Why impurity atom's loss of electron doesn't create a hole?

Question

What I know about holes:I have read that in any intrinsic semiconductor if electron comes out of the bonded situation between two atoms then the electron is said to be a free electron and is said to possess an energy state in conduction band and the empty space left due to removal of electron due to any reason say temperature reason is called hole and in a collective manner we say electron-hole pair is created.

What I want to ask:Now lets say an intrinsic conductor is doped with an donor impurity say with antimony then out of $5$ antimony electrons $4$ are bonded to the main atom say germanium and the 5th electron is loosely bonded to antimony.Now if we apply say electric field or increase the temperature that loosely bonded electron will be excited from valence band to conduction band. Now my book says in this way a free electron is created without creating a hole. So,my question is

Why won't the hole be created now in the antimony case as the process is similar to what happened in the germanium atom without any doping due to say temperature?

Answer 1

Good question.I will try to explain it in the simplest way possible.

We have to take dilution approximation first(very important)..Since a crystal structure is unaffected by impurity concentration the value of Ec and Ev doesn't change. We don't have energy bands for the impurity atoms, we only have a single level outside the conduction and the valence band.

Recall the concept of a hole, an empty state that is created when a valence electron was elevated into the conduction band.For T>0K, all the valence electron may gain thermal energy, if a valence electron gains a small amount of thermal energy it hops into the empty state(hole movement)

Now coming to the main part of the question, since the impurity atoms don't have an energy band rather they have a level, the vacancy formed after ionization is not filled up by an electron, because for electrons it is easier for them to move to a nearby bond(very less energy is required, it is obvious) than to jump up to a level and form a bond.So because for the level of energy, they don't have a mobile vacancy(i.e holes).

Answer 2

In an n-type semiconductor like the one you describe the donor atoms occupy gap states in between the valence and conduction bands and the charges associated with these states are not mobile. It is certainly true that when an electron from the donor (antimony in this case) is thermally promoted into the conduction band it leaves behine a positive charge. However that positive charge is localised in a gap state and isn't mobile so it cannot act as a conductor in the way a hole does.