5) Fabricate a PN junction in silicon. (a) Calculate the junction depth, Xi, for

Question

5) Fabricate a PN junction in silicon. (a) Calculate the junction depth, Xi, for a boron dopant that has been diffused into n-type silicon. Assume that the surface concentration of boron is held constant and that annealing is for 30 min at 1150°C. The n-type silicon initially has a uniform concentration of another dopant, 1015 atoms/cm3. (see attachment for additional data) (b) Calculate the total amount of boron that has diffused into the n-type Si. (c) Compare the "exact" junction depth from 5a with that estimated from the characteristic diffusion distance. (d) How long would it take for the composition Cos to penetrate 1 micron at 1150°C? Cos is the composition midway between the initial boron concentration in the silicon, and the boron concentration at the surface. Boron gas ambient in diffusion tube SiO pt n-type Si Diffusion of Boron into the source and drain region

Explanation / Answer

D = Do exp [-Ea/kB *T] T Temparature in kelvin 1423K

D = (1.0 cm^2/s) * [-3.5eV/ 8.4617 *10^-5 * 1423K] = 4.01532*10^-13 cm^2/s

Dt = D * (Time in seconds) =  4.01532*10^-13 cm^2/s * 1800 = 7 *10^(-10) cm^2/s

Assuming surface concentration of boron to be 2.4x10^(20) cm–3.

xj junction depth = 2Dt [erf^(-1)(1-Nb/Ns]; 1– NB/No = 0.999792;  erf (2.63) = 0.9998  

xj = 27 *10^(-10) * 2.68 * = 139 µm

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