Nondegenerate Electron Gas Research Articles

Light absorption by free charge carriers in the presence of phonons in an anisotropic quantum wire

The absorption of light by free charge carriers has been theoretically studied considering the processes related to scattering from phonons in an anisotropic parabolic quantum wire. The case in which the electromagnetic wave is polarized along the axis of the wire and the case of non-degenerate electron gas statistics have been considered. In this work, it was determined that the dependence of the location of the peaks of the intraband optical absorption coefficient on the characteristic frequency of the confinement potential in quantum wires with asymmetric parabolic potential was .

Influence of Boundary Conditions on Quantum Magnetotransport in a Thin Film

Analytical expressions are obtained for the Hall coefficients and the magnetoresistance of a thin semiconductor film. The case of a weak magnetic field is considered and the effects related to the splitting of the energy spectrum of charge carriers into Landau levels are not taken into account. The isoenergetic surface of a semiconductor material is an ellipsoid of revolution (spheroid). The transition to the limiting cases of degenerate and nondegenerate electron gases and mirror boundaries is carried out. The behavior of charge carriers is described by the quantum Liouville equation. The effect of the surface scattering of charge carriers is taken into account through the Soffer boundary conditions. The dependence of the Hall coefficients and magnetoresistance on the film thickness, induction of an external magnetic field, and film surface roughness is analyzed.

Identical and nonidentical superlattice on the surface of nanotubes: Specific heat and magnetization

The thermodynamic and magnetic properties of electrons in superlattices on the surface of a nanotube in a longitudinal magnetic field are investigated. It is shown that the specific heat of nondegenerate electron gas in superlattice on the surface of a nanotube oscillates with the change in the magnetic flux. With the increase in effective mass, the magnetization in identical and nonidentical superlattices on the surface of a nanotube are close to each other. Magnetization has a “saw-tooth” form as a function of a magnetic field. For the lattice of nanotubes with two different radii, ordinary compensation points, at which the magnetization vanishes at fixed values of the magnetic field strength, are found.

Взаимодействие электромагнитной Н-волны с наноструктурой "диэлектрик-полупроводник-диэлектрик" с учетом анизотропии зонной структуры полупроводника

The problem of electromagnetic H-wave interaction with a layered "insulator-semiconductor- insulator" nanostructure is solved. We assume that the semiconductor layer thickness can be comparable to or less than the charge carrier de Broglie wavelength. Charge carrier surface scattering is taken into account by the Soffer boundary conditions. The electromagnetic wave frequency is less than the plasma resonance frequency. The constant energy surface is an ellipsoid of revolution. Analytical expressions are obtained for the reflection, transmission and absorption coefficients. Calculations are performed for the limiting cases of a degenerate and nondegenerate electron gas. We analyze the dependences of the optical coefficients on dimensionless parameters: the semiconductor layer thickness, the electromagnetic wave frequency and incidence angle, the chemical potential, the ellipticity parameter, the insulating layer permittivities, and the semiconductor-insulator interface roughness parameters.

Compensation points in the lattice of semiconductor nanotubes

In the present work, we investigated the thermodynamic properties of the lattice formed by noninteracting nanotubes using a single-walled nanotube model in a longitudinal magnetic field. We show that the specific heat of nondegenerate electron gas in semiconductor nanotubes changes from kB/2 to kB as temperature increases. Magnetization has a “saw-tooth” form as a function of the magnetic field. For the lattice of nanotubes with two different radii, we found ordinary compensation points, points at which the magnetization vanishes at fixed values of the magnetic field strength.

Screened Potential by Electron Gas

Donors and acceptors in semiconductors are charged impurities with a Coulomb potential and, therefore, are screened by free charge carriers – electrons. An analytical description of the oscillations of the screened external potential by the electron gas is considered in this paper. Using the inverse transformation of the Fourier component, the screened Coulomb Potential U(r) and the value of the screening radius rs for the degenerate and nondegenerate electron gas are found. The dependence of rs on potentials is also given. It is shown that the screening radius decreases with increasing the electron density.

