Lei-Ting Balance Equation Research Articles

Effects of two-mode transverse optical phonons in bulk wurtzite AlGaN on electronic mobility in AlGaN/GaN quantum wells

The two-mode property of bulk transverse optical (TO) phonons in ternary mixed crystals of wurtzite AlxGa1-xN has been investigated by introducing impurity modes in a modified random-element isodisplacement model. Based on the dielectric continuous model, the uniaxial model, and the Lei-Ting balance equation, the effects of the two-mode property on electrostatic potentials of interface optical and confined optical phonons in AlGaN/GaN quantum wells, as well as their influences on the electronic mobility (EM), are discussed by a component-dependent weight model. Our results indicate that the total EM decreases to a minimum at first and then increases slowly with x under the influences of the competitions from the eight branches of phonons. The further calculation shows that the total EM decreases with the increment of temperature in the range of 200 K < T < 400 K and reduction of well width d. As a comparison, the EM is calculated for an Al0.58Ga0.42N/GaN quantum well at room temperature, and our result is 1263.0 cm2/Vs, which is 1.44 times of the experiment value. Our result is expected since the difference between our theory and the experiment is mainly due to the neglect of interface-roughness and other secondary scattering mechanisms. Consequently, the two-mode property of bulk TO phonons in ternary mixed crystals does affect obviously on the electron transport in the quantum wells. And our component-dependent weight model could be extended to study the electric properties influenced by optical phonons in other related heterostructures.

Influence of optical-phonon scattering on electron mobility in wurtzite AlGaN/AlN/GaN heterostructures

Adopting a numerical method of solving self-consistently the Schrdinger equation and Poisson equation through taking into account the realistic heterostructure potential, which includes the influences of energy band bending and the finite thickness of barriers, and through considering the built-in electric field induced by spontaneous and piezoelectric polarization, the eigenstates and eigenenergies of electrons in two-dimensional electron gas (2DEG) are obtained for wurtzite AlxGa1-xN/AlN/GaN heterostructures with an inserted AlN layer. Based on the continuous dielectric model and the Loudon's uniaxial crystal model, optical-phonon modes and their ternary mixed crystals effect are discussed using the transfer matrix method. Furthermore, the Lei-Ting balance equation is extended in order to investigate the distribution of 2DEG and its size effect as well as ternary mixed crystals effect on electron mobility, which under the influence of each branch of optical-phonon modes are analyzed at room temperature. The results show that the increases of the thickness of inserted AlN layer and the Al component of AlxGa1-xN in the barrier enhance the built-in electric field in the GaN layer, leading 2DEG to be much closer to the interface of a heterostructure. In addition, it can also be found that the scattering from the interface phonons is stronger than from other optical-phonons, the interface phonons play a dominant role in the total mobility. A higher electron mobility can be obtained by adjusting appropriately the thickness of inserted AlN layer and Al component.

Double-resonant structure in the high-frequency transresistance of coupled electron-hole systems

The linear dc and high-frequency transresistivity of coupled electron-hole systems are investigated using the Lei-Ting balance equations approach extended to include many-body corrections. A possible indirect method of experimentally measuring the dynamical transresistivity in the high frequency (terahertz) regime is designed basing on the detailed analysis on the relationship between the directly measurable resistivities in the electron- and hole-layer and the dynamical transresistance. The theoretically predicted dc transresistance is in good agreement with the experimental data for the given electron-hole system experimentally investigated. The calculated dynamical transresistance exhibits pronounced double-resonant structure, which can be attributed to the cooperation and competition between the two plasmon modes. It is pointed out that the behavior of the frequency-dependent transresistance is temperature-sensitive and the dynamical transport properties are essentially influenced by the short range correlations.

