Theory of parametric amplification in superlattices

We consider a high-frequency response of electrons in a single miniband of superlattice subject to dc and ac electric fields. We show that Bragg reflections in miniband result in a parametric resonance which is detectable using ac probe field. We establish theoretical feasibility of phase-sensitive THz amplification at the resonance. The parametric amplification does not require operation in conditions of negative differential conductance. This prevents a formation of destructive domains of high electric field inside the superlattice.     

On a superlattice bloch oscillator

The differential dc and hf conductivities of semiconductor superlattices with various electron miniband dispersion relations are studied. It is shown that, due to the anharmonicity of Bloch oscillations, the hf conductivity can be negative at frequencies equal to integral multiples of the Bloch frequency. This effect can arise even in the regions where the differential dc conductivity is positive. The results of the study suggest that superlattices with a miniband dispersion law in which the effective electron mass is positive in a sizable part of the miniband and decreases as the electron energy increases can be used to generate and amplify terahertz-range (microwave) fields.     

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.     

Steady-state and transient electron transport in bulk GaN employing an analytic bandstructure

We have studied the steady-state and transient electron transport in bulk gallium nitride using an ensemble two valley Monte-Carlo approach. We employ an analytic form for the bandstructure which is non-parabolic and includes the inflection point predicted by empirical pseudopotential methods. It has been suggested that the inflection point could give rise to a negative effective mass which would, in turn, give rise to a negative-differential conductivity (NDC). We examine the character of the NDC by varying the energy separation to the upper valleys. We find that for steady-state velocity field characteristics, the transferred electron effect dominates over the negative mass effect. However, the transient characteristics show a small temporary dominance of the negative mass effect when the valley separation is 1.9 eV.     

Microscopic Three-Dimensional Theory of Space-Charge-Wave Modes in GaAs-Based Planar Superlattices

We report a systematic, fully three-dimensional thkoreticd examination of convective space-charge wave modes of a planar superlattice subject to negative differential miniband conductance (NDC) in a dc bias electric field. Our analysis is based on a set of hydrodynamic balance equations for system having an arbitrary energy band, with an accurate microscopic treatment of phonon and impurity scatterings. When applied to the longitudinal transport of an unconfined planar superlattice, these equations, which take full account of the role of carrier transverse motion, give rise to bulk NDC in the dc steady state conduction and provide a unified formulation to analyze the small-signal ac response in the space homogeneous case and the drift-relaxational modes under spatidy inhomogeneous condition.     

Ballistic electron transport in lateral antidot arrays investigated by scattering-matrix method

A scattering-matrix method is formulated for the study of ballistic electron transport in a lateral quantum system. It is shown that the physically important and less localized states are allowed to dominate in the implementation of the formalism and, therefore, the method remains numerically stable. As an example of its application, the method has been used to study electron transport in both weakly and strongly modulated one-dimensional antidot arrays defined in a two-dimensional electron-gas (2DEG) constriction. For the arrays with a weak modulation, we show that the conductance bands can appear at the edges of the conductance plateaux of the 2DEG constriction. For the arrays with a strong modulation, a more complicated conductance structure has been found. The conductance at high Fermi energies is seen to be characterized by two kinds of fluctuations, namely slow and rapid fluctuations. The slow fluctuations result from wave interferences in a form of Bragg reflections, while the rapid fluctuations reflect the formation of electron minibands. However, due to strong overlaps between the minibands, regular miniband formation may only be observed in the low Fermi energy range.     

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.     

Magnetotransport in a semconductor superlattice with transverse magnetic field

Magnetotransport in a semiconductor superlattice (SL) under transverse magnetic field has been investigated. It is shown that in weak magnetic and electric fields there is negative magnetoresistivity along the SL layers and positive magnetoresistivity along the SL axis. The Hall resistivity is much less than the usual semiconductor value. With an increase of electric field, there appears a negative differential conductivity (NDC) along the SL layers, and the Hall voltage depends nonlinearly on current density. In higher electric field, destroying the miniband structure, the magnetoresistivity along the SL axis is negative. The magnetoresistivity along the SL axis in strong magnetic field is positive for any current density. The Hall resistivity in strong magnetic (electric) field equals the classical value.     

Generation of direct current in a semiconductor superlattice under the action of a bichromatic field as a parametric effect

Generation of direct current in a semiconductor superlattice under the action of an ac bichromatic field is considered in the most general case of an arbitrary ratio of the frequencies of the fields being mixed. It is shown that this effect is of parametric origin associated with oscillations of the electron effective mass in the miniband of the superlattice.     

含各向异性左手材料一维光子晶体微腔的Wannier-Stark态

通过传输矩阵方法,研究了含各向异性左手材料的一维光子晶体耦合微腔结构。结果表明,该结构中存在两类微带,一类位于常规的Bragg带隙,另一类位于零均值折射率带隙。当腔的厚度发生调制时,两类微带变成两类Wannier-Stark态。耦合微腔厚度梯度因子增大时,两类带隙中Bragg振荡周期都减小,而且透过率降低。     

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.     

