Effect of Miniband Dispersion on Inelastic Scattering of Superlattice Electrons by Acoustic Phonons

Within the framework of the Boltzmann equation, formulas for calculating the effective relaxation time and mobility of superlattice electrons are derived with allowance for inelastic scattering on acoustic phonons and dispersion of the miniband energy spectrum depending on the longitudinal wave vector. The dependences of longitudinal and transverse mobilities of the nondegenerate electronic gas of the GaAs/Al_0.36Ga_0.64As superlattice with the quantum well 5 nm wide on the potential barrier width and temperature are analyzed numerically. It is demonstrated that inelasticity of scattering and miniband dispersion significantly increase the electron mobility, and its temperature dependence becomes more pronounced at low temperatures.     

Electron-confined LO-phonon scattering in GaAs-Al0.45Ga0.55As superlattice

We develop a theoretical model to the scattering time due to the electron-confined LO-phonon in GaAs-Al_xGa_1-xAs superlattice taking into account the sub-band parabolicity. Using the new analytic wave function of electron miniband conduction of superlattice and a reformulation slab model for the confined LO-phonon modes, an expression for the electron-confined LO-phonon scattering time is obtained. In solving numerically a partial differential equation for the phonon generation rate, our results show that forx = 0.45, the LO-phonon in superlattice changes from a bulk-like propagating mode to a confined mode. The dispersion of the relaxation time due to the emission of confined LO-phonons depends strongly on the total energy.     

A Ground Miniband Width of a Superlattice with Rectangular Quantum Wells versus Constructive Parameters

A convenient formula for the ground miniband width as a function of constructive parameters of the superlattice is derived from the solution of the Kronig–Penney equation using the perturbation theory. The conditions of applicability of this formula are verified for the GaAs/Al_xGa_1–x As superlattices used as infrared photodetectors.     

Scattering of Quasi-Two-Dimentional Electrons of the GaAs/Al x Ga1–x As Superlattice by Polar Optical Phonons in the Dielectric Continuum Model

The longitudinal and transverse mobility of electrons in the ground miniband of the GaAs/AlGaAs superlattice (SL) is calculated for the case of scattering on the long-range potential of polar optical (PO) phonons at T = 300 K. The partial contributions of different oscillation modes of the long-range PO-phonon potential to the mobility and effective relaxation time are analyzed. The dependences of the mobility and pulse effective relaxation time on the SL parameters are investigated. The calculation is made using a linearized Boltzmann equation. The scalar PO-phonon potential is calculated within the dielectric continuum model.     

Electron energy states and miniband parameters in a class of non-uniform quantum well and superlattice structures

A simple method to compute the carrier energy states, miniband parameters and dispersion characteristics for single and multiple quantum well and superlattice structures is presented. The method utilizes the continuity of the envelope function across the heterojunctions according to the boundary conditions that both the wavefunction ψ and the particle current density $\text{ψ′}\text{m}{}^{\mathrm{★}}$ be continuous at each interface. The nonuniform potential distribution encountered in doped or compositionally graded materials is approximated by piecewise constant potential functions. In addition to being conceptually simple, the method is readily adopted to fairly complex structures where other more sophisticated methods such as LCAO, reduced Hamiltonian and tight binding theories may become unfeasible or unmanageable. It is shown that for an arbitrary stepped potential variation, the eigenvalues (or the energy states) of quantum wells or a finite number of coupled quantum wells can be found by utilizing a transverse resonance method which is readily implemented on a digital computer for the computation of these eigenvalues. For the case of periodic superlattices, the miniband parameters and the dispersion characteristics are computed from a suitably defined transmission matrix associated with a unit cell of the superlattice which may itself consist of multiple layers. Typical results for the computed parameters for several wells and simple, biperiodic, binary and polytype superlattices consisting of various Al_xGa_1?xAs and In_xGa_1?xAs alloys are presented.     

