Help with semiconductor physics

Bad Chemicals

Can anyone explain what the equation np=Nc^2(e^(-Eg/kT)) signifies. I know np = ni^2. Is Nc^2 here ni^2 (i.e. free charge carriers) or is it the overall number of charge carriers? I assumed that Nc^2 was the total number of charge carriers, so that Nc^2(e^(-Eg/kT))=ni^2, but that is not the case.

Also can anyone explain, if given ni=1.5x10^16m^-3, and electron and hole mobilities are 0.13m^2V^-1s^-2 and 0.05m^2V^-1s^-1 respectively, how to find the conductivity of the doped silicon at 300K, if there is one donor impurity per 10^8 silicon atoms. I looked up the density and found the carrier concentration that way, but there must be some way to do it given the info above!
Thanks anyone who can help.

citrus burst

Bad Chemicals wrote: »

Can anyone explain what the equation np=Nc^2(e^(-Eg/kT)) signifies. I know np = ni^2. Is Nc^2 here ni^2 (i.e. free charge carriers) or is it the overall number of charge carriers? I assumed that Nc^2 was the total number of charge carriers, so that Nc^2(e^(-Eg/kT))=ni^2, but that is not the case.

Also can anyone explain, if given ni=1.5x10^16m^-3, and electron and hole mobilities are 0.13m^2V^-1s^-2 and 0.05m^2V^-1s^-1 respectively, how to find the conductivity of the doped silicon at 300K, if there is one donor impurity per 10^8 silicon atoms. I looked up the density and found the carrier concentration that way, but there must be some way to do it given the info above!
Thanks anyone who can help.

At 0 K all the electrons in a semiconductor material are in the valence band and none are in the conduction band. The difference between in energy between the valence band and conduction band, known as the band gap is given by [Latex]E_g = \Delta E=E_c - E_v[/Latex].

To get an electron to the conduction band, the material must be thermally excited. When an electron has enough energy to go into the conduction band, it leaves behind a hole in the valence band. So [Latex]n=p[/Latex], where n is the number of electrons and p is the number of hole. When n is the same as p this is known as an intrinsic semiconductor.

The carrier concentration (or the free charge carriers) [Latex]n_i[/Latex] is given by:

[Latex]n_i = \sqrt{N_vN_c}exp \frac{-\Delta E}{2kT}[/Latex]

where [Latex]N_v[/Latex] is the hole concentration in the valence band and [Latex]N_c[/Latex] is the electron concentration in the conduction band. In this case they are the same.

The product of electron and hole concentrations [Latex]np[/Latex] is given by:

[Latex]np = n_i^2 = N_vN_c exp \frac{-\Delta E}{kT}[/Latex]

And since [Latex]N_v=N_c [/Latex]

[Latex]np = n_i^2 = N_c^2 exp \frac{-\Delta E}{kT}[/Latex]

as you have. I don't see what is wrong with what you have above.

This basically says that the electron/hole concentration is constant at a given temperature and doesn't depend on the Fermi level. It's known as the mass-action law.

In the second part are you given the carrier concentration [Latex]n_i[/Latex] or did you work it out? If you are given it then the conductivity is just;

[Latex]\sigma = n_i(\mu_e + \mu_p)q[/Latex]

If this isn't the case there are a few ways to work it out depending on whether the material is p type or n type. Here is a good website that might help you understand better.

Bad Chemicals

Hi, thank you for that and the website is great.
In the second part below, I was given the intrinsic carrier concentration, but from that I don't know how to work out the overall carrier concentration (whether free or not) in order to get the conductivity. This may be a misunderstanding of mine. Am I right in saying that the intrinsic carrier concentration is the number of thermally excited carriers? Also I think there is an overall carrier concentration from which the level of doping can be calculated given one donor impurity per 10^8 silicon atoms.
Thank you again.