Thermodynamic model for metalorganic vapor-phase epitaxy of N-polar group-III nitrides in step-flow growth mode: Hydrogen, competitive adsorption, and configuration entropy

Abstract

A thermodynamic model for metalorganic vapor-phase epitaxy (MOVPE) of the N-polar $(000\overline{1})$ binary group-III nitrides (AlN, GaN, and InN) in the step-flow growth mode is proposed based on the Burton, Cabrera, and Frank (BCF) theory. The coverages of the group-III adatoms are thermodynamically evaluated under competitive adsorption with hydrogen, which is used as a carrier gas or dissociated from the ${\mathrm{NH}}_{3}$ source gas during MOVPE. The chemical potentials of the group-III and H adatoms on N-polar group-III nitride surfaces are modeled using the respective bond energies with the surface N atoms of the nitride and the vibrational frequencies of the adatoms. The coverages of the coadsorbed group-III and H adatoms are calculated using the Langmuir adsorption isotherm with these chemical potentials. The configuration entropy of the group-III adatoms bridges the gap between the thermodynamic model and the BCF theory. The coverage of the group-III adatoms plays a role like partial pressure of the group-III gas in the thermodynamics. The equilibrium coverage of the group-III adatoms and the equilibrium pressure of the ${\mathrm{NH}}_{3}$ gas are evaluated from the conditions of Gibbs energy balance between the sources (group-III adatom and ${\mathrm{NH}}_{3}$ gas molecule) and products (group-III nitride and $3/2\phantom{\rule{0.28em}{0ex}}{\mathrm{H}}_{2}$ gas molecules) and of speed balance between group-III and N incorporation into step kinks. Fair agreements with the experimentally optimized growth conditions for MOVPE of N-polar GaN and InN are obtained by this method. Among the examined binary group-III nitrides, AlN growth is hardly affected by ${\mathrm{H}}_{2}$ gas pressure, GaN growth is controlled well by ${\mathrm{H}}_{2}$ gas pressure, and InN growth is strongly inhibited by ${\mathrm{H}}_{2}$ gas. A criterion for selecting the ${\mathrm{NH}}_{3}$/group-III flow ratio for maximum products/cost and minimum waste of the materials is demonstrated using the growth model and the estimated growth parameters. The offcut angle dependence of the growth rate on the vicinal substrates is also investigated.