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Electrical Properties of Metals and Semiconductors
Published in Yip-Wah Chung, Monica Kapoor, Introduction to Materials Science and Engineering, 2022
Consider a metal with n conduction electrons per unit volume, to which an electric field E is applied. This causes acceleration of these conduction electrons equal to eE/m, where e is the electron charge and m its mass. Figure 3.1 shows schematically how the velocity of a conduction electron varies with time: the electron velocity increases linearly with time, suddenly decreases to some value due to collision with obstacles in the solid (which include lattice vibrations, impurities, interfaces, or other electrons), then re-accelerates and so on. Define τ as the average time between collisions (also known as mean free time or relaxation time). The average drift velocity vd acquired by electrons is given by: vd=eEmτ
Introduction
Published in DAVID K. FERRY, Semiconductor Transport, 2016
The density is the sheet density of carriers in the qua si-two-dimensional electron gas at the interface discussed above. The actual density can usually be varied by an order of magnitude on either side of this value; for example, 1010-10'3 cm"2 are possible in Si and somewhat lower at the upper end in GaAs (2 x 1012 cm-1}. Again the mobility is a typical value, but in high- mobility structures, as much as 107 cm2/Vs has been achieved in GaAs, and 2 x 105 cm2/Vs has been achieved in Si (modulation doped with SiGe at the interface) at low temperature. Finding the scattering time from the mobility is straightforward, and masses of 0.067m0 and 0.19m0 are used for GaAs and Si, respectively. The Fermi wave vector is determined by the density through kF = (2jws)> , (It is often not appreciated that the inversion layer in an Si MOSFET is degenerate even at room temperature at relatively moderate densities.) The Fermi velocity is vF = kfh/m. The elastic mean free path is then defined by the scattering time and the Fermi velocity as lt - vrx„. The inelastic mean free path is estimated for the two materials based upon experiments (Ferry and Goodnick, 1997), but it also should be recognized that there will be a range of values for this parameter. The inelastic mean free time, often called the phase-breaking or coherence time, is found through the relationship lm = vrzm, and the inelastic, or phase-breaking, time is found from the estimate of the inelastic mean free path.
Basic Electronic Structures and Charge Carrier Generation in Organic Optoelectronic Materials
Published in Sam-Shajing Sun, Larry R. Dalton, Introduction to Organic Electronic and Optoelectronic Materials and Devices, 2016
where is the electron velocityis the average electron transport relaxation time, also called mean free time (MFT), defined as the average time an electron travels between the two scattering centers [6,7]
Analysis of Population Control Techniques for Time-Dependent and Eigenvalue Monte Carlo Neutron Transport Calculations
Published in Nuclear Science and Engineering, 2022
Ilham Variansyah, Ryan G. McClarren
Note that particle position and time are respectively measured in mean free path () and mean free time [], where is particle speed. We also have the typical scattering parameter . The scalar flux solution of this time-dependent problem is
Beyond direct simulation Monte Carlo (DSMC) modelling of collision environments
Published in Molecular Physics, 2019
O. Schullian, B. R. Heazlewood
The density of all three gases in the box is found to be uniform, with the temperature and velocity of each species converged and stable (see Figure 3). A numerical estimate of how well the simulation reproduces the properties expected from a quantitative theoretical treatment of the system can be derived from considering the mean free path, mean free time and collision frequency per unit volume. This information can be straightforwardly obtained from the simulation, although it is worth commenting on the collision frequency calculations. The frequency of collisions between two different species can be obtained in two ways – by following the trajectories of species 1 and monitoring interactions with the mean field gas of species 2, or by following species 2 and tracking its interactions with the mean field gas of species 1. While either approach will yield the same result, it is much more efficient to follow the lower density particle, species 2 (He), as it propagates through the high-density field of species 1 (Ar), as far more collisions of interest occur per trajectory than would take place in the reverse situation. The collision frequency between each of the gases is shown in Figure 4, with the exception of N –N collisions (species 3 colliding with species 3). This is because no N –N collisions took place over the length of the simulation – as expected, given that the mean free time for such collisions is approximately 13 s. The simulated collision frequencies between all other collision partners, Ar–Ar, Ar–He, Ar–N, He–He, and He–N, are in excellent agreement with theoretical values (within 0.5%). As Table 3 shows, the mean free path and mean free time established from the simulations are also in line with the expected theoretical values.