Carrier Distribution Function Research Articles

Tunable High-Frequency Acoustoelectric Current Oscillations in Fluorine-Doped Single-Walled Carbon Nanotubes

Herein, we report on a fluorine-doped single-walled carbon nanotube (FSWCNT) phenomenon, that yields tunable high-frequency self-sustained acoustoelectric direct current (ADC) oscillations. A tractable analytical method was used in the hypersound domain, to base the calculations on carriers in the lowest miniband. Hypothetically, the energy of interaction between the carriers and the acoustic phonons is less than the energy of the typical carriers. High-order harmonics of the acoustic phonons’ effective field could be disregarded under this supposition. The ADC was observed to exhibit a nonlinearity, that resulted from the carrier distribution function’s distortion as a result of interaction with the acoustic phonons, which had strong nonlinear effects. Theoretically, we demonstrated that the dynamics of space charge instabilities, due to Bragg reflection of Bloch oscillating carriers in the FSWCNT’s miniband, were the only factors which contributed to the creation of radiation in the terahertz (THz) frequency range. The study also investigated the influence of various FSWCNT parameters such as the overlapping integrals (Δs and Δz), ac-field E1, and carrier concentration noon the behaviour of the ADC. The results showed that the intensity of the ADC oscillation Jzzae/Joae could be tuned by adjusting Δs, Δz, E1, and no.This tunability suggests that FSWCNTs could be used as an active device operating at very high frequencies, potentially reaching the submillimeter wavelength range. The study also suggests the possibility of domain suppression and acoustic Bloch gain through dynamic ADC stabilisation.

Acoustoelectric direct current density in fluorine doped single-walled carbon nanotubes due to harmonic mixing of bichromatic fields with commensurate frequencies

Herein, we theoretically report on the acoustoelectric direct current (ADC) generation in a non-degenerate fluorine doped single-walled carbon nanotubes (FSWCNTs), due to mixing of waves with commensurate harmonics in the hypersound regime, qℓ≫1 (where q is the acoustic wavenumber and ℓ is the carrier mean free path). The only restriction of the theory on the sound intensity was that, the interaction energy between the carrier and the acoustic phonons must be small in comparison with the characteristic carrier energy. It was observed that in this situation, the higher harmonics of the effective field of the acoustic wave can be neglected; the origin of the nonlinearity was due to the distortion of the distribution function for carriers moving in phase with the phonons, as a result of interaction with the acoustic wave; the nonlinear effects can then be very important. The ADC generated was highly nonlinear and non-ohmic and depended on the amplitude of the bichromatic fields (i.e., pump and probe field), overlapping integral for jumps (Δs and Δz), carrier concentration (no), Bloch frequency (Ω), photon frequency (ω) and acoustic phonon frequency (ωq). The strong nonlinearity and non-ohmicity of the I-V characteristic of the FSWCNTs may be associated with a number of nonlinear phenomena including the non-parabolic band relation, carrier heating due to distortion in carrier distribution function, Stark component, and Bloch oscillations of intraminiband carriers. It was possible to alter the magnitude and direction of the rectified ADC by adjusting the phase of the fields, and the generation of ADC corresponded to even instability zones in the FSWCNTs. Thus, based on the high ADC obtained, we propose FSWCNTs for ADC generation under bichromatic fields with commensurate harmonics.

Trapping of Hot Carriers in the Forksheet FET Wall: A TCAD Study

We simulate the spatial profile of trapped charge in the forksheet FET wall under hot-carrier stress by calculating carrier distribution functions and using a non-radiative multiphonon model. We observe charge trapping above and below the horizontal projection of the sheet in the wall. We find the charge profile not to depend on the sheet width and the trapping in the forksheet FET wall to be significantly smaller than the trapping in the gate stack.

Effects of the Nature of Boundaries Conditions and Their Truncation Errors on the Distribution of Minority Carriers in Silicon Solar Cell

In this work, the effects of boundaries conditions and truncation errors in the distribution of minority carriers in the semiconductor are studied. It is a one-dimensional digital study of a polycrystalline silicon solar cell under polychromatic illumination in a dynamic state. Starting from the Boltzmann equation of semiconductors, the author establishes the general equation of particle transport. Assumptions made on the latter allow it to give the equation of distribution of minority carriers in a general way in its case to be studied. This dimensioned distribution equation reveals the parameters of influences on the distribution of carriers. It obtains a partial derivative equation for the carrier distribution function. The boundary conditions are then discretized to order one and then to order two. By considering boundary conditions and the nature of the carriers, the author numerically resolves the discretized general equation by assessing the influence of the nature of the boundary conditions and truncation errors and the influence of the discretization step on the density of the charge carriers by setting certain parameters and varying others. The work ends with a conclusion and logical follow-up to this work.

