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How to calculate the mean free time in Drude model?

Physics Asked on May 10, 2021

According to Drude model, the average electron takes some time to go from one ion to another: this time is called mean free time. The problem is there isn’t a satisfactory definition of this mean free time.
Let’s say there are two electrons.
The first electron takes 30 seconds to go from one ion to another for the first path.
For the second path, it takes only 40 seconds.

The second electron takes 40 seconds to go from one ion to another fot the first path.
For the second path, it takes 30 seconds.

Now, there are two ways to calcolare the mean free time.

  1. I can sum the times taken by each electron for only the first path (or the second) divided by the number of electrons (in our case there are two electrons);
  2. I can calculate the average time of each electron independently and then I can calculate the mean free time by averaging the average times above.

One Answer

Mean free time means a mean time between collisions. Note that these are not collisions with every lattice ion that electron encounters on its path, but collisions with randomly spread impurities, phonon-emission events, etc. Thus, mean here means averaging over the distribution of electron velocities, over the distribution of impurities, and over the probabilities of other collision events.

Answered by Vadim on May 10, 2021

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