Ultrafast creation and annihilation of space-charge domains in a semiconductor superlattice observed by use of Terahertz fields

We report an experimental study indicating ultrafast creation and annihilation of space-charge domains in a semiconductor superlattice under the action of a THz field. Our experiment was performed for an InGaAs/InAlAs superlattice with the conduction electrons undergoing miniband transport. We applied to a superlattice a dc bias that was slightly smaller than a critical bias necessary for the formation of space-charge domains caused by a static negative differential conductivity. Additionally subjecting the superlattice to a strong THz field, resulted in a dc transport governed by the formation of domains if the frequency of the field was smaller than an upper frequency limit (~3 THz). From this frequency limit for the creation and annihilation of domains we determined the characteristic time of the domain buildup. Our analysis shows that the buildup time of domains in a wide miniband and heavily doped superlattice is limited by the relaxation time due to scattering of the miniband electrons at polar optic phonons. Our results are of importance for both an understanding of ultrafast dynamics of pattern formation in nanostructures and the development of THz electronic devices.Received: 25 March 2004, Published online: 23 July 2004PACS: 72.20.Ht High-field and nonlinear effects - 72.30. + q High-frequency effects; plasma effects - 73.21.Cd SuperlatticesK.N. Alekseev: Permanent address: Department of Physical Sciences, P.O. Box 3000, University of Oulu FIN-90014, Finland.     

Modeling of the energy spectrum of the CdTe/Hg1-xCdxTe/CdTe quantum well by varying the band offset, well width, and composition x

Currently, CdTe/Cd _x Hg_1-x Te/CdTe heterostructures attract particular interest and are very promising for developing the next-generation terahertz radiation detectors. However, properties of such structures have not yet been studied in sufficient detail. The energy spectrum and wave functions of the CdTe/Cd _x Hg_1-x Te/CdTe heterostructure were theoretically modeled for various well widths, the valence band offset, and composition x in the range 0<x<0.16. Characteristic features of the behavior of energy levels of two-dimensional electrons in such structures were studied with respect to x variation. A criterion for determining the number of electronic levels below the conduction band bottom, applicable to compositions 0<x<0.16 was obtained. The time of two-dimensional electron relaxation by longitudinal optical phonons was calculated.     

InAs/InxGa1－xSb二类超晶格红外探测器的吸收波长与电子-空穴波函数交叠的研究

运用包络函数模型和传输矩阵方法计算了二类超晶格的能级结构.考虑到InAs与In_xGa_1-xSb结合存在应变,在计算中InAs/In_xGa_1-xSb二类超晶格的带阶采用模型固体理论处理.因为吸收系数与电子-空穴波函数交叠成正比,所以研究了InAs/In_xGa_1-xSb二类超晶格红外探测器的吸收波 关键词： 二类超晶格 红外探测器 波函数的交叠 传输矩阵     

Influence of magnetic quantization on the effective mass in semiconductor superlattices

An attempt is made to study the effect of a quantizing magnetic field on the effective electron mass in a semiconductor superlattice at low temperatures. It is found on the basis of the tight-binding approximation, taking GaAs-Ga_1–x Al _x As an example, that the effective mass at the Fermi level depends on the magnetic quantum number due to the cosine dependence of the wave-vector in the superlattice direction. The mass also exhibits oscillatory features in the presence of magnetic quantization because of its dependence on Fermi energy which oscillates with changing magnetic field.     

Magnetic octupole order in : A polarized neutron diffraction study

Recently, in phase IV of Ce_xLa_1-xB₆, weak but distinct superlattice reflections from the order parameter of phase IV have been detected by our unpolarized neutron scattering experiment [K. Kuwahara, K. Iwasa, M. Kohgi, N. Aso, M. Sera, F. Iga, J. Phys. Soc. Japan 76 (2007) 093702]. The scattering vector dependence of the intensity of superlattice reflections is quite unusual; the intensity is stronger for high scattering vectors. This result strongly indicates that the order parameter of phase IV is the magnetic octupole. However, the possibility that the observed superlattice reflections are due to lattice distortions could not be completely ruled out only on the basis of the unpolarized neutron scattering experiment. To confirm that the superlattice reflections are magnetic, therefore, we have performed a single crystal polarized neutron diffraction experiment on Ce_0.7La_0.3B₆. The obtained result has clearly shown that the time reversal symmetry is broken by the order parameter of phase IV. This is further evidence for the magnetic octupole order in Ce_xLa_1-xB₆.     

