One-band Effective-mass Approximation Research Articles

A study on the electronic properties of A site and B site doped SrTiO3 for thermoelectric applications using first-principles calculations

In SrTiO3, the nature of dopants and their substitution at the A or B site becomes a critical factor in determining the electrical conductivity, Seebeck coefficient, and thermal conductivity. The electronic band structure and the density of states (DOS) for the ab-initio study using different dopants were estimated using PBE-GGA approximation. The size, site of substitution, and nature of dopants cause significant changes in the lattice dimensions, band structure, band curvatures, and the density of states, which reflect as changes in the effective mass The effective mass is calculated from the curvature of the bottom-most conduction band using the one-band effective mass approximation. Pentavalent substitutions on the B site of SrTiO3 affect the conduction band’s curvature differently than with trivalent substitutions on the A site. They also exhibit an opposite trend in the change in band curvature according to the dopant’s ionic radius. In contrast, isovalent dopants showed no change in the band curvature except for the bandgap modification. In this paper, we have provided a semi-quantitative understanding regarding the thermoelectric properties like conductivity and Seebeck coefficient that get affected due to the substituent’s nature and site at which it substitutes.

Effect of conduction band nonparabolicity on Aharonov-Bohm oscillations in n-type InAs/GaAs quantum ring

We study the effect of nonparabolicity of the conduction band on the energy spectrum of the off-axis donors in InAs crater-like quantum rings in framework of the Kane Hamiltonian. By using ta simple numerical procedure we find the low-lying energies dependencies on the radius, height and width of the ring and on the distance of the donor location from the axis. The comparison of our results with those obtained in one-band effective mass approximation reveals an essential influence of the non-parabolicity of the conduction band on the off-axis energy spectra in InAs/GaAs quantum rings. In addition, we analyse the effect of the external magnetic field applied along the symmetry axis on the Aharonov-Bohm oscillations of lower energy levels.

The effect of density-of-state tails on band-to-band tunneling: Theory and application to tunnel field effect transistors

It is demonstrated how band tail states in the semiconductor influence the performance of a Tunnel Field Effect Transistor (TFET). As a consequence of the smoothened density of states (DOS) around the band edges, the energetic overlap of conduction and valence band states occurs gradually at the onset of band-to-band tunneling (BTBT), thus degrading the sub-threshold swing (SS) of the TFET. The effect of the band tail states on the current-voltage characteristics is modelled quantum-mechanically based on the idea of zero-phonon trap-assisted tunneling between band and tail states. The latter are assumed to arise from a 3-dimensional pseudo-delta potential proposed by Vinogradov [1]. This model potential allows the derivation of analytical expressions for the generation rate covering the whole range from very strong to very weak localization of the tail states. Comparison with direct BTBT in the one-band effective mass approximation reveals the essential features of tail-to-band tunneling. Furthermore, an analytical solution for the problem of tunneling from continuum states of the disturbed DOS to states in the opposite band is found, and the differences to direct BTBT are worked out. Based on the analytical expressions, a semi-classical model is implemented in a commercial device simulator which involves numerical integration along the tunnel paths. The impact of the tail states on the device performance is analyzed for a nanowire Gate-All-Around TFET. The simulations show that tail states notably impact the transfer characteristics of a TFET. It is found that exponentially decaying band tails result in a stronger degradation of the SS than tail states with a Gaussian decay of their density. The developed model allows more realistic simulations of TFETs including their non-idealities.

Transverse laser dressing effects on the subband density of states in a 20-nm-wide GaAs/Al0.3Ga0.7As quantum well wire

The electronic subband structure of a relatively thick cylindrical quantum well wire irradiated by a non-resonant laser field is calculated within the one-band effective-mass approximation by using a finite element method. For the first time, the problem is solved for a large number of transverse electron modes in the wire. Exact laser-dressing effects on the lateral confinement potential are considered by using an analytical function. Important changes of the electron localization probability under intense laser field are described. The study reveals a competition between the quantum confinement and the laser field which breaks down the cylindrical symmetry of the wire and splits the degenerate electronic levels. A proper analysis of these results is accomplished by calculating the density of states function. Our central prediction is the non-uniform blueshift of the conduction subband structure which may be valuable for an active control of the optoelectronic properties related to intersubband and interband transitions in semiconductor quantum wires.

Direct tunneling hole currents through ultrathin gate oxides in metal-oxide-semiconductor devices

We present a physical model to calculate the direct tunneling hole current through ultrathin gate oxides from the inversion layer of metal–oxide–semiconductor field-effect transistors. A parametric self-consistency method utilizing the triangular well approximation is used for the electrostatics of the inversion layer. For hole quantization in the inversion layer, an improved one-band effective mass approximation, which is a good approximation to the rigorous six-band effective mass theory, is used to account for the band-mixing effect. The tunneling probability is calculated by a modified Wentzel–Kramers–Brilliouin (WKB) approximation, which takes the reflections near the Si/SiO2 interfaces into account. It is found that the parabolic dispersion in the SiO2 band gap used in the WKB approximation is only applicable for hole tunneling in oxides thinner than about 2 nm and for low gate voltage. A more reasonable Freeman–Dahlke hole dispersion form with significantly improved fitting to all experimental data for different oxide thickness and gate voltage range is adopted and discussed.

