Solid State Physics (Instrinsic->Extrinsic)

[pghaffari]

Solid State Physics Help Please! (Instrinsic->Extrinsic)

Homework Statement

3 samples of silicon with donor densities of:

1st sample: 10^18 cm^-3
2nd sample: 10^16 cm^-3
3rd sample: 10^14 cm^-3

for each, find out at what temp the sample transitions from intrinsic to extrinsic behavior

Homework Equations

this is what i need help with.. I read the section of intrinsic->extrinsic behavior but I can't find any equations that relate donor densities with temperature..

the equations i know/see from the section:

for instrinsic: n = p (concentration of electron in conduction band = concentration of holes in valence band )

r_i = g_i (regeneration rate of EHP (electron hole pairs) = recombination rate of EHP)

from those 2 and equilibrium we can get :

r_i = alpha_r n_0 p_0 = alpha_r (n_i)^2 = g_i (at any temperature we can predict that the rate of recombination of electrons and holes r _i is proportional to the equalibrium concentration of electrons n_0 and the concentration of holes p_0)for extrinsic materials, it just talks about what it is (when a crystal is doped s uch that the equilibrium carrier concentrationns n_0 and p_0 are different from the intrinsic carrier concentration n_i )

After this section it goes on and tals about Fermi energy and levels..

So I'm not quite sure how I can apply the equations I have to solve this problem..

Please advise.
Thank you

 

[NateD]

!The Attempt at a SolutionI'm not sure how to solve this problem.. I feel like I'm missing something..