Showing papers by "Alex Zunger published in 2000"

First-principles calculation of band offsets, optical bowings, and defects in CdS, CdSe, CdTe, and their alloys

Abstract: Using first principles band structure theory we have calculated (i) the alloy bowing coefficients, (ii) the alloy mixing enthalpies, and (iii) the interfacial valence band offsets for three Cd-based (CdS, CdSe, CdTe) compounds. We have also calculated defect formation energies and defect transition energy levels of Cd vacancy VCd and CuCd substitutional defect in CdS and CdTe, as well as the isovalent defect TeS in CdS. The calculated results are compared with available experimental data.

Theoretical interpretation of the experimental electronic structure of lens shaped, self-assembled InAs/GaAs quantum dots

Abstract: We adopt an atomistic pseudopotential description of the electronic structure of self-assembled, lens-shaped InAs quantum dots within the ``linear combination of bulk bands'' method. We present a detailed comparison with experiment, including quantites such as the single-particle electron and hole energy level spacings, the excitonic band gap, the electron-electron, hole-hole, and electron-hole Coulomb energies and the optical polarization anisotropy. We find a generally good agreement, which is improved even further for a dot composition where some Ga has diffused into the dots.

Microscopic Origin of the Phenomenological Equilibrium "Doping Limit Rule" in n-Type III-V Semiconductors

Abstract: The highest equilibrium free-carrier doping concentration possible in a given material is limited by the "pinning energy" which shows a remarkable universal alignment in each class of semiconductors. Our first-principles total energy calculations reveal that equilibrium n-type doping is ultimately limited by the spontaneous formation of close-shell acceptor defects: the (3-)-charged cation vacancy in AlN, GaN, InP, and GaAs and the (1-)-charged DX center in AlAs, AlP, and GaP. This explains the alignment of the pinning energies and predicts the maximum equilibrium doping levels in different materials.

Pseudopotential calculations of electron and hole addition spectra of InAs, InP, and Si quantum dots

Abstract: The electron and hole addition energies, the quasiparticle gap, and the optical gap of InAs, InP, and Si quantum dots are calculated using microscopic pseudopotential wave functions. The effects of the dielectric mismatch between the quantum dot and the surrounding material are included using a realistic profile for the dielectric constant e(r). We find that the addition energies and the quasiparticle gap depend strongly on the dielectric constant of the environment eout , while the optical gap is rather insensitive to eout . We compare our results with recent tunneling spectroscopy measurements for InAs nanocrystals, finding excellent agreement. Our calculations for the addition energies and the quasiparticle gap of InP and Si nanocrystals serve as predictions for future experiments.

Electronic structure of BAs and boride III-V alloys

Abstract: Boron arsenide, the typically ignored member of the Group-III--V arsenide series BAs-AlAs-GaAs-InAs is found to resemble silicon electronically: its $\ensuremath{\Gamma}$ conduction-band minimum is p-like $({\ensuremath{\Gamma}}_{15}),$ not s-like $({\ensuremath{\Gamma}}_{1\mathrm{c}}),$ it has an ${X}_{1\mathrm{c}}$-like indirect band gap, and its bond charge is distributed almost equally on the two atoms in the unit cell, exhibiting nearly perfect covalency. The reasons for these are tracked down to the anomalously low atomic $p$ orbital energy in the boron and to the unusually strong $s--s$ repulsion in BAs relative to most other Group-III--V compounds. We find unexpected valence-band offsets of BAs with respect to GaAs and AlAs. The valence-band maximum (VBM) of BAs is significantly higher than that of AlAs, despite the much smaller bond length of BAs, and the VBM of GaAs is only slightly higher than in BAs. These effects result from the unusually strong mixing of the cation and anion states at the VBM. For the BAs-GaAs alloys, we find (i) a relatively small $(\ensuremath{\sim}3.5 \mathrm{eV})$ and composition-independent band-gap bowing. This means that while addition of small amounts of nitrogen to GaAs lowers the gap, addition of small amounts of boron to GaAs raises the gap; (ii) boron ``semilocalized'' states in the conduction band (similar to those in GaN-GaAs alloys); and (iii) bulk mixing enthalpies that are smaller than in GaN-GaAs alloys. The unique features of boride Group-III--V alloys offer new opportunities in band-gap engineering.

