I would like to get an idea about the mean free path of the electrons in doped ZnO thin films.
I have the electrical data obtained from the Hall Effect measurement.
How can I find the mean free path of the charge carriers??
If you have the value of the DC conductivity σ, density of the carriers n, and their effective mass m, you can from these deduce the value of the relaxation time τ -- using the relationship σ = nq2τ/m, where q denotes the charge of the carriers, equal to e < 0 for electrons and -e > 0 for holes. Knowledge of this and of the value of the Fermi velocity v provides you with the value of the mean-free path l -- using the relationship l = vτ. The relaxation time τ is related to the mobility μ through the equality μ = qτ/m (since one has σ = nqμ), so that knowledge of the mobility makes knowledge of the carrier density for the calculation of τ or l redundant. Since you mention that have made Hall measurements, you can deduce the density of the carries in your samples from the Hall coefficient.
For details, you may wish to consult the book Solid State Physics by Ashcroft and Mermin.
If you have the value of the DC conductivity σ, density of the carriers n, and their effective mass m, you can from these deduce the value of the relaxation time τ -- using the relationship σ = nq2τ/m, where q denotes the charge of the carriers, equal to e < 0 for electrons and -e > 0 for holes. Knowledge of this and of the value of the Fermi velocity v provides you with the value of the mean-free path l -- using the relationship l = vτ. The relaxation time τ is related to the mobility μ through the equality μ = qτ/m (since one has σ = nqμ), so that knowledge of the mobility makes knowledge of the carrier density for the calculation of τ or l redundant. Since you mention that have made Hall measurements, you can deduce the density of the carries in your samples from the Hall coefficient.
For details, you may wish to consult the book Solid State Physics by Ashcroft and Mermin.
Thank you.
But can I find the Fermi velocity for my films??
I have n, σ, μ and I can find τ from plasma energy calculation.
You are welcome Arindam.
If you have μ and τ, then you can deduce m. Assuming a single parabolic band, m completely fixes this band and therefore the Fermi velocity v. For non-parabolic bands, you need more work to do, since once you have fixed its functional form, you will have to use the value of n to determine the relevant Fermi surface, at which the gradient of your band will provide you with the information regarding the Fermi velocity (in general, this will depend on the direction).
Dear Arindam,
The problem is that if you have a semiconductor you need to distinguish clearly the different density of n and p carriers that you have on your transport. The mobility for them is quite different as they mass, therefore also their mean path.
I want to find out the mean free path of the electrons only.
and my film is highly conducting (n-type).
In such a case you have only n-type but you need to take care with the components of the conductivity that you are considering: transvers or longitudinal.
How can carrier mobility μ and relaxation time τ can be measured for p type semiconductor?
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