88
4 Measurement of Work Function
specimen
Energy analyzer
good
poor
(a)
(b)
Fig. 4.20 a Schematic illustration of electric potential for the measurement setup in secondary
electron cutoff spectroscopy; b examples of good and poor sample mounting for measurements to
avoid disturbing the electric field
4.3 Utilizing Contact Potential Difference Measurement
The methods described in Sects. 4.1 and 4.2 enable the measurement of the absolute
value of the work function in principle. However, there are many cases where only
relative values or changes in the work function are important and absolute values are
not necessary in experiments. In particular, when the change in the work function with
time is measured, quick measurements are important rather than obtaining absolute
values. For such cases, the contact potential difference (CPD) between two materials,
a reference material (reference) and a specimen, is measured. In Fig. 4.21, the energy
diagram for the generation of a CPD is schematically illustrated. It can be seen from
the figure that the CPD is the difference in the work function between two materials.
Either the Kelvin probe method or the diode method is used to measure the CPD.
4.3.1 Kelvin Probe Method
When there is a CPD between two metals, as in Fig. 4.21, a capacitor is formed. When
the reference side of one of the metals vibrates so that the distance (x) between the
two metals changes with time, a current (i) is induced in the circuit (Fig. 4.22). The
induced current is expressed by the following equation:
i =
dQ
dt
= ×
d
dt
εε 0 A
x
,
(4.13)
4 Measurement of Work Function
specimen
Energy analyzer
good
poor
(a)
(b)
Fig. 4.20 a Schematic illustration of electric potential for the measurement setup in secondary
electron cutoff spectroscopy; b examples of good and poor sample mounting for measurements to
avoid disturbing the electric field
4.3 Utilizing Contact Potential Difference Measurement
The methods described in Sects. 4.1 and 4.2 enable the measurement of the absolute
value of the work function in principle. However, there are many cases where only
relative values or changes in the work function are important and absolute values are
not necessary in experiments. In particular, when the change in the work function with
time is measured, quick measurements are important rather than obtaining absolute
values. For such cases, the contact potential difference (CPD) between two materials,
a reference material (reference) and a specimen, is measured. In Fig. 4.21, the energy
diagram for the generation of a CPD is schematically illustrated. It can be seen from
the figure that the CPD is the difference in the work function between two materials.
Either the Kelvin probe method or the diode method is used to measure the CPD.
4.3.1 Kelvin Probe Method
When there is a CPD between two metals, as in Fig. 4.21, a capacitor is formed. When
the reference side of one of the metals vibrates so that the distance (x) between the
two metals changes with time, a current (i) is induced in the circuit (Fig. 4.22). The
induced current is expressed by the following equation:
i =
dQ
dt
= ×
d
dt
εε 0 A
x
,
(4.13)