Development of Interdigitated Electrode Sensors for Monitoring the  
Dielectric Properties of Lubricant Oils 
 
by 
 
Jacob Wade Craft 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
December 13, 2010 
 
 
 
 
 
 
 
 
 
Copyright 2010 by Jacob Wade Craft 
 
 
Approved by 
 
Dong-Joo Kim, Chair, Associate Professor of Materials Engineering 
Jeffrey Fergus, Professor of Materials Engineering 
Barton Prorok, Associate Professor of Materials Engineering 
 
 
 
 
 
 
ii 
 
 
 
 
 
 
Abstract 
 
 
 Proper lubrication is a necessary step in protecting the engine of any vehicle. Regular 
changing of the lubricating oil becomes an important part of keeping the vehicle running for an 
extended life. Currently, lubricant oil is changed based on a scheduled time frame or set mileage. 
It would be advantageous, however, to be able to detect the properties of oil and tell when 
lubricant change is necessary to reduce waste and excess cost. 
 The goal of this research is to develop and optimize an IDT sensor to measure the change 
in the capacitance value of lubricant oil. To optimize the sensor, four design parameters were 
chosen and varied between several series of IDT electrodes. The electrodes were fabricated and 
tested to observe how each of the parameters, electrode width, finger thickness, finger spacing 
and number of fingers, would affect the sensitivity of the capacitance measurements. Several 
trends of how they affect the sensitivity were observed and the relative importance of each factor 
was determined. In general, a maximization of the sensing area by increasing electrode width and 
finger thickness was the most influential. The spacing of the electrode fingers is also a very 
important factor though the biggest changes are only seen at very small spacing?s. The effect of 
substrate material was also studied and was found to have some effect. 
 
 
 
 
 
 
 
 
 iii 
 
 
 
 
 
Acknowledgments 
 
 
I would like to thank Dr. Kim and the members of my committee, Dr. Fergus and Dr. 
Prorok for all of their help and guidance. I would also like to thank my group members, Dr. 
Wikle, L.C. Mathison, Joshua, Dan, Ho Sang, Seon Bae and Ishita for their help and support. 
Finally, I would like to thank my friends and my family for their love and support throughout 
this process.  
 iv 
 
 
 
 
 
Table of Contents 
 
 
Abstract ......................................................................................................................................... ii 
Acknowledgments........................................................................................................................ iii  
List of Tables ............................................................................................................................... vi  
List of Figures ............................................................................................................................. vii  
List of Abbreviations ................................................................................................................... ix 
Chapter 1  Introduction ................................................................................................................. 1 
 1.1 Overview  .................................................................................................................... 1 
 1.2 Thesis Structure   ........................................................................................................ 2 
Chapter 2  General Background .................................................................................................... 3 
2.1 Oil Degradation and Current Testing Methods ........................................................... 3 
2.1.1 Oil Degradation ............................................................................................ 3 
2.1.2 Current Testing Methods ............................................................................. 5 
2.1.3 Current Research .......................................................................................... 7 
2.1.4 Commercially Available Sensor Systems .................................................. 17 
2.2 Capacitance Sensors.................................................................................................. 18 
2.2.1 General Principles ...................................................................................... 18 
2.2.2 IDT Structure ............................................................................................. 19 
2.2.3 IDC Model ................................................................................................. 21 
Chapter 3 Experimental Setup and Techniques  ......................................................................... 25 
 v 
3.1 Artificial Aging of Oil Samples ................................................................................ 25 
3.2 Fabrication of Sensors............................................................................................... 28 
3.3 Measurements ........................................................................................................... 30 
Chapter 4 Results and Discussion ............................................................................................... 32 
4.1 Capacitance Measurements ....................................................................................... 33 
4.1.1 Effect of IDT Geometry ............................................................................. 33 
4.1.2 Effect of Substrate Material ....................................................................... 55 
4.2 Optimization of Sensor ............................................................................................. 55 
Chapter 5 Conclusions and Future Studies ................................................................................. 57 
References   ................................................................................................................................. 59 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 vi 
 
 
 
 
 
 
List of Tables 
 
 
Table 2.1 ASTM standard test methods for determining the condition of lubricant oils ............. 7 
Table 2.2 Equations needed for calculation of CI and CE for finite and infinite layers. ............. 24 
Table 3.1 Data for BP turbo oil 2380 .......................................................................................... 26 
Table 3.2 Sputter Conditions for Metal Depositions .................................................................. 30 
Table 4.1  Design parameters for Original IDT electrodes  ........................................................ 33 
Table 4.2  Design parameters for the second set of IDT electrodes. .......................................... 36 
Table 4.3  Design parameters for the final IDT electrode design.  ............................................. 42 
Table 4.4 Effect of design factors on capacitance measurements. ............................................. 52 
Table 4.5 Capacitance per unit area for the 2nd electrode series ................................................. 54 
Table 4.6 Capacitance per unit area for the 3rd electrode series ................................................. 54 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 vii 
 
 
 
 
 
 
List of Figures 
 
 
Figure 2.1 Reaction scheme for oxidation-polymerization reaction sequence ............................. 5 
Figure 2.2 Lubricating oil viscosity vs. dielectric constant .......................................................... 8 
Figure 2.3 Change of dielectric constants with temperature of fresh oil ...................................... 9 
Figure 2.4 Correlation between the measured dielectric constant and the sensing capacitance . 10 
Figure 2.5 Characteristics of dielectric constant vs. temperature for engine oil ......................... 11 
Figure 2.6 Dielectric constant vs. driving distance and its variance with temperature .............. 11 
Figure 2.7 Measured Dielectric Constant for grid capacitance sensor in various media ............ 12 
Figure 2.8 Change in the dielectric constant with different concentrations of contaminant 
particles. .................................................................................................................... 13 
 
Figure 2.9 Relationship between permittivity (Dielectric Constant) and acid number .............. 14 
Figure 2.10 Relationship between permittivity (Dielectric Constant) and iron content ............. 15 
Figure 2.11 Relationship between permittivity (Dielectric Constant) and moisture content ..... 15 
Figure 2.12 Relative dielectric constant variation of different polluted oil samples from fresh oil 
sample ...................................................................................................................... 16 
 
Figure 2.13 Illustration of Delphi Oil Quality Sensor ................................................................ 18 
Figure 2.14 Schematic diagram of an interdigitated electrode. .................................................. 20 
Figure 2.15 Plot of Calculated Capacitance vs. Finger spacing using equation 2.1  .................. 21 
Figure 2.16 (a) Layout of electrode (b) Cross section of electrode. ........................................... 22 
Figure 2.17 Equivalent circuit for IDC model. ........................................................................... 22 
Figure 3.1 Schematic diagram of the oil degradation vessel. ..................................................... 27 
 viii 
Figure 3.2 Photo of the oil degradation vessel.  .......................................................................... 27 
Figure 3.3 Schematic of Fabrication Process .............................................................................. 29 
Figure 4.1 Capacitance vs. Frequency curve for 40s electrode  ................................................. 34 
Figure 4.2 Capacitance vs. Frequency curve for 60s electrode .................................................. 34 
Figure 4.3 Capacitance vs. Frequency curve for 80s electrode .................................................. 35 
Figure 4.4 Capacitance vs. Frequency curve for 100s electrode ................................................ 35 
Figure 4.5 Capacitance vs. Frequency curve for T4S6F3 electrode ........................................... 37 
Figure 4.6 Capacitance vs. Frequency curve for T4S6F6 electrode. .......................................... 37 
Figure 4.7 Capacitance vs. Frequency curve for T4S6F9 electrode. .......................................... 38 
Figure 4.8 Capacitance vs. Frequency curve for T4S6F6L electrode......................................... 38 
Figure 4.9 Change in capacitance vs. finger spacing. ................................................................. 39 
Figure 4.10 Plot of number of fingers vs. the change in capacitance. ........................................ 40 
Figure 4.11 Plot of change in capacitance vs. the electrode width. ............................................ 40 
Figure 4.12 Finger thickness vs. Change in capacitance. ........................................................... 41 
Figure 4.13 Capacitance vs. Frequency curve for T2S5F6 Electrode ........................................ 43 
Figure 4.14 Capacitance vs. Frequency curve for T2S10F6 Electrode ...................................... 44 
Figure 4.15 Capacitance vs. Frequency curve for T4S5F6 Electrode ........................................ 45 
Figure 4.16 Capacitance vs. Frequency curve for T4S10F6 Electrode ...................................... 46 
Figure 4.17 Capacitance vs. Frequency curve for T4S10F6L Electrode .................................... 47 
Figure 4.18 Comparison between measured value and the various models used. ...................... 49 
Figure 4.19 Change in capacitance vs. Finger Width ................................................................. 50 
Figure 4.20 Change in capacitance vs. Finger spacing ............................................................... 50 
Figure 4.21 Change in capacitance vs. Electrode Width ............................................................ 51 
 ix 
 
