Electric Subbands Research Articles

Observation of ballistic transport in the upper subband of a two-dimensional electron system.

We report a specially designed transverse magnetic focusing experiment on a two-dimensional electron system confined to a square quantum well with two electric subbands occupied. The reflecting barrier of a usual magnetic focusing device is replaced by a surface-gate-induced, tunable potential barrier that allows us to selectively reflect and magnetically focus the upper subband electrons while the lower subband electrons pass over the barrier and are not focused. We observe the focusing of the upper subband electrons. The weakness of the focusing signal for the upper subband ballistic electrons suggests that they have a surprisingly short ballistic mean free path compared to the lower subband electrons.

Influence of light on the confinement potential of GaAs/AlxGa1-xAs heterojunctions.

The energy levels of confined subbands in very-high-mobility GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructures are experimentally determined using the resonant coupling between the electric subbands and Landau levels that occurs in tilted magnetic-field measurements. Theoretical subband energies are calculated self-consistently taking into account wave penetration into the barrier and exchange effects. A comparison between theory and experiment enables the shape of the confinement potential to be determined for these samples which are extensively used in studies of the fractional quantum Hall effect and possible Wigner crystallization. Illumination of the samples with light whose energy is greater than the band gap of the ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As is shown to dramatically affect the shape of the confinement potential and cause large reductions in carrier density for continuous illumination.

Magnetotransport and electric subband studies of Si-delta-doped Al0.27Ga0.73As/GaAs single quantum wells grown by metalorganic chemical vapour deposition

Shubnikov-de Haas and Van der Pauw Hall effect measurements at 1.5 K have been carried out to investigate the existence of a two-dimensional electron gas and to determine subband energies in an Si-delta-doped Al0.27Ga0.73As/GaAs single quantum well. Capacitance-voltage profiling measurements have been performed to characterize the properties of centre delta-doped Al0.27Ga0.73As/GaAs quantum wells. The subband energies, energy wavefunctions and subband carrier densities were determined using the experimental results and a self-consistent calculation taking into account the exchange correlation effects.

Energy-momentum relation for polarons in quantum-well wires

The interaction of quasi-one-dimensional electrons and longitudinal-optical (LO) phonons is calculated. Results are presented for the polaron correction to the electric subbands and the polaron effective mass. Using improved Wigner-Brillouin perturbation theory, we have investigated in detail the energy-momentum relation for quasi-one-dimensional polarons. It is shown that the dispersion curves of all subbands bend over and are pinned at the phonon continuum above the renormalized ground state. This should result in a spatial oscillation of the electron group velocity in real quantum-well wires.

Energy-dependant cyclotron mass in InAs/AlSb quantum wells

The influence of conduction band non-parabolicity on the cyclotron resonance of a two-dimensional electron system in InAs quantum wells is investigated. We demonstrate that the experimentally determined dependence of the cyclotron mass on the carrier density in the well can be excellently described using a two-band k.p model. In contrast to previously studied systems our experimental results allow us to deduce quantitatively the quantization energy of the first electrical subband for wells of different width.

Low-temperature carrier distributions in wide quantum wells of different shapes from capacitance-voltage measurements

The carrier distributions in modulation-doped wide graded quantum wells that a measurement of the capacitance C between a surface gate and an ohmic contact to the carriers as a function of the applied bias V would yield are calculated. These capacitance-voltage (C-V) distributions are found to agree inexactly, but closely, with the calculated true carrier distributions. Density modulation features, induced by superlattices or by abrupt changes in the curvature of band-gap grading, are strikingly reproduced. Electron distributions extracted from actual measurements on a wide parabolic well and on a parabolic well with superimposed superlattice are in good agreement with theory. For the case of the parabolic well, the occupancy of a finite number of subbands is manifested as structure in the C-V distributions. This technique is relevant to the measurement of carrier distributions in any wide carrier system with more than one electric subband occupied.

