Fundamentals of Semiconductor Physics

Introduction

The basic materials used for integrated circuit (IC) device fabrication are conductors, semiconductors, and insulators creating desired electrical properties to manufacture very large scale integrated (VLSI) circuits with target performance objective. Thus, the characteristics of an IC device depend on the properties of its constituent materials along with its geometrical and structural information. And, in atomic level, the IC device characteristics are modulated by the transport of current carrying fundamental constituents of materials, referred to as the electrons and holes. Again, the electronic properties of semiconductors primarily depend on the transport of the majority carrier electrons or holes. The semiconductors with majority carrier concentration as electrons are referred to as the /г-type, whereas the semiconductors with majority carrier concentration as holes are referred to as the //-type. Thus, in order to understand the performance of IC transistors in general, and “fin” field- effect transistor (FinFET) devices in particular, it is essential to understand the basic physics of the и-type and //-type semiconductors along with the transport properties of electrons and holes in building IC devices. Though a number of published titles are available on the subject [1-16], the objective of this chapter is to present a brief overview of semiconductor physics, basics of и-type and //-type semiconductors, and the characteristics of an и-type and a //-type semiconductor in contact forming a //и-junction that are necessary to understand the theory and operations of FinFET devices in VLSI circuits and systems.

Semiconductor Physics

Crystalline silicon is widely used as the starting semiconducting material for manufacturing VLSI devices and system-on-chips (SoCs). Thus, unless otherwise specified, in this book, the semiconductor physics is described with reference to silicon material. Thin silicon wafers used in the IC fabrication processes are cut parallel to either the (111) or (100) crystal planes. However, the (100) material is most commonly used due to the fact that during IC fabrication processes, (100) wafers produce the lowest amount of charge at the silicon/silicon dioxide (Si/SiO,) interface and offer higher carrier mobility [17,18]. Thus, it is of great interest to study how the electrons and holes are bonded in a silicon atom and understand their transport mechanism in a silicon crystal. And therefore, in this section, the energy band model and transport properties of electrons and holes are discussed.

Energy Band Model

In a silicon crystal, each atom has four valence electrons and four nearest neighboring atoms. Each atom shares its valence electrons with its four neighbors in a paired configuration called a covalent bond. It is predicted by quantum mechanics (QM) that the allowed energy levels of electrons in a solid are grouped into two bands, called the valence band (VB) and the conduction band (CB) as shown in Figure 2.1. These bands are separated by an energy range that the electrons in a solid cannot possess and is referred to as th& forbidden band or forbidden gap. The VB is the highest energy band and its energy levels are mostly filled with electrons forming the covalent bonds. The CB is the next highest energy band with its energy levels nearly empty. The electrons which occupy the energy levels in the CB are called the free electrons or conduction electrons.

Typically, the energy is a complex function of momentum in a three-dimensional space and there are many allowed energy levels for a large number of electrons in silicon and therefore, the energy band diagram is also complex [19]. For the simplicity of representation, only the edge levels of each of the allowed energy bands are shown in the energy band diagram (Figure 2.1). In Figure 2.1, Ec and £„ are the bottom-edge of the CB and the top-edge of the VB, respectively, and Eg is the bandgap energy separating Ec and £,, And, at any ambient temperature T(K), Eg is given by

When a valence electron is given sufficient energy (> £), it can break out of the chemical bonding state and excite into the CB to become a free electron leaving behind a vacancy, or hole, in the VB. A hole is associated with a positive charge since a net positive charge is associated with the atom from which the electron broke away. Note that both the electron and hole are generated simultaneously from a

Energy band diagram of a semiconductor like silicon

FIGURE 2.1 Energy band diagram of a semiconductor like silicon: Ec is the bottom-edge of the conduction band and £,, is the top-edge of the valance band which are separated by an energy gap Eg = Ec - £,,; in the figure, represents the electrons and “O” represents the holes.

single event. The electrons move freely in the CB and holes move freely in the VB. In silicon, the bandgap is small (~1.12 eV), therefore, even at room temperature a small fraction of the valence electrons are excited into the CB generating electrons and holes. This allows limited conduction to take place from the motion of the electrons in the CB and holes in the VB. As shown in Figure 2.1, when an electron in the CB gains energy, it moves up to an energy £ > Ec, while when a hole in the VB gains energy, it moves down to an energy E < £,, Thus, the energy of the electrons in the CB increases upward while the energy of the holes in the VB increases downward.

The bandgap energy £sfor silicon at room temperature (300 °K) is ~1.12 eV. As the temperature increases, the value of Eg for most semiconductors decreases due to the increase in the crystal lattice spacing by thermal expansion. For silicon, the

dE

temperature coefficient of Eg at 300 °K temperature is: = -2.73 x 1СГ* eVKT1

[20] . The temperature dependence of Eg for silicon can be modeled by using polynomial functions valid for different range of temperatures [16,20]. However, in a circuit simulation tool like SPICE (Simulation Program with Integrated Circuit Emphasis)

[21] , the temperature dependence of Eg is modeled by [22]

where:

T is the temperature in Kelvin (K)

Eg(T) is the energy gap in eV

 
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