Issues

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2019

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vol. 17 / 

Issue 2

 



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Yu. O. Kruglyak
«Physics of Nanotransistors: Scattering of Electrons and Model of Transmission of Metal–Oxide–Semiconductor Field-Effect Transistor»
225–253 (2019)

PACS numbers: 72.10.-d, 72.20.Dp, 73.23.Ad, 73.40.-c, 73.50.Bk, 84.32.Ff, 85.35.-p

A qualitative pattern of electron-scattering phenomena in the conduction channel of nanotransistors is considered in detail, and important results are formulated in the form of a summary of formulas (18), in which the concept of the transmission coefficient T(E) connecting the mean free path ?(E) with the conduction channel length L is key. Then, the generalized theory of Landauer–Datta–Lundstrom (LDL) transport enables to construct a model for the MOSFET transmission with allowance for the scattering of electrons. The limitations imposed by the MOS electrostatics are taken into account in the Landauer expression for the current (19). The result is a model for passing the MOSFET in the form of a summary of formulas (36) for calculating both the linear region and the saturation region of the output characteristic of a nanotransistor, which can be compared with the ballistic model of a MOSFET (69/[1]). If the transistor operates in a subthreshold mode, one can use nondegenerate statistics. However, in the regime above the threshold, the conduction band at the barrier top is close to or even below the Fermi level, so we need to use the Fermi–Dirac statistics. Nevertheless, it has become a practice in the theory of MOS devices to use the nondegenerate Maxwell–Boltzmann statistics, since its use greatly simplifies calculations, leads to simpler formulas, and makes the theory more understandable. In practice usually, some parameters of the transistor are not known with sufficient accuracy, and in the case of using nondegenerate statistics, they can be considered as fitting parameters, providing quite acceptable results. The obtained equations are in a good agreement with the physics of processes in the linear region as well as in the saturation region that cannot be said concerning the whole region of voltage variation in the drain, since we do not have a sufficiently reliable model for the T(VDS) dependence. Next, we show how you can combine the penetration model and the virtual source model, and thus to simulate the entire MOSFET output characteristic.


Key words: nanoelectronics, field effect transistor, MOSFET, LDL model, transistor metrics, electron scattering, penetration model.

https://doi.org/10.15407/nnn.17.02.225

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