 
 
 
 
List of Abbreviations 
 
 
IDT Interdigitated Transducer    
IDC Interdigitated Capacitor 
TAN Total Acid Number 
TBN  Total Base Number 
ASTM American Society for Testing and Materials 
 
GPC Gel Permeation Chromatography  
 
FTIR Fourier Transform Infrared Spectroscopy 
1 
 
 
 
 
CHAPTER 1 
INTRODUCTION 
 
1.1 Overview 
 Proper lubrication is a necessary step in protecting the engine of any vehicle. Regular 
changing of the lubricating oil becomes an important part of keeping the vehicle running for an 
extended life. Currently, most engine manufacturers recommend a scheduled approach to 
changing the engine lubricant. This scheduled maintenance is an effective way of making sure 
that the engine stays properly lubricated but can lead to wastefulness if the lubricant is changed 
before it is necessary. Condition based maintenance and oil changes would be preferable. It 
allows the engine lubricant to be changed only when needed and would save on maintenance 
costs in the long run. 
With this in mind, a sensor to monitor the condition of the lubricant in situ has been 
studied. By using an interdigitated electrode structure as a capacitance sensor, the change in the 
capacitance value of oil with its degradation can be monitored. By determining at what point the 
lubricant becomes unfavorable for use in vehicle the engine lubricant can be changed at a point 
in time when it is necessary and save on maintenance costs. 
 The goal of the research is to study and develop this sensor to be implemented in the 
field. The theory behind how the sensor works is relatively simple and the main challenges were 
to determine how the geometrical and other parameters of the sensor affect the response and how 
to optimize the sensor for increased performance in the field. The geometry of the sensor used 
 2 
has a large effect on the sensitivity of the device as well as the type of substrate material used in 
fabrication. 
 
1.2 Thesis Structure 
Chapter 2 includes a literature survey from which this thesis work is based. The chemical 
degradation of oil based lubricants is discussed as well as general information on capacitance 
sensors and interdigitated electrodes. 
Chapter 3 discusses the fabrication process for the sensors as well as the testing procedures 
for the finished products. 
Chapters 4 and 5 present the results of the research and a discussion of the findings as well as 
a summary of the work and conclusions. 
  
 3 
 
 
 
CHAPTER 2 
GENERAL BACKGROUND 
 
2.1 Oil Degradation and Current Testing Methods 
 Lubrication is an essential part of any type of machinery. One of the major types of 
lubricants in use currently is polyol ester based synthetic lubricants. The degradation and 
oxidation of these lubricants are of major concern to ensure that machinery stays properly 
lubricated with timely lubricant changes. In this section, the types of degradation that lubricants 
undergo and different methods of characterizing and analyzing that degradation will be 
discussed. 
2.1.1 Oil Degradation 
 The degradation of polyol ester based lubricants involves a complex series of reactions 
that have been the subject of much study.[1-5] When exposed to oxygen at high temperatures 
(over 200?C), lubricant oils will undergo a series of free radical chain reactions. Three major 
events occur in the breakdown: evaporation, oxidation and thermal degradation. The most 
influential of these is the oxidation reaction which is what causes the sludge and varnish build up 
that is detrimental to the effectiveness of the lubrication.[3,5] 
 All lubricant oils consist of long chain hydrocarbons that are susceptible to oxidation. 
Most engine oil manufacturers take this into account and use oxidation inhibitors in their 
products which will protect the lubricant from oxidation for some time and prolong its useful 
 4 
life. However, when exposed to sufficient heat these oxidation inhibitors become unable to 
protect against the hydrocarbon chains becoming oxidized. The first step in the oxidation 
reaction for these oils is a free-radical chain reaction that will result in the production of 
hydroperoxides which will decrease the effectiveness of the lubricant. The hydroperoxides are 
unstable, however, and will convert to acids and ketones leading to an increased acid content in 
the oil. The products from the initial oxidation reactions that are now present in the lubricant are 
of low molecular weight. These byproducts will generally do one of two things; either evaporate 
into the gas phase or polymerize and form the high molecular weight products that are the cause 
of the increased viscosity of degraded oil and of the sludge and varnish deposits that are 
detrimental to the machinery in which the lubricant is being employed.[3,5] 
 Figure 2.1 shows the basic reaction scheme for the oxidation and polymerization of 
lubricant oil. As the oil is used part of it is lost to evaporation and part is oxidized into the low 
molecular weight liquid phase oxidation products. Again, some of these low molecular weight 
products will evaporate and the rest will polymerize into the high molecular weight liquid phase 
products. Finally, the high molecular weight products will continue to polymerize and eventually 
form as sludge and varnish on surfaces they are supposed to be lubricating.[3,5] 
 
