Electronic Subband Structure Research Articles

Electron subband structure and controlled valley splitting in silicon thin-body SOI FETs: Two-band k · p theory and beyond

We use a two-band k · p Hamiltonian to describe the subband structure in strained silicon thin films. The model describes the dependence of the transversal effective mass on strain and film thickness. However, it is found that the two-band k · p model is unable to describe recently observed large valley splitting. Therefore a generalization of the model is necessary. To go beyond the k · p theory, an auxiliary tight-binding model defined on a lattice of sites containing two localized orbitals is introduced in such a way that it reproduces the bulk dispersion obtained from the two-band k · p model. Corresponding dispersion relations including strain are obtained. We discuss an alternative mechanism to create and control the valley splitting by applying shear strain. The valley splitting increases with increased shear strain and decreasing film thickness and can be larger than the spin splitting. This makes silicon-based quantum devices promising for future applications in quantum computing.

Electron subband dispersions in ultra-thin silicon films from a two-band k⋅p theory

The electron subband structure in a thin (100) silicon film is analyzed based on a two-band k⋅p theory. For unprimed subbands the dependence of the nonparabolicity parameter on film thickness is obtained. The two-band k⋅p theory gives a thickness dependence of the effective masses for primed subbands. Limitations of the model are discussed. The importance of the nonparabolicity parameter dependence on the film thickness for transport is demonstrated.

Electron Raman scattering in semiconductor quantum wire in an external magneticfield

The differential cross-section for an electron Raman scattering process in a semiconductorquantum wire in the presence of an external magnetic field perpendicular to the plane ofconfinement is calculated. We assume a single parabolic conduction band. Theemission spectra for different scattering configurations and the selection rules forthe processes are studied. Singularities in the spectra are found and interpreted.The electron Raman scattering studied here can be used to provide directinformation about the electron band and subband structure of these confinementsystems. The magnetic field distribution is considered constant with valueB0 inside the wire and zero outside.

ELECTRON SUBBAND STRUCTURE AND MOBILITY TRENDS IN P-N DELTA-DOPED QUANTUM WELLS IN SI

We present the electronic spectrum of a n-type delta-doped quantum well in Si coupled to a p-type delta-doped barrier within the envelope function efiective mass approximation. We applied the Thomas-Fermi approximation to derive an analytical expression for the conflning potential, and thus, we obtain the electronic structure in a simple manner. We analyzed the electron subband structure varying the distance between the doping planes (l) as well as the impurity density in them (n2D; p2D). We also study the mobility trends through an empirical formula that is based on the electron levels, the electron wave functions and the Fermi level. We flnd a monotonic decrease in the mobility as the p-type barrier moves away from the n-type well, and optimum parameters, l = 70 and n2D = 5 £ 10 12 cm i2 and p2D = 5 £ 10 13 cm i2 , for maximum mobility.

Electronic subband structure of InAs/GaSb-based type II and broken-gap quantum well systems

We present a simple theoretical approach to calculate electronic subband structure in InAs/GaSb-based type II and broken-gap quantum well systems. The theoretical model is developed through solving self-consistently the Schrödinger equation for the eigenfunctions and eigenvalues coupled with the Poisson equation for the confinement potentials, in which the effects such as charge distribution and depletion are considered. In particular, we examine the effect of a GaSb cap layer on electronic properties of the quantum well systems in conjunction with experiments and experimental findings. The results obtained from the proposed self-consistent calculation can be used to understand important experimental findings and are in line with those measured experimentally.

Self-consistent electronic subband structure of undoped InAs/GaSb-based type II and broken-gap quantum well systems

Motivated by a very recent experimental work on investigating electronic properties of InAs/GaSb-based type II and broken-gap quantum well structures, in this article we present a simple and transparent theoretical approach to calculate electronic subband structure in such device systems. The theoretical model is developed on the basis of solving self-consistently the Schrödinger equation for the eigenfunctions and eigenvalues coupled with the Poisson equation for the confinement potentials, in which the effects such as charge distribution and depletion are considered. In particular, we examine the effect of a GaSb cap layer on electronic properties of the quantum well systems in conjunction with experiments and experimental findings. The results obtained from the proposed self-consistent calculation can be used to understand important experimental findings and are in line with those measured experimentally.

