We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other.

Band parameters for III–V compound semiconductors and their alloys

Polarity discontinuities at the interfaces between different crystalline materials (heterointerfaces) can lead to nontrivial local atomic and electronic structure, owing to the presence of dangling bonds and incomplete atomic coordinations. These discontinuities often arise in naturally layered oxide structures, such as the superconducting copper oxides and ferroelectric titanates, as well as in artificial thin film oxide heterostructures such as manganite tunnel junctions. If polarity discontinuities can be atomically controlled, unusual charge states that are inaccessible in bulk materials could be realized. Here we have examined a model interface between two insulating perovskite oxides--LaAlO3 and SrTiO3--in which we control the termination layer at the interface on an atomic scale. In the simple ionic limit, this interface presents an extra half electron or hole per two-dimensional unit cell, depending on the structure of the interface. The hole-doped interface is found to be insulating, whereas the electron-doped interface is conducting, with extremely high carrier mobility exceeding 10,000 cm2 V(-1) s(-1). At low temperature, dramatic magnetoresistance oscillations periodic with the inverse magnetic field are observed, indicating quantum transport. These results present a broad opportunity to tailor low-dimensional charge states by atomically engineered oxide heteroepitaxy.

A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

Recent technical advances in the atomic-scale synthesis of oxide heterostructures have provided a fertile new ground for creating novel states at their interfaces. Different symmetry constraints can be used to design structures exhibiting phenomena not found in the bulk constituents. A characteristic feature is the reconstruction of the charge, spin and orbital states at interfaces on the nanometre scale. Examples such as interface superconductivity, magneto-electric coupling, and the quantum Hall effect in oxide heterostructures are representative of the scientific and technological opportunities in this rapidly emerging field.

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Emergent phenomena at oxide interfaces

The most widely used oxide for photocatalytic applications owing to its low cost and high activity is TiO2. The discovery of the photolysis of water on the surface of TiO2 in 19721 launched four decades of intensive research into the underlying chemical and physical processes involved2, 3, 4, 5. Despite much collected evidence, a thoroughly convincing explanation of why mixed-phase samples of anatase and rutile outperform the individual polymorphs has remained elusive6. One long-standing controversy is the energetic alignment of the band edges of the rutile and anatase polymorphs of TiO2 (ref. 7). We demonstrate, through a combination of state-of-the-art materials simulation techniques and X-ray photoemission experiments, that a type-II, staggered, band alignment of ~ 0.4 eV exists between anatase and rutile with anatase possessing the higher electron affinity, or work function. Our results help to explain the robust separation of photoexcited charge carriers between the two phases and highlight a route to improved photocatalysts.

Band alignment of rutile and anatase TiO2

A study of heterojunction interface geometry based on our measured differences in $3d$ core-state binding energies for germanium and gallium at Ge-GaAs heterojunctions of different crystallographic orientations is reported. For the interfaces which have been studied, i.e., (110), (100) Ga, (100) As, (111) Ga, and ($\overline{1}\overline{1}\overline{1}$) As, orientation-dependent variations in dipole contributions to valence-band discontinuities of about 0.2 eV have been observed. From electrostatic considerations we deduce the simplest interface geometries consistent with the facts that the differences are small and no large charge accumulations can occur at the junction. An abrupt planar junction is allowed for the (110) interface, but the polar interfaces require at least two transition planes of atoms with compositions which are deduced from the two conditions above. The electrostatic calculations were based upon the differences in nuclear charge and are unaffected by the resulting polarization of the bonds if that polarization is described in an "electronegativity" approximation. In this approximation there would in fact be no dipole shift for the ideal geometries proposed. An improved treatment of the bond polarization based upon the bond-orbital model gives residual dipole shifts somewhat smaller than those observed, and in poor agreement with our measurements. Inclusion of lattice-distortion effects at the interface also fails to account for the observed dipole shifts. We conclude that the experimentally prepared junctions must contain deviations from the ideal atom arrangements. The number of these deviations required to account for the observed shifts is on the order of one for every fifteen interface atoms.

