Resistivity Ratios: Germanium Homework Statement

[beesher]

Homework Statement

(a) A sample of n-type Germanium contains 10²³ ionized donors per cubic meter. Estimate the ratio at room temperature (300K) of the resistivity of this material to that of high purity intrinsic Germanium. The Electron hole product for Germanium is 10³⁸m^-6 and it can be assumed that the mobility of the electrons and the mobility of the electrons in the hole are similar at 300K.

(b) Suppose it takes an energy of 2eV to create a vacany in a certain solid. Show that the relative density of the vacanies of the atoms will always be less than 10^-8 per cent unless the melting point is higher than 1000K.

The Attempt at a Solution

Well, I thought since the electron hole product is 10³⁸ then that gives:

Intrinsic - N_e=N_n = 10¹⁹
Extrinsic - N_e=10²³ therefor N_n=10¹⁵

relitive resistivity can be given as P_Extrinsic/P_Intrinsic.

I'm not really sure how I continue from there. Do I disregard the mobilities because the are similiar?

(b) I'm really unsure how to complete (b), I think it might be something to do with manipulation of n=Ne^-E/kT.

Any help would be much appreciated

 

[beesher]

anyone?