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Interdigital Sensors and Transducers
Interdigital Sensors and Transducers
ALEXANDER V. MAMISHEV
, MEMBER, IEEE
,
KISHORE SUNDARA-RAJAN
, STUDENT MEMBER, IEEE
, FUMIN YANG
, STUDENT MEMBER, IEEE
,
YANQING DU
, MEMBER, IEEE
,
AND
MARKUS ZAHN
, FELLOW, IEEE
Invited Paper
This review paper focuses on interdigital electrodesa geo-
metric structure encountered in a wide variety of sensor and
transducer designs. Physical and chemical principles behind the
operation of these devices vary so much across different fields of
science and technology that the common features present in all
devices are often overlooked. This paper attempts to bring under
one umbrella capacitive, inductive, dielectric, piezoacoustic, chem-
ical, biological, and microelectromechanical interdigital sensors
and transducers. The paper also provides historical perspective,
discusses fabrication techniques, modeling of sensor parameters,
application examples, and directions of future research.
KeywordsDielectric measurements, interdigital sensors, non-
destructive testing (NDT), sensor design, sensor modeling, spec-
troscopy, surface acoustic waves (SAWs), transducers.
I. I
NTRODUCTION
A. Motivation for This Paper
Interdigital electrodes are among the most commonly used
periodic electrode structures. Recent advances in such fields
as nondestructive testing (NDT), microelectromechanical
systems (MEMS), telecommunications, chemical sensing,
piezoacoustics, and biotechnology involve interdigital elec-
trodes in very different ways. At the same time, a number of
Manuscript received February 16, 2003; revised December 30, 2003. This
work was supported in part by the National Science Foundation under CA-
REER Award 0093716, in part by the Center for Process Analytical Chem-
istry, in part by the Electric Power Research Institute, in part by the Univer-
sity of Washington Royalty Research Fund, in part by the Link Foundation,
in part by the Air Force Office of Sponsored Research, and in part by the
American Public Power Association.
A. V. Mamishev, K. Sundara-Rajan, and F. Yang are with the Sensors,
Energy, and Automation Laboratory (SEAL), Department of Elec-
trical Engineering, University of Washington, Seattle, WA 98195 USA
(e-mail:
mamishev@ee.washington.edu;
kishore@ee.washington.edu;
fuminy@ee.washington.edu).
Y. Du is with Underwriters Laboratories, Santa Clara, CA 95050 USA
(e-mail: Yanqing.Du@us.ul.com).
M. Zahn is with the Department of Electrical Engineering and Computer
Science, Massachusetts Institute of Technology, Cambridge, MA 02139
USA (e-mail: zahn@mit.edu).
Digital Object Identifier 10.1109/JPROC.2004.826603
common features are shared among these applications. The
purpose of this paper is to outline common features and to
highlight the differences of sensor geometry, manufacturing
techniques, choice of materials, analytical and numerical
modeling, design optimization, system integration, and
data analysis. It is difficult and perhaps even excessive to
maintain equally deep and comprehensive treatment of all
these subjects. Instead, the fringing electric field sensors are
given the deepest emphasis in this manuscript. Significant
aspects of other types of sensors are discussed, while repe-
tition is avoided. References are provided to major review
papers and books in each section devoted to a particular
field of interdigital electrode applications, such as dielectric
imaging, acoustic sensors, and MEMS.
It is not possible to develop a universal sensor and a uni-
versal parameter estimation algorithm that would provide
the maximum information about material properties in all
applications. Each application requires a judicious choice
of sensor design and associated parameter estimation algo-
rithms. As a technical system develops, the requirements for
each element become clearer and affect the requirements for
each element of the trinity shown in Fig. 1. For example, it
may become clear during the development stage that the one-
sided access to the material under test (MUT) is not necessary
due to the specifics of the manufacturing process. In this case,
the electrode layout design should not be limited to interdig-
ital structures only. The dual-sided access has advantages of
larger, easily measurable capacitances and a more uniform
field distribution. The examples of appropriate matching of
sensors and parameter estimation algorithms with different
applications are encountered throughout this paper.
