Analysis of Quantum Confinement and Carrier Transport of Nano-Transistor in Quantum Mechanics

Quantum mechanics is the branch of physics that consists of laws explaining the physical properties of the nature of nano-particles and their characteristics on an atomic scale. The study of nano-particles significantly challenges our current perception of the universe and the fabric of reality itself. Quantum particles have both wave-like and particle-like characteristics. The fundamental equation that predicts the physical behaviour of a quantum system is the Schrödinger equation and the Poisson equation using Monte Carlo simulations. This gives rise to the wavefunction, electron and hole densities, energy levels and band structure of the system which contains all the measurable information about the particle such as time and position, where position is represented using probabilities. This is because particles do not have one definite position during the time before measurement. In fact, they exist as a fuzzy distribution of all possible states where the likelihood of finding the particle in some states is more probable than others. This is known as being in a superposition of all states. When the quantum system is observed, however, its wavefunction collapses so it consequently falls into one specific position. Moreover, in this chapter we present the simulation results of conduction band profile, electron density (classical and quantum mechanical), eigenstate and eigenfunctions for Si, SOI and III-V MOSFET structures at bias voltage 1.0 V using 1D Poisson-Schrödinger solver