Showing papers by "Alex Zunger published in 1992"

Zinc-blende-wurtzite polytypism in semiconductors.

Abstract: The zinc-blende (ZB) and wurtzite (W) structures are the most common crystal forms of binary octet semiconductors. In this work we have developed a simple scaling that systematizes the T=0 energy difference \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ between W and ZB for all simple binary semiconductors. We have first calculated the energy difference \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}^{\mathrm{LDF}}$(AB) for AlN, GaN, InN, AlP, AlAs, GaP, GaAs, ZnS, ZnSe, ZnTe, CdS, C, and Si using a numerically precise implementation of the first-principles local-density formalism (LDF), including structural relaxations. We then find a linear scaling between \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}^{\mathrm{LDF}}$(AB) and an atomistic orbital-radii coordinate R\ifmmode \tilde{}\else \~{}\fi{}(A,B) that depends only on the properties of the free atoms A and B making up the binary compound AB. Unlike classical structural coordinates (electronegativity, atomic sizes, electron count), R\ifmmode \tilde{}\else \~{}\fi{} is an orbital-dependent quantity; it is calculated from atomic pseudopotentials. The good linear fit found between \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ and R\ifmmode \tilde{}\else \~{}\fi{} (rms error of \ensuremath{\sim}3 meV/atom) permits predictions of the W-ZB energy difference for many more AB compounds than the 13 used in establishing this fit. We use this model to identify chemical trends in \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ in the IV-IV, III-V, II-VI, and I-VII octet compounds as either the anion or the cation are varied. We further find that the ground state of MgTe is the NiAs structure and that CdSe and HgSe are stable in the ZB form. These compounds were previously thought to be stable in the W structures.

Efficient cluster expansion for substitutional systems.

Abstract: We demonstrate a cluster expansion technique that is capable of accurately predicting formation energies in binary substitutional systems---even for those with large atomic relaxations. Conventional cluster expansions converge rapidly only in the absence of atomic relaxations, and they fail for long-period lattice-mismatched superlattices. When combined with first-principles total-energy methods, our method allows for very fast calculations for structures containing hundreds or thousands of atoms. The convergence and effectiveness of the cluster expansion are enhanced in two ways. First, the expansion is recast into reciprocal space, which allows for the inclusion of all important pair interactions. Second, a reciprocal space formulation for elastic strain energy is introduced, allowing accurate predictions for both long- and short-period superlattices. We illustrate the power of the method by performing a cluster expansion that requires total-energy calculations for only 12 simple input structures, with at most eight atoms per unit cell. We then correctly predict the formation energies of relaxed long-period superlattices, low-symmetry intermixed superlattices, structures with varied compositions, substitutional impurities, and a [ital im]1000 atom/cell simulation of the random alloy.

First-principles calculation of the order-disorder transition in chalcopyrite semiconductors.

Abstract: We describe the polymorphic order-disorder transition in the chalcopyrite-type semiconductor Cu{sub 0.5}In{sub 0.5}Se through a Monte Carlo simulation of a generalized Ising Hamiltonian whose interaction energies are determined from {ital ab} {ital initio} total-energy calculations. The calculated transition temperature ({ital T}{sub {ital c}}=1125{plus minus}10 K) compares well with experiment ({ital T}{sub {ital c}}=1083 K). Unlike the analogous phenomena in isovalent III-V alloys, we find that the transition is dominated by electronic compensation between donor and acceptor states, leading to strong correlations in the disordered phase, and a {ital decrease} in the optical band gap upon disordering.

Predictions and systematizations of the zinc-blende-wurtzite structural energies in binary octet compounds.

Abstract: To systematize the wurtzite (W) versus zinc blende (ZB) structural preferences among the binary octet compounds, we have calculated the correponding energy difference \ensuremath{\Delta}${\mathit{E}}_{\mathit{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}^{\mathrm{LDF}}$(AB) for thirteen AB compounds using the local-density formalism (LDF). We then uncovered a linear scaling betwteen \ensuremath{\Delta}${\mathit{E}}_{\mathit{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}^{\mathrm{LDF}}$ and an atomistic orbital-radii coordinate R\ifmmode \tilde{}\else \~{}\fi{}(A,B) that can be simply calculated from the properties of the free A and B atoms. This permits predictions of W-ZB energy differences for all binary compounds and exposes simple chemical trends, including the stabilization of the ZB form in the sequence B=O\ensuremath{\rightarrow}S\ensuremath{\rightarrow}Se\ensuremath{\rightarrow}Te for ${\mathit{A}}^{\mathrm{II}}$${\mathit{B}}^{\mathrm{VI}}$ and A=Ga\ensuremath{\rightarrow}Al\ensuremath{\rightarrow}In for ${\mathit{A}}^{\mathrm{III}}$${\mathit{B}}^{\mathrm{V}}$'s. We propose new structural assignments for the low-temperature ground state of CdSe (ZB) and MgTe (NiAs type).

Electronic structure of ordered and disordered Cu3Au and Cu3Pd.