B. Terminology
The explosion in the quantity of scientific information has
brought its share of confusion to the subject of interdigital
sensors. As a result, lack of coordination of research efforts
is not uncommon in this field. For example, theoretical
0018-9219/04$20.00 � 2004 IEEE
808
PROCEEDINGS OF THE IEEE, VOL. 92, NO. 5, MAY 2004 Fig. 1.
Every sensing application requires an optimum
combination of inherently dependent elements of the measurement
system comprising sensor design and parameter estimation
algorithms.
expressions obtained for capacitance of interdigital piezo-
electric sensors are rarely mentioned in papers published in
the fields of dielectrometry or MEMS; researchers in one
country are often unaware of efforts in other countries; and
sensor designers repeat mistakes of previous generations.
Ambiguity of terminology does not help this situation: not
everyone associates periodic microstrip electrode structures
with interdigital patterns. Moreover, the word interdigital
itself does not have direct analogs in other languages. Thus,
this most frequent term is often replaced by such equivalents
as periodic, microstrip, comb, and grating, as well
as such variations as interdigitated and combed. The
overlap of the terms is not complete, for example, not every
microstrip circuit is interdigital, and not every interdigital
circuit is strictly periodic.
The term interdigital, selected for use throughout this
paper, refers to a digitlike or fingerlike periodic pattern of
parallel in-plane electrodes used to build up the capacitance
associated with the electric fields that penetrate into the
material sample or sensitive coating.
Another term frequently misunderstood in context of
interdigital sensors is wavelength. One should distinguish
between the radiation wavelength of electromagnetic waves
and the wavelength of the spatial periodicity, or spatial
wavelength, of the geometrical structure. The former is the
wavelength
with the frequency equal to the frequency of
the voltage source applied to the sensor electrodes
(1)
where
is the speed of light and
is the frequency of the
voltage source. This variable is typically discussed in con-
text of radio frequency (RF) and microwave circuits. For ex-
ample, a 600-MHz electromagnetic wave has the wavelength
of 50 cm. The spatial wavelength of the periodic interdigital
structure is the distance between the centerlines of the adja-
cent fingers belonging to the same electrode.
Using the terms capacitance and conductance for the de-
scription of terminal characteristics of an interdigital sensor
may be misleading, especially when one encounters effec-
tive negative values of capacitance or conductance. Strictly
speaking, these are mutual capacitance (or transcapacitance)
and mutual conductance (or transconductance), as defined
in multielectrode circuits. For the overwhelming majority of
cases, this distinction is not important enough to justify the
use of longer, more cumbersome terms.
Sensors
, transducers, and detectors, as explained below,
are related; hence, these terms are often used interchange-
ably. The choice of the term usually depends on the function
of the device that one wants to emphasize.
A sensor is a device whose output can be quantified and
changes with one or more physical phenomena. This output
information can be used for process monitoring and control.
A transducer is a device that converts one form of energy into
another form. The measurement of physical variables asso-
ciated with the resulting form of energy allows estimation of
the physical variables associated with the input energy. A de-
tector is a device indicating presence, absence, or change of
the signal qualitatively, either as a binary signal or as a low
resolution signal with several states.
C. Historical Perspective
Historically, the first and still the most common reason
for making an interdigital electrode structure is to increase
the effective length, and, therefore, the capacitance between
the electrodes. Perhaps the earliest example of interdigital
electrode design is found in the patent of N. Tesla, issued
in 1891 [1]. In this example, each finger is a rectangular
plate, immersed in an insulating liquid. The total capaci-
tance of the electrical condenser proposed by Tesla in-
creases approximately linearly with the number of plates.
This principle is sometimes used in modern capacitors as
well. Theoretical expressions for calculation of capacitance
between coplanar strips appeared in the 1920s [2]. Antenna
designers use such periodic strip patterns to control the radia-
tion patterns. The technology, later named microdielectrom-
etry, started more than 20 years ago as a modification of the
charge-flow transistor (CFT), originally developed for mon-
itoring the sheet resistance of thin-film materials [3]. The
CFT was an MOS-compatible device based on contempo-
rary principles of transistor electronics [4], [5]. In this device,
the time delay between the application of the gate voltage
and a complete inversion of the channel region is dependent
on the sheet resist