Question

2. b) An n-type silicon wafer undergoes a pre-deposition diffusion process with a constant surface concentration of boride gas; the resulting concentration of boron in silicon at the surface is estimated to be 1x1018 atoms cm-3. The background concentration of trace boron atoms in the silicon wafer is estimated to be 1x1014 cm-3. Estimate the depth of the p-n junction below the surface when the background doping concentration of the n-type impurity is 3.45 x1016 cm-3; assume the diffusion process proceeds for 10 minutes and has a diffusion parameter given by 10-12 cm2s-1.

Estimate the number of boron atoms (per cm2) introduced in this thin surface layer following the pre- deposition step.

Cont. If a drive-in diffusion process continues at the same temperature for 3 hours, estimate the concentration of the boron atoms at the surface on completion of this step, assuming there are no losses through the surface. How far has the pn junction diffused into the material after this process ?

Answer 1

2. b) Surface concentration, N_S = 1*10¹⁸ atoms cm^-3

​Background doping concentration, N_B = 3.45*10¹⁶ atoms cm^-3

^​​Diffusion time, t = 10 mins = 600 s

Diffusion co-efficient, D = 10^-12 cm²s^-1

Junction depth, x_j = 2 (Dt)^1/2​[erf^-1(1-(N_B ​/ N_S​))] = 2 (10^-12 cm²s^{-1 *} 600 s)^1/2​[erf^-1(1-(3.45*10¹⁶ atoms cm^-3 ​/ 1*10¹⁸ atoms cm^-3​))]

x_j = 2(6*10^-10 cm²)^1/2​ ​[erf^-1(1-(0.0345))] = 2 (2.45*10^-5 cm)​ ​[erf^-1(0.9655)] = 2 (2.45*10^-5 cm)​ ​[1.5]

Refer erf below erf table for erf (z) = 0.96

x_j = 2 (2.45*10^-5 cm)​ ​[1.5]​ = 7.35*10^-5 cm = 0.735 μ​m

Depth of the p-n junction​ = 0.735 μ​m​