H. Ehrenreich

Bio: H. Ehrenreich is an academic researcher from General Electric. The author has contributed to research in topics: Electron & Electronic band structure. The author has an hindex of 11, co-authored 11 publications receiving 4850 citations.

Optical Properties of Semiconductors

Abstract: Reflectance data are presented for Si, Ge, GaP, GaAs, InAs, and InSb in the range of photon energies between 1.5 and 25 eV. The real and imaginary parts of the dielectric constant and the function describing the energy loss of fast electrons traversing the materials are deduced from the Kramers-Kronig relations. The results can be described in terms of interband transitions and plasma oscillations. A theory based on the frequency-dependent dielectric constant in the random phase approximation is presented and used to analyze these data above 12 eV, where the oscillator strengths coupling the valence and conduction bands are practically exhausted. The theory predicts and the experiments confirm essentially free electron-like behavior before the onset of $d$-band excitations and a plasma frequency modified from that of free electrons due to oscillator strength coupling between valence and $d$ bands and $d$-band screening effects. These complications are absent in Si. The energy loss functions obtained from optical and characteristic energy loss experiments are also found to be in good agreement. Arguments for interpreting structure in the reflectance curves above 16 eV in terms of $d$-band excitations are given.

Self-Consistent Field Approach to the Many-Electron Problem

Abstract: The self-consistent field method in which a many-electron system is described by a time-dependent interaction of a single electron with a self-consistent electromagnetic field is shown to be equivalent for many purposes to the treatment given by Sawada and Brout. Starting with the correct many-electron Hamiltonian, it is found, when the approximations characteristic of the Sawada-Brout scheme are made, that the equation of motion for the pair creation operators is the same as that for the one-particle density matrix in the self-consistent field framework. These approximations are seen to correspond to (1) factorization of the two-particle density matrix, and (2) linearization with respect to off-diagonal components of the one-particle density matrix. The complex, frequency-dependent dielectric constant is obtained straight-forwardly from the self-consistent field approach both for a free-electron gas and a real solid. It is found to be the same as that obtained by Nozi\'eres and Pines in the random phase approximation. The resulting plasma dispersion relation for the solid in the limit of long wavelengths is discussed.

Optical Properties of Ag and Cu

Abstract: Experimental data for the optical constants of Ag and Cu extending to 25 eV are discussed in terms of three fundamental physical processes: (1) free-electron effects, (2) interband transitions, and (3) collective oscillations. Dispersion theory is used to obtain an accurate estimate of the average optical mass characterizing the free-electron behavior over the entire energy range below the onset of interband transitions. The values are ${m}_{a}=1.03\ifmmode\pm\else\textpm\fi{}0.06$ for Ag and 1.42\ifmmode\pm\else\textpm\fi{}0.05 for Cu. The interband transitions to 11 eV are identified tentatively using Segall's band calculations. Plasma resonances involving both the conduction band and $d$ electrons are identified and described physically.

Optical Properties of Aluminum

Abstract: The frequency-dependent complex dielectric constant $\ensuremath{\epsilon}(\ensuremath{\omega})={\ensuremath{\epsilon}}_{1}+i{\ensuremath{\epsilon}}_{2}$ and associated functions are derived in the range 0 to 22 eV by application of the Kramers-Kronig relations to existing reflectance data for clean Al surfaces. The results are quantitatively interpreted in terms of intra- and interband transitions as well as plasma oscillations. The decomposition of $\ensuremath{\epsilon}(\ensuremath{\omega})$ into intra- and interband parts given here is seen to be valid in the presence of electron-electron interactions. Due to these interactions the optical effective mass ${m}_{a}=1.5$, deduced from experiment in the free-carrier region, is appreciably larger than that obtained using Segall's band calculations (${m}_{\mathrm{ac}}\ensuremath{\cong}1.15$). The band calculations are extended to higher energies in order to examine the effect of interband transitions for the range of interest. It is found that the only interband transitions which lead to significant structure in ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$ are those that occur around $W$ and $\ensuremath{\Sigma}$ in the vicinity of $K$ in the Brillouin zone and that these produce a peak near 1.4 eV. These conclusions are in accord with the experimentally determined ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$ which exhibits a peak at 1.5 eV and has no further structure at higher energies. The result of a quantitative calculation of the structure in ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$ using a fine mesh of points in k space and an approximate variation of the momentum matrix element with k is in good agreement with the experimental results with respect to shape but has a magnitude which is somewhat too low. From the known influence of many-electron effects on the intraband contribution to $\ensuremath{\epsilon}(\ensuremath{\omega})$ and a general sum rule, the corresponding effect on interband transitions may be estimated and shown roughly to account for the difference. The derived $\ensuremath{\epsilon}(\ensuremath{\omega})$ indicates the presence of a sharp plasma resonance at $\ensuremath{\hbar}{\ensuremath{\omega}}_{p}=15.2$ eV, in excellent agreement with the results of characteristic energy loss experiments. It is shown that this resonance may be interpreted either in terms of electrons characterized by the low-frequency optical mass and screened by the interband dielectric constant at ${\ensuremath{\omega}}_{p}$ or, since the $f$ sum has been essentially exhausted, in terms of the exact asymptotic formula for $\ensuremath{\epsilon}$ in which all carriers are unscreened and have the free-electron mass.

