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Homework Help: Measuring minority carrier density and mobility

  1. Feb 28, 2016 #1
    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. jcsd
  3. Mar 4, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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