Mean free path

About: Mean free path is a research topic. Over the lifetime, 4412 publications have been published within this topic receiving 114418 citations.

Transport properties of silicon

Abstract: Electrical conductivity, thermal conductivity, and thermoelectric power of single-crystalline silicon are investigated at temperatures between 2 and 300 K. From the measured data we calculate the mean free path of electrons and phonons and separate diffusion part and phonon-drag part of the thermoelectric power. Using a new method, we evaluate the mean free path of those phonons which are responsible for the phonon drag effect.

Emission probability of hot electrons from silicon into silicon dioxide

Abstract: An experimental method is described for directly measuring the probability of electron emission from the silicon substrate into the SiO2 layer after the electron has fallen through a certain potential drop in traversing the depletion layer and reached the Si‐SiO2 interface. The method is based on optically induced hot‐electron injection in polysilicon‐SiO2‐silicon field‐effect‐transistor structures of reentrant geometry. The emission probability was studied as a function of substrate doping profile, substrate voltage, gate voltage, and lattice temperature. It was found that the hot electrons could be emitted by tunneling as well as by surmounting the Schottky‐lowered barrier. Over‐the‐barrier emission dominates at large substrate voltages, where the emission probability is high, and tunnel emission becomes appreciable and may even dominate at small substrate voltages where the emission probability is low. A simple model was developed based on the assumption that only those hot electrons lucky enough to escape collision with optical phonons were emitted. Using this model, we found that the expression P=A exp(−d/λ) described very well the dependence of the emission probability on doping profile, substrate voltage, and gate voltage. Here A=2.9 is a constant, λ is the optical‐phonon‐electron collision mean free path, d is the distance from the Si‐SiO2 interface where the potential energy is equal to the ’’corrected’’ barrier of (3.1 eV−βEOX1/2 −αEOX2/3ox), βEOX1/2 is the Schottky lowering of the barrier, and αEOX2/3 is a ’’barrier‐lowering’’ term introduced to account for the probability of tunneling. The temperature dependence of the collision mean free path was found to follow the theoretical relationship λ=λo tanh(ER/2kbT), with λo=108 A and ER=0.63 eV. This model is useful for evaluating potential hot‐electron‐related instability problems in IGFET and similar structures.

Critical behavior of disordered degenerate semiconductors. II. Spectrum and transport properties in mean-field theory

Abstract: The critical behavior of disordered degenerate semiconductors is studied within a mean-field theory valid when the number of degeneracy points is large I show that above two dimensions there is a semimetal-metal transition at a critical impurity concentration The mean free path and the one-particle density of states exhibit scaling behavior with universal exponents The transition is smeared at nonzero temperature An equation of state, relating temperature, disorder, and bare conductivity, is presented In two dimensions, the semimetallic phase is unstable I show that a localization transition follows except in two dimensions where all states are localized The bare conductivity appears to be a universal number in two dimensions Applications to zero-gap semiconductors and other systems are discussed

Models of Synchrotron X-Rays from Shell Supernova Remnants

Abstract: The diffusive shock acceleration process can accelerate particles to a maximum energy depending on the shock speed and age and on any competing loss processes on the particles The shock waves of young supernova remnants can easily accelerate electrons to energies in excess of 1 TeV, where they can produce X-rays by the synchrotron process I describe a detailed calculation of the morphology and spectrum of synchrotron X-rays from supernova remnants Remnants are assumed to be spherical and in the Sedov evolutionary phase, though the results are insensitive to the detailed dynamics The upstream magnetic field is assumed uniform; downstream it is assumed to be compressed but not additionally turbulently amplified In all cases, spectra begin to depart from power laws somewhere in the optical to UV range and roll off smoothly through the X-ray band I show that simple approximations for the electron emissivity are not adequate; a full convolution of the individual electron synchrotron emissivity with a calculated electron distribution at each point in the remnant is required Models limited by the finite shock age, by synchrotron or inverse Compton losses on electrons, or by escape of electrons above some energy have characteristically different spectral shapes, but within each class, models resemble one another strongly and can be related by simple scalings The images and spectra depend primarily on the remnant age, the upstream magnetic field strength, and the level of magnetic turbulence near the shock in which the electrons scatter In addition, images depend on the viewing or aspect angle between the upstream magnetic field and the line of sight The diffusion coefficient is assumed to be proportional to particle energy (or mean free path proportional to gyroradius), but I investigate the possibility that the proportionality constant becomes much larger above some energy, corresponding to an absence of long-wavelength MHD waves Models producing similar spectra may differ significantly in morphology, which allows for possible discriminations I parameterize the model spectra in terms of a slope at 4 keV and a factor by which the X-ray flux density at that energy falls below the extrapolated radio spectrum Synchrotron radiation may contribute significantly to the X-ray emission of remnants up to several thousand years old