Miniband Transport In Superlattices Research Articles

Recent results on superlattice transport and optoelectronics applications

Recent results involving miniband transport in superlattices at millimetre (mm) wave frequencies are reviewed. The miniband negative differential conductance up to very high frequencies allows for a new kind of device, the superlattice photo-oscillator. A practical application for optical to mm-wave conversion is demonstrated. An analysis of the intrinsic limitations in the transport processes led to recent progress in the understanding of superlattices physics involving Zener inter-miniband tunneling.

Balance equations for electron transport in an arbitrary energy band driven by an intense terahertz field. Application to superlattice miniband transport

We suggest a balance-equation approach to hot-electron transport in a single arbitrary energy band subject to an intense radiation field of terahertz (THz) frequency, including all the multiphoton emission and absorption processes and taking account of realistic scatterings due to impurities and phonons. This approach, which allows one to calculate THz-driving, time-averaging transport based on a set of time-independent equations, provides a convenient method to study the effect of an intense THz electric field on carrier transport in a nonparabolic energy band. As an example, these fully three-dimensional, acceleration- and energy-balance equations are applied to the discussion of superlattice miniband transport at lattice temperature T=77 and 300 K driven by the THz radiation field of varying strengths. It is shown that the current through a dc biased miniband superlattice is greatly reduced by the irradiation of an intense THz electric field.

Absolute Instability in Superlattice Miniband Transport

The possible absolute instability in superlattice miniband transport using the hydrodynamic balance equations for arbitrary energy dispersion is investigated. In contrast to the prediction of the drift-diffusion model that in doped semiconductor superlattices absolute instability occurs closely following the onset of negative differential mobility (NDM), the present analysis shows that a wide-miniband planar superlattice may become absolutely unstable only when it is biased deep in the NDM regime. This result is in agreement with recent experimental findings.

Superlattice space-charge-wave analyses in a modified drift-diffusion model and in a simplified balance-equation formulation

Unstable space-charge-waves in superlattice miniband transport are investigated using a modified drift-diffusion model and using a simplified one-dimensional hydrodynamic balance-equation formulation with a relaxation-time approximation. We point out that the earlier widely accepted notion, that in the small wavevector limit the space-chargewave (SCW) propagates at a phase velocity equal to the carrier drift velocity and with an amplitude-growth rate equal to the negative value of the mobility frequency, -ωc, was crucially based on the implicit assumption that the system momentum relaxation time τm is extremely small. Taking account of a finite momentum relaxation time, we find that even the drift-diffusion model would yield results significantly different from the above predictions: the phase velocity of a long-wavelength traveling SCW can be much slower than the carrier drift velocity and its amplitude-growth rate much smaller than -ωc. A hydrodynamic balance-equation formulation, which properly treats energy dissipation and further reduces the amplitude-growth rate, provides a convenient tool for improved qualitative analyses in SCW-related problem in semiconductor superlattices.

Strongly driven quantum wells: An analytical solution to the time-dependent Schrödinger equation.

An analytical solution is found for the lowest Floquet state in a single quantum well which is strongly driven by an external laser field of form $\mathrm{eFz}\mathrm{cos}\ensuremath{\omega}t$. The spectral weights of the photon sidebands vary in a highly nonlinear fashion with $F$, exhibiting strong quenchings close to roots of the Bessel functions ${J}_{n}({k}_{0}eF/m{\ensuremath{\omega}}^{2})$, where $n$ is the sideband index and ${k}_{0}$ is the wave vector of the centerband resonance. The ${\ensuremath{\omega}}^{\ensuremath{-}2}$ scaling behavior of the roots is qualitatively different from the ${\ensuremath{\omega}}^{\ensuremath{-}1}$ dependence found in the coherent miniband transport in superlattices.

Bragg scattering and effective force-balance equations in superlattice miniband transport

The two existent balance-equation methods for electron transport, which incorporate Bragg scattering and give rise to bulk negative differential mobility, are further investigated using the Boltzmann transport equation for Bloch electrons. We point out that the ansatz employed in the earlier Büttiker–Thomas (BT) scheme to relate the average drift velocity and the average momentum, should be modified for a general energy band. Numerical calculation of superlattice miniband conduction shows that the modified BT force-balance method yields a velocity–field behavior almost equivalent to that predicted by the acceleration-balance method of Lei, if the appropriate momentum function is used in the calculation of the BT frictional force, such that Bragg scattering is properly taken into account in the process of electron scattering.