Short-wave sectioned free-electron masers with Bragg resonators based on the traveling and quasi-critical wave coupling

We consider the possibility of implementation of a free-electron maser with a two-mirror resonator composed of modified and conventional Bragg mirrors, operated in the short-wave part of the millimeter-wave range. The use of a modified Bragg mirror based on the traveling and quasicritical wave coupling at the input of the interaction space permits the transverse-index selection of modes. Amplification of the synchronous co-propagating wave by an electron beam is reached mainly in the regular part of the resonator. Even slight reflections from the conventional output Bragg cavity, which directly couples the co- and counter-propagating traveling waves, turn out to be sufficient for generation of self-excited oscillations. It is shown that the new scheme of a free electron maser ensures the oscillation frequency stabilization with respect to the electron-energy variation. With the optimal choice of the parameters, the oscillation frequency is close to the cutoff frequency of a quasi-critical wave excited in the modified Bragg structure.     

Engineering negative differential conductance with the Cu(111) surface state

Low-temperature scanning tunneling microscopy and spectroscopy are employed to investigate electron tunneling from a C60-terminated tip into a Cu(111) surface. Tunneling between a C60 orbital and the Shockley surface states of copper is shown to produce negative differential conductance (NDC) contrary to conventional expectations. NDC can be tuned through barrier thickness or C60 orientation up to complete extinction. The orientation dependence of NDC is a result of a symmetry matching between the molecular tip and the surface states.     

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     

Experimental contribution to the relaxation problem on the (100) and (110) surfaces of aluminum by LEED data reduction

It is shown that low-energy electron diffraction intensities off crystal surfaces can, despite their apparent complexity, be fully understood with such simple and familiar concepts as Bragg reflections, zero-angle scattering phase shifts, electron penetration depth, and intdermediate beams in multiple scattering. Our emphasis is on direct physical understanding rather than on calculational methods.     

TEM image contrast from antiphase domains in GaAs: Ge(001) grown by MBE

Antiphase domains occur in thin GaAs epitaxial films grown on Ge(001) by molecular beam epitaxy. The domains have been imaged by transmission electron microscopy using 200-type reflections in dark field. The carefully chosen imaging conditions with convergent illumination ensure that doubly diffracted beams from a pair of first order Laue zone discs contribute to the singly diffracted 200-type beams. The three Bragg reflections may add in or out of phase to give domains in either light or dark contrast depending on their polarity.     

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.     

Nonlinear theory of coaxial free-electron masers with 2D distributed feedback (quasi-optical approximation)

The nonlinear dynamics of coaxial free-electron masers with 2D distributed feedback, which is realizable in 2D Bragg structures, is analyzed in terms of a quasi-optical approximation. It is shown that feedback with the spatial synchronization of radiations from tubular electron beams with a perimeter exceeding 1000 wavelengths can be provided under such conditions. The objects of investigation are the one-section design of a free-electron maser with 2D distributed feedback and a design with a combined two-mirror resonator. In the latter, an entrance 2D Bragg mirror provides the spatial synchronization of radiation and weak reflections from a conventional exit Bragg mirror are sufficient for the self-excitation of the oscillator. The advantage of the two-mirror design is a decrease in ohmic losses. The adequacy of the geometric optics approximation used earlier to describe the dynamics of such self-excited oscillators is demonstrated under various boundary conditions for transverse (azimuthal) energy fluxes at the edges of a Bragg structure.     

Negative differential conductance and effective electron mass in highly asymmetric ballistic bilayer graphene nanoribbon

We present a simplified theory of the effective momentum mass (EMM) and ballistic current-voltage relationship in a degenerate two-folded highly asymmetric bilayer graphene nanoribbon. With an increase in the gap, the density-of-states in the lower set of subbands increases more than that of the upper set. This results in a phenomenological population inversion of carriers, which is reflected through a net negative differential conductance (NDC). It is found that with the increase of the ribbon width, the NDC also increases. The population inversion also signatures negative values of EMM above a certain ribbon-width for the lower set of subbands, which increases in a step-like manner with the applied longitudinal static bias. The well-known result for symmetric conditions has been obtained as a special case.     

Superlattice vertical transport with high-lying minibands

We examine the role of high-lying minibands in superlattice vertical transport using a nonparabolic balance-equation approach. We find that the inclusion of high-lying minibands results in a decrease of the electron temperature, a reduction of the peak drift velocity and a slow-down of the velocity-drop rate in the negative differential mobility (NDM) regime, in comparison with those predicted by a single miniband model. These effects become significant when the strength of the electric field gets close to or falls in the NDM regime.