Phosphorous is an n-type dopant in Si since it introduces extra electrons to Si (an P atom has 1 more valence electron than Si). It is widely used in making semiconductor devices (p-n junctions for example). The diffusivity of phosphorus in Si is given by: D0=3.85 cm2/s, and activation energy Qa=3.65 eV. The initial P concentration in Si can be considered 0. Let us consider two cases:

(1) A Si wafer is treated in phosphorus vapor at 1000o C so that the phosphorus concentration at the surface is kept at the solubility limit of 1021/cm3.

(a) Plot the concentration profile of phosphorus after 1h diffusion (i.e. concentration vs. distance from the surface. You can use matlab, excel, etc to obtain it.)

(b) How many P atoms per cm2 have been diffused into Si during this 1h?

(2) We deposit 1015/cm2 phosphorus atoms on Si surface (you can consider that they are adsorbed on Si surface, forming a single atomic layer on Si). Then a 1h annealing is conducted at 1000o C for 1h to "drive-in" the dopants.

(a) Plot the concentration profile of phosphorus after 1h diffusion and compare it to the case of 1(a)

(b) Conventionally, dopant concentration of >1018 cm-3 is considered to be "heavily doped". What is the depth of the heavily doped region after this 1h annealing?