Nonparabolic Energy Bands Research Articles

Temperature Damping of Plasmons in Nonparabolic Band

Collective excitations influence many effects observed in quantum free-carrier semiconductor plasmas, like, for example, the impurity scattering of carriers for radiation frequencies close to the plasma frequency. Recent studies on linear-conduction-band materials [1, 2] indicate that the free-carrier band nonparabolicity may have a strong impact on the plasmons behaviour. In the present paper the influence of the nonparabolic structure of the free-carrier band on the dispersion of plasmons and their temperature damping is considered. The temperature-dependent formfactor —Im[1/e(q, ω)], where e(q, ω) is the wavevectorand frequency-dependent RPA [3] longitudinal complex dielectric function, is used to examine the properties of the collective excitations. The nonparabolic energy band of the form E(k) = (1/2)[(E8 + 4Ρ2k2)1/2 — Eg] is assumed and the overlap integrals of the electronic wave functions calculated from the Kane model are taken into account in the free-carrier polarizability. The calculations were performed for the plasma in n-PbSe in isotropic approximation [4], with P 2 = ħ2Eg/2m*, where Eg is the energy gap and m* is the effective mass at the bottom of the conduction band. The dielectric function included also the optical-phonon contribution [e.g. 4] i.e. we account for the plasmon-phonon coupling. For the degenerate plasma the nonparabolicity of the free-carrier band was found to extend the range of the wavevectors and energies where the plasmons

Quasi-elastic light scattering from electrons in semiconductors with nonparabolic energy bands

Quasi-elastic light scattering from electrons in semiconductors with nonparabolic energy bands

Inducing normally forbidden transitions within the conduction band of GaAs quantum wells

Six heretofore unobserved envelope state transitions within the conduction band of an AlAs/GaAs quantum well are reported, two of which are forbidden in a symmetric quantum well. The highest energy transition is resonant with 2.86 μm wavelength light. These resonant energies and absorption strengths agree with predictions based on a many-body theory of electrons in nonparabolic energy bands. A new type of infrared modulator is possible via absorption changes in the ‘‘forbidden’’ transition between the first and the third conduction subbands.

On electronic Raman scattering from high-Tc layered superconducting materials

The nature of electronic Raman scattering from anisotropic layered high- T c materials has been considered. Approximate expressions for the electronic Raman scattering from both charge-density fluctuations (CDF) and spin-density fluctuations (SDF) in these materials with nonparabolic energy bands and anisotropic Fermi surfaces have been derived. It is shown that in the normal state the unscreened part of the single-particle electronic Raman scattering has a width of about 2ω cn in the collision-dominated regime in which the normal state collision frequency ω cn ⪢ q · v f , where ħ q is the momentum transfer in the scattering process and v F is the Fermi velocity. Although, the normal state Raman spectrum is not as flat as observed experimentally, the possibility that most of the spectrum may be arising from such collision-dominated single-particle excitations, cannot be ruled out completely. More careful experimentation is required to confirm unambiguously the existence of any novel type of electronic excitations in the system.

Multiphoton transitions in semiconductors in the non-perturbative approach

Transition rates for multiphoton absorption via direct band-to-band excitation have been calculated using a non-perturbative approach due to Jones and Reiss [3], based on the Volkov type final state wave functions. Both cases of parabolic and non-parabolic energy bands have been included in our calculations. Absorption coefficients have been obtained for the cases of plane polarized and circularly polarized light. In particular, two-photon absorption coefficients are derived for the two cases of polarization for the parabolic band approximation as well as for non-parabolic bands and compared with the results based on perturbation theory. Numerical estimates of the two-photon absorption coefficients resulting from our calculations are also provided.

Properties of liquid-phase epitaxy grown Pb1−xSnxTe homostructure diode lasers with Ga-doped cladding layer

The properties of homostructure Pb1−xXnxTe diode lasers with tin compositions x=0.126, 0.182, 0.210, and 0.238 fabricated from liquid-phase epitaxy grown p+-p-n+ layer structure with Ga-doped n-type cladding layer were investigated. Threshold current density (Jth) and quantum efficiency (ηext) was measured as a function of temperature in the range 10≤T≤140 K. Current versus voltage (I-V) and product derivative I dV/dI vs I characteristics were measured at T=10 and 40 K. Jth was evaluated from basic principles taking into account intrinsic radiative and nonradiative Auger recombination lifetime, where the last was calculated using both parabolic and nonparabolic energy band structures. Satisfactory agreement was obtained between the calculated and measured Jth for temperatures above 40 K, while at low temperatures the theory underestimates Jth significantly. Using an electrical equivalent model of the diode laser and best fit procedure the I-V and I dV/dI vs I characteristics were analyzed and the various current components and diode laser parameters were obtained. It was qualitatively shown that the discrepancy at low temperatures follows from the presence of large leakage and tunneling currents. The temperature dependence of the observed ηext, which exhibits a maximum between 40 and 50 K, was shown to be related to a filamentary lasing process.