 5 
 
Figure 2.1 Reaction scheme for oxidation-polymerization reaction sequence.[3] 
2.1.2 Current Testing Methods 
 There are many methods in use currently to monitor the condition of used oil once a 
sample has been taken from the vehicle. In this section some of the more prominent methods will 
be discussed along with the underlying principles that make the methods a useful indicator of the 
remaining useful life of the lubricant. 
 The first and most obvious test to run on a sample of lubricant oil is to measure its 
viscosity. The viscosity can be tested in a number of ways outlined by ASTM standards. The 
viscosity of the oil will tell a great deal about how much degradation has occurred. A fresh oil 
sample will usually be a light color and have a lower viscosity to aid in the lubrication and 
wetting of parts inside of the engine or machinery. An oil sample taken from an engine that has 
been used extensively will be dark and much thicker. This increase in viscosity is a result of the 
polymerization of the oxidation byproducts. The low molecular weight byproducts react and 
form long chain molecules with high molecular weights that can eventually become sludge and 
varnish deposits if allowed to react for too long.[3,5] The change in viscosity is the most 
 6 
immediately apparent from a visual standpoint and is useful to determine if further testing is 
necessary. 
 Another valuable test that is often preformed is the determination of the total acid number 
(TAN) or the total base number (TBN). These tests determine the pH of the oil which is very 
telling as to the amount of degradation that has taken place. As the oil oxidizes, the 
hydroperoxides that are formed are converted into acids which will raise the pH level of the 
oil.[3,5] As the degradation increases the TAN will increase and be a very good indicator of the 
amount of useful life that remains in the oil sample. 
Another less commonly used method is gel permeation chromatography (GPC). GPC is 
most often used to determine the molecular weights of the byproducts of the degraded oil. As a 
sample is degraded, the byproducts will contain products with lower molecular weights, products 
with the same molecular weight, and products with high molecular weight. The GPC separates 
and collects data on the amounts of each present. An increase in the high molecular weight 
products will indicate a rise in the viscosity and a decrease in the lubrication potential of the 
oil.[2] 
Various types of spectroscopy have been utilized in lubricant characterization as well 
including: visible, UV, infrared, and Fourier transformation infrared (FTIR). The spectroscopic 
techniques are easy ways to determine the amount of degradation of a sample in a short amount 
of time. Different peaks in these spectra relate to types of bonds that exist in the sample. By 
monitoring how the peaks change, a determination can be made as to what is taking place in the 
sample.[6] 
Table 2.1 shows a summary of the common ASTM standard tests that can be performed 
on a lubricant oil to help to determine its condition. Some or all may be used to gather enough 
 7 
information to determine if the oil is still useable. These tests are used to detect the amount of 
water in the oil, its TAN and TBN, its viscosity and color and the presence of wear metals and 
other contaminants. These are the type of tests that a commercial company would perform in a 
standard oil analysis. 
Table 2.1 ASTM standard test methods for determining the condition of lubricant oils. 
Standard Description 
ASTM D 4377 Standard Test Method for Water in Crude Oils by Potentiometric Karl 
Fischer Titration 
ASTM D 974 Standard Test Method for Acid and Base Number by Color-Indicator 
Titration 
ASTM D 445 Standard Test Method  for Kinematic Viscosity of Transparent and Opaque 
Liquids 
ASTM D 5185 Standard Test Method  for Determination of additive elements, Wear Metals, 
and Contaminants in Used Lubricating Oils by Inductively Coupled Plasma 
Atomic Emission Spectroscopy 
ASTM D 1500 Standard Test Method for ASTM Color of Petroleum Products 
 
A newer method for detecting the quality of an oil sample is to measure the electrical 
properties of the oil to determine the extent of degradation. In this method, a sensor of some type 
is used to measure the dielectric constant or the change in the dielectric constant of the oil 
sample. Tests of this method on used oil samples have shown that as an oil sample is degraded, 
the dielectric constant of the sample will show a marked increase over a similar sample of fresh 
oil. The underlying principle behind this measurement is not fully understood as of yet but, the 
leading and most logical theory is that as the oil is degraded, it will take on a stronger dipole 
characteristic and increase the dielectric constant of the material. [7-19] 
2.1.3 Current Research 
 There is much current and recent research in the field of sensors for measuring oil 
quality. Some commercial sensors are even available at a premium price. In this section I will 
discuss some of the more relevant information that I have used as guidance for my project. 
 8 
 Research published by Turner and Austin has shown a distinct and definite correlation 
between increased use and thus degradation of an oil sample and an increase in the dielectric 
constant of used oil samples. In their research, used oil samples of a known mileage were 
collected and the viscosity and dielectric constant of each sample was taken and plotted against 
one another. The resultant plot (Figure 2.2) showed that the more the oil was used and the greater 
the degradation, the higher the measured dielectric constant was.[7] 
 
Figure 2.2 Lubricating oil viscosity vs. dielectric constant.[7] 
 Research performed by Lee, Kim and Semenov has shown some other useful information 
regarding the measurement of the dielectric properties of lubricant oils.[8] First, they showed how 
the dielectric constant of lubricant oil changes with temperature. They measured 14 types of 
fresh oil at temperatures ranging from room temperature to 100 C. The results, shown in Figure 
2.3, show that the dielectric constant change is related to the type of oil and the chemical makeup 
of it but, at temperatures less than 60 C, the dielectric constant stays in a range between 2.2 and 
 9 
2.4 depending on manufacturer. This will determine how the sensor can be implemented, if 
placed in too warm of an environment, the data collected might be misleading. 
 
Figure 2.3 Change of dielectric constants with temperature of fresh oil.[8] 
 The three researchers also developed a sensor to detect the deterioration of oil in situ. 
Their approach was to use a coil capacitive sensor that was inserted into the oil pan. Their sensor 
uses two enamel coils wound together to measure the cross capacitance of the oil. They 
compared these measurements to independent measurement of dielectric constant to determine if 
the sensor was detecting the change. Their results show the sensor capacitance at 11pF in air, 22 
pF in the fresh oil and 23.6 pF in oil that had been used for 16,000 km. The tests were done for 
different oils and different distances travelled. Figure 2.4 shows the plot of the their results, it 
shows the correlation between the measured capacitance and the independently measured 
dielectric constant of the oils.[8] Overall, their research helps to show the feasibility of using a 
capacitance sensor to measure the deterioration of engine oil. 
 10 
 
Figure 2.4 Correlation between the measured dielectric constant and the sensing capacitance.[8] 
 Additional researchers have also investigated the coil type capacitive sensor and the 
relationship between the dielectric constant of oil and its temperature.[9] Their data on dielectric 
constant and temperature correlates with that of Lee, Kim and Semenov shown in Figure 2.5. Up 
until about 55 or 60 C, the dielectric constant remains relatively stable but it increases above that 
temperature, varying with the composition of the oil. They continued on by investigating how the 
dielectric constant changed with use. The oil was run in engines on a dynamometer for up to 
20,000 km and then the dielectric constant was measured at various temperatures. This again 
shows in Figure 2.6 that the dielectric constant will increase with use and also that the 
temperature that the constant is measured at has an effect on the result. 
 11 
 
Figure 2.5 Characteristics of dielectric constant vs. temperature for engine oil.[9] 
 
Figure 2.6 Dielectric constant vs. driving distance and its variance with temperature.[9] 
 The work of Raadnui and Kleesuwan[10] also shows that the dielectric constant of oil will 
change as it is used and is degraded. Their experiment used a grid capacitor to measure the 
change in capacitance and then determine the resulting change in dielectric constant. By taking 
measurements in air as a control and then in fresh and used engine oil they showed that the 
 12 
change in the dielectric constant and thus the condition of the oil can be monitored with a 
capacitance sensor. Figure 2.7 shows their results for measured dielectric constant in air and in 
fresh and used oil at several frequencies. 
 
Figure 2.7 Measured Dielectric Constant for grid capacitance sensor in various media.[10] 
 Raadnui and Kleesuwan have also done investigations on the effects of various 
contaminants in lubricant oils and how they affect the dielectric constant. In the study, ferrous 
particles, water and silicon dioxide particles were each introduced into oil samples. Each was 
mixed in three levels of concentration and the dielectric constant of the sample was measured. 
The investigation showed that each of the three contaminants had an effect on the dielectric 
constant. In each case, as the concentration of the contaminant rose, the dielectric constant 
followed in the same way. However, with the addition of water, there was no change between the 
first and second concentration.  
 13 
 
Figure 2.8 Change in the dielectric constant with different concentrations of contaminant 
particles.[10] 
 Keller and Saba[11] also investigated the changes in dielectric constant with degradation 
of lubricant oil samples. In their tests, they used a dielectric constant meter and also measured 
the TAN of the samples. Their results again show that the increased degradation leads to an 
increase in the dielectric constant of the sample. Plots of change in dielectric constant vs. the 
TAN show that the two are correlated. 
 Another important aspect shown in their work is that the dielectric constant is not 
affected only by the degradation of the oil but also the introduction of contaminants that come 
from natural wear on the moving parts inside of machinery. Their investigation focused on ferro 
particles suspended in the oil. The results showed a dependence on the particle size, 
concentration and the amount of time that the sensor was exposed to the oil. With regard to size, 
bigger particles had the greater effect while the concentration had some, but little effect. The 
time aspect of the experiment showed that as the particles are allowed to collect onto the sensor, 
the greater the change in the dielectric constant. [11] 
 14 
 Another research group has investigated how dielectric constant and different 
contaminants are directly related using a capacitance sensor. [12] This research lays groundwork 
for determining that the dielectric constant can be used as an indicator of oil degradation. The 
researchers tested water contamination, ferrous metal contamination and change in acid number 
which seem to be the three most important factors in determining the useful remaining life of 
lubricant oils. The oils that were tested were SF20W/30(A), SF 15W/30(B), SE10W/30(C) and 
SE5W/30(D). For each of the factors tested, a mostly linear relationship exists between the 
dielectric constant and an increase in the concentration of the contaminant. Figures 2.9, 2.10 and 
2.11 show these relationships graphically for each of the four oil types A-D. Knowing that this 
correlation exists will allow for further experimentation with capacitive sensors to determine the 
quality of oil in situ. 
 
