# Chapter 2: Semiconductor Fundamentals

## 2.1 Introduction

 To understand the fundamental concepts of semiconductors, one must apply modern physics to solid materials. More specifically, we are interested in semiconductor crystals. Crystals are solid materials consisting of atoms, which are placed in a highly ordered structure called a lattice. Such a structure yields a periodic potential throughout the material, which results in some remarkable properties.
 Two properties of crystals are of particular interest, since they are needed to calculate the current in a semiconductor. First, we need to know how many fixed and mobile charges are present in the material. Second, we need to understand the transport of the mobile carriers through the semiconductor.
 In this chapter we start from the atomic structure of semiconductors and explain the concepts of energy bands, energy band gaps and the density of states in an energy band. We also show how the current in an almost filled band can more easily be analyzed using the concept of holes. Next, we discuss the probability that energy levels within an energy band are occupied. We will use this probability density to find the density of electrons and holes in a band.
 Two carrier transport mechanisms will be considered. The drift of carriers in an electric field and the diffusion of carriers due to a carrier density gradient will be discussed. Recombination mechanisms and the continuity equations are then combined into the diffusion equation. Finally, we present the drift-diffusion model, which combines all the essential elements discussed in this chapter.
 Boulder, December 2004