Modeling and characterization of direct tunneling hole current through ultrathin gate oxide in p-metal–oxide–semiconductor field-effect transistors

We report the calculation of hole direct tunneling (DT) current from the inversion layer in a p-metal–oxide–semiconductor field-effect transistor based on a solid physical background. Our results are in good agreement with those obtained from carrier separation measurements over a wide range of oxide thicknesses in the ultrathin regime. The effect of valence band mixing on hole quantization in an inversion layer in a Si substrate is properly accounted for by an improved one-band effective mass approximation. A modified Wentzel–Kramers–Brillouin approximation to calculate the hole transmission probability is used by adopting a more accurate dispersion equation in the oxide gap. Our method is general, simple, and computationally efficient. It may even be used to calculate the hole DT current in other gate dielectric materials.

Hole quantization effects and threshold voltage shift in pMOSFET-assessed by improved one-band effective mass approximation

Threshold voltage (V/sub T/) shift due to quantum mechanical (QM) effects in pMOSFET is investigated based on a six-band effective mass approximation (EMA). Due to the valence band mixing, both subband energies and density of states (DOS) show remarkable difference from those derived from traditional one-band EMA using the bulk Si effective masses. In comparison with the experimental results, it is found that V/sub T/ Shift in pMOSFET is significantly overestimated by the traditional one-band EMA, however it corresponds with our six-band EMA calculation. Based on the numerical results of our six-band EMA, new effective masses are determined empirically and their electric field dependence is also evaluated. Using these new effective masses instead of the bulk effective masses, one-band EMA still display effectiveness in describing hole quantization and V/sub T/ Shift in an empirical manner. A set of constant energy quantization/DOS effective masses (0.29/1.14, 0.22/0.75, 0.24/0.66 m/sub 0/) for the first three subbands, neglecting their electric field dependence, is proposed for the modeling of QM effects in pMOSFET in this improved version of the one-band EMA formula. Computing time is minimized and results can be obtained with sufficient accuracy and correspond well with reported experimental data, thus the improved one-band EMA formula provide a firm ground in routine device simulation for deep submicron MOS devices.

A simple and efficient model for quantization effects of hole inversion layers in MOS devices

A simple and efficient model is introduced to study the hole quantization effects in the inversion layer of p-MOS devices. It is based on a six-band effective mass equation and a zigzag potential. The strong mixing between the heavy, light, and split-off hole bands is emphasized and quantitatively assessed. All subband dispersions are found to be anisotropic, far from parabolic, and electric field dependent. In addition, there are camel-back structures at some subband minima. The density of states (DOS) profiles show strong deviations from the step-like functions and one or two peaks may appear at the subband minima of the DOS, corresponding to the camel-back band structures. The traditional one-band effective mass approximation (EMA) using effective mass values extracted from bulk Si underestimates and oversimplifies the subband DOS. We justify this model by applying it to the capacitance of hole inversion layer and the threshold voltage shifts due to quantum mechanical (QM) effect. The model simulation shows good agreement with experimental results, demonstrating the accuracy of this model. The model and the characterization of the band structure of Si valence hole quantization lay the ground work in routine simulation of deep submicrometer MOS devices.

Infrared Absorption of Multiple Quantum Wells: Bound to Continuum Transitions

-heterojunction quantum structures are numerically investigated. In the con- duction band energy range the absorption to continuum is studied within one-band effective-mass approximation. By changing the shape of quan- tum wells, we can tune the energy corresponding to absorption peak. We also show low the absorption is modified in the case of annealed struc- tures. The inter-subband transitions in the energy range of valence band in Si/Si 1— x Gex /Si quantum well are described with the help of multiband Luttinger—Kohn Hamiltonian. Particular attention is paid to transitions to resonant states.

Resonance Spectra of Quantum Dots in Magnetic Field

Influence of magnetic field on the energy positions and widths of one- -electron resonance states in a multi-shell spherical quantum dot is inves- tigated. The one-band effective mass approximation is assumed. The com- plex-eigenvalue Schrodinger equation approach involving complex rotation of coordinates is used to obtain complex eigenenergies, Er - i²/2, corre- sponding to resonance states. We show how the magnetic field changes the resonance energy, Er, and decay rate, Γ, yielding bound states for some particular cases.