Figure 2.9 Relationship between permittivity (Dielectric Constant) and acid number.[12] 
 15 
 
Figure 2.10 Relationship between permittivity (dielectric constant) and iron content.[12] 
 
Figure 2.11 Relationship between permittivity (dielectric constant) and moisture content. [12] 
 Yang and his collaborators have also worked at testing the feasibility of using capacitive 
sensors to detect the change in the dielectric constant of oil. [13] Their focus was on how different 
contaminants affected the dielectric constant measurement. By using a cylindrical capacitive 
sensor and a series of digital signal manipulations they were able to detect small variances in the 
 16 
capacitance and thus the dielectric constant of oil samples. They contaminated 4 different oil 
samples and took measurements, one with water, two with varying amounts of ferrous particles 
and one with used engine oil. The resulting plot, Figure 2.12, of the relative change in dielectric 
constant for each contaminant shows that all of these will have an effect on the overall 
measurement and that the dielectric constant of the oil is a suitable measurement for determining 
the deterioration of an oil sample. It not only shows chemical changes but also outside pollutants 
like metal particles and water contamination. 
 
Figure 2.12 Relative dielectric constant variation of different polluted oil samples from fresh oil 
sample. [13] 
 From all the current research it is clear that a capacitive sensor of some type can be 
implemented to monitor the condition of lubricant oil in situ. The effects of the oils deterioration 
chemically and its contamination due to wear and introduction of moisture and other liquid 
contaminants have been shown to cause increases in the dielectric constant of the oil and thus 
 17 
related increases in the capacitance. The previous research has used many types of capacitance 
sensors all based on similar parallel plate concepts. What remains is trying to simplify the design 
by creating a planar interdigitated electrode to be used as a capacitance sensor and implemented 
onto a dipstick. The fabrication of such a device would be easier to accomplish and be relatively 
inexpensive when done on an industrial scale. By taking the research that has already been done 
and advancing it in this new direction, a new device can be designed and fabricated to achieve 
similar results in a new form factor using the existing established principles. 
2.1.4 Commercially Available Sensor Systems 
 Several models of vehicles currently in production have what are called oil life monitors. 
These devices are based on the engine computer measurements. The vehicle?s computer collects 
data on the number of cold starts, the time and distance travelled, the RPMs generated and 
various other factors. These measurements are then run through an algorithm that can estimate 
the remaining useful life of the oil. These devices can be useful but a sensor to measure the 
actual physical condition of the oil, and not an estimate, would be preferable. 
 One option that is currently commercially available to directly monitor the condition of 
lubricant automotive and machine oil in situ is from Delphi.[20] The Delphi oil quality sensor 
monitors electrochemical materials that are present in degraded oil. The sensor uses a triangular 
waveform to make the materials of interest interact with the sensing electrodes and create a 
current flow. The current flow is measured by the electrode and the oil quality can be 
determined. Their literature indicates that the magnitude of the current will be proportional to the 
concentration of the material that is being measured and inversely proportional to the viscosity of 
the oil. The sensor itself is installed in the oil reservoir and measures in real time. The sensor 
 18 
measures the TAN, viscosity, water content, temperature and oil level. An illustration of the 
sensor is given in Figure 2.13. 
 
Figure 2.13 Illustration of Delphi Oil Quality Sensor. [20] 
2.2 Capacitance Sensors 
 Sensors for the measurement of capacitance values are commonplace in modern devices. 
The operation is based on a simple formula and can be easily implemented in a variety of 
situations. 
 
2.2.1 General Principles 
 Capacitance sensors can vary in their type and structure. However most are based on a 
parallel plate structure that is basic and common. Parallel plate capacitors consist of two plates of 
a given area set at a distance apart from one another with a dielectric medium of some sort in 
between the two. The useful part of this relationship is that the capacitance can be calculated by 
the formula: 
 (2.1) ??? AC r0?
 19 
where C is the capacitance, ?0 is the permittivity of free space (a constant), A is the area of the 
plates, d is the spacing of the plates and ?r is the dielectric constant of the media between the two 
plates. By knowing the constant values of ?0, A and d, we can determine the dielectric constant 
of the media that is in between the plates of the capacitor. This also means that the capacitance 
and the dielectric constant of a material are related. So, as the oil in the experiment ages, the 
dielectric constant will change and the capacitance of the oil in the sensor will change as well. 
 
 
2.2.2 IDT Structure 
 For this application, an interdigitated electrode design was chosen. IDTs have been widely 
used and studied in a variety of capacities.[21-34] In this case, it will be used as a capacitive sensor. 
The IDT design consists of two sets of fingers that interpenetrate making a comb structure. This 
sets up a series of parallel plate capacitors that can be used as a sensing area. The geometry of 
the IDT plays a large role in the sensitivity of the structure. The main aspects of the design are 
the thickness of the fingers, the spacing between the fingers, the width of the electrode and the 
number of fingers that are used. Each of these factors will affect the measurements that are taken 
and the sensitivity of the sensor. The sensitivity of the sensor should increase with decreased 
finger spacing, an increased number of fingers, and increased width and finger thickness. 
 
 20 
 
Figure 2.14  Schematic diagram of an interdigitated electrode. 
 Starting with equation 2.1, it can be seen that by changing the variables that we have 
control over, namely the area, A, and the spacing, d, we can control the expected capacitance 
measurement of the sensor. In general, increasing the area of the fingers, (this can be done by 
increasing the thickness, increasing the width and increasing the number of fingers) will increase 
the capacitance value that the sensor will measure under a given condition. The capacitance 
measurement can also be increased by decreasing the spacing of the fingers. The increase in the 
value of the capacitance is beneficial to the sensor because the independent variable, namely the 
dielectric constant of the surrounding fluid, will multiply that value with its change. This means 
that as the measured capacitance value increases, the sensitivity to change will also increase. 
Figure 2.15 illustrates this. In the figure, the capacitance value vs. finger spacing is plotted for 
constant finger area. The value for the dielectric constant for air used in the calculation is 1 and 
the value for the dielectric constant for oil used is 2.1. The figure clearly shows an expected 
trend of increased capacitance values and sensor sensitivity with decreased finger spacing. 
 21 
 
Figure 2.15  Plot of Calculated Capacitance vs. Finger spacing using equation 2.1 
 
2.2.3 IDC Model 
 
 The modeling of interdigitated capacitors has been the subject of much study. An 
accurate mathematical model of the IDC would allow for a valuable comparison between the 
calculated value and the eventual measured value. The model that will be used here was 
developed by Igreja and Dias and is based on the conformal mapping technique.[22] The model is 
able to take into account a layered structure which gives it an advantage over other IDC models. 
Figure 2.16 shows the layout of the electrode and the cross section. This model assumes that we 
can consider the thickness of the substrate as infinite if the thickness is much greater than the 
spatial wavelength (?=2(W+G)). In addition, the thickness of the fingers can be ignored because 
it is much less than the width. Figure 2.17 shows the equivalent circuit used in the model. 
 
