Pendulum limit,chaos and phase-locking in the dynamics of ac-driven semiconductor superlattices

We describe a limiting case when nonlinear dynamics of an ac-driven semiconductor superlattice in the miniband transport regime is governed by a periodically forced and damped pendulum equations. We find analytically the conditions for a transition to chaos. With increasing temperature the chaos disappears. We also discuss fractional dc voltage states in a superlattice originating from phase-locked states of the pendulum.     

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.     

Current oscillation and chaotic dynamics in superlattices driven by crossed electric and magnetic fields

We have theoretically studied current oscillation and chaotic dynamics in doped GaAsAlAs superlattices driven by crossed electric and magnetic fields. When the superlattice system is driven by a dc voltage, a stationary or dynamic electric-field domain can be obtained. We carefully studied the electric-field-domain dynamics and current self-oscillation which both display different modes with the change of magnetic field. When an ac electric field is also applied to the superlattice, a typical nonlinear dynamic system is constructed with the ac amplitude, ac frequency, and magnetic field as the control parameters. Different nonlinear behaviors show up when we tune the control parameters.     

Observation of negative differential conductivity in a FET with structured gate

Using electron beam lithography, we have fabricated a novel quantum device in which a lateral surface superlattice (LSSL) replaces the gate of a high electron mobility transistor (HEMT). We have observed strong negative differential conductivity (NDC) which we believe could be due to the onset of Bloch oscillations. Other devices, identical in all ways except that the gates are solid instead of grid-like as in the BlochFET, did not show NDC. Alternative explanations for the NDC are discussed and discounted for various reasons. Dedicated to Professor Karlheinz Seeger on the occasion of his 60th birthday     

离子型声子晶体的光学性质

提出了离子型声子晶体的概念,发展了相应的理论：在实验上证实了离子型声子晶体中存在超晶格振动与电磁波的强烈耦合,观察到原先存在于离子晶体中的极化激元等长波光波行为;预言了一些可能的物理效应,离子型声子晶体超晶格振动和电磁波的耦合方程与黄昆方程在形式上完全一致,说明了超晶格与实际晶格在物理上的相似性。     

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     

Dynamic conductivity of ac–dc-driven graphene superlattice

The dynamic conductivity of graphene superlattice in the presence of ac electric field and dc electric field with longitudinal and transversal components with respect to superlattice axis was calculated. In the case of strong transversal component of dc field conductivity of graphene superlattice was shown to be such as if the electrons had got the effective mass. In the case of weak transversal component of dc field conductivity was shown to change its sign if the frequency of ac field was an integer multiple of half of Bloch frequency.     

Infrared absorption and Raman scattering on coupled plasmon-phonon modes in superlattices

We theoretically consider a superlattice formed by thin conducting layers spatially separated between insulating layers. The dispersion of two coupled phonon-plasmon modes of the system is analyzed by using the Maxwell equations, with the retardation effect included. Both transmission for the finite plate and the absorption for the semi-infinite superlattice in the infrared are calculated. Reflectance minima are determined by the longitudinal and transverse phonon frequencies in the insulating layers and by the density-state singularities of the coupled modes. We also evaluate the Raman cross section from the semi-infinite superlattice. The text was submitted by the authors in English.     

Polariton modes in superlattice media

The propagation characteristics of electromagnetic waves in superlattice media are discussed and various polariton modes with corresponding equations fixing their dispersion relations are derived.     

Theory of electromagnetic wave propagation in superlattices with optically anisotropic layers

A formalism is developed to find the photon dispersion relations in superlattice systems having layers with low optical symmetry or having magnetic layers. This formalism is an exact solution of the first order Maxwell's equations including all the information for the anisotropic optical response tensors and including the coupling of the TE and TM modes. Based on a 4×4 matrix approach for solving complicated reflection and transmission problems in stratified anisotropic media and employing a plane wave expansion of the field components to take into account the periodicity of the superlattices, the photon dispersion relation can be obtained numerically with a simple algorithm. This result is useful in predicting the absence of certain electromagnetic modes along the superlattice axis, and in identifying observed resonances with a particular excitations of the system.     