Band Structure and Electron Transport of GaAs

Abstract: Existing experimental data on GaAs are reviewed and analyzed to yield the band structure in the vicinity of the band edges as well as the parameters characterizing the bands summarized in Fig. 1 of this paper. On the basis of presently existing experimental evidence, chiefly the behavior of the optical band gap in Ga(As, P) alloys and the deduced pressure shift and density of states effective mass, it is thought likely that the subsidiary conduction band minima lie along [100] directions. Analytical expressions including nonparabolic effects are given for the energy and density of states of the [000] conduction band and used to obtain a better value of the effective mass from optical reflectivity data. The experimentally observed structure in the Hall effect in $n$-type material at elevated temperatures is shown to result from excitation of carriers into the subsidiary conduction band. Changes of resistivity with pressure are explained on the basis of an increase of the [000] effective mass at low pressures and the transfer of carriers to the subsidiary minima at higher pressures. The scattering mechanisms, which are important in connection with transport phenomena, are shown to be polar lattice scattering and charged impurity scattering in the highest mobility samples. The transport calculations leading to the mobility and thermoelectric power as a function of temperature and impurity concentrations are performed using variational techniques, and shown to agree well with experiment. The apparently low mobility in the subsidiary minima is attributed at least in part to the large effective mass and relatively small anisotropy ratio. An estimate shows scattering between the two conduction bands probably to be unimportant.

Optical properties of metallic films for vertical-cavity optoelectronic devices.

Abstract: We present models for the optical functions of 11 metals used as mirrors and contacts in optoelectronic and optical devices: noble metals (Ag, Au, Cu), aluminum, beryllium, and transition metals (Cr, Ni, Pd, Pt, Ti, W). We used two simple phenomenological models, the Lorentz-Drude (LD) and the Brendel-Bormann (BB), to interpret both the free-electron and the interband parts of the dielectric response of metals in a wide spectral range from 0.1 to 6 eV. Our results show that the BB model was needed to describe appropriately the interband absorption in noble metals, while for Al, Be, and the transition metals both models exhibit good agreement with the experimental data. A comparison with measurements on surface normal structures confirmed that the reflectance and the phase change on reflection from semiconductor-metal interfaces (including the case of metallic multilayers) can be accurately described by use of the proposed models for the optical functions of metallic films and the matrix method for multilayer calculations.

Electronic excitations: density-functional versus many-body Green's-function approaches

Abstract: Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green’s-function equations, starting with a one-electron propagator and considering the electron-hole Green’s function for the response. Key ingredients are the electron’s self-energy S and the electron-hole interaction. A good approximation for S is obtained with Hedin’s GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of S. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green’s functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green’s functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV

Abstract: We report values of pseudodielectric functions $〈\ensuremath{\epsilon}〉=〈{\ensuremath{\epsilon}}_{1}〉+i〈{\ensuremath{\epsilon}}_{2}〉$ measured by spectroscopic ellipsometry and refractive indices $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}=n+ik$, reflectivities $R$, and absorption coefficients $\ensuremath{\alpha}$ calculated from these data. Rather than correct ellipsometric results for the presence of overlayers, we have removed these layers as far as possible using the real-time capability of the spectroscopic ellipsometer to assess surface quality during cleaning. Our results are compared with previous data. In general, there is good agreement among optical parameters measured on smooth, clean, and undamaged samples maintained in an inert atmosphere regardless of the technique used to obtain the data. Differences among our data and previous results can generally be understood in terms of inadequate sample preparation, although results obtained by Kramers-Kronig analysis of reflectance measurements often show effects due to improper extrapolations. The present results illustrate the importance of proper sample preparation and of the capability of separately determining both ${\ensuremath{\epsilon}}_{1}$ and ${\ensuremath{\epsilon}}_{2}$ in optical measurements.

Electronic Structure: Basic Theory and Practical Methods

Abstract: 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.

Semiconducting and other major properties of gallium arsenide

Abstract: This review provides numerical and graphical information about many (but by no means all) of the physical and electronic properties of GaAs that are useful to those engaged in experimental research and development on this material. The emphasis is on properties of GaAs itself, and the host of effects associated with the presence of specific impurities and defects is excluded from coverage. The geometry of the sphalerite lattice and of the first Brillouin zone of reciprocal space are used to pave the way for material concerning elastic moduli, speeds of sound, and phonon dispersion curves. A section on thermal properties includes material on the phase diagram and liquidus curve, thermal expansion coefficient as a function of temperature, specific heat and equivalent Debye temperature behavior, and thermal conduction. The discussion of optical properties focusses on dispersion of the dielectric constant from low frequencies [κ0(300)=12.85] through the reststrahlen range to the intrinsic edge, and on the ass...