Doped Semiconductor Superlattices Research Articles

Influence of confined acoustic phonons on the acousto-electric field in doped semiconductor superlattices

By using a quantum kinetic equation for electrons, the expression of the acoustoelectric field under the influence of confined acoustic phonons in doped semiconductor superlattices (DSSL) is obtained. From these expressions, the acousto-electric field depends on temperature, acoustic wave frequency, Fermi energy level, doped concentration, and quantum number m characterizing the phonons confinement. The results are numerically calculated for the GaAs:Be/GaAs:Si DSSL and show that the appearance of phonons confinement makes the acousto-electric field value become different than the cases of unconfined phonons.

The influence of confined acoustic phonon on the quantum Peltier effect in doped semiconductor superlattice in the presence of electromagnetic wave

Based on the kinetic equation method, the quantum Peltier effect has been theoretically studied under the influence of confined acoustic phonon in doped semiconductor superlattice in the presence of the electromagnetic wave (laser radiation). There were complicated dependences of the analytical expression of the Peltier coefficient (PC) on quantities such as doped concentration of the superlattice, amplitude of the laser radiation, the cyclotron frequency of electrons and temperature of the system. In detailed consideration, the quantum number m was changed in order to characterize the influence of confined acoustic phonon. When setting the m to zero, we obtained the results that corresponded to the case of unconfined phonon. The theoretical results have been numerically evaluated and discussed for the GaAs:Si/GaAS:Be doped semiconductor superlattice (DSS). We found the oscillation of the PC according to enhancement of cyclotron frequency of electrons. Moreover, position of resonant peaks has shifted under the influence of phonon confinement. In the case of low doped concentration (n D), the PC decreased in non-linear way; then it reached a negative constant in high n D value. The non-linear change of the PC also has been detected when investigating its dependence on the laser amplitude. All numerical results have shown that the magnitude of the PC decreased due to the increase of phonon confinement effect. In short, the confinement of acoustic phonon caused the change of the quantum Peltier effect in DSS of GaAs:Si/GaAS:Be in quantitatively as well as qualitatively.

The Ettingshausen effect in doped semiconductor superlattice under the influence of confined optical phonon

The electron – optical phonon scattering is considered in detail to studying the Ettingshausen effect in doped semiconductor superlattice under the influence of phonon confinement and laser radiation. The analytical expressions for tensors and the Ettingshausen coefficient are obtained by using the kinetic equation method. The Ettingshausen coefficient depends on temperature of the sample, amplitude and frequency of laser radiation, magnetic field and the quantum number m specific for the confinement of phonon. The dependences are clearly displayed in the numerical results for GaAs:Be/GaAs:Si doped semiconductor superlattice. The magnetic field makes the Ettingshausen coefficient change in quantitative under the influence of temperature or laser amplitude and change the resonance condition. The numerical results show that both resonance condition and resonance peaks position are affected by the increase of quantum number m. We also get the result corresponding to the unconfined optical phonon case when m is set to zero. Due to the change of the wave function and energy spectrum of electrons, most of results for the Ettingshausen effect in doped semiconductor superlattice obtained are different from the case of bulk semiconductor. Moreover, in comparison with the case of unconfined optical phonon, under the influence of phonon confinement effect, the Ettingshausen coefficient changes in magnitude, the number and position of resonance peaks.

Parametric resonance of acoustic and optical phonons in a doped semiconductor superlattice in the presence of a laser field

In this paper, we analytically investigated the possibility of parametric resonance of acoustic and optical phonons. We obtained a general dispersion equation for parametric amplification and transformation of phonons. The dispersions of the resonant acoustic phonon modes and the threshold amplitude of the field for acoustic phonon parametric amplification are obtained. The parametric amplification for acoustic phonons in a doped semiconductor superlattice can occur under the condition that the amplitude of the external electromagnetic field is higher than the threshold amplitude.

