2. MOSFET: Basics, Characteristics, and Characterization

This chapter attempts to provide a theoretical basis for the Metal Oxide (Insulator) Semiconductor (MOS/MIS) Structure and the MOS/MIS Field Effect Transistor (MOSFET/MISFET), their characteristics, and their characterization (parameter extraction); the theoretical treatment starts from the first principles. While deriving the mathematical relations, assumptions have been avoided as far as possible. A comprehensive treatment is included which covers the important aspects of the function, mechanism, and operation of the MOS/MIS devices; in particular topics have been covered which are relevant to all the later chapters of the book and which will aid in reading the rest of this book. We begin this chapter with the theory of the classical MOS structure (non-leaky and SiO₂ single gate dielectric) and the classical MOSFET and then graduate to the MOS structure and the MOSFET with the high-k gate stack and the high mobility channels. Various aspects of the MOS/MOSFET devices analyzed in this chapter include the energy band profiles, circuit representations, electrostatic analysis (charge–voltage and capacitance–voltage relations), drain current versus drain voltage relation, quantum-mechanical phenomena (wave function penetration, tunneling, carrier confinement), nature of the high-k gate stack traps, and the pseudo-Fermi function inside the gate stack and the occupancy of the gate stack traps. Features such as capacitance–voltage (C–V) characteristics, flat-band and threshold voltages (V_FB and V_T), V_T versus EOT characteristics permeate the chapters; hence these features and characteristics such as conductance–voltage (G–V) characteristics have been discussed. A significant part of this chapter contains topics which are rarely seen in the literature and are yet to be well understood. As these topics (composition of the high-k gate stack, nature of the high-k gate stack charges, effects of the degradation factors) are of vital significance for the progress of the high-k gate stack technology, we have tried to analyze these issues. The final part of this chapter treats the various methods available for characterization of the high-k gate stacks, in particular, for the determination of the trap parameters—trap density, trap energy, trap capture cross-section, and the trap location inside the gate stack.