Quantum Kinetic Equation For Electrons 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.

Theoretical Study of the Nernst Effect in Compositional Superlattices in the Presence of Strong Electromagnetic Wave

The Nernst effect has been theoretically studied in compositional superlattice in the presence of a strong electromagnetic wave. Using the quantum kinetic equation for electrons with two cases electrons-acoustic phonons scattering and electrons-optical phonons scattering, we obtained the analytic expression of the Nernst coefficient and kinetic tensors as a function of the magnetic field, temperature, frequency, and amplitude of the electromagnetic wave and parameters of the compositional superlattice. The dependence of the Nernst coefficient on the magnetic field and temperature is achieved by numerical calculations for AlGa/AlGaAs material. The result indicates that in the case of electron-acoustic phonon scattering, the Shubnikov-de Hass oscillation appears. Whereas, in the case of electrons-optical phonons scattering, the peak of magneto-photon-phonon resonance appears. In both cases, when temperature increases, the Nernst coefficient decreases rapidly, and for electrons-optical phonons scattering, the resonance peak has a movement.

Theoretical study of nonlinear absorption of a strong electromagnetic wave in infinite semi-parabolic Plus Semi-inverse Squared Quantum Wells by using quantum kinetic equation

General analytic expressions for the total absorption coefficient of strong electromagnetic waves caused by confined electrons in Infinite semi-parabolic plus Semi-inverse Squared Quantum Wells (ISPSISQW) are obtained by using the quantum kinetic equation for electrons in the case of electron-optical phonon scattering. A second-order multi-photon process is included in the result. The dependence of the total absorption coefficient on the intensity E0, the photon energy ħΩ of an SEMW, and the temperature T for a specific GaAs/GaAsAl ISPPSISQW is achieved by using a numerical method. The computational results demonstrate that the total absorption coefficient’s dependence on photon energy can be utilized for optically detecting the electric sub-bands in an ISPPSISQW. Besides, we also give theoretical rules on the dependence of the Full Width at Half Maximum on important external parameters such as temperature and perpendicular magnetic field. Furthermore, the obtained results are consistent with prior theoretical and experimental findings.

Influence of a Strong Electromagnetic Wave on the Nonlinear Absorption coefficient of Strong lectromagnetic Waves Caused by Electrons Confined in Cylindrical Quantum Wires

The nonlinear absorption coefficient of a strong electromagnetic wave caused by electrons confined in cylindrical quantum wires is theoretically studied by using the quantum kinetic equation for electrons. Analytic expressions of the nonlinear absorption coefficient of a strong electromagnetic wave caused by electrons confined in a cylindrical quantum wire with a parabolic potential for electron-optical phonon scattering is obtained, that the dependence of the nonlinear absorption coefficient on the intensity E0 and the frequency Ω of the external strong electromagnetic wave is strongly and nonlinearly. The analytic expressions are numerically calculated and discussed for a GaAs/GaAsAl quantum wire. The results are compared with those for normal bulk semiconductors and quantum wells to show the differences.

Conductivity tensor in semiconductor with the presence of a laser field and an electromagnetic wave field for the case of scattering on ionized impurities

There are a lot of studies on semiconductors and in semiconductors also appear many dynamic effects, from the research results that have many applications in science and technology. Conductivity tensor is a familiar concept in physics in general and semiconductors in particular, but research on scattering on ionized impurities is still limited. This paper presents the influence of laser field and electromagnetic waves on conductivity tensor for the case of scattering on ionized impurities in semiconductor. The particle system is placed in an electromagnetic wave field and a laser field. Using quantum kinetic equations for electrons in semiconductor under the action of an electromagnetic wave field, a laser field, the conductivity tensor is calculated with case of scattering on ionized impurities. Conductivity tensor depends on the frequency of the laser field, the laser field amplitude, the electromagnetic wave frequency and typical parameters for semiconductor system. With different frequency bands, the dependence of tensor conductivity on the frequency is different, and the special conductivity tensor is strongly dependent on the amplitude of the laser field but depends very little on its frequency. The results will be plotted and discussed with GaAs semiconductor case and compared with studies for different scattering cases.

