Quantum Mechanics for Tomorrow's Engineers

The current–voltage characteristics of modern electronic devices consisting of semiconductor heterostructures, such as resonant tunneling diodes, quantum cascade lasers, and tandem solar cells, are determined by the dynamics of electrons propagating through quantum-engineered 1D potential landscapes. In this chapter, we will develop a general formalism with which to describe transmission probabilities for electron waves propagating through arbitrary potentials, which can be used for analyzing electron motion in semiconductor devices. Furthermore, we will extend our formalism to 1D electrons moving in a general spatially periodic potential, based on which we will describe the basic concepts of the band theory of solids. The central theorem in band theory is the Bloch theorem, which we will derive and then use for discussing the dynamics of electrons in crystalline solids (or Bloch electrons).