(surface concentration)

we aim to amplify electrical signals by using transistors through doping impurity atoms like P into Si. For this purpose, you would need to meet the requirements of 1.3 x 10^4 P atoms/cm^3 at the depth of 50 m. Let us assume that the diffusion coefficient of P in Si is 2.3 x 10^-12 cm^2 /s at the processing temperature. Calculate the surface concentration of P that must be maintained constant to meet this requirement in a time of 75 min. Assume that the initial concentration of P in Si is zero.