Semiconductors

In this chapter we develop a basic understanding of the properties of intrinsic and extrinsic semiconductors. Although most of our discussions and examples will be based on Si, the ideas are applicable to Ge and to the compound semiconductors such as GaAs, InP, and others. By intrinsic Si we mean an ideal perfect crystal of Si that has no impurities or crystal defects such as dislocations and grain boundaries. The crystal thus consists of Si atoms perfectly bonded to each other in the diamond structure. At temperatures above absolute zero, we know that the Si atoms in the crystal lattice will be vibrating with a distribution of energies. Even though the average energy of the vi­brations is at most 3kT and incapable of breaking the Si-Si bond, a few of the lattice vibrations in certain crystal regions may nonetheless be sufficiently energetic to “rup­ture” a Si-Si bond. When a Si-Si bond is broken, a “free” electron is created that can wander around the crystal and also contribute to electrical conduction in the presence of an applied field. The broken bond has a missing electron that causes this region to be positively charged. The vacancy left behind by the missing electron in the bonding orbital is called a hole. An electron in a neighboring bond can readily tunnel into this broken bond and fill it, thereby effectively causing the hole to be displaced to the orig­inal position of the tunneling electron. By electron tunneling from a neighboring bond, holes are therefore also free to wander around the crystal and also contribute to elec­trical conduction in the presence of an applied field. In an intrinsic semiconductor, the number of thermally generated electrons is equal to the number of holes (broken bonds). In an extrinsic semiconductor, impurities are added to the semiconductor that can contribute either excess electrons or excess holes. For example, when an impurity such as arsenic is added to Si, each As atom acts as a donor and contributes a free elec­tron to the crystal. Since these electrons do not come from broken bonds, the numbers of electrons and holes are not equal in an extrinsic semiconductor, and the As-doped Si in this example will have excess electrons. It will be an n-type Si since electrical con­duction will be mainly due to the motion of electrons. It is also possible to obtain a p-type Si crystal in which hole concentration is in excess of the electron concentration due to, for example, boron doping.

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