Biomedical Engineering Reference
In-Depth Information
used to investigate the dynamics of bound or mobile charges in bulk or interface regions of
any kind of ionic solids, or liquid materials, semiconductors, mixed ionic-electronic materials,
and insulators (dielectrics). The technique measures the impedance as a function of frequency
automatically in the range of 0.1 Hz to 10 MHz and is easily interfaced to the computer.
The complex impedance measurements are capable of separating the various contribu-
tions such as bulk, grain boundary, and electrode, to total conductivity. Hence, this tech-
nique is able to extract the data that allow these phenomena to be isolated. Spectroscopic
impedance studies on diamond films form the basis of this chapter; as such, the current
status, models, and fundamental applications and interpretations related to this technique
are crucial to the chapter. This chapter provides detailed background information based
on both theoretical and empirical knowledge in this area.
Starting with general concepts of electrochemical impedance, the principle of this technique
is presented. The utilization of this technique to characterize the grains and grain boundaries
contribution are discussed in details. The equivalent electrical circuits are presented to com-
pare with real materials systems. Next, formulae for the capacitance of one-layer and two-layer
dielectrics models, with either in-plane or cross-section electrode configuration, are presented
as references for the following chapters. Finally, from the microscopic point of view, different
mechanisms on dielectric relaxation and polarization are summarized.
Case studies on impedance spectroscopy of diamond films have been presented includ-
ing single-crystalline, polycrystalline, and nanocrystalline. The potential applications for
both diamond-based materials and non-diamond-based materials have been reviewed.
ImpedanceTheory
Impedance Principle
Electrochemical impedance is the frequency-dependent complex-valued proportionality
factor that is a ratio between the applied potential and current signal. For the sake of sim-
plicity, the impedance plots for the resistor-capacitor (
R
-
C
) in parallel with a series resistor
network (see Figure 4.1) will be considered in some detail. The reason for choosing this
circuit is because many of the electrochemical systems encountered in practice are actually
modeled using this network [1].
The terms “resistance” and “impedance” both imply an obstruction to current or electron
flow. When dealing with a direct current (DC), only resistors provide this effect. However,
for the case of an alternating current (AC), circuit elements such as capacitors and induc-
tors can also influence the electron flow. These elements can affect not only the magnitude
of an AC wave form but also its time-dependent characteristics or phase. In DC theory,
where the frequency equals 0 Hz, a resistance is defined by the Ohm's law:
E = IR
(4.1)
where
E
is the applied potential,
I
is the resulting current, and
R
denotes resistance.
For an AC current, where the frequency exceeds zero, this is represented by
E = IZ
Ohm's law with frequency > 0
(4.2)
