TABLE OF CONTENTS It was stated in Section 2.1.3 that carrier motion in silicon consists of drift in the presence of an electric field and diffusion in the presence of a concentration gradient. Drift is characterized by the mobility defined in Eq. (2.18), and diffusion by the diffusion coefficient defined in Eqs. (2.28) and (2.29). Since both mechanisms are closely tied to the random thermal motion of electrons (or holes), the diffusion coefficient and the mobility are related by the Einstein relations, Eqs. (2.30) and (2.31). In this appendix, we briefly describe the physical picture of the drift and diffusion processes, leading to the basic concept behind the Einstein relations. Note that MKS units are used throughout this appendix (i.e., length must be in meters, not centimeters).
Under thermal equilibrium, electrons possess an average kinetic energy proportional to kT. They move in random directions through the silicon crystal with an average thermal velocity ? th. At room temperature, ? th is of the order of 10 7 cm/s. Electrons scatter frequently with the lattice (phonons) and ionized impurity atoms. The average distance electrons travel between collisions is called the mean free path l, and the average time between collisions is called the mean free time ?=l/ ? th. Typically, l ? 100 and ? ? 0.1 ps.
In the absence of electric field, the net velocity of electrons in any particular direction is zero, since the thermal...