Abstract: In ordered L${1}_{2}$-type ${\mathit{A}}_{3}$B compounds, each A atom is coordinated by 8A+4B atoms, while each B atom is coordinated by 12A atoms. By symmetry, all A-A, A-B, and B-B bond lengths are equal. When this structure disorders to form the substitutionally random ${\mathit{A}}_{0.75}$${\mathit{B}}_{0.25}$ alloy, each atom acquires a distribution of different types of coordination shells. Concomitantly with this reduction in site symmetries, (i) topologically different A atoms (and separately, different B atoms) can have unequal charges, and (ii) the various bonds need not be of equal average lengths 〈R〉 (i.e., 〈${\mathit{R}}_{\mathit{A}\mathrm{\ensuremath{-}}\mathit{A}}$〉\ensuremath{ e}〈${\mathit{R}}_{\mathit{A}\mathrm{\ensuremath{-}}\mathit{B}}$〉\ensuremath{ e} 〈${\mathit{R}}_{\mathit{B}\mathrm{\ensuremath{-}}\mathit{B}}$〉). Furthermore, (iii) there can be a distribution of bond-length values around 〈${\mathit{R}}_{\mathit{i}\mathit{j}}$〉 for each of the three chemical bond types. In this work we study the effects of such charge fluctuations (i) and relaxational fluctuations [(ii) and (iii)] on the electronic structure of ${\mathrm{Cu}}_{3}$Au and ${\mathrm{Cu}}_{3}$Pd. The random alloys are modeled by the special quasirandom structure (SQS), whereby the sites of a periodic supercell are occupied by A and B atoms so that the first few radial correlation functions closely reproduce the average correlation functions in an infinite substitutional random network. Instead of requiring that each atom ``see'' an identical, average medium, as is the case in the homogeneous site-coherent-potential approximation (SCPA), we thus create a distribution of distinct local environments whose average corresponds to the random alloy.Application of a first-principles local-density method (linearized augmented-plane-wave method) to the SQS then provides the energy-minimizing equilibrium relaxations, charge density, density of states, and formation enthalpy. We find that charge and relaxational fluctuations neglected in the SCPA lead to a significant stabilization of the alloy (\ensuremath{\sim}30% lowering in mixing enthalpy) and to substantial (\ensuremath{\sim}1 eV) nonrigid shifts in the electronic energy levels.

Evolution of alloy properties with long-range order.

Abstract: We present a general theory of compounds with partial long-range order. We derive a simple formula that determines the properties of a partially ordered compound from those of the perfectly random alloy and the fully ordered compound. The formula makes accurate predictions of both formulation energies and electronic band structures. We also use the formula to predict the band gaps of Al[sub 1[minus][ital x]]Ga[sub [ital x]]As/GaAs superlattices.

Interfacial atomic structure and band offsets at semiconductor heterojunctions

Abstract: The relationship between interfacial atomic structure and band offsets at semiconductor heterojunctions is explored through first‐principles local density functional calculations. In particular, the effects of variations in interfacial geometry are analyzed for (001) interfaces between III–V/III–V materials. For the AC/BC case of a common atom, isovalent A–B intermixing in the noncommon atomic planes near the interface does not affect the band offset, even in the case of large lattice‐mismatched systems. For quaternary AB/CD systems, there are two possible chemically abrupt interfaces (A–D or B–C); these can have offsets that differ by up to 80 meV. In those cases where the chemically abrupt AB/CD offset depends on the interfacial identity, intermixing leads to offset variations which are directly related to the offset difference between the chemically abrupt A–D and B–C interfaces. The differing behavior of common‐atom versus noncommon‐atom systems is analyzed in terms of the symmetry of the nearest‐neig...

Ordering thermodynamics of surface and subsurface layers in the Ga1-xInxP alloy.

Abstract: Although bulk III-V alloys exhibit phase separation, vapor-phase epitaxial growth of Ga 0.5 In 0.5 P/GaAs (001) at ≃900-1000 K shows spontaneous ordering into the (111)-oriented mono-layer (GaP) 1 (InP) 1 superlattice (the «CuPt» structure). Only two superlattice directions ([111] and [111], which define the CuPt B variant) out of four possible are seen. Both [111] and [111] subvariants are observed on flat surfaces or when surface steps are perpendicular to the cation dimers

Theory of bonding charge density in β′ NiAl

Abstract: Fox and Tabbernor [Acta metall. mater.39, 669 (1991)] have recently measured the four lowest structure factors F(G) of NiAl using highly accurate high energy electron diffraction. We present here a systematic comparison of their results with ab initio band theory, in the context of the local density formalism. We find very good agreement for the three of the four lowest measured structure factors, while our F(200) is ∼0.4 e/cell higher. We tentatively attribute this difference to uncertainties in the treatment of the temperature factors in non-monoatomic compounds. Indeed, comparing with experiment our calculation for the monoatomic Si crystal (where the temperature term factors out), we find that theory reproduces the measured structure factors to within a very small deviations of ∼0.02 e/atom. We have also examined the effect of high Fourier components that are not currently amenable to measurements on the ensuing NiAl deformation electron density distribution (DEDD) maps. We find that the truncation of the Fourier series after four structure factors misses the directional d-like charge lobes near the Ni sites. We show that static and dynamic DEDD give a similar picture of the bonding.

