This chapter brings together the physical underpinnings of field-effect transistors operating in their nanoscale limits. It tackles the change in dominant behavior from scattering-limited long-channel transport to mesoscopic and few scattering events limits in quantized channels. It looks at electrostatics and a transistor’s controllability as dimensions are shrunk—the interplay of geometry and control—and then brings out the operational characteristics in “off”-state, e.g., the detailed nature of insulator’s implications or threshold voltage’s statistical variations grounded in short-range and long-range effects, and “on”-state, where quantization, quantized channels, ballistic transport and limited scattering are important. It also explores the physical behavior for zero bandgap and monoatomic layer materials by focusing on real-space and reciprocal-space funneling as one of the important dimensional change consequences through a discussion of parasitic resistances.
