Mean Free Time Silicon (PURCELL 4.12)

[NullSpace0]

Homework Statement

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.

Homework 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.

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?

 

[schaefera]

Are you sure that the holes count as mobile? What is their mass? Would counting them effectively halve the time you're looking for?

 

[TSny]

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.

 

[schaefera]

Ah! So the OP's problem was conversion.

What about that factor of 2?

 

[TSny]

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.