If aluminum is diffused into a thick slice of silicon with no previous aluminum in it at a temperature of 1100°C for 206 minutes, what is the depth below the surface at which the concentration is 1016 atoms/cm3? if the surface concentration is 1018 atoms/cm^3?

the depth below the silicon surface at which the aluminum concentration would be atoms/ is

Explanation:

The concentrations of a diffusing element in a silicon wafer at any particular position below the surface and  the time it takes to reach that concentration has a relationship given by Fick's second law

Where

The concentration of the carbon on the gear surface is

The initial uniform (normal) concentration of carbon in the gear is

The  concentration of carbon at a distance x below the gear surface after time t is

 Distance below the gear surface is x

Diffusivity of carbon at a given temperature is D

Time is t

erf is a mathematical function called error function

The impurity diffusion is a method in which an impurity is diffused into a silicon wafer at a very high temperature.The given values are

            = atoms/

          = 0 atoms/

          = atoms/

         t = 206 minutes = 12360 s  [1 minutes= 60 seconds ]

For an aluminum diffusing in silicon at 11100°C  Diffusivity is

Substituting these values we have

Let assume

  Hence

To determine for what number the  error function is 0.99

The table on the first uploaded image is a table that error function for some number

Where z is the same thing as R

calculating the R (i.e z) value whose error function is 0.99 , using the interpolation method we have

Substituting the value of R in the equation 2 we have

So therefore the value of  x is

Hence the depth below the silicon surface at which the aluminum concentration would be atoms/ is

po-215 i got it right on the quiz