6.3 Charge Neutrality Level (CNL) and S Parameter
119
6.3 Charge Neutrality Level (CNL) and S Parameter
In Sect. 6.2, the CNL was introduced as the origin of nonideality in the MIGS
model. If the position of the CNL is different from that of the Fermi level, the
distribution of metal electrons penetrating into the semiconductor at the interface
changes, generating the potential in Fig. 6.4. By using an analogy of a capacitor
where the potential between the two plates depends on the dielectric constant of the
material between them, it is reasonable to expect that the potential will depend on
the dielectric constant of the semiconductor in contact with the metal. In Fig. 6.6,
the effective work function φ m,eff for different metals is plotted as a function of the
dielectric constant for some oxides (calculated from data in Ref. [10]). The value of
φ m,eff at a dielectric constant of 1 is for the interface with a vacuum and the value
of φ m,eff is φ m . On the basis of more detailed discussion, the following empirical
relationship has been proposed [1, 11].
S =
1
1 + 0.1(ε ∞ − 1)
2
(6.10)
Here, ε ∞ is the optical dielectric constant. Figure 6.7 shows the experimentally
obtained relationship between the dielectric constant and the S parameter for various
semiconductors and insulators [3].
When Fermi level pinning occurs, i.e., the SBH does not change upon modification
of the metal work function, the S value is nearly zero. This means that in Fig. 6.4
increases linearly with φ m . In practice, the range of φ m modification is about 3 eV.
If the S value is 0.01, the SBH changes by at most 0.03 V, which can be regarded
as strong Fermi level pinning. According to Eq. (6.10), a dielectric constant of 32.5
will give an S value of 0.01. For readers’ convenience, some materials with relatively
Fig. 6.6 Effective work function φ m,eff for different metals in contact with several oxides plotted
as a function of dielectric constant of the oxides (see text for explanation)
119
6.3 Charge Neutrality Level (CNL) and S Parameter
In Sect. 6.2, the CNL was introduced as the origin of nonideality in the MIGS
model. If the position of the CNL is different from that of the Fermi level, the
distribution of metal electrons penetrating into the semiconductor at the interface
changes, generating the potential in Fig. 6.4. By using an analogy of a capacitor
where the potential between the two plates depends on the dielectric constant of the
material between them, it is reasonable to expect that the potential will depend on
the dielectric constant of the semiconductor in contact with the metal. In Fig. 6.6,
the effective work function φ m,eff for different metals is plotted as a function of the
dielectric constant for some oxides (calculated from data in Ref. [10]). The value of
φ m,eff at a dielectric constant of 1 is for the interface with a vacuum and the value
of φ m,eff is φ m . On the basis of more detailed discussion, the following empirical
relationship has been proposed [1, 11].
S =
1
1 + 0.1(ε ∞ − 1)
2
(6.10)
Here, ε ∞ is the optical dielectric constant. Figure 6.7 shows the experimentally
obtained relationship between the dielectric constant and the S parameter for various
semiconductors and insulators [3].
When Fermi level pinning occurs, i.e., the SBH does not change upon modification
of the metal work function, the S value is nearly zero. This means that in Fig. 6.4
increases linearly with φ m . In practice, the range of φ m modification is about 3 eV.
If the S value is 0.01, the SBH changes by at most 0.03 V, which can be regarded
as strong Fermi level pinning. According to Eq. (6.10), a dielectric constant of 32.5
will give an S value of 0.01. For readers’ convenience, some materials with relatively
Fig. 6.6 Effective work function φ m,eff for different metals in contact with several oxides plotted
as a function of dielectric constant of the oxides (see text for explanation)