Impact of dopants in GaN on the formation of two-dimensional electron gas in AlGaN/GaN heterostructure field-effect transistors

The two-dimensional electron gas distribution in AlGaN/GaN high electron mobility transistors is determined from the solution of the coupled Schr?dinger’s and Poisson’s equations. Considering the piezoelectric effect, the two-dimensional electron gas concentration is calculated to be as high as 7.7×10¹⁹ cm^-3. In order to obtain an understanding of how the two-dimensional electron gas distribution is influenced by dopants in GaN, we observed the two-dimensional electron gas concentration and occupation of sub-bands versus dopant concentration in the GaN layer of an AlGaN/GaN heterostructure. Our results show that the two-dimensional electron gas concentration is slightly increased at higher doping levels in GaN, while the quantum confinement in the AlGaN/GaN heterostructure is weakened with the increase of donor concentration in the GaN layer. Received: 26 May 2001 / Accepted: 23 July 2001 / Published online: 23 January 2002     

Conditions of existence of oscillatory phenomena in an electron gas

The thermodynamics of an electron gas in an arbitrary magnetic field is investigated for arbitrary values of the thermodynamic parameters. It is demonstrated that the oscillatory phenomena in the electron gas occur only for positive values of the chemical potential. Oscillations at the boundary of the region of existence of the oscillatory phenomena are considered. The thermodynamic characteristics of the electron gas in the magnetic field are expressed through the special functions introduced in the present work. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 17–24, June, 2008.     

Hartree-Fock approximation for the one-dimensional electron gas

The Hartree-Fock calculation on the one-dimensional electron gas is done on the basis of the method analogous to that applied by Bloch and Wigner and Seitz for the three-dimensional gas. The boundary conditions of the standing wave are taken for the wave function and the bare Coulomb interaction between electrons is assumed. The parameterr _s of the three-dimensional gas is replaced by the ratio between the cross-section radius and the length of the potential tube filled by the one-dimensional gas. Excepting for a special case of the excitement of an electron pair put on one electron level the excitation energies of the non-magnetic gas are found to be very much higher than these of the ferromagnetic gas. A similar relation holds between the ground state energies of the non-magnetic and magnetic gases.     

Minimum magnetocapacitance of a screened two-dimensional electron gas

A theory for the magnetocapacitance of a partially screened two-dimensional (2D) electron gas is proposed. The model investigated is sensitive to different types of screening in a 2D electron gas with an integer filling factor: the so-called conventional approach and the self-consistent approximation introduced in the present paper. The calculations point to the importance of the self-consistent treatment of the magnetocapacitance of a 2D electron gas under the conditions of an integer filling factor. The final self-consistent results are qualitatively consistent with the available experimental data. Fiz. Tverd. Tela (St. Petersburg) 39, 742–745 (April 1997)     

Potential of an insulated electrode in a high-energy electron flow under a gas pressure of 0.1–1.0 Pa

We analyze the variation of the floating potential of an insulated metallic electrode in a flow of electrons with an energy of up to 300 eV under a gas pressure of 0.1–1.0 Pa at a current density lower than 0.1 A/cm². It is shown that the dependence of the floating potential on the initial electron energy is non-monotonic; this fact is explained by the variation of the ratio of the ion current density to the density of fast electron current in the plasma. The balance of the electron and ion currents on the surface of an insulated electrode is ensured by the cutoff of the low-energy part of the electron flow at the level determined by the magnitude of the floating potential. The maximal value of the floating potential increases upon a decrease in the gas pressure; this is due to a decrease in the ion current density. The interval of energy variation in which the floating potential decreases from the maximal value (50–250 eV) to 5–6 eV increases with the electron current density and the gas pressure. The electrode material and the type of the gas do not noticeably affect the variation of the floating potential.     

