Kane Dispersion Relation Research Articles

Non-Parabolic Band Hydrodynamic Model for Silicon Quantum Wires

ABSTRACTElectron transport phenomena in silicon nanowires are investigated for square and equilateral triangle cross-sections of the wire by using an Extended Hydrodynamic model coupled to the Schrödinger–Poisson system. This model has been formulated by closing the moment system derived from the Boltzmann equation on the basis of the maximum entropy principle of Extended Thermodynamics, including scattering of electrons with acoustic and non-polar optical phonons and by considering the conduction band described by the Kane dispersion relation. Applications to the case of bulk silicon for different cross-sections of the wire are presented.

Simulation of a double-gate MOSFET by a non-parabolic energy-transport subband model for semiconductors based on the maximum entropy principle

A nanoscale double-gate MOSFET is simulated with an energy-transport subband model for semiconductors including the effects of non-parabolicity by means of the Kane dispersion relation. The closure relations are derived on the basis of the maximum entropy principle and all the relevant scattering mechanisms of electrons with acoustic and non polar optical phonons are taken into account. The model is shown to form a system of nonlinear parabolic partial differential equations.The results of the simulations validate the robustness of the numerical scheme and the accuracy of the model. In particular, the importance of taking into account the non-parabolicity is assessed, since a relevant difference in the currents is obtained in comparison with the parabolic band case.

Electronic structure of chromium-doped lead telluride-based diluted magnetic semiconductors

The crystal structure, composition, galvanomagnetic, and oscillatory properties of Pb1−x−ySnxCryTe (x=0,0.05–0.30; y⩽0.01) alloys are studied for different matrices and chromium impurity concentrations. It is shown that impurity chromium ions dissolve in the lattice in amounts below 1mol.%, while higher chromium concentrations lead to the appearance of microscopic regions with elevated chromium contents and inclusions of chromium-tellurium compounds. Reductions in the hole concentration, p−n conversion of the conductivity type, and stabilization of the Fermi level by the resonance level of chromium are observed with increasing chromium content. The initial rates of change of the charge carrier concentrations during doping are determined. A two-band Kane dispersion relation is used to calculate the electron concentration and Fermi level as functions of the tin content. A diagram showing the rearrangement of the electronic structure of the chromium doped alloys with varying matrix composition is constructed.

On the nature of charge carrier scattering in Ag2Se at low temperatures

The electric and thermoelectric properties of silver selenide in the temperature range of 4.2–300 K have been studied. The data obtained are interpreted within the theory of one-type carriers and Kane dispersion relation, with allowance for the character of electron-electron interaction. It is established that, for the concentrations n ≤ 7.8 × 1018 cm−3, charge carriers are scattered by impurity ions at T ≤ 30 K and by acoustic and optical phonons and point defects at T ≥ 30 K. Electron-electron interactions are found to be elastic at T < 30 K.

Electronic structure of diluted magnetic semiconductors Pb1–x –yGex Cry Te under pressure

AbstractThe galvanomagnetic properties of Pb1–x –y Gex Cry Te in the temperature range 4.2–300 K under variation of the alloy composition (x ≤ 0.13, y ≤ 0.05) and under hydrostatic compression (P ≤ 17 kbar) have been investigated. Pressure dependences of the electron concentration and Fermi energy were obtained. In the frame of the Kane dispersion relation theoretical dependences of electron concentration and Fermi energy were calculated and parameters of chromium impurity band were estimated. Magnetic field dependences of the Hall coefficient under variation of germanium content and under pressure were measured. It is shown, that existence of two conductivity mechanisms should be taken into account: conduction band conductivity and electron‐type conductivity via chromium impurity band states. In terms of the two‐band conduction model the main parameters of charge carriers were obtained. Experimental results are discussed taking into account the diagram of the electronic structure reconstruction under pressure, assuming finite capacity, electron filling and widening of the impurity band. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Insulator-metal transition in Pb1-xGexTe doped with chromium under pressure

The galvanomagnetic effects in the n-Pb1-xGexTe (x=0.02-0.13) alloys, doped with chromium, at the temperatures in the range of 4.2≤T≤300 K and under hydrostatic compression of up to 17 kbar have been investigated. The insulator-metal transition, induced by pressure in Pb1-xGexTe: Cr (x=0.10) alloy, was revealed. Using the experimental data in the frame of two-band Kane dispersion relation the pressure dependences of electron concentration and Fermi energy were calculated. The pressure coefficient of chromium deep level energy was obtained and the diagram of the electronic structure reconstruction under pressure was proposed.

