Subband Energy Separation Research Articles

Unusual energy separation of subbands in Si(111) p-channels induced by In adsorption

We investigated the dispersion structure of the hole subbands in vicinal Si(111)4 × 1-In surfaces directly by angle-resolved photoelectron spectroscopy. In this study, three inversion layers with different impurity concentrations and numbers of times of flash annealing (FA) were investigated. We observed wider energy separations of subbands levels for the sample with a less number of FA and a higher impurity concentration. However, the observed energy levels and separations had smaller binding energy than those calculated by triangle potential approximation. We found that the discrepancies were due to the out-diffusion of Arsenic atoms from the sub-surface region of silicon via high temperature FA. The possible potential profile of the space charge layer after considering the out-diffusion of Arsenic dopant atoms at the sub-surface region was proposed.

Combined effect of electron and lattice temperatures on the long intersubband relaxation times of Ge/SixGe1−xquantum wells

In this paper, we have experimentally and numerically studied the nonradiative intersubband (ISB) relaxation in $n$-type Ge/SiGe quantum well (QW) systems. Relaxation times have been probed by means of pump-probe experiments. An energy balance model has been used to interpret the experimental differential transmission spectra and to assess the relevance in the nonradiative relaxation dynamics of both electron and lattice temperature as well as of the carrier density. The comparison between experimental data and theoretical simulation allowed us to calibrate the interaction parameters which describe the electron-optical phonon scattering in two-dimensional (2D) Ge systems. Characteristic relaxation times has been calculated and compared with those of GaAs QWs as a function of the 2D electron density, of the subband energy separation, and of the lattice and electronic temperature. We found that ISB relaxation times for the Ge/SiGe systems are generally shorter than that previously calculated when the electron distribution was neglected. Nonetheless, our main result is that the relaxation time in Ge/SiGe QW systems is longer than 10 ps, also for transition energies above the Ge optical phonon energy, up to 300 K. Furthermore, we obtained that the relaxation times are at least one order of magnitude longer than in GaAs-based systems.

Tailoring electron–phonon interaction in nanostructures

Efficient design of optoelectronic devices based on electron intersubband transitions depends critically on the knowledge of the intersubband relaxation times which in turn, depends on electron scattering with LO and acoustic phonons. In this article the intersubband scattering time associated with electron–acoustic-phonon interaction has been discussed in terms of phonon mode quantization and phonon confinement with describing the acoustic phonon dispersion relation in detail by introducing the cut-off frequency for each mode. It has been shown that the quantization of acoustic phonon modes lead to an enhancement in electron–phonon scattering time in AlGaAs quantum well structures. Based on the presented model, a new tailoring method has presented to adjust the electron–phonon scattering time in intersubband-transition-based structures while keeping the electronic properties unaltered. Also, we illustrated that for a quantum well with subband energy separation of ∼30meV, the intersubband scattering time with acoustic-phonon-assisted transitions could be tailored from ∼120ps to increased value of ∼400ps or reduced value of ∼45ps by inserting a 1nm-thickacoustically soft or hard layers, respectively, while keeping the same the initial energy separation.

Local Carrier Recovery Acceleration in Quantum Well Semiconductor Optical Amplifiers

Based on the concept of local carrier density, intraband carrier dynamic characteristics of quantum well (QW) semiconductor optical amplifiers (SOAs) are theoretically investigated. In our numerical model, electron energy relaxation processes via electron-polar optical phonon interactions are also calculated. It is found that, the electron wave function and the subband energy separation have significant effects on electron energy relaxation rate, especially when the subband energy separation between state |1 〉 and |2 〉 is nearly the same as the longitudinal optical phonon energy, the electron energy relaxation rate in SOAs can be maximized. Finally, for comparison, we analyze the intraband effects in three different SOA samples. The effects of QW designs of SOAs on local carrier density recovery time have been discussed. The recovery time can be reduced to 700 fs from 1.5 ps when the optimized SOA sample is chosen.