Erratum: Signatures of Discontinuity in the Exchange-Correlation Energy Functional Derived from the Subband Electronic Structure of Semiconductor Quantum Wells [Phys. Rev. Lett.98, 066806 (2007)

The discontinuous character of the exact exchange-correlation $(xc)$ energy functional of Density Functional Theory is shown to arise naturally in the subband spectra of semiconductor quantum wells. Using an \emph{ab-initio} $xc$ functional, including exchange exactly and correlation in an exact partial way, a discontinuity appears in the $xc$ potential, each time a subband becomes slightly occupied. Exchange and correlation give opposite contributions to the discontinuity, with correlation overcoming exchange. The jump in the intersubband energy is in excellent agreement with experimental data.

Subband structure and transport properties of two‐dimensional electron gas in Al x Ga 1–x N/GaN heterostructures

We report on Hall mobility and Shubnikov-de Haas (SdH) measurements of the two dimensional electron gas (2DEG) formed in a series of AlxGa1–xN/GaN heterostructures with different Al composition grown on sapphire substrates. In samples of x = 0.15 and 0.20, we found single periodical oscillations. In a sample of x = 0.30 a double periodical one was clearly resolved, which indicates that more than one subband has been occupied by electrons. Fast Fourier transform (FFT) analysis yielded information about the electron density and subband structure of the 2DEGs. The oscillatory part of the SdH signal was analyzed to extract the quantum scattering time at 4.2 K. It was found that as the increase of the Al content, quantum scattering time of the ground subband decreases gradually. We attributed it to the enhanced interface roughness scattering and the onset of the inter-subband scattering in the sample with higher Al content. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Signatures of Discontinuity in the Exchange-Correlation Energy Functional Derived from the Subband Electronic Structure of Semiconductor Quantum Wells

The discontinuous character of the exact-exchange-correlation (xc) energy functional of density functional theory is shown to arise naturally in the subband spectra of semiconductor quantum wells. Using an ab initio xc functional, including exchange exactly and correlation in an exact partial way, a discontinuity appears in the xc potential, each time a subband becomes slightly occupied. Exchange and correlation give opposite contributions to the discontinuity, with correlation overcoming exchange. The jump in the intersubband energy is in excellent agreement with experimental data.

Scanned electrical probe characterization of carrier transport behavior in InAs nanowires

Conductive atomic force microscopy combined with detailed calculations of electronic subband structure has been used to analyze electron transport behavior across the transition between ballistic and drift/diffusive motion in InAs nanowires grown by metal organic chemical vapor deposition. Using a conducting tip in an atomic force microscope as a local, positionable electrical probe, InAs nanowire resistance as a function of electron transport distance within the nanowire has been measured. For distance of ∼200nm or less, this resistance is observed to be nearly independent of distance, while for larger distances the resistance increases linearly with distance. Analytical calculations indicate that a resistance only weakly dependent on distance should be observed for distances up to a few times the electron mean free path, and calculations of the mean free path using a variety of approaches yield values in the range of ∼50nm, very consistent with the observation of distance-independent resistance for transport distances up to ∼200nm.

Terahertz electron distribution modulation in piezoelectricInxGa1−xN∕GaNmultiple quantum wells using coherent acoustic nanowaves

We observed ultrafast electron distribution modulation following the strain oscillation of coherent acoustic nanowaves up to a THz frequency range. Through piezoelectric effects, the acoustic nanowave modifies the electronic subband structure, and further modulates the energy distributions of electrons and holes. With amplitude-fixed acoustic waves, a pronounced enhancement of transmission modulation due to acoustic modulation of electron distribution was observed when the optically probed energy position is close to the Fermi level.

