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Nanowire FETs for Healthcare Applications
Published in Balwinder Raj, Brij B. Gupta, Jeetendra Singh, Advanced Circuits and Systems for Healthcare and Security Applications, 2023
Experimentally, charge carriers in semiconductors scatter because of vibrations in the lattice, impurities due to ionized ions, and other structural defects in the lattice. The scatterings result in the charge carriers or electrons moving from one path to another, as shown in Figure 3.1. The critical dimensions of semiconductor devices should be larger than the mean free path. The mean free path is defined as the average distance between two different scattering events. Charge carriers i.e. electrons and holes have random motion into the semiconductor devices in a specific direction, which is directed by the applied electric field (Anantram et al., 2008).
Vacuum and Gas Kinetics
Published in Eiichi Kondoh, Micro- and Nanofabrication for Beginners, 2021
Molecular collisions are purely stochastical and the molecular speeds have a distribution; and therefore, the free path has a distribution. The average of this distribution is called the mean free path, frequently abbreviated as MFP. The mean free path is a crucial quantity needed to describe the behavior of gas molecules at reduced pressure. The mean free path is also closely related to viscosity and thermal conductivity of a gas.
Micro/Nano Heat Transfer
Published in Sadık Kakaç, Hongtan Liu, Anchasa Pramuanjaroenkij, Heat Exchangers, 2020
Sadık Kakaç, Hongtan Liu, Anchasa Pramuanjaroenkij
When the gas is at very low pressure, the interaction between gas molecules and the wall becomes as frequent as intermolecular collisions so the effects of boundaries and the molecular structure become more important on the flow. This type of flow is known as rarefied flow, and these effects are called rarefaction effects. The Knudsen number, which is an dimensionless number defined as the ratio of the mean free path of the molecules to the characteristic length of the flow channel, is used to represent rarefaction effects, and the Knudsen number is defined as4Kn=λL
Photon, neutron absorption capabilities of Y2O3-Al2O3-P2O5 glasses
Published in Radiation Effects and Defects in Solids, 2022
M.W. Aladailah, O.L. Tashlykov, M.W. Marashdeh, H. Akhdar
The Δ0.5 of a gamma-ray is described as the quantity of shielding material necessary to reduce the beam's intensity to half of its original value. Similarly, the mean free path (MFP) is the average distance traveled by a particle between two successive collisions. The sample with the lower values of the half-value layer (Δ0.5) and MFP is the most efficient radiation protection. The following (3) and (4) equations are used to determine Δ0.5and MFP (30, 31). Here µ – linear attenuation coefficient(cm−1). The interaction of a portion of the total number of electrons in the shielding sample with a gamma photon is described by Zeff. As a result, we can calculate the effective atomic number using the mass attenuation coefficient values of each constituent element as Eq (5) (32, 33): where denotes the weight fraction of element denotes the atomic weight, and Zi denotes the atomic number.
Study of Shock Structures Using the Unified Gas-Kinetic Wave-Particle Method with Various BGK Models
Published in International Journal of Computational Fluid Dynamics, 2022
Guochao Fan, Wenwen Zhao, Zhongzheng Jiang, Weifang Chen
The Knudsen number (Kn), defined as the ratio of the molecular mean free path to the object characteristic length, is used to preliminarily evaluate the degree of gas rarefaction and distinguish the flow regime from continuum flow to free molecular flow correspondingly. As Kn increases, beyond the hydrodynamic scale, the widely used Navier–Stokes equations with linear constitutive relations become incompetent in those non-equilibrium flows due to the breakdown of continuum assumption. For example, Navier–Stokes equations cannot correctly reproduce the behaviour of shock thickness for increasing Mach number (Gilbarg and Paolucci 1953). As the foundation of gas-kinetic theory, however, the Boltzmann equation is capable of describing the non-equilibrium processes from continuum flow to free molecular flow. After this kinetic equation is formed, the crucial problem in academia is how to solve it accurately and efficiently.
High order parallelisation of an unstructured grid, discontinuous-Galerkin finite element solver for the Boltzmann–BGK equation
Published in International Journal of Computational Fluid Dynamics, 2019
B. Evans, M. Hanna, M. Dawson, M. Mesiti
The dimensionless coefficient, Knudsen number, allows the classification of a fluid flow in terms of the degree of rarefaction (Niimi). The Knudsen number, Kn, is defined as , where λ is the mean free path of molecules in the flow and L is a suitable reference length scale. From kinetic theory, the mean free path, λ, can be computed as where is the Boltzmann constant ( J/K), T is the gas temperature, p the gas pressure and d the molecular diameter.