Quantum transport in graphene nanoribbons patterned by metal masks

Graphene nanoribbons (GNRs) were fabricated by metal mask lithography and plasma etching. GNRs with width ∼20 nm show field-effect conductance modulation of ∼12 at room temperature and >106 at 4.2 K. Conductance quantization due to quantum confinement in low field transport was observed. Landauer formula was utilized to fit the experimental data and excellent agreement was obtained. The extracted subband energy separation was found to deviate from the predicted values of perfect armchair GNRs. Transmission probability is much smaller than unity due to scattering by GNR edge/bulk disorder and impurities, indicating a mean free path ∼40 nm. High field family I-Vs exhibited current saturation tendency and current density as high as 2 A/mm has been measured at low temperature.

Effect of electron-electron scattering on magnetointersubband resistance oscillations of two-dimensional electrons in GaAs quantum wells

The low-temperature $(4.2lTl12.5\text{ }\text{K})$ magnetotransport $(Bl2\text{ }\text{T})$ of two-dimensional electrons occupying two subbands (with energy ${E}_{1}$ and ${E}_{2}$) is investigated in GaAs single quantum well with AlAs/GaAs superlattice barriers. Two series of Shubnikov-de Haas oscillations are found to be accompanied by magnetointersubband (MIS) oscillations, periodic in the inverse magnetic field. The period of the MIS oscillations obeys condition ${\ensuremath{\Delta}}_{12}=({E}_{2}\ensuremath{-}{E}_{1})=k\ensuremath{\cdot}\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$, where ${\ensuremath{\Delta}}_{12}$ is the subband energy separation, ${\ensuremath{\omega}}_{c}$ is the cyclotron frequency, and $k$ is the positive integer. At $T=4.2\text{ }\text{K}$ the oscillations manifest themselves up to $k=100$. Strong temperature suppression of the magnetointersubband oscillations is observed. We show that the suppression is a result of electron-electron scattering. Our results are in good agreement with recent experiments, indicating that the sensitivity to electron-electron interaction is the fundamental property of magnetoresistance oscillations, originating from the second-order Dingle factor.

Two-subband-populated AlGaN∕GaN heterostructures probed by electrically detected and microwave-modulated magnetotransport measurements

The authors apply the microwave-modulated technique to study the transport properties of two-subband-populated AlGaN∕GaN heterostructures. The microwave modulation enhances the small Shubnikov–de Haas oscillations at low magnetic fields, providing a direct way to compare the mobilities of different subbands from the experimental data. In addition, this technique can help us to determine the subband-energy separation, especially when the population of the second subband is much lower than that of the first one. Variation of subband-energy separation due to different spacer thicknesses is obtained. Therefore, the authors showed a powerful way to probe parameters of two-subband-populated AlGaN∕GaN heterostructures.

Electronic transport characteristics in a one-dimensional constriction defined by a triple-gate structure

We investigate the electronic transport characteristics of a one-dimensional (1D) narrow constriction defined in a GaAs∕AlxGa1−xAs heterostructure by a simple triple-gate structure consisting of a pair of split gates and an additional surface Schottky gate (center gate) between them. Comparison between devices with and without a center gate reveals that the center gate, even when zero biased (VCG=0V), significantly modifies the surface potential and facilitates the 1D confinement in a deep two-dimensional electron system. The pinch-off voltages at VCG=0V for various channel widths W (=0.4–0.8μm) and lengths L (=0.2–2μm) are well described by the analytical formula based on the pinned-surface model [J. H. Davies et al., J. Appl. Phys. 77, 4504 (1995)]. Nonlinear transport spectroscopy with an additional dc bias shows that the lowest 1D subband energy separation (ΔE1,2) changes linearly with VCG and can be enhanced by 70% for VCG=0.8V. A simple model assuming an infinitely long channel and no self-consistent potential well reproduces the overall behavior of the measured ΔE1,2. In addition, effects of impurities, occasionally found for long-channel devices (L⩾1μm), are found to be greatly reduced by applying positive VCG and thereby enhancing ΔE1,2. Data are also presented for the transport anomaly below the first conductance plateau, the so-called “0.7 anomaly,” demonstrating that the triple-gate structure is useful for the study of density-dependent phenomena in a 1D system.

