Overview

Conventional device analysis begins by assuming that carriers behave as classical particles which obey Newton s laws. A more fundamental treatment describes the electron by its wave function, ?( r, t), which is obtained by solving the Schr dinger equation,

(1.1)

The quantity ?*( r, t) ?( r , t)d r is the probability of finding the electron between r and r+d r. Three different potential energies appear in the wave equation; the first, E _C0 (r), describes potentials that are built-in or applied to the device. (The energy band diagram of a semiconductor device is just a plot of this potential versus position. Device engineers usually refer to this potential as E _C (r), but in this text E _C will refer to the position and momentum-dependent conduction band potential; it contains a potential energy component, E _C0 ( r ), and a kinetic energy component.) The second potential is the crystal potential, U _C (r), which describes the electrostatic potential due to the atoms. (Since eq. (1.1) is a wave equation for a single electron, U _C (r) also includes the average potential due to the other electrons in the solid.) Finally, U _S is a scattering potential due to random deviations in potential caused by ionized impurities or by lattice vibrations. Device analysis is usually based on an approximate solution to eq. (1.1) known as the semiclassical treatment which describes...