Dark excitons due to direct Coulomb interactions in silicon quantum dots

Abstract: Electron-hole exchange interactions can lead to spin-forbidden ''dark'' excitons in direct-gap quantum dots. Here, we explore an alternative mechanism for creating optically forbidden excitons. In a large spherical quantum dot made of a diamond-structure semiconductor, the symmetry of the valence band maximum (VBM) is t{sub 2}. The symmetry of the conduction band minimum (CBM) in direct-gap material is a{sub 1}, but for indirect-gap systems the symmetry could be (depending on size) a{sub 1}, e, or t{sub 2}. In the latter cases, the resulting manifold of excitonic states contains several symmetries derived from the symmetries of the VBM and CBM (e.g., t{sub 2}xt{sub 2}=A{sub 1}+E+T{sub 1}+T{sub 2} or t{sub 2}xe=T{sub 1}+T{sub 2}). Only the T{sub 2} exciton is optically active or ''bright,'' while the others A{sub 1}, E, and T{sub 1} are ''dark.'' The question is which is lower in energy, the dark or bright. Using pseudopotential calculations of the single-particle states of Si quantum dots and a direct evaluation of the screened electron-hole Coulomb interaction, we find that, when the CBM symmetry is t{sub 2}, the direct electron-hole Coulomb interaction lowers the energy of the dark excitons relative to the bright T{sub 2} exciton. Thus, the lowest energy exciton ismore » forbidden, even without an electron-hole exchange interaction. We find that our dark-bright excitonic splitting agrees well with experimental data of Calcott et al., Kovalev et al., and Brongersma et al. Our excitonic transition energies agree well with the recent experiment of Wolkin et al. In addition, and contradicting simplified models, we find that Coulomb correlations are more important for small dots than for intermediate sized ones. We describe the full excitonic spectrum of Si quantum dots by using a many-body expansion that includes both Coulomb and exchange electron hole terms. We present the predicted excitonic spectra. (c) 2000 The American Physical Society.« less

Pseudopotential study of electron-hole excitations in colloidal free-standing InAs quantum dots

Abstract: Excitonic spectra are calculated for free-standing, surface passivated, InAs quantum dots using atomic pseudopotentials for the single-particle states and screened Coulomb interactions for the two-body terms. We present an analysis of the single particle states involved in each excitation in terms of their angular momenta and Bloch-wave parentage. We find that (i) in agreement with other pseudopotential studies of CdSe and InP quantum dots, but in contrast to $k\ensuremath{\cdot}p$ calculations, the dot wave functions exhibit strong odd-even angular momentum envelope function mixing (e.g., s with $p)$ and large valence-conduction coupling. (ii) While the pseudopotential approach produced very good agreement with experiment for free-standing, colloidal CdSe and InP dots, and for self-assembled (GaAs-embedded) InAs dots, here the predicted spectrum does not agree well with the measured (ensemble average over dot sizes) spectra. (1) Our calculated excitonic gap is larger than the photoluminescence measured one, and (2) while the spacing between the lowest excitons is reproduced, the spacings between higher excitons is not fit well. Discrepancy (1) could result from surface state emission. As for (2), agreement is improved when account is taken of the finite-size distribution in the experimental data. (iii) We find that the single-particle gap scales as ${R}^{\ensuremath{-}1.01}$ (not ${R}^{\ensuremath{-}2}),$ that the screened (unscreened) electron-hole Coulomb interaction scales as ${R}^{\ensuremath{-}1.79}$ ${(R}^{\ensuremath{-}0.7}),$ and that the excitonic gap scales as ${R}^{\ensuremath{-}0.9}.$ These scaling laws are different from those expected from simple models.

Comparison of the k⋅p and direct diagonalization approaches to the electronic structure of InAs/GaAs quantum dots

Abstract: We present a comparison of the 8-band k⋅p and empirical pseudopotential approaches to describing the electronic structure of pyramidal InAs/GaAs self-assembled quantum dots. We find a generally good agreement between the two methods. The most significant differences found in the k⋅p calculation are (i) a reduced splitting of the electron p states (3 vs 24 meV), (ii) an incorrect in-plane polarization ratio for electron-hole dipole transitions (0.97 vs 1.24), and (iii) an over confinement of both electron (48 meV) and hole states (52 meV), resulting in a band gap error of 100 meV. We introduce a “linear combination of bulk bands” technique which produces results similar to a full direct diagonalization pseudopotential calculation, at a cost similar to the k⋅p method.

Addition Spectra of Quantum Dots: the Role of Dielectric Mismatch

Abstract: Using atomistic pseudopotential wave functions, we calculate the electron and hole addition energies and the quasi-particle gap of InAs quantum dots. We find that the addition energies and the quasi-particle gap depend strongly on the dielectric constant eout of the surrounding material, and that when eout is much smaller than the dielectric constant of the dot the electron−electron and hole−hole interactions are dominated by surface polarization effects. We predict the addition energies and the quasi-particle gap as a function of size and eout, and compare our results with recent single-dot tunneling spectroscopy experiments.

