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# Effective mass (solid-state physics)

About: Effective mass (solid-state physics) is a research topic. Over the lifetime, 12539 publications have been published within this topic receiving 295485 citations.

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TL;DR: This review analyzes recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.

Abstract: Graphene is a wonder material with many superlatives to its name. It is the thinnest known material in the universe and the strongest ever measured. Its charge carriers exhibit giant intrinsic mobility, have zero effective mass, and can travel for micrometers without scattering at room temperature. Graphene can sustain current densities six orders of magnitude higher than that of copper, shows record thermal conductivity and stiffness, is impermeable to gases, and reconciles such conflicting qualities as brittleness and ductility. Electron transport in graphene is described by a Dirac-like equation, which allows the investigation of relativistic quantum phenomena in a benchtop experiment. This review analyzes recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.

12,117 citations

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TL;DR: In this article, the authors present a comprehensive, up-to-date compilation of band parameters for the technologically important III-V zinc blende and wurtzite compound semiconductors.

Abstract: 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.

6,349 citations

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TL;DR: In this article, a character table for the group of the wave vector at certain points of symmetry in the Brillouin zone is given, and a possible reason for the complications which may make a simple effective mass concept invalid for some crystals of this type structure is presented.

Abstract: Character tables for the "group of the wave vector" at certain points of symmetry in the Brillouin zone are given. The additional degeneracies due to time reversal symmetry are indicated. The form of energy vs wave vector at these points of symmetry is derived. A possible reason for the complications which may make a simple effective mass concept invalid for some crystals of this type structure will be presented.

2,833 citations

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TL;DR: In this article, a review of the properties of the Al x Ga1−x As/GaAs heterostructure system is presented, which can be classified into sixteen groups: (1) lattice constant and crystal density, (2) melting point, (3) thermal expansion coefficient, (4), lattice dynamic properties, (5) lattices thermal properties,(6) electronic-band structure, (7) external perturbation effects on the bandgap energy, (8) effective mass, (9) deformation potential, (10) static and

Abstract: The Al x Ga1−x As/GaAs heterostructure system is potentially useful material for high‐speed digital, high‐frequency microwave, and electro‐optic device applications Even though the basic Al x Ga1−x As/GaAs heterostructure concepts are understood at this time, some practical device parameters in this system have been hampered by a lack of definite knowledge of many material parameters Recently, Blakemore has presented numerical and graphical information about many of the physical and electronic properties of GaAs [J S Blakemore, J Appl Phys 5 3, R123 (1982)] The purpose of this review is (i) to obtain and clarify all the various material parameters of Al x Ga1−x As alloy from a systematic point of view, and (ii) to present key properties of the material parameters for a variety of research works and device applications A complete set of material parameters are considered in this review for GaAs, AlAs, and Al x Ga1−x As alloys The model used is based on an interpolation scheme and, therefore, necessitates known values of the parameters for the related binaries (GaAs and AlAs) The material parameters and properties considered in the present review can be classified into sixteen groups: (1) lattice constant and crystal density, (2) melting point, (3) thermal expansion coefficient, (4) lattice dynamic properties, (5) lattice thermal properties, (6) electronic‐band structure, (7) external perturbation effects on the band‐gap energy, (8) effective mass, (9) deformation potential, (10) static and high‐frequency dielectric constants, (11) magnetic susceptibility, (12) piezoelectric constant, (13) Frohlich coupling parameter, (14) electron transport properties, (15) optical properties, and (16) photoelastic properties Of particular interest is the deviation of material parameters from linearity with respect to the AlAs mole fraction x Some material parameters, such as lattice constant, crystal density, thermal expansion coefficient, dielectric constant, and elastic constant, obey Vegard’s rule well Other parameters, eg, electronic‐band energy, lattice vibration (phonon) energy, Debye temperature, and impurity ionization energy, exhibit quadratic dependence upon the AlAs mole fraction However, some kinds of the material parameters, eg, lattice thermal conductivity, exhibit very strong nonlinearity with respect to x, which arises from the effects of alloy disorder It is found that the present model provides generally acceptable parameters in good agreement with the existing experimental data A detailed discussion is also given of the acceptability of such interpolated parameters from an aspect of solid‐state physics Key properties of the material parameters for use in research work and a variety of Al x Ga1−x As/GaAs device applications are also discussed in detail

2,671 citations

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Bell Labs

^{1}TL;DR: In this article, the authors used the method of effective mass, extended to apply to gradual shifts in energy bands resulting from deformations of the crystal lattice, to estimate the interaction between electrons of thermal energy and the acoustical modes of vibration.

Abstract: The method of effective mass, extended to apply to gradual shifts in energy bands resulting from deformations of the crystal lattice, is used to estimate the interaction between electrons of thermal energy and the acoustical modes of vibration. The mobilities of electrons and holes are thus related to the shifts of the conduction and valence-bond (filled) bands, respectively, associated with dilations of longitudinal waves. The theory is checked by comparison of the sum of the shifts of the conduction and valence-bond bands, as derived from the mobilities, with the shift of the energy gap with dilation. The latter is obtained independently for silicon, germanium and tellurium from one or more of the following: (1) the change in intrinsic conductivity with pressure, (2) the change in resistance of an $n\ensuremath{-}p$ junction with pressure, and (3) the variation of intrinsic concentration with temperature and the thermal expansion coefficient. Higher mobilities of electrons and holes in germanium as compared with silicon are correlated with a smaller shift of energy gap with dilation.

2,530 citations