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Mean Free Time Silicon (PURCELL 4.12)

  1. Oct 3, 2012 #1
    1. The problem statement, all variables and given/known data
    This is Purcell 4.12... Given that conductivity in silicon at 500K is 0.3 sec-1, deduce the mean free time between collisions of an electron.


    2. Relevant equations
    Electron mass is 9.1x10-28 grams (mass of a hole is exactly the same), the charge on an electron is 4.8x10-10, the density of electrons and holes is each 1015.


    3. The attempt at a solution
    I solved Purcell's equation for conductivity to find mean free time instead:

    T=(Mass*σ)/(2Ne2)... and I get something like 5.92x10-25 seconds. Isn't this way too small? Or did I do something wrong?
     
  2. jcsd
  3. Oct 6, 2012 #2
    Are you sure that the holes count as mobile? What is their mass? Would counting them effectively halve the time you're looking for?
     
  4. Oct 6, 2012 #3

    TSny

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    According to page 147 of Purcell, the conductivity of pure silicon at 500 K is 0.3 (ohm-cm)-1 rather than 0.3 sec-1.
     
  5. Oct 7, 2012 #4
    Ah! So the OP's problem was conversion.

    What about that factor of 2?
     
  6. Oct 7, 2012 #5

    TSny

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    I believe the factor of 2 is there because an electron could collide with either another electron or a hole. So, the number density of particles that the electron could collide with would be twice that of just the number density of electrons alone.
     
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