Stabilization of the fermi level by a resonant gallium level in Pb1−x SnxTe alloys

Electrical properties of gallium-doped n-Pb1−xSnxTe alloys (x=0.09−0.21) are studied. Ahomalous temperature dependences of the Hall coefficient which indicate the Fermi level pinning by a resonant gallium level in the conduction band were detected. The dependences of the electron concentration and Fermi energy on the alloy composition and temperature are calculated from experimental data in terms of the two-band Kane dispersion relation. It is shown that the gallium resonant level position relative to the valence band top is almost independent of the matrix composition. The dependence of the thermal coefficient of the resonant level shift with respect to the midgap on the alloy composition is obtained.

Chromium Impurity States in Pb1-xGexTe Alloys Under Pressure

AbstractThe galvanomagnetic effects in the n-Pb1-xGexTe:Cr (x=0.02-0.13) alloys at the temperatures 4.2≤T≤300 K and under hydrostatic compression up to 17 kbar have been investigated. The metal-insulator transition under the increase of germanium content in the alloys and insulator-metal transition, induced by pressure in Pb1-xGexTe:Cr (x=0.10) alloy, were revealed. Using the experimental data in the frame of two-band Kane dispersion relation the dependences of the free electron concentration and the Fermi level position on the matrix composition and on the pressure were calculated. The composition and pressure coefficients of chromium deep level movement were obtained and the models of the electronic structure reconstruction under varying the alloy composition and under pressure were proposed.

Simulation of Gunn oscillations with a non‐parabolic hydrodynamical model based on the maximum entropy principle

PurposeOn the basis of the maximum entropy principle, seeks to formulate a hydrodynamical model for electron transport in GaAs semiconductors, which is free of any fitting parameter.Design/methodology/approachThe model considers the conduction band to be described by the Kane dispersion relation and includes both Γ and L valleys. Takes into account electron‐non‐polar optical phonon, electron‐polar optical phonon and electro‐acoustic phonon scattering.FindingsThe set of balance equation of the model forms a quasilinear hyperbolic system and for its numerical integration a recent high‐order shock‐capturing central differencing scheme has been employed.Originality/valuePresents the results of simulations of n+ ‐n‐n+ GaAs diode and Gunn oscillator.

Si and GaAs mobility derived from a hydrodynamical model for semiconductors based on the maximum entropy principle

Consistent hydrodynamical models for electron transport in Si and GaAs semiconductors, free of any fitting parameter, have been formulated in (Cont. Mech. Thermodyn. 11 (1999) 307; Contemp. Mech. Thermodyn. 12 (1999) 31; Contemp. Mech. Thermodyn. 14 (2002) 405; COMPEL (to appear)) on the basis of the maximum entropy principle (MEP), by describing the valleys in the energy conduction band by means of the Kane dispersion relation. Explicit constitutive functions for fluxes and production terms appearing in the macroscopic balance equations of density, crystal momentum, energy and energy-flux have been obtained. Scatterings of electrons with polar (in the case of GaAs) and non-polar optical phonons, both for intervalley and intravalley interactions, and with acoustic phonons and impurities have been taken into account. Here we derive from the previous hydrodynamical models both low- and high-field mobilities. The results are compared with those given by the Caughey–Thomas formula and eventually the validity of the Einstein relation is investigated.

2D Simulation of a Silicon MESFET with a Nonparabolic Hydrodynamical Model Based on the Maximum Entropy Principle

A hydrodynamical model for electron transport in silicon semiconductors, which is free of any fitting parameters, has been formulated on the basis of the maximum entropy principle. The model considers the energy band to be described by the Kane dispersion relation and includes electron–nonpolar optical phonon and electron–acoustic phonon scattering. The set of balance equations of the model forms a quasilinear hyperbolic system and for its numerical integration a recent high-order shock-capturing central differencing scheme has been employed. Simulations of an n+–n–n+ silicon diode have been presented and comparison with Monte Carlo data shows the good accuracy of the model and performance of the numerical scheme. Here the results of simulations of a silicon MESFET in the two-dimensional case are presented. Both the model and the numerical scheme demonstrate their accuracy and efficiency as CAD tools for modeling realistic submicron electron devices.