Photocurrent generation in graphene/h-BN heterostructures under solar illumination

Graphene/h-BN tunneling heterostructures have considerable potential for developing future optoelectronic devices including solar cells because of their unique properties. To date, theoretical studies have been constrained to a single graphene insulator graphene-tunneling junction. We demonstrate how photocurrents can be generated in multilayer graphene/h-BN heterostructures. We compute the steady-state carrier occupation in graphene by solving the Boltzmann transport equation under a standard 1 sun illumination with electron–phonon and electron–electron scattering. An energy balance equation is used to normalize the carrier distribution function. The effect of the heterostructure and rotational alignment on the photocurrent is discussed. We obtained heterostructure designs to produce photocurrents above 17 mA/cm2. Our approach based on the formation of a graphene/h-BN multilayer structure is a promising candidate for high-performance photovoltaic devices.

Electrical conductivity of a thin film in the case of an arbitrarily oriented ellipsoidal isoenergetic surface of a conductor

The static electrical conductivity of a thin conducting film is calculated using the kinetic approach. The model of diffuse boundary conditions is used as boundary conditions for the charge carrier distribution function. The isoenergetic surface of the conducting film material is an ellipsoid of rotation that is arbitrarily oriented in the pulse space. The volume of the conductor is dominated by scattering on impurity atoms and on dislocations of electrons (holes). The electrical conductivity of the film is analyzed depending on the angles that determine the direction of the ellipsoid axis of rotation, and a comparison with the results for the case of a macroscopic sample is presented. A comparison is made with experimental data for the electrical conductivity of Bi and Si thin films.

SmB6: A material with anomalous energy distribution function of charge carriers?

We argue that the ground state energy distribution function of the subsystem of localized charge carriers in valence fluctuating semiconductors is qualitatively different from that for conventional semiconductors at T=0 K. As follows from our analysis, both occupied and unoccupied sites can be found above as well as below the Fermi level in the ground state as a consequence of dynamical changes of impurity energies due to valence fluctuations. Such anomalous energy distribution of charge carriers sheds new light on interpretation of experimental results of valence fluctuating semiconductors, e.g. SmB6 and YbB12.

The backward Monte Carlo method for semiconductor device simulation

A backward Monte Carlo method for the numerical solution of the semiconductor Boltzmann equation is presented. The method is particularly suited to simulate rare events. The general theory of the backward Monte Carlo method is described, and several estimators for the contact current are derived from that theory. The transition probabilities for the construction of the backward trajectories are chosen so as to satisfy the principle of detailed balance. This property guarantees stability of the numerical method and allows for a clear physical interpretation of the estimators. A symmetric sampling method which generates wave vectors always in pairs symmetric to the origin can be shown to yield zero current exactly as thermal equilibrium is approached. The properties of the different estimators are evaluated by simulation of an n-channel MOSFET. Quantities varying over many orders of magnitude can be resolved with ease. Such quantities are the drain current in the sub-threshold region, the high-energy tail of the carrier distribution function, and the so-called acceleration integral which varies over 30 orders in the example shown.

Valley Hall transport of photon-dressed quasiparticles in two-dimensional Dirac semiconductors

We present a theory of the photovoltaic valley-dependent Hall effect in a two-dimensional (2D) Dirac semiconductor subject to an intense near-resonant electromagnetic field. Our theory captures and elucidates the influence of both the field-induced resonant interband transitions and the nonequilibrium carrier kinetics on the resulting valley Hall transport in terms of photon-dressed quasiparticles (PDQs). The non-perturbative renormalization effect of the pump field manifests itself in the dynamics of the PDQs, with a quasienergy spectrum characterized by dynamical gaps δη (η is the valley index) that strongly depend on field amplitude and polarization. Nonequilibrium carrier distribution functions are determined by the pump field frequency ω as well as the ratio of intraband relaxation time τ and interband recombination time τrec. We obtain analytic results in three regimes, when (I) all relaxation processes are negligible, (II) τ ≪ τrec, and (III) τ ≫ τrec, and display corresponding asymptotic dependences on δη and ω. We then apply our theory to 2D transition-metal dichalcogenides, and find a strong enhancement of valley-dependent Hall conductivity as the pump field frequency approaches the transition energies between the pair of spin-resolved conduction and valence bands at the two valleys.

