Showing papers by "Alex Zunger published in 1994"

Solving Schrödinger’s equation around a desired energy: Application to silicon quantum dots

Abstract: We present a simple, linear‐in‐size method that enables calculation of the eigensolutions of a Schrodinger equation in a desired energy window. We illustrate this method by studying the near‐gap electronic structure of Si quantum dots with size up to Si1315H460(≊37 A in diameter) using a plane wave pseudopotential representation.

Electronic Structure Pseudopotential Calculations of Large (.apprx.1000 Atoms) Si Quantum Dots

Abstract: The electronic structure of quantum dots containing N [ge] 1000 atoms is difficult to calculate by conventional molecular methods since the effort scales as N[sup 3]. Our newly developed method allows calculation of eigenstates within a desired [open quotes]energy window[close quotes] and thus has a linear-in-N scaling. This method is applied here to Si quantum dots using a plane wave basis expansion and an empirical pseudopotential Hamiltonian. Hydrogen atoms passivate the surface dangling bonds using a realistic surface relaxation geometry. We investigate the dependences of energy gaps and radiative recombination rates on the size, shape, and orientation of the Si quantum dots. We find that (1) a unified curve exists for band gap vs size of quantum spheres, cubes, and rectangular boxes; (2) the band edge states of Si quantum dots are bulklike, not surfacelike; (3) the band gap is insensitive to the surface orientation and to the overall shape of the quantum dot as long as it is not too prolate; (4) the radiative lifetime is sensitive to the shape and orientation; and (5) effective mass and single band truncated crystal models describe inadequately the electronic structure of Si quantum dots in the size range ([approx lt]40 [angstrom]) studiedmore » here. 52 refs., 8 figs., 2 tabs.« less

Dielectric constants of silicon quantum dots

Abstract: Quantum mechanical pseudopotential calculations of the absorption spectra and static dielectric constant ${\ensuremath{\epsilon}}_{s}$ of Si quantum dots with \ensuremath{\sim}100-1300 atoms are presented. The predicted ${\ensuremath{\epsilon}}_{s}$ is found to be significantly reduced relative to the bulk value, but is considerably larger than the value deduced from currently available model calculations. A convenient parametrization of ${\ensuremath{\epsilon}}_{s}$ vs size $R$ is provided. We find that for quantum dots with $Rl20$ \AA{} the electron-hole pair is confined by the physical dimension of the dot, not by the Coulomb attraction.

Relationships between the band gaps of the zinc-blende and wurtzite modifications of semiconductors

Abstract: While the direct band gaps of wurtzite (W) and zinc-blende (ZB) structures are rather similar, the W and ZB gaps can differ enormously (e.g., \ensuremath{\sim}1 eV in SiC) in indirect gap materials. This large difference is surprising given that the structural difference between wurtzite and zinc blende starts only in the third neighbor and that total energy differences are only \ensuremath{\sim}0.01 eV/atom. We show that zinc-blende compounds can be divided into five types (I--V) in terms of the order of their ${\mathrm{\ensuremath{\Gamma}}}_{1\mathit{c}}$, ${\mathit{X}}_{1\mathit{c}}$, and ${\mathit{L}}_{1\mathit{c}}$ levels and that this decides the character (direct, indirect, pseudodirect) of the wurtzite band gap. The observation of small ${\mathit{E}}_{\mathit{g}}^{\mathrm{W}}$-${\mathit{E}}_{\mathit{g}}^{\mathrm{ZB}}$ differences in direct band-gap systems (``type II,'' e.g., ZnS), and large differences in indirect gap systems (``type IV,'' e.g., SiC) are explained. We further show that while both type-III systems (e.g., AIN) and type-V systems (e.g., GaP) have an indirect gap in the zinc-blende form, their wurtzite form will have direct and pseudodirect band gaps, respectively. Furthermore, a direct-to-pseudodirect transition is predicted to occur in type-I (e.g., GaSb) systems.

First-Principles Statistical Mechanics of Semiconductor Alloys and Intermetallic Compounds

Abstract: A binary substitutional system can exist in 2N configurations that can be formed by occupying any of the N sites of a lattice by either an A or a B atom. Substitutional configurations include compounds, alloys, superlattices, and substitutional impurities. This article addresses the questions of (i) finding the lowest energy configuration of a given A/B substitutional system, (ii) calculating its composition-temperature phase diagram, and (iii) its finite-temperature thermodynamic properties, using the first-principles local density approximation (LDA). Mapping of the LDA energies of 10–20 ApBq compounds onto an Ising-like “cluster expansion” enables use of lattice statistical mechanics techniques that elegantly solve the above problems. This extends the utility of the LDA from simple, perfectly-ordered compounds to truly complex structures. We illustrate the method for semiconductor systems and transition-metal intermetallic systems, emphasizing the role of lattice relaxation.