Influence of noble gases on electron cyclotron heated hydrogen plasma

A quartz-chamber 2.45-GHz electron cyclotron resonance ion source (ECRIS) is designed at Peking University for the diagnostic purpose. Experimental results show that the added noble gases in hydrogen could cause a decrease of electron temperature and an increase of electron density. In this work, a numerical model is upgraded for ECR plasma generated by mixed gases. On this basis, the model is applied for the composed hydrogen plasma with additional noble gases. And dependences of neutral gas density and electron density on electron temperature are presented for individual gas (He, Ar, and H₂) and gas mixture, respectively. The calculated results are basically in accordance with the diagnostic results of ECRIS.     

Influence of the state of the electron gas on dispersion curves of ionization waves in neon

On the example of neon the onset of a transition is described from a non-hydrodynamic state of the electron gas, which exists at low pressures and currents, to a state where a local hydrodynamics is applicable. In the non-hydrodynamic state the ionization waves are influenced by resonant properties of the electron gas which means that several varieties can be selected on each of the two dispersion curves. With growing current the two parts of dispersion curve of the fast varieties (r and s) merge and this is interpreted as disappearance of the spatial resonance of the electron gas due to an enhancement of the electron Coulomb collisions.The author expresses his gratitude to K.Rohlena and L.Pekárek for helpful discussions.     

二维电子体系在高密度下的稳定性

本文计算了高密度的二维电子体系的边缘能(将二维体系沿某一直线解离成两片时,形成单位长度新边缘所需要的能量)。结果发现,当r_ss^(c)(约0.415)时,边缘能变负,从而表明在高密度下,二维电子气的基态有可能发生不稳。我们分别讨论了二维非束缚的电子气和束缚的电子气基态的稳定性,并在一个简化的模型下给出了束缚的电子气基态稳定性的判据。 关键词：     

Some methods of electron-beam entry into a dense gas

A system is considered of pumping a laser with an electron beam that moves relative to the active medium. The problem of planar two-dimensional gas flow through a bounded heat-releasing medium, a problem analogous to that of rectilinear motion of a beam with constant velocity, is solved analytically. It is proposed to admit an electron beam into a dense gas through aerodynamic ports. The effect of perturbations induced by the beam passage on the flow of gas in an aerodynamic port with a rarefaction wave is analyzed.Translated from Trudy Ordena Lenina Fizicheskogo Institute im. P. N. Lebedeva AN SSSR, Vol. 145, pp. 160–171, 1984.     

Rigorous solution of a Hubbard model extended by nearest‐neighbour Coulomb and exchange interaction on a triangle and tetrahedron

The Hubbard model extended by both nearest‐neighbour (nn) Coulomb correlation and nearest‐neighbour Heisenberg exchange is solved rigorously for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the model parameters in a closed analytical form. For fixed electron numbers we found a multitude of level crossings, both in the ground state and in the excited states in dependence on the various model parameters. By coupling an ensemble of clusters to an electron bath we get the cluster gas model or the cluster gas approximation, if an extended array of weak‐interacting clusters is considered. The grand‐canonical potential Ω (μ, T, h) and the electron occupation N (μ, T, h) of the related cluster gases were calculated for arbitrary values (attractive and repulsive) of the three interaction constants. For the cluster gases without the additional interactions we found various steps in N (μ, T = 0, h = 0) higher than one. The reason is the degeneration of ground states differing in their electron occupation by more than one electron. For the triangular cluster gas we have one such degeneration point. For the tetrahedral cluster gas two. As a consequence, we do not find areas with one electron in the μ‐U ground‐state phase diagram of the triangular cluster gas or with one, two and five electrons in the case of the tetrahedral cluster gas. The degeneration point of the triangular cluster gas can not be destroyed by an applied magnetic field. This holds also for the lower degeneration point of the tetrahedral cluster gas. Otherwise, the upper degeneration point breaks down at a critical magnetic field h_c. The dependence of h_c on U shows a maximum for strong on‐site correlation. The influence of nn‐exchange and nn‐Coulomb correlation on the ground‐state phase diagrams is calculated. Whereas antiferromagnetic nn‐exchange breaks the degeneration points of the tetrahedral cluster gas partially only, a repulsive nn‐Coulomb correlation lifts the underlying degeneracies completely. Otherwise both ferromagnetic nn‐exchange and attractive nn‐Coulomb interaction stabilise the degeneration points. The consequences of the cluster gas results for extended cluster arrays are discussed.     

