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#### Abstract

When analyzing semiconductor devices, the traditional approach is to assume that carriers scatter frequently from ionized impurities, phonons, surface roughness, etc. so that the average distance between scattering events (the so-called mean-free-path, λ) is much shorter than the device. When these conditions hold, we can describe carrier transport with drift-diffusion equations. The traditional derivation of the MOSFET I-V characteristic above threshold assumes that the drift current dominates [1]. For the subthreshold current, we usually assume that diffusion dominates [2]. Numerical simulation programs include both drift and diffusion under all bias conditions (e.g. MINIMOS [3]). As devices shrink, however, we should consider the possibility that the device dimensions become comparable to the mean-free-path for scattering. In the limit, L << λ, where the channel length is much shorter than the mean-free-path, we can ignore scattering completely. In this case, the operation of a MOSFET would be more like a vacuum tube than like a conventional semiconductor device. In practice, scattering always occurs, but it is common now for the critical, current-limiting part of the device to be comparable in size to a mean-free-path. Modern devices, therefore, operate between the drift-diffusion and ballistic regimes. Drift-diffusion theory continues to provide insights into the operation of small semiconductor devices, but a ballistic treatment provides new insights that may prove useful as MOSFETs are scaled to their limits and as new devices are explored. The modern device engineer should be familiar with both approaches. In these notes, we develop a simple theory for the ballistic MOSFET.

- Introduction
- The MOSFET as a bipolar transistor
- Generic model for a nanotransistor
- Application to a ballistic MOSFET
- Discussion
- Relation to traditional MOSFET theory
- Summary

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