6.1 S Parameter: Indicator of Nonideality
115
Table 6.1 Several reported S
values [1]
Material
S value
Si
~0.05
GaAs
~0.09
GeSe
~0.06
GaS
~0.9
SiO 2
~1.0
In some references, the S parameter is defined using electronegativity instead of
φ m . This is based on the relationship between electronegativity and φ m as discussed
in Chap. 2. Hereafter, the discussion is based on SBH , but the same discussion
applies for V FB . In Table 6.1, some reported S values are listed [1]. The S values are
material-dependent. When S = 0, the SBH is constant regardless of the value of φ m ,
and this situation is called Fermi level pinning. The S parameter has been defined
from experiments. The physical meaning of the S parameter is discussed later in
Sect. 6.3. Some examples of SBH plotted against φ m or φ m,eff are shown in Fig. 6.3
[2–4].
A band diagram of a nonideal Schottky contact is drawn by introducing a potential
difference , as in Fig. 6.4. Here, SBH = φ m − EA − . Therefore, from Eq. (6.3),
φ m,eff = φ m −
(6.7)
S ≡
d (SBH )
d φ m
=
d φ m,eff
d φ m
(6.8)
= 1 −
d
d φ m
.
(6.9)
The ideal case is = 0, for which S = 1. For S = 0, meaning that any change
in the metal work function does not affect the band alignment, changes with the
metal work function as
d
d φ m
= 1. For 0 < S < 1,
d
d φ m
is less than 1 but constant,
meaning that is linearly dependent on φ m , making it possible to tune the SBH via
φ m . In some cases is not a simple function of φ m and is affected by other factors,
which will be discussed in Chap. 7.
6.2 Origin of Nonideality
Many ideas have been proposed to explain nonideality from different viewpoints.
One viewpoint is that the origin of nonideality is either intrinsic or extrinsic. Here,
an “intrinsic origin” means that nonideality originates from the nature of the materials and cannot be changed by changing the process of interface formation. On
the other hand, an “extrinsic origin” is the process of interface formation and can
115
Table 6.1 Several reported S
values [1]
Material
S value
Si
~0.05
GaAs
~0.09
GeSe
~0.06
GaS
~0.9
SiO 2
~1.0
In some references, the S parameter is defined using electronegativity instead of
φ m . This is based on the relationship between electronegativity and φ m as discussed
in Chap. 2. Hereafter, the discussion is based on SBH , but the same discussion
applies for V FB . In Table 6.1, some reported S values are listed [1]. The S values are
material-dependent. When S = 0, the SBH is constant regardless of the value of φ m ,
and this situation is called Fermi level pinning. The S parameter has been defined
from experiments. The physical meaning of the S parameter is discussed later in
Sect. 6.3. Some examples of SBH plotted against φ m or φ m,eff are shown in Fig. 6.3
[2–4].
A band diagram of a nonideal Schottky contact is drawn by introducing a potential
difference , as in Fig. 6.4. Here, SBH = φ m − EA − . Therefore, from Eq. (6.3),
φ m,eff = φ m −
(6.7)
S ≡
d (SBH )
d φ m
=
d φ m,eff
d φ m
(6.8)
= 1 −
d
d φ m
.
(6.9)
The ideal case is = 0, for which S = 1. For S = 0, meaning that any change
in the metal work function does not affect the band alignment, changes with the
metal work function as
d
d φ m
= 1. For 0 < S < 1,
d
d φ m
is less than 1 but constant,
meaning that is linearly dependent on φ m , making it possible to tune the SBH via
φ m . In some cases is not a simple function of φ m and is affected by other factors,
which will be discussed in Chap. 7.
6.2 Origin of Nonideality
Many ideas have been proposed to explain nonideality from different viewpoints.
One viewpoint is that the origin of nonideality is either intrinsic or extrinsic. Here,
an “intrinsic origin” means that nonideality originates from the nature of the materials and cannot be changed by changing the process of interface formation. On
the other hand, an “extrinsic origin” is the process of interface formation and can