The general analytical expression for computation of generalized relativistic Fermi-Dirac functions

In this paper, general sufficiently analytical formulae are developed for the arbitrary order generalized relativistic Fermi-Dirac (FD) functions. Analytical assessment of relativistic FD function is very important for various fields of physics especially in the theory of relativistic nondegenerate and degenerate electron gas systems. One of the more appropriate and correct approximations is based on a binomial expansion method and incomplete Gamma functions that have been used in the calculations of the generalized relativistic FD functions. Note that, the established expression in special cases of specific values of parameters becomes the evaluation formulae of other type FD functions. Calculation results of the generalized relativistic FD functions are compared with the other approximations methods and available numerical approaches and demonstrated satisfactory agreement.

Взаимодействие электромагнитной H-волны с полупроводниковым нанослоем

A theoretical model of the electromagnetic H-wave interaction with a semiconductor nanolayer, the thickness of which can be comparable to or less than charge carrier de Broglie wavelength is constructed. We assume the frequency range of the electromagnetic wave to be much less than the plasma frequency. Analytical expressions are derived for optical coefficients as the functions of the dimensionless thickness, electromagnetic wave frequency and incidence angle, chemical potential, and surface roughness parameters. The results derived for the limiting cases of degenerate and nondegenerate electron gas are analyzed.

Interaction of an electromagnetic H-wave with a semiconductor nanolayer

A theoretical model of the electromagnetic H-wave interaction with a semiconductor nanolayer, the thickness of which can be comparable to or less than charge carrier de Broglie wavelength is constructed. We assume the frequency range of the electromagnetic wave to be much less than the plasma frequency. Analytical expressions are derived for optical coefficients as the functions of the dimensionless thickness, electromagnetic wave frequency and incidence angle, chemical potential, and surface roughness parameters. The results derived for the limiting cases of degenerate and nondegenerate electron gas are analyzed. Keywords: nanolayer, Liouville equation, de Broglie wavelength, Soffer model, optical coefficients.

Electrical properties of strained germanium nanofilm

Dependences of the concentration of intrinsic current carriers, electron and hole mobilities and specific conductivity for strained germanium nanofilms grown on the Si, Ge(0,64)Si(0,36) and Ge(0,9)Si(0,1) substrates with crystallographic orientation (001), on their thickness at different temperatures were calculated on the basis of the statistics of non-degenerate two-dimensional electron and hole gas in semiconductors. The electrical properties of such nanofilms are determined by the peculiarities of their band structure. It is established that the effects of dimensional quantization, the probability of which increases with decreasing temperature, become significant for germanium nanofilms with the thickness of d<7 nm. The presence of such effects explains the significant increase in the specific conductivity and the decrease in the intrinsic concentration of current carriers for these nanofilms. The electron and hole mobility in the investigated germanium nanofilms is lower in relation to such unstrained nanofilms. Only for the strained germanium nanofilm with the thickness of d> 50 nm grown on the Ge(0,9)Si(0,1) substrate, an increase in the hole mobility at room temperature of more than 1.5 times was obtained. The obtained results of the electrical properties of strained germanium nanofilms can be used in producing on their basis new elements of nanoelectronic.

Квантовый транспорт в полупроводниковом нанослое с учетом поверхностного рассеяния носителей заряда

The problem of the conductivity of a thin conductive nanolayer is solved taking into account the quantum theory of transport processes. The layer thickness can be comparable to or less than the de Broglie wavelength of charge carriers. The constant-energy surface has the form of an ellipsoid of revolution with the main axis parallel to the layer plane. Analytical expressions are obtained for the conductivity tensor components as a function of dimensionless thickness, chemical potential, ellipticity parameter, and surface roughness parameters. The conductivity analysis for the limiting cases of a degenerate and non-degenerate electron gas are conducted. The results are compared with known experimental data for a silicon layer.

