Chapter 6
Advanced Models for Practical Devices
6.1 S Parameter: Indicator of Nonideality
In this chapter, nonideal band alignment, which is often observed in practical devices,
will be discussed. As mentioned in Sect. 5.1, the following equations are satisfied in
the case of ideal band alignment.
SBH = φ m − EA
(6.1)
Here, SBH , φ m , and EA are the Schottky barrier height, the work function of the
metal, and the electron affinity of the semiconductor, respectively (Fig. 6.1a).
V FB = φ m − φ s
(6.2)
Here, V FB and φ s are the flat-band voltage and the work function of the
semiconductor, respectively (Fig. 6.1b).
When ideal band alignment is realized, the desired SBH or V FB can be achieved
by tuning φ m , because SBH or V FB linearly increases with φ m (Fig. 6.2a).
In practical cases, the above equations are often not satisfied. In such cases, the
effective work function φ m,eff is sometimes defined for metals such that it satisfies
Eqs. (6.3) or (6.4).
SBH = φ m,eff − EA
(6.3)
V FB = φ m,eff − φ s
(6.4)
Even in a nonideal case, it is often observed that SBH or V FB (or the effective work
function) is linearly dependent on φ m , although the proportionality coefficient is not
equal to 1 but less than 1 in most cases (Fig. 6.2b). The proportionality coefficient is
called the S parameter, which is defined as
© National Institute for Materials Science, Japan 2021
M. Yoshitake, Work Function and Band Alignment of Electrode Materials,
NIMS Monographs, https://doi.org/10.1007/978-4-431-56898-8_6
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