Effects of screening on the rate of energy loss in degenerate surface layers of compound semiconductors at low lattice temperatures

The energy loss rate of an electron in degenerate surface layers of a compound semiconductor for inelastic interaction with deformation and piezoelectric acoustic phonons is calculated with due account of the screening of the perturbing potential under the condition of low lattice temperature when the approximations of the well known traditional theory is not valid. The numerical results obtained for GaAs and CdS exhibits interesting features, significantly different from what follows if one either makes the traditional approximation of negligible phonon energy or disregards the screening of the scattering potential.     

Effects of screening of the interaction potential on the mobility characteristics of degenerate surface layers in compound semiconductors at low lattice temperatures

The rates of scattering of the conduction electrons in degenerate two-dimensional electron gas in the surface of compound semiconductors at low lattice temperatures have been obtained for interaction with the piezoelectric and deformation potential acoustic phonons, under different prevailing conditions. The calculations have been carried out taking due account of the screening of the interaction potential at low temperatures where again the phonon energy cannot be neglected in comparison to the average thermal energy of the electrons and, as a result, the equipartition approximation for the phonon distribution can hardly be valid. The scattering rates thus obtained for inversion layers in GaAs and ZnO are found to depend upon the carrier energy, the lattice temperature and the level of degeneracy in quite involved manners, which are very different from what follows if one makes the simplifying approximation of negligible phonon energy or disregards the effects of screening. The mobility characteristics are then obtained using these scattering rates. The results show how the screening of the interaction potential and the finite energy of the intravalley acoustic and piezoelectric phonons significantly change the mobility characteristics of the degenerate surface layers at low lattice temperatures. The inadequacies of the present theory are pointed out and recommendations for possible refinements are discussed.     

Lattice-controlled electron transport characteristics in quantized surface layers at low temperature

A theory of intravalley acoustic scattering of the carriers in a non-degenerate two-dimensional electron gas is developed here under the condition of low lattice temperature when the assumptions of the well-known traditional theory are not valid. The scattering rates thus obtained are then used to estimate the zero-field mobility characteristics in an n-channel Si inversion layer. It is found that the finite energy of the phonons makes the energy and lattice temperature dependence of the scattering rate, and consequently the lattice temperature dependence of the mobility, significantly different from what follows, in the light of traditional theory which assumes equipartition law for the phonon distribution and neglects the phonon energy in comparison to the carrier energy.     

Two-dimensional electronic transport in In0.53Ga0.47As quantum Wells

Transport properties of the electrons itinerant two dimensionality in a square quantum well of In_0.53Ga_0.47As are studied in the framework of Fermi-Dirac statistics including the relevant scattering mechanisms. An iterative solution of the Boltzmann equation shows that the ohmic mobility is controlled by LO phonon scattering at room temperature, but below 130 K alloy scattering is predominant. The calculated mobilities with a suitable value of the alloy scattering potential agree with the experimental results over a range of lattice temperature. For lattice temperatures below 25 K where the carrier energy loss is governed by the deformation potential acoustic scattering, the warm electron coefficient is found to be negative. Its magnitude decreases with increasing lattice temperature and is greater for larger channel widths. Values of the small-signal AC mobility of hot electrons at a lattice temperature of 4.2 K are obtained for different sheet carrier densities and channel widths. Cut-off frequencies around 100 GHz are indicated.Dedicated to H.-J. Queisser on the occasion of his 60th birthday     

Transient response of hot electrons in narrow-gap semiconductors at low temperatures in the presence of a longitudinal quantizing magnetic field

Transient response of hot electrons in narrow-gap semiconductors to a step electric field in the presence of a longitudinal quantizing magnetic field has been studied at low temperatures using displaced Maxwellian distribution. The energy and momentum balance equations are used assuming acoustic phonon scattering via deformation potential responsible for the energy relaxation and elastic acoustic phonon scattering together with ionized impurity scattering for momentum relaxation. The calculations for the variation of drift velocity and electron temperature as functions of time are made for n-Hg_0.8Cd_0.2 Te in the extreme quantum limit at 1.5 K and 4.2 K. The momentum and energy relaxation times are found to be of the same order of magnitudes as with the experimental values. The magnetic field and lattice temperature dependences of the relaxation rates have been investigated.One of the authors, Suchandra Bhaumik, acknowledges the Council of Scientific and Industrial Research (New Delhi) for financial support.     

