Page 376 - Book Hosokawa Nanoparticle Technology Handbook

FUNDAMENTALS CH. 6 EVALUATION METHODS FOR PROPERTIES OF NANOSTRUCTURED BODY
electron depletion layers cover the entire region of
these particles. For particles with intermediate sizes,
effective electron density changes markedly depend-
ing on the amount of adsorbed oxygen. For electrical
conduction through a porous structure, as shown in
Fig. 6.4.7, electric current flows by crossing electron
depletion layers or through paths narrowed by elec-
tron depletion layers. Accordingly, highly resistive
electron depletion layers on the surface contribute
largely to the overall resistance, and electrical con-
ductivity changes markedly depending on particle
E c size, particle configuration and surface acceptor den-
E c sity. When adsorbed water layers exist on the surface
E F of insulating particles, electric current flows mainly
E F through these layers. Also, in this case, highly con-
ductive water layers on the surface contribute largely
E
V
E V to the overall resistance.
Figure 6.4.7 6.4.2.2 Direct current (DC) measurement
Structural schema of porous sintered bodies and their band By DC measurement, the overall conduction proper-
structures. Insulating electron depletion layer is formed on ties including the contributions of interfaces and sur-
grain surface (white region). E : Fermi level, E : energy faces are measured as described above. Fig. 6.4.9
C
F
level at the bottom of conduction band, E : energy level at shows general measurement methods for resistivity
V
1
the top of valence band. [ m], which is the inverse of conductivity [S m ]
and their features [2]. It also shows the measurement
methods for sheet resistance [ / ] ( /d) used
s
s
for the evaluation of thin films and surfaces. The two-
probe and four-probe methods are used for high-
resistance and low-resistance samples, respectively.
Particle size (nm)
10 17 The Van der Pauw method can be applied to the meas-
urement of film samples of any shape. In the Van der
Pauw method, electrodes are provided at any of the
100 four positions A, B, C and D on the edge of a film
10 15 sample, the voltage V CD between electrodes C and D
is measured when an electric current I AB is made to
flow between electrodes A and B, and the resistance
is determined using V /I . The resistance
R
70
neff (cm -3 ) 10 13 R BC,DA is determined in the same way, and the resis-
CD AB
AB,CD
tivity of the sample can be obtained from the two
resistances. f is the coefficient related to the sample
configuration and electrode position, and f 1 when
50 R R . In most cases, measurement is con-
BC,DA
AB,CD
10 11 ducted for samples with the shape shown in
Fig. 6.4.9f.
When leakage current is made to flow in the volt-
age measurement circuit, a conductivity larger than
10 9
T = 400K 30 the true value is estimated. Accordingly, it is neces-
= 8.6 20 sary for all measurement methods to use a voltmeter
r
= 1×10 17 10
N D with a high internal impedance. It is also necessary to
E = 0.05ev maintain the atmosphere (e.g., water vapor pressure
D
and oxygen partial pressure) unchanged and to con-
10 11 10 12 10 13
duct measurement in a dry atmosphere, especially for
-2
Nss (cm ) high-resistance samples. The following treatments
are effective in improving accuracy: (1) two meas-
Figure 6.4.8 urements are conducted in opposite current direc-
Relationship between effective electron density n and tions and the average is adopted to avoid the effect of
eff
surface acceptor density N for ZnO particles of various thermoelectric power and (2) an electric shield is
ss
sizes [1]. T: temperature, : dielectric permittivity N : applied to avoid the effect of the electric field from
D
r
donor density, E : donor level. the outside.
D
350