Question on donor concentration in thermal equilibrium

[snoothie]

Homework Statement

In a sample of GaAS at T=200k, we have experimentally determined that n₀=5p₀ and that N_a=0. Calculate n₀,p₀, and N_d.

Homework Equations

The Attempt at a Solution

Have solved that n_i for GaAS at 200k is 1.2687cm^-3.
And using the mass action law equation, p₀=n_i²/5p₀. I derived p₀=0.567cm^-3 , n₀=5p₀= 2.8363cm^-3.

Can someone confirm if it is right to say that the donor concentration, N_d is approximately equal to n₀ in this case? Since the equilibrium equation state, if N_d >> n_i, then n₀ is approximately equal to N_d.

 

[anathema]

Yes, your understanding is correct. In this case, since Nd is much larger than ni, n0 can be approximated as equal to Nd. This is because the majority of the carriers in the material are coming from the donors, and the contribution from the intrinsic carriers (n0) is relatively small. So, for practical purposes, you can consider n0 and Nd to be approximately equal.

 

[tomcue]

I would say that your calculations appear to be correct based on the given information. However, I would also suggest double-checking your calculations and equations to ensure accuracy. Additionally, it is important to note that the donor concentration, Nd, is not necessarily equal to n0 in all cases. It is only approximately equal when Nd is much larger than the intrinsic carrier concentration, ni. It would be beneficial to also consider the temperature and other factors that may affect the equilibrium concentrations.