Influence of Confined Acoustic Phonons on the Nonlinear Acousto-electric Effect in Doped Semiconductor Superlattices

Abstract: By using a quantum kinetic equation for electrons, we have studied the Acousto-electric effects in doped semiconductor superlattice (DSSL) under the influence of confined phonon. Considering the case of the electron - acoustic phonon interaction, we have found the expressions of the nonlinear quantum acousto-electric current. From these expression, the acousto-electric current (AEC) depends nonlinearly on temperature, acoustic wave frequency and the characteristic parameters of DSSL (For example: the doped concentration ). Moreover, the expression of the AEC under the influence of confined phonons fairly different from the case of unconfined phonons.
 The results are numerically calculated for the GaAs:Be/ GaAs:Si DSSL; therefore, it can be easily seen that the dependence of the acousto-electric current on the characteristic parameters of the acoustic wave, temperature, the characteristic parameters of DSSL and the quantum number m characterizing the phonons confinement. The results have showed that the appearance of phonons confinement make the AEC value changes remarkably. The AEC is almost stable in low acoustic wave frequency condition and changes as a parabolic curve when move up. On the other hand, in case of low doped concentration number the AEC surges as a parabolic function in the dependence on , then it remains stability at just below zero in high value.
 Keywords: Acousto-electric field, Quantum kinetic equation, Doped superlattices, Electron - phonon interaction.

Theoretical Study of the Magneto-Thermoelectric Effect in Doped Semiconductor Superlattices under the Influence of an Electromagnetic Wave by Using a Quantum Kinetic Equation

By using a quantum kinetic equation for electrons, we studied magneto - thermoelectric effects in the doped semiconductor superlattice (DSSL) under the influence of electromagnetic waves (EMW). In case of the electron - acoustic phonon interaction, we have also figured out analytical expressions of the Ettingshausen coefficient (EC) in DSSL. These expressions are quite different from those which were obtained in the case of bulk semiconductors. The results are numerically calculated for the GaAs:Be/ GaAs:Si DSSL; we found that the EC depends on the characteristic parameters of EMW, temperature and the characteristic parameters of DSSL. The results are consistent with recently experimental observations but the EC is different from that in the bulk semiconductors or bismuth. In addition, the impact of the EMW on the Ettingshausen effect was also discovered. These are latest results which have been studied in terms of Ettingshausen effect in DSSL.

Impact of confined LO-phonons on the Hall effect in doped semiconductor superlattices

Abstract Based on the quantum kinetic equation method, the Hall effect in doped semiconductor superlattices (DSSL) has been theoretically studied under the influence of confined LO-phonons and the laser radiation. The analytical expression of the Hall conductivity tensor, the magnetoresistance and the Hall coefficient of a GaAs:Si/GaAs:Be DSSL is obtained in terms of the external fields, lattice period and doping concentration. The quantum numbers N, n, m were varied in order to characterize the effect of electron and LO-phonon confinement. Numerical evaluations showed that LO-phonon confinement enhanced the probability of electron scattering, thus increasing the number of resonance peaks in the Hall conductivity tensor and decreasing the magnitude of the magnetoresistance as well as the Hall coefficient when compared to the case of bulk phonons. The nearly linear increase of the magnetoresistance with temperature was found to be in good agreement with experiment.

A novel exact solution to transmission problem of electron wave in a nonlinear Kronig-Penney superlattice

Nonlinear Kronig-Penney model has been frequently employed to study transmission problem of electron wave in a doped semiconductor superlattice or in a nonlinear electrified chain. Here from an integral equation we derive a novel exact solution of the problem, which contains a simple nonlinear map connecting transmission coefficient with system parameters. Consequently, we propose a scheme to manipulate electronic distribution and transmission by adjusting the system parameters. A new quantum coherence effect is evidenced by the strict expression of transmission coefficient, which results in the aperiodic electronic distributions and different transmission coefficients including the approximate zero transmission and total transmission, and the multiple transmissions. The method based on the concise exact solution can be applied directly to some nonlinear cold atomic systems and a lot of linear Kronig-Penney systems, and also can be extended to investigate electronic transport in different discrete nonlinear systems.

