3.1 Mixing Elements
45
Fig. 3.10 a Calculated band structure of some transition metal carbides [10]. b Calculated band
structure of some transition metal nitrides [10]. Red lines are the Fermi level and red arrows show
the bulk term of the work function
A similar discussion is possible for HfCx but with the work function changing
in the opposite direction. The position of the Fermi level is shifted toward the right
(shallower energy level) by the introduction of vacancies both in the bulk and at the
surface, resulting in a decrease in the bulk term of the work function, as shown in
Fig. 3.15a [13]. Taking into account the origin of electrons composing the DOS near
the Fermi level of HfC without vacancies (Fig. 3.15b [14]), which is Hf, we can
deduce again that the vacancies at the surface should not affect the surface term of
the work function of HfC. Hence, it is expected that the introduction of vacancies in
HfC will result in a decrease in the work function through the decrease in the bulk