Measuring minority carrier density and mobility

[OnesieWithaZ]

Homework Statement

Hi all,

I'm currently working on a Hall effect lab in which I analyze a p-type sample of germanium (I know it's p-type because I observe a hall voltage inversion point around 350 K which can only happen for a p-type sample). From the Hall and resistivity data I can obtain hole the dopant concentration and hole mobility, but when I try to obtain the electron concentration and mobility I run into a lot of trouble.

My questions are 1) is it possible to obtain values for electron mobility and concentration as a function of temperature from measurements of only a P-type sample? and if so 2) what is going wrong in my approach?

Homework Equations

eq 1) Hall coef = (thickness)*Vh/(I*B) = (n*mu_n^2 - p*mu_hole^2)*e/sigma^2 = 1/(e*p)

eq 2) n_i^2 = (const)*T^3*exp(-Eg/kT)

The Attempt at a Solution

I have obtained the hall voltage and conductivity of the sample. From the hall voltage I obtain the Hall coefficient. This gives a means of finding the concentration of dopants, NA.

From resistivity data in the intrinsic region I have obtained the band gap energy.

I now assume (this could be where I'm messing up) that the carrier concentrations are:

p = NA + N
n = N

Where NA is the number of acceptors from impurities and N is the number of electrons thermally excited from the valance band to the conduction band.

Electron Concentration
Plug these into equation 2 from the relevant equations section - and solve for N.

Electron mobility
From equation 1 in the intrinsic region, we have the equality on the far right. I have mu_hole as a function of temperature. When I solve for mu_n, however, I get nonsense results (mobilities of 10^24 cm^2/(V*s) at low temperatures. I have thoroughly checked my math and code... this is what the math puts out. The reason being that I get extremely low values of n at low temperature (which is how it should be by equation 2)

Sorry for not expressing things well - as you can probably tell this is not clear in my head at all - so I'm having trouble expressing it coherently... Thanks for any help!

 

[mark726]

Hello!

Thank you for sharing your work and questions with the forum. It sounds like you have a good understanding of the Hall effect and the equations involved, but you are running into some trouble when trying to determine the electron concentration and mobility in your p-type sample.

To answer your first question, yes, it is possible to obtain values for electron mobility and concentration from measurements of only a p-type sample. In fact, this is a common practice in semiconductor research, as it allows for a direct comparison between the hole and electron transport properties of the material.

Now, let's address your second question. It seems like you are on the right track with your approach, but there are a few things that may be causing issues with your results. First, when you say that you "assume" the carrier concentrations, are you assuming that N is equal to zero? If so, this may be causing problems with your calculations. In reality, there will always be some thermally excited electrons in the conduction band, even in a p-type sample. So, it may be more accurate to say that:

p = NA + N
n = N + n0

where n0 is the thermally excited electron concentration at a given temperature.

Additionally, when solving for N in equation 2, it is important to make sure that you are using the correct units for all the variables (e.g. temperature in Kelvin, energy in eV, etc.). If any of your units are incorrect, it could lead to nonsensical results.

Finally, it is also possible that there may be errors in your experimental data or calculations that are causing issues with your results. I would recommend double checking all of your data and calculations to make sure everything is correct.

I hope this helps and good luck with your lab!