Wannier-Stark Levels Research Articles

Transport and stimulated THz emission in simple weak barrier superlattices

Emissions at 2.6 – 2.8 THz are observed from liquid helium cooled disk chips with metal - superlattice - metal cavities made of two low n type doped wafers with weak barrier GaAs-GaAlAs superlattice of 1000 periods. The emissions are at 8.6 – 18.8 Volts within region of rising chip current (at positive chip differential conductivity) that guarantees absence of inhomogeneous electric field domains. At 2.6 – 2.7 THz the emission tunable by 8 – 10 Volts voltage change is higher than the Bloch oscillations frequency; while at 2.8 THz at 12 – 18 Volts it is lower than ωB, The THz frequency bands are measured with a cyclotron resonance filter; the band width is of about that of the THz quantum cascade laser. By using long voltage pulses the chip heating above 100 K is achieved without substantial change in chip THz emission power. We speculate that the emission is super luminescence (amplification) of whispering gallery modes in the chips as a result of inverted Wannier-Stark level transitions under bias. The results advocate development of THz and higher frequency sources based on such simple superlattices; the sources should well compete with the THz quantum cascade lasers in particular at elevated temperatures.

THz Stimulated Emission from Simple Superlattice in Positive Differential Conductivity Region

Narrow band emissions at 2.6–2.8 THz are observed out of liquid helium cooled 1 mm disk chips prepared of a wafer with the very low n type doped weak barrier GaAs–GaAlAs superlattice of 1000 periods. The emissions are at about 8.0–18.0 V pulsed voltage applied to the chips in region of the chips positive DC differential conductivity that guaranties absence of inhomogeneous electric field domains in the chips. The emission frequency bands are estimated with a cyclotron resonance filter; the measurements show that the band width is of about that of the THz quantum cascade laser. By using long voltage pulses the chip heating above 100 K is achieved without substantial change in emission power. We speculate that the emission is super luminescence (amplification) of whispering gallery modes in the chips as a result of inverted Wannier-Stark level transitions under bias. The results are the first world demonstration of THz stimulated emission in a simple superlattice within region of positive DC differential conductivity; they give strong impetus for development of THz and higher frequency sources based on such simple superlattices; the sources should well compete with the THz quantum cascade lasers in particular at elevated temperatures.

THz stimulated emission from simple superlattice in positive differential conductivity region

AbstractNarrow band emissions at 2.6–2.8 THz are observed out of liquid helium cooled 1 mm disk chips prepared of a wafer with the very low n type doped weak barrier GaAs–GaAlAs superlattice of 1000 periods. The emissions are at about 8.0–18.0 V pulsed voltage applied to the chips in region of the chips positive DC differential conductivity that guaranties absence of inhomogeneous electric field domains in the chips. The emission frequency bands are estimated with a cyclotron resonance filter; the measurements show that the band width is of about that of the THz quantum cascade laser. By using long voltage pulses the chip heating above 100 K is achieved without substantial change in emission power. We speculate that the emission is super luminescence (amplification) of whispering gallery modes in the chips as a result of inverted Wannier-Stark level transitions under bias. The results are the first world demonstration of THz stimulated emission in a simple superlattice within region of positive DC differential conductivity; they give strong impetus for development of THz and higher frequency sources based on such simple superlattices; the sources should well compete with the THz quantum cascade lasers in particular at elevated temperatures.

Stimulated emission at transitions between Wannier–Stark ladders in semiconductor superlattices

New intraband semiconductor lasers—Wannier–Stark lasers—based on simple GaAs (150 A, quantum well)/GaAlAs (19 A with an aluminum fraction of 12%, barrier) superlattices have been demonstrated. The amplification mechanism in these lasers is based on population inversion between the ground Wannier–Stark level in the superlattice quantum wells and the weakly populated upper Wannier–Stark level in the wells two, three, or four periods down in the applied potential. Multiple regions of intense stimulated microwave emission near voltages of 8, 13, and 20 V (i.e., in the vicinity of resonances between these Wannier–Stark levels of the superlattice) have been discovered in the laser chips. The stimulated emission emerges in the circuit formed by the chip and its wiring. The emission from one of the chips at a temperature of up to 150 K (near 20 V applied to the chip) occurs at a frequency of about 7.3 GHz and has an estimated power of up to 1 W. It has been shown that the negative conductivity responsible for the emission still persists at 300 K but the emission is unseen owing to high losses in the circuit at this temperature. The superlattice wafer has been grown by metalorganic chemical vapor deposition. It consists of 1000 periods and a stop layer, to produce a metal–superlattice–metal terahertz resonator. Terahertz radiation has not been observed owing to a low amplification, as compared to losses in the resonator. According to the performed experiments, calculations, and discussions, such superlattices as radiation sources in gigahertz, terahertz, and higher frequency ranges could compete with quantum cascade lasers under appropriate optimization of their parameters.

