TABLE OF CONTENTS This chapter is a review of (or introduction to) some key concepts that will be needed as we examine nanotransistors. For the most part, concepts will be stated, not derived. A thorough introduction to these concepts can be found in Datta [1.1]. We also assume that the reader is acquainted with the basics of semiconductor physics (as discussed, for example, in [1.2]). For the quantum mechanical underpinning, see Datta [1.3] and for a more extensive discussion of semiclassical transport theory, see Lundstrom [1.4].
In equilibrium, the probability that a state at energy, E, is occupied is given by the Fermi function as
| (1.1) |  |
where the subscript, 0, reminds us that the Fermi function is defined in equilibrium, and T L is the lattice temperature. When states in the conduction band are located well above the Fermi level, the semiconductor is nondegenerate and eqn. (1.1) can be approximated as
| (1.2) |  |
By writing the energy as the sum of potential and kinetic energies,
| (1.3) |  |
where E C is the bottom of the conduction band, eqn. (1.2) can be written as
| (1.4) |  |
where C is a constant. Equation (1.4) states that in a nondegenerate semiconductor, the carrier velocities are distributed in a Gaussian (or Maxwellian) distribution with the spread of the distribution related to the temperature of the carriers. Since 
,we can also write
| (1.5) |  |
which shows that the carrier velocities are distributed symmetrically about the x-axis (or for that matter, the y- and...
