Temperature dependence on intrinsic carrier concentration

[elimenohpee]

How does one calculate the intrinsic carrier concentration Ni for silicon as a function of temperature? I know the equation ni^2 = Nc*Nv exp(-Eg/kT) can be used, but then another equation is needed to find the energy band gap Eg. The effective density of states values Nc and Nv are well defined, but I can't seem to find out how to calculate Eg.

 

[jimmy neutron]

The band (or energy) gap, Eg, for silicon is taken from experiment and is about 1.1-1.2 eV and is known to within 5%. It only has a relatively weak dependence upon temperature.

According to Aschrcoft and Mermin (Solid State Physics, Saunders Coolege Publishing, ):
Eg (0K) = 1.17 eV, Eg(300K) = 1.12 eV.

The band gap can be measured in several ways, eg by its optical properties. When the frequency of an incident photon becomes large enough to excite electrons across the energy gap there is an abrupt increase in the absorption coefficient of the incident radiation.

 

[elimenohpee]

So basically there is no real "equation" that can be used to specifically calculate bandgap energy? It looks as if Ni isn't susceptible to much change when temperature drops, but I was more interested when temperature increases, which theoretically should shrink the gap. I just need a precise way to calculate by how much.

 

[jimmy neutron]

The band gaps are properties of the material and ultimately relatedto its structure.

 

[jimmy neutron]

According to Pierret ("Advanced Semiconductor Fundamentals", Prentice Hall 2003, see pp 82-83) the manner that the band gap for a large number of semiconductors varies with T can be modeled by the empirical relationship
Eg(T) = Eg(0) - alpha*T^2/(T + beta)
where alpha and beta are constants chosen to obtain the best fit to the experimental data. For silicon Pierret gives
Eg(300 K) = 1.125 eV, Eg(0) = 1.170 eV, alpha = 4.730X10^(-4) eV/K, beta = 636 K.
(Please check before using.)