Influence of the Miniband Width on the Relaxation Time of Superlattice Electrons Scattered by Impurity Ions

Based on the Boltzmann equation, the influence of the miniband width on the relaxation time of nondegenerate electrons scattered by impurity ions in the GaAs/Al _x Ga_1–x As superlattice with doped quantum wells is numerically analyzed. The wave function being the eigenfunction of the ground state of the lower miniband of the superlattice is used to calculate the scattering probability. The dispersion of the longitudinal and transverse relaxation times versus the longitudinal wave vector is investigated.     

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-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.     

Franz–Keldysh oscillations at the above-barrier miniband in a GaAs/AlxGa1 − xAs superlattice

We report on the observation of the Franz–Keldysh oscillations associated with the second-electron and heavy-hole minibands, in which the second-electron miniband lies above the barrier potential, in a GaAs(7.0 nm)/Al_0.1Ga_0.9As (3.5 nm) superlattice by using electroreflectance spectroscopy. The reduced mass estimated from the Franz–Keldysh oscillations is consistent with that estimated from the miniband–dispersion relation based on the effective mass approximation around a zero-electric field, and becomes heavier with an increase in the electric field. The electric-field dependence of the reduced mass correlates with the localization of the electron envelope function. We discuss these results from an envelope-function forms calculated by a transfer-matrix method.     

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.     

Quantum tunnel reflectors and superlattices on their basis

A dispersion relation ε (q) is derived for electrons in a planar superlattice constructed in the form of a quantum well that is coupled by tunneling with a periodic array of parallel strip-shaped quantum wires. A narrow miniband inside of the substantially wider gap is demonstrated for special resonance conditions. Since the obtained spectra are very sensitive to correlation of different array parameters they can be tuned and detuned easily.     

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.     

Minibands of p-type δ-doping superlattices in GaAs

A microscopic theory is presented for high-field miniband transport in a two-dimensional superlattice. The energy transfer to the lateral electron motion is taken into account as well as scattering on polar optical phonons. Oscillatory current anomalies appear when the optical phonon frequency is a multiple of the Bloch frequency. The current oscillations, which are due to Wannier–Stark localization, are much more pronounced in a two-dimensional than in a three-dimensional system with a superlattice structure in one direction.     

Transport in superlattices in the stark ladder regime

The current-voltage characteristic of a semiconductor superlattice in the Stark ladder regime has been calculated. It is shown that the negative differential conductivity onset electric field is defined by the scattering time, which depends only very slightly on the superlattice miniband width.     

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.     

On the dispersion relation of magnetoplasmons in a planar graphene-based superlattice

The dispersion relation for magnetoplasmons in a planar superlattice with periodically alternating regions of gapless and gapped modifications of graphene has been derived within the frame of the random-phase approximation. The contribution of virtual transitions between the lower electron miniband and the upper hole miniband to the polarization operator has been taken into account in addition to the contribution of virtual intra-miniband transitions.     

Dynamic localization and self-induced transparency in a two-dimensional superlattice with a nonadditive dispersion law

Electron dynamics and the nonlinear effects of electric conduction in a two-dimensional semiconductor superlattice with nonadditive miniband dispersion relations have been studied in the case of strong high-frequency electric fields applied to the superlattice. The conditions for dynamic electron localization and electromagnetic transparency in such superlattices have been revealed.     

X-Ray diffraction and Raman spectroscopy studies of superlattices BaTiO3/(Ba0.5,Sr0.5)TiO3/SrTiO3

The structural characteristics of the BaTiO₃/(Ba_0.5,Sr_0.5)TiO₃/SrTiO₃ superlattice on a (001) MgO substrate have been studied using X-ray diffraction. The modulation period and unit cell parameters of layers forming the superlattice have been measured. The sizes of coherent scattering regions and average microstrains in the direction perpendicular to the surface have been estimated. The obtained characteristics are compared to those of the two-layer BaTiO₃/(Ba_0.5,Sr_0.5)TiO₃ superlattice. The Raman spectra demonstrate a substantial shift of the soft E(TO) mode in the three-layer superlattice as compared to the position in the two-layer superlattice. The effects observed are associated with a substantial increase in the temperature of the phase transition of the three-layer superlattice to the paraelectric phase.     