Temperature dependent energy relaxation time in AlGaN/AlN/GaN heterostructures

The two-dimensional (2D) electron energy relaxation in Al_0.25Ga_0.75N/AlN/GaN heterostructures was investigated experimentally by using two experimental techniques; Shubnikov-de Haas (SdH) effect and classical Hall Effect. The electron temperature (T_e) of hot electrons was obtained from the lattice temperature (T_L) and the applied electric field dependencies of the amplitude of SdH oscillations and Hall mobility. The experimental results for the electron temperature dependence of power loss are also compared with the current theoretical models for power loss in 2D semiconductors. The power loss that was determined from the SdH measurements indicates that the energy relaxation of electrons is due to acoustic phonon emission via unscreened piezoelectric interaction. In addition, the power loss from the electrons obtained from Hall mobility for electron temperatures in the range T_e > 100 K is associated with optical phonon emission. The temperature dependent energy relaxation time in Al_0.25Ga_0.75N/AlN/GaN heterostructures that was determined from the power loss data indicates that hot electrons relax spontaneously with MHz to THz emission with increasing temperatures.     

An analysis of phonon emission as controlled by the combined interaction with the acoustic and piezoelectric phonons in a degenerate III–V compound semiconductor using an approximated Fermi–Dirac distribution at low lattice temperatures

Compound semiconductors being piezoelectric in nature, the intrinsic thermal vibration of the lattice atoms at any temperature gives rise to an additional potential field that perturbs the periodic potential field of the atoms. This is over and above the intrinsic deformation acoustic potential field which is always produced in every material. The scattering of the electrons through the piezoelectric perturbing potential is important in all compound semiconductors, particularly at the low lattice temperatures. Thus, the electrical transport in such materials is principally controlled by the combined interaction of the electrons with the deformation potential acoustic and piezoelectric phonons at low lattice temperatures. The study here, deals with the problem of phonon growth characteristics, considering the combined scattering of the non-equilibrium electrons in compound semiconductors, at low lattice temperatures. Beside degeneracy, other low temperature features, like the inelasticity of the electron–phonon collisions, and the full form of the phonon distribution have been duly considered. The distribution function of the degenerate ensemble of carriers, as given by the heated Fermi–Dirac function, has been approximated by a simplified, well-tested model. The model which has been proposed earlier, makes it much easier to carry out analytically the integrations without usual oversimplified approximations.     

Polar optic phonon scattering of two dimensional electron gas in a rectangular potential well

The mobility of a two-dimensional electron gas (2DEG) in a rectangular potential well formed in a AlGaAs/GaAs/AlGaAs structure scattered by polar-optic phonon is calculated by an iterative solution of Boltzmann equation. The values are significantly different from those calculated by using a relaxation time. The polar-optic mobility is found to dominate over acoustic mobility over a temperature range of 100–300 K when the well thickness is about 10 nm. The mobility values for 2DEG are, however, found to be lower than the bulk values.     

Electron mobility in a modulation doped AlGaN/GaN quantum well

We consider a two dimensional electron gas confined to a modulation doped AlGaN/GaN quantum well and study the dependence of low field mobility on various parameters such as composition, well width, remote impurity and interface roughness as a function of temperature. GaN is assumed to be in the zincblende structure. Acoustic and optical phonon, ionized remote impurity and interface roughness scatterings are taken into account in mobility calculations. The scattering rates are calculated using the self-consistently calculated wave functions obtained from the numerical solution of Poisson and Schr?dinger equations. Also found from the self-consistent solutions are the potential profile at the junction, the energy levels in the well and electron concentrations in each level. Ensemble Monte Carlo method is used to find the drift velocities of the two dimensional electrons along the interface under an applied field. The mobility of two dimensional electrons is obtained from the drift velocity of electrons. It is found that while remote impurity scattering is very effective for small values of spacer layer and doping concentrations, increasing Al concentration reduces the mobility of electrons. The effect of surface roughness, on the other hand, on mobility is almost independent of well width. The results of our simulations are compatible with the existing experimental data.     