Plasmon modes of a superlattice — Classical vs quantum limits

The collective plasmon excitations of a superlattice are investigated in both the classical and quantum limits. Using a model that is applicable to superlattices whose constituent layers are either semiconductor- semiconductor, semiconductor-metal, or metal-metal, we show that the surface plasmon interface modes of each layer (slab) couple via the long range Coulomb interaction into two bands of plasmons with dispersion along the superlattice axis. Results for plasmon dispersion are presented for the classical limit (de Broglie wavelength less than the layer width) where the response is treated via a solution of Maxwell's equations using the bulk 3-D dielectric constant to describe each intervening layer. These results are compared to the plasmon dispersion in the quantum regime where the wave-vector frequency dependent dielectric constant of the superlattice is calculated taking into account quantization effects (subband structure). The relationship between the modes in both limits is derived.     

Radioelectric effect in a superlattice under the action of an elliptically polarized electromagnetic wave

The density of the current associated with the drag of charge carriers in a superlattice by an elliptically polarized electromagnetic wave is calculated. Two cases of the mutual orientation of the Umov-Poynting vector and the superlattice axis, i.e., their parallel and perpendicular orientations, are analyzed. It is shown that, for the parallel orientation, the radioelectric effect can change sign. The influence of the longitudinal dc electric field on the radioelectric effect is investigated under the conditions where a circularly polarized electromagnetic wave propagates along the superlattice axis. The current density is studied as a function of the electric field strength and the electromagnetic wave intensity. It is demonstrated that the direction of the electric current is changed at specific values of the dc field strength and the wave intensity.     

Quasiclassical Describing of the Bloch Oscillation in a Superlattice by Fokker-Planck Equation

A theoretical study of Bloch electron transport in a superlattice miniband driven by an electric field parallel to the growth axis is carried out, by Fokker-Planck equation (FPE) in momentum space with the averaged momentum relaxation time (γ) approximation. Steadystate drift-velocity/field characteristics exhibit the expected maximum followed by negative differential conductivity (NDC), and then followed by drift-velocity oscillation when γ or electric field is large. The oscillation frequency is an increasing function of γ, and when γ → ∞, the limit of the oscillation frequency is the Bloch frequency as expected.     

The defect structure of AlGaN/GaN superlattices grown on sapphire by the MOCVD method

High-resolution x-ray diffractometry and electron microscopy are used to study the defect structure and relaxation mechanism of elastic stresses in AlGaN/GaN superlattices grown by the MOCVD method on sapphire covered with a preliminarily deposited GaN and AlGaN buffer layer. Based on an analysis of the half-widths of three-crystal scan modes of x-ray reflections measured in different diffraction geometries, the density of different dislocation families is determined. For all the dislocation families, the density is shown to increase with the Al concentration in the solid-solution layers and depend only weakly on the superlattice period. From the electron-microscopic patterns of planar and cross sections, the types of dislocations and their distribution in depth are determined. It is shown that, in addition to high-density vertical edge and screw dislocations, which nucleate in the buffer layer and propagate through the superlattice layers, there are sloped intergrowing dislocations with a large horizontal projection and bent mixed dislocations with a Burgers vector $\left\langle {11\overline 2 3} \right\rangle $ at the interface between individual superlattice layers. The former dislocations form at the interface between the buffer layer and the superlattice and remove misfit stresses between the buffer and the superlattice as a whole, and the latter dislocations favor partial relaxation of stresses between individual superlattice layers. In samples with a high Al concentration (greater than 0.4) in AlGaN layers, there are cracks surrounded by high-density chaotic horizontal dislocations.     