Runaway of electrons in dense gases and mechanism of generation of high-power subnanosecond beams

New understanding of mechanism of the runaway electrons beam generation in gases is presented. It is shown that the Townsend mechanism of the avalanche electron multiplication is valid even for the strong electric fields when the electron ionization friction on gas may be neglected. A non-local criterion for a runaway electron generation is proposed. This criterion results in the universal two-valued dependence of critical voltage U _cr on pd for a certain gas (p is a pressure, d is an interelectrode distance). This dependence subdivides a plane (U _cr , pd) onto the area of the efficient electron multiplication and the area where the electrons leave the gas gap without multiplication. On the basis of this dependence analogs of Paschen’s curves are constructed, which contain an additional new upper branch. This brunch demarcates the area of discharge and the area of e-beam. The mechanism of the formation of the recently created atomospheric pressure subnanosecond e-beams is discussed. It is shown that the beam of the runaway electrons is formed at an instant when the plasma of the discharge gap approaches to the runaway electrons is formed at an instant when the plasma of the discharge gap approaches to the anode. In this case a basic pulse of the electron beam is formed according to the non-local criterion of the runaway electrons generation. The role of the discharge gap preionization by the fast electrons, emitted from the plasma non-uniformities on the cathode, as well as a propagation of an electron multiplication wave from cathode to anode in a dense gas are considered.     

Position passage through an electron gas

The analysis of the passage of a charged particle through an electron gas is given in this paper. The electron gas is considered as a plasma which oscillates with the Debye frequency. At the same time the electron gas polarization by the electric field of a passing positron is taken into account. The positron energy loss per unit time is calculated. The thermalization time of high velocity positrons is obtained. This time depends on the density of a metal, namely on the electron gas density according to the experimental data.     

Particle‐in‐cell/Monte Carlo simulation of electron and ion currents to cylindrical Langmuir probe

Electron and ion currents to a cylindrical Langmuir (electrostatic) probe were calculated using the particle‐in‐cell/Monte Carlo (PIC/MC) self‐consistent simulation for a neutral gas in the pressure range 2–3,000 Pa. The simulation enables us to calculate the probe currents even at high neutral gas pressures when the collisions of collected charged particles with neutral gas particles near the probe are important. The main aim of this paper is the calculation of probe currents at such high gas pressures and the comparison of the results with experimentally measured probe currents. Simulations were performed for two cases: (a) probes with varying radii in a non‐thermal plasma with high electron temperature at low neutral gas pressure of 2 Pa (in order to verify the correctness of our simulations), and (b) probe with the radius of 10 μm in the afterglow plasma with low electron temperature and a higher neutral gas pressure (up to 3,000 Pa). The electron probe currents obtained in case (a) show good agreement with those predicted by the orbital motion limited current (OMLC) theory for probes with radii up to 100 μm for the given plasma conditions. At larger probe radii and/or at higher probe voltages, the OMLC theory incorrectly predicts too high an electron probe current for the plasma parameters studied. Additionally, a formula describing the spatial dependence of the electron density in the presheath in the collisionless case is derived. The simulation at higher neutral gas pressures, i.e. case (b), shows a decrease of the electron probe current with increasing gas pressure and the creation of a large presheath around the probe. The simulated electron probe currents are compared with those of measurements by other authors, and the differences are discussed.     

Längsfeldstärke,Elektronentemperatur, mittlere Neutralgasdichte,Ionenstromdichte auf die Wand und mittlere Entladungsstromdichte in der Freifallsäule bei hohem Ionisationsgrad

On the basis of a foregoing paper new theoretical results for the positive column at low pressure and strong ionization, especially for discharges in noble gas ion lasers, are given. The mean velocity v_n0 of the neutral atoms reemitted from the wall is taken into account. The electric conductivity is calculated for an argon plasma. The formulas connecting the electron temperature, the mean neutral gas density, and the electric field strength are derived. The electron temperature, the axial electric field intensity, the degree of ionization, the axial electron drift velocity, the ion flux to the wall, and the force density causing the main part of gas pumping along the column are calculated as functions of the product of the mean current density and the tube radius, and of v_n0 for argon. The axial drift velocity of the electrons is still smaller than the mean thermal electron velocity for high discharge currents, except at very low gas pressures. In general, the ion flux to the wall is not directly proportional to the discharge current. The factor for the determination of the charged particle density by means of probe measurements at the wall is discussed. The self-magnetic field affects the discharge only at high electron temperature, high degree of ionization, and relatively large tube radius, i.e. at high current density and low gas pressure in not too narrow discharge channels.     

