Semiconductors: Find maximum Operating temp.

[papasmurf]

Homework Statement

"A GaAs device is doped with a donor concentration of 3x10^15 cm^-3.For the device to operate properly, the intrinsic carrier concentration must remain less than 5% of the total electron concentration. What is the maximum temperature that the device can operate?"

Homework Equations

N_D=3 x 10¹⁵ cm^-3

n₀*p₀ = n_i²

n_i=0.05n₀ or 20n_i=n₀

n_i=sqrt(N_CN_V)*exp(E_g / 2kT)

N_C=2(m*_dsekT / 2pi(h-bar)²)^3/2

N_V=2(m*_dshkT / 2pi(h-bar)²)^3/2

N_D - N_A -n₀ + p₀ = 0

k = boltzman's constant

I think that's all the equations that will be needed?

The Attempt at a Solution

Honestly, I've just been rearranging equations and plugging things in up to this point. My teacher said we will need MATLAB to find the final solution, not sure if that really is the case or not. Really, I have no idea where to start. I've just been looking at it for a solid hour and haven't written much down. I will start that now and post updates, I just wanted to get this up and let people look at it I guess.

Actually, I take some of that back. I substituted and rearranged the last equation I put up there.
3 x 10¹⁵ cm^-3 = N_A + 20n_i - n_i/20 = N_A - (399/20)*n_i

I'm going to work on this now. Any help/advice/stimulating conversation will be greatly appreciated. Thanks.

 

[papasmurf]

How do I know if I can neglect N_A? In a lot of the example problems in the book, it always talks about neglecting one thing or another because it small, but I don't see where it says what "small" means, or how you know something is small based on another value.