Electron energy distributions, transport parameters, and rate coefficients in GaAs

Monte Carlo methods have been used to obtain the electron energy distributions, transport parameters, and rate coefficients for electrons in a three-valley model of GaAs with nonparabolic energy bands in the presence of an external electric field. A technique has been developed which reduces the computation time when using self-scattering algorithm. Consequently, for a given computation time, more test particles can be used in the simulation. This results in a reduction in the fluctuation of the calculated quantities. In this paper, the Monte Carlo technique is presented for two generic time variations of the applied field: (a) dc and (b) a step change. The results shown are for the steady-state behavior of electrons in GaAs, for dc electric fields with values up to 70 kV/cm.

Monte Carlo Study of Hot Electron Transport in Quantum Wells

Monte Carlo simulations of hot electron transport in AlGaAs/GaAs /AlGaAs quantum wells were carried out in order to clarify the drift velocity overshoot and steady state drift velocity versus the electric-field relation. In the simulations, we took into account the nonparabolic isotropic energy band structures. Results are given for GaAs well widths of 500 and 100 Å and an electron sheet density of 1.0×1012 cm-2 at 77 K. The drift-velocity overshoot reaches about 7×107 cm/s at an electric field of 10 kV/cm in both quantum well structures. A negative differential mobility appears beyond 3 kV/cm in both structures due to electron transfer from the Γ valley to the L valleys.

Nonlinear response of electron-phonon interaction inn-type nondegenerate piezoelectric semiconductors

The nonlinear response of the electron-phonon interaction in nondegenerate piezoelectric semiconductors such asn-type InSb in the presence of a dc magnetic fieldB directed along the propagation of acoustic waves has been studied by using a quantum mechanical treatment. The effect of electron scattering in solids has been taken into consideration, so the electron relaxation time cannot be neglected. The nonlinear nature of the energy band is corrected for, using the Heisenberg equation of motion. It is found that the nonlinear response is proportional to a nonlinear longitudinal conductivity tensor τ zzz when acoustic waves propagate parallel to the [111] direction for both piezoelectric and deformation-potential couplings. Numerical calculations for τ zzz of n-type InSb at low temperatures are presented. Results show that the nonlinear response decreases rapidly with the sound frequency, and decreases slowly with the dc magnetic field and temperature. Therefore, the electron relaxation time and the nonparabolicity of energy bands play important roles for the electron-phonon interaction due to the piezoelectric and deformation-potential couplings in the microwave region.

Theory of the cyclotron resonance spectrum of a polaron in two dimensions.

The magneto-optical absorption spectrum of a two-dimensional polaron is calculated by using a memory-function approach. The cyclotron resonance frequency and the cyclotron resonance mass of the polaron are obtained for weak electron-phonon coupling. The absorption spectrum exhibits peaks around the cyclotron frequency ${\ensuremath{\omega}}_{c}$ and the LO-phonon-assisted harmonics ${\ensuremath{\omega}}_{\mathrm{LO}+\mathrm{n}{\ensuremath{\omega}}_{c}}$ (n=1,2,. . .). The oscillator strength and the position of the peaks are investigated as a function of the magnetic field strength. A Landau-level broadening parameter is introduced phenomenologically in order to remove the divergencies in the magneto-optical absorption spectrum. The effect of the nonzero width of the two-dimensional electron layer is also investigated. After taking into account the effect of the nonparabolic energy band of the electron, the calculated cyclotron resonance masses are compared to the experimental data for GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructures and InSb inversion layers. In order to explain the experimental results for GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructures with our one polaron theory an effective electron-phonon coupling constant has to be used which is smaller than generally accepted. Many-body effects are expected to be responsible for this reduction.

Current, carrier concentration, Fermi energy, and related properties of binary compound polar semiconductors with nonparabolic energy bands

Using Kane’s energy–wave-vector relation (k.P model), it is shown that the nonparabolic band structure of binary compound polar semiconductors (BCPSCs) is, in fact, a perturbed parabolic band structure. The formula for this ‘‘parabolic’’ band structure is used to derive current, carrier concentrations, Einstein equation, and others. The formula for the Einstein equation is found to be of the same form as that for wide-gap semiconductors. Simplified relations for nonparabolicity coefficients have been derived. It is shown that these coefficients compare well with similar coefficients derived earlier from different considerations. Numerical calculations of effective mass, density of states, Fermi energy, and electron-impurity interaction energy have been carried out for a number of representative compounds. Good correspondence of theoretical results with available experiments indicates that the present model is quite useful for describing properties of BCPSCs.