Optical resonance identification of long-range electron tunneling between superlattice levels in an electric field

A method for diagnostics of the interaction of electron states in multilayer heterostructures in a dc electric field is suggested. The method is based on measurements of the resonance response of the harmonic amplitude of the current in a heterostructure to modulated laser radiation. The method is used for studying tunneling between the Wannier-Stark levels in the superlattice with strongly coupled quantum wells.

Master equation approach of classical noise in intersubband detectors

Electronic transport in intersubband detectors is investigated theoretically and experimentally. Within the framework of inter--Wannier-Stark levels electron scattering, consistent dark current and low-frequency noise expressions are obtained through the resolution of the two first moments of a master equation for classical particles. In particular, the formulation of noise bridges over the vision of uncorrelated Johnson and shot contributions. Theoretical predictions are compared to measurements for five quantum well detectors, either photovoltaic or photoconductive, whose detection wavelength span from $8\phantom{\rule{0.222222em}{0ex}}\ensuremath{\mu}\text{m}$ to $17\phantom{\rule{0.222222em}{0ex}}\ensuremath{\mu}\text{m}$. Quantitative agreement with experiment is found for a broad range of biases and temperatures. Correlation effects are discussed and proven to either reduce or enhance the noise.

Zener tunneling in semiconductor superlattices

Characteristics of miniband tunneling and Wannier–Stark levels in semiconductorsuperlattices are studied as regards their dependence on the symmetry of the unit cells andthe type of miniband structure. We modify the k ⋅ p method into a k ⋅ v form and on this basis generalize the Zener formula for the inter-band tunneling inhomogeneous semiconductors to the case of inter-miniband tunneling in superlattices,account being taken of the inhomogeneity of the electron effective mass. The correspondingsum rule for the effective masses in such structures is obtained. We develop a unifiedmatrix approach for the calculation of the inter-miniband tunneling and Wannier–Starklevels in the case of an arbitrary number of minibands. We study the electric fielddependence of the probability of inter-miniband tunneling for an electron transferredthrough the Brillouin minizone only once. The peculiarities of the inter-minibandtransitions for the case where this transfer is repeated are also examined for various unitcells and miniband structures of the superlattice. In addition, we discuss mechanisms andspecific features of the resonant Zener tunneling and its manifestations in electrontransport.

Transport in GaAs/Al x Ga1−x As superlattices with narrow minibands: Effects of interminiband tunneling

The results of experimental investigations for the I–V characteristics are presented for superlattices based on GaAs/AlxGa1−xAs with thin barriers in the electric-field region with an intense interminiband tunneling. The regular features for the I–V characteristics are found in the voltage range adequate to the static positive differential conductivity in the superlattice. On the basis of calculations for the Wannier-Stark levels, it is established that the observed features are associated with the resonant tunneling between these levels belonging to quantum wells located at a distance from 6–13 superlattice periods from each other. It is noted that the similar resonant delocalization of Wannier-Stark wave functions can lead to the existence of dynamic negative differential conductivity for the laser type of an appreciable value in such superlattices.

High-field transport in semiconductor superlattices for interacting Wannier–Stark levels

We developed a microscopic theory of electron transport in superlattices within the Wannier–Stark approach by including the interaction associated with Zener tunneling between the energy levels pertaining to adjacent quantum wells. By using a Monte Carlo technique we have simulated the hopping motion associated with absorption and emission of polar optical phonons and determined the main transport parameters for the case of a GaAs/GaAlAs structure at room temperature. Interaction between the levels is found to be responsible for a systematic increase of the level energy with respect to the bottom of the quantum well at electric fields above about 20 kV/cm. When compared with the non-interacting case, at the highest fields the average carrier energy evidences a consistent increase, which leads to a significant softening of the negative slope of both the drift velocity and diffusivity versus electric field behavior.

