doping of semiconductors

neu

I understand the principle behind p and n type doping, but I don't understand how such a small amount, 1ppm, can cause such a massive change in the fermi energy.



as I understand it:

for the intrinsic case the number of electrons exactly matches the number of holes and the fermi energy is equal to the mid-gap energy.

When a very small amount of atoms are added which have an extra electron/hole then electrons/holes are added to system which adds extra levels (as in diagram).

But how can such a small addition of electrons/holes have such a large change in the fermi energy?

marcusl

It's because it introduces a lot of excess charge carriers over that of the intrinsic material. Silicon at 300K has about 10^10 carriers per cc, while 1ppm of dopant donates or accepts about 10^-6 x 10^22 = 10^16 electrons per cc so it significantly changes the Fermi level (chemical potential).