3.1 Mixing Elements
43
Fig. 3.8 Calculated work
function values for 3d, 4d,
and 5d transition metals and
their carbides, together with
some experimental values
Now, we discuss the effect of defects (carbon and nitrogen atom vacancies) on
the work function. In Table 3.2, both experimental [12] and theoretical [13] work
functions of tantalum carbides (TaCx) and hafnium carbides (HfCx) (100) with and
without carbon vacancies are listed. For TaCx, an increase in the work function is
obtained by the introduction of vacancies both experimentally and in theory, whereas
a decrease in the work function of HfCx is obtained by the introduction of vacancies
both experimentally and in theory. These vacancies are formed both inside the bulk
and at the surface.
Because the work function is composed of the bulk term and the surface term, the
location of vacancies, either in the bulk or at the surface, is significant. Figure 3.12
shows the densities of states (DOSs) near the Fermi level for TaCx without vacancies,
with vacancies only at the surface, and with vacancies both in the bulk and at the
surface [13]. In Fig. 3.13, the corresponding cross sections of the electron density
of TaCx (a) without vacancies and (b) with vacancies both in the bulk and at the
surface are displayed [13]. From Fig. 3.12, it can be seen that the introduction of
surface vacancies causes almost no change in the position of the Fermi level or the
DOS (Fig. 3.12 middle). However, the position of the Fermi level is shifted to the