Calculation of the conductivity of a thin conductive layer taking into account Soffer boundary conditions and isoenergy surface anisotropy of conductor

The task about the conductivity of a thin conductive layer in a longitudinal alternative electric field is solved. The relationship between layer thickness and charge carrier mean free path is arbitrary. The Soffer model is used as boundary conditions for Boltzmann equation. The isoenergy surface of a semiconductor is an ellipsoid of revolution. Analytical expressions are obtained for conductivity tensor components as functions of layer thickness, isoenergy surface anisotropy parameter, electric field frequency, surface roughness parameters, and chemical potential. The limiting cases of a degenerate and non-degenerate electron gas are considered. The dependences of conductivity tensor components on the above parameters are analyzed. The results obtained for cases of a degenerate and non-degenerate electron gas are compared. A comparative analysis of results is made with calculations in the view of diffuse-mirror boundary conditions and with known experimental data.

Effect of the Boundary Conditions on the High-Frequency Electrical Conductivity of a Thin Conducting Layer in a Longitudinal Magnetic Field

The problem of the high-frequency conductivity of a thin conducting layer in a longitudinal magnetic field is solved using a kinetic approach taking into account the mirror-diffusion boundary conditions. The specularity coefficients of the layer surfaces are assumed to be different. An analytical expression is derived for the dimensionless integrated conductivity as a function of the dimensionless parameters, including the layer thickness, electric-field frequency, magnetic induction, chemical potential, and surface specularity coefficients. The limiting cases of a degenerate and nondegenerate electron gas are considered. A comparative analysis of theoretical calculations with the experimental data is made. A method for determining the specularity coefficients and the carrier mean free path using the longitudinal magnetoresistance of a thin metallic film is demonstrated.

Calculation of thin wire conductivity in a longitudinal magnetic field taking into account Fuchs boundary conditions

The task about thin wire conductivity in a longitudinal stationary magnetic field and alternative electrical field is solved by the kinetic method in the view of Fuchs model. The ratio between the wire radius and the charge carrier mean free path is arbitrary. Electric and magnetic fields are homogeneous. The wire radius is much less than the skin layer depth, i.e. the skin effect is neglected. The limiting cases of a degenerate and nondegenerate electron gas are considered. The conductivity dependences on the magnetic field induction, electric field frequency, wire radius and surface specularity coefficient are investigated. Results obtained for limiting cases of degenerate and nondegenerate electron gas are compared. Also, these results are compared with experimental data. An effective method for determining the surface specularity coefficient and charge carrier mean free path is illustrated. The dependence of the charge carrier mean free path in a sample volume on the wire radius is analyzed.

XXIV Международный симпозиум Нанофизика и наноэлектроника", Нижний Новгород, 10-13 марта 2020 г. Влияние граничных условий на высокочастотную электропроводность тонкого проводящего слоя в продольном магнитном поле

The problem of the high-frequency conductivity of a thin conductive layer in a longitudinal magnetic field is solved in terms of kinetic approach taking into account diffuse-mirror boundary conditions. Specularity coefficients of layer surfaces are assumed to be different. An analytical expression is derived for dimensionless integral conductivity as a function of dimensionless parameters: layer thickness, electric field frequency, magnetic induction, chemical potential and surface specularity coefficients. The limiting cases of a degenerate and non-degenerate electron gas are considered. A comparative analysis of theoretical calculations with experimental data is carried out. The method to determine specularity coefficients and mean free path of charge carriers from the longitudinal magnetoresistance of a thin metal film is illustrated.