Conductivity tensor in cylindrical quantum wire with infinite potential for the case of electron-optical phonon scattering

Conductivity tensor characterizes the conductivity of the material, this work calculates the conductivity tensor in a cylindrical quantum wire with infinite potential in the presence of two external fields, the laser field and linearly polarized electromagnetic wave field. The problem is also only considered for the case of electron-optical phonon scattering. By using a quantum kinetic equation for electrons in a quantum wire in the presence of two external fields, the conductivity tensor is calculated. The expression for conductivity tensor shows its dependence on the frequency and amplitude of the external field as well as other parameters specific to the system The figure of the dependence of the conductivity tensor to the external field will be investigated and plotted for the quantum wire GaAs/GaAsAl.

The influence of electromagnetic waves and laser fields on conductivity tensor for the case of electron - optical phonon scattering in quantum wells with a parabolic potential

This paper studies the influence of electromagnetic waves and laser fields on conductivity tensor with the case of electron - optical phonon scattering in quantum wells. Because electrons are confined in the quantum well in one direction, the conductivity tensor in the quantum well is different from the conductivity tensor in the bulk semiconductor. The carrier system in a quantum well is located in an electromagnetic wave field and a laser field. Using quantum kinetic equation for electrons in quantum wells in the presence of an electromagnetic wave and a laser field, from the quantum kinetic equation it is possible to calculate the conductivity tensor. The conductivity tensor expression is a function of the electromagnetic wave frequency, laser field frequency and quantum well characteristic parameters. Survey and plot the dependence of conductivity tensor on electromagnetic wave frequency, laser field frequency, laser field amplitude with GaAs / GaAsAl quantum well case.

The influence of electromagnetic waves on conductivity tensor in the presence of laser field in quantum wells with parabolic potential for the case of electrons-acoustic phononscattering

In quantum well studies, the conductivity tensor problem is one of the fundamental problems. In this work the topic covered here is the effect of electromagnetic waves on the conductivity tensor with the presence of a laser field in a quantum well with a parabolic potential considering the case ofelectrons-acoustic phonon scattering. By using quantum kinetic equations for electrons in quantum wells with parabolic potential, the author has calculated conductivity tensor with electrons–acoustic phonon scattering in the presence of an electromagnetic wave field and a laser field. The expression tensor for conductivity shows its dependence on the frequency of the electromagnetic wave field, the frequency of the laser field, and other parameters specific to the system. From the conductivity tensor expression plotted the effect of the electromagnetic wave field on the conductivity tensor in the presence of the laser field. The quantum well is discussed and plotted here is the GaAs/GaAsAl quantum well.

The dependence of the conductivity tensor on electromagnetic waves and laser fields in a quantum well with infinite potential in the case of electrons - optical phonon scattering

There are many studies on low-dimensional semiconductors, including quantum wells. Conductivity tensor is one of the key concepts in materials research. This work studies the dependence of the conductivity tensor on electromagnetic waves and laser fields in a quantum well with infinite potential in the case of electrons - optical phonon scattering. Results are obtained using the quantum kinetic equation for electrons in a quantum well, the particle system is placed in an electromagnetic wave field and a laser field, from solving the quantum kinetic equation yields conductivity tensor expressions.This work also only considers the case of electron scattering - optical phonon and with quantum well there can be infinite potential. The conductivity tensor expression shows its dependence on the electromagnetic wave frequency, laser field frequency, laser field amplitude, and other parameters that characterize the quantum well.A graph of the dependence of the conductivity tensor on electromagnetic wave frequency, laser field frequency, and laser field amplitude will be plotted and examined. The semiconductor investigated here is the GaAs/GaAsAl quantum well.

Magneto-thermoelectric Effects in Cylindrical Quantum Wire under the Influence of Electromagnetic Wave for Electron-optical Phonon Scattering

Based on the quantum kinetic equation for electrons, we have theoretically studied the influence of a Strong Electromagnetic Wave (EMW) on the Magneto-Thermoelectric Effects in a cylindrical quantum wire with an infinite potential (CQWIP) (for electron - optical phonon scattering) under the influence of electric field E1=(0,0,E1), magnetic field B=(0,B,0) and a strong EMW (laser radiation) E= (0,0,E0sinΩt) (where and are amplitude and frequency of EMW, respectively). We obtain the analytic expressions for the kinetic tensors sik, bik, gik, xik and the Ettingshausen coefficient (EC) in the CQWIP with the dependence on the frequency, the amplitude of EMW, the Quantum Wire (CQWIP) parameters, the magnetic field and the temperature. The results are numerically evaluated and graphed for GaAs/GaAsAl quantum wire. Then, the results in this case are compared with the case of the bulk semiconductors and others low-dimension system in order to show the difference and the novelty of the results. Moreover, we realize that as the EMW frequency increases, the EC fluctuates with a stable trend and the appearance of the Shubnikov-de Haas (SdH) oscillations pattern when we survey the dependence of EC on the magnetic field.

