Simple theoretical analysis of the Einstein’s photoemission from quantum confined superlattices

In this paper, we study the Einstein’s photoemission from III–V, II–VI, IV–VI and HgTe/CdTe quantum well superlattices (QWSLs) with graded interfaces and quantum well effective mass superlattices in the presence of a quantizing magnetic field on the basis of newly formulated dispersion relations in the respective cases. Besides, the same has been studied from the afore-mentioned quantum dot superlattices and it appears that the photoemission oscillates with increasing carrier degeneracy and quantizing magnetic field in different manners. In addition, the photoemission oscillates with film thickness and increasing photon energy in quantum steps together with the fact that the solution of the Boltzmann transport equation will introduce new physical ideas and new experimental findings under different external conditions. The influence of band structure is apparent from all the figures and we have suggested three applications of the analyses of this paper in the fields of superlattices and microstructures.     

Properties of InGaN/GaN quantum wells and blue light emitting diodes

We have reported the effects of growth interruption time on the optical and structural properties of high indium content In_xGa_1−xN/GaN (x>0.2) multilayer quantum wells (QWs). The InGaN/GaN QWs were grown on c-plane sapphire by metal organic chemical vapor deposition. The interruption was carried out by closing the group-III metal organic sources before and after the growth of the InGaN QW layers. The transmission electron microscopy (TEM) images show that with increasing interruption time, the quantum-dot-like region and well thickness decreases due to indium reevaporation or the thermal etching effect. As a result the photoluminescence (PL) peak position was blue-shifted and the intensity was reduced. The sizes and number of V-defects did not differ with the interruption time. The interruption time is not directly related to the formation of defects. The V-defect originates at threading dislocations and inversion domain boundaries due to higher misfit strain. Temperature dependent PL spectra support the results of TEM measurements. Also, the electroluminescence spectra of light-emitting diode show that dominant mechanism in InGaN/GaN QWs is a localized effect in the quantum-dot-like regions.     

Simple theoretical analysis of the Fowler-Nordheim field emission from microstructures and quantum wires of optoelectronic materials

We present a simplified theoretical formulation of the Fowler-Nordheim field emission (FNFE) under magnetic quantization and also in quantum wires of optoelectronic materials on the basis of a newly formulated electron dispersion law in the presence of strong electric field within the framework of k.p formalism taking InAs, InSb, GaAs, Hg_1−xCd_xTe and In_1−xGa_x As_yP_1−y lattice matched to InP as examples. The FNFE exhibits oscillations with inverse quantizing magnetic field and electron concentration due to SdH effect and increases with increasing electric field. For quantum wires the FNFE increases with increasing film thickness due to the existence van-Hove singularity and the magnitude of the quantum jumps are not of same height indicating the signature of the band structure of the material concerned. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the field current varies in various manners with all the variables in all the limiting cases as evident from all the curves, the rates of variations are totally band-structure dependent. Under certain limiting conditions, all the results as derived in this paper get transformed in to well known Fowler-Nordheim formula.     

Tilted magnetic field effect on the subbands of a GaAlAs diode with a GaAs quantum well

We have calculated the subbands in the GaAs quantum well at the n-side of the junction in a Ga_1−xAl_xAs diode. We show that the density of carriers confined in the quantum well increases by the increasing magnetic field strength but also decreases depending on the magnetic length. We have observed oscillatory behavior of the density of carriers due to the in-plane magnetic field.     

Polar propagating optical phonon states and their dispersive spectra in wurtzite nitride superlattices: Quantum size effect

The polar optical phonon states of propagating (PR) modes in wurtzite GaN/Al_xGa_1−xN superlattices (SLs) are investigated within the dielectric continuum model framework. It is proved that the PR phonon modes only appear in wurtzite GaN/Al_xGa_1−xN SL with a small x$x$ Al mole ratio concentration (such as x<0.34$x<0.34$). The analytical phonon states of PR modes and their dispersive equation in the wurtzite GaN/Al_xGa_1−xN SL structures are obtained. Numerical calculations on the dispersive spectra of PR modes and their electrostatic potential properties as well as the quantum size effect are performed for a wurtzite GaN/Al_0.15Ga_0.85N SL. Results reveal that dispersive curves of PR modes in SLs form frequency bands. As the well width of GaN well-layer increases, the frequency bands of PR modes become steeper and narrower. The discussion of electrostatic potentials shows that the wavelength of PR phonon modes with a phase qL=π$qL=\pi$ (0) is 2L$2L$ (L$L$). With the increase of the SL well width, the wave-node number of the PR phonon modes in the barrier regions increases. The present theoretical scheme and numerical results are quite useful for analyzing the dispersive spectra of PR phonon modes and their polaronic effect in wurtzite GaN/AlGaN SL structures.     

