Gateways Into Electronics

6

MODELS OF SEMICONDUCTOR DEVICES

6-1 SEMUCONDUCTORS

If electronics is unthinkable without amplifiers, it is nowadays virtually unthinkable without semiconductor devices such as transistors. Our purpose here is to gain sufficient insight into the physics of semiconductor devices that we can accept the simple models used to represent them.

We will concentrate on silicon because it is the most widely used semiconductor. Germanium is important for historical reasons, and other semiconductors are increasingly used for special purposes—high speed in the case of gallium arsenide—but devices based on these materials can be readily understood using the concepts we will develop.

6-1-1 Intrinsic Silicon

Pure crystalline silicon (intrinsic silicon) is a three-dimensional lattice in which each atom is at the center of a regular tetrahedron formed by its four nearest neighbors. Silicon is element 14 in the periodic table; like carbon, which is in the same column of the table and is thus chemically similar, it has four valence electrons. Each atom in intrinsic silicon forms four covalent bonds with its nearest neighbors. For our purposes, it will be sufficient to think in terms of the two-dimensional lattice shown in Fig. 6-1, in which each atom is also linked to four neighbors.

The energy required to break a covalent bond in silicon is the bandgap energy Σ_G = 1.1 eV (expressed in electron-volts, which is the energy gained by an electron of charge –e = –1.6 · 10⁻¹⁹ C when it climbs through 1 ...