Determination of the basic parameters of pseudomorphic GaInAs quantum wells by means of simultaneous transport and optical investigations

Combined studies of GaAlAs/GaInAs/GaAs pseudomorphic structures have been performed by means of transport under hydrostatic pressure, luminescence and cyclotron resonance emission experiments. The structures investigated were 130 Å quantum wells. They were δ-doped outside of the quantum well, with the spacer thickness ranging between 20 and 60 Å. These structures allowed us to study the influence of the carrier density N s on mobility and on the position of the Fermi level E F above the first electrical sub-hand E 0. By using pressure and illumination, we changed N s from 0.5 to 1.8 × 10 12 cm −2. In this range, only the first electric sub-band is populated. A strong decrease of mobility at higher concentrations was shown and depended essentially on correlation effects. High magnetic field transport measurements confirmed that only the lowest sub-band was populated. Moreover, cyclotron resonance emission gave the effective mass as a function of the carrier density in the well. On this basis, the importance of the non parabolicity effect was estimated. All these results were interpreted within the framework of the variational method leading to a determination of the most important physical parameters describing this system.

Electronic and optical properties of PbTe/Pb1-xEuxTe multiple-quantum-well structures.

The frequency dependence of the absorption constant \ensuremath{\alpha}(\ensuremath{\omega}) and the enhancement of the refractive index n(\ensuremath{\omega}) in the region of interband transitions between confined quasi-two-dimensional states of the valence and conduction bands of PbTe/${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Eu}}_{\mathit{x}}$Te multiple-quantum-well (MQW) structures is studied experimentally as well as theoretically. Transmission, reflectivity, and photoconductivity spectra of several MQW's with PbTe well widths from 62 to 118 \AA{} and ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Eu}}_{\mathit{x}}$Te barrier widths from 486 to 621 \AA{} (x\ensuremath{\approxeq}3%) are compared with calculated spectra. The experimental data are compared to calculations of the transmission and reflectivity of the multilayer structures based on frequency-dependent dielectric functions \ensuremath{\epsilon}(\ensuremath{\omega}) of the buffer and MQW layers. For the buffer layer experimentally determined values for \ensuremath{\epsilon}(\ensuremath{\omega}) are used, whereas for the MQW system the sum of a background dielectric function and an additional term, which takes into account the electronic contribution due to interband transitions between electric subbands in the valence band (VB) and conduction band (CB), are used.For calculating the second term two approaches were followed. The conventional approach is based on treating these interband transitions as originating from confined states within the PbTe wells only. The second, more realistic, approach is based on a complete calculation of the band structure of the MQW systems using a k\ensuremath{\cdot}p envelope function approximation which yields proper energy eigenstates, eigenfunctions, and oscillator strengths. The absorption constant \ensuremath{\alpha}(\ensuremath{\omega}) is then obtained from an integration in k space. The electronic contribution \ensuremath{\delta}${\mathrm{\ensuremath{\epsilon}}}^{\mathrm{VB}\mathrm{\ensuremath{-}}\mathrm{CB}}$(\ensuremath{\omega}) to the total dielectric function is independent of the position z along the growth direction in the MQW structure, i.e., in this respect the MQW is treated as being optically homogeneous. The calculated transmission and reflectivity data fit the experimental data very well. The steplike changes in \ensuremath{\alpha}(\ensuremath{\omega}) result in cusplike changes of the refractive index n(\ensuremath{\omega}). From a comparison of the experimentally determined interband transition energies with the calculated values on several samples, the conduction-band offset is determined to be \ensuremath{\Delta}${\mathit{E}}_{\mathit{c}}$/\ensuremath{\Delta}${\mathit{E}}_{\mathit{g}}$=0.55\ifmmode\pm\else\textpm\fi{}0.2.