Electron–hole superlattices in GaAs/Al x Ga1− x As multiple quantum wells

A GaAs/Al _x Ga_{1? x} As semiconductor structure is proposed, which is predicted to superconduct at T _c?≈?2?K. Formation of an alternating sequence of electron- and hole-populated quantum wells (an electron–hole superlattice) in a modulation-doped GaAs/Al _x Ga_{1? x} As superlattice is considered. This superlattice may be analogous to the layered electronic structure of high-T _c superconductors. In the structures of interest, the mean spacing between nearest electron (or hole) wells is the same as the mean distance between the electrons (or holes) in any given well. This geometrical relationship mimics a prominent property of optimally doped high-T _c superconductors. Band bending by built-in electric fields from ionized donors and acceptors induces electron and heavy-hole bound states in alternate GaAs quantum wells. A proposed superlattice structure meeting this criterion for superconductivity is studied by self-consistent numerical simulation.     

High resolution x-ray diffractometry of the structural characteristics of a semiconducting (InGa)As/GaAs superlattice

A statistical approach is used to construct a kinematic theory of x-ray diffraction on a semiconducting superlattice with a two layer period. This theory takes two types of structural deformations into account: crystal lattice defects caused by microdefects distributed chaotically over the thickness of the superlattice, and periodicity defects of an additional superlattice potential owing to random deviations in the thicknesses of the layers of its period from specified values. Numerical simulation is used to illustrate the effect of structural defects on the development of the diffraction reflection curve. The theory is used to analyze experimental x-ray diffraction spectra of semiconducting In_xGa_1−x As/GaAs superlattices. Zh. Tekh. Fiz. 69, 44–53 (February 1999)     

Piezoresistivity in GaAs/InxGa1–xAs/AlAs superlattice structures

We report on a strong piezoresistive effect in GaAs/ In_x Ga_1–x As/AlAs superlattice structures fabricated on a GaAs‐base cantilever. The measurements of the piezoresistive properties were performed for tensile strains by static pressure experiments. The maximum gauge factor (GF) for the GaAs/In_x Ga_1–x As/AlAs epilayer can be estimated to 200, which is higher than the value of the gauge factor reported for Si transducers. Our results demonstrate a higher potential of GaAs/In_x Ga_1–x As/AlAs superlattice structures for the development of piezoresistive sensors. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Longitudinal Wave Propagation in Dielectric Waveguide Array

Based on the established rigorous theory for two-dimensionally periodic (2DP) medium, Longitudinal propagation in Dielectric Waveguide Array (DWA) was analyzed in detail. Firstly, given longitudinal wave vector (k _z), Brillouin dispersion relations between transversal wave vectors were analyzed. Interactions between space harmonics were also studied. Secondly, on condition that transversal wave vector k _x equaled k _y, dispersion relations between longitudinal and transversal wave vectors were analyzed in detail. Because of interactions between space harmonics increasingly getting stronger with k _z or modulation coefficients increasing, stop-bands could be distinctly displayed and thus longitudinal propagation in DWA could be comprehensively analyzed. The applications about longitudinal propagation in DWA were also discussed.     

Suppression of the singularly localized states in dimer quasiperiodic Fibonacci superlattices

Using the transfer-matrix technique, we have numerically investigated the effect of introducing the dimer on the nature of the states across Dimer Fibonacci semiconductor superlattices on the miniband structure of the GaAs/Al_xGa_1?xAs superlattices. By the introduction of the dimer model, the transmission spectra reveal the appearance of a miniband structure with a concomitant disappearance of the singularly localized states. This behavior is due to the interaction between the states of the dimer wells inside the potential and, therefore, the system is seen by the particle as two overlapped ordered structures.     

