Semiconductors, minimum conductivity

1. Mar 12, 2015

leonmate

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 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. Mar 12, 2015

phyzguy

Do you remember that in a semiconductor n*p = ni2?

3. Mar 12, 2015

leonmate

yeah, i have that eq written down, trying to work out where to go from that...

4. Mar 12, 2015

phyzguy

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.

5. Mar 12, 2015

leonmate

σ = e(n0μe + ni2/n0 μh)

I'm not really sure what to do with this, also where did n = n0 come from?

6. Mar 12, 2015

leonmate

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!

7. Mar 13, 2015

phyzguy

Great!

8. Feb 14, 2016

nishant619

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.