In intrinsic semiconductors Fermi level is ammost in the middle of the band gap and hence at a particular temperature , conductivity will decrease exponentially with band gap. But the axact value of conductivity can not be calculated unless one knows the pre- exponential factor of conductivity. In extrinsic semiconductors there is no direct relation between conductivity and band gap as Fermi level is not at the middle of the band gap. For detail read any elementary book on semiconductors or solid state physics.

In intrinsic semiconductors Fermi level is ammost in the middle of the band gap and hence at a particular temperature , conductivity will decrease exponentially with band gap. But the axact value of conductivity can not be calculated unless one knows the pre- exponential factor of conductivity. In extrinsic semiconductors there is no direct relation between conductivity and band gap as Fermi level is not at the middle of the band gap. For detail read any elementary book on semiconductors or solid state physics.

thank you very much for your answer

As suggested by Dr. A. Kumar, there is no direct relation between conductivity and band gap as the position of Fermi level depends on dopant type and its concentration. However, you can better understand the relationship by visiting the web pages as suggested by Saeidh Hosseini. It may help you to formulate the a relationship between conductivity and band gap in your case.

Dear Sayed,

The conductivity of as semiconductor material is given by

sigma= q un n0+ qup p0,

where mu is the mobility n0 and p0 are the electron concentration and hole concentration at thermal equilibrium. According to doping if one is majority the other will be minority and its conductivity is negligible. This is because of the mass action law p0 n0=ni^2.

So if the material is doped its conductivity will be controlled by doping and this is the strength of the semiconductors.

However if the material is intrinsic p0=n0=ni and the conductivity will be determined by the energy gap since ni^2 is proportional to exp - Eg/kT. So, as Eg increases the intrinsic material conductivity will be appreciably reduced.

For more information please refer to the book: Book Electronic Devices

Best wishes

Dear Prof. Zekry thank you very much for your answer

For polymeric materials, the value of electrical conductivity was enhanced as the Eg value decreased. This is due to incorporation of filler within the polymeric matrix. Several works were published on this.

Do you know a mathematical equation to calculate the conductivity from energy band gap of polymeric materials?

As pointed out by colleagues

sigma = n*q*mew+p*q*mew

Consider a germanium crystal containing 2×1014 phosphorous atoms /cm3 which have ionization energy of 12 meV .

1- At what temperature the complete ionization will occur?

2-Calculate the majority and the minority carrier concentration at 300 K?

3- What happens for a low-doped germanium as the temperature increases?