32
2 What is the Work Function?: Definition and Factors …
whereas the temperature derivative of the work function increases approximately
linearly with temperature for temperatures above 9.2 K.
2.5 Inhomogeneity of the Work Function
Up to this point, we have discussed theoretical aspects or rather controlled surfaces.
However, practical surfaces are inhomogeneous in many aspects such as polycrystallinity, irregular roughness, uneven bulk/surface composition, and uneven surface
contamination. Here, we briefly discuss the work function of such inhomogeneous
surfaces. Figure 2.24a shows a schematic potential diagram of a polycrystalline
sample with three different crystal orientations in contact. In this figure, the potential
of each crystal orientation is connected with the vacuum level reference. However,
where grains with different crystal orientations are in contact, the electrons inside
each grain try to maintain chemical equilibrium so that the Fermi level of each grain
is aligned in the same energy level. As a result, the vacuum level outside the sample
is similar to that shown in Fig. 2.24b. This means that the work function of a polycrystalline sample is inhomogeneous. When the size of one grain is sufficiently large
to satisfy the definition of the work function in Sect. 2.2 and the work function
measurement method with lateral resolution is applied, such inhomogeneity in the
work function is actually observed. However, the work function obtained by usual
methods is considered to be an averaged value obtained from surfaces with different
b) Fermi level referenced
a) Vacuum level referenced
Vacuum level
Fig. 2.24 Inhomogeneity with multiple grains having different crystal orientations. The vacuum
level is position-dependent. See text for explanation
2 What is the Work Function?: Definition and Factors …
whereas the temperature derivative of the work function increases approximately
linearly with temperature for temperatures above 9.2 K.
2.5 Inhomogeneity of the Work Function
Up to this point, we have discussed theoretical aspects or rather controlled surfaces.
However, practical surfaces are inhomogeneous in many aspects such as polycrystallinity, irregular roughness, uneven bulk/surface composition, and uneven surface
contamination. Here, we briefly discuss the work function of such inhomogeneous
surfaces. Figure 2.24a shows a schematic potential diagram of a polycrystalline
sample with three different crystal orientations in contact. In this figure, the potential
of each crystal orientation is connected with the vacuum level reference. However,
where grains with different crystal orientations are in contact, the electrons inside
each grain try to maintain chemical equilibrium so that the Fermi level of each grain
is aligned in the same energy level. As a result, the vacuum level outside the sample
is similar to that shown in Fig. 2.24b. This means that the work function of a polycrystalline sample is inhomogeneous. When the size of one grain is sufficiently large
to satisfy the definition of the work function in Sect. 2.2 and the work function
measurement method with lateral resolution is applied, such inhomogeneity in the
work function is actually observed. However, the work function obtained by usual
methods is considered to be an averaged value obtained from surfaces with different
b) Fermi level referenced
a) Vacuum level referenced
Vacuum level
Fig. 2.24 Inhomogeneity with multiple grains having different crystal orientations. The vacuum
level is position-dependent. See text for explanation