Optical properties of zinc-blende semiconductor alloys: Effects of epitaxial strain and atomic ordering.

Abstract: Spontaneous ordering of III-V alloys is known to cause a band-gap reduction \ensuremath{\Vert}\ensuremath{\Delta}${\mathit{E}}_{\mathit{g}}$\ensuremath{\Vert} and a splitting \ensuremath{\Delta}${\mathit{E}}_{12}$ of the valence-band maximum. Strain also leads to a valence-band splitting and, depending on the sign of the strain \ensuremath{\epsilon}, to an increase (for \ensuremath{\epsilon}0) or decrease (for \ensuremath{\epsilon}g0) in the band gap. We present a general theory explaining how the strain produced by lattice mismatch with the substrate interacts with ordering effects. We find for (001) strain and (111) ``CuPt'' ordering that (i) atomic ordering removes the cusp in the band gap vs strain curve of random alloys; (ii) epitaxial strain always leads to an increase in the ordering-induced valence-band splitting \ensuremath{\Delta}${\mathit{E}}_{12}$; (iii) atomic ordering reduces the slope of \ensuremath{\Delta}${\mathit{E}}_{12}$ vs strain; (iv) while (a) strain, (b) ordering, and (c) clustering can all lead to a band-gap reduction, we show here that the three effects can be partially distinguished on the basis of a \ensuremath{\Delta}${\mathit{E}}_{12}$ vs \ensuremath{\Vert}\ensuremath{\Delta}${\mathit{E}}_{\mathit{g}}$\ensuremath{\Vert} plot; (v) the wave-function type at the valence-band maximum (VBM) (and, hence, the cause of the splitting) can be further determined by measuring the polarization dependence of the intensities of the transitions between the VBM split components and the conduction-band minimum; (vi) we predict that ordering can significantly enhance the degree of spin polarization of photoelectrons emitted from the VBM. Ordered III-V alloys can thus be used as a good polarized electron source. These general results open avenues of band-gap engineering by combining epitaxial strain with atomic ordering. Specific experimentally testable predictions are presented.

Confinement, surface, and chemisorption effects on the optical properties of Si quantum wires

Abstract: We have used the empirical pseudopotential method to study the electronic and optical properties of [001] Si quantum wires with (110)--([bar 1]10) square cross sections ranging from 4[times]4 to 14[times]14 monolayers (7.7[times]7.7 to 26.9[times]26.9 A, respectively). We present energy levels, band gaps, oscillator-strength, and charge-density distributions. To understand the electronic structure of these systems we calculate their properties in a stepwise process, considering (1) wires with a free surface but without hydrogen and (2) wires with hydrogen chemisorption on the surface. We find that (i) in both cases, the band gap between bulklike states increases as the wire size is reduced (due to quantum confinement). However, (ii) hydrogen chemisorption acts to reduce the gap. (iii) Whereas the low-energy states near the valence-band [ital minimum] are effective-mass-like, the near-band-gap states with or without H on the surface can be decisively non-effective-mass-like. The lowest conduction states are pseudodirect, not direct. (iv) The calculated energy dependence of the transition lifetimes is too strong to explain the observed low-energy slow'' emission band in porous Si purely in terms of transitions in an ideal wire. However, an alternative model, which introduces a mixture of wires and boxes, can account for the experimental slope.

First-principles simulated-annealing study of phase transitions and short-range order in transition-metal and semiconductor alloys

Abstract: Total-energy local-density calculations on approximately 20 periodic crystal structures of a given AB compound are used to define a long-range Ising Hamiltonian which correctly represents atomic relaxations. This allows us to accurately calculate structural energies of relaxed substitutional ${\mathit{A}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathit{B}}_{\mathit{x}}$ systems containing thousands of transition-metal atoms, simply by adding up spin products in the Ising Hamiltonian. The computational cost is thus size independent. We then apply Monte Carlo and simulated-annealing techniques to this Ising Hamiltonian, finding (i) the T=0 ground-state structures, (ii) the order-disorder transition temperatures ${\mathit{T}}_{\mathit{c}}$, and (iii) the Tg${\mathit{T}}_{\mathit{c}}$ short-range-order parameters. The method is illustrated for a transition-metal alloy (${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Pd}}_{\mathit{x}}$) and a semiconductor alloy (${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{In}}_{\mathit{x}}$P). It extends the applicability of the local-density method to finite temperatures and to huge substitutional supercells. We find for ${\mathrm{Cu}}_{0.75}$${\mathrm{Pd}}_{0.25}$ a characteristic fourfold splitting of the diffuse scattering intensity due to short-range order as observed experimentally.

