Temperature dependence of the energy gap in semiconductors
TL;DR: In this article, a relation for the variation of the energy gap (E g ) with temperature (T ) in semiconductors is proposed. And the equation satisfactorily represents the experimental data for diamond, Si, Ge, 6H-SiC, GaAs, InP and InAs.
About: This article is published in Physica D: Nonlinear Phenomena.The article was published on 1967-01-01. It has received 4451 citations till now. The article focuses on the topics: Band gap & Diamond.
Citations
More filters
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
TL;DR: In this paper, the authors provide numerical and graphical information about many physical and electronic properties of GaAs that are useful to those engaged in experimental research and development on this material, including properties of the material itself, and the host of effects associated with the presence of specific impurities and defects is excluded from coverage.
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...
2,115 citations
TL;DR: Optical spectroscopy is used to estimate the exciton binding energy in the mixed-halide crystal to be in the range of 50 meV, and it is shown that such a value is consistent with almost full ionization of the excitonic population under photovoltaic cell operating conditions.
Abstract: Excitonic solar cells, within which bound electron-hole pairs have a central role in energy harvesting, have represented a hot field of research over the last two decades due to the compelling prospect of low-cost solar energy. However, in such cells, exciton dissociation and charge collection occur with significant losses in energy, essentially due to poor charge screening. Organic-inorganic perovskites show promise for overcoming such limitations. Here, we use optical spectroscopy to estimate the exciton binding energy in the mixed-halide crystal to be in the range of 50 meV. We show that such a value is consistent with almost full ionization of the exciton population under photovoltaic cell operating conditions. However, increasing the total photoexcitation density, excitonic species become dominant, widening the perspective of this material for a host of optoelectronic applications.
1,473 citations
TL;DR: A comprehensive overview of the progress that has been made within the context of 1D ZnO nanostructures synthesized via wet chemical methods can be found in this paper, where the synthetic methodologies and corresponding growth mechanisms, different structures, doping and alloying, position-controlled growth on substrates, and finally, their functional properties as catalysts, hydrophobic surfaces, sensors, and in nanoelectronic, optical, optoelectronics, and energy harvesting devices.
Abstract: One-dimensional (1D) ZnO nanostructures have been studied intensively and extensively over the last decade not only for their remarkable chemical and physical properties, but also for their current and future diverse technological applications. This article gives a comprehensive overview of the progress that has been made within the context of 1D ZnO nanostructures synthesized via wet chemical methods. We will cover the synthetic methodologies and corresponding growth mechanisms, different structures, doping and alloying, position-controlled growth on substrates, and finally, their functional properties as catalysts, hydrophobic surfaces, sensors, and in nanoelectronic, optical, optoelectronic, and energy harvesting devices.
1,247 citations
TL;DR: This work describes recent progress in the understanding of the prescription, morphology, structure, spectrum, and packaging of phosphors and suggests avenues for further development and the scientific challenges that must be overcome before phosphors can be practically applied in LEDs.
Abstract: Light-emitting diodes (LEDs) are excellent candidates for general lighting because of their rapidly improving efficiency, durability, and reliability, their usability in products of various sizes, and their environmentally friendly constituents. Effective lighting devices can be realized by combining one or more phosphor materials with chips. Accordingly, it is very important that the architecture of phosphors be developed. Although numerous phosphors have been proposed in the past several years, the range of phosphors that are suitable for LEDs is limited. This work describes recent progress in our understanding of the prescription, morphology, structure, spectrum, and packaging of such phosphors. It suggests avenues for further development and the scientific challenges that must be overcome before phosphors can be practically applied in LEDs.
1,077 citations
References
More filters
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
TL;DR: The optical absorption coefficient of high resistivity gallium arsenide has been measured over the range of photon energy 0.6 to 2.75 eV, at temperatures from 10 to 294\ifmmode^\circ\else\textdegree\fi{}K as mentioned in this paper.