Intense laser effects on nonlinear optical absorption and optical rectification in single quantum wells under applied electric and magnetic field

In this work the effects of intense laser on the electron-related nonlinear optical absorption and nonlinear optical rectification in GaAs-Ga_1−xAl_xAs quantum wells are studied under, applied electric and magnetic field. The electric field is applied along the growth direction of the quantum well whereas the magnetic field has been considered to be in-plane. The calculations were performed within the density matrix formalism with the use of the effective mass and parabolic band approximations. The intense laser effects are included through the Floquet method, by modifying the confining potential associated to the heterostructure. Results are presented for the nonlinear optical absorption, the nonlinear optical rectification and the resonant peak of these two optical processes. Several configurations of the dimensions of the quantum well, the applied electric and magnetic fields, and the incident intense laser radiation have been considered. The outcome of the calculation suggests that the nonlinear optical absorption and optical rectification are non-monotonic functions of the dimensions of the heterostructure and of the external perturbations considered in this work.     

Barrier height effect on binding energies of shallow hydrogenic impurities in coaxial GaAs/ AlxGa1−xAs quantum well wires under a uniform magnetic field

The ground state binding energies of axial hydrogenic impurities in a coaxial cylindrical quantum well wire are reported as a function of the barrier height and the radius of wire in the presence of a uniform magnetic field applied parallel to the wire axis. The quantum well wire (QWW) is assumed to be an infinitely long cylinder of GaAs material surrounded by Al_xGa_1−xAs (for finite case and vacuum for infinite case). Binding energy calculations were performed with the use of a variational procedure in the effective mass approximation. We observed that the binding energy is sensitive to well radius only for both larger R$R$ values and small magnetic fields. We also compared the infinite and finite case binding energies and showed that increasing the Al concentration in the finite barrier case, binding energies are increased as expected. Our results are in good agreement and complementary with the previous theoretical works.     

Theoretical study on InxGa1−xN/GaN quantum dots solar cell

In this work, the structure of In_xGa_1−xN/GaN quantum dots solar cell is investigated by solving the Schrödinger equation in light of the Kronig-Penney model. Compared to p-n homojunction and heterojunction solar cells, the In_xGa_1−xN/GaN quantum dots intermediate band solar cell manifests much larger power conversion efficiency. Furthermore, the power conversion efficiency of quantum dot intermediate band solar cell strongly depends on the size, interdot distance and gallium content of the quantum dot arrays. Particularly, power conversion efficiency is preferable with the location of intermediate band in the middle of the potential well.     

Donor impurity states in coupled quantum well wires under hydrostatic pressure and applied electric field

In this work we study the binding energy of the ground state for a hydrogenic donor impurity in laterally coupled GaAs/Ga_1−xAl_xAs quantum well wires, considering the simultaneous effects of hydrostatic pressure and applied electric field. We have used a variational method and the effective mass and parabolic band approximations. The low dimensional structure consists of two quantum well wires with rectangular transverse section coupled by a central Ga_1−xAl_xAs barrier. Our results are reported for several sizes of the structure and we have taken into account variations of the impurity position along the growth direction of the heterostructure.     

Size dependent effective band gap,optical absorption coefficients and refractive index changes in a wide ZnS/Zn1−xMgxS strained quantum well

Exciton binding energy of a confined heavy hole exciton is investigated in a Zn_1−xMg_xS/ZnS/Zn_1−xMg_xS single strained quantum well with the inclusion of size dependent dielectric function for various Mg content. The effects of interaction between the exciton and the longitudinal optical phonon are brought out. The effect of exciton is described by the effective potential between the electron and hole. The interband emission energy as a function of well width is calculated for various Mg concentration with and without the inclusion of dielectric confinement. Non-linear optical properties are carried out using the compact density matrix approach. The dependence of nonlinear optical processes on the well width is investigated for different Mg concentration. The linear, third order non-linear optical absorption coefficients values and the refractive index changes of the exciton are calculated for different concentration of magnesium content. The results show that the exciton binding energy is found to exceed LO phonon energy of ZnS for x>0.2 and the incorporation of magnesium ions and the effect of phonon have great influence on the optical properties of ZnS/Zn_1−xMg_xS quantum wells.     

Simultaneous effects of temperature and pressure on diamagnetic susceptibility of a shallow donor in a quantum antidot

The effect of temperature and pressure, simultaneously, on the diamagnetic susceptibility and binding energy of a hydrogenic donor impurity at the center of a GaAs/Ga_1−xAl_xAs quantum antidot is studied within the effective mass approximation. For this goal, we first analytically solve the Schrödinger equation to obtain wavefunctions and energy levels. Then, using the electronic states, we can calculate the diamagnetic susceptibility. The results obtained from the present work reveals that (i) the diamagnetic susceptibility increases with increasing pressure, (ii) the diamagnetic susceptibility decreases by increasing temperature, (iii) the value of 〈r²〉 decreases with increasing pressure due to the quantum confinement, and (iv) an increase in the pressure enhances the binding energy for a constant temperature.     

