Oxidation and diffusion

When diffusing impurities at the same temperature, if the diffusion time is quadrupled, by roughly what factor does the spreading distance change?

  1. A4 times
  2. B16 times
  3. C2 times
Show answer and explanation

Answer: C. 2 times

The characteristic diffusion distance is √(Dt), proportional to the square root of time. Quadrupling the time doubles the distance (√4 = 2). Note that to keep diffusion shallow, temperature (which sets D) matters more than time.

  • A. The distance is proportional to the square root of time, not to time.
  • B. 16 times assumes the distance scales with the square of time.
  • C. Correct. √4 = 2 times.
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