The electronic charge distribution in crystalline silicon : comparison of Ab initio theory and experiment

Abstract: Recent consolidation by Cummings & Hart [Aust. J. Phys. (1988), 41, 423–431] of five measured data sets of high-precision Si structure factors and subsequent analysis by Deutsch [Phys. Lett. A (1991), 153, 368–372] produced information on the charge density of Si with precision that is unmatched by any other system. A detailed comparison with newly performed ab initio electronic structure calculation within the local density formalism (LDF) is presented here. The convergence of the calculation is extended to the limit at which the results reflect the predictions of the underlying LDF, unobscured by computational uncertainties. Excellent agreement (e.g. R = 0.21% which is three to five times better than previous calculations) is found. This allows the effects of high-index structure factors to be assessed (currently beyond the reach of high-precision measurements) on both static and dynamic deformation charge densities.

Theory of interfacial stability of semiconductor superlattices.

Abstract: With few exceptions, abrupt isovalent {ital AC}/{ital BC} semiconductor superlattices (SL's) were predicted to be {ital globally} unstable at {ital T}=0 with respect to the random alloy. We examine the stability of these SL's with respect to {ital local} swaps of atoms near the interface, leading to interface-broadening reconstructions. For lattice-mismatched GaP/InP SL's, we find that reconstruction is most energetically favorable for SL's in the (111) and (011) directions, and somewhat less favorable for SL's in the (001) direction. These results are indepenent of period {ital p} for {ital p}{gt}3; for {ital p}{lt}3, reconstruction results in large energy gains (nearly 60% for {ital p}=1 (111)), in the (001) and (111) directions, but reconstruction is unfavorable for short-period (011) and (201) SL's. For monolayer SL's reconstruction is accompanied by a large increase in the electronic band gap. The stability of abrupt SL's with respect to reconstruction shows a strong dependence on the substrate lattice constant on which the SL is grown; SL's grown in a GaP substrate are the most stable, while those grown on InP are the least stable. For {ital lattice}{minus}{ital matched} AlAs/GaAs SL's, small energy lowerings are found for some SL's with {ital p}{le}3, while no reconstructions aremore » found for longer periods.« less

Identity of the conduction-band minimum in (AlAs)1/(GaAs)1 (001) superlattices: Intermixing-induced reversal of states.

Abstract: First-principles pseudopotential calculations on the (001) (AlAs){sub 1}/(GaAs){sub 1} superlattice (SL) shows that {ital partial} intermixing of the Al and Ga atoms relative to the abrupt case lowers its formation energy, making this SL even stabler at low {ital T} than the fully randomized Al{sub 0.5}Ga{sub 0.5}As alloy. Concomitantly, the conduction-band minimum (CBM) reverts from the GaAs {ital L}-derived state, to the {ital X}{sup {ital x}{ital y}}-derived AlAs state. The previously noted discrepancy between theory (pertinent to abrupt SL's and yielding an {ital L}-derived CBM) and experiment (yielding an {ital X}{sup {ital x}{ital y}}-derived CBM) is therefore attributed to insufficient interfacial abruptness in the samples used to date in experimental studies.

Surface energetics and ordering in GaInP

Abstract: Although bulk III-V semiconductor alloys generally exhibit phase separation, vapor-phase epitaxial growth of Ga0.5In0.5P on GaAs (001) shows spontaneous ordering into a [111] oriented monolayer superlattice. This ordering is believed to be induced at the surface during growth. We have performed total-energy first-principles pseudopotential calculations for the surface layers of cation- and anion-terminated (001) surfaces of Ga0.5In0.5P on GaAs substrates and valence-forcefield model calculations for deeper layers. These calculations show that the relative stability of the various Ga/In arrangements is a strong function of the layer depth below the surface. At the cation-terminated surface a Ga/In atomic arrangement corresponding to the observed bulk ordering is preferred over other arrangements by 90 meV per surface atom. This preference is intimately tied to electronically driven surface reconstructions. For subsurface Ga/In layers the energy differences are generally small (<30 meV per atom), but at the fourth subsurface layer they play a critical role in controlling the three-dimensional stacking of the ordered (001) layers. Finally, thermodynamic calculations based on a configurational Hamiltonian whose interaction energies are fit to the total energy calculations show that the observed ordering can be explained as a thermodynamically stable surface phase at growth temperatures, which, depending on the atomic mobilities, may remain as a metastable bulk phase as the growth proceeds. On the basis of these results we propose a possible mechanism for the development of the ordered phase.

Thermodynamics of surface‐induced ordering in the Ga1−xInxP alloy

Abstract: The occurrence of spontaneous CuPt‐like ordering in epitaxial Ga1−xInxP alloys is examined by means of a thermodynamic theory. We treat both cation‐ and anion‐terminated surfaces. We find that the order parameter of the observed CuPtB variant is significant for reconstructed cation‐terminated surfaces even at preparation temperatures. A possible mechanism for the formation of the three‐dimensional CuPtB structure involves partial equilibration of the cation‐terminated reconstructed surface followed by freezing of the cations as the surface is buried by newly deposited layers.