Mean Free Time Silicon (PURCELL 4.12)

Click For Summary

Homework Help Overview

The discussion revolves around a problem from Purcell regarding the mean free time between collisions of electrons in silicon at a temperature of 500K, given a specific conductivity value. Participants are examining the implications of the conductivity measurement and the role of both electrons and holes in the calculations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to derive the mean free time using a formula related to conductivity but questions the validity of their result, suggesting it may be too small. Other participants question the treatment of holes as mobile charge carriers and the implications of their mass on the calculations. There is also a discussion about the correct interpretation of the conductivity value provided in the problem.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the assumptions made about the charge carriers. Some guidance has been offered regarding the factors influencing the calculations, particularly concerning the number density of particles involved in collisions.

Contextual Notes

There is a noted discrepancy regarding the units of conductivity, with participants clarifying the correct interpretation as ohm-cm instead of sec-1. The role of holes in the calculation and their impact on the mean free time is also under consideration.

NullSpace0
Messages
25
Reaction score
0

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?
 
Physics news on Phys.org
Are you sure that the holes count as mobile? What is their mass? Would counting them effectively halve the time you're looking for?
 
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.
 
Ah! So the OP's problem was conversion.

What about that factor of 2?
 
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.
 

Similar threads

Replies
1
Views
5K
  • · Replies 7 ·
Replies
7
Views
11K
  • · Replies 0 ·
Replies
0
Views
3K
  • · Replies 1 ·
Replies
1
Views
5K
  • · Replies 5 ·
Replies
5
Views
10K
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 4 ·
Replies
4
Views
5K
Replies
1
Views
13K