Simple theoretical analysis of the thermoelectric power in quantum dot superlattices of non-parabolic heavily doped semiconductors with graded interfaces under strong magnetic field

We study theoretically the thermoelectric power in the presence of a large magnetic field (TPM) in heavily doped III–V, II–VI, PbTe/PbSnTe, strained layer and HgTe/CdTe quantum dot superlattices (QDSLs) with graded structures on the basis of newly formulated electron energy spectra and compare the same with that of the constituent materials. It has been found, taking heavily doped GaAs/Ga_1−xAl_xAs, CdS/CdTe, PbTe/PbSnTe, InAs/GaSb and HgTe/CdTe QDSLs as examples, that the TPM increases with increasing inverse electron concentration and film thickness, respectively, in different oscillatory manners and the nature of oscillations is totally band structure dependent. We have also suggested the experimental methods of determining the Einstein relation for the diffusivity–mobility ratio, the Debye screening length and the electronic contribution to the elastic constants for materials having arbitrary dispersion laws.     

Fabrication and hard X-ray photoemission analysis of photocathodes with sharp solar-blind sensitivity using AlGaN films grown on Si substrates

Photocathode devices operating in reflection-mode, where the photoemission is detected on the same side as the light irradiation, were developed for the detection of deep ultraviolet light by using p-Al_xGa_1−xN films grown on Si(1 1 1) substrates. The external quantum efficiencies were as high as 20-15% at 200 nm and 280 nm, while the value was as low as 10⁻²% at 310 nm. The on-off ratio was more than four orders of magnitude, which represents high solar-blind sensitivity. The escape probability of Al_xGa_1−xN photocathode was decreased with increase of AlN mole fraction. The effective barrier potential against the photoelectron emission near the surface was reduced due to the upward shift of conduction band of Al_xGa_1−xN. The photoemission from the Al_xGa_1−xN films terminated with Cs-O adatoms will be discussed in terms of band diagrams that were evaluated by hard X-ray photoelectron spectroscopy.     

Combined effects of magnetic and electric fields on the interband optical transitions in InAs/InP quantum wire

Combined effects of magnetic and electric fields on the confined exciton in an InAs_1−xP_x/InP (x=0.2) quantum well wire are investigated taking into account the geometrical confinement effect. Variational formulism, within the frame work of effective mass approximation, is applied to obtain the exciton binding energy. The second order harmonic generation and the optical gain are carried out using compact density method. The strain effects are included with the confinement potential in the Hamiltonian. The energy difference of the ground and the first excited state is found in the presence of magnetic and electric fields taking into the consideration of spatial confinement effect. The result shows that the optical properties are more influenced taking into account the effects of geometrical confinement, magnetic field and electric field. It is shown that the telecommunication wavelength can be achieved with the suitable doping barrier material with the wire material and the external perturbations.     

Spin transistor and quantum spin Hall-effects in CdBxF2−x–p-CdF2–CdBxF2−x sandwich nanostructures

Planar CdB_xF_2−x–p-CdF₂–CdB_xF_2−x sandwich nanostructures prepared on the surface of the n-type CdF₂ bulk crystal are studied to register the spin transistor and quantum spin Hall-effects. The current–voltage characteristics of the ultra-shallow p⁺–n junctions verify the CdF₂ gap, 7.8 eV, and the quantum subbands of the 2D holes in the p-type CdF₂ quantum well confined by the CdB_xF_2−xδ-barriers. The temperature and magnetic field dependencies of the resistance, specific heat and magnetic susceptibility demonstrate the high temperature superconductor properties for the CdB_xF_2−xδ-barriers. The value of the superconductor energy gap, 2Δ = 102.06 meV, determined by the tunneling spectroscopy method appears to be in a good agreement with the relationship between the zero-resistance supercurrent in superconductor state and the conductance in normal state, πΔ/e, at the energies of the 2D hole subbands. The results obtained are evidence of the important role of the multiple Andreev reflections in the creation of the high spin polarization of the 2D holes in the edged channels of the sandwich device. The high spin hole polarization in the edged channels is shown to identify the mechanism of the spin transistor and quantum spin Hall-effects induced by varying the top gate voltage, which is revealed by the first observation of the Hall quantum conductance staircase.     

