By theory of energy bands we know that conduction band is half completed so there are available higher energy states for the electrons
-
The 3p band is not continuous, but instead has a gap. The gap is due to the structure which allows a separation of the lower bonding half of the band and the upper antibonding half of the band. Qualitatively, it is what you expect from the use of Zintl rules: in the structure of phosphorus every phosphorus atom makes 3 bonds to nearby neighboring atoms and has a lone-pair of electrons as well. (This local bonding description is true of all of phosphurus's allotropes: red, white, or black P - see the Wiipedia link.) When main-group elements or compounds form such "octet-consistent" structures, you inevitably get a band gap (though sometimes the valence and conduction bands overlap a bit and you get a semi-metal).