Fraction of ionized atoms in an intrinsic semiconductor

[theBEAST]

Homework Statement

Here is the problem in the book:

Here is the solution:

What I don't get is why the solution defines the fraction to be n_i/(5*10²²). Shouldn't it be 2*n_i/(5*10²²) since we have both donors and acceptors, so there are actually twice the number of atoms.

Also, intrinsic means that the silicon is not doped right? If that is the case why are there even donors and acceptors, shouldn't the concentrations be zero?

 

[ehild]

What I don't get is why the solution defines the fraction to be n_i/(5*10²²). Shouldn't it be 2*n_i/(5*10²²) since we have both donors and acceptors, so there are actually twice the number of atoms.

Also, intrinsic means that the silicon is not doped right? If that is the case why are there even donors and acceptors, shouldn't the concentrations be zero?

There are no donors, no acceptors in an intrinsic semiconductor. Some silicon atoms get ionized by thermal energy. One of the electrons of a silicon atom gains enough energy to escape from its ion, which means leaving the valence band and becoming a "free" electron in the conduction band. The escaped electron leaves a positive ion behind, which means lack of an electron, a "hole" in the valence band.

So excitation of a silicon atom produces an electron-donor pair and leaves one positive ion behind.

ehild