Chapter 5
Modification of Band Alignment
via Work Function Control
In this chapter, the band alignment in an ideal case will be discussed. Ideally, the band
alignment is solely determined by the work functions of the materials in contact. In
many cases, however, the interface band alignment deviates from the ideal condition
for many intrinsic and extrinsic reasons. Even in such nonideal cases, an ideal contact
is considered as a starting point. Therefore, ways of modifying the band alignment
through work function control in an ideal case are of great importance.
5.1 Ideal Band Alignment
The band alignment between a metal (work function of φ m ) and an n-type semiconductor (work function of φ s ) in an ideal case is shown in Fig. 5.1. Similarly to the
surface discussed in Chap. 2 (Fig. 2.8a), the electron distribution at an edge where
the surrounding electric condition changes sharply deviates from that in a uniform
region, forming an interface dipole and an interface potential due to the dipole. In the
case of an interface, electron redistribution occurs so that the Fermi level of the metal
aligns with that of the semiconductor (or insulator) in order to realize thermodynamic
equilibrium in the electronic system. The Fermi level is aligned by introducing an
interface potential so that the vacuum level at the contact is continuous. This electron redistribution or the interface potential causes band bending at the interface.
Therefore, the amount of band bending E is equal to the difference in the work
function between the metal and semiconductor (φ m − φ s ). As a result, the Schottky
barrier height (SBH), which is the activation energy needed to excite an electron
in the Fermi level of the metal to the conduction band of the semiconductor (E C ),
is equal to {(E C − E F ) + E}. Using the relationships EA = φ s − (E C − E F ) and
E = (φ m − φ s ), the SBH is expressed as (φ m − EA), where EA is the electron
affinity of the semiconductor.
© 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_5
97
Modification of Band Alignment
via Work Function Control
In this chapter, the band alignment in an ideal case will be discussed. Ideally, the band
alignment is solely determined by the work functions of the materials in contact. In
many cases, however, the interface band alignment deviates from the ideal condition
for many intrinsic and extrinsic reasons. Even in such nonideal cases, an ideal contact
is considered as a starting point. Therefore, ways of modifying the band alignment
through work function control in an ideal case are of great importance.
5.1 Ideal Band Alignment
The band alignment between a metal (work function of φ m ) and an n-type semiconductor (work function of φ s ) in an ideal case is shown in Fig. 5.1. Similarly to the
surface discussed in Chap. 2 (Fig. 2.8a), the electron distribution at an edge where
the surrounding electric condition changes sharply deviates from that in a uniform
region, forming an interface dipole and an interface potential due to the dipole. In the
case of an interface, electron redistribution occurs so that the Fermi level of the metal
aligns with that of the semiconductor (or insulator) in order to realize thermodynamic
equilibrium in the electronic system. The Fermi level is aligned by introducing an
interface potential so that the vacuum level at the contact is continuous. This electron redistribution or the interface potential causes band bending at the interface.
Therefore, the amount of band bending E is equal to the difference in the work
function between the metal and semiconductor (φ m − φ s ). As a result, the Schottky
barrier height (SBH), which is the activation energy needed to excite an electron
in the Fermi level of the metal to the conduction band of the semiconductor (E C ),
is equal to {(E C − E F ) + E}. Using the relationships EA = φ s − (E C − E F ) and
E = (φ m − φ s ), the SBH is expressed as (φ m − EA), where EA is the electron
affinity of the semiconductor.
© 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_5
97