48
3 Modification of the Work Function
Table 3.1 Calculated work functions (eV) for carbide and nitride surfaces
Relaxed
Unrelaxed
Theory
Exp.
TiC
4.62
4.19
4.7 [14]
3.8 [16]
TiN
3.25
3.03
2.92 [13]
TaC
4.16
3.85
4.24 [15]
4.3 [17]
(3.86: unrelaxed)
TaN
3.45
3.79
4.0 [13]
HfC
4.28
3.86
4.5 [17]
HfN
2.79
3.13
3.85–3.90 [13]
NbC
4.26
3.85
4.2 [17]
NbN
3.33
3.59
3.92 [13]
ZrC
4.30
3.94
4.0 [17]
ZrN
2.79
2.84
2.94 [13]
Table 3.2 Work functions of (100) plane of TaCx and HfCx
Experiment
Theory
x
φ
φ
TaCx
1.0
4.38
1
3.84
0.5
4.73
Vacancy in bulk and surface
4.11
(+0.35)
(+0.27)
HfCx
1.0
4.63
1
4.31
0.6
3.87
Vacancy in bulk and surface
3.35
(−0.76)
(−0.96)
was defined in Ref. [15]. The method of obtaining the VEC for each material is as
follows: the VECs of a d
n metal, carbon, and nitrogen are equal to n + 2, 4, and 5,
respectively. According to this definition, the VECs of TaC 1.0 , HfC 1.0 , and HfC 0.5 are
9, 8, and 6 (4 + 4 × 0.5), respectively. The VECs of these stoichiometric carbides are
decreased by introducing carbon vacancies. Therefore, as seen from Fig. 3.16a, the
hardness of TaC increases with vacancy introduction, whereas that of HfC decreases;
accordingly, the bulk term also decreases. The above results agree with the previously
mentioned calculations. From Fig. 3.16c, the hardness as a measure of the bulk term
may provide a way of estimating the effect of mixing metals or carbon/nitrogen on
the work function.
First-principles calculations on stoichiometric carbides and nitrides are useful for
clarifying the effect of vacancy introduction on the surface term, as demonstrated
for TaCx and HfCx. For carbides and nitrides whose DOS near the Fermi level is
mainly composed of electrons from the metal, the surface term is unaffected by
the introduction of vacancies. Calculation results in the case of vacancies are not
necessary, and therefore, the results for a rather large variety of materials are available.
3 Modification of the Work Function
Table 3.1 Calculated work functions (eV) for carbide and nitride surfaces
Relaxed
Unrelaxed
Theory
Exp.
TiC
4.62
4.19
4.7 [14]
3.8 [16]
TiN
3.25
3.03
2.92 [13]
TaC
4.16
3.85
4.24 [15]
4.3 [17]
(3.86: unrelaxed)
TaN
3.45
3.79
4.0 [13]
HfC
4.28
3.86
4.5 [17]
HfN
2.79
3.13
3.85–3.90 [13]
NbC
4.26
3.85
4.2 [17]
NbN
3.33
3.59
3.92 [13]
ZrC
4.30
3.94
4.0 [17]
ZrN
2.79
2.84
2.94 [13]
Table 3.2 Work functions of (100) plane of TaCx and HfCx
Experiment
Theory
x
φ
φ
TaCx
1.0
4.38
1
3.84
0.5
4.73
Vacancy in bulk and surface
4.11
(+0.35)
(+0.27)
HfCx
1.0
4.63
1
4.31
0.6
3.87
Vacancy in bulk and surface
3.35
(−0.76)
(−0.96)
was defined in Ref. [15]. The method of obtaining the VEC for each material is as
follows: the VECs of a d
n metal, carbon, and nitrogen are equal to n + 2, 4, and 5,
respectively. According to this definition, the VECs of TaC 1.0 , HfC 1.0 , and HfC 0.5 are
9, 8, and 6 (4 + 4 × 0.5), respectively. The VECs of these stoichiometric carbides are
decreased by introducing carbon vacancies. Therefore, as seen from Fig. 3.16a, the
hardness of TaC increases with vacancy introduction, whereas that of HfC decreases;
accordingly, the bulk term also decreases. The above results agree with the previously
mentioned calculations. From Fig. 3.16c, the hardness as a measure of the bulk term
may provide a way of estimating the effect of mixing metals or carbon/nitrogen on
the work function.
First-principles calculations on stoichiometric carbides and nitrides are useful for
clarifying the effect of vacancy introduction on the surface term, as demonstrated
for TaCx and HfCx. For carbides and nitrides whose DOS near the Fermi level is
mainly composed of electrons from the metal, the surface term is unaffected by
the introduction of vacancies. Calculation results in the case of vacancies are not
necessary, and therefore, the results for a rather large variety of materials are available.