Polar heterojunction interfaces

Angle-resolved core-level and valence-band x-ray photoelectron spectroscopy (XPS) data for GaAs(110), Ge(110), and Ge(111) surfaces are analyzed to determine core-level to valence-band maximum binding-energy differences to a precision of the order of the room-temperature thermal energy. A method for markedly improving the precision with which the position of the valence-band maximum in XPS data can be located is presented. This method is based on modeling the XPS valence-band spectrum in the vicinity of the valence-band maximum by an instrumentally broadened theoretical valence-band density of states and fitting this model to the experimental data by using the least-squares method. The factors which influence the attainable precision for determining core-level to valence-band maximum binding-energy differences are quantitatively discussed. These factors include the presence of occupied surface states, band bending, surface chemical shifts, background effects associated with inelastic processes, instrumental line shape, and spectrometer calibration accuracy. The spin-orbit-split components of the Ga, As, and Ge $3d$ core lines are resolved and binding energies of these components, measured relative to the valence-band maxima in GaAs and Ge, are reported.

Semiconductor core-level to valence-band maximum binding-energy differences: Precise determination by x-ray photoelectron spectroscopy

X-ray photoemission spectroscopy was used to measure directly the CdTe-HgTe (\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}1) heterojunction valence-band discontinuity (${\ensuremath{\Delta}E}_{v}$) with the result ${\ensuremath{\Delta}E}_{v}=0.35\ifmmode\pm\else\textpm\fi{}0.06$ eV. On the basis of the frequently applied common-anion rule, it has generally been assumed that ${\ensuremath{\Delta}E}_{v}$ would be small; the large value of ${\ensuremath{\Delta}E}_{v}$ will affect predicted CdTe-HgTe heterojunction and superlattice properties. In conjunction with recent ${\ensuremath{\Delta}E}_{v}$ measurements on the $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}\ensuremath{-}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ heterojunction system, the large ${\ensuremath{\Delta}E}_{v}$ result for the CdTe-HgTe (\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}1) heterojunction provides direct experimental evidence in contradiction to the common-anion rule for lattice-matched heterojunction interfaces.

CdTe-HgTe (¯1¯1¯1) Heterojunction Valence-Band Discontinuity: A Common-Anion-Rule Contradiction

Accurate knowledge of the band discontinuities at a heterojunction interface and the factors that affect their magnitude are of both fundamental and practical interest. The application of x‐ray photoemission spectroscopy (XPS) to the direct, contactless, and quantitative measurement of the valence band discontinuity (ΔEv) at abrupt heterojunctions is discussed. The topics covered include a description of a method to achieve precise measurement, results of ΔEv measurements for many heterojunction pairs selected from the lattice‐matched semiconductor series Ge, GaAs, ZnSe, CuBr, and AlAs, and a comparison of experiment to models that predict ΔEv. Examples are given to illustrate the effect on ΔEv of such preparation‐dependent parameters as growth sequence and interface crystallographic orientation.

Measurement of semiconductor heterojunction band discontinuities by x-ray photoemission spectroscopy

X‐ray photoelectron spectroscopy was used to study the growth and energy‐band alignment of ZnSe–GaAs(110) and ZnSe–Ge(110) heterojunctions. The ZnSe–GaAs heterojunctions were formed by growing ZnSe on GaAs(110). Growth temperatures were varied to produce both epitaxial and nonepitaxial interfaces. For ZnSe grown at ∠300 °C on GaAs(110), the valence‐ band discontinuity ΔEv was 0.96 eV; for ZnSe deposited at room temperature and crystallized at ∠300 °C, ΔEv is 1.10 eV. The Ge–ZnSe(110) interfaces were formed by depositing Ge(ZnSe) on ZnSe(Ge)(110) at room temperature, followed by ∠300 °C crystallization. The corresponding ΔEv’s were 1.52 and 1.29 eV, respectively. Our measured ΔEv values for epitaxial heterojunctions are compared with the predictions of theoretical models. Our results demonstrate that substantial interface structure dependent contributions to ΔEv can occur at Ge–ZnSe(110) and GaAs– ZnSe(110) heterojunctions.

E. A. Kraut

Papers

Polar heterojunction interfaces

Semiconductor core-level to valence-band maximum binding-energy differences: Precise determination by x-ray photoelectron spectroscopy

CdTe-HgTe (¯1¯1¯1) Heterojunction Valence-Band Discontinuity: A Common-Anion-Rule Contradiction

Measurement of semiconductor heterojunction band discontinuities by x-ray photoemission spectroscopy

Measurement of ZnSe–GaAs(110) and ZnSe–Ge(110) heterojunction band discontinuities by x‐ray photoelectron spectroscopy (XPS)