Silicon oxidation parabolic rate constant

The most predominant effect of H20 in the oxidizing ambient is to increase the parabolic rate constant (90). As a result, the effect of the interface reaction as the rate-controlling process increases with increasing H20 content. A relatively small HzO concentration (25 ppm) in 02 is already sufficient to increase the parabolic rate constant by factors of 1.3 and 1.6 for <111>-and <100>-oriented silicon wafers, respectively (99). The linear rate constant increases more gradually over the range of added H20 (0-2000 ppm) (90). 

These results indicate that is very sensitive to diffusion of cations since the parabolic rate constant depends on the diffusivity. For instance, chromium and silicon in Figure 10.12 are the fastest and the slowest elements that oxidize in oxygen, respectively. Therefore, Dcr -Dsi from Figure 10.12. Since weight gain and oxide thickness are related through eq. (1026) with n = 1/2, it is convenient to combine eqs. (1026) and 10.19) or (10.67) to get... 

Figure 7-16. The effect of the partial pressure of oxidant on the parabolic rate constant of silicon. (Adapted from Deal and Grove, 1965.)...

The terms B and BIA can be referred to as the parabolic and linear rate constants for describing the oxide growth kinetics. The physical meanings of the rate constants B and BjA are the oxidant diffusion and interface reaction rate, respectively. The corresponding values for B and BIA for dry and wet oxidation of (111) silicon are plotted in Fig. 3. For (100) silicon, these values should be divided by 1.68. These expressions are better fit for the cases of a very thin oxide layer and in dry O2 conditions. Solving Eq. 13 leads to the relationship between the oxide thickness and the growth time ... 

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