On the differential conductivity of semiconductor superlattices

The nature of negative differential conductivity (NDC) of a semiconductor superlattice was studied. It is shown that the presence of regions with a negative effective mass in a Brillouin miniband is not necessary for NDC to set in. NDC exists even in superlattices with parabolic and superquadratic miniband dispersion relations, where the electron effective mass is positive everywhere and, in this case, is fully determined by Bragg reflections of the electron. When the electron Bragg reflections are suppressed by optical phonons, NDC can disappear completely. NDC is retained only if there is a sizable region with a negative effective mass in the miniband.     

Inverse dielectric function of a superlattice including local field effects and spatial dispersion

The inverse longitudinal dielectric function of a superlattice is calculated. Local field effects due to the superlattice structure and spatial dispersion due to both the superlattice and atomic structure are taken into account. Two applications are treated i) density Raman scattering from interface and bulk plasmons and ii) optical dielectric constants of superlattices.     

THz-field induced nonlinear transport and dc voltage generation in a semiconductor superlattice due to Bloch oscillations

We report on a theoretical analysis of terahertz (THz-) field induced nonlinear dynamics of electrons in a semiconductor superlattice that are capable to perform Bloch oscillations. Our results suggest that for a strong THz-field a dc voltage should be generated. We have analyzed the real-time dynamics using a balance equation approach to describe the electron transport in a superlattice miniband. Taking account of both Bloch oscillations of electrons in a superlattice miniband and dissipation, we studied the influence of a strong THz-field on currently available superlattices at room temperature. We found that a THz-field can lead to a negative conductance resulting in turn in a THz-field induced dc voltage, and that the voltage per superlattice period should show, for varying amplitue of the THz-field, a form of wisted plateaus with the middle points being with high precision equal to the photon energy divided by the electron charge. We show voltage to the finite voltage state, and that in the finite voltage state dynamic localization of the electrons in a miniband occurs.     

Modeling and experimental study of 780–808-nm AlGaAs/GaAs injection lasers with electron superlattice barriers

Electron superlattice barriers (ESBs) were used in AlGaAs/GaAs injection lasers to improve the electron confinement of the active layer by Bragg reflection of electron waves. The design of a separate-confinement heterostructure (SCH) laser with ESBs operating at 780–808 nm was optimized. Conventional SCH and SCH-ESB were prepared by low-pressure MOCVD epitaxy. Oxide stripe lasers with stripe widths of 100 and 200µm were prepared. The threshold current density of 0.3 kA/cm² and the characteristic temperature constantT ₀=220 K were measured at a wavelength of 808 nm for SCH-ESB lasers with an active-layer thickness of 40 nm and a resonator length of 0.4–0.5 mm. For conventional SCH lasers with the same geometry, a threshold current density of 0.42 kA/cm² andT ₀=160 K were obtained. Experimental results on the low-temperature photoluminescence characterizing ESB regions are presented and are compared with the calculated miniband energy spectrum of the superlattice structure. The leakage currents for ordinary SCH and SCH-ESB lasers were analyzed. Experimental verification of a reduction in the leakage current for SCH-ESB lasers was obtained.     

Magnetic structure simulation of Fe/V superlattices with a variable thickness of iron layers

The model of the magnetic structure of Fe/V superlattices is discussed. The discrepancy in estimation of the critical temperature for the Fe₂/V _n /Fe₃/V _n superlattice obtained by neutron scattering and the magneto-optical Kerr effect is caused by inhomogeneity of the magnetization distribution in a finite superlattice.     

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. Received: 23 January 1998 / Revised: 31 March 1998 / Accepted: 20 April 1998