0
5E-12
1E-11
1.5E-11
2E-11
2.5E-11
3E-11
3.5E-11
0.00E+00 5.00E-06 1.00E-05 1.50E-05 2.00E-05
Cap
ac
itan
ce
 (F)
Finger Spacing (m)
Air
Oil
 22 
 
Figure 2.16 (a) Layout of electrode (b) Cross section of electrode.[22] 
 
 
Figure 2.17 Equivalent circuit for IDC model. [22] 
 
 The capacitance of an IDC (CIDC) is given by the model as  
 
                                
            
                                   (2.2) 
 
where CI,IDC is the capacitance for a pair of inside electrodes as shown in Figure 2.17 and given 
as 
 
                             
                    
    
                            
      
      
      
                       (2.3) 
 
and CE,IDC is the capacitance of an outside electrode and given as 
 
 
 
 23 
 
                             
                    
    
                            
      
      
      
                      (2.4) 
 
The terms kI,? and kE,? are given by 
 
                                                                   (2.5) 
 
and 
 
                                                                        (2.6) 
 
The k? is the complex modulus of k and is equal to the square root of (1-k2). The variable ? is the 
metallization ratio which is given by W/W+G which are shown in Figure 2.16. The values for kI 
and kE for the finite silicon dioxide layers are much more complex to calculate but take into 
account the thickness of the layer. A detailed description of how to calculate each is given in 
Igreja and Dias. In all equations ? is the dielectric constant of the material and ?0 is the 
permittivity of free space. Additionally, Table 2.2 gives the relevant equations for both the finite 
and infinite conditions.[22] 
 This model can be easily adapted for different structures and add any number of finite 
layers. It will be used as a point of comparison for the measurements that will be taken with the 
actual sensors later. 
 
 
 
 
 
 24 
Table 2.2 Equations needed for calculation of CI and CE for finite and infinite layers.[22] 
 
 
 
 
  
 25 
 
 
 
 
CHAPTER 3 
 
EXPERIMENTAL SETUP & TECHNIQUES 
 
 
 
 
3.1 Artificial Aging of Oil Samples 
 In order to properly test the function of the electrodes, testing must be done on oils that 
have undergone various amounts of use. This should allow for the observation of how the oil 
changes with its degradation and what we should look for to tell if the oil is past its useable 
lubricant level. Instead of placing the lubricants into a functioning engine and allowing them to 
age naturally, it would be of use to be able to artificially age them in a controlled setting. To do 
this, the oil is heated beyond its normal use temperature and oxygen is bubbled through it at this 
elevated temperature. This allows for faster aging times for a greater quantity and for more 
control over the condition of the oil.[1-5] 
 With this in mind, an oil degradation chamber was constructed to artificially age the oil in 
a controlled environment. The chamber consists of a stainless steel vessel to contain the oil and a 
band heater to increase the temperature to a controlled point. Dry oxygen was also introduced 
into the chamber to allow the oil to oxidize as it would in an engine under normal use. A device 
to stir and agitate the oil was added to insure that the oil was evenly aged. A valve at the bottom 
of the container allowed for easy removal of samples without having to shut down the device. 
Samples of the oil were taken at various time intervals for different aging temperatures usually 
after 24, 48 and 72 hours. This provides a series of oils at different levels of degradation to test. 
The oil samples that were used for this experiment were manufactured by British Petroleum 
 26 
(BP). BP 2380 turbo engine oil was used for test runs. The oil was aged at 200 C for periods of 
24, 48 and 72 hours. Data for the fresh oil used is given in Table 3.1. [35] 
Table 3.1 Data for BP turbo oil 2380 
BP Turbo Oil 2380 Test Method Result 
Density @ 15?C, Kg/l ASTM D1298 0.9749 
Kinematic Viscosity, cSt, mm2/sec 
@ 100?C 
@ 40?C 
@ -40?C 
 
ASTM D445 
ASTM D445 
ASTM D-2532 
 
4.97 
24.2 
7950 
Total Acid N?, mgKOH/g SAE-ARP5088 0.43 
Pour Point, ?C ASTM D97 -57 
Flash Point, ?C ASTM D92 265 
Evaporative Loss, % (6.5h, 204?C) ASTM D972 3.0 
 
 
 
 27 
 
Figure 3.1. Schematic diagram of the oil degradation vessel. 
 
Figure 3.2. Photo of the oil degradation vessel. 
 
 
 28 
3.2 Fabrication 
 The fabrication of the IDT electrodes used for the experiment was performed using 
standard photolithography techniques to form the patterns and sputter deposition to deposit the 
metal electrodes. Photomasks from Covalent Coated Products and Photo Sciences Inc. were used 
in the lithography process with an nLOF 2035 photoresist. Two substrates were used for the 
electrodes, SiO2 and Al2O3. The SiO2 for the substrates was thermally grown on silicon wafers 
and had a nominal thickness of 500 nm. The Al2O3 substrates were deposited via sputter onto 
silicon wafers and had a nominal thickness of 500 nm as well. 
 29 
 
Figure 3.3 Schematic of Fabrication Process. [36] 
 The metallic electrodes were deposited via a DC magnetron sputter system made by 
Denton Vacuum Inc. The processing is carried out under a high vacuum and high purity argon 
gas is used as the atmosphere in the chamber. For the SiO2 substrates, an adhesion layer of either 
titanium or chromium is deposited first with a thickness of 10 nm. This is followed by the 
deposition of gold with a thickness of 100 nm. For the Al2O3 substrates, titanium and chromium 
 30 
did not have the proper adhesion and aluminum was used instead, again with a thickness of 10 
nm. In all instances, pre-sputtering was used to clean the target and to stabilize the power to the 
cathode. All sputter targets are 3 inch diameter. The sputter conditions for the various deposition 
processes are given in Table 3.2.[37-43] 
Table 3.2 Sputter Conditions for Metal Depositions. 
Material Pre-Sputter 
Power (W) 
Pre-Sputter 
Time (Sec) 
Sputter 
Power 
(W) 
Sputter 
Time 
(Sec) 
Ar Flow 
Rate 
(SCCM) 
Deposition 
Pressure 
(mTorr) 
Temp 
(C) 
Ignition 
Pressure 
(mTorr) 
Gold 100 180 100 180 25 5.0 25 50 
Aluminum 200 30 200 30 25 5.0 25 50 
Titanium 200 30 200 30 25 5.0 25 50 
Chromium 300 30 300 10 25 5.0 25 50 
 
 After deposition of the metallic electrodes, the excess metal and photoresist was lifted off 
in acetone. The wafer was then diced into individual electrodes for testing using a diamond 
tipped pen to split the silicon wafers. 
 
3.3 Measurements 
 The electrodes that were fabricated for this project are designed to measure the electrical 
properties of the fluid sample that the electrode is immersed in. In this case, oil is the fluid of 
interest. For testing, an HP 4192A LF impedance analyzer was used. The instrument can 
measure a number of variables against a sweep in AC or DC voltage as well as frequency. For 
this particular experiment, different electrical properties are measured vs. a sweep in the 
frequency. The electrical properties of major interest are the capacitance, the dielectric loss and 
the impedance. 
 The procedure that was used throughout the testing was to first measure the variable that 
was being tested for the electrode in air. After the air sample was collected, the electrode was 
 31 
placed in a sample of fresh oil. For this experiment, BP 2380 Turbo engine oil was used. After a 
fresh oil measurement, the electrode was rinsed in methanol to clean it and then placed in oil that 
had been artificially aged and another measurement was taken. This was repeated for three 
different levels of aging and then once more in an oil sample that was aged regularly in a turbo 
engine. 
  
