Page 379 - Book Hosokawa Nanoparticle Technology Handbook

6.4 ELECTRIC PROPERTIES FUNDAMENTALS

C C
R 0 1 2 CPE
R 1 R 2 R 3
Subscript Resistance R(Ω) Capacitance C(F)
0 1.51×10 2 ⎯
1 1.11×10 2 1.02×10 −10
2 4.65×10 3 2.3×10 −5
-4
3 6.41×10 14 3.34×10 (CPE−T)
-1
5.02×10 (CPE−P)
2,500

2,000
(Ω) 1,500
200
150
1,000 (Ω)
Ζ″ 100
50
500 0
Ζ″
-50
150 200 250 300 350 400
0 Ζ′ (Ω)
0 500 1,000 1,500 2,000 2,500
Ζ′ (Ω)

Figure 6.4.11
Equivalent circuit and impedance plot for WO ·2H O
2
3
(5.5 vol%) epoxy resin composite [4]. Circles and solid
lines indicate measured values and calculated values,
respectively. CPE: constant phase element.
Figure 6.4.12
The mapping of conduction regions in lead titanate Simulated impedance plot (a) and modulus plot (b) for an
zirconate (PZT) thin films on a Si/Pt substrate has equivalent circuit with largely different component
been reported, in which electrical conduction was resistances R and the same component capacitance C. is
measured in the vertical direction of the films by the time constant. The modulus is represented as the
attaching and scanning a conductive cantilever [8]. inverse of the complex permittivity.
A conductive area of approximately 100 nm width
was distributed along grain boundaries. The results
showed that the grain boundaries work as current
paths, degrading the insulating/ferroelectric proper-
ties of the PZT thin films.
Two microscopic four-point probe methods of
examining the electrical conductivity of silicon
crystal surfaces, have been developed (Fig. 6.4.13)
[9]. One uses linearly arranged monolithic four-point
probes fabricated on one tip, whose probe spacing is
fixed around several micrometers. The other one uses
four probes on four independently driven STM tips,
whose probe spacing can be changed from 1 m to
1 mm. In the latter method, a square arrangement of
the probes is possible [10]; thus, this method can be
regarded as a modified, infinitesimal Van der Pauw
method. When the probe spacing is very small, only Figure 6.4.13
current flowing near the surface is detected. Schematic drawings of the four-point probe method in
Accordingly, the method can accurately determine (a) linear and (b) square arrangements.

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