Is there an elastic anomaly for a (001) monolayer of InAs embedded in GaAs

Abstract: When a coherently grown (001)‐oriented layer of InAs is embedded in a GaAs host, the coherency strain induces a perpendicular distortion of the embedded layer, predicted by continuum elasticity theory to be e⊥=7.3%. Brandt, Ploog, Bierwolf, and Hohenstein, [Phys. Rev. Lett. 68, 1339 (1992)] have described a high‐resolution electron microscopic analysis of such buried layers that appears to reveal a breakdown of continuum elasticity theory in the limit of monolayer films. In particular, they found for a single monolayer of InAs a lattice distortion that corresponds to e⊥=12.5%. Here we report on an investigation into whether a first‐principles local‐density total energy minimization shows such an elastic anomaly in the monolayer limit. We find that it does not.

Absolute deformation potentials of Al, Si, and NaCl.

Abstract: We present an approach to the calculation of absolute deformation potentials (ADP's) based on ab initio all-electron methods. The ADP of a given single-particle state is obtained from the variation of its energy between a compressed and an expanded region of the same material. Core levels are used to calculate the band offset at the compressed-expanded homojunction. We present results for a simple metal (Al), a semiconductor (Si), and an insulator (NaCl) under uniaxial strain. We find that (i) the ADP of the valence-band maximum is positive in Si, as predicted by a simple tight-binding model, but it is negative in NaCl, in conflict with tight binding; (ii) while most conduction-band states have negative ADP's, in agreement with the tight-binding picture, some conduction states have positive ADP's; (iii) core levels have nonvanishing ADP's, so they cannot be used as ``absolute'' reference energies in the presence of strain.

Effects of atomic clustering on the optical properties of III-V alloys

Abstract: Self-consistent electronic structure calculations together with a structural model are used to study the effect of short-range atomic order on the optical properties of otherwise random Al(0.5)Ga(0.5)As, Ga(0.5)In(0.5)P, and Al(0.5)In(0.5)As alloys. We find that clustering can reduce the direct band gap of these alloys by as much as 100 meV. Furthermore, sufficiently strong clustering is predicted to transform Al(0.5)Ga(0.5)As into a direct gap material.

Effects of atomic clustering on the optical properties of iii-v alloys

Abstract: Self‐consistent electronic structure calculations together with a structural model are used to study the effect of short‐range atomic order on the optical properties of otherwise random Al05Ga05As, Ga05In05P, and Al05In05As alloys We find that clustering can reduce the direct band gap of these alloys by as much as 100 meV Furthermore, sufficiently strong clustering is predicted to transform Al05Ga05As into a direct gap material

Unequal wave vectors in short- versus long-range ordering in intermetallic compounds.

Abstract: The sign of the formation energy [Delta][ital H][sub [ital F]] of a compound indicates if the low-temperature long-range order (LRO) corresponds to compound formation (when [Delta][ital H][sub [ital F]][lt]0) or to phase-separation (when [Delta][ital H][sub [ital F]][gt]0). However, [Delta][ital H][sub [ital F]] by itself does not tell us what type (ordering or clustering) of high-temperature short-range order (SRO) can be expected. The reason is that [Delta][ital H][sub [ital F]] contains two [ital types] of contributions: an elastic,'' volume-deformation energy [ital G]([ital x]) that reflects the energy invested in deforming the constituents [ital A] and [ital B] to the volume [ital V]([ital x]) of the [ital A][sub 1[minus][ital x]][ital B][sub [ital x]] alloy, and a chemical'' energy [var epsilon] that reflects [ital A]-[ital B] interactions (charge transfer and atomic relaxations) at a [ital fixed] [ital V]([ital x]). We show that the LRO and the SRO have the same behavior only when the signs of [Delta][ital H][sub [ital F]] and [var epsilon] are the same: ordering tendencies ( type I'') when both [Delta][ital H][sub [ital F]][lt]0 and [var epsilon][lt]0, or phase-separating/clustering tendencies ( type III'') when both [Delta][ital H][sub [ital F]][gt]0 and [var epsilon][gt]0. However, type II'' systems ([Delta][ital H][sub [ital F]][gt]0;more » [var epsilon][lt]0) can exhibit a phase-separating LRO and an ordering-type SRO. Direct self-consistent local-density calculations of the total energy coupled with Monte-Carlo simulated annealing calculations of the ensuing Ising-like cluster expansion illustrate these type I, II, and III behaviors in Ni-V, Ni-Au, and Pd-Rh, respectively.« less