Modeling gate leakage current in nMOS structures due to tunneling through an ultra-thin oxide

For the first time, the tunneling current in silicon nMOS structures with ultra-thin gate oxides has been studied both by numerically solving Schrödinger's equation and by using the WKB approximation, which explicitly includes the size quantization effects in the inversion layers. The numerical solution employs first-order perturbation within the one-band effective-mass approximation to calculate the lifetime of an inversion-layer quasi-bound state. The good agreement in the tunneling currents estimated with these two methods justifies the use of the WKB approximation in the direct tunneling regime. The range of validity of the WKB approximation is also discussed.

Quantum-confinement-induced Gamma -->X transition in GaAs/AlGaAs quantum films, wires, and dots.

Large GaAs domains embedded in an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As matrix act as potential wells for both electrons and holes, resulting in a direct band-gap system. When the GaAs domains become small, however, quantum-confinement effects may push the \ensuremath{\Gamma}-like conduction-band state localized on GaAs above the X-like conduction-band state of the ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As alloy, leading to an indirect band-gap system. Using a pseudopotential band-structure method, as well as the conventional one-band effective-mass approximation, we investigate the nature of the direct\ensuremath{\rightarrow}indirect (\ensuremath{\Gamma}\ensuremath{\rightarrow}X) transition in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum films, wires, and dots. In the case of an isolated GaAs quantum structure embedded in AlAs, we find that the critical size for the onset of the \ensuremath{\Gamma}\ensuremath{\rightarrow}X transition increases from \ensuremath{\sim}31 \AA{} in a two-dimensional film through \ensuremath{\sim}56 \AA{} in a one-dimensional cylindrical wire to \ensuremath{\sim}80 \AA{} in a zero-dimensional spherical dot. The interaction between GaAs quantum structures tends to reduce the critical size for the \ensuremath{\Gamma}\ensuremath{\rightarrow}X transition. We further study the effect of the alloy composition on the \ensuremath{\Gamma}\ensuremath{\rightarrow}X transition, finding that the critical size decreases when the Ga concentration of the alloy increases. In the case of spherical GaAs quantum dots embedded in an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As alloy, we show that, as a function of the dot radius and the alloy composition, different alignments of the band-edge states lead to different regimes of the lowest-energy optical transition.

Beyond the Virtual Crystal Approximation in Diluted Magnetic Semiconductors

We present a new model approach which goes beyond the virtual crystal approximation and the molecular field approximation in the description of the spin splitting of band states in diluted magnetic semiconductors. The theory is formulated within a one-band effective mass approximation and explicitly takes into account a chemical and magnetic disorder caused by substitutional ions. The results confirm the apparent dependence of the p-d exchange integral on x in Cd1-xMnxS for small concentrations of Mn ions and we predict the asymmetric field and temperature dependence of the spin splitting in this compound.

Formation Time of Magnetic Polarons

Progress in the application of short light pulses for monitoring of dynamical processes has made it possible to trace the emerging of exciton magnetic polarons (EMP) after optical injection of carriers across the band gap in diluted magnetic semiconductors (DMS) [1-6]. In this paper we discuss mechanisms which might account for the fast dynamics of the polaron formation in DMS. Consider a carrier trapped at t = O in a localized state. Its adiabatic wave function is described by a Schrodinger equation which contains: (i) kinetic energy, taken here in the one-band effective-mass approximation, (ii) potential energy that includes the localizing and confining potential, (iii) a nonlinear term HM = HM(r, t), which describes the exchange interaction with the time-dependent polarization of the surrounding localized spins,

Coupled cyclotron-intersubband resonances in parabolic wells with tilted valleys

The influence of the subband-Landau level coupling resulting from the tilted configuration of the valleys on the intraband magneto-optical transitions in PbTe and Si parabolic quantum wells is discussed. The calculations are performed in the framework of the one-band effective-mass approximation for the case of normal magnetic field. in the range of the strong field the absorption spectrum consists of two hybridized cyclotron-intersubband modes. It has features similar to that observed for the case when the magnetic field but not the valley is tilted.

Surface cyclotron resonance on InSb in Voigt configuration.

Magnetic fields parallel to space-charge layers on semiconductors define a crossed-field configuration with strong electric fields. Analytical expressions for the resulting hybrid electric-magnetic surface band structure and its optical transitions are derived in the triangular-well approximation of the electrostatic potential. The results of the one-band effective-mass approximation are extended to a two-level model that accounts for the nonparabolicity of narrow-band-gap semiconductors such as InSb. In the hybrid surface band structure, electrons with bulklike wave functions exist, allowing the experimental study of conduction-band cyclotron resonance in crossed fields. This is done in a wide range of frequencies, magnetic fields, and inversion electron densities, i.e., electric field strengths. The experimental results are discussed within the proposed models and are compared with experiments on other semiconductors. Specifically, the destruction of the Landau quantization in crossed electric and magnetic fields is investigated, both theoretically and experimentally; polarons are also studied. This is possible because of the absence of coupled plasma cyclotron--LO-phonon modes in the present degenerate electron system.