Non-linear generation of alternating current harmonics in quantum dot superlattice miniband transport

We have analyzed vertical miniband transport in GaAs-based superlattices subject to a d.c. field E 0 which drifts the system into the regime of negative differential mobility jointly with a perturbing single-frequency electric field E ω sin(2Ω t). Our balance equation formulation takes account of strong electron-electron interactions which tend to thermalize the system rapidly about the center-of-mass motion. In this, we consider E ω ⩾ E 0, so that the perturbing a.c. field is strong, and the responding steady periodic miniband current (evolving after transients relax) exhibits harmonic content beyond the impressed single frequency, characteristic of non-linear time harmonic generation. The scattering mechanisms are bulk phonons and random impurities. The superlattice treated here is a one-dimensional line of periodically spaced quantum dots of period d = 15 nm, lateral diameter d r = 10 nm, quantum well width a = 8 nm, carrier line density N 1 d = 0.314 and miniband with δ = 220 K. The impressed period of oscillation is taken as 2π ω = 4 ps, and, using material parameters appropriate to GaAs, we determine the harmonic composition of the periodic miniband current as a function of the high frequency amplitude E ω .

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.

Three-dimensional boltzmann-bloch theory of miniband transport in superlattices with elastic scattering

Elastic scattering couples the quasi one-dimensional (1D) motion of electrons responding to an applied electric field in growth direction of a semiconductor superlattice effectively to the lateral degrees of freedom. We describe the superlattice by a simple miniband and elastic scattering explicitly by an appropriate collision term in Boltzmann's equation. As a function of the applied field, we calculate the heating of the electron system and its drift velocity, which shows pronounced negative differential conductance. Our results are qualitatively different from those of previous ID theories, but compare favorably with results of recent experiments and balance-equation calculations.

Effect of elastic scattering on miniband transport in semiconductor superlattices.

Within the quasiclassical Boltzmann-Bloch approach to nonlinear miniband transport in superlattices, elastic scattering is included in a relaxation-time approximation. Elastic scattering makes the problem truly three dimensional and leads in the regime of negative differential conductance to results that are qualitatively different from those of the quasi-one-dimensional models considered previously and compare favorably with recent experiments and balance-equation calculations.

Effect of a transverse magnetic field on superlattice miniband transport.

A semiclassical theory for the superlattice miniband transport in crossed magnetic and electric field is developed here using the nonlinear balance-equation dynamics. Numerical calculations are carried out for the case pertinent to that of the measurement reported recently [Sibille et al., Europhys. Lett. 13, 279 (1990)]. The present theoretical predictions are in good agreement with the experimental observations.

Balance-Equation Approach to Hot-Carrier Transport in Semiconductors

The balance-equation approach to nonlinear hot-carrier transport theory, formulated by Lei and Ting (1984), is addressed in this comprehensive review. A central feature is the role of strong electron-electron interactions in promoting rapid thermalization about the drifted transport state and the concomitant substantial simplification of the transport theory. This physical feature is embodied in the initial density matrix chosen to represent the unperturbed carrier system. Force and energy balance equations are formulated for the dc steady state, ac dynamic and transient cases of charge conduction, including memory effects. The scattering mechanisms include impurity and phonon interactions along with dynamic nonlocal screening effects due to carrier-carrier interactions. Both linear and nonlinear resistivities are discussed in the degenerate and nondegenerate statistical regimes. Interesting phenomena such as electron cooling and thermal noise and diffusion are discussed as well. Semiconductor microstructure transport is described for both linear and nonlinear hot carrier conduction. In this connection, quasi-2D-systems, heterojunctions, and quantum well superlattices are treated with attention to steady state, transient and high frequency transport, including, for example, superlattice plasmon resonance structure. Type-II superlattice transport is reviewed as well as type-I, and electron-hole drag is treated in conjunction with negative minority electron mobility in a quantum well. Multivalley semiconductors are discussed in some detail. Furthermore, attention is also focused on the center-of-mass velocity fluctuation, Langevin-type equation and thermal noise and diffusion for microstructures and multivalley systems. A number of particularly important phenomena are examined from the balance-equation point of view, such as nonequilibrium phonons, higher order scattering effects and weak localization, hydrodynamic equations for weakly nonuniform systems, and the intracollisional field effect. Alternative formulations and interpretations of the balance-equation approach are reviewed. The distinction between this many-particle, isothermal, balance-equation theory and the noninteracting (single-particle) adiabatic transport theory is discussed to clarify issues subject to controversy in the literature. Finally, we give a brief review of recent developments in the balance-equation approach: investigation of the distribution function in balance-equation theory, improved calculations for GaAs/AlGaAs heterojunctions, extension of the balance equations to an abitrary energy band and recent work on superlattice miniband transport.