HIGH TEMPERATURE RESISTANCE MEASUREMENT SYSTEM FOR SOLID OXIDE FUEL CELL CIRCUIT PASTES By Aishwarya Vidyachandra Bhatlawande A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Electrical Engineering - Master of Science 20 20 A BSTRACT HIGH TEMPERATURE RESISTANCE MEASUREMENT SYSTEM FOR SOLID OXIDE FUEL CELL CIRCUIT PASTES By Aishwarya Vidyachandra Bhatlawande Solid oxide fuel cells (SOFCs) are one of the most promising energy conversion technologies which convert chemical energy directly to electric al energy. SOFCs have high efficiency, high fuel flexibility, low fabrication cost and high potential for co - generation . Although the solid oxide fuel cells have high efficiency, they operate on a low open circuit voltage. Several individual cells are connected in series in order to achieve the required voltage level. These cells are linked together using an appropriate metallic interconnect. However, the weak contact/adhesion as well as the oxid e formation between the metal cera mic interface can affect the overall performance. T o alleviate this, a current collecting layer that reduces the overall electrical contact resistance and exhibits good stability is needed. S ilver nickel circuit pastes are expected to be den se, mechanically strong and have higher conductivity than other high temperature alloys, or conductive ceramics . High performance silver pastes should exhibit properties such as good printability, high efficiency, reliability, durability and long - life even after exposure to high temperatures. The performance of the silver paste has a profound effect on the efficiency and the performance to cost ratio of SOFCs. The objective of this work is to build a measurement system for electrical characterization (shee t resistivity and contact resistivity) of silver nickel circuit pastes and compare the performance with commercially available silver pastes (Heraeus and DAD87) iii ACKNOWLEDGEMENT S I would like to express my deepest appreciation to my advisor Dr. Tim Hogan for giving me the opportunity to work on this project. Without his help and guidance, this thesis would not have been possible. He taught me a great deal throughout the course of this research which extends beyond t he scope of this project. I would also like to thank my committee members - Dr. Jason Nicholas and Dr. Timothy Grotjohn for their invaluable suggestions and expertise. I would like to express my sincere gratitude to members of DOE circuit paste team. It has been a pleasure working alongside and getting to know you all. I had the opportunity to learn so much from each team meeting that we had. Thanks to Genzhi Hu for his patience and extreme sincerity in preparing the samples and performing the SEM . I wou ld like to acknowledge the help extended by Brian Wright and Nina Baule for their assistance in profilometer measurements. A big thank you to my parents and sister for never ever giving up on me, especially on days where I failed to believe in myself. I feel extremely lucky to have your unwavering and unconditional support by my side. To my extended family - Bansari Chauhan, Aishwarya Paraspatki , Iravati Ambike , Shardool Mehta, Anish Natu , Omkar Thatte , Harish Chakravarty, and Snehal Borana, I have no r ight words to express my gratitude. All I would like to say is each one of you has contributed in bringing me to a place in life that I might not have otherwise found. iv TABLE OF CONTENT LIST OF TABLES ................................ ................................ ................................ ......................... vi LIST OF FIGURES ................................ ................................ ................................ ...................... vii KEY TO SYMBOLS AND ABBREVIATIONS ................................ ................................ .......... ix CHAPTER 1 ................................ ................................ ................................ ................................ ... 1 INTRODUCTION, BACKGROUND, AND MOTIVATION ................................ ....................... 1 1.1 Rationale and Research objective ................................ ................................ ......................... 1 1.2 Choice of substrate and silver inks ................................ ................................ ........................ 6 1.3 Evaluation of electrical performance of circuit pastes on SOFC substrates ......................... 9 1.4 Thesis Content ................................ ................................ ................................ ..................... 12 CHAPTER 2 ................................ ................................ ................................ ................................ . 14 EXPERIMENTAL PROCEDURES ................................ ................................ ............................. 14 2.1 Sa mple Preparation ................................ ................................ ................................ ............. 14 2.2 Measurement of sheet resistivity ................................ ................................ ......................... 18 2.2.1 Apparatus and system design ................................ ................................ ....................... 19 2.2.2 Temperature stabilization ................................ ................................ ............................. 21 2.2.3 Process and Methodology ................................ ................................ ............................. 25 2.2.4 Calculations ................................ ................................ ................................ .................. 26 2.2.5 Profilometer for thickness measurement ................................ ................................ ...... 28 2.3 Measurement of contact resistivity ................................ ................................ ..................... 31 2.3.1 Apparatus and System Design ................................ ................................ ...................... 31 2.3.2 Process and Method ology ................................ ................................ ............................. 32 2.3.3 Calculations ................................ ................................ ................................ .................. 33 2.3.4 Measurement of gap - spacing ................................ ................................ ........................ 35 2.3.5 Measurement of contact resistivity at room temperature using four probes ................ 37 2.3.6 Preparation of reference sample ................................ ................................ ................... 38 CHAPTER 3 ................................ ................................ ................................ ................................ . 40 RESULTS AND DISCUSSION ................................ ................................ ................................ ... 40 3.1 Sheet resistivity results ................................ ................................ ................................ ........ 40 3.1.1 Sheet resistivity of Heraeus paste screen printed on alumina ................................ ...... 40 3.1.2 Sheet resistivity of DAD87 paste screen printed on alumina ................................ ....... 42 3.1.3 Sheet resistivity of silver nickel paste screen printed on alumina ................................ 43 v 3.1 .4 Summary of sheet resistance samples ................................ ................................ .......... 44 3.2 Contact resistivity results ................................ ................................ ................................ .... 46 3.2.1 DAD87 screen printed on LSM ................................ ................................ .................... 46 3.2.2 Heraeus screen printed on LSM ................................ ................................ ................... 47 3.2.3 Silver nickel screen printed on LSM ................................ ................................ ............ 48 3.2.4 Contact resistivity (Heraeus, DAD87, silver nickel screen printed on LSM) ............ 50 3.3 Resistivity of reference sample ................................ ................................ ........................... 52 3.4 Probable errors in the measuring instr ument ................................ ................................ ....... 59 3.5 Tensile test results ................................ ................................ ................................ ............... 66 CHAPTER 4 ................................ ................................ ................................ ................................ . 67 CONCLUSIONS AND FUTURE SCOPE ................................ ................................ ................... 67 BIBLIOGRAPHY ................................ ................................ ................................ ......................... 70 vi LIST OF TABLES Table 1. 1 Important characteristics of DAD87 7 Table 1. 2 Important characteristics of Heraeus C8710 8 Table 2. 1 Calculation of PID gain values using the ultimate gain and ultimate period [ 4 4 . ..2 5 Table 2. 2 Readings for gap spacing on J - Image (Heraeus sample 2, gap spacing 1) 36 vii LIST OF FIG URES Figure 1. 1 Basic operation of SOFC operating on H2 fuel [1 0 2 Figure 2.1 Basic screen - printing process [3 8 ] 1 5 Figure 2.2 Pattern for test sample for measurement of sheet resistivit y ... 1 7 Figure 2.3 Pattern for test sample for measurement of contact resistivity 7 Figure 2.4 van der Pauw resistivity measurement configurations [3 6 ] 1 8 Figure 2.5 Switching diagram for Keithley 7002 switch syst 2 0 Figure 2.6 Resistivity measurement set - up 2 1 Figure 2.7 Response of a PID controller [ 41 ] 2 2 Figure 2.