Temperature-tunable semiconductor metamaterial

We propose a novel class of temperature-tunable semiconductor metamaterials that exhibit negative refraction in the terahertz spectral range. These metamaterials are based on doped semiconductor superlattices with ultrathin barriers of about 1 nm thickness. Due to the tunnel transparency of the barriers, layers of the superlattice cannot be considered as isolated and, therefore, the classical homogenization approach is inapplicable. We develop a theory of quantum homogenization which is based on the Kubo formula for conductivity. The proposed approach takes into account the wave functions of the carriers, their distribution function and energy spectrum. We show that the components of the dielectric tensor of the semiconductor metamaterial can be efficiently manipulated by external temperature and a topological transition from the dielectric to hyperbolic regime of metamaterial can be observed at room temperature. Using a GaAs/Al$_{0.3}$Ga$_{0.7}$As superlattice slab as an example, we provide a numerical simulation of an experiment which shows that the topological transition can be observed in the reflection spectrum from the slab.

Coherent phonon optics in a chip with an electrically controlled active device.

Phonon optics concerns operations with high-frequency acoustic waves in solid media in a similar way to how traditional optics operates with the light beams (i.e. photons). Phonon optics experiments with coherent terahertz and sub-terahertz phonons promise a revolution in various technical applications related to high-frequency acoustics, imaging, and heat transport. Previously, phonon optics used passive methods for manipulations with propagating phonon beams that did not enable their external control. Here we fabricate a phononic chip, which includes a generator of coherent monochromatic phonons with frequency 378 GHz, a sensitive coherent phonon detector, and an active layer: a doped semiconductor superlattice, with electrical contacts, inserted into the phonon propagation path. In the experiments, we demonstrate the modulation of the coherent phonon flux by an external electrical bias applied to the active layer. Phonon optics using external control broadens the spectrum of prospective applications of phononics on the nanometer scale.

Hall Effect on the Doped Semiconductor Superlattice with an In-plane Magnetic Field Under Influence of an Intense Electromagnetic Wave

The Hall effect is studied theoretically in a doped semiconductor superlattice (DSSL) subjected to a crossed dc electric field and magnetic field in the presence of an intense electromagnetic wave (EMW). By using the quantum kinetic equation for electrons interacting with acoustic phonons at low temperature, we obtain expressions for the magnetoresistance as well as the Hall coefficient in dependence on the external fields and characteristic parameters of the DSSL. Analytical results are numerically evaluated for the GaAs:Si/GaAs:Be DSSL. The dependence of the magnetoresistance on the magnetic field is consistent with the result obtained for some two-dimensional electron systems. The Hall coefficient depends weakly on the magnetic field and its value in the presence of the EMW is smaller than that of the case without EMW.

Dependence of the Hall Coefficient on Doping Concentration in Doped Semiconductor Superlattices with a Perpendicular Magnetic Field under the Influence of a Laser Radiation

The dependence of the Hall coefficient on doping concentration in doped semiconductor superlattices (DSSLs) under a crossed dc electric field and magnetic field in the presence of a laser radiation, is investigated by using a quantum kinetic equation for electrons. Analytical results for the resistance and the Hall coefficient (HC) are computationally evaluated and graphically plotted for the GaAs:Si/GaAs:Be DSSL. Numerical results for the magnetoresistance are in accordance with available theories. The dependence of the HC on the doping concentration shows an oscillation whose phase is strongly affected by the laser radiation.

ELECTROPHONON RESONANCE IN DOPED SEMICONDUCTOR SUPERLATTICES

The electrophonon resonance (EPR) effect in doped semiconductor superlattices (DSSL) are investigated by using the quantum kinetic equation (QKE) for electrons to obtain the general analytic expression for optical absorption coefficient. We also obtain an EPR condition as a function of the photon energy and plasma energy. In particular, anomalous behaviors of the EPR effect such as the splitting of EPR peaks for incident photon energy or plasma energy are discussed. This raises a possibility of detecting electric subbands in DSSLs experimentally by utilizing EPR effects.

