Homework Help: Solid State Physics Help Please (Instrinsic->Extrinsic)

1. Apr 21, 2012

pghaffari

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

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

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

2. Relevant 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..