Sketch, using either Matlab or Excel on the same axes, the energy/probability distribution curve for n-type silicon at two temperatures T1 and T2 (where T2 > T1) to show the effect of temperature upon the position of the Fermi level. (Hint: where would the Fermi level be if all the silicon atoms contributed a hole-electron pair?).
Fermi function f(E) specifies how many of the existing states at the energy E will be filled with an electron, or equivalently, f(E) specifies ,under equilibrium conditions, the probability that an available states at an energy E will be occupied by an electron. Mathematically speaking the Fermi function is simply a probability density
function. in mathematical symbols,
f(E) = 1/( 1+exp (E-Ef)/kT )
Ef=Fermi energy of Fermi level
See the 2 attachments. First with some explanation and some other references, the second the f(E) plots using Si at 50K, 300K and 1000K. Using the Excel you can enter in the relevant cells any temperature in K you want and the resultant plot should be produced. You will need to change the legend filed as well though which are referenced under the actual plot.
Fermi Energy ...
The expert examines fermi functions versus energy.