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Ю. А. Кругляк
«Учёт рассеяния в обобщённой модели транспорта электронов в микро- и наноэлектронике»
PACS numbers: 72.10.-d, 72.20.Dp, 72.20.Fr, 73.23.-b, 73.63.-b, 85.35.-p
When describing the transport of electrons through a conductor in the diffusion regime, an important role is played by the average mean free path ?, which determines the transmission coefficient T. For a deeper understanding of how the average electron velocity and average scattering time, which determine the magnitude of ?, both the scattering of current carriers and the heat transport are qualitatively described within the Landauer–Datta–Lundstrom (LDL) model in the course of change of scattering times in the process of collisions. The basic relationship between the transmission coefficient and the average mean free path is proved for 1D resistor as the simplest example. A connection is established between ? and the time ?m of momentum relaxation for conductors of different dimensions. There is given an estimation of the averaged values for the mean free path ? from experimental measurements using the diffusion coefficient, and the connection between the mean free path and mobility is established. As an example, the experimental data for Si MOSFET at different approximations along the LDL theory of transport involving models of different accuracy are analysed. The analysis sought to answer two questions: 1) how many modes provide a current conduction? and 2) how the measured resistance is close to the ballistic limit? Answers to these questions are given with different degrees of reliability. To simplify the calculations, the simplest model at T???0 K was initially used that is certainly not sufficiently satisfactory, especially for the room temperature. Further, we assume the Maxwell–Boltzmann statistics for the charge carriers (non-degenerate conductors); the calculations in this case do not cause difficulties, however, the assumption of non-degeneracy is also inadequate above the voltage threshold. Finally, abandon any assumptions and simply calculate the Fermi–Dirac integrals to get the value of equal to 15 nm, which is the best possible estimation for a given resistor length of 60 nm. The length of this resistor cannot be considered too large compared to the mean free path, so it is physically correct to assume that this resistor operates in a quasi-ballistic regime.