 32 
 
 
 
CHAPTER 4 
RESULTS & DISCUSSION 
 
 The objective for this research is to develop and optimize an IDT sensor electrode to 
achieve the highest sensitivity to a change in capacitance. The sensitivity of this measurement is 
important because in future studies it will allow for more accurate determination of the amount 
of degradation in the oil sample. To reach this goal, it must be determined what factors 
contribute to the sensitivity and how they can be changed to fit the goals and constraints of this 
project. 
 From the study of literature, it has been shown that an interdigitated electrode can be used 
to successfully measure the capacitance value of a dielectric media. It is also known that the 
sensitivity of the electrode changes with its design.[21-34] The geometry of the electrode will 
affect its sensitivity so by changing the design parameters of the electrode, an optimum design 
should be able to be produced. 
 We can treat the basic interdigitated electrode like a parallel plate capacitor and use the 
equation for capacitance to predict how it will behave as the design is changed. This will give a 
starting point for our design and allow for the prediction of expected trends with design change. 
From the equation, we see that the two variables that can be changed with the design are the area, 
A and the spacing of the plates, d. The spacing will correspond to the spacing between the 
 33 
fingers in the electrode and the area will correspond to a combination of the electrode?s width, 
finger thickness and number of fingers. 
 From this, we now have four design parameters that can be easily changed. It is now left 
to determine what effect each parameter has and how important it will be to the sensitivity of the 
electrode when tested. To optimize the sensor, each will be tested to determine how it affects the 
capacitance sensitivity and which are most important to the design. From here, various stages of 
the testing process are presented.  
4.1 Capacitance Measurements 
4.1.1 Effect of IDT Geometry 
 The original electrode design was a rough starting point to test some of the information 
gathered from the literature and try and determine some trends in the design. The design 
parameters are given in Table 4.1. These electrodes are large and have finger spacing?s ranging 
from 40 to 100 microns. Using these electrodes, capacitance vs. frequency curves were 
generated, see figures 4.1 ? 4.4 below. The values that were obtained are very low and may be 
inaccurate, especially when comparing them to the curves generated by taking the same 
measurement with the later electrode designs. The measurements for the first set of electrodes 
are less than a picofarad at most points and the separation between them is even smaller. 
 
Table 4.1  Design parameters for Original IDT electrodes 
Sample 
Identification 
Space between 
electrode (?m) 
Width (?m) Length (mm) # of fingers 
(Total) 
40S 40 40 5 30 (60) 
60S 60 60 7.5 30 (60) 
80S 80 80 10 30 (60) 
100S 100 100 12.5 30 (60) 
 
 34 
 
Figure 4.1  Capacitance vs. Frequency curve for 40s electrode. 
 
 
 
Figure 4.2   Capacitance vs. Frequency curve for 60s electrode. 
0.00E+00
1.00E-14
2.00E-14
3.00E-14
4.00E-14
5.00E-14
6.00E-14
7.00E-14
8.00E-14
9.00E-14
1.00E+04 1.00E+05 1.00E+06
Capacitan
ce
Frequency
40s C-F
Air
Fresh 
Oil
0.00E+00
2.00E-14
4.00E-14
6.00E-14
8.00E-14
1.00E-13
1.20E-13
1.40E-13
1.00E+04 1.00E+05 1.00E+06
Capacitan
ce
Frequency
60s C-F
Air
Fresh 
Oil
 35 
 
Figure 4.3   Capacitance vs. Frequency curve for 80s electrode. 
 Figure 4.4   Capacitance vs. Frequency curve for 100s electrode. 
 
 
 After the initial testing with the original electrode design, a new design was planned. For 
this design, it was decided to create the electrodes and vary the four test parameters to determine 
how changing them would affect the sensitivity and if the trend generated by the sensors would 
match the expected trend. The design table, Table 4.2, shows the four parameters that are 
considered. It was decided to vary the thickness of the fingers, the spacing of the fingers, the 
0.00E+00
2.00E-14
4.00E-14
6.00E-14
8.00E-14
1.00E-13
1.20E-13
1.40E-13
1.00E+04 1.00E+05 1.00E+06
Capcit
ance
Frequency
80s C-F
Air
Fresh 
Oil
0.00E+00
2.00E-14
4.00E-14
6.00E-14
8.00E-14
1.00E-13
1.20E-13
1.00E+04 1.00E+05 1.00E+06
Capacitan
ce
 (F
)
Frequency (Hz)
Capacitance vs. Frequency 100s Electrode
Air
Fresh 
Oil
 36 
number of fingers and the width of the electrode. By testing these parameters it could be 
determined how each affects the sensitivity of the sensor. 
Table 4.2  Design parameters for the second set of IDT electrodes. 
Finger 
Thickness(um) 
Finger 
Spacing (um) 
IDT 
Width 
(mm) 
Number of 
Fingers 
ID 
40 100 4.25 60 T4S10F6 
40 80 4.25 60 T4S8F6 
40 60 4.25 60 T4S6F6 
40 40 4.25 60 T4S4F6 
40 20 4.25 60 T4S2F6 
40 80 8.5 60 T4S8F6L 
40 60 8.5 60 T4S6F6L 
40 40 8.5 60 T4S4F6L 
40 80 4.25 30 T4S8F3 
40 60 4.25 30 T4S6F3 
40 40 4.25 30 T4S4F3 
40 80 4.25 90 T4S8F9 
40 60 4.25 90 T4S6F9 
40 40 4.25 90 T4S4F9 
80 80 4.25 60 T8S8F6 
80 60 4.25 60 T8S6F6 
80 40 4.25 60 T8S4F6 
 
The following section shows some capacitance vs. frequency curves for these electrodes. 
In general, they all show the same basic trend. The figures show the series of IDTs with a 
constant finger width of 40 microns and a spacing of 60 microns. The variation is first, in the 
number of fingers and then in the length of the fingers. With increasing number of fingers, the 
capacitance that is measured becomes greater as it also does with the increase in the length. 
 
 37 
 Figure 4.5  Capacitance vs. Frequency curve for T4S6F3 electrode. 
 Figure 4.6   Capacitance vs. Frequency curve for T4S6F6 electrode. 
 38 
 Figure 4.7  Capacitance vs. Frequency curve for T4S6F9 electrode. 
 Figure 4.8 Capacitance vs. Frequency curve for T4S6F6L electrode. 
 39 
 
 From this and the other similar series, it can be shown that some relevant trends are 
present in the data. By taking the difference between the capacitance value measured in air and 
the capacitance value measured in fresh oil, the parameter delta C can be used to determine the 
sensitivity of the sensors and what kind of trend the sensors follow.  First, the trend with finger 
spacing can be shown in Figure 4.9 to have a strong relationship with the sensitivity, as expected. 
As the finger spacing decreases, the amount of change in the capacitance increases. 
 Figure 4.9  Change in capacitance vs. finger spacing. 
 
 Figures 4.10 and 4.11 show the trends with change in number of fingers and change in 
electrode width respectively. Figure 4.10 shows that the sensitivity is maximum at a 60 finger 
electrode design. This does not agree with what is expected from the literature and the model. 
The sensitivity should be increased with the number of fingers due to an increase in the overall 
 40 
area of the electrode that comes with additional fingers. Figure 4.11 shows the increase in 
sensitivity with increase in electrode width as expected. 
 
Figure 4.10  Plot of number of fingers vs. the change in capacitance. 
 Figure 4.11  Plot of change in capacitance vs. the electrode width. 
 41 
 
Figure 4.12  Finger thickness vs. Change in capacitance. 
 