Non‐parabolic band hydrodynamical model of silicon semiconductors and simulation of electron devices

AbstractA consistent hydrodynamical model for electron transport in silicon semiconductors, free of any fitting parameter, has been formulated in Anile and Romano (Continuum Mechanics Thermodynamics 1999; 11:307–325) and Romano (Continuum Mechanics Thermodynamics 1999; 12:31–51) on the basis of the maximum entropy principle, by considering the energy band described by the Kane dispersion relation. Explicit constitutive functions for fluxes and production terms in the macroscopic balance equations of density, crystal momentum, energy and energy flux have been obtained. Scatterings of electrons with non‐polar optical phonons (both for intervalley and intravalley interactions), acoustic phonons and impurities have been taken into account.In this article we show the link with other macroscopic models describing the motion of charge carriers. In particular, under suitable scaling assumptions, an energy transport model is recovered. An analysis of the formal properties is given by showing that the evolution equations form a hyperbolic system in the physically relevant region of the space of the dependent variables. At last, by using the numerical method developed in Liotta et al. (International Series of Numerical Mathematics 1999; 130:651–660) and Liotta et al. (SIAM Journal on Numerical Analysis 1999, to appear) simulations for bulk silicon and n+–n–n+ silicon diode are performed. The obtained results are in good agreement with the Monte Carlo data. Copyright © 2001 John Wiley &amp; Sons, Ltd.

Simulation of Submicron Silicon Diodes with a Non-Parabolic Hydrodynamical Model Based on the Maximum Entropy Principle

A hydrodynamical model for electron transport in silicon semiconductors, free of any fitting parameters, has been formulated in [1,2] on the basis of the maximum entropy principle, by considering the energy band described by the Kane dispersion relation and by including electron-non polar optical phonon and electron-acoustic phonon scattering.In [3] the validity of this model has been checked in the bulk case. Here the consistence is investigated by comparing with Monte Carlo data the results of the simulation of a submicron n+–n–n+ silicon diode for different length of the channel, bias voltage and doping profile.The results show that the model is sufficiently accurate for CAD purposes.

Moment Equations with Maximum Entropy Closure for Carrier Transport in Semiconductor Devices: Validation in Bulk Silicon

Balance equations based on the moment method for the transport of electrons in silicon semiconductors are presented. The energy band is assumed to be described by the Kane dispersion relation. The closure relations have been obtained by employing the maximum entropy principle.The validity of the constitutive equations for fluxes and production terms of the balance equations has been checked with a comparison to detailed Monte Carlo simulations in the case of bulk silicon.

Non parabolic band transport in semiconductors: closure of the moment equations

The problem of the closure of the moment equations of the semiconductor Boltzmann equation is studied in the framework of the Kane dispersion relation (therefore avoiding the limitations of the parabolic band approximation). By using the maximum entropy ansatz for the closure one obtains, in the limit of small anisotropy, explicit constitutive relations for the stress tensor and the flux of energy flux tensor. The results obtained are in remarkable agreement with those arising from Monte Carlo simulations.

Comparison of Non‐Parabolic Hydrodynamic ModelsBased On Different Band Structure Models

This paper presents two non‐parabolic hydrodynamic model formulations suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship, (ℏk)2/2m = W(1+αW). The second formulation makes use of a power law, (ℏk)2/2m = xWy, for the dispersion relation. The non‐parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation is limited. The power law formulation produces closed form coefficients similar to those under the parabolic band approximation but the carrier concentration can deviate. An extended power law dispersion relation is proposed to account for band structure effects, (ℏk)2/2m = xW1+yW. This dispersion relation closely matches the calculated band structure over a wide energy range and may lead to closed form coefficients for the hydrodynamic model.

On a Simplified Form of Kane's Dispersion Relation for Semiconductors

On a Simplified Form of Kane's Dispersion Relation for Semiconductors