Piezoelectric scattering limited mobility characteristics of a degenerate surface layer in compound semiconductors at low lattice temperatures

The theory is developed for piezoelectric scattering rate of carriers in a degenerate surface layer under the condition of low temperature when the approximations of the well-known traditional theory are not valid. The scattering rates thus obtained are then used to estimate the zero-field mobility characteristics for the surface layers under similar condition of low temperature. The results for the surface layers in GaAs and ZnO show that when one takes into account either the degeneracy of the carrier ensemble or the finite energy of the phonons or both, the energy dependence of the scattering rates changes significantly from what follows for a non-degenerate ensemble or from the traditional theory, where one makes use of the high-temperature approximation and thus assumes equipartition law for the phonon distribution, and neglects the phonon energy in the energy balance equation of the electron–phonon system. It is observed that the zero-field mobility characteristics that follow from these scattering rates are interesting in that they are quite different from what turns out either for a non-degenerate ensemble or in the high-temperature approximations.     

极化子效应对ZnS/CdSe核壳量子点光吸收系数的影响

在有效质量近似下,利用量子力学密度矩阵理论,从理论上研究了考虑极化子效应后核壳量子点中线性、三阶非线性以及总的光吸收系数在不同条件下随入射光能量变化的关系。通过数值计算,分析了电子-LO声子和电子-IO声子相互作用对ZnS/CdSe柱型核壳结构量子点光吸收系数的影响。结果表明,极化子效应对光吸收系数有很大影响,不同声子模式对光吸收系数影响大小不同。考虑电子-LO声子后,光吸收系数被大大提高。另外,入射光强和弛豫时间对系统的吸收系数也有很大影响。     

Energy loss to intravalley acoustic modes in nano-dimensional wire structures at low temperatures

The theory of rate of loss of energy of non-equilibrium electrons due to inelastic interaction with the intravalley acoustic phonons in a nano-dimensional semiconductor wire has been developed under the condition of low lattice temperature, when the approximations of the well known traditional theory are not valid. Numerical results are obtained for narrow-channel GaAs-GaAlAs wires structures. On comparison with other available results it is revealed that the finite energy of the intravalley acoustic phonons and, the use of the full form of the phonon distribution without truncation to the equipartition law, produce significant changes in the energy loss characteristics at low temperatures.     

Magnetic susceptibility and short-range order in iron pnictides: Anisotropic J1-J2 Heisenberg model

The electron spin relaxation times by piezoelectric and polar optical phonon scattering in GaAs are calculated using the formula derived from the projection-reduction method. The temperature, magnetic field, and electron density dependences of the relaxation time are investigated. The electrons are found to be scattered mostly by piezoelectric phonons at low temperatures and polar optical phonons at high temperatures. The electron density affects the magnetic field dependence of the relaxation time at low temperatures but have only slight affects at high temperatures.     

Mobility as controlled by the transverse component of phonon wave vector in quantum layers at low temperatures

Without resorting to either the Kawaji’s simplified model of interaction with only two-dimensional phonons or to the equipartition approximation for the phonon distribution, the characteristics of the momentum relaxation time of the conduction electrons in a quantized surface layer for interaction with intravalley acoustic phonons have been analysed under the condition of low temperature. The scattering and the mobility characteristics thus obtained for an n-channel (1 0 0)-oriented Si inversion layer are apparently quite different from what follows in the traditional framework.     

Effects of non-equilibrium polar optic phonons and the band non-parabolicity on small signal high-frequency hot electrons ac mobility in narrow gap semiconductors in high magnetic fields

The small signal high-frequency ac mobility of hot electrons in n-HgCdTe in the extreme quantum limit at low and high temperatures have been calculated considering the non-equilibrium phonon distribution as well as the thermal phonon distribution .The energy loss rate has been calculated considering only optical phonon scattering while the momentum loss rate has been calculated considering acoustic phonon scattering and piezoelectric scattering together with polar optical phonon scattering and separately considering only the polar optical scattering. The results have been discussed and compared. It has been observed that at 20 K, the normalized mobility considering all the three scattering mechanisms differs appreciably from that considering only the polar optical phonon scattering. However, at 77 K, there is no difference in the normalized mobility. This establishes the fact that at higher temperature, the effect of acoustic phonon scattering and piezoelectric coupling is negligible, compared to the polar optical phonon scattering. So the ac mobility considering only polar optical phonon scattering has been studied at 77 and 20 K. The ac mobility is found to remain constant up to 100 GHz and thereafter it started decreasing at higher frequencies at 77 K whereas the ac mobility reduces at much lower frequencies at lower temperature at lower field. The non-parabolicity of the band structure enhances the normalized mobility.     

