A 0.2-mm-thick wafer of silicon is treated so that a uniform concentration gradient of antimony is produced. One surface contains 1 Sb atom per 108 Si atoms and the other surface contains 500 Sb atoms per 108 Si atoms. The lattice parameter for Si is 5.4307 Å (Appendix A). Calculate the concentration gradient in (a) at% Sb per cm; and (b) Sb atoms cm ? cm3 .

- 0.0249% Sb/cm

Explanation:

Given that:

One surface contains 1 Sb atom per  10⁸  Si atoms and the other surface contains 500 Sb atoms per  10⁸ Si atoms.

The concentration gradient in atomic percent (%) Sb  per cm can be calculated as follows:

The difference in concentration =

The distance = 0.2-mm = 0.02 cm

Now, the concentration of silicon at one surface containing  1 Sb atom per 10⁸ silicon atoms and at the outer surface that has 500 Sb atom per   10⁸ silicon atoms can be calculated as follows:

= - 0.0249% Sb/cm

b) The concentration of Sb in atom/cm³ for the surface of 1 Sb atoms can be calculated by using the formula:

Lattice parameter = 5.4307 Å;  To cm ; we have

=

=

The concentration of Sb in atom/cm³ for the surface of 500 Sb can be calculated as follows:

   =  

   =

Finally, to calculate the concentration gradient

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