Question

The diffusion coefficient for aluminum in silicon is D (Al in Si) = 4 × 10-13 cm2/s at 1300 K. What is a reasonable value for D (Al in Si) at 1600 K ?

Answer 1

Given data

diffusion coefficient for aluminum in silicon

D1 = 4 × 10^-13 cm2/s

T1 = 1300 K

T2 =1600 K

D2 =?

Qd = 3.41 eV for Al in Si

Boltzmann's constant k = 8.62 x 10^-5 eV/atom-K

However we can estimate that at increasing temperature value of D will also increase.

At 1600 K, value of D2 > 4 × 10-13 cm2/s

Now we can prove

We know that

D1 = D0 exp(-Qd/kT1)

D2 = D0 exp(-Qd/kT2)

Divide both equations

D1/D2 = exp(-Qd/kT1 + Qd/kT2)

ln D1/D2 = (Qd/k) (1/T2 - 1/T1)

ln ( 4 × 10^-13/D2) = (3.41/8.62*10^-5) (1/1600 - 1/1300)

ln ( 4 × 10^-13/D2) = (-5.706)

4 × 10^-13/D2 = 0.003326

D2 = 1.20 x 10^-10 m2/s