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Semiconductors, minimum conductivity

  1. Mar 12, 2015 #1
    1. The problem statement, all variables and given/known data

    Show that the minimum conductivity of a semiconductor occurs when n0 = ni√(μhe)

    Derive an equation for the minimum conductivity

    Calculate the (i) minimum and (ii) intrinsic conductivity for silicon. State the assumptions you make and the origin of any material properties used

    2. Relevant equations
    Some equations I've dug out of my notes that look revelant:

    conductivity, σ = enμe + epμh = σe + σh
    Number of electrons in conduction band: n0 = niexp(Ei - Ef / kT)

    3. The attempt at a solution

    I'm a little stuck on where to start with this one,
    I know that ni is the intrinsic carrier concentration, n0 is the carrier concentration in the conduction band.

    μh and μe are hole and electron mobility. This is the constant of proportionality between the drift velocity and the electric field. So the some of the electrons drift into the conduction band

    Seems obvious that conductivity is at a minimum when there is as few electrons as possible in the conduction band, so I guess I need to do something with that. But I really need a hint or two here as I'm struggling to solve this problem. It's due tomorrow! >_<

    Cheers
     
  2. jcsd
  3. Mar 12, 2015 #2

    phyzguy

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    Do you remember that in a semiconductor n*p = ni2?
     
  4. Mar 12, 2015 #3
    yeah, i have that eq written down, trying to work out where to go from that...
     
  5. Mar 12, 2015 #4

    phyzguy

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    So write n = n0 and p = ni2 / n0, then write σ in terms of n0 (eliminating n and p), then find the value of n0 that minimizes σ.
     
  6. Mar 12, 2015 #5
    σ = e(n0μe + ni2/n0 μh)

    I'm not really sure what to do with this, also where did n = n0 come from?
     
  7. Mar 12, 2015 #6
    Ah, brainwave...

    σ = e(n0μe + ni2/n0 μh)

    Then differentiate wrt n and set equal to zero to find the minimum. Rearrange and got it!
     
  8. Mar 13, 2015 #7

    phyzguy

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    Great!
     
  9. Feb 14, 2016 #8
    a. Calculate conductivity σ as function of temperature σ(T) for following semiconductors:


    Eg=0.4 eV, Nd=1e15 cm-3; Ec-Ed=0.02, Nc=Nv=1e19;
    Use temperature from 80K to 500K, step 1K. For mobility, use µ=µoT-0.6 with µo=20,000.

    can anybody help me out with this question.
     
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