Anode plasma structure in a gas discharge with neutral density depleted by ionization

We consider the anode plasma structure in a gas discharge with density of neutral atoms (neutrals) depleted by strong ionization. We obtain analytical solutions of the quasi-neutrality equation for the potential distribution and a condition for the existence of anode plasma in the one-dimensional case for arbitrary potential dependences of the neutral depletion frequency and the electron density. We consider the special cases of a constant neutral depletion frequency, ionization by Maxwellian electrons, and ionization by an intense electron beam under the conditions of collisionless ion motion and Boltzmann thermal electron distribution. The solutions for the first two cases at zero depletion parameter, i.e., at constant gas density, match those obtained in [1] by a power series expansion. In the case of ionization by Maxwellian electrons, the formation of anode plasma at reasonable working-gas flow rates is shown to be possible only at a fairly high electron temperature (if, e.g., xenon is used as the working gas, then T _e ≥ 5 eV). Steady-state solutions of the quasi-neutrality equation under ionization by an intense electron beam exist only if the ratio of the electron beam density to the maximum thermal electron density does not exceed a certain limiting value.     

The surface energy of an electron gas in model crystals

The surface energy of an electron gas in a crystal is considered. The results obtained for a quadratic spectrum are generalized to an arbitrary energy spectrum in certain crystal models. The surface energy of an electron gas with a quadratic spectrum is found for a sample with a rough boundary when the height of irregularities is small compared with the electron wavelength.     

Magnetic bloch electron states and spin polarization in 2D superlattices without an inversion center with Rashba spin-orbit interaction in an electron gas

The quantum states of carriers in 2D doubly periodic n-type semiconducting superlattices without spatial inversion symmetry in an external magnetic field are calculated in the one-electron approximation. It is shown that the spin-orbit interaction and spin splitting in the magnetic field may lead to the occurrence of the photovoltaic effect in a 2D electron gas without an inversion center and to a nonzero spin magnetization of the electron gas in the plane perpendicular to the magnetic field.     

相对论简并电子气体的磁化

中子星内部的致密电子是高度简并的相对论气体, 其输运性质与中子星磁或热的观测现象密切相关, 被认为是中子星磁场的主要载体. 外磁场中电子的朗道能级是分立的且高度简并的, 与无外场时的能量差决定 了系统的磁化程度, 用量子统计的方法可计算理想相对论电子气体的磁化率. 结果表明弱场条件下的磁化率在数量级上接近白矮星的10^-3. 强磁场下的磁化呈现出类似在某些低温金属中出现的de Haas-van Alphen 震荡效应, 高次谐频的震荡幅度有可能超出临界磁化时的磁化率. 表明中子星内部有可能存在非稳定的磁化过程, 发生类似气液转化的一级相变过程, 出现两种磁化共存的稳定态或过冷磁化的亚稳态(若不同磁化态间存在表面能). 从亚稳态向稳定态的突然转化可能与磁星的辐射有关, 可以解释在磁星巨闪过程中观测到的额外辐射问题.     

Resonant transmittance through periodically modulated films

We analyze the optical transmittance at normal incidence for an electron gas without losses. The electron gas is supposed to have a plane parallel slab geometry and its dielectric permittivity is assumed to be periodically modulated in one direction parallel to the interfaces. Due to surface plasmon polariton mode excitation, there exist resonance frequencies where the transmittance equals to unity. The number and positions of peaks are investigated analytically and a comparison with the analytic theory by Dykhne et al. [6] is made.