Optical transitions in charged CdSe quantum dots

Abstract: Using a many-body approach based on single-particle pseudopotential wave functions, we calculate the dependence of the optical transitions in CdSe nanocrystals on the presence of ‘‘spectator’’ electrons or holes. We find that~i! as a result of the different localization of the electron and hole wave functions, the absorption lines shift by as much as 22 meV/unit charge when electrons or holes are loaded into the quantum dot. ~ii! The lowest emission line is significantly red shifted with respect to the lowest allowed absorption line. ~iii! Trapping of a ‘‘spectator’’ hole in a surface state is predicted to lead to dramatic changes in the absorption spectrum, including the appearance of new transitions. Semiconductor quantum dots can be charged by deliberate injection of carriers ~via electrical contacts, 1 or via a scanning-tunneling-microscopy tip, 2 ! by photoionization processes removing one or more carriers from the quantum dot, 3 or by capture of external charges. 4 The effects of charging on the optical properties of self-assembled InAs/GaAs quantum dots have been recently measured both in absorption 5 and emission. 6 It was found that when electrons are progressively loaded into the quantum dots, the absorption and emission energies are redshifted relative to the neutral dots. Furthermore, low-energy lines disappear from the absorption spectrum, 5 while new high-energy lines appear in the photoluminescence spectrum. 6 In colloidal quantum dots, charging of surface states is believed to be at the origin of a variety of unusual phenomena, including the occurrence of a permanent dipole moment even in zincblende dots, 7 intermittency ~blinking! of photoluminescence, 3 spectral diffusion and Stark shift, 8 upconversion of photoluminescence, 9 and possibly even the occurrence of long spin lifetimes. 10 However, there are still no reports on the absorption or emission spectra of charged colloidal dots. The effects of charging on the interband optical transitions can be examined using a screened Hartree-Fock model, where the initial and final states are expressed as Slater determinants. The energy DEh,e(Nes ) required to optically excite an electron from the valence-band state h to the conduction-band state e in the presence of N es ‘‘spectator electrons’’ ( e s ) is:

Short-range-order types in binary alloys: a reflection of coherent phase stability

Abstract: The short-range order (SRO) present in disordered solid solutions is classified according to three characteristic system-dependent energies: (1) formation enthalpies of ordered compounds, (2) enthalpies of mixing of disordered alloys, and (3) the energy of coherent phase separation (the composition-weighted energy of the constituents each constrained to maintain a common lattice constant along an A/B interface) These energies are all compared against a common reference, the energy of incoherent phase separation (the composition-weighted energy of the constituents each at their own equilibrium volumes) Unlike long-range order (LRO), short-range order is determined by energetic competition between phases at a fixed composition , and hence only coherent phase-separated states are of relevance for SRO We find five distinct SRO types, and give examples showing each of these five types, including Cu-Au, Al-Mg, GaP-InP, Ni-Au, and Cu-Ag The SRO is calculated from first principles using the mixed-space cluster expansion approach combined with Monte Carlo simulations Additionally, we examine the effect of inclusion of coherency strain in the calculation of SRO, and specifically examine the appropriate functional form for accurate SRO calculations

L-to-X crossover in the conduction-band minimum of Ge quantum dots

Abstract: Screened-pseudopotential calculations of large ((less-or-similar sign)3000 atoms) surface-passivated Ge quantum dots show that below a critical dot diameter that depends on the passivant, the character of the lowest conduction state changes from an L-derived to an X-derived state. Thus, in this size regime, Ge dots are Si-like. This explains the absence, in a pseudopotential description, of a crossing between the band gaps of Si and Ge dots as a function of size, predicted earlier in single-valley effective-mass calculations. The predicted L{yields}X crossing suggests that small Ge dots will have an X-like, red shift of the band gap with applied pressure, as opposed to an L-like blue shift of large dots. (c) 2000 The American Physical Society.

Addition energies and quasiparticle gap of CdSe nanocrystals

Abstract: Using atomistic pseudopotential wave functions we calculate the quasiparticle gap, the optical gap and the electron and hole addition energies of CdSe nanocrystals. We find that the quasiparticle gap and the addition energies depend strongly on the dielectric constant of the surrounding material, while the optical gap is rather insensitive to the environment. We provide scaling lows for these quantities as a function of the quantum dot size, and compare our results with recent scanning tunneling spectroscopy experiments.

