Lecture Problem 30

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Lecture Problem 30

• Noel Godinez

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Problem Statement

• Phosphorus is diffused into a thick slice of
  silicon with no previous phosphorus in it at a
  temperature of 1100C. If the surface
  concentration of the phosphorus is 1.0x1018
  atoms/cm3 and its concentration at 1µm is
  1.0x1015 atoms/cm3, how long must the diffusion
  time be? D 3.0x10-13 cm2/s for P diffusing into
  Si at 1100C. If the temperature is dropped to
  1050C, what is the diffusion time? If the
  temperature remains at 1100C but the depth is
  increased to 2µm, what is the diffusion time?

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Theory

• Solution to Ficks 2nd Law for a semi-infinite
  solid in which the surface concentration is held
  constant

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Theory

• Temperature dependence of diffusivity

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Solution

• What we know

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Solution x 1 µm, T 1100oC

• Plug into Solution to Ficks 2nd Law

What happens to the diffusion time when the
temperature drops to 1050oC?
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Solution x 1 µm, T 1050oC

• Calculate the new diffusivity

Over 3 times longer with only a 4.5 drop in
temperature!!
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Solution x 2 µm, T 1100oC

• The depth is now doubled

4 times as long with a 100 increase in depth!
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Conclusion

• Diffusion time is much more sensitive to
  temperature changes than to depth changes.
• Activation energy for diffusion is specific to
  what is being diffused as well as the host
  substance (in this case P into Si).