Quantum transport equations for high electric fields.

We develop a formalism for studying the motion of nondegenerate electrons in semiconductors, which allows a nonperturbative description of the effects of an external high electric field on electron-phonon scattering within the Kadanoff-Baym-Keldysh nonequilibrium Green's-function approach. Based on the exact solutions of Schr\odinger's equation, we solve Dyson's equation for the single-particle retarded Green's function ${G}^{r}$${(\mathrm{k}}_{\ensuremath{\perp}}$,z,z',\ensuremath{\omega}). Recognizing that high fields break the translational symmetry of the system and that momentum is no longer a good quantum number, we use Airy transforms to handle the position dependence parallel to the applied high field. From this we are able to derive a model for the spectral density function A${(\mathrm{k}}_{\ensuremath{\perp}}$,s,\ensuremath{\omega}) through which we can account for quantum effects such as collisional broadening and the intracollisional field effect in a simple and rigorous way. We demonstrate the theory by considering only weak scattering with nonpolar optical phonons and restrict ourselves to fields that are constant in space and time. Our formulation suggests the presence of a novel quantum effect induced by the simultaneous presence of scattering and electric field which produces a discontinuous trajectory of the electron path along the field direction.

The influence of a high average electric field (∼1 V/nm) in the hydrophobic interior of a bilayer lipid membrane on short-wavelength in-plane phononic motions of lipid chains is considered. The average electric field is assumed to be nearly constant on a picosecond time scale and a nanometer length scale. This field may be induced, for instance, by externally applied subnanosecond electric pulses or the membrane dipole potential. Using a generalized hydrodynamic approach, we derive a corresponding electrohydrodynamic model generalized to high wave numbers. In the considered approximation, all electric field effects are reduced only to a constant contribution to the generalized isothermal compressibility modulus. The corresponding dynamic structure factor for a lipid bilayer is derived. We show that due to polarization effects, the high field can critically impact the dynamics of longitudinal acousticlike modes at wave numbers near the major peak of the static structure factor. We estimate quantitatively that for typical lipid bilayers, transverse high electric fields can cause strong phonon energy softening, enhancement of phonon population, and formation of a gap in the dispersion of excitation frequency. The results obtained agree with simulations of the initiation of lipid bilayer electropores, suggesting that the proposed model reproduces the essential features of the field's impact on atomic density fluctuations. The proposed mechanism may have significant implications for the understanding of electroporation, passive molecular transport, and spontaneous pore formation in lipid bilayers.

The influence of high electrical DC fields (>20 kV/mm) on aging, polarization and on the morphology of polyethylene (PE) is discussed. Infrared and positron annihilation spectroscopy measurements as well as capacitance measurements tend to suggest that the polymer morphology is modified by high fields. The author shows that the accelerated electrical aging characteristics of PE are linked directly to the morphology changes induced by the field. Below a so-called critical field, the activation volume of the aging process is dependent on the field-induced strain. Above the critical field, the amorphous phase is deformed significantly, and weak van der Waals bonds are broken, leading to another, faster, aging regime. There is an excellent agreement between the proposed model and experimental data obtained with various PE samples. The possible relation between the submicrocavity formation proposed in his aging model and various polarization measurements is discussed. It is his contention that strong charge injection occurs only after submicrocavity formation, i.e. after weak bond breakage. As is well known, the polarization currents obtained under high fields are controlled by space charges. It seems that the wave packets and the negative resistance observed at >100 kV/mm in PE are associated with a steady state in field-induced defect formation. This suggests that space charges are related to the formation of submicrocavities and, therefore, are a consequence, not a cause, of high field aging.

We have investigated quantum corrections to the Boltzmann equation for transport in high, spatially uniform electric fields, with weak scattering. Parabolic bands show no effects for constant fields up to ${10}^{7}$ V/cm; nonparabolic bands or time-varying fields give quantum corrections by dis- torting the energy-conserving \ensuremath{\delta} function in semiclassical transition rates. We have found that in practical cases the scale of this is less than that from collisional broadening, almost invariably neglected. These results extend greatly the known range of validity of the Boltzmann equation in semiconductors.