Coherent Delocalization of Atomic Wave Packets in Driven Lattice Potentials

Atomic wave packets loaded into a phase-modulated vertical optical-lattice potential exhibit a coherent delocalization dynamics arising from intraband transitions among Wannier-Stark levels. Wannier-Stark intraband transitions are here observed by monitoring the in situ wave-packet extent. By varying the modulation frequency, we find resonances at integer multiples of the Bloch frequency. The resonances show a Fourier-limited width for interrogation times up to 2 s. This can also be used to determine the gravity acceleration with ppm resolution.

Multiphoton exciton absorption in a semiconductor superlattice in a dc electric field

An analytical approach to the problem of the multiphoton exciton absorption in biased narrow-well superlattices (SLs) induced by the optical transitions to the localized resonant exciton states is developed. Both the ac electric field of the intense optical wave and the dc electric field are directed parallel to the SL axis. The SL is formed by a periodic sequence of quantum wells (QWs) whose widths are taken to be much less than the exciton Bohr radius. The model of the SL potential employs a limiting form of the Kronig-Penney potential, i.e., a periodic chain of QWs separated by $\ensuremath{\delta}$-function-type barriers. A sufficiently strong dc electric field provides the localization of the carriers within one period of the SL. Analytical dependencies of the coefficient of the multiphoton exciton absorption on the characteristics of the dc and ac electric fields and on the parameters of the SL in the approximation of both isolated and interacting Wannier-Stark levels are obtained in the nearest-neighbor tight-binding approximations. Our analytical results correlate well with those obtained in numerical investigations. Estimates of the expected experimental values are performed for the parameters of a $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ SL.

Simple theoretical analysis of the interband optical absorption coefficient in wide-gap semiconductors in the presence of an external electric field and its dependence on a longitudinal magnetic field

An attempt is made to present a simplified theoretical analysis of the interband optical absorption coefficient (OAC) due to a constant uniform electric field on the basis of the electron wave vector dependence of the optical matrix element (OME) for the incident photon energy, ( ℏ ω ), below and above the band-gap ( E g). It has been found, taking n-GaAs as an example for numerical computation, that the expression of the OAC exhibits an exponential fall-off with the electric field and the photon energy without the consideration of the Wannier–Stark levels, which generally exists in a band due to the external electric field. The effect of a longitudinal magnetic field on the OAC is also studied on the basis of the fact that the transverse wave vector ( k ⊥) is quantized due to parallel magnetic field and is conserved in the interband optical transition of electrons. Similar results, such as singularity for the case ℏ ω < E g in the OAC and the oscillations in the OAC for the case ℏ ω ⩾ E g in presence of electric field are also obtained with modifications in the expressions for the OAC in presence of electric and parallel magnetic fields. Present study explains the modification of the band-gap of the semiconductor in the presence of electric and parallel magnetic fields, respectively. The numerical analyses are performed and discussed in details taking n-GaAs as an example.

Zener tunneling between Wannier–Stark levels in GaAs/AlGaAs superlattices

We have performed a detailed calculation of the inter-Wannier–Stark-ladder Zener tunneling probability P( F) in a wide-miniband GaAs/Al 0.3Ga 0.7As superlattice under a strong electric field F, the terahertz emission spectrum I( F) of which was measured experimentally. By comparing P( F) and I( F), we confirm that the oscillating behavior of I( F) is due to the Zener tunneling between Wannier–Stark levels.

Scattering-assisted electric current in semiconductor superlattices in the Wannier-Stark regime

We have used the Monte Carlo technique to investigate the mechanism of scattering-assisted charge transport in semiconductor superlattices under a strong applied electric field in the Wannier-Stark (WS) regime. The distribution function of quasi-two-dimensional carriers localized in each WS level is calculated, and the contributions of different scattering mechanisms to the total scattering probability are analyzed. Based on these results, the drift velocity is derived as a function of the applied electric field. Due to the LO-phonon-induced resonant transfer of electrons between different spatially localized WS states, our calculated I-V characteristics oscillates with clear negative differential velocity behavior. At the electric field strength such that the Bloch oscillation energy is equal to an integer multiple of the LO phonon energy, a peak appears in the I-V curve. Our theoretical result agrees with the experimental data which was obtained from analyzing the terahertz response of superlattices to picosecond optical pulse excitation. (Less)

Simple theory of the interband optical absorption in an external electric field for optoelectronic materials

