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[...]... 298 11.5 Conclusion 301 References 301 Copyright © 2006 Taylor & Francis Group, LLC 1 Physics of Silicon Nanodevices David K Ferry, Richard Akis, Matthew J Gilbert, and Stephen M Ramey 1.1 INTRODUCTION For the past several decades, miniaturization in silicon integrated circuits has progressed steadily with an exponential scale described by Moore’s Law.1 This incredible progress... metaloxide-semiconductor field-effect transistors (MOSFETs) and then turn to the much more important role in small transistors We follow this with a discussion of the 1 Copyright © 2006 Taylor & Francis Group, LLC 2 Silicon Nanoelectronics ultimately small device—the quantum dot and single-electron tunneling Finally, a discussion is given of many-body effects in such small devices Each of these topics will be discussed... the channel, and µ V 2L (2.5) is the (average) velocity in the channel Hence, we may rewrite Equation (2.3) once again as I D = We nS v S Copyright © 2006 Taylor & Francis Group, LLC nD v D (2.6) 4 Silicon Nanoelectronics Decoherence regions L FIGURE 1.1 A conceptual device under bias The source is at the left and the drain at the right, as indicated by the two gray areas, which may be considered to... given another version of a ballistic transport treatment for the MOSFET, and has used this to some success in fitting to experimental data19 Although Copyright © 2006 Taylor & Francis Group, LLC 6 Silicon Nanoelectronics Natori developed his expression with a full quantum mechanical basis, the approach is an outgrowth of the Duke tunneling formula,20 and we can follow a variation of the semiclassical... above derivations, then we must account for the higher electron temperature in this region Each carrier that exits the channel into the drain brings Copyright © 2006 Taylor & Francis Group, LLC 8 Silicon Nanoelectronics with it an excess, directed energy of eVD This extra energy is rapidly thermalized by carrier-carrier scattering,25 which provides an elevated electron temperature Te > T in the drain... as the full quantum treatment is discussed in a later section 1.3 GRANULARITY By granularity, we refer to the failure of thermodynamic averaging in small devices If we consider a silicon- on-insulator (SOI) MOSFET, with the silicon channel 10 nm thick, 20 nm wide and 10 nm long, and doped to 1019 cm-3, then there are only 20 dopant atoms in the channel If the carrier density is 1013 cm-2, then there... model of the surface height variation to study thickness variations in SOI MOSFETs It is quite clear that a truly small semiconductor device can no Copyright © 2006 Taylor & Francis Group, LLC 10 Silicon Nanoelectronics longer be considered as a generic entity It will have its own characteristic performance that will depend upon the configuration of the dopants, the variations of the oxide thickness... this approach to be valid, we must have wave packets that do not have coherence among the packets This really means that the eigenvalue spectrum of the Copyright © 2006 Taylor & Francis Group, LLC 12 Silicon Nanoelectronics Schrödinger equation must be washed out by the thermal smearing If this spectrum is distinguishable, then a single wave packet for each particle is not a valid approach, and our effective... kinetic energy quadratic in the momenta and a coordinate-only dependence in the potential energy That is, it is clear that some modifications will have Copyright © 2006 Taylor & Francis Group, LLC 14 Silicon Nanoelectronics to be made when nonparabolic energy bands, or a magnetic field, are present However, the Gaussian approximation is well established as the method for incorporating the purely quantum... compared the density gradient approach and the effective potential approach and obtained similar results, which is to be expected This is because the Copyright © 2006 Taylor & Francis Group, LLC 16 Silicon Nanoelectronics Z Y X FIGURE 1.3 Crystal orientation of the SOI MOSFET for the quantum simulation (the directions are not to scale) The overlay shows how the six conduction band valleys . Cataloging-in-Publication Data Silicon nanoelectronics / edited by Shunri Oda and David Ferry. p. cm. ISBN 0-8247-2633-2 1. Molecular electronics. [DNLM: 1. Nanotechnology. 2. Silicon Compounds. ] I novel func- tions for silicon- based devices. Among various candidate materials for nanometer scale devices, silicon nanodevices are particularly promising because of the existing silicon process infrastructure. perfect interface between the natural oxide and silicon. The goal of this book is to give an update of the current state of the art in the field of silicon nanoelectronics. This book is a compact reference