During ultra high voltage (UHV) transmission, the discharge caused by high intensity electric fields aggravates the aging process of external insulation materials used for composite insulators. The microstructural characteristics of its base material polymer—methyl vinyl silicone rubber—are the key basis for the performance of insulation materials under electric field exposure. Based on molecular dynamics simulations, a molecular model of methyl vinyl silicone rubber was established. Mechanisms influencing the microstructure evolution under electric fields had been studied at the atomic level. The results showed that the initial reaction characteristics of silicone rubber molecules involve the violent vibrated of all the methyl and vinyl atoms, and shortening of the chemical bonds. The neighboring groups were close to each other and generated different amounts of -Si-Si- bonds. This promoted the helical shrinkage of the molecule, and protrusion of the middle of the molecule which presented an inverted U shape. The high electric field greatly reduced the total energy of molecules, and the potential energy in particular was more severely destroyed, resulting in degradation of its structure. Besides, as the electric field intensity increased, the elastic modulus of the molecule gradually increased. It was shown that high electric fields would make the stiffness of silicone rubber become larger, and the brittleness to become stronger, which reduced the mechanical properties of materials, accelerating its aging. The results provide a theoretical basis for establishing the connection between the micro appearance and macro characteristics of materials, as well as reference values for the optimization of base materials used for making composite insulators.

High electric fields, that are characteristic of sub-micron devices, produce highly energetic electrons, lack of equilibrium between electrons, optical phonons, and acoustic phonons, and high rates of heat generation. A simple coupled thermal and electrical model is developed for sub-micron silicon semiconductor devices consisting of the hydrodynamic equations for electron transport and energy conservation equations for different phonon modes. An electron Reynolds number is proposed and used to simplify the electron momentum equation. On a case study of the metal-oxide-semiconductor field-effect transistor with 0.24 μm gate length, the calculated transconductance of 0.175 1/Ω m agreed well with measured value of 0.180 1/Ω m at 2 V drain voltage. The maximum electron temperature is found to occur under the drain side of the gate where the electric field is the highest. Comparison with experimental data shows the predictions of optical and acoustic phonon temperature distributions to have the correct trend and the observed asymmetric behavior. Increase in substrate boundary temperature by 100 °C reduces the drain current by 17% and decreases the maximum electron temperature by 8%. The first effect increases device delay and the second effect decreases the possibility of device degradation by charge trapping in the gate oxide.

In ferroelectric switching experiments with stretched and unstretched PVDF-foils we have measured the time dependent growth of the polarization after applying a high electric field (of about 200 MV/m). These experiments were performed between 300 K and about 140 K. During the dipolar re-orientation (p=dipol moment per monomer) in the high field regime (E = electric field) the liberated energy p»E per monomer is of the same order as kT, and therefore the process of polarization in high fields is expected to be strongly influenced by the liberated energy and thus to proceed in a cooperative way. This cooperative polarization process is demonstrated in the strongly field dependent growth time of the polarization which rapidly decreases when higher fields are applied as can be best observed at temperatures above 200 K.

Transport equations are derived for particles, momentum, and energy of electrons in a semiconductor with two distinct valleys in the conduction band, such as GaAs. Care is taken to state and discuss the assumptions which are made in the derivation. The collision processes are expressed in terms of relaxation times. The accuracy is improved by considering these to depend on the average kinetic energy rather than the electron temperature. Other transport equations used in the literature are discussed, and shown to be incomplete and inaccurate in many cases. In particular, the usual assumption that the mobility and diffusion constant depend locally on the electric field strength is shown to be incorrect. Rather, these quantities should be taken as functions of the local average velocity of electrons in the lower valley.

Electric-field-induced polarization fatigue of [001]-oriented [formula omitted] single crystals

The effective medium theory is extended to the calculation of the dc conductivity and Hall effect of macroscopic inhomogeneous semiconductors in high (just after ohmic region) electrical fields. A cubic network of the macroscopic barriers with random heights is used as a model of the considered semiconductors. The electrical field dependences of the direct and Hall current densities are calculated. As it follows from calculations on the direct and Hall current differential conductivities and also the Hall angle decrease with increasing electrical field in the non‐ohmic region.

The development of high-voltage DC cables is mainly limited by the properties of insulating materials. Adding an appropriate amount of nanoparticles can improve the dielectric properties of materials. To study the effect of high temperature and nano-filler concentration on the conductivity characteristics of the dielectric, LDPE/Sio <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> nanocomposites with the particle size of 7 nm and mass fraction of 0.5wt%, lwt%, and 3wt% were prepared by filling LDPE with nano- Sio <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> particles. The DC conductance at 90°C and 100°C was measured at the electric field strength of1-100 kV/mm, and the temperature sensitivity of the samples were analyzed. The results show that in the condition of high temperature and low electric field, the nanocomposite can effectively reduce the conductivity current density and improve the conductivity performance, and the first threshold electric field increases with the increase of nano-filling concentration. Under the high electric field at high temperatures, temperature becomes one of the main factors that affect the carrier transport process. Among all samples, the LDPE/Sio <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> nanocomposite with a mass fraction of 3wt% has the best conductivity and the lowest temperature sensitivity.