Design of a GaN∕AlGaN intersubband Raman laser electrically tunable over the 3–5μm atmospheric transmission window

Design results aimed at achieving tunable high-temperature operation in the 3–5μm atmospheric transmission window are presented for the intersubband Raman lasers based on GaN∕AlGaN coupled quantum wells. The ultrafast longitudinal-optical-phonon (LO-phonon) scattering in GaN∕AlGaN quantum wells (QWs) can be used for the rapid depopulation of the lower laser state, while the large LO-phonon energies (∼90meV) allow for a design to minimize the thermal population of the lower laser state, and are therefore beneficial for obtaining high-temperature operation. The Raman gain is proportional to the difference between the virtual lifetime of the upper laser state and the effective lifetime of the lower laser state instead of the real lifetimes. The advantage is that these lifetimes can be tuned with the detuning of the pump photon energy from the subband energy separation. At a fixed pumping wavelength of 2.7μm, the tuning range of 3.6–5.2μm is predicted with a moderate Raman gain of at least 100∕cm as the electric field is varied. Furthermore, the output power of this laser is unlikely to saturate because of the intrinsically short intersubband lifetimes in the GaN-based QWs.

Dual-gate GaAs/AlGaAs quantum point contact with tuneable subband energy separation

A quantum point contact is formed whose confining potential is controlled in addition to the electron density. Split-gate contacts are etched from a highly p-type doped epitaxial GaAs surface layer, and a Schottky-type top and centre gate is inserted using a thin calixarene resist layer as insulator. In this way, the energy separation between the lowest one-dimensional subbands can be tuned from 5.5 to 10 meV.

Observation of capacitance?voltage oscillations in porous silicon

This paper presents the experimental observation of room temperature capacitance–voltage oscillations in porous silicon (PS). Analysis of the experimental data suggests density-of-states discontinuities in the PS nanostructures to be the likely origins of the oscillations. From the experimental data, a sub-band energy separation of 0.19 eV is estimated for the dominant silicon nanostructures. This corresponds to a nanostructure dimension of approximately 3 nm , which agrees well with the value expected for the PS fabrication conditions.

Observation of capacitance–voltage oscillations in porous silicon

This paper presents the experimental observation of room temperature capacitance–voltage oscillations in porous silicon (PS). Analysis of the experimental data suggests density-of-states discontinuities in the PS nanostructures to be the likely origins of the oscillations. From the experimental data, a sub-band energy separation of 0.19 eV is estimated for the dominant silicon nanostructures. This corresponds to a nanostructure dimension of approximately 3 nm , which agrees well with the value expected for the PS fabrication conditions.

Optimized energy separation for phonon scattering in three-level terahertz intersubband lasers

We examine the impact of the complex phonon spectrum on the design rules for three-level THz intersubband emitters that utilize resonant optical phonon scattering to obtain intersubband population inversion. In GaAs/AlxGa1−xAs multiple quantum wells, electron–optical phonon scattering occurs due to interaction with “GaAs-like” modes at ℏωLO∼36 meV and “AlAs-like” modes at ℏωLO∼47 meV. Scattering rates are calculated for interface and confined phonon modes to determine the optimal subband energy separations for enhancement of fast depopulation scattering and reduction of parasitic nonradiative scattering. While the results depend sensitively on details of the structure, we find that, for electrically pumped THz lasers, there is not an overwhelming advantage in increasing the subband separation to allow scattering by the higher energy modes. © 2001 American Institute of Physics.

Optical and transport studies of hot electrons in modulation-doped quantum wires

We describe recent progress in producing quantum wires by modulation-doping v-groove structures. Strong lateral confinement is observed, with subband energy separation of 40 meV. The high quality 1D electron system shows pronounced singularities in the photoluminescence spectrum near the Fermi energy. Energy relaxation has been investigated by electrical heating, where we find clear evidence of LO-phonon scattering and real space transfer. Time-resolved photoluminescence reveals intersubband relaxation within the 1D levels.