Optical anisotropy and spin polarization in ordered GaInP

Abstract: Spontaneous CuPt‐like ordering of GaxIn1−xP causes a splitting at the valence band maximum (VBM) and induces an anisotropy in the intensities of the transitions between these split VBM components and the conduction band minimum. We calculate these intensities as function of ordering parameter η, and show that the transition intensities depend strongly on the light polarization e and the degree of long‐range order η in the sample. Furthermore, for sufficiently ordered single‐subvariant sample, 100% spin polarization of emitted photoelectrons is predicted.

Comparison of two cluster-expansion methods for the energetics of Pd-V alloys

Abstract: The formation energies of substitutional transition-metal alloys are examined by several means. First, two types of direct total-energy calculations are considered, namely, (i) the local-density approximation (LDA), and (ii) a tight-binding (TB) approximation thereof. Second, these directly calculated total energies are used to construct two Ising-like cluster expansions that, if sufficiently accurate, could be used to construct the full statistical mechanics of transition-metal alloys. These are (a) the Connolly-Williams (CW) method, and (b) direct configurational averaging (DCA). Finally, the ability of these two cluster expansions [(a) and (b)] to fit and predict a large number of the underlying directly calculated [(i) and (ii)] total energies is tested, by the average prediction error [chi]. These tests are performed for a large number of Pd-V alloys, and also, to a more limited extent, for the Pd-Rh, Pd-Ti, and Pt-V systems. We find for Pd-V that (i) direct TB calculations show significant overbinding (too-negative formation energies) relative to the LDA, with average error of [chi]=112 meV/atom (a typical formation energy of Pd[sub 0.50]V[sub 0.50] is [similar to][minus]250 meV/atom); (ii) the CW cluster expansion mimics quite well the results of the respective direct calculations, whether LDA ([chi]=19 meV/atom) or TB ([chi]=19 meV/atom); (iii) themore » DCA cluster expansions provides a less accurate depiction of the TB energies on which it is based ([chi]=65 meV/atom); (iv) the prediction errors for the equimolar random alloys are significantly larger using the DCA than using the CW method. In light of (i) above, it appears that the tight-binding model needs to be refined before it can be used systematically for (either DCA or CW) cluster expansions.« less

Strain effects on the spectra of spontaneously ordered GaxIn1−xP

Abstract: Spontaneous (111) CuPt‐like ordering has been widely observed in GaxIn1−xP lattice matched (x=x0) to a GaAs(001) substrate. This leads to a band‐gap reduction ΔEg and to a valence‐band splitting ΔE12. We explore here the consequence of the coexistence of (001) epitaxial strain (produced by selecting x≠x0) and (111) chemical ordering. This leads to distinct changes in ΔEg and ΔE12 which could serve as new fingerprints of ordering.

Comparison of experimental and theoretical electronic charge distribution in γ-TiAl

Abstract: Using critical voltage electron diffraction, Fox has recently determined the lowest seven X-ray structure factors of [gamma]-TiAl (L1[sub 0] structure). The authors present here a comparison of these accurately measured (0.15%) structure factors with first-principles local density calculations, finding an agreement within 0.7% and an r.m.s. error of 0.013 e/atom. While such measurements are limited to the first few structure factors [rho](G) (where G is the crystal momentum), theory is able to obtain [rho](G) for arbitrarily high G. If they construct charge density deformation maps by Fourier summations up to the lowest measured G, the calculated and experimental density deformation maps agree very closely. However, if they include in the theoretical density deformation map high G values (outside the range accessible to experiment), qualitatively different bonding patterns appear, in particular between Ti atoms. Systematic study of the total, valence, and deformation charge densities as well as comparison with result for NiAl in the hypothetical L1[sub 0] structure elucidate the bonding patterns in these transition metal aluminides.

Long- versus short-range order in Ni3V and Pd3V alloys.