Hot-electron transport and impact ionization process inHg0.8Cd0.2Te

We present an expression for the electron impact ionization rate under moderate electric field within the framework of the Lei-Ting balance equation approach. We consider the case where the hole gas is cold and in thermal equilibrium, and the final electrons are located near the conduction-band edge. Using the Kane band model to describe the conduction band, we calculate the conduction\char21{}conduction\char21{}heavy-hole\char21{}conduction electron-hole pair generation rate and current-voltage characteristics of n-type ${\mathrm{Hg}}_{0.8}{\mathrm{Cd}}_{0.2}\mathrm{Te}.$

Modelling semiconductor device using the hydrodynamic balance equations with accurate collision integral terms

The paper presents new hydrodynamic balance equations for semiconductor device simulation, which stem from the Lei–Ting balance equations for spatially inhomogeneous device structures. Their main characteristics, which differ from those of the conventional hydrodynamic equations, is the inclusion of accurate momentum and energy collision terms at the microscopic level. With the help of the nonlinear frictional force and energy transfer functions, the collision terms as well as the relaxation times can be self-consistently calculated from the primary physical parameters, taking full account of dynamical screening and other quantum-mechanical effects. A solution method for this set of differential–integral equations is proposed and applied to a one-dimensional simulation of a submicron Si n+nn+n structure diode. The numerical results for various applied voltages are presented.

Onsager relations and hydrodynamic balance equations.

In this paper we clarify the role of heat flux in the hydrodynamic balance equations, facilitating the formulation of an Onsager relation within the framework of this theory. Previously thought to be unobtainable from the present form of the theory [X.L. Lei, J. Cai, and L.M. Xie, Phys. Rev. B {\bf 38},1529 (1988)], our verification of the Onsager relation for linear particle and heat flux currents driven by electric fields and temperature gradients resolves a puzzling issue of long standing. Our results show that, for any temperature, when electron density is sufficiently high, the linear predictions of balance equation theory exactly satisfy the Onsager relation. The condition of high density is consonant with the requirement of strong electron-electron interactions for the validity of the Lei-Ting balance equations. Our results support the validity of this theory for a weakly nonuniform system. We also discuss a possible method of extending this theory to a system further removed from thermal equilibrium.

Semiconductor device simulation with the Lei–Ting balance equations

A hydrodynamical simulation model of carrier transport in semiconductor devices based on the Lei–Ting balance equations is presented. Unlike conventional hydrodynamical models derived from moments of the Boltzmann transport equation, where collisions with impurities and phonons are represented by momentum and energy relaxation times, we represent the scattering interaction in terms of frictional forces acting on the carriers and energy-loss rate of the carriers. As such, these quantities are calculated within the model itself, as functions of the carrier drift velocity and carrier temperature, along with the carrier density, which are themselves solved for self-consistently within our hydrodynamical model. In addition to the usual advantages of hydrodynamical approach, such as its capability to deal with high-field, nonlinear, nonstationary, and hot-electron effects, along with its modest computational cost, the new model incorporates electron–electron interactional effects (e.g., nonlocal, dynamical screening).

Impact ionization in balance equation theory

We present a theoretical investigation of electron impact ionization processes under a high electric field within the framework of the Lei-Ting balance equation approach in the case where the hole gas is approximately in thermal equilibrium. An expression for the impact ionization coefficient for an arbitrary conduction band is obtained. As an example, the impact ionization coefficient of bulk InSb is calculated in the approximation of a parabolic conduction band and the result is compared with existing experimental data.

Distribution functions and balance equations of drifting Bloch electrons in an electric field.

The Lei-Ting balance-equation method for high-field electron transport in semiconductors has recently been extended to general energy bands by several authors with different results. We present a test of these extensions, especially those proposed by Lei [Phys. Status Solidi B 170, 519 (1992)] and by Huang and Wu [Phys. Rev. B 49, 2223 (1994)], by applying them to superlattice miniband transport. It is shown that except for Lei's nonparabolic method, none of them is able to produce the well-established negative differential mobility of the Esaki-Tsu type in the vertical conduction of a semiconductor superlattice. Some confusions concerning the nature of the distribution functions in the balance-equation theory are discussed.