A theoretical model for calculating the effects of carrier heating with nonequilibrium hot phonons on semiconductor devices and the current-voltage relations

A theoretical model is proposed and presented to calculate carrier heating with nonequilibrium hot-phonon effects on semiconductor devices. The effects of nonequilibrium hot phonons are incorporated in the calculation of the intraband energy relaxation rates of the interactions between carriers and polar longitudinal optical (LO) phonons. This model and its rate equations of carrier number and energy densities are employed for the numerical calculation of the magnitude of carrier heating and its effects on the current-voltage relation of semiconductor devices. Simulation results show that the effects of carrier heating significantly make the current-voltage relation deviate from the exponential form of an ideal diode and the output current saturate at high applied voltages. Carrier temperatures are shown to reach several thousand degrees for devices with small active regions. The results suggest that carrier heating will become more severe and noticeable for semiconductor devices with active regions of nano-size structures. The results conclude that the methods of using the classical Maxwell-Boltzmann distribution function for carriers with a single energy relaxation time or theoretical models without hot-phonon effects are both inadequate and questionable for studying carrier heating problems.

In English

Relaxation of the excess minority carrier distribution in macroporous silicon structure was calculated using the finite difference method. The initial distribution of the excess minority carriers has two maxima after carrier generation by electromagnetic wavelength 0.95 μm with small absorption depth. The first maximum of the initial distribution function is in macroporous layer, the second one is in monocrystalline substrate. Surface recombination leads to the diffusion of excess charge carriers to recombination centers and creates the non-homogeneity of the excess charge carrier distribution. A rapid maximum decrease of the excess carrier distribution function in a macroporous layer and near the boundary of a macroporous layer and monocrystalline substrate is found. The slow decrease of the distribution function in a monocrystalline substrate is evaluated. We observed one maximum of the excess minority carrier distribution after homogeneous carrier generation by electromagnetic wavelength 1.05 μm with big absorption depth. The rate of change in the concentration of excess minority carriers decreases in time in macroporous silicon layer due to high recombination and increases due to diffusion to the surface of silicon substrate after generation by the electromagnetic wave 0.95 μm with small absorption depth. The rate of change in the concentration of excess minority carriers decreases in time in the entire structure after generation by the electromagnetic wave 1.05 μm with big absorption depth and small non-homogeneity.

In English

We have obtained a simple expression that determines the effective minority carrier lifetime in macroporous silicon with periodic arrangement of infinitely long macropores as a function of bulk lifetime, surface recombination velocity of minority carriers, pore radius and the distance between the centers of macropores. This expression can be applied also to macroporous silicon with randomly distributed pores by replacing the pore radius and the distance between the centers of macropores with their average values. The distribution of steady-state excess minority carriers in macroporous silicon is calculated for the analytical model proposed by us. The calculation is made for the case when both the outer surface of macroporous silicon and the bottom of pores are illuminated with light. We observed two peaks of the distribution of steady-state excess minority carriers in macroporous silicon near the surfaces illuminated with light of wavelength 0.95 m. At the same time, if macroporous silicon was illuminated with light with the wavelength of 1.05 μm, we observed only one maximum in the distribution function of the excess minority carriers, in spite of the fact that the pore bottom was also illuminated with light. It is shown that the distribution of excess minority carriers in macroporous silicon with through pores is similar to the distribution in single crystal silicon. But in this case, the effective lifetime of minority charge carriers in the effective medium of macroporous silicon, which includes silicon and the surface of pores, corresponds to the bulk minority-carrier lifetime in monocrystalline silicon.

On the propagation of charge carriers fluxes in the thin layer of a plane-parallel solid-state structure with scattering at the boundaries of the layer taken into account

The composition of the thin layer of a plane-parallel solid-state structure affects the propagation of differential charge carriers fluxes in the thickness of the layer and through it. Scattering of these fluxes at the boundaries of the thin layer affects also the distribution function of charge carriers. This scattering is correctly taken into account in integrated boundary conditions for the kinetic equation. For a plane-parallel layer, the kinetic equation (in the approximation of the relaxation time) is reduced to a convenient form, which describes the propagation of differential fluxes in the thickness of the layer. The solution for thick and thin layers of different types (metal, insulator, semiconductor) is analyzed. Practically important problems, in which the obtained solutions can be effectively used, are specified.

