46
3 Modification of the Work Function
LaN
LaC
(b)
(a)
HfC
HfN
Fig. 3.11 Fermi level positions of carbide (red lines) and nitride (blue lines) for a La [10], b Hf
[10], c Ta [10], and d Ti [11]
term owing to the Fermi level shift toward a shallower energy. This change in the
work function agrees with Table 3.2.
In the cases of TaCx and HfCx, the introduction of carbon vacancies does not
affect the surface term of the work function, but it does affect the bulk term, where
the effect is opposite for TaCx and HfCx. Here, we discuss a general procedure for
estimating the effect of carbon/nitrogen vacancies on the surface and bulk terms
of the work function. If the effect of vacancy introduction on the Fermi level is
calculated for all carbides and nitrides, the change in the bulk term upon vacancy
introduction can be estimated directly from the shift of the Fermi level. However, the
effect of vacancy introduction has been calculated for a limited number of carbides
and nitrides. Therefore, we search for experimental values that indicate the size of the
bulk term. Experimental studies on transition metal carbides and nitrides are mostly
conducted from the viewpoint of hard coatings. A very large number of results on