# Measuring minority carrier density and mobility

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1. Feb 28, 2016

### OnesieWithaZ

1. The problem statement, all variables and given/known data
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?

2. Relevant 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)
3. 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!

2. Mar 4, 2016