Plasmon-polariton modes and optical properties of metallic superlattices

The plasmon-polariton modes in metallic superlattices are studied using coupled hydrodynamic and electromagnetic equations. At spatial periods of the order of 1000Å, we find important influences of the artificial superlattice modulation on the dispersions, which have interesting implications on the optical properties. We also find anisotropic behavior in the study of helicon modes in the presence of a static magnetic field.     

Effect of a dc electric field on the high-frequency conductivity of a graphene superlattice

Longitudinal and transverse high-frequency conductivities of a graphene superlattice placed in an additional dc electric field are calculated. It is shown that in a sufficiently strong transverse field, the dependence of the longitudinal high-frequency conductivity of the superlattice on the ac field frequency changes. This effect is explained by the nonadditivity of the electronic spectrum of the investigated structure.     

Intraband dynamics and terahertz emission in biased semiconductor superlattices coupled to double far-infrared pulses

This paper studies both the intraband polarization and terahertz emission of a semiconductor superlattice in combined dc and ac electric fields by using the superposition of two identical time delayed and phase shifted optical pulses. By adjusting the delay between these two optical pulses, our results show that the intraband polarization is sensitive to the time delay. The peak values appear again for the terahertz emission intensity due to the superposition of two optical pulses. The emission lines of terahertz blueshift and redshift in different ac electric fields and dynamic localization appears. The emission lines of THz only appear to blueshift when the biased superlattice is driven by a single optical pulse. Due to excitonic dynamic localization, the terahertz emission intensity decays with time in different dc and ac electric fields. These are features of this superlattice which distinguish it from a superlattice generated by a single optical pulse to drive it.     

Response of a Bloch oscillator to a THz-field

In this paper we report on the observation of response of a Bloch oscillator at room temperature to a THz-field of a frequency larger than the Bloch frequency. The oscillator consisted of a semiconductor superlattice structure, with an applied dc voltage giving rise to a dc electron drift current. Submitting the oscillator to a field at a frequency of 3.3 THz caused a sizeable reduction of the current; the THz-field was generated by use of intense THz-radiation pulses focused on an antenna coupled to the superlattice. We attribute the THz-field induced reduction of the current to a frequency modulation of the Bloch oscillations of electrons at the frequency of the THz-field, leading to reduction of the electron drift velocity and, consequently, of the current.     

A theoretical study of harmonic generation in a short period AlGaN/GaN superlattice induced by a terahertz field

Based on an improved energy dispersion relation, the terahertz field induced nonlinear transport of miniband electrons in a short period AlGaN/GaN superlattice is theoretically studied in this paper with a semiclassical theory. To a short period superlattice, it is not precise enough to calculate the energy dispersion relation by just using the nearest wells in tight binding method: the next to nearest wells should be considered. The results show that the electron drift velocity is 30% lower under a dc field but 10% higher under an ac field than the traditional simple cosine model obtained from the tight binding method. The influence of the terahertz field strength and frequency on the harmonic amplitude, phase and power efficiency is calculated. The relative power efficiency of the third harmonic reaches the peak value when the dc field strength equals about three times the critical field strength and the ac field strength equals about four times the critical field strength. These results show that the AlGaN/GaN superlattice is a promising candidate to convert radiation of frequency ω to radiation of frequency 3ω or even higher.     

Giant magnetoresistance of iron-chromium superlattices at microwaves

Interaction between an rf electromagnetic field and the Fe/Cr superlattice placed in a rectangular waveguide so that a high-frequency current passes in the plane of superlattice layers is considered. The transmission coefficient versus the magnetic field strength is found at centimeter waves, and a correlation between this dependence and the field dependence of the dc magnetoresistance is established. It is shown that a change in the transmission coefficient may greatly exceed the giant magnetoresistance of the superlattice. The frequency dependence of the microwave measurements has an oscillatory character. The oscillation frequencies are analyzed in terms of wavelet transformation. Two types of oscillation periods are found to exist, one of which corresponds to the resonance of waves traveling in the superlattice along the direction parallel to the narrow wall of the waveguide.