CALCULATION OF THE INTENSITY-DEPENDENT ABSORPTION SPECTRUM IN TWO-DIMENSIONAL ELECTRON SYSTEMS

General analytic expression for the intensity-dependent absorption coefficient (IDAC) of an intense electromagnetic wave (IEMW) in two-dimensional electron systems (2DES) is obtained by using the quantum kinetic equation (QKE) for electrons in the case of electron–optical phonon scattering in a doped semiconductor superlattice (DSSL). The dependence of IDAC on the amplitude E0 and the photon energy ℏΩ of an IEMW, the energy ℏωp and the temperature for a specific n-i-p-i superlattice of GaAs : Si / GaAs : Be is achieved due to a numerical method. The computational results show that not only the dependence of IDAC on ℏΩ but also the dependence of IDAC on ℏωp can be applied to optically detect the electric subbands in a DSSL.

Calculation of the Nonlinear Absorption Coefficient of an Intense Electromagnetic Wave Caused by Confined Electrons in Doped Semiconductor Superlattices

Calculation of the Nonlinear Absorption Coefficient of an Intense Electromagnetic Wave Caused by Confined Electrons in Doped Semiconductor Superlattices

Optical detection of folded mini-zone-edge coherent acoustic modes in a doped GaAs/AlAs superlattice

A coherent phonon mode with frequency corresponding to the first mini Brillouin-zone edge stop gap is observed in ultrafast pump-probe measurements on a doped semiconductor superlattice structure. It is proposed that the optical detection of the mode is facilitated by interactions with the free carriers present in the superlattice.

Parametric Resonance of Acoustic and Optical Phonons in a Doped Semiconductor Superlattice

Parametric Resonance of Acoustic and Optical Phonons in a Doped Semiconductor Superlattice

Numerical Methods for a Quantum Drift–diffusion Equation in Semiconductor Physics

We present the numerical methods and simulations used to solve a charge transport problem in semiconductor physics. The problem is described by a Wigner–Poisson kinetic system we have recently proposed and whose results are in good agreement with known experiments. In this model, we consider doped semiconductor superlattices in which electrons are supposed to occupy the lowest miniband, exchange of lateral momentum is ignored, the electron–electron interaction is treated in the Hartree approximation and elastic and inelastic collisions are taken into account. Nonlocal drift-diffusion equations derived systematically elsewhere from the hyperbolic limit of a kinetic Wigner–Poisson model are solved. The nonlocality of the original quantum kinetic model equations implies that the derived drift-diffusion equations contain spatial averages over one or more superlattice periods. Numerical methods are based upon prior knowledge on physical properties of the phenomenon and have shown to be effective in validating our formulation. Numerical solutions of the equations show self-sustained oscillations of the current through a voltage biased superlattice, in good agreement with known experiments.

Relocation dynamics and multistable switching in semiconductor superlattices

A numerical study of electric field domain relocation during slow voltage switching is presented for a spatially discrete model of doped semiconductor superlattices. The model is derived from the Poisson's equation and the charge continuity equation. It consists of an Ampère equation for the current density and a global summatory condition for the electric field and it has been particularly effective in the prediction and reproduction of experimental results. We have designed a fast numerical scheme based on the use of an explicit expression for the current density. The scheme reproduces both previous numerical and experimental results with high accuracy, yielding new explanations of already known behaviors and new features that we present here.

Voltage switching and domain relocation in semiconductor superlattices

A numerical study of domain wall relocation during voltage switching with different ramping times is presented for weakly coupled, doped semiconductor superlattices exhibiting multistable domain formation in the first plateau of their current-voltage characteristics. Stable self-oscillations of the current at the end of stable stationary branches of the current-voltage characteristics have been found. These oscillations are due to periodic motion of charge dipoles near the cathode that disappear inside the SL, before they can reach the receiving contact. Depending on the dc voltage step, the type of multistability between static branches and the duration of voltage switching, unusual relocation scenarios are found including changes of the current that follow adiabatically the stable I--V branches, different faster episodes involving charge tripoles and dipoles, and even small amplitude oscillations of the current near the end of static I--V branches followed by dipole-tripole scenarios.