Infrared-Photoconductivity Due to Sub-Band Transitions in PbTe/Pb1−xEuxTe and PbSe/Pb1−xMnxSe

AbstractThe photoconductive (PC) properties of MBE grown PbTe/Pb1−xEuxTe (x<6.7%) and of PbSe/Pb1−xMnxSe (x<3%) multi quantum (MQW) well samples were investigated in the midinfrared region from 100 meV to 500 meV in the temperature range from 5 K up to 210 K. Whereas in PbTe/Pb1−xEuxTe MQW's electrons and holes are confined in the PbTe layers, PbSe/Pb1−xMnxSe forms a staggered system with electrons confined in the PbSe/Pb1−xMnxSe layers and holes confined in the PbSe layers. Consequently, the transitions between electric subbands in the PbTe/Pb1−xEuxTe MQW's give rise to a step like increase of the PC signal whenever the photon energy hv coincides with the interband transition energies between hole and electron subbands (selection rule Δn = 0). For the range of well widths investigated (42 Å to 91 Å ) distinctive steps in the photoconductivity spectra were observed. In the PbSe/Pb1−xMnxSe MQW's the absorption signals show a typical type II superlattice (SL) behaviour and thus the photoconductivity response is also much weaker than for the PbTe/Pb1−xEuxTe MQW's.

On the absorption of infrared radiation by electrons in semiconductor inversion layers

Resonances in the inversion layer for infrared fields normal to the interface do not occur at the electric subband splittings. They are shifted from the subband splittings by resonant screening of the infrared field. The corrections for (100) Si surfaces are shown to be comparable to the shifts ascribed to many-body effects.

Heavily accumulated surfaces of mercury cadmium telluride detectors: Theory and experiment

Some processes used to passivate n-type mercury cadmium telluride photoconductive infrared detectors produce electron accumulation layers at the surfaces, which result in 2D electron gases. The dispersion relations for the electric subbands that occur in these layers have been calculated from first principles. Poisson's equation for the built-in potential and Schroedinger's equation for the eigenstates have been solved self-consistently. The cyclotron effective masses and Fermi energies have been computed for each subband density for 12 total densities between 0.1 to 5.0×1012 cm−2. The agreement with Shubnikov-de Haas measurements is very good at lower densities with possible improvement if band-gap narrowing effects were to be included. At higher densities, larger differences occur. The simple 2D description is shown to break down as the density increases because the wave functions of the conduction and valence bands cannot be well separated by the narrow band gap of long-wavelength detectors. These results provide a basis for characterizing the passivation processes, which greatly affect device performance.

Electrophonon resonances in a quasi-two-dimensional electron system.

When the energy difference between two electric subbands in a quasi-two-dimensional electron system equals a LO-phonon energy, resonant scattering will occur. This leads to an enhancement of the scattering rate and, consequently, to a suppression of the conductivity. Changing the energy difference between the electric subbands (e.g., through a gate) leads to a series of electrophonon resonances in the conductivity. A detailed study is made of this effect for different confinement potentials. We found that the scattering processes where the emission of a phonon is involved are very important for the electrophonon resonance and that the size of the effect decreases with increasing temperature.

Normal and hot electro-phonon resonance effect in a quasi-two-dimensional semiconductor system

The electro-phonon resonance effect is a consequence of a resonant interaction between two electric subbands mediated by an optical phonon. It occurs in a quasi-two-dimensional electron system each time the energy difference between two electric subbands equals the energy of a LO phonon. The authors study the influence of this effect on the electron mobility by using the momentum balance equation. The temperature and electron density dependences of the resonances are studied in the linear and non-linear response regimes.

Probing the subband structure of a wide electron system in a parabolic quantum well via capacitance-voltage measurements.

Low-temperature capacitance-voltage measurements in an electron system realized in a remotely doped, wide AlGaAs parabolic quantum well show small (\ensuremath{\sim}1%) capacitance steps whose positions coincide with the calculated and independently measured front gate voltages at which the electric subbands are depopulated. The step positions respond to an applied in-plane magnetic field or a back-gate bias, in a manner consistent with the magnetic or electric depopulation of the subbands, respectively. We conclude that these steps are indeed related to the subband structure of the electron system.

