How can doped semiconductor be neutral?

The terms n- and p-type doped do only refer to the majority charge carriers. Each positive or negative charge carrier belongs to a fixed negative or positive charged dopant.

p and n type materials are NOT positively and negatively charged.

An n-type material by itself has mainly negative charge carriers (electrons) which are able to move freely, but it is still neutral because the fixed donor atoms, having donated electrons, are positive.

Similarly p-type material by itself has mainly positive charge carrier (holes) which are able to move relatively freely, but it is still neutral because the fixed acceptor atoms, having accepted electrons, are negative.

http://www.halbleiter.org/en/fundamentals/doping/

http://uk.answers.yahoo.com/question/index?qid=20110422034224AAINiGl

Google is your friend, too.

Well there is no reason for the doped semi-conductor to be charged; either positive, or negative. Every single atom in the semiconductor came with its full complement of electrons, so the whole thing has no charge surplus or deficiency.

For example, if the semiconductor is say Silicon, every Si atom has 4 valence electrons. If you dope it P type with boron, which is a group III atom, each B atom has just 3 valence electrons. If you dope it N type with phosphorus, that is a group V element so each atom comes with 5 valence electrons. But either type of dopant atom is still charge neutral.

If a B atom replaces a Si atom in the crystal, one of the Si valence electrons has no mate from the Boron, and if a P atom replaces a Si atom, then the P atom has one electron with no mate from a Si atom; but it is always electrically neutral (the whole crystal)

Simply- intrinsic semi conductor is neutral to that if we add a neutral dopant then it is obvious that the overall charge will be neutral :)