The kinetics of diffusion are strongly dependent on temperature. The
diffusion coefficient D is related to temperature by an Arrhenius-type
equation,
(5-4)
where Q is the activation energy (in units of cal/ mol) for diffusion of the
species under consideration (e.g., Al in Si), R is the gas constant ,
and T is the absolute temperature (K). D0 is the pre-exponential term,
similar to c0 in Equation 5-1. D0 is a constant for a given diffusion system
and is equal to the value of the diffusion coefficient at 1/ T = 0 or T =?.
Typical values for D0 are given in Table 5-1, while the temperature
dependence of D is shown in Figure 5-12 for some metals and ceramics.
Covalently bonded materials, such as carbon and silicon (Table 5-1), have unusually high
activation energies, consistent with the high strength of their atomic bonds. Figure 5-13 shows the diffusion coefficients for different dopants in silicon. In ionic materials, such as some of the oxide ceramics, a diffusing ion only enters a site having the same charge. In order to reach that site, the ion must physically squeeze past adjoining ions, pass by a region of opposite charge, and move a relatively long distance (Figure 5-14). Consequently, the activation energies are high and the rates of diffusion are lower for ionic materials than those for metals (Figure 5-15 on page 171). We take advantage of this in many situations. For example, in the processing of silicon (Si), we create a thin layer of silica (SiO2) on top of a silicon wafer (Chapter 19). We then create a window
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