Abstract: The optical absorption coefficient of high-resistivity gallium arsenide has been measured over the range of photon energy 0.6 to 2.75 eV, at temperatures from 10 to 294\ifmmode^\circ\else\textdegree\fi{}K. The main absorption edge shows a sharp peak due to the formation of excitons. The energy gap and exciton binding energy are deduced from the shape of the absorption curve above the edge. Their values at 21\ifmmode^\circ\else\textdegree\fi{}K are 1.521 and 0.0034 eV, respectively. Absorption from the split-off valence band is observed, the spin-orbit splitting being 0.35 eV at the center of the zone. The exciton line shows unexplained structure on the low-energy side. Application of a stress splits the exciton line by 12 eV per unit [111] shear, and shifts it by -10 eV per unit dilation. Absorption due to the ionization of deep-lying impurity levels is observed, with thresholds at 0.70, 0.49, and 0.27 eV from the main absorption edge.
865 citations
TL;DR: The effect of lattice vibrations on the energy gap has been treated previously on the basis of broadening rather than shifting of the energy levels as mentioned in this paper, and the effect was found to be negligible for nonpolar crystals, whereas according to their treatment it should be much larger.
Abstract: The problem treated is the effect of lattice vibrations in producing a shift of the energy levels which results in a temperature dependent variation of the energy gap in semiconductors. Calculations for silicon and germanium give results of the same order of magnitude as the observed temperature dependent shift of the absorption band edge. The effect of lattice vibrations on the energy gap has been treated previously on the basis of broadening rather than shifting of the energy levels. The effect was found to be negligible for non-polar crystals, whereas according to our treatment it should be much larger. For polar crystals our result turns out to be essentially the same as was given by the previous treatment.
466 citations
TL;DR: In this article, the residual ray bands have been observed for the ordinary and extraordinary rays for green alpha (hexagonal) SiC and the resonance frequencies are 2.380 and 2.356, respectively.
Abstract: Infrared transmission and reflectivity measurements from 1 to 25 \ensuremath{\mu} (microns) have been made on several samples of green alpha (hexagonal) SiC. The residual ray bands have been observed for the ordinary and extraordinary rays. The resonance frequencies are 2.380\ifmmode\times\else\texttimes\fi{}${10}^{13}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ (12.60 \ensuremath{\mu}) and 2.356\ifmmode\times\else\texttimes\fi{}${10}^{13}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ (12.73 \ensuremath{\mu}), respectively. From the reflectivity the high-frequency dielectric constant is found to be 6.7. A careful analysis shows that the residual ray bands can be fitted within experimental error by the classical dispersion theory within the correct choice of the dispersion parameters. From the parameters the value 10.0 is obtained for the low-frequency dielectric constant. The effective charge is $0.94e$. Complete description of the residual ray band for the extraordinary ray required, in addition to the main resonance, a weak resonance at 2.647\ifmmode\times\else\texttimes\fi{}${10}^{13}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ (11.33 \ensuremath{\mu}). A study on the effects of several different surface treatments shows the reflectivities reported here are an intrinsic property of the crystal. The room-temperature absorption coefficient as a function of wavelength in the range 1 to 10 \ensuremath{\mu} has been determined from transmission measurements. A number of weak lattice bands are observed between 5 and 10 \ensuremath{\mu}.
362 citations
TL;DR: In this article, the authors measured the heat capacity of pure silicon and germanium with accuracy of ± 0.5% for 10° 20°K and 2.5° and 300°K, respectively.
Abstract: Heat capacities of pure silicon and germanium have been measured between 2.5° and 300°K. The estimated accuracies of the measurements are ±0.5% for 10° 20°K. The results for silicon were anomalous in the region T <7°K; it is suggested that this behaviour resulted from adsorption and desorption of exchange gas in the calorimeter vessel. No anomalies were observed in the measurements on germanium; their accuracy at the lowest temperatures is estimated to be ±2%. The results for both substances are significantly different from previously published values. The temperature variation of ΘD of both silicon and germanium below about T= ΘD/3 is consistent with general harmonic theory, but at high temperatures ΘD decreases with increasing temperature. This appears to be a clearly marked anharmonic effect of a type that cannot be explained by change of volume alone. The results for T < ΘD/3 are therefore extrapolated to high temperatures to give a heat capacity consistent with h...
259 citations