In this paper, we present numerical results for steady-state and time-dependent currents as well as for a long-time average current in strong nonlinear dc and ac electric fields for an electron gas in a one-dimensional (1D) quantum-dot superlattice. A microscopic model is employed for the scattering of electrons by phonons and static impurities by means of the Boltzmann equation method. The dc results are favorably compared with recent exact analytic results based on a relaxation-time model for electron-phonon scattering. Our results demonstrate the different roles played by elastic and inelastic scattering on the damped Bloch oscillations as well as the nonlinear steady-state current and their opposite roles on the damped dynamical localization. We also find a suppression of dynamical localization by strong Bloch oscillations and features in the Esaki-Tsu peaks in the presence of an ac electric field when electron scattering is included. On the basis of a nonequilibrium electron distribution obtained from the Boltzmann equation, a self-consistent-field approach is employed to establish a general formalism for the optical response of current-driven electrons in both the linear and nonlinear regimes to a 1D quantum-dot superlattice. The dc-field dependences of both the peak energy and peak strength in the absorption spectrum for a 1D quantum-dot superlattice are calculated, from which we find: (1) both the peak energy and its strength are significantly reduced with increasing dc electric field; and (2) the peak energy and peak strength are anomalously enhanced by raising the temperature for the nonlinear transport of electrons when a strong dc electric field is applied.

Electrical conduction of poly (methyl methacrylate) (PMMA) is considered to be ionic from low to very high fields near breakdown. Support for the ionic mechanism can be supplied from the compensation law, and from the temperature dependence of the electrical conductivity and the breakdown field. In high electric fields above the ohmic region, it was observed that the apparent activation energy decreased with increasing electric field. A simplified equation for the activation energy was derived in which the dependence of the electric field on ionic jump energy and ionic dissociation energy was taken into consideration. The ionic jump distance between equilibrium positions computed from the equation was 10 to 20 Å and was in good agreement with periodic structure of PMMA.

One of the major problems of polymeric insulation is their tendency to accumulate space charge at higher electric fields, especially in HVDC (High Voltage DC) applications. Nanodielectrics are an emerging area of research because of their potential as a novel insulating material in electrical apparatus and systems. Understanding space charge behavior in these new materials is crucial to their application in high field environment. In the present work, space charge behavior in epoxy alumina nanocomposites is investigated by using Pulse Electro Acoustics (PEA), Conduction Current (CC), and Electroluminescence techniques in conjunction. The PEA technique is used to measure accumulated charge density, and maps the space charge distribution in the volume of the dielectric. Polarization- Depolarization current measurements are carried out to extract conduction current density, dc conductivity, and permittivity. Electroluminescence measurements are related to injection and impact ionization of charge carriers. Space charge density, conduction current density, and electroluminescence counts, show a transition above a certain electric field. The electric field above which all three characteristics undergo a transition is associated with the threshold field for accumulation of space charge. Nano-dielectrics show lower space charge, and lower conductivity at higher fields than neat epoxy. The permittivity of the nanodielectrics is seen to be higher than neat epoxy at lower electric fields. At higher fields their permittivities are comparable. The complementary findings from all three techniques prove to be effective in characterizing the space charge in the nano dielectrics.

A treatment of magnetoconductivity is developed for high electric fields and general energy-band structure using a partial solution of the Boltzmann equation in a form similar to that set up by McClure for low electric fields. The present treatment is valid when the scattering processes are such that the distribution function varies but a small amount over an entire constant-energy surface, or, in the case of the many-valley band structure, over the part of a constant-energy surface within each valley. In the latter case, different distribution functions must be used for the different valleys. The elements of the magnetoconductivity matrix that results are expressed in terms of carrier concentration, total or within each valley, and averages over the carriers of a quantity involving the momentum relaxation time and the S tensor defined by McClure. This tensor, which depends on the shape of the constant-energy surfaces and on the magnetic-field strength, is evaluated for the individual valleys in a nondegenerate many-valley semiconductor. The magnetoconductivity matrix is then in a form convenient for calculation of conductivity and galvomagnetic effects for either low or high electric fields. It is used to obtain expressions for anisotropy voltage and Hall coefficient in high electric fields involving the number of carriers in each valley, orientation of the valleys, and valley averages over quantities involving relaxation time and energy.