Dear  Prasenjit 

Some materials are naturally p or n-type materials. As a result of the fermi level being close to the valence bands for PbSe it seems that PbSe is a p-type semiconductor without doping.

Dear Prasenjit;

In general words, some of undoped semiconductors are naturally n-type and p-type, respectively. I agree with Mr. Abdulsattar and want to say that the nonzero n

and p are the results of thermal excitation, which moves some electrons from the

valence band into the conduction band. So the thermal effects show the semiconductor as p-type or n-type and the Fermi level of the structure take place close to CB or VB.   

Hi,

I don't know about PbSe but GaSb also shows similar result. Undoped grown GaSb is generally p type. This is due to lattice defects(vacancy defect of Ga or a Ga atom on Sb site) of grown crystal.This defects act as acceptor and that's why it's fermi level lies close to the valence band.  

Have a look at Fig. 1(a) of the publication you referred to: There you see that the LDA-calculated band gap is zero. Therefore, here the Fermi energy lies directly at the highest occupied level. Moreover, this means that Figs. 1(a) and 1(b) are not consistent: According to Fig. 1(a), there should be no gap in the total DOS, Fig. 1(b). Maybe in the calculation of the DOS there was a similar problem as discussed recently for graphene, where also the DOS did not match the band structure (cf. https://www.researchgate.net/post/Inconsistency_between_DOS_and_Band_structure/1).