Auger transitions in semiconductors and their computation

To obtain an accurate theoretical determination of Auger transition rates from first principles it is essential that the multidimensional integral of the transition probabilities should not be approximated, particularly with regard to the overlap functions, as has been done previously. In considering general interband Auger transitions (with direct or indirect bands) the difficulty of complicated limits imposed by energy and momentum conservation is removed by a transformation of the variables, resulting in an integration over a complete six-dimensional solid angle. This makes accurate computation possible without approximating the integrand-within the limitation of the best available overlap functions and band structure. The initial application is to InSb where small- and large-signal Auger lifetimes, mass-action constants and impact ionisation rates are determined using Fermi-Dirac statistics, non-parabolic energy bands for all states and overlap functions derived from the four-band k.p model.

Three-photon absorption in direct-gap crystals

Third-order time-dependent perturbation theory, utilizing parabolic and nonparabolic energy bands and calculated (from band structure) higher bands as intermediate levels, and a Keldysh first-order model are used to calculate three-photon-absorption coefficients of several direct-gap crystals. Third-order perturbation results for CdS at 1.06 microm agree well with the experimental data.

Effect of size quantization on the Einstein relation in ultrathin films of non-parabolic semiconductors

An attempt is made to investigate the effect of size quantization on the diffusivity-mobility ratio of the carriers in ultrathin films of semiconductors having Kane-type nonparabolic energy bands. It is shown, takingn-type InSb as an example, that the ratio oscillates both with increasing film thickness and with increasing carrier concentration under degenerate conditions and remains unaffected otherwise. The corresponding results for parabolic semiconductors are also obtained from the expressions derived.

Influence of alloy composition on the diffusivity-mobility ratio in n-channel inversion layers on ternary semiconductors

An expression is derived for the diffusivity-mobility ratio of the carriers in n-channel inversion layers on semiconductors like the ternary compounds which have strongly non-parabolic energy bands. The dependence of the ratio on alloy composition is also studied under the weak-field limit taking n-channel Hg1−xCdx.Te as an example.

Two-photon absorption in several direct-gap crystals

The formulas for describing two-photon absorption in direct-gap crystals, developed by Keldysh, Braunstein, and Basov, are compared. It is shown that the Keldysh formula is closely related to Braunstein's for allowed-allowed transitions, while Basov's proposed formula more closely corresponds to Braunstein's for allowed-forbidden transitions. A number of suggested improvements are introduced in Braunstein's formula and corrections to Basov's are presented. The two-photon absorption coefficients for several direct-gap semiconductors and alkali halides are calculated from these formulas and compared with the available experimental data. The formulas of Keldysh and Braunstein for describing allowed-allowed transitions, where one considers excitonic intermediate states and nonparabolic energy bands, are found to give results in fair agreement with published experimental results. It is noted, in comparison, that Basov's and Braunstein's absorption coefficients for allowed-forbidden transitions are smaller than available experimental data by orders of magnitude.

Theory of a solid-state cyclotron maser

Abstract : A theory is developed for the cyclotron maser interaction between an electron beam and the electromagnetic waves in a cavity formed with a semiconductor having nonparabolic energy bands. The interaction originates from the dependence of the effective mass of the electron (hence cyclotron frequency) on its velocity due to nonparabolic energy-momentum relation. This mechanism is very similar to that for the cyclotron maser radiation in vacuum tubes where the relativistic variation of mass with velocity is utilized. The linear response of the electron beam to the cavity fields are obtained from Vlasov equation and the Maxwell's equations while collisions are treated with an approximate model. Analytical expressions for the beam-wave coupling coefficient, beam energy loss and the threshold power are derived for the fundamental and higher cyclotron harmonics. The dependence of these quantities on the various parameters such as cavity length, beam position, beam energy, magnetic field, etc. are discussed. (Author)

On the relation between the fermi energies in the presence and absence of magnetic quantization in degenerate semiconductors having non-parabolic energy bands

An investigation is made of the influence of band non-parabolicity on the relation between the Fermi energies in the presence and absence of magnetic quantization in degenerate semi-conductors through derivation of a simplified form of the relation.

Effects of energy-band nonparabolicity on the free-carrier absorption inn-type GaP

The effects of nonparabolicity on the free-carrier absorption in $n$-type GaP are analyzed on the basis of quantum-mechanical results. It is shown that the absorption coefficient is reduced by about 10-15% in the wavelength range 4-10 \ensuremath{\mu}. The index of wavelength dependence is also somewhat increased.

On the theory of electron diffusion under a temperature gradient in degenerate semiconductors having non-parabolic energy bands

The theory of electron diffusion under a temperature gradient (Soret effect) in degenerate semiconductors having non-parabolic energy bands and spherical constant-energy surfaces is worked out for the first time. An expression is given for the Soret coefficient which may be determined from the knowledge of the energy dependence of the relaxation time and can be related to the thermoelectric power.