Screened shallow impurity properties of quantum well heterosystems with high-κ dielectric barrier environment

The effect of high-κ dielectric mismatch on the impurity states screened by free electron gas is investigated theoretically in high-κ dielectric barrier/quantum well/high-κ dielectric barrier (hh-κ) and low-κ dielectric barrier/quantum well/high-κ dielectric barrier (lh-κ) types of quasi two-dimensional (Q2D) heterostructures. A restriction of the characteristic long-range nature of the impurity Q2D screened interaction due to the high-κ dielectric mismatch has been revealed here - atypical of the Q2D dielectrically homogeneous systems. Accordingly, for the hh-κ type heterostructure, an impurity screened interaction potential at moderately large (relative to the quantum well width values) in-plane distances behaves as the Q2D Debye-Hückel potential, while at rather large distances falls off on the background of the high-κ dielectric constant of the barrier medium. The screened impurity ground state energy in the framework of the Q2D Debye-Hückel potential has been investigated variationally for the first time. A role of high-κ dielectric mismatch is exposed when comparing the results for the discussed heterostructures based on the realistic InSb/HfO2 interface. The characteristic ranges where the quantum confinement effect, enhancing the Coulomb interaction, balances the joint weakening influence of the impurity screening and high-κ dielectric mismatch effects are revealed. The received admissible values of the in-plane density/temperature ratio parameter for the hh-κ type heterostructure typically refer to non-degenerate electron gas while for the lh-κ type both electron gas statistics are significant. Due to the high-κ dielectric mismatch a binding energy sufficient decline with reducing of the quantum well width has been established. In the hh-κ type heterostructure an impurity binding is quite sizable at the wide quantum wells (d ∼8 ÷ 10 nm). Meanwhile, for the lh-κ-type heterostructure, an impurity binding energy is enough large (∼10 meV) in both wide and narrow quantum well cases.

Resonance Absorption of Electromagnetic Radiation in a Phosphorene Single Layer

The absorption coefficient of the electromagnetic radiation in a phosphorene single layer placed in a magnetic field is found. A degenerate and nondegenerate electron gas is considered. The resonant dependences of the absorptance on the radiation frequency and applied magnetic field are found. Taking into account electron scattering at an ionized impurity leads to oscillation dependences of the absorption coefficient on the radiation frequency and external magnetic field. The resonance character of the absorption curve is shown. The conditions of resonances and position of resonance peaks are found.

Terahertz conductivity and coupling between geometrical and plasmonic resonances in nanostructures

Terahertz conductivity spectra of charges moving ballistically in one-, two-, and three-dimensional infinitely deep rectangular potential wells were investigated theoretically using semiclassical and quantum Kubo formulas. The conductivity spectrum of a degenerate electron gas in these nanostructures exhibits a series of geometrical resonances. These further couple with plasmon resonances occurring in isolated structures: qualitatively different interaction regimes are found in one-, two-, and three-dimensional nanostructures. In contrast, the response of a nondegenerate electron gas smears into a single broad band due to the excessive spectral broadening caused by the wide distribution of charge velocities.

Резонансное поглощение электромагнитного излучения в монослое фосфорена

AbstractThe absorption coefficient of the electromagnetic radiation in a phosphorene single layer placed in a magnetic field is found. A degenerate and nondegenerate electron gas is considered. The resonant dependences of the absorptance on the radiation frequency and applied magnetic field are found. Taking into account electron scattering at an ionized impurity leads to oscillation dependences of the absorption coefficient on the radiation frequency and external magnetic field. The resonance character of the absorption curve is shown. The conditions of resonances and position of resonance peaks are found.

Electrical conductivity of a nondegenerate electron gas with a complex shaped quantum well

In this paper, the electrical conductivity of a nondegenerate electron gas with a complex shaped quantum well is calculated. The conductivity’s dependences on the temperature and on the parameters of the quantum well are studied in the case of electron-phonon scattering. For scattering of electrons by polar optical phonons, the conductivity is shown to depend essentially on the temperature, as distinct from acoustical phonon scattering and to decrease with increasing temperature. Also, the conductivity decreases down to zero, with increasing potential of quantum well.