The Coleman book gives the energy gap for silicon as 11 eV t

The Coleman book gives the energy gap for silicon as 1.1 eV, the effective electron mass as 0.26 me and the effective hole mass as 0.49 me. Using these numbers, you can show that the Fermi energy for intrinsic Silicon at 300K is 0.562 eV above the top of the valence band. Suppose you doped silicon in such a way that the Fermi energy at 300K moved down by 0.350 eV (so that the final Fermi energy is 0.212 eV). What is the concentration and type of dopant that you would need to use?

Solution

1) according to the formula

Ei= Emidgap + 3/4(ln kT mh /me) where k =1.3807 x 10 ^-23= boltzman constant mh = effective mass of hole and me=effective mass of electron

Ei - Emidgap = 0.012 ( puttig the value of mh , me ,k , T= 300k)

since Emidgap is 0.55 (1.1/2) eV above valence band so intrinsic fermi level Ei = 0.562 eV above valence Band

we know that Ef = Ei + kT ln n/ni

and   Ef = Ei - kT ln p/ni

therefore in order to bring down the impurity should be p type that is may be boron

from the equation  Ef = Ei - kT ln p/ni

=> Ef - Ei = - kT ln p/ni => 0.350 = kT ln p/ni

thus we can get p from this formula