We study theoretically the interband optical-absorption coefficient (OAC) of optoelectronic materials within the framework of the three-band model of Kane [J. Phys. Chem. Solids 12, 181 (1959)] in the presence of an external electric field for modified photon energy (ℏω1) below and above the band gap (Eg), respectively. The optical matrix element depends on the electron wave vector k and this practical aspect has been incorporated in the present analysis. It has been found, taking InAs, InSb, Hg1−xCdxTe, and In1−xGaxAsyP1−y lattice matched to InP as examples of optoelectronic compounds for numerical computations, that for modified photon energies below the band gap, the OAC exhibits an exponential fall off with the electric field and the photon energy, respectively. For the opposite inequality, the OAC oscillates with the modified photon energy without the consideration of the Wannier-Stark levels, which generally exist in a band due to the presence of an external electric field. In both cases, the OAC exhibits the singularity when the incident photon energy (ℏω0) tends to Eg and the magnitude of the OAC depends to a large extent on the numerical values of the energy-band constants of the said compounds. In addition, the simplified results of the OAC for materials having parabolic energy bands have also been obtained from the present generalized analysis under certain limiting conditions.

Influence of a strong magnetic field on the Wannier-Stark states of an electrically biasedGaAs/AlxGa1−xAssuperlattice

We present experimental and theoretical photocurrent spectra of a GaAs/AlGaAs superlattice under the influence of electric and magnetic fields parallel to the growth axis. In this field configuration, the charge carriers are subjected to zero-dimensional confinement. Depending on the fields, we observe a complicated interplay of Wannier-Stark and Landau levels. The experimental spectra are found to be in good agreement with numerical results.

Theoretical analysis of interband optical absorption in an external electric field

We study theoretically the interband optical absorption coefficient of semiconductors described within the two-band Kane model in the presence of an external electric field for photon energy below and above the semiconductor band gap. The optical matrix element depends on the momentum vector, and this important aspect has been incorporated in the present analysis. For photon energies below the band gap, the absorption coefficient exhibits an exponential falloff with the electric field and the photon energy. For the opposite inequality, the same coefficient oscillates with the photon energy without consideration of the Wannier–Stark levels, which generally exists in a band due to the presence of an external electric field. Additional oscillations are expected in the above two cases because of the formation of the discrete Stark ladders.

Field-induced delocalization of Eu 2+ and Ce 3+ impurity levels in II a–VI b semiconductors

We proposed a model for the light emission from II a –VI b semiconductors doped with Eu 2+ and Ce 3+ ion, considering the mixing interaction between the conduction electrons and the localized d electrons under the high-electric fields. Introducing the modified Anderson Hamiltonian and Wannier–Stark levels, we obtained the thermal Green's function and the self-energy for the localized electrons. Using asymptote of the Airy function we calculated the energy shift of the localized level and delocalization probability, and found that they depend strongly on the mixing interaction and the electric field intensity. Moreover, we estimated the electroluminescent relaxation time by using the delocalization probability and found, comparing the calculational relaxation time with the experimental one, that the excited levels of Eu 2+ and Ce 3+ ions in the CaS : Eu and SrS : Ce,Cl devices are placed below 0.15–0.4 eV from the bottom of the conduction band of the host materials and their mixing interaction with conduction electrons is expected to be 0.5–0.8 eV.

Excitonic influences on the anticrossing gap of Wannier–Stark levels in a wide well superlattice

In this paper we compare different theoretical calculations with experimental data of anticrossings of a wide well semiconductor superlattice in the Wannier–Stark regime. Calculations have been performed by using a variation method and a numerical method. For the variation method we used different approaches to minimize energy. With the numerical model, continuum states were calculated and anticrossing of 1s states with continuum states were found. Calculations have been performed for h1e1(0)–h1e2(−1) and h1e1(1)–h1e2(0) anticrossings and are compared with data from photocurrent experiments.

TRANSPORT IN EXCITED STATES OF SEMICONDUCTOR SUPERLATTICES

The electronic conduction processes in the minibands and excited states of semiconductor superlattices are reviewed and discussed. The paper includes an introduction on miniband conduction and hopping conduction between localized states. It focusses subsequently on interminiband transport, both in the context of theoretical approaches and of experimental observations of these effects. Rabi oscillations between interacting Wannier–Stark levels are considered in detail. The role of scattering, and the manifestation of multipeaked velocity-field relationships on carrier and electric field profiles are evidenced. The final part concerns transport above the superlattice barriers, and quasi-ballistic transport in excited superlattice minibands.