Magneto – thermoelectric Effects in Compositional Superlattice in the Presence of Electromagnetic Wave

Ettingshausen coefficient (EC) in the compositional semiconductor superlattice under the influence of electromagnetic wave (EMW) is surveyed by using the quantum kinetic equation for electrons. The analytical expressions of the Ettingshausen coefficient are numerically calculated for the GaAs/AlGaAs compositional semiconductor superlattice. It have been showed that the appearance of EMW has changed the EC’s value and the EC decreases nonlinearly when the temperature increases. Studying the dependence of EC on the magnetic field, we discovered that the resonance peaks have appeared and the superlattice period strongly affects the Ettingshausen coefficient.

Influence of Confined Phonons on the Hall Coefficient in a Cylindrycal Quantum wire with an infinite potential (for electron – confined optical phonon scattering)

The influence of confined optical phonons on the Hall Coefficient (HC) in a Cylindrycal Quantum Wire (CQW) with an infinite potential (for electron – confined optical phonons scattering). Consider a case where CQW is placed in a perpendicular magnetic field , a constant - electric field and an intense electromagnetic wave . By using the quantum kinetic equation for electrons interacting with Confined Optical Phonon (COP), we obtain analytical expressions for (HC), which are different from in comparison to those obtained for the HC in the case of normal bulk semiconductor and in the case of cylindrycal quantum wire with electron – unconfined phonons scattering mechanism. Numerical calculations are also applied for AlGaAs/GaAs/AlGaAs cylindrycal quantum wire, we see the HC depends on magnetic field B, temperature T, frequency Ω and amplitude E0 of laser radiation and especially quantum index m1 and m2 characterizing the phonon confinement. This influence is due to the quantum index m1 and m2, which makes an increase of Hall coefficient by 2,3 times in comparition with the case of unconfined phonons. When the quantum number m1 and m2 goes to zero, the result is the same as in the case of unconfined phonons.

Magneto-thermoelectric effects in rectangular quantum wire with an infinitely high potential in the presence of electromagnetic wave (electron - acoustic phonon interaction)

Based on the quantum kinetic equation for electrons, we have theoretically studied the influence of a Strong Electromagnetic Wave on the Ettingshausen Effect (EC) in a rectangular quantum wire with an infinite potential (RQWIP). We obtain the analytic expressions for the kinetic tensor as well as the Ettingshausen coefficient in the rectangular quantum wire with an infinite potential with the dependence on B and Ω…… The results are numerically evaluated and graphed for GaAs/GaAs:Al quantum wire. We survey the electrical and thermal conductivity tensor depend on Electromagnetic Wave frequency and temperature. The results give us appearance of the Shubnikov–de Haas oscillations when we survey the dependence of Ettingshausen coefficient on the magnetic field. Then, we realize that as the temperature increases, the Ettingshausen coefficient decreases. This shows that the Electromagnetic Wave have a clear impact on the effects. These are latest results which have been studied in terms of Ettingshausen effect in rectangular quantum wire.

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.

Interaction of External Acoustic Waves - Confined Electrons - Internal Phonons in a Cylindrical Quantum Wire with an Infinite Potential in the Presence of an External Magnetic Field

Interaction of external acoustic waves - confined electrons - internal phonons in a cylindrical quantum wire with an infinite potential (CQWIP) has been theoretically studied via the quantum kinetic equation for electrons in the presence of an external magnetic field (EMF). The quantum kinetic equation for the distribution function of electrons interacting with internal and external acoustic phonons is obtained from the Heisenberg equation of motion and the model of CQWIP. The density of acoustomagnetoelectric (AME) current and the analytical expressions for the AME field in the CQWIP in the presence of the EMF are obtained. The theoretical results are numerically evaluated for the specific CQWIP of GaAs/GaAsAl. It is shown that the AME field strongly depends on the system temperature in both cases of the strong magnetic field and the weak magnetic field. However, the graph showing the relationship between the AME field and the system temperature has the peaks in case of the strong magnetic field. The reason may be due to movement of the electrons between the mini-bands. The AME field obtained in this work are then compared with those of bulk semiconductors, superlattices, quantum wells (QW) and rectangular quantum wire (RQW).

