy. With this method, we can investigate the influence of growth conditions, such as partial pressure and temperature, on the surface stability and growth kinetics. First, we examine the feasibility of this approach by comparing calculated surface phase diagrams of GaAs(001) with experimental results. In addition, the Ga diffusion length on GaAs(001) during molecular beam epitaxy is discussed. Next, this approach is systematically applied to the reconstruction, adsorption and incorporation on various nitride semiconductor surfaces. The calculated results for nitride semiconductor surface reconstructions with polar, nonpolar, and semipolar orientations suggest that adlayer reconstructions generally appear on the polar and the semipolar surfaces. However, the stable ideal surface without adsorption is found on the nonpolar surfaces because the ideal surface satisfies the electron counting rule. Finally, the stability of hydrogen and the incorporation mechanisms of Mg and C during metalorganic vapor phase epitaxy are discussed.