This is a rather interesting question, which is another way of saying "I don't know."
If the truth be told, I hadn't really thought about this topic in this way before.
One thing to remember is that the doping only affects a very (VERY) thin layer at the top of the semiconductor substrate (typically silicon). Also that it involves the doping gas and silicon wafer being maintained at rather high temperatures (600 to 800C I think) for quite a long time (6 to 12 hours).
Also, we're only talking about relatively few dopant atoms entering the silicon matrix -- say 1 dopant atom per 100 million substrate atoms for light doping and 1 dopant atom per 10 thousand atoms for heavy doping.
So, at these temperatures, the atoms in the silicon matrix are vibrating around like crazy and the bonds between them are stressed to their breaking point -- thereby allowing the dopant atoms to work their way into the matrix.
Having said all this, I don't know if the dopant atoms simply squeeze their way in pushing the silicon atoms aside and creating minor discontinuities in the silicon matrix, or if some silicon atoms "evaporate" off the surface of the substrate.
I'll be interested to see what others say -- plus I'll ask a few friends. I'll post a follow-up comment if I hear anything useful.