Relaxation processes and mobility of electrons in a semiconductor quantum well with the modified Pöschl-teller confining potential

Relaxation processes and mobility of electrons in a semiconductor quantum well are studied. The modified Pöschl-Teller potential is used as a confining potential. Scattering rates due to impurity ions, acoustic and piezoacoustic phonons are calculated taking into account the screening of scattering potentials by charge carriers. It is shown that when degenerate electrons are scattered by acoustic phonons, the dependence of scattering rate on electron wave number ν_ac(k) is almost linear. At small k, the acoustic phonon piezoelectric scattering rate of degenerate electrons increases with k, and then it decreases slightly when k > 8 × 10⁷ m⁻¹. The ionized impurity scattering rate of degenerate electrons does not depend on temperature, is directly proportional to the electron density, and decreases with increasing k. Dependences of electron mobility on surface ion density and temperature are studied. It is shown that in the case of non-degenerate or slightly degenerate electron gas, a maximum appears in the temperature dependence of the mobility, and the screening effect is negligible. The screening significantly increases the mobility of electrons in the case of high degeneration. Obtained results are applied to GaAs-based quantum wells.     

Electron-acceptor luminescence from a non-Maxwellian distribution of photoexcited electrons in GaAs

Distribution functions are calculated for photoexcited electrons in GaAs, under conditions of continuous, monochromatic excitation. The lattice temperature is taken to be 1.2 K and the excitation intensity such that the density of photoexcited carriers is insufficient for the distribution to be affected by intercarrier scattering. A Boltzmann equation approach is used to take account of the effects of, injection of electrons into the conduction band, at an energy below the threshold for longitudinal optical phonon emission, scattering by acoustic phonons, via the deformation potential and piezoelectric interactions, and recombination. The equation is solved numerically using an iterative technique and the distribution functions are found to differ significantly from a Maxwellian form. Emission spectra due to conduction band to neutral acceptor transitions are derived from the computed distribution functions and are compared with recent experimental results.     

Temperature relaxation and energy loss of hot carriers in graphene

The temperature relaxation and energy loss of hot Dirac fermions are investigated theoretically in graphene with carrier–optical phonon scattering. The time evolutions of temperature and energy loss for hot Dirac fermions in graphene are calculated self-consistently. It shows that the carrier–optical phonon coupling results in the energy relaxation of hot carriers excited by an electric field, and the relaxation time for temperature is about 0.5–1 ps and the corresponding energy loss is about 10–25 nW per carrier for typically doped graphene samples with a carrier density range of 1–5×10¹² cm^?2. Moreover, we analyze the dependence of temperature and energy relaxation on initial hot carrier temperature, lattice temperature and carrier density in detail.     

Effect of electrostatic screening due to non-equilibrium carriers on the lattice scattering rate at low temperatures

The intravalley acoustic scattering rate has been calculated here taking the screening by non-equilibrium electrons into account under the condition when the lifetime of the electrons is controlled by shallow attractive traps at low lattice temperature. The scattering rates now turn out to be field dependent and the characteristics are significantly different from what follows when the electron ensemble is in equilibrium with the lattice. The results indicate the possibility of interesting non-ohmic transport characteristics under these conditions. Numerical results are obtained for high purity samples of Si.     

High field transport properties in a GaN/AlGaN heterostructure

The drift velocity, electron temperature, electron energy and momentum loss rates of a two-dimensional electron gas are calculated in a GaN/AlGaN heterojunction (HJ) at high electric fields employing the energy and momentum balance technique, assuming the drifted Fermi–Dirac (F–D) distribution function for electrons. Besides the conventional scattering mechanisms, roughness induced new scattering mechanisms such as misfit piezoelectric and misfit deformation potential scatterings are considered in momentum relaxation. Energy loss rates due to acoustic phonons and polar optical phonon scattering with hot phonon effect are considered. The calculated drift velocity, electron temperature and energy loss rate are compared with the experimental data and a good agreement is obtained. The hot phonon effect is found to reduce the drift velocity, energy and momentum loss rates, whereas it enhances the electron temperature. Also the effect of using drifted F–D distribution, due to high carrier density in GaN/AlGaN HJs, contrary to the drifted Maxwellian distribution function used in the earlier calculations, is brought out.