Electron transport in non-parabolic Kane bands

Linear and non-linear transport properties of carriers in non-parabolic Kane bands are investigated using the two extended balance equations introduced by Magnus, Sala and De Meyer (MSD) (1990) and by Lei (1992,1994). Formally, the MSD equations describe the motion of a single particle with fixed charge and fixed mass, while the Lei equations describe the motion of a single particle having fixed charge but variable effective mass. In the parabolic limit these two sets of equations are identical and reduce to the original Lei-Ting balance equations. In the non-parabolic case, although the linear resistivities predicted by the Lei and MSD equations are nearly the same for weakly to medially non-parabolic systems, non-linear drift-velocity-field behaviour obtained from these two sets of equations shows marked differences for medial and strong non-parabolicity. The reasons for these differences are discussed.

Hot-electron mobility in laterally confined systems

Hot-electron transport in GaAs/AlGaAs quantum wires and quantum wells having various lateral confinements are investigated systematically using the Lei-Ting balance equation theory. Intrasubband and intersubband transitions of up to 21 electron subbands in quantum wires and seven subbands in quantum wells due to acoustic phonons, optic phonons and impurities are taken into account. Linear and non-linear electron mobilities are presented as functions of carrier density, electron field (or drift velocity), temperature and lateral confinement for these one-dimensional (1D) and two-dimensional (2D) systems, and compared with those in bulk material. At low temperatures, the electron mobility in quantum wires can be much higher than that in quantum wells or in bulk material in optimum conditions. However at high temperatures, when optic phonon scattering dominates the other scattering mechanisms, the mobility in quantum wires can hardly exceed the value in quantum wells or in bulk material.

Distribution function of a drifting electron gas for general energy-band structures.

The usual application of the Lei-Ting balance equation method for treating electron transport problems makes use of a Fermi distribution function for the electron motion relative to the center of mass. It is pointed out that this presumes the existence of a moving frame of reference that is dynamically equivalent to the rest frame of reference, and this is only true for electrons with a constant effective mass. The method is thus inapplicable to problems where electrons governed by a general energy-band dispersion E(k) are important (such as in miniband conduction). It is demonstrated that this difficulty can be overcome by introducing a distribution function for a drifting electron gas by maximizing the entropy subject to a prescribed average drift velocity. The distribution function reduces directly to the usual Fermi distribution for electron motion relative to the center of mass in the special case of E(k)=${\mathrm{\ensuremath{\Elzxh}}}^{2}$\ensuremath{\Vert}k${\mathrm{\ensuremath{\Vert}}}^{2}$/2${\mathit{m}}^{\mathrm{*}}$. This maximum entropy treatment of a drifting electron gas provides a physically more direct as well as a more general basis for the application of the balance equation method.

Recent Developments in Magnetotransport Theory

A selection of topics recently examined in the literature of normal, dissipative magnetotransport is reviewed here, principally from the perspective of the Lei-Ting balance equation approach. We employ this isothermal formalism to revisit linear and nonlinear bulk 3D magnetoresistance, discussing longitudinal impurity limited conduction and magnetophonon resonance structure. For the transverse configuration, the characteristic linear impurity magnetoresistance log-divergence is seen to be removed by nonlinearity alone, with or without screening. At high magnetic fields, prominent hot-electron magnetophonon resonance structure is discussed for transverse transport as well as thermal noise. Another principal focus of concern here is the role of Landau quantization in linear and nonlinear transport in semiconductor microstructures, particularly quantum well superlattices (Type-I and Type-II) and heterostructures, including magnetoplasmon and cyclotron resonances as well as Shubnikov-de Haas oscillations. Electron-hole drag and negative absolute minority carrier mobility are discussed. Finally, we briefly discuss the density modulated 2DEG having magnetoresistance commensurability oscillations due to the interplay of the length scales of the cyclotron radius and the modulation period (superposed as an envelope upon Shubnikov-de Haas oscillations).