Influence of effective mass and energy band splittings on the radiative characteristics of QW lasers at transparency

The effect of degenerate light- and heavy-hole bands on the carrier and current density and the differential gain are studied and compared with the nondegenerate case in semiconductor quantum-well (QW) lasers. It is demonstrated that the presence of the degenerate bands at the valence band (VB) maximum will always lead to an increased threshold radiative current density compared to the case where only one band is significantly populated. When the valence bands are separated by an energy E s, the current density decreases rapidly with increasing E s, with greater reductions being achieved for a given tensile than compressive strain. The effect of the second subband becomes less important with increasing E s, and the radiative current density reverts to that of the one VB case, demonstrating the importance of maximising the subband energy separation to optimize laser characteristics.

Many-body optical gain of wurtzite GaN-based quantum-well lasers and comparison with experiment

The optical gain of wurtzite InxGa1−xN/In0.02Ga0.98N and GaN/AlxGa1−xN quantum well (QW) lasers taking into account many-body effects is investigated. The valence band structures are calculated as a function of strain and well thickness. The inclusion of compressive strain shows better lasing performance because of the increase of the subband energy separation in the valence band. Our theoretical gain spectra of In0.15Ga0.85N/In0.02Ga0.98N QW lasers are in good agreement with measured ones reported by Nakamura, IEEE J. Sel. Top. Quantum Electron. 3, 712 (1997). It is also shown that there is a universal relation governing the dependence of the band-gap renormalization on the two-dimensional carrier density for GaN-based QW lasers as there is for the infrared III-V systems.

Quantum transport in a Schottky in-plane-gate controlled GaAs/AlGaAs quantum well wires

Transport properties of a novel GaAs/AlGaAs quantum well wires (QWWs) with Schottky in-plane gates were investigated. The QWW was realized by a combination of a electron beam lithography and the in situ electrochemical technology. Clear quantized conductance in units of 2 e 2/ h was observed up to 100 K. Nonlinearities are found in the current-voltage characteristics at a small applied voltage, resulting in conductance deviation from the value of the quantized conductance. From the breakdown voltage of conductance quantization, a subband energy separation is estimated to be 10 meV or higher.

Electrical transport properties and confinement potential analysis of buried AlGaAs/GaAs quantum wires

Buried wires with lateral potential barriers provided by AlGaAs/GaAs heterointerfaces have been fabricated by wet etching and metalorganic chemical vapor deposition regrowth. Burying the wire was proven to enhance the electrical transport properties; for example, it decreased the critical width and increased the subband energy separation. Two-dimensional simulation using the Poisson equation was performed to obtain the potential profile of both as-etched and buried wires. The quantum energy levels corresponding to the lateral confinement were calculated for the obtained potential profiles. The calculated energy separations agreed well with the experimental ones and the subband energy separation of the buried wire was larger than that of the as-etched wire for the same effective width. These results show that burying wire is effective for creating strong lateral confinement.

Origin of the nu =1/2 fractional quantum Hall state in wide single quantum wells.

We study the effect of subband energy separation and asymmetry on the quasiparticle excitation gaps of the \ensuremath{\nu}=1/2 and coexisting fractional quantum Hall (FQH) states in wide single quantum wells. A new even-denominator FQH state at \ensuremath{\nu}=3/2 and a dramatic subband-mixing-driven phase transition from a one- to two-component FQH state at \ensuremath{\nu}=2/3 are observed. Our results reveal the two-component origin of the \ensuremath{\nu}=1/2 FQH state, and allow us to construct an experimental phase diagram for electron states at half filling.

Transport Properties of Buried AlGaAs/GaAs Quantum Wires

Buried wires with lateral interfaces consisting of AlGaAs/GaAs heterointerfaces are fabricated using wet etching and regrowth by MOCVD. The critical width of the buried wires was decreased to 0.1 µm, which was less than third of that of as-etched wires. The energy separation of one-dimensional subbands obtained from the Landau plots of Shubnikov-de Haas oscillations for the buried wires was increased to 2.8 meV, which was about two and half times larger than that of the as-etched wire. These results show that the buried quantum wire structure improves electrical transport properties.