Doping of semiconductors and fermi energy.

[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).

 

[charng]

I can explain this phenomenon by looking at the underlying principles of doping and its effect on the Fermi energy in semiconductors. First, it is important to understand that doping introduces impurity atoms into the crystal lattice of a semiconductor material. These impurity atoms have either one extra electron (for n-type doping) or one missing electron (for p-type doping) compared to the host atoms.

In an intrinsic semiconductor, the Fermi energy is located at the mid-gap energy level because the number of electrons and holes are equal. However, when we introduce impurity atoms, they create additional energy levels in the band structure of the semiconductor. These energy levels are located closer to either the conduction band (for n-type doping) or the valence band (for p-type doping).

Now, when we add a very small amount of impurity atoms, such as 1ppm, these additional energy levels are still present but they are not fully occupied or depleted. This means that there is still a significant number of electrons or holes available at these energy levels. This leads to a change in the Fermi energy, as it shifts towards the energy level with the majority of carriers (electrons or holes).

To put it simply, the small amount of dopant atoms creates a large number of additional energy levels in the band structure, which in turn affects the distribution of electrons and holes and ultimately leads to a change in the Fermi energy. This is why even a small amount of doping can have a significant impact on the Fermi energy in semiconductors.