# Semiconductor physics: Resistivity,mobility and concentration.

1. Apr 30, 2013

### Aerozeppelin

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

If a sample of pure silicon at 300 Kelvin has a resistivity of 950Ωm, and if the electron-to-hole mobility ration is 3:1, with the electron mobility equal to 0.12m2V-1s-1, what are the intrinsic hole and electron concentrations?

2. Relevant equations

I know resistivity is equal to
$\frac{ρL}{A}$. But I dont think this is applicable. I cannot find any equations in books or on the internet connecting these properties (concentration, mobility and resistivity).

3. The attempt at a solution

Well considering the ratio of electron to hole mobility is 3:1, I presume that the hole mobility is 0.04m2V-1s-1 (ie. electron mobility divided by 3). After that, I'm completely lost!
Any help would be appriciated!

2. Apr 30, 2013

### phyzguy

You should be able to write the conductivity of the silicon (inverse of the resistivity) in terms of the concentration of carriers and their mobility. If you haven't learned this, Google it.

3. May 2, 2013

### Aerozeppelin

Can't believe I didn't think of that!
Thanks a million.

Here's my answer if anyone wants it.

σ=$\frac{1}{ρ}$

1.053x10-3 = q (nμn + pμp)
Where:

q is the charge of an electron.
μn is the mobility of electron. = 0.12
And μp is the mobility of holes. = 0.04

To solve for concentrations (n and p),

Rearranging,

0.12n + 0.04p = 6.579x1015

N = P in intrinsic.

∴ 0.16n = 6.579x1015

& p = n = 4.118x1016

4. May 2, 2013

### phyzguy

Looks good, I think you did it all correctly. However, there are no units on the answer. I always take off points for a number with no units.