Which area of physics deals with principle of work of BJTs, diodes and other semiconductor elements and which book do you suggest covering this?
If you are really talking about the low-level device physics: Semiconductor Physics. They tend to sit close to quantum mechanics and such. Band diagrams, energy levels, tunneling, are all common. 

There are a few good books out there. It is always interesting to look at wikipedia and start form there. Just google around, there are likely many pages dedicated to the field of semiconductor physics and technology.