52
3 Modification of the Work Function
Fig. 3.16 a Hardness of various carbides as a function of valence electron concentration (VEC)
(see text for explanation of VEC). b Hardness of various nitrides as a function of valence electron
concentration (VEC) (see text for explanation of VEC). c Hardness of three carbonitrides as a
function of valence electron concentration (VEC) (see text for explanation of VEC)
work functions of YN, ZrN, NbN, MoN, PdN, and AgN are unaffected by nitrogen
vacancy introduction, but those of TcN, RuN, and RhN are. For TaN, the surface
term of the work function will not be affected by vacancy introduction but that of
WN will be affected, although if the structure of WN is hexagonal, the surface term
will not be affected by nitrogen vacancies. Most of the transition metal carbides and
nitrides in practical use are composed of low-d metals. Therefore, there is almost
no effect of vacancy introduction on the surface term of the work function in most
cases.
In summary, we can estimate the effect of vacancy introduction on the work
function in the following way. First, determine the direction in which the Fermi
level is shifted by vacancy introduction (bulk term). Then, find whether the DOS
is composed of electrons from carbon (surface term). When electrons from carbon
are not involved in the Fermi level, there is no effect of vacancy introduction on
the surface term of the work function; this appears to be the case for most practical
transition metal carbides. Then, the change in the work function owing to vacancy
introduction is determined by the bulk term. It may be possible to estimate the