There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

http://www.phys.ttu.edu/%7Ecmyles/Phys5335/Lectures/Lecture02k%20-%20Vogl,%20Hjalmarson%20&%20Dow.%20Tightbinding%20Bands.%20JPCS%201983.pdf

A Semi-empirical tight-binding theory of the electronic structure of semiconductors†☆

In this article we review the experimental and theoretical investigations of the linear and nonlinear optical properties of semiconductor quantum well structures, including the effects of electrostatic fields, extrinsic carriers and real or virtual photocarriers.

Linear and nonlinear optical properties of semiconductor quantum wells

▪ Abstract Photoexcitation of a semiconductor with photons above the semiconductor band gap creates electrons and holes that are out of equilibrium. The rates at which the photogenerated charge carriers return to equilibrium via thermalization through carrier scattering, cooling by phonon emission, and radiative and nonradiative recombination are important issues. The relaxation processes can be greatly affected by quantization effects that arise when the carriers are confined to regions of space that are small compared with their deBroglie wavelength or the Bohr radius of bulk excitons. The effects of size quantization in semiconductor quantum wells (carrier confinement in one dimension) and quantum dots (carrier confinement in three dimensions) on the respective carrier relaxation processes are reviewed, with emphasis on electron cooling dynamics. The implications of these effects for applications involving radiant energy conversion are also discussed.

Spectroscopy and hot electron relaxation dynamics in semiconductor quantum wells and quantum dots.

Idealized Quantum Wells and Superlattices: A Summary. Band Structure of Bulk III-V Compounds. Envelope Function Description of Heterostructure Electronic States. Coulombic Bound States and Interface Defects in Heterostructures. Energy Levels in Modulation-Doped Heterostructures. Electrical Conductivity of Quasi Bi-Dimensional Electron Gases. Optical Properties of Quasi Bi-Dimensional Systems. Effect of Static External Electric and Magnetic Fields on the Energy Levels of Quasi Bi-Dimensional Electron Gases. Appendices.

/pdf/wave-mechanics-applied-to-semiconductor-heterostructures-58lh0kvzim.pdf

Wave Mechanics Applied to Semiconductor Heterostructures

The resonant tunneling diode (RTD) has been widely studied because of its importance in the field of nanoelectronic science and technology and its potential applications in very high speed/functionality devices and circuits. Even though much progress has been made in this regard, additional work is needed to realize the full potential of RTD's. As research on RTD's continues, we will try in this tutorial review to provide the reader with an overall and succinct picture of where we stand in this exciting field or research and to address the following questions: What makes RTD's so attractive? To what extent can RTD's be modeled for design purposes? What are the required and achievable device properties in terms of digital logic applications? To address these issues, we review the device operational principles, various modeling approaches, and major device properties. Comparisons among the various RTD physical models and major features of RTD's, resonant interband tunneling diodes, and Esaki tunnel diodes are presented. The tutorial and analysis provided in this paper may help the reader in becoming familiar with current research efforts, as well as to examine the important aspects in further RTD developments and their circuit applications.

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Resonant tunneling diodes: models and properties

We propose a new material which could be useful in a number of infrared optoelectronic devices. The material consists of alternating (100) layers of CdTe and HgTe. The band gap of this superlattice is adjustable from 0 to 1.6 eV depending on the thicknesses of the CdTe and HgTe layers. Details of the band‐gap variation and the character of the band‐edge states are presented.

The CdTe/HgTe superlattice: Proposal for a new infrared material

An analytic expression for the current-voltage characteristics of resonant tunneling diodes is derived from basic principles. The form is ideal for insertion into circuit simulation models. It is demonstrated for a conventional InGaAs-AlAs RTD and for an InAs-AlSb-GaSb RIT diode. The expression is based on the quantum tunneling formalism and contains parameters that originate from physical quantities, but which can also be treated as empirical. Empirical fitting is straightforward and results in an excellent match to the data. Additional levels of physical realism can be incorporated in a natural way.

Physics-based RTD current-voltage equation

Much understanding of the electronic and optical properties of a semiconductor superlattice can be obtained by relating the superlattice electronic wave functions and band structure to those of the two bulk semiconductors from which it is constructed. In this paper, the relationship is studied within the framework of the empirical tight-binding model, which is solved using the reduced Hamiltonian technique. The superlattice wave functions are described as linear combinations of bulk Bloch functions with complex wave vectors, twenty (including spin) for each of the two constituent materials. The bulk Bloch-function composition of the superlattice wave function is studied as a function of layer thickness, alloy composition, and energy. The GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As and InAs-GaSb superlattices are examined in detail. Comparisons with simpler Kronig-Penney and envelope-function models are made. It is found that the lowest superlattice conduction-band states are primarily derived from the expected bulk states with wave vectors near the center of the Brillouin zone, with a small admixture of zone-edge components. The energies and general form of the wave functions are modified only slightly, except close to the interfaces. There, the admixture can significantly affect the interfacial boundary conditions beyond those employed by commonly used envelope-function approximations. Valence-band states are more complicated in that the superlattice periodic potential mixes the bulk heavy-hole, light-hole, and spin-orbit split-off bands, even at the superlattice Brillouin-zone center. Crossover effects occur in which a given superlattice subband can have a varying proportion of light-hole-like or heavy-hole-like character depending on superlattice layer thickness. The dispersion of the subbands away from the zone center also causes the mixing of bands and results in modifications of the superlattice band structure as compared with band structures produced by simpler models.

Joel N. Schulman

Papers

Wave Mechanics Applied to Semiconductor Heterostructures

Resonant tunneling diodes: models and properties

The CdTe/HgTe superlattice: Proposal for a new infrared material

Physics-based RTD current-voltage equation

Band mixing in semiconductor superlattices.