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# Quasi Fermi level

About: Quasi Fermi level is a research topic. Over the lifetime, 2795 publications have been published within this topic receiving 79565 citations.

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General Electric

^{1}TL;DR: The band structure of InSb is calculated using the k ·. p perturbation approach and assuming that the conduction and valence band extrema are at k = 0 as mentioned in this paper.

Abstract: The band structure of InSb is calculated using the k ·. p perturbation approach and assuming that the conduction and valence band extrema are at k = 0. The small band gap requires an accurate treatment of conduction and valence band interactions while higher bands are treated by perturbation theory. A highly nonparabolic conduction band is found. The valence band is quite similar to germanium. Energy terms linear in k which cannot exist in germanium are estimated and found to be small, though possibly of importance at liquid-helium temperature. An absolute calculation of the fundamental optical absorption is made using the cyclotron resonance mass for n-type InSb. The agreement with experimental data for the fundamental absorption and its dependence on n-type impurity concentration is quite good. This evidence supports the assumptions made concerning the band structure.

2,905 citations

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Bell Labs

^{1}TL;DR: Detailed calculations of the shift of exciton peaks are presented including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations ofexciton binding energy in a field.

Abstract: We report experiments and theory on the effects of electric fields on the optical absorption near the band edge in GaAs/AlGaAs quantum-well structures. We find distinct physical effects for fields parallel and perpendicular to the quantum-well layers. In both cases, we observe large changes in the absorption near the exciton peaks. In the parallel-field case, the excitons broaden with field, disappearing at fields \ensuremath{\sim}${10}^{4}$ V/cm; this behavior is in qualitative agreement with previous theory and in order-of-magnitude agreement with direct theoretical calculations of field ionization rates reported in this paper. This behavior is also qualitatively similar to that seen with three-dimensional semiconductors. For the perpendicular-field case, we see shifts of the exciton peaks to lower energies by up to 2.5 times the zero-field binding energy with the excitons remaining resolved at up to \ensuremath{\sim}${10}^{5}$ V/cm: This behavior is qualitatively different from that of bulk semiconductors and is explained through a mechanism previously briefly described by us [D. A. B. Miller et al., Phys. Rev. Lett. 53, 2173 (1984)] called the quantum-confined Stark effect. In this mechanism the quantum confinement of carriers inhibits the exciton field ionization. To support this mechanism we present detailed calculations of the shift of exciton peaks including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations of exciton binding energy in a field. We also calculate the tunneling lifetimes of particles in the wells to check the inhibition of field ionization. The calculations are performed using both the 85:15 split of band-gap discontinuity between conduction and valence bands and the recently proposed 57:43 split. Although the detailed calculations differ in the two cases, the overall shift of the exciton peaks is not very sensitive to split ratio. We find excellent agreement with experiment with no fitted parameters.

1,731 citations

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TL;DR: In this paper, two distinct mechanisms have been suggested for the sudden increase of the number of electrons in an unfilled band, which occurs when the field strength passes a critical value, analogous to the electrical breakdown of gases.

Abstract: In the modern theory of metallic conduction initiated by Bloch, conductors, semi-conductors, and non-conducting crystals may be represented by the same model. In this model each electron is supposed to move freely in the periodic field of the lattice. Owing to this field, not all electronic energy levels are allowed; the allowed levels are grouped into bands, separated by energy intervals which are disallowed. If all the energy levels of a given band are occupied by electrons, then, according to the theory, these electrons can make no contribution to an electric current in the crystal. If all the bands are full, the crystal must be an insulator. Thus in an insulator there exist a number of energy bands which are completely full, and a number of bands of higher energy which, for a perfect crystal at the absolute zero of temperature, are empty. In a real non-conducting crystal, however, there will be a few electrons in the first unfilled band, owing to thermal excitation, impurities, etc. Their number is, however, too small to give an appreciable current at ordinary field strengths. As the field strength is increased, the current due to these few electrons increases steadily, but it will not show the sudden rise observed in dielectric breakdown. For this sudden rise it is necessary that the number of electrons in an unfilled band should suddenly increase as the field strength passes a critical value. Two distinct mechanisms have been suggested for this sudden increase. Of these, the first is a process analogous to the electrical breakdown of gases. In the absence of an external field, the few electrons in the upper band are in the lowest energy state of this band; under the action of an electric field, they are raised to higher levels. When one of these electrons reaches a sufficiently high level, it will give up energy to an electron in a lower (full) band, both electrons making a transition to a low level of the upper band. The process will then be repeated; the number of electrons in the upper band will thus increase exponentially with time as long as the electric field is maintained.

1,095 citations

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TL;DR: In this paper, the authors derived the effective mass Hamiltonian for wurtzite semiconductors, including the strain effects, using the k-ensuremath{\cdot}p perturbation method, which is then checked with that derived using an invariant method based on the Pikus-Bir model.

Abstract: We derive the effective-mass Hamiltonian for wurtzite semiconductors, including the strain effects. This Hamiltonian provides a theoretical groundwork for calculating the electronic band structures and optical constants of bulk and quantum-well wurtzite semiconductors. We apply Kane's model to derive the band-edge energies and the optical momentum-matrix elements for strained wurtzite semiconductors. We then use the k\ensuremath{\cdot}p perturbation method to derive the effective-mass Hamiltonian, which is then checked with that derived using an invariant method based on the Pikus-Bir model. We obtain the band structure ${\mathit{A}}_{\mathit{i}}$ parameters in the group theoretical model explicitly in terms of the momentum-matrix elements. We also find the proper definitions of the important physical quantities used in both models and present analytical expressions for the valence-band dispersions, the effective masses, and the interband optical-transition momentum-matrix elements near the band edges, taking into account the strain effects. \textcopyright{} 1996 The American Physical Society.

924 citations

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TL;DR: Amorphous covalent alloys particularly of group-IV, -V, and -VI elements are readily formed over broad ranges of composition and have been described as low-mobility electronic intrinsic semiconductors with a temperature-activated electrical conductivity σ = σ 0×exp(-ΔE/kT) which sometimes extends well into the molten state as discussed by the authors.

Abstract: Amorphous covalent alloys particularly of group-IV, -V, and -VI elements are readily formed over broad ranges of composition.1–6 They have been described as low-mobility electronic intrinsic semiconductors with a temperature-activated electrical conductivity σ = σ 0×exp(-ΔE/kT) which sometimes extends well into the molten state.2,3,7 They remain intrinsic with changed ΔE when their composition is changed.1,5,7 These alloys transmit infrared light up to an exponential absorption edge from which an energy gap E g is estimated.1,2 The value of E g usually is smaller than 2ΔE, often by as much as 10–20%.7,8 Photoconductivity9 and recombination-radiation10 measurements have been interpreted as giving evidence for the presence of localized states in the gap.

828 citations