Nonradiative capture and recombination by multiphonon emission in GaAs and GaP

Data are presented for 9 capture cross sections of deep levels in GaAs and 4 in GaP which can be interpreted as capture by multiphonon emission (MPE). At high temperatures the cross sections have the form $\ensuremath{\sigma}={\ensuremath{\sigma}}_{\ensuremath{\infty}}{e}^{\frac{\ensuremath{-}{E}_{\ensuremath{\infty}}}{\mathrm{kT}}}$ where ${\ensuremath{\sigma}}_{\ensuremath{\infty}}={10}^{\ensuremath{-}14}\ensuremath{-}{10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ and ${E}_{\ensuremath{\infty}}=0\ensuremath{-}0.56$ eV. A simple theory of MPE capture is presented in which vibrations of a single lattice coordinate modulate the depth of the potential well binding the carrier. In this model capture results from lattice vibrations causing the crossing of free- and bound-carrier levels. The breakdown of the adiabatic approximation near the crossing is discussed. The calculated cross sections have the form $\ensuremath{\sigma}=Af(0)$ where $f(h\ensuremath{\nu})$ is the normalized line shape for radiative capture. The lattice relaxation properties of the center determine $f(0)$. The temperature dependence of $f(0)$ correctly accounts for the thermally activated behavior of the cross sections at high temperatures. Classical and quantum treatments of the lattice motion give the same expression for $\ensuremath{\sigma}$ at high temperature. A detailed calculation of $A$ is made for the capture of a carrier by an attractive neutral impurity in the case where both the free-carrier and bound-carrier wave functions are describable in a one-band effective-mass approximation. The theoretical value of $A$ leads to ${\ensuremath{\sigma}}_{\ensuremath{\infty}}\ensuremath{\approx}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$, the same order of magnitude as the experimental values. However, many of the experimental cross sections involve complexities not accounted for in this simple model such as charged impurities and transitions between free states and bound states of different symmetry. The lattice relaxation parameters are experimentally determined for the Zn-O and O centers in GaP. Lattice relaxation is found adequate to explain the large cross sections for electron capture by the Zn-O center and hole capture by the two-electron state of O. The studies of the O and Zn-O centers also provide evidence for nonlinear changes in the impurity energy level with lattice displacement which decrease the electron capture cross sections and greatly enhance the hole recombination cross sections. The source of this nonlinearity is discussed.

Low-frequency electronic resistivity of crystals due to the scattering from dipoles

The screened potential of an electrical dipole impurity in crystalline solids is obtained in the Debye-Hückel approximation. In the one-band effective-mass approximation and Born approximation of the scattering, the low-frequency transport relaxation time of current-carriers, electrical conductivity and the electronic part of permittivity of crystals are calculated when the scattering mechanism is connected with the randomly distributed screened dipole centres. It is shown that in some cases the scattering from dipole impurity centres may be essential and even more effective than the other scattering mechanisms.

Theory of metal-insulator-metal tunneling for a simple two-band model

The one-band effective mass approximation for the dispersion relationship in the barrier of a metal-insulator-metal (MIM) tunnel junction fails if the barrier height is a considerable portion of the band gap of the insulator. This paper reports on results when the more realistic dispersion relation of Franz and Kane is used and displays the sensitivity of the tunnel effect to the band model. We illustrate some examples of the energy distribution of the current. Characteristic features of tunneling through trapezoidal-like barriers will be discussed, including maxima in the logarithmic derivative curves, in the thermal I-V characteristics, and the zero-bias offset of the conductance minimum. Calculations are performed by integrating the tunnel equation numerically, and analytical approximations for this equation are also presented from which the effect of various parameters on the tunneling characteristic can be estimated.

Nonlinear electromagnetic response of bloch electrons in a magnetic field

A general self-consistent method has been developed to calculate optical nonlinearities of a solid in presence of a d.c. magnetic field. This method has been used to calculate linear as well as bilinear induced current densities in the one-band effective-mass approximation for Bloch electrons in the solid. The result for the linear current density gives familiar expressions for the Faraday effect and cyclotron resonance when the incident wave is polarized in the direction other than that of the d.c. magnetic field. However, it is shown that even if two fundamental waves of frequencies ω 1 and ω 2 are polarized in the direction of the d.c. magnetic field, the bilinear current density induced in the solid has cyclotron resonance denominators at the combination frequencies 2ω 1 , 2ω 2 and ω 1 ± ω 2 . When the fundamental waves are polarized in arbitrary directions cyclotron resonance denominators occur in the bilinear current density also at frequencies ω 1 and ω 2 .