 Figure 4.12 also shows a useful trend in the data. It shows that as the thickness of the 
fingers is increased, the sensitivity is increased as well. This is again as expected; the increase in 
the thickness of the fingers will yield a greater area in the capacitor and thus a greater 
capacitance measurement and more sensitivity for detection. 
 In Figures 4.9 through 4.12, the values gained from studying the model are shown in 
addition to the measured values that were discussed. In all cases, the measured change is greater 
than that predicted by the model. The possible causes and factors that may contribute to this will 
be discussed in more detail later. Important to note is that the model and measured values do 
show the same trends in all but the case for number of fingers. 
 After analyzing the trends that were observed by testing this series of electrodes, a third 
and final series was designed and fabricated. The dimensions of these electrodes are given in 
 42 
Table 4.3. For this set, the finger spacings were minimized to try and achieve maximum 
sensitivity, with sizes ranging from 15 microns to as small as 3 microns. 
 
Table 4.3  Design parameters for the final IDT electrode design. 
Finger 
Thickness(um) 
Finger 
Spacing (um) 
IDT 
Width 
(mm) 
Number of 
Fingers 
ID 
20 15 4.25 60 T2S15F6 
20 10 4.25 60 T2S10F6 
20 5 4.25 60 T2S5F6 
20 3 4.25 60 T2S3F6 
20 10 8.5 60 T2S10F6L 
40 15 4.25 60 T4S15F6 
40 10 4.25 60 T4S10F6 
40 5 4.25 60 T4S5F6 
40 3 4.25 60 T4S3F6 
40 10 8.5 60 T4S10F6L 
 
 From the previous data and the information collected in the literature review, it should be 
clear that the design of the new sensors should provide an increased resolution and ability to 
detect the changes in the capacitance of the oil samples. The same types of tests were run with 
the new sensors as for the previous sets. Capacitance vs. Frequency curves for these are shown in 
Figures 4.13-4.17. Also included is the plots are the values predicted by the model. A large 
discrepancy between the measured and calculated value is seen in all cases. To determine the 
problem, different methods of attaching the sensors to the impedance analyzer were tried first. 
This yielded the same results as previous. Next, a new impedance analyzer was used, and again 
the same measurements were gathered leading me to believe that the measurements are accurate 
and that something must be causing the discrepancy between the measurements and the model. 
 43 
 
Figure 4.13 Capacitance vs. Frequency curve for T2S5F6 Electrode. 
 
 44 
 
Figure 4.14 Frequency vs. Capacitance curve for T2S10F6 Electrode. 
 45 
 
Figure 4.15 Capacitance vs. Frequency curve for T4S5F6 electrode. 
 
 46 
 
Figure 4.16 Capacitance vs. Frequency curve for T4S10F6 electrode. 
 47 
 
Figure 4.17 Capacitance vs. Frequency curve for T4S10F6L electrode. 
The gap between the measured values and the calculated values from the model are much 
too large to be ignored. As previously discussed, the measurements have been taken with a 
variety of methods and using separate impedance analyzers so it seems that the equipment is not 
a major cause of the problem. 
The first possible cause that was investigated was to recalculate the model values without 
assuming that the silicon layer was infinite. Originally the capacitance values were calculated 
using this assumption and it was thought that changing to a finite layer would both better show a 
correct prediction of the value and decrease the gap between the measured and modeled values. 
For this, the model equation 2.3 was modified and became 
 
 48 
 
                             
                    
    
                            
      
      
        
                  (4.1) 
and the value for kI,Si and k?I,Si were calculated using the equations from Table 2.2. The new 
model takes into account the finite thickness and no longer assumes an infinite substrate as 
before.[22] 
The result was that there was an increase in the value of the model capacitance but the 
increase was quite small, at around 5%. This could be a factor but is most likely not the main 
thing affecting the measurements. Related to this is the actual dielectric constant of the silicon 
being used. In the model, the assumption was that bare silicon with a silicon dioxide layer was 
used. However, the wafers used were actually doped. This change could lead to an increased 
dielectric constant in the silicon and a higher value for the model as well. 
 Another possible factor that was explored was that the adhesion layer might be causing 
an increase in the measured capacitance values. The adhesion layer that is present between the 
silicon dioxide and the gold metallization layer may have oxidized and be causing an increase in 
the measured capacitance value that is not considered in the original model. To take this into 
account, Equation 4.1 was further modified to include the additional layer. The new equation is 
given as 
                                             
                    
    
                                        
        
          
         ,  02   ,  02,+      ,     ,  ?                               (4.2) 
 49 
which now takes the addition of the adhesion layer into account.[22] The dielectric constants of 
titanium and chromium oxides are very high and could easily cause a large increase in the 
measured capacitance if they are present. When the model was adjusted to include an oxidized 
adhesion layer, the capacitance values of the model increased by up to 5 times the original value. 
This large increase due to a very thin layer leads me to believe that this is the major cause of the 
gap between the calculated values of the model and the actual measured values. 
 Figure 4.18 Below shows a comparison of the different models to each other and the 
expected value. There is still quite a large gap, but the oxidation of the adhesion layer and taking 
into consideration that the silicon layer is finite explains what should be causing a large part of 
the gap. 
 
Figure 4.18. Comparison between measured value and the various models used. 
The trends in the data for the final electrode design again show what is expected, that a 
decrease in the spacing between the electrode fingers and an increase in the electrode?s sensing 
area are preferable. Plots of the change in capacitance vs. the various parameters are shown in 
Figures 4.19 ? 4.21. 
0.00E+00
1.00E-10
2.00E-10
3.00E-10
4.00E-10
5.00E-10
6.00E-10
7.00E-10
8.00E-10
9.00E-10
1.00E-09
T4S5F6
Cap
citan
ce
 (F)
Axis Title
Measured
Original Model
Finite Si Model
Adhesion Layer Model
 50 
 
Figure 4.19 Change in capacitance vs. Finger Width. 
 
Figure 4.20 Change in capacitance vs. Finger spacing. 
 51 
 
Figure 4.21 Change in Capacitance vs. Electrode Width. 
 From observing the trends in the data it is clear that by increasing the sensing area and 
decreasing the spacing between the electrode fingers, the greatest resolution will be possible. 
This is also shown in the data that is shown in Figures 4.19-4.21.  In these plots, the difference is 
again seen between the modeled values and the measured values like before. This should again 
be caused mainly by the adhesion layer oxidation and the assumption of the substrate layer to be 
infinite. The T4S10F6L electrode preformed the best when comparing oil to fresh air. It had a 
difference of 11.8 pF between the two. However, it would be beneficial to determine how much 
influence each parameter has on the sensitivity measurement and how best to design the 
electrodes to increase sensitivity. Table 4.4 shows a summary of how each of the factors affects 
the measurement. 
 
