Why is black phosphorus semiconductor with direct bandgap?

[Douasing]

Why is black phosphorus a semiconductor with a direct bandgap?

The problem is mentioned by the two following references:
"The three bonds take up all three valence electrons of phosphorus,so, unlike graphene, monolayer black phosphorus is a semiconductor with a predicted direct bandgap of 2 eV at the G point of the first Brillouin zone."
(see http://www.nature.com/nnano/journal/v9/n5/full/nnano.2014.35.html)

"Unlike carbon, phosphorus has only three valance electrons which leads to BP being semiconducting since each atom is bonded to three neighboring atoms."
(see http://scitation.aip.org/content/aip/journal/apl/104/10/10.1063/1.4868132)

In order to check the point,I input the keyword "valence" in wiki:
http://en.wikipedia.org/wiki/Valence_(chemistry)

I found that typical valencies are three and five for phosphorus,but only four for carbon.I somehow doubt the explanation in the references and some meticulous and clear details shoud be supplied.

 

[DrDu]

p has a full s orbital and 3 additional electrons in the remaining three p orbitals. Hence these three orbitals can form 3 covalent bonds with neighbouring atoms. There are also 3 anti-bonding orbitals at higher energy. The bonding orbitals will form a full valence band and the anti-bonding orbitals an empty conduction band.