Abstract: Measurements of the short-range-order (SRO) diffuse scattered intensity show peaks at the 〈11/20〉 and 〈100〉 points in ${\mathrm{Ni}}_{3}$V and ${\mathrm{Pd}}_{3}$V, respectively, although the stable ground state in both systems (D${0}_{22}$) is a 〈11/20〉-type structure. Mean-field theory predicts 〈11/20〉 SRO in both materials, in contradiction with experiment for ${\mathrm{Pd}}_{3}$V. The 〈100〉-type SRO in ${\mathrm{Pd}}_{3}$V has been explained previously as a non-mean-field effect. Via a combination of first-principles total-energy calculations and Monte Carlo simulated annealing, we show that non-mean-field effects are insufficient to explain the observed SRO of ${\mathrm{Pd}}_{3}$V. However, the inclusion of electronic excitations leads to a temperature dependence in the interaction energies which correctly explains both the SRO and phase stability in ${\mathrm{Pd}}_{3}$V and ${\mathrm{Ni}}_{3}$V.

Pressure dependence of optical transitions in ordered GaP/InP superlattices

Abstract: We have calculated the pressure coefficients α of a few optical transitions in (001), (111), (110), and (201) GaP/InP ordered superlattices using ab initio methods. The equilibrium atomic geometries under hydrostatic pressure are obtained by direct minimization of the elastic enthalpy. We find that (i) the pressure coefficient of the lowest energy transition is uniformly high, due to the Γ1c character of the conduction‐band minimum; (ii) the pressure coefficient of the transition to the second lowest conduction state at Γ distinguishes the (111)‐oriented (CuPt) superlattice (α=4.0 meV/kbar) from the remaining structures (α≂−2 meV/kbar). This is so because in CuPt we have L folding, while in the other structures we have X folding; (iii) the calculated pressures for the Γ→X crossover are 45, 43, 12, and 16 kbar for the (001), (111), (110), and (201) superlattices, respectively. These trends reflect the zero‐pressure Γ1c–X1c energy separation and the Γ1c pressure coefficient of these structures.

Pressure dependence of the band gaps in Si quantum wires

Abstract: The pressure coefficients a of interband transitions in (001) silicon wires are calculated using a plane‐wave basis and carefully fitted empirical pseudopotentials. We find purely red shifts (a<0). Their magnitudes, as well as changes with wire sizes can be interpreted in terms of the ‘‘truncated crystal model’’ which describes the wire conduction bands as linear combination of the lowest bulk conduction bands along the Γ‐X line.

Type-II-->type-I transition in (GaX)n/(InX)n (001) superlattices (X=P, Sb) as a function of period n.

Abstract: Coherently strained GaX/InX interfaces (X=P, Sb) lattice matched to a (001)-oriented substrate are predicted to have a type-I band-gap alignment, with both the valence-band maximum and the conduction-band minimum (CBM) located on the In-rich material. At the same time, the CBM wave function of short-period (GaX${)}_{\mathit{n}}$/(InX${)}_{\mathit{n}}$ superlattices is predicted to have larger amplitude on the GaX layers, leading to a type-II alignment. We show that (i) a type-II\ensuremath{\rightarrow}type-I transition occurs around the period n=4; (ii) this transition has a different origin with respect to the well-known case of GaAs/AlAs superlattices; (iii) the band structure of ultrathin superlattices cannot be explained in terms of a simple effective-mass theory; (iv) the wave-function localization in short-period superlattices is determined by the atomic orbital energies.

Of semiconductor alloys and intermetallic compounds

Abstract: A binary substitutional system can exist in 2N configurations that can be formed by occupying any of the N sites of a lattice by either an A or a B atom Substitutional configurations include compounds, alloys, superlattices, and substitutional impurities This article addresses the questions of (0 finding the lowest energy configuration of a given NB substitutional system, (ii) calculating its composition-temperature phase diagram, and (iii) its finite-temperature thermodynamic properties, using the first-principles local density approximation (LDA) Mapping of the LDA energies of 10-20 ~Bq compounds onto an Ising-like "cluster expansion" enables use of lattice statistical mechanics techniques that elegantly solve the above problems This extends the utility of the LDA from simple, perfectly-ordered compounds to truly complex structures We illustrate the method for semiconductor systems and transition-metal intermetallic systems, emphasizing the role of lattice relaxation

Structural instability in zinc-blende semiconductors

Abstract: The conditions for the occurrence of off-center atomic displacements in pure zinc-blende semiconductors have been studied. A coupling of a chemically active valence d band with an s-like conduction band is predicted to lead to such a metastability. Total energy calculations confirm that this is the case in CuCl and CuBr. The unusual experimental manifestations of this metastability are outlined.