 
 
 52 
Table 4.4. Effect of design factors on capacitance measurements. 
Parameter  Parameter 
Value 1 (?m) 
Delta C 
1 (pF)  
Parameter 
Value 2 (?m) 
Delta C 2 
(pF)  
% Change  Expected % 
Change  
Finger Spacing  10  5.59 5  6.46  15.5%  26.1%  
Finger Thickness  20 6.46  40  9.51 47.3%  23.3%  
Electrode Width  4,250  5.59  8,500  11.8 111%  100%  
 
 First, if the finger spacing is considered, in both sets of electrodes a strong trend is shown 
toward an increased resolution with decreased spacing, which is to be expected. It can also be 
seen that the change in sensitivity that is caused by changing the spacing depends very much on 
size. For example, the change from a 100 micron gap to a 20 micron gap results in only a about a 
13% change in resolution while the change from 10 microns to 5 microns results in almost a 19% 
increase in resolution. As the spacing becomes smaller, a small change has a much greater effect 
on the resolution. 
 Next, if the finger thickness is considered, the trend that is shown is that an increase in 
the thickness will result in improved resolution, which again is what was expected. For this 
parameter, the effect seems to not be influenced as much by the absolute size of the electrode. 
For example, when the thickness of the fingers is doubled from 20 microns to 40 microns, the 
increase in sensitivity is about 45% and when the thickness is increased from 40 microns to 80 
microns the sensitivity increase is about 25%. So, there is still dependence on size but not as 
much as with the finger spacing. 
 53 
 Finger spacing and finger thickness each have a measureable effect on the capacitance 
but are not independent of one another. They are more correctly described by the metallization 
ratio, ?. The metallization ratio is equivalent to the thickness divided by the combined value of 
the thickness and the spacing. It is a measurement of the amount of area covered by the 
electrode. The capacitance value will increase with an increase in the metallization ratio. 
 The next parameter to consider is the sensor width. By increasing the width of the sensor, 
the area is increased and the sensitivity will go up. This has been shown in both the literature and 
in the experimental process. The effect of the electrode width has a very strong influence on the 
sensitivity. From the experimental data, at every electrode size, when the width was doubled 
from 4.25 mm to 8.50 mm the sensitivity value increased by at least 111%. This seems to be the 
most effective way to greatly increase sensitivity in the easiest way. 
 The final parameter, the number of fingers, is also important to consider. It should be that 
the sensitivity increases with the number of fingers due to the increased area of the electrode. 
However, it shows that there is a maximum in sensitivity at 60 fingers which is unexpected 
although the raw capacitance measurements do continue to increase with number of fingers as is 
expected. This maximum in the sensitivity value lets us know that when designing an electrode 
that we can increase the value to a maximum number of 60 fingers. 
 Looking at the data, it seems that the value for the 2nd and 3rd set of electrodes are about 
the same, but upon further comparison there is an improvement in performance per unit area 
between the two sets. Tables 4.5 and 4.6 show the change in capacitance per unit area for each of 
the sets. 
 
 
 54 
Table 4.5. Capacitance per unit area for the 2nd electrode series. 
Electrode ID  Delta C (pF)  Sensor Area (mm2)  ?C/Unit Area 
(pF/mm2)  
T4S2F6  7.95 15.3 0.52 
T4S6F6  7.76 25.5 0.30 
T8S6F6  9.40 35.7 0.26 
T4S6F6L  12.46 51.0 0.24 
 
Table 4.6. Capacitance per unit area for the 3rd electrode series. 
Electrode ID Delta C (pF) Sensor Area (mm2) ?C/Unit Area 
(pF/mm2) 
T2S5F6 6.46 6.38 1.01 
T4S5F6 9.51 11.48 0.83 
T2S10F6 5.59 7.65 0.73 
T2S10F6L 11.81 15.30 0.77 
 
 By taking into account the change in capacitance compared to the size and area of the 
sensor, the final set of electrodes has a higher change in capacitance per unit area. It shows that 
with better design, a smaller electrode can be as effective at detecting the change in capacitance 
as a larger electrode. It also allows for determining how small of a sensor that we may be able to 
make and still be able to detect a given threshold in capacitance change. 
 
 
 
 55 
4.1.2  Effect of Substrate Material 
 So far, all of the models that have been used have not taken into account that the electric 
field applied to the sensor not only penetrates into the oil or air, but also into the substrate when 
the tests are being run. To make an effort to determine how the substrate material effects the 
measurements and the sensitivity of the device, the same electrodes were patterned onto an 
alumina substrate as well and similar measurements were made. In this section, the effect that the 
substrate has on the sensitivity will be investigated and discussed and how the dielectric constant 
of the substrate might affect the outcome of the results. 
 Measurements were taken with the same electrodes patterned on alumina substrates 
instead of silicon dioxide. The results showed that in most cases the sensitivity was increased 
when using the alumina substrates. However, the increase in the measured value did not have a 
common trend. In some cases the increase was as little as about 5% while some cases resulted in 
increases in sensitivity of up to 25%. In general though it can be seen that the substrate material 
does have some effect on the measurements and further study may be helpful in determining 
what the exact relationship is. 
 
4.2 Optimization of Sensor 
 From what has been learned from the literature and from experiments, some rules about 
how to optimize this type of sensor have become apparent. First, a minimum spacing between 
the fingers of the interdigitated electrode is critical. It has been shown that the capacitance values 
measured and the sensitivity of the sensor is inversely proportional to the spacing. Second, the 
area of the sensor should be maximized. The overall width of the electrode and the thickness of 
 56 
the fingers themselves will both come into play here. By making each large, the overall area of 
the sensor will be increased and thus increase the measurements taken and the sensitivity. 
 Further analysis of the data shows some other important information for optimization of 
the sensor. Each of the parameters will affect the sensitivity in varying amounts and will 
ultimately vary in the importance of design. From the data collected, the most important factor in 
increasing sensitivity is to increase the electrode width. By increasing the width of the electrode, 
the area is greatly increased and will lead to the largest increase in sensitivity of all the 
parameters. The next most important parameter to consider is the metallization ratio which takes 
into account both the finger thickness and finger spacing. As the metallization ratio is increased 
an increase in the capacitance will also be seen. The metallization ratio can be increased by 
either increasing finger thickness or decreasing finger spacing.  Finally, the number of fingers is 
also important, however from the data it can be seen that a maximum sensitivity seems to be 
reached at 60 fingers so it leaves little to decide upon in a design. The fifth factor, substrate type, 
showed mixed results. However, the use of alumina most definitely had an effect on the 
measurements and generally caused the sensitivity to increase. Finding a better substrate may 
also prove useful once a suitable geometric design is established. 
 
  
 57 
 
 
 
CHAPTER 5 
CONCLUSIONS AND FUTURE STUDIES 
 
 An interdigitated electrode sensor was studied and optimized to be used as a sensor for 
detecting the dielectric properties of lubricant oils. The various design parameters were tested 
and the trends garnered from those experiments allowed for the optimization of capacitance 
measurements to be used as a basis for determining the quality of the oil. It was shown that by 
minimizing the spacing between the fingers of the interdigitated electrode and increasing the 
electrode area that greater resolution could be achieved. Furthermore, it was shown that the 
metallization ratio which includes both finger thickness and spacing was a major factor affecting 
the sensitivity. The number of fingers used in the electrode showed maximum sensitivity at 60 
fingers. The effect of substrate material was also studied. The results showed that there was a 
noticeable effect but it was not constant. 
 A gap between the expected values that were generated using the mathematical IDC 
model of Igreja and Dias, and the measured value was observed. Several reasons for the gap and 
additions to the model were discussed. A large part of the gap seems to be due to the oxidation of 
the adhesion layer used to get the gold electrodes to adhere to the silicon dioxide substrate. The 
model did not take this into account originally and when it was added showed a definite increase 
in the model value for capacitance. 
 58 
 Future studies in this area should include the testing of several additional components to 
the degradation of oil. It has been shown that the inclusion of wear particles and moisture content 
will also affect the electrical properties of the oil as it degrades. The sensor should also be used 
to test how these variables affect the measurements taken by the sensor. The temperature of the 
sample should also be taken into consideration. Again, literature shows that the dielectric 
constant of oil is sensitive to temperature increase above 55 C. The sensor should be tested to see 
how the temperature affects its readings and where in the oil reservoir it can be successfully 
implemented. Finally, a threshold for when oil becomes unusable should be established and how 
the sensor responds at that point of degradation should be determined. 
  
 59 
 
 
 
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