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.

Calculation of the Ettingshausen coefficient in a Rectangular quantum wire with an infinite potential in the presence of an Electromagnetic wave (the electron - optical phonon interaction )

The Ettingshausen coefficient (EC) in a Rectangular quantum wire with an infinite potential (RQWIP)in the presence of an Electromagnetic wave (EMW) is calculated by using a quantum kinetic equation for electrons. Considering the case of the electron - optical phonon interaction, we have found the expressions of the kinetic tensors . From the kinetic tensors, we have also obtained the analytical expression of the EC in the RQWIP in the presence of EMW as function of the frequency and the intensity of the EMW, of the temperature of system, of the magnetic field and of the characteristic parameters of RQWIP. The theoretical results for the EC are numerically evaluated, plotted and discussed for a specific RQWIP GaAs/GaAsAL. We also compared received EC with those for normal bulk semiconductors and quamtum wells to show the difference. The Ettingshausen effect in a RQWIP in the presence of an EMW is newly developed.

Magneto – thermoelectric effects in quantum well in the presence of electromagnetic wave

Abstract. We have studied magneto-thermoelectric effects in quantum well in the presence of electromagnetic wave. The analytic expression for Ettingshausen coefficient (EC) in the Quantum Well with parabolic potential (QWPP) in the presence of Electromagnetic wave (EMW) is calculated by using the quantum kinetic equation for electrons. The dependence of EC on the frequency, the amplitude of EMW, the Quantum Well parameters and the temperature are obtained. The results are numerically calculated, plotted, and discussed for GaAs/GaAsAl Quantum Well to clearly show the dependence of EC on above parameters and the results in this case are compared with the case in the bulk semiconductors. We realize that as the temperature increases, the EC decreases. The results show appearance of the Shubnikov–de Haas (SdH) oscillations when we survey the dependence of EC on the magnetic field.
 Keywords: Ettingshausen, Quantum well, Electromagnetic wave, parabolic potential, GaAs/GaAsAl.

Nonlinear absorption coefficient and optically detected electrophonon resonance in cylindrical GaAs/AlAs quantum wires with different confined phonon models

A quantum kinetic equation for electrons interacting with confined phonons is used to investigate the nonlinear absorption of an intense electromagnetic wave by electrons in cylindrical GaAs/AlAs quantum wires. The analytic expression for absorption coefficient is calculated for three models of confined optical phonons: the dielectric continuum (DC), hydrodynamic continuum (HC), and Huang-Zhu (HZ) models. The absorption coefficient depends on the square of the electromagnetic wave amplitude. The electrophonon resonance and optically detected electrophonon resonance (ODEPR) are observed through the absorption spectrum. The full width at half maximum (the line-width) of the ODEPR peaks is obtained by a computational method. The line-width is found to increase with increasing temperature and decrease with increasing the quantum wire radius. In particular, numerical results show that the DC and HZ models lead to a similar behaviour of electron - confined phonon interaction whereas the HC model results in a quite different one, especially at small quantum wire radius. For large quantum wire radii, above mentioned phonon models have equivalent contributions to the ODEPR line-width.

Dependence of the Hall Coefficient on a length of rectangular quantum wires with infinitely high potential under the influence of a Laser Radiation

The Hall coefficient (HC) of a strong electromagnetic wave (EMW) caused by confined electrons in a rectangular quantum wire (RQW) is theoretically studied by using the quantum kinetic equation for electrons. The problem is considered in the case of electrons - acoustic phonons scattering. Wave function and energy spectrum in a RQW are different from those in a cylindrical quantum wire (CQW) or two dimensional systems (2D). Therefore analytical expressions for the HC in a RQW is obtained, different from CQW or 2D. Numerical calculations are carried out with a specific GaAs/GaAsAl RQW to show clearly the dependence of HC on a length Lx (Ly) RQW with different low temperature values. We can see that the length Lx (Ly) increases in value within the domain that HC increases. The HC reaches a peak before slightly decreases when the length Lx (Ly) continues going up. However, the HC depends on the radius and the length of CQW and wire size of RQW Lx and Ly at different values of temperatures; this is the fundamental difference between CQW and RQW. If the length Lx (Ly) continues to increase, the HC remains constant. It means that HC is no longer dependent on the length of quantum wires (This behavior is similar to the case of the independence of the HC on the length in bulk semiconductor).