Debye model

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

Abstract: The Reuss-Voigt approximations are well known methods whereby the isotropic polycrystalline elastic constants can be calculated from the single crystal elastic constants. It is shown here that the Reuss and the Voigt approximations can be used to estimate, accurately, the mean sound velocity of a crystal. Using this method, the Debye Temperature, which is proportioned to the mean sound velocity, can be determined without recourse to the published tables or high speed computers. This approximation is valid for all crystal classes.

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...

Abstract: Given the energy of a solid (E) as a function of the molecular volume (V), the gibbs program uses a quasi-harmonic Debye model to generate the Debye temperature Θ(V), obtains the non-equilibrium Gibbs function G★(V;p,T), and minimizes G★ to derive the thermal equation of state (EOS) V(p,T) and the chemical potential G(p,T) of the corresponding phase. Other macroscopic properties are also derived as a function of p and T from standard thermodynamic relations. The program focuses in obtaining as much thermodynamical information as possible from a minimum set of (E,V) data, making it suitable to analyse the output of costly electronic structure calculations, adding thermal effects at a low computational cost. Any of three analytical EOS widely used in the literature can be fitted to the p−V(p,T) data, giving an alternative set of isothermal bulk moduli and their pressure derivatives that can be fed to the Debye model machinery.

Abstract: The energy gap and other parameters of the superconducting state are calculated from the Bardeen-Cooper-Schrieffer theory in Gor'kov-Eliashberg form, using a realistic retarded electron-electron interaction via phonons and including the Coulomb repulsion. The solution is facilitated by observing that only the local phonon interaction, mediated entirely by short-wavelength phonons, is important, and that a good approximation for the phonon spectrum is therefore an Einstein model rather than Debye model. The resulting equation is solved by an approximate iteration procedure. The results are similar to earlier gap equations but the derivation gives a precise meaning to the interaction and cutoff parameters of earlier theories. The numerical results are in good order-of-magnitude agreement with the observed transition temperatures but lead to an isotope effect at least 15% less than the accepted -\textonehalf{} exponent (${T}_{c}$ proportional to ${M}^{\ensuremath{-}\frac{1}{2}}$). Also, the present theory predicts that all metals should be superconductors, although those not observed to do so would have remarkably low transition temperatures.