Anticrossing semiconducting band gap in nominally semimetallic InAs/GaSb superlattices

Abstract: While $(\mathrm{InAs}{)}_{n}/(\mathrm{GaSb}{)}_{n}$ (001) superlattices are semiconducting for $nl{n}_{c}\ensuremath{\approx}28\mathrm{ML},$ for $ng{n}_{c}$ the InAs electron level ${e}_{\mathrm{InAs}}$ is below the GaSb hole level ${h}_{\mathrm{GaSb}},$ so the system is converted to a nominal semimetal. At nonzero in-plane wave vectors $({\mathbf{k}}_{\ensuremath{\Vert}}\ensuremath{ e}0),$ however, the wave functions ${e}_{\mathrm{InAs}}$ and ${h}_{\mathrm{GaSb}}$ have the same symmetry, so they anticross. This opens up a ``hybridization gap'' at some ${\mathbf{k}}_{\ensuremath{\Vert}}={\mathbf{k}}_{\ensuremath{\Vert}}^{*}.$ Using a pseudopotential plane-wave approach as well as a (pseudopotential fit) eight-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ approach, we predict the hybridization gap and its properties such as wave-function localization and out-of-plane dispersion. We find that recent model calculations underestimate this gap severely.

Indium-indium pair correlation and surface segregation in InGaAs alloys

Abstract: In-In pair correlations and In surface segregation in In xGa 1-xAs alloys are studied by first-principles total-energy calculations. By calculating the substitution energy of a single In atom, we find that the near-surface energetics explains the observed In segregation on InGaAs(001)-beta2(2x4) surfaces. Indium surface segregation further enhances the In site selectivity, thus the long-range ordering. We find that the [110] and [001] In-In pair correlations are repulsive and nearly isotropic in bulk but are highly anisotropic near the (001) surface. The sign of the [110] In-In interaction energies vs the distance from the surface is oscillatory. These findings explain the recent puzzling cross-sectional x-STM results.

Anticrossing and coupling of light-hole and heavy-hole states in (001) GaAs/Al x Ga 1-x As heterostructures

Abstract: Heterostructures sharing a common atom such as AlAs/GaAs/AlAs have a ${D}_{2d}$ point-group symmetry which allows the bulk-forbidden coupling between odd-parity light-hole states (eg, lh1) and even-parity heavy-hole states (eg, hh2) Continuum models, such as the commonly implemented (``standard model'') $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ theory miss the correct ${D}_{2d}$ symmetry and thus produce zero coupling at the zone center We have used the atomistic empirical pseudopotential theory to study the lh1-hh2 coupling in (001) superlattices and quantum wells of $\mathrm{GaAs}/{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ By varying the Al concentration x of the barrier we scan a range of valence-band barrier heights $\ensuremath{\Delta}{E}_{v}(x)$ We find the following: (i) The lh1 and hh2 states anticross at rather large quantum wells width or superlattice periods $60l{n}_{c}l70$ monolayers (ii) The coupling matrix elements ${V}_{\mathrm{lh}1,hh2}^{{\mathbf{k}}_{\ensuremath{\Vert}}=0}$ are small (002--007 meV) and reach a maximum value at a valence-band barrier height $\ensuremath{\Delta}{E}_{v}\ensuremath{\approx}100 \mathrm{meV},$ which corresponds to an Al composition ${x}_{\mathrm{Al}}=02$ in the barrier (iii) The coupling matrix elements obtained from our atomistic theory are at least an order of magnitude smaller than those calculated by the phenomenological model of Ivchenko et al [Phys Rev B 54, 5852 (1996)] (iv) The dependence of ${V}_{\mathrm{lh}1,hh2}$ on the barrier height $\ensuremath{\Delta}{E}_{v}(x)$ is more complicated than that suggested by the recent model of Cortez et al, [J Vac Sci Technol B 18, 2232 (2000)], in which ${V}_{\mathrm{lh}1,hh2}$ is proportional to the product of $\ensuremath{\Delta}{E}_{v}(x)$ times the amplitudes of the lh1 and hh2 envelopes at the interfaces Thus, atomistic information is needed to establish the actual scaling

Hund's rule, spin blockade, and the Aufbau principle in strongly confined semiconductor quantum dots

Abstract: The ground-state configuration of a system of N electrons or holes (N = 1⋯8) in strongly confined InAs, InP, and Si quantum dots (diameter ~ 30 A) is calculated using pseudopotential single-particle energies and wave functions as input to the many-body expansion of the total energy The validity of generally accepted "rules of level occupation" (Hund's rule, Aufbau principle, and single spin-flip rule) is examined We find that while Hund's rule is generally obeyed, deviations from the Aufbau principle are common when single-particle energy levels are separated by a few meV We also find a few instances where the single spin-flip rule is violated, leading to "spin blockade" in linear conductance

BAs-GaAs Semiconductor Alloys as a Photovoltaic Alternative to Nitride Alloys

Abstract: Nitrogen alloyed III-V semiconductor compounds have been intensely studied in recent years due to unusual effects caused by nitrogen alloying. These effects are exploited in band gap engineering for specific applications such as solar cells and blue lasers.