# Doping of semiconductors

#### Niles

Hi all

It can be shown that the product of the hole and electron concentration is constant at a given temperature in a semiconductor, as long as the Fermi level is in the ~middle of the gab.

When we dope semiconductors, do we use the above argument? I.e., does doping work because of this argument?

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#### Niles

If my question is unclear, I can explain it in a new way.

#### ZapperZ

Staff Emeritus
2018 Award
It is puzzling because of your last statement in the OP. When you dope a semiconductor, the Fermi level (or more precisely, the chemical potential) is no longer in the middle of the band gap. So I'm not sure how using "the above argument" would explain doping, i.e I'm not sure what you're getting at.

Zz.

#### Niles

My book says (and I am quoting): "Because the product of the electron and hole concentration is a constant independent of impurity concentration at a given temperature, the introduction of a small proportion of a suitable impurity to increase n, say, must decrease p." Here n is the concentration of electrons, and p is the concentration of holes.

And the correct assumption in the OP is: The distance of the Fermi level (i.e. the chemical potential, since we are dealing with semiconductors) from the edge of both bands is large in comparision with T.

I am using Kittel (it's page 207).

What I don't understand is, when we have a donor atom in a semiconductor, then the extra electron gets thermally excited to the conduction band. But that still brings down a hole to the donor energy level, right?

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#### ZapperZ

Staff Emeritus
2018 Award
I still don't see how that passage that you quoted implied that the chemical potential doesn't change with doping. The fact that you now have more charge carriers in the conduction band when you n-doped means that the statistical count of charge carriers that determines the chemical potential has changed.

Zz.

#### Niles

You make a good point.

When we have a donor atom in a semiconductor, then the extra electron gets thermally excited to the conduction band. Does that bring down a hole to the donor energy level?

#### ZapperZ

Staff Emeritus
2018 Award
You make a good point.

When we have a donor atom in a semiconductor, then the extra electron gets thermally excited to the conduction band. Does that bring down a hole to the donor energy level?
This is not similar to an intrinsic semiconductor where an electron promoted to the conduction band leaves behind a hole. The "donor" by definition, "donates" electrons to the conduction band. It doesn't leave any holes in the donor level.

Zz.

#### Niles

Disregard my OP, but substitute it with the following statement: "It can be shown that the product of the hole and electron concentration is constant at a given temperature in a semiconductor, independent of impurity concentration at a given temperature." This is shown it both Kittel and Ashcroft and Mermin (standard textbooks within this field).

Is it because of this fact (i.e. that np=constant, where n is electron concentration and p is hole concentration) that we have a n-type semiconductor, when it contains donor atoms? I mean, if 1 donor atom donates 1 electron to the conduction band, does this imply that there is 1 hole less in the valence band, and thus we have a n-type semiconductor?

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#### d logician

how does the acceptor atom get negatively charged ? can u guys answer the question

#### Niles

We regard the acceptor atom (e.g. gallium in germanium) as being a germanium atom, but with a negative charge in the nucleus and a missing electron (hole) orbiting the nucleus.

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