Considerations for surface reconstruction stability prediction on GaAs(001)

John C. Thomas, Anton Van der Ven, Joanna Mirecki Millunchick, Normand A. Modine
2013 Physical Review B  
We present a theoretical analysis of the finite temperature equilibrium surface reconstruction stability of GaAs(001) from first principles, encompassing the As-rich regime relevant to lowtemperature grown (LTG) GaAs. Experimental evidence points to the thermodynamic stability of a (4×3) reconstruction in this regime, but density functional theory (DFT) calculations predict all (4×3) reconstructions to be metastable relative to the β2(2×4) and c(4×4). We employ statistical mechanical
more » ... chanical simulations, parameterized by density functional theory (DFT) to study the combined effects of configurational disorder and vibrational excitations on surface phase stability. The calculated finite-temperature surface free energies of the various reconstructions indicate that if a small constant energy shift is used to enforce stability of the lowest-energy (4×3), the resultant phase diagram is consistent with experiment, with the c(4×4) overwhelming (4×3) at high temperature. This behavior is due to competition between configurational entropy, which favors c(4×4) and vibrational entropy, which favors (4×3). The broad importance of III-V compound semiconductors for device applications is due to their wide variety of realizable, tunable alloys. However, because useful III-V alloys and heterostructures require precisely controlled layer-by-layer synthesis, their resultant properties and quality are largely limited by our understanding of structure and ordering phenomena at the crystalline growth surface. The structure and composition of the surface play an important role in the injection of point defects and antisites, particularly at low temperatures. Increasingly, these surface-induced defects are exploited for their beneficial consequences, as in low-temperature grown (LTG) GaAs, which is an important material for THz emitters and detectors. 1 LTG GaAs is typically grown in the [001] orientation at temperatures below 300 • C and under As-rich conditions. 2,3 In this regime excess surface As becomes kinetically trapped in the growing film, incorporating at up to 1 at-% above bulk stoichiometry in the form of both antisite defects and metallic As precipitates. 2,4 The high charge mobility and very low carrier lifetime in defected LTG GaAs make it particularly well suited for THz-range heterodyne photomixers. 5,6 The low-temperature growth regime is also used to enhance incorporation in low-solubility alloy systems, such as Ga 1−x Bi x As 7 and the ferroelectric semiconductor Ga 1−x Mn x As 8 Significant theoretical study of GaAs(001) has previously identified only two stable As-rich surface reconstructions, relative to bulk stoichiometry: the c(4×4) and β2(2×4), illustrated in Figs. 1(a) and 1(b), respectively. 9-11 Experimental observations, however, indicate the existence of a stable "×3" surface reconstruction on GaAs(001) with an As coverage intermediate to that of the β2(2×4) and c(4×4). 12-15 Scanning tunneling microscopy (STM) experiments strongly suggest that the GaAs "×3" surface is actually comprised of a (4×3) reconstruction. 14 Any complete description of GaAs(001) surface stability must account for this (4×3) reconstruction. This report presents our rigorous and comprehensive theoretical analysis of surface reconstruction stability on GaAs(001). We identify the low-energy As-rich GaAs(001) reconstruction prototypes and calculate their finitetemperature surface free energies from first principles, taking into account the combined effects of configurational disorder and vibrational excitations. By considering small relative shifts to the reconstruction surface free energies calculated from first principles we reproduce the experimentally-observed sequence of reconstruction stability with respect to temperature and surface composition. By relating the surface free energies to the finite-temperature partial pressure of As 4 we obtain a GaAs(001) surface phase diagram that is easily relatable to experimental results, with which we find good agreement. By elucidating the link between thermal disorder and surface reconstruction stability, our results provide crucial insight about the role of thermal excitation when targeting desirable growth regimes. Traditionally, surface reconstruction stability has been determined by comparing energies obtained from electronic structure calculations for a collection of reconstruction hypotheses. The reconstructions hypotheses are conjectured a posteriori based on limited empirical evidence. Consequently, constructing a hypothesis and verifying its stability is complicated by a number of factors. On a multicomponent surface, a well-specified surface reconstruction is comprised of a reconstruction prototype, which defines the bonding topology of surface atoms, and a species configuration that decorates it; if a prototype specifies an arrangement of dimers on the surface, each possible configuration of that prototype specifies whether each dimer is a homodimer, comprised of like species, or a heterodimer, composed of unlike species. Energy differences between reconstructions are calculated from DFT, which reliably predicts many groundstate properties of III-V compounds but provides no direct information about thermally excited behavior. Thermal effects, including lattice vibrations and fluctuations in species configuration, contribute an entropic component to the surface free energy that may alter reconstruction stability. Consequently, zero-K surface energies calculated from DFT are an insufficient predictor of reconstruction stability. At typical synthesis temperatures (k B T ∼ 50-80 meV) a sufficient entropy difference between surface reconstructions can overwhelm the difference in their 0-K surface energies, resulting in entropic stabilization of one reconstruction relative to another. Recent advances have resulted in a catalogue of all plausible III-V surface reconstructions, enabling an exhaustive search for a low-energy (4×3) reconstruction on GaAs(001). 11 Among the 124 conceivable (4×3) reconstruction prototypes that are charge-balanced, DFT calculations indicate that the prototype depicted in Fig. 1(c) has the lowest surface energy. Two species configurations of this prototype, the α(4×3) and β(4×3), have previously been predicted to be stable on the GaSb(001) and AlSb(001) surfaces. 16 These are illustrated in Fig. 1(c) inset. However, DFT predicts all species configurations of this (4×3) to be metastable on GaAs(001) relative to either the β2(2×4) or at least one species configuration of the c(4×4) prototype. The difference in surface free energy between the (4×3) and c(4×4) prototypes is very small, though-approximately 7 meV/A (1×1) over a sizeable range of chemical potential, where A (1×1) is the area of the surface primitive cell. Our calculations for the 123 other charge-balanced (4×3) prototypes show them to have much higher surface energy with respect to the c(4×4). 17 Consequently, the only (4×3) prototype that merits consideration is the one depicted in Fig. 1(c) . The multicomponent surface is an open system at fixed temperature, such that the surface free energy γ(T, µ As ) is minimized at equilibrium for fixed temperature T and As chemical potential µ As . 17 γ is comprised of contributions from electronic structure (i.e., the zero-K surface enthalpy), configurational excitations, and lattice vibrations. Electronic structure calculations were performed using a surface/slab geometry within the DFT local density approximation (LDA), as implemented in the Vienna ab initio Simulation Package (vasp). 18 Procedures and parameters are well
doi:10.1103/physrevb.87.075320 fatcat:3bzkia4xbng65hberjxktbamva