If aluminum is diffused into a thick slice of silicon with no previous aluminum

Question

If aluminum is diffused into a thick slice of silicon with no previous aluminum in it at a temperature of 1100?C for 8 hours, what is the depth below the surface at which the concentration is 1016 atoms/cm3 if the surface concentration is maintained at 1018 atoms/cm3?  Use D = 2 x 10-12 cm2/s for aluminum diffusing in silicon at 1100?C.

If aluminum is diffused into a thick slice of silicon with no previous aluminum in it at a temperature of 1100?C for 8 hours, what is the depth below the surface at which the concentration is 1016 atoms/cm3 if the surface concentration is maintained at 1018 atoms/cm3? Use D = 2 x 10-12 cm2/s for aluminum diffusing in silicon at 1100?C.

Explanation / Answer

C=c"erf(x/2*sqrt(d*t))

10^16=10^18erf(x/2*sqrt((2*10^-12)*8*3600

=>x=2.13micrometer

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