The effects of pressure and hydrogenic donor impurity on the linear and nonlinear optical properties of a GaAs/GaAlAs nanowire superlattice

The combined effects of hydrostatic pressure, presence and absence of hydrogenic donor impurity are investigated on the linear and nonlinear optical absorption coefficients and refractive index changes of a GaAs/Ga_1−xAl_xAs nanowire superlattice. The wave functions and corresponding eigenvalues are calculated using finite difference method in the framework of effective mass approximation. Analytical expressions for the linear and third order nonlinear optical absorption coefficients and refractive index changes are obtained by means of compact-density matrix formalism. The linear and third order nonlinear absorption coefficient and refractive index changes are presented as a function of photon energy for different values of hydrostatic pressure, incident photon intensity and relaxation time in the presence and absence of hydrogenic donor impurity. It is found that the linear and third order nonlinear absorption coefficients, refractive index changes and resonance energy are quite sensitive to the presence of impurity and applied hydrostatic pressure. Moreover, the saturation in optical spectrum and relaxation time can be adjusted by increasing pressure in presence of impurity whereas the effect of hydrostatic pressure is negligible in the case of absence of hydrogenic impurity.     

Dynamical Properties of Coherent Plasmons Coupled with LO Phonons in an InAs/GaAs Strained Superlattice

We have investigated the coherent plasmon photoexcited in the electron miniband of an InAs/GaAs strained superlattice (SL) using a reflection-type pump-probe technique. Under the condition that the center energy of the pump pulses is tuned to the fundamental transition energy of the SL, the coherent plasmon coupled with the longitudinal optical (LO) phonon of GaAs that is the barrier layer is observed. The time-domain signals of the coherent plasmon coupled with the GaAs-like LO phonon drastically change with varying the generation and detection energies. From the energy dependence of the time-domain signals, we discuss the relaxation process of the carriers photoexcited in the miniband of the SL.     

Study of period number effect in the superlattice infrared photodetector

Superlattices have been demonstrated previously by our group in the design of the multicolor infrared photodetector. In general, the period number of the superlattice may be up to several dozens. In this paper, we have investigated the performance of the infrared photodetectors especially with 3, 5 and 15 periods. The detector structure contains a thick blocking barrier embedded between two superlattices with different period numbers but with the same well and barrier widths. This double-superlattice structure shows switchable spectral responses between two spectral regions by the voltage polarities. The photoresponse in each spectral region is also tunable by the magnitude of the applied voltage. The voltage-dependent behavior reveals the photoelectron relaxation and transport mechanism in the superlattice miniband. Superlattice with few periods has high electron group velocity, less relaxation effect and less collection efficiency. Therefore the superlattice with few periods may have better responsivity and narrower photoresponse range than the one with many periods. Based on the experimental results of our devices, it is observed that the superlattice with fewer periods has better detectivity, responsivity, wider range of the operational temperature, and more flexible miniband engineering than the conventional multiple quantum well infrared photodetector.     

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, -ω _c, was crucially based on the implicit assumption that the system momentum relaxation time τ_m 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 -ω_c. 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.     

Raman scattering from GaAs-InxGa1−xAs strained-layer superllatices

Measurements of Raman scattering were performed on GaAs-In_xGa_1?xAs strained-layer superlattices, grown by molecular beam epitaxy, with lattice periods ranging from 30 ～ 250 Å and In concentrations x, 0.22 and 0.37. Only one GaAs-like longitudinal optical phonon peak was observed in each strained-layer superlattice, in contrast to the well-known result that two peaks were observed in GaAs-Al_xGa_1?xAs superlattices. The GaAs-like phonon frequencies shifted from those of bulk GaAs to those of bulk In_xGa_1?xAs alloys as the ratio of the one-layer thickness of In_xGa_1?xAs to the lattice period increases from zero to one. We conclude that the GaAs-like phonon mode is a uniform mode of the whole strained-layer superlattice and the phonon frequency is determined by the averaged In concentration.