Magnetotransport measurements and electric subbands in an Al x Ga1?x As(x= 0.3)/GaAs one-side-modulation-doped quantum well

Magnetotransport measurements and electric subbands in an Al x Ga1?x As(x= 0.3)/GaAs one-side-modulation-doped quantum well

Electric subband studies in an In 0.53Ga 0.47As/InP one-side-modulation-doped quantum well

Shubnikov-de Haas and Van der Pauw Hall-effect measurements on In 0.53Ga 0.47As/InP one-side-modulation-doped quantum wells grown by metalorganic chemical vapor deposition have been carried out to investigate the magnetotransport properties of an electron gas and to determine the subband energies and wave functions in a single quantum well. The Shubnikov-de Haas measurements have demonstrated the existence of a two dimensional electron gas in the In 0.53Ga 0.47As potential well. The electric subband energies, energy wavefunctions, and subband carrier densities were determined using the experimental results and a self-consistent method by taking into account the exchange-correlation effects.

Electric subbands in Si-delta-doped GaAs grown by metalorganic chemical vapor deposition

Shubnikov-de Haas and Van der Pauw Hall effect measurements at 1.5 K have been carried out to investigate the existence of a two-dimensional electron gas and to determine subband energies in Si-delta-doped GaAs grown by atmospheric pressure metalorganic chemical vapor deposition. The Shubnikov-de Haas measurements clearly show multiple oscillation periods, which vary dramatically with the angle between the magnetic field and the normal to the sample surface, indicative of the occupation of several subbands by quasi-two-dimensional electrons in a potential well. With the magnetic field in the plane of the interface, magnetoresistance oscillations are also clearly observed that are not periodic in the reciprocal of the magnetic field. Using these experimental results and a self-consistent numerical method which took into account the exchange-correlation effects, the electrical subband energies were also determined.

Electric subbands in a strained InAs0.6P0.4/InP single quantum well

Shubnikov-de Haas and Van der Pauw Hall effect measurements on strained InAs0.6P0.4/InP one-side-modulation-doped quantum wells grown by metalorganic chemical vapour deposition have been performed in order to investigate the properties of an electron gas in an InAs0.6P0.4 single quantum well. Hall effect measurements showed that the mobility and the carrier concentration were 40800 cm2 V-1 s-1 and 1.43*1012 cm-2 at 1.5 K, respectively. The Shubnikov-de Haas measurements and fast-Fourier analyses clearly showed an oscillation frequency, which changes with the angle between the magnetic field and the surface normal, indicative of the occupation of the InAs0.6P0.4 potential well by two-dimensional electrons. The subband energies and energy wavefunctions were determined using the experimental results and a self-consistent method taking into account the exchange-correlation effects.

Magneto-optical studies of screened excitons in GaAs/AlxGa1-xAs modulation-doped quantum wells.

Asymmetric GaAs/Al x Ga 1-x As quantum wells were studied by photoconductivity and photoluminescence in magnetic fields up to 15 T. The sample chosen had only one occupied electric subband, with a high density of 8.2×10 12 cm -2 , which allowed a study of the empty E2-H1 transitions by photoconductivity. This showed that there was a small but finite binding energy of 1.5±0.5 meV for the 1s state, which increased very rapidly at high fields in agreement with theory, due to the changing effects of the screening on the exciton

Electric subbands in a both-side-modulation-doped In0.52Al0.48As/In0.65Ga0.35As single quantum well

Shubnikov-de Haas and Van der Pauw Hall effect measurements on an In0.52Al0.48As/In0.65Ga0.35As lattice-mismatched single quantum well grown by molecular beam epitaxy have been carried out to investigate the electrical properties of an electron gas and subband energies in a unique potential well. The measurements at 1.5 K have demonstrated clearly the existence of a quasi-two-dimensional electron gas in the quantum well. It is found that three subbands in the quantum well are occupied. Electron energy subbands in the quantum well were calculated by a self-consistent method taking into account exchange-correlation effects and making use of the experimentally determined carrier density.