Effect of non-abrupt doping profiles on the carrier sheet density in one-side modulation-doped GaAs/AlGaAs quantum wells

A theoretical study on the influence of non-abrupt doping profiles on the electronic subband structure in one-side modulation-doped GaAs/AlGaAs quantum wells with graded interfaces is presented. Emphasis is given on the dependence of the carriers sheet density on both the spacer thickness and the donors diffusion length. A proper discretization method for solving the coupled Schrodinger and Poisson equations self-consistently over a nonuniform grid is proposed. This furnishes numerically stable results for the electron sheet density even when non-abrupt doping and heterointerface profiles are included in the model calculation. The depletion approximation is surpassed and a significant increase in the electron sheet density is obtained when non-abrupt doping profiles are taken into account. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of conduction-band nonparabolicity on electron confinement and effective mass inGaNxAs1−x∕GaAsquantum wells

We derive an analytical model to describe the conduction-band states of GaNAs-based quantum well structures, including the band anticrossing effect between N resonant states and the conduction-band edge. The predictions of the model are compared to those obtained using a full ten-band k·p model based on the same set of parameters. Both methods are then tested by comparison with the experimentally determined ground- and excited-state interband transition energies of GaNxAs1−x quantum wells of different well widths and N composition x obtained at 300 K and under hydrostatic pressures up to 2.0 GPa . We show that the transition energies can be described by a consistent set of material parameters in all the samples studied, and present how the conduction to valence-band offset ratio varies strongly with x in GaNxAs1−x∕GaAs quantum well structures. We conclude that the model presented can be used to predict the transition energies and electron subband structure of any GaNxAs1−x∕GaAs quantum well with well width between 2 and 25 nm , and N composition x between 1 and 4% , although further work is still required to confirm the optimum choice for the variation of band offset ratio with composition.

Atomic arrangements, electronic parameters, and electronic structures in modulation-doped Al xGa 1− xAs/In yGa 1− yAs/Al xGa 1− xAs step quantum wells

Strain effects and electronic parameters of delta-modulation-doped Al x Ga 1− x As/In y Ga 1− y As/Al x Ga 1− x As step quantum wells were investigated by high-resolution transmission electron microscopy (HRTEM) and Shubnikov-de Haas (S-dH) measurements. An atomic crystal structure for the quantum wells was described based on the HRTEM results, and the carrier density and the effective mass of the two-dimensional electron gas (2DEG) occupied in the In y Ga 1− y As quantum wells were determined from the S-dH data. The electronic parameters in delta-modulation-doped Al x Ga 1− x As/In y Ga 1− y As/Al x Ga 1− x As step quantum wells were compared with those in GaAs/In y Ga 1− y As/Al x Ga 1− x As step quantum well. The electronic subband structures in the quantum wells were calculated by a self-consistent method. The present results can help to improve the understanding of the microstructural and electronic properties in delta-modulation-doped Al x Ga 1− x As/In y Ga 1− y As/Al x Ga 1− x As step quantum wells.

Electronic parameters and electronic structures in modulation-doped highly strained In xGa 1− xAs/In yAl 1− yAs coupled double quantum wells

Electronic parameters of a two-dimensional electron gas (2DEG) in modulation-doped highly strained In x Ga 1− x As/In y Al 1− y As coupled double quantum wells were investigated by performing Shubnikov–de Haas (S–dH), Van der Pauw Hall-effect, and cyclotron resonance measurements. The S–dH measurements and the fast Fourier transformation results for the S–dH at 1.5 K indicated the electron occupation of two subbands in the quantum well. The electron effective masses of the 2DEG were determined from the cyclotron resonance measurements, and satisfied qualitatively the nonparabolicity effects in the quantum wells. The electronic subband structures were calculated by using a self-consistent method.

Spin-orbit-split subbands in IV-VI asymmetric quantum wells

Analytical solutions for the spin-orbit-split electron and hole subband structure in IV-VI lead-salt semiconductor asymmetric quantum wells (QW's) are obtained within the envelope function approximation and the Dimmock four-band $k\ensuremath{\cdot}p$ model for the bulk, around the four equivalent L points. Contrary to the III-V and II-VI QW's, the spin-orbit interaction in the these rocksalt QW's is purely Rashba, although multivalley and anisotropic. The Rashba splitting in these QW's is shown to be highly dependent on the structure parameters and can be much larger than those in similar III-V structures. In particular, specific results for the energy spectrum of ${\mathrm{Pb}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}\mathrm{Te}/\mathrm{PbTe}/{\mathrm{Pb}}_{1\ensuremath{-}y}{\mathrm{Eu}}_{y}\mathrm{Te}$ QW's show that the Rashba splitting is approximately linear (and changes sign) with $\ensuremath{\delta}Q,$ the difference between the band offsets at the two interfaces, independently of the valley and growth direction. The well width and ${k}_{\ensuremath{\Vert}}$ dependences of the Rashba splitting are also investigated, for the ground and excited states confined in IV-VI QW's, and experimental verification of the main predictions is discussed.

