Interstitial position probability?

[fordahwin]

Homework Statement

A silicon crystal is being doped with Ni atoms. The formation energies for substitutional and interstitial Ni atoms are Es= 0.74 eV and Ei=0.16 eV, respectively. At 320 centigrade, what is the probability for a Ni atom to be placed in an interstitial configurations?

Homework Equations

$\frac{n_v}{N} = e^{-\frac{Q}{RT}}$

The Attempt at a Solution

I started this problem by calculating the number of vacancies for the substitutional and interstitial energy at 320 C. However, I am not so sure where to go from there. Would would I use this equation to get a probability?

 

[nilesh_pat]

Do I need to use a different equation? Es = 0.74 eVEi = 0.16 eVT = 320 C$n_v = N * e^{-\frac{Es}{RT}}$$n_v = N * e^{-\frac{Ei}{RT}}$$n_v(substitutional) = N * e^{-\frac{0.74eV}{8.617*10^{-5}eV/K * 593K}} = N * 0.033$$n_v(interstitial) = N * e^{-\frac{0.16eV}{8.617*10^{-5}eV/K * 593K}} = N * 0.323$