Dimerization on GaN(001) Surfaces
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DIMERIZATION ON GaN(001) SURFACES MIN-HSIUNG TSAI AND JOHN D. DOW Department of Physics and Astronomy, Arizona State University, Tempe, Arizona 85287-1504, U.S.A. ABSTRACT The GaN(001) surface is polar with either N- or Ga-termination. We predict that the Ga-terminated surface does not dimerize, but instead the surface Ga atoms relax into the vacuum by about ;0.38 A. The N-terminated surface is predicted to form a c(2x4) structure with N2 dimers in rows of length two. This is to be contrasted with the (2x1) Si(001) surface, on which the dimer rows are infinitely long, and with the (2x4) GaAs(001) surface, on which the rows are three dimers long. I. INTRODUCTION GaN, a wide band-gap semiconductor that normally occurs in the wurtzite phase, has recently been grown in the zinc-blende crystal-structure, in the form of thin (001) films, on substrates such as GaAs(001) [1], buffered Si(001) [2], and sapphire(0001) [3]. These achievements have rekindled interest in GaN, and also ARxGal-xN and InxGa1_xN alloys, as potential materials with optoelectronic applications in the blue to ultra-violet [4], and have highlighted the need for a better scientific understanding of both the GaN(001) surface itself and how GaN grows in the (001) direction. In this paper we predict the equilibrium geometries of the GaN N-terminated and Ga-terminated (001) perfect surfaces, using a theory that also obtains the observed (2xl) structure of the Si(001) surface and the observed (2x4) structure of the Asterminated GaAs(001) surface. II. MOLECULAR DYNAMICS WITH CHARGE TRANSFER GaN is a relatively ionic III-V compound semiconductor with a band gap of 3.4 eV at 300 0 K. Because of GaN's ionicity and strong long-ranged Coulomb forces in the bulk, both covalent bonding and ionic bonding determine the surface atoms' equilibrium positions. The surface crystal structure represents the minimum free-energy atomic configuration, and the internal energy, which is equal to the free-energy at zero temperature, can be computed reliably using the a priori local-density approximation [5]. However, until recently [6], implementation of the local-density approximation to find the equilibrium position of a structure of atoms (such as a surface) was computationally forbidding; instead, one would guess several likely equilibrium configurations, compute the internal or total energy of each, and select the one with the lowest total energy. However, with the development of a new, computationally efficient, self-consistent, local-density-approximation, a priori molecular dynamics with charge transfer [7], we are now able to reliably compute the net interatomic force Fi on the i-th atom of mass Mi, and then numerically solve Newton's law, Fi=Mi d2 Ri/dt 2 , for the atomic trajectories Ri(t), assuming that all atoms initially occupy the sites of a perfect, quiescent, unrelaxed zinc-blende (001) surface. After a time, the surface will pass through or near its maximum-kinetic-energy equilibrium configuration, as indicated by a decrease in total kinetic energy from one time-
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