Anisotropic size quantization and semimetal–semiconductor phase transition in bismuth-like cylindrical nanowires

The electronic subband structure of carriers in bismuth-like cylindrical nanowires is investigated analytically, using an anisotropic effective mass model. Quantum confinement effects are found to be significantly enhanced over the results of a quasi-isotropic approach, due to the correct consideration of both the mass anisotropy and the boundary shape of the wire. The size quantization problem for a carrier with anisotropic effective mass parameters in a cylindrical well is shown to be equivalent to that of a carrier with some isotropic effective mass in an elliptical well. Detailed study of the energy levels reveals their orbital degeneracy is lifted by the elliptic symmetry, where the degree of ellipticity corresponds to the mass anisotropy. Carrier motion is analysed by analogy to the geometrical optics of elliptic waveguides, with bounding caustic curves defining two groups inside the wire that correspond to ‘whispering gallery’ and ‘jumping ball’ modes. The additional confinement, arising from the mass anisotropy, leads to larger critical wire diameters for the semimetal-to-semiconductor transition, which is investigated for wires of different crystallographic orientation.

High‐pressure photoluminescence study of the electronic structure of InP/GaP quantum dots

AbstractThe electronic subband structure of self‐assembled InP/GaP quantum dots (QDs) has been investigated by means of photoluminescence (PL) measurements as a function of hydrostatic pressure up to 8 GPa and temperature. At ambient pressure the PL emission of the sample arises from direct optical transitions between the lowest electron and hole Γ‐point states confined in the QDs. At a very low pressure of about 0.15 GPa, the Γ–X conduction band crossover occurs, after which the PL emission of the dots becomes roughly 20 times weaker in intensity and its energy exhibits the slight redshift typical of indirect recombination processes from the conduction band X valleys. Our results indicate a type‐I band alignment for the strained InP/GaP dot structure at low pressure and yield a value of 300 ± 30 meV for the valence‐band offset.

Population inversion in an optically pumped single quantum well

An optically pumped intersubband laser generator is proposed in which the continuum states above an Al0.2Ga0.8As–GaAs–Al0.2Ga0.8As single quantum well with a width of L=17 nm serve as the highest level in a four-level laser system. The design allows much greater flexibility in the choice of pumping source and simplifies considerably the device fabrication. We have obtained the electronic subband structure of the proposed device and utilized a simple rate equation approach to examine the electron density in different states under optical pumping.

Gas source molecular beam epitaxy of InP-based microstructures: material growth, characterization and device applications

InP epitaxial layers and InGaAs/InAlAs/InP modulation doped heterostructures were grown by gas source molecular beam epitaxy, in which arsenic and phosphorus beams were obtained by thermal cracking of AsH 3 and PH 3. High purity InP layers have been obtained by optimizing growth parameters. To identify the species of impurity and defect in high quality InP layers, low temperature photoluminescence (PL) and photothermal ionization spectroscopy measurements were carried out. The residual donors were determined to be silicon and sulfur. To obtain a deep insight to the electronic subband structure of the two-dimensional electron gas (2DEG) system, Shubnikov-de Haas, quantum Hall effect measurements and field-dependent cyclotron resonance measurements were conducted. The electron density on each subband in 2DEG was determined to be 2.84×10 12 and 3.4×10 11 cm −2, respectively. The effective masses of the two subbands are (0.061±0.001) m 0 for the zero subband and (0.049±0.001) m 0 for the first subband. An optoelectronic integrated circuit (OEIC) structure consisting of high electron mobility transistor (HEMT) and metal semiconductor metal photo detector (MSM-PD) was achieved by gas source molecular beam epitaxy with one growth run. The responsibility of MSM-PD is 0.5 A/ W. DC transconductance of an InGaAs/InAlAs HEMT with 1.5-μm gate length is 305 mS mm −1; the maximum saturation current is 350 mA mm −1 and the pinch-off voltage is −1.4 V. The gain of the HEMT amplifier is 14 dB. The integrated photoreceiver could successfully operate at a data rate of 622 Mbit s −1.