Band Theory of Electrical Conductivity

In Section 11.6 we saw that the ability of metals to conduct heat and electricity can be explained with molecular orbital theory. To gain a better understanding of the conductivity properties of metals we must also apply our knowledge of quantum mechanics. The model we will use to study metallic bonding is band theory, so called because it states that delocalized electrons move freely through bands formed by overlapping molecular orbitals. We will also apply band theory to certain elements that are semiconductors. 

A number of elements are semiconductors, that is, they normally are not conductors, but will conduct electricity at elevated temperatures or when combined with a small amount of certain other elements. The Group 4A elanents silicon and germanium are especially suited for this purpose. The use of saniconductors in transistors and solar cells, to name two applications, has revolutionized the electronic industry in recent decades, leading to iuCTeased miniaturization of electronic equipment. 

The opposite effect occurs if boron is added to silicon. A boron atom has three valence electrons ls 2s 2p ). Thus, for every boron atom in the silicon crystal there is a single vacancy in a bonding orbital. It is possible to excite a valence electron from a nearby Si into this vacant orbital. A vacancy created at that Si atom can then be flUed by an electron from a neighboring Si atom, and so on. In this manner, electrons can move through the crystal in one direction while the vacancies, or positive holes, move in the opposite direction, and the solid becomes an electrical conductor. Impurities that are electron deficient are called acceptor impurities. Semiconductors that contain acceptor impurities are called p-type semiconductors, where p stands for positive. 

In both the p-type and n-type semiconductors, the energy gap between the valence band and the conduction band is effectively reduced, so that only a small amount of energy is needed to excite the electrons. Typically, the conductivity of a semiconductor is increased by a factor of 100,000 or so by the presence of impurity atoms. 

The growth of the semiconductor industry since the early 1960s has been truly remarkable. Today semiconductors are essential components of nearly all electronic equipment, ranging from radios and television sets to pocket calculators and computers. One of the main advantages of solid-state devices over vacuum-tube electronics is that the former can be made on a single chip of silicon no larger than the cross section of a pencil eraser. Consequently, much more equipment can be packed into a small volume—a point of particular importance in space travel, as well as in hand-held calculators and microprocessors (computers-on-a-chip). 

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