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Semiconductors-Introduction

Nearly everything that we use contains semiconductors. From old relics such as "Transistor Radios", to computers, and everything in between, semiconductors make modern human technology operate. Before this book, wikibooks had a number of sources on semiconductors, scattered as stub pages and individual chapters in other books. However, this book is an attempt to bring all that information together into a single resource, and therefore become more valuable to the wikibooks community at large. Now, other books that used to provide their own mini discussions of semiconductors can instead link to this book in an effort to save time and space.

Semiconductors are special materials (frequently silicon-based) that conduct differently under different conditions. This is, of course, only a partial definition, but it is certainly an important part. Semiconductors can be used to control the flow of electricity in a circuit, they can be used to amplify a signal, or they can be used to switch current flow on or off. In fact, this is only a small subset of the things that semiconductors can do. This book will explain what semiconductors are, and how they are used.

It is the intent of this book to become a thorough and complete reference resource on semiconductors. The first section will discuss what semiconductors are, and how they are constructed physically. The second section will begin to discuss transistors, first through the use of specific models (Transistors as a switch, and Transistors as an amplifier). Section 3 will talk about Field Effect Transistors (FET), how they operate, and how they are made. Section 4 will talk further about the use of transistors as amplifiers, and will discuss Op-Amp circuits in detail. Section 5 will discuss rectifier circuits and regulator circuits. Section 6 will talk more in depth about using transistors as switches, and will discuss the popular CMOS and TTL design methodologies. Finally, section 7 will discuss the use of light with semiconductors, including phototransistors, photodiodes, and LEDs. In the future, additional topics may be covered.

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.

Solid materials are classified by the way the atoms are arranged within the solid. Materials in which atoms are placed at random are called amorphous. Materials in which atoms are placed in a highly ordered structure are called crystalline. Poly-crystalline materials are materials with a high degree of short-range order and no long-range order. These materials consist of small crystalline regions with random orientation called grains, separated by grain boundaries. Crystals naturally form as liquid material cools down, since the close proximity of atoms lowers their energy. However, since crystallization typically occurs in multiple locations simultaneously, one finds that the poly-crystalline structure is quite common except for materials such as glass which tend to be amorphous. Crystalline silicon dioxide does occur in the form of quartz but only if the temperature and pressure promote crystal formation.

Of primary interest in this text are crystalline semiconductors in which atoms are placed in a highly ordered structure. Crystals are categorized by their crystal structure and the underlying lattice. While some crystals have a single atom placed at each lattice point, most crystals have a combination of atoms associated with each lattice point. This combination of atoms is also called the basis.

The classification of lattices, the common semiconductor crystal structures and the growth of single-crystal semiconductors are discussed in the following sections.

2.2.1 Bravais lattices

The Bravais lattices are the distinct lattice types, which when repeated can fill the whole space. The lattice can therefore be generated by three unit vectors,

and a set of integers k, l and m so that each lattice point, identified by a vector

, can be obtained from:

(2.2.1)

The construction of the lattice points based on a set of unit vectors is illustrated by Figure 2.2.1.

Figure 2.2.1:

The construction of lattice points using unit vectors

In two dimensions, there are five distinct Bravais lattices, while in three dimensions there are fourteen. The lattices in two dimensions are the square lattice, the rectangular lattice, the centered rectangular lattice, the hexagonal lattice and the oblique lattice as shown in Figure 2.2.2.It is customary to organize these lattices in groups, which have the same symmetry. An example is the rectangular and the centered rectangular lattice. As can be seen on the figure, all the lattice points of the rectangular lattice can be obtained by a combination of the lattice vectors

. The centered rectangular lattice can be constructed in two ways. It can be obtained by starting with the same lattice vectors as those of the rectangular lattice and then adding an additional atom at the center of each rectangle in the lattice. This approach is illustrated by Figure 2.2.2 c). The lattice vectors

generate the traditional unit cell and the center atom is obtained by attaching two lattice points to every lattice point of the traditional unit cell. The alternate approach is to define a new set of lattice vectors, one identical to

and another starting from the same origin and ending on the center atom. These lattice vectors generate the so-called primitive cell and directly define the centered rectangular lattice.

Figure 2.2.2.:

The five Bravais lattices of two-dimensional crystals: (a) square, (b) rectangular, (c) centered rectangular, (d) hexagonal and (e) oblique

These five lattices are summarized in Table 2.2.1. a₁ and a₂ are the magnitudes of the unit vectors and a is the angle between them.

Table 2.2.1.:

Bravais lattices of two-dimensional crystals

The same approach is used for lattices in three dimensions. The fourteen lattices of three-dimensional crystals are classified as shown in Table 2.2.2, where a₁, a₂ and a₃ are the magnitudes of the unit vectors defining the traditional unit cell and a, b and g are the angles between these unit vectors.

Table 2.2.2.:

Bravais lattices of three-dimensional crystals

The cubic lattices are an important subset of these fourteen Bravais lattices since a large number of semiconductors are cubic. The three cubic Bravais lattices are the simple cubic lattice, the body-centered cubic lattice and the face-centered cubic lattice as shown in Figure 2.2.3. Since all unit vectors identifying the traditional unit cell have the same size, the crystal structure is completely defined by a single number. This number is the lattice constant, a.