Semiconductor physics: Resistivity,mobility and concentration.

[Aerozeppelin]

Homework Statement

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?

Homework Equations

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

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!

 

[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.

 

[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 (nμ_n + pμ_p)
Where:

q is the charge of an electron.
μ_n is the mobility of electron. = 0.12
And μ_p 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

 

[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.

 

[paranormal]

You are on the right track in calculating the hole mobility based on the given ratio with electron mobility. The next step would be to use the relationship between resistivity, mobility, and concentration in a semiconductor. The formula is as follows:

ρ = 1/qμnN + 1/qμpP

Where ρ is the resistivity, q is the elementary charge, μn and μp are the electron and hole mobilities respectively, and N and P are the electron and hole concentrations.

Since we know the resistivity, electron mobility, and the ratio of electron to hole mobility, we can solve for the intrinsic hole concentration (P) using the above equation. Once we have P, we can then use the given ratio again to calculate the intrinsic electron concentration (N).

I hope this helps guide you in the right direction. Remember to always check your units and use the appropriate values for the constants. Good luck!