The quantum acoustomagnetoelectric field in a quantum well with a parabolic potential

The acoustomagnetoelectric (AME) field in a quantum well with a parabolic potential (QWPP) has been studied in the presence of an external magnetic field. The analytic expression for the AME field in the QWPP is obtained by using the quantum kinetic equation for the distribution function of electrons interacting with external phonons. The dependence of the AME field on the temperature T of the system, the wavenumber q of the acoustic wave and external magnetic field B for the specific AlAs/GaAs/AlAs is achieved by using a numerical method. The problem is considered for both cases: The weak magnetic field region and the quantized magnetic field region. The results are compared with those for normal bulk semiconductor and superlattices to show the differences, and we use the quantum theory to calculate the AME field in the QWPP.     

Exciton effects on the refractive index and optical absorption in wurtzite quantum wells via a fractional-dimensional space approach

The optical refractive index changes and absorption coefficients of quantum wells (QWs) are theoretically investigated with considering exciton effects within the framework of the fractional-dimensional space approach. The exciton wave functions and bound energies are obtained as a function of spatial dimensionality, and the dimension increases with the well width increasing. Then optical properties are obtained by using the compact-density matrix approach and an iterative method. Numerical results are presented for wurtzite ZnO/Mg_xZn_1−xO QWs. The calculated results show that the changes of refractive index and absorption coefficients are greatly enhanced due to the quantum confinement of exciton. And the smaller the QW width (dimension) is, the larger influence of exciton on the optical properties will be. Furthermore, the exciton effects make the resonant peaks move to a lower energy. In addition, the optical properties are related to the QW width, the incident optical intensity and carrier density.     

Non-Fermi-liquid behavior in UCu4+xAl8−x compounds

We report on experimental studies of the Kondo physics and the development of non-Fermi-liquid scaling in UCu_4+xAl_8−x family. We studied 7 different compounds with compositions between x=0 and 2. We measured electrical transport (down to 65 mK) and thermoelectric power (down to 1.8 K) as a function of temperature, hydrostatic pressure, and/or magnetic field.Compounds with Cu content below x=1.25 exhibit long-range antiferromagnetic order at low temperatures. Magnetic order is suppressed with increasing Cu content and our data indicate a possible quantum critical point at x_cr≈1.15. For compounds with higher Cu content, non-Fermi-liquid behavior is observed. Non-Fermi-liquid scaling is inferred from electrical resistivity results for the x=1.25 and 1.5 compounds. For compounds with even higher Cu content, a sharp kink occurs in the resistivity data at low temperatures, and this may be indicative of another quantum critical point that occurs at higher Cu compositions.For the magnetically ordered compounds, hydrostatic pressure is found to increase the Néel temperature, which can be understood in terms of the Kondo physics. For the non-magnetic compounds, application of a magnetic field promotes a tendency toward Fermi-liquid behavior. Thermoelectric power was analyzed using a two-band Lorentzian model, and the results indicate one fairly narrow band (10 meV and below) and a second broad band (around hundred meV). The results imply that there are two relevant energy scales that need to be considered for the physics in this family of compounds.     

All-optical control of the time delay in a one-dimensional photonic bandgap formed by double-quantum-wells

In this work, we show the feasibility of all-optical control of time delay in a Bragg grating with an active defect that consists in an asymmetric double quantum-well GaAs/Al_xGa_1−xAs. The double quantum-well is modeled as a Λ-V-type four level system. The refractive index of the defect can be modified by a control field due to the tunneling-induced quantum interference. It is shown that index changes as large as 0.4 can be obtained via cross-phase modulation. This allows for the development of a propagating mode at the selected wavelength. The existence of the mode permits the slow-down of light pulses, thus the system may act as a delay line with a group index as high as 100 operating at bandwidths of tens of GHz. We demonstrate that this defective photonic bandgap structure could enable ultrafast and ultrasensitive nonlinear all-optical switching at moderate powers of the control field.     

Thermoelectric power in superlattices of nonparabolic semiconductors with graded interfaces under magnetic quantization

Summary We study the thermoelectric power of the electrons under magnetic quantization in III–V, II–VI, PbTe/PbSnTe and strained layer superlattices with graded interfaces and compare the same with the corresponding bulk specimens of the constituent materials by formulating the respective expressions incorporating the broadening. It is found, by taking GaAs/Ga_1−x Al _x As, CdS/CdTe, PbTe/PbSnTe and InAs/GaSb superlattices with graded interfaces as examples, that the thermoelectric power exhibits oscillatory dependence with the inverse quantizing magnetic field due to Shubnikov-de Hass effect and increases with decreasing electron concentration in an oscillatory manner in all the aforementioned cases. The thermopower in graded superlattices is greater than that of constituent bulk materials together with the fact that the oscillations in superlattices show up much more significantly as compared to the respective constituent materials. In addition, the well-known expressions for bulk specimens of wide-gap semiconductors have also been obtained as special cases from our generalized expressions under certain limiting conditions.