Question

Temperature dependent extrinsic and intrinsic carrier concentrations:

Answer 1

This is a Edx Solid Chem exam question, but I think it's okay to post since the deadline is now over.

A 27 g sample of germanium crystal contains 44 mg of arsenic. The arsenic is substitutionally incorporated into the crystal. Germanium has a band gap of 0.66 eV and an intrinsic carrier concentration at 25o C of 4.2e+13 cm-3. At what temperature (in oC) will the intrinsic carrier concentration equal the extrinsic carrier concentration?

First I found the number of As atoms per cm^3 , which equalled 7*10^19 atoms/ cm^3

At that point, I'm pretty sure I used the wrong equation, and got the wrong answer. I think I should have used

Intrinsic Carrier Concentration = \[A *T^{3/2} * e ^{\frac{band-gap}{ 2KT }}\]

At which point I should get:

\[4.2*10^{13} = A * 298.16^{3/2} * e^{\frac{ 0.66 }{ 2 * (8.62*10^{-5}*298.16}}\]

Therefore A = 3.07 * 10^15

If the extrinsic = intrinsic

\[7*10^{19} = 3.07*10^{15} * T^{3/2} * e^{\frac{ 0.66 }{ 2*(8.62*10^-5)*T}}\]

=\[10.034 = lnT^{3/2} * \frac{ 0.66 }{ 1.72*10^{-4}T}\]

Unfortunately, at this point I get a bit bogged down and I'm not sure how to proceed, any help would be appreciated.

Thanks in advance!

Answer 2

shouldnt you bee asking this is math????

Answer 3

be*