Microscopic Hot-Carrier Degradation Modeling of SiGe HBTs Under Stress Conditions Close to the SOA Limit

We present and validate a physics-based model to describe the underlying mechanisms of hot-carrier degradation in bipolar transistors. Our analysis is based on a deterministic solution of the coupled system of Boltzmann transport equations for electrons and holes. The full-band transport model provides the energy distribution functions of the charge carriers interacting with the passivated Si–H bonds along the oxide interface. The simulation results assert the dominant role of hot holes along the emitter–base spacer oxide interface in the long-term degradation of an n-p-n SiGe heterojunction bipolar transistor under low and high-current conditions at the border of the safe-operating area. The interface trap density is calculated by incorporating an energy driven paradigm for the microscopicmechanisms of defect creation into a reaction-limitedmodelwith dispersive reaction rates. These interface traps increase the forward-mode base current via Shockley–Read–Hall recombination and degrade the overall device performance. The Gummel characteristics of a degraded device and time evolution of the excess base current for different stress conditions are verified versus the experimental data obtained for a state-of-the-art toward-terahertz SiGe HBT.

Hot-Carrier Degradation Modeling of Decananometer nMOSFETs Using the Drift-Diffusion Approach

We extend our previously suggested drift-diffusion (DD)-based hot-carrier degradation model to the case of decananometer transistors. Special attention is paid to the effect of electron-electron scattering, which populates the high energy tail of the carrier distribution function, by using a rate balance equation. We compare the results of the DD-based model with the results obtained from a spherical harmonics expansion of the Boltzmann transport equation as well as experimental data. We also study the accuracy and limits of the applicability of the DD-based model and conclude that this model is able to capture hot-carrier degradation in nMOSFETs over a range of gate lengths from 65 to 300 nm with excellent accuracy.

Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors

In the presented report, the Nernst-Ettingshausen effect in layered conductors is investigated. Considering a Fermi surface (FS) consisting of a slightly corrugated cylinder and two corrugated planes distributed periodically in the momentum space, the thermoelectric effects are considered under general assumptions for the value of a magnetic breakdown probability. As a result of an external generalized force, the FS sheets in layered conductors with a multisheet FS appear to be so close that the charge carriers (as a result of magnetic breakdown) can move from one FS sheet to another. In addition, the distribution functions of the charge carriers and the magnetic breakdown oscillations of thermoelectrical field along the normal to the layer, under different values and orientations of the magnetic field, $B$, are calculated. It is shown that if the magnetic field is deflected from the $xz$-plane at an angle $\varphi$, the oscillation part of a thermoelectrical field along the normal to the layer under condition $\sin\varphi\tan\vartheta \gg 1$ is mainly determined with the Nernst-Ettingshausen effect.

Magnetoresistance of organic conductors in the vicinity of a topological phase transition

We analyze the effect of magnetic breakdown on the resistance of layered organic conductors with a multisheet Fermi surface consisting of a cylinder and two slightly corrugated planes along the projection of the momentum onto the normal to the layers. Analytic expressions are derived for the charge carrier distribution function, and the dependences of the interlayer and intralayer conductivities on the magnitude and orientation of the external magnetic field in the immediate vicinity of a topological phase transition are determined when the distance between the different sheets of the Fermi surface is quite small, but the topological structure of the Fermi surface is still intact.

The influence of boundary conditions on the electrical conductivity of a thin cylindrical wire

Within the kinetic approach, the high-frequency electrical conductivity of a thin semiconductor circular cross-section wire is calculated. The radius of the wire is assumed to be small compared with the characteristic skin depth that allows neglecting the skin effect. A model taking into account the dependence of the reflectivity coefficient on the surface roughness factor and the angle of incidence of the charge carriers at the inner border of the wire was used as the boundary conditions for the nonequilibrium distribution function of the charge carriers The extreme cases of a degenerate semiconductor and a nondegenerate one are considered. The results obtained are compared to the calculations for the model of Fuchs diffuse-specular boundary conditions.

Dominant role of many-body effects on the carrier distribution function of quantum dot lasers

The effects of free-carrier-induced shift and broadening on the carrier distribution function are studied considering different extreme cases for carrier statistics (Fermi–Dirac and random carrier distributions) as well as quantum dot (QD) ensemble inhomogeneity and state separation using a Monte Carlo model. Using this model, we show that the dominant factor determining the carrier distribution function is the free carrier effects and not the choice of carrier statistics. By using empirical values of the free-carrier-induced shift and broadening, good agreement is obtained with experimental data of QD materials obtained under electrical injection for both extreme cases of carrier statistics.

Polyaryzatsiyni zalezhnosti vyprominyuvannya haryachymy nosiyamy v InSb

Polarization dependences of the spontaneous radiation emitted by hot carriers in p- and n-InSb have been measured experimentally and explained theoretically. A periodic dependence of the spontaneous radiation intensity on the polarizer rotation angle with respect to the direction of the heating electric field is found. This dependence is associated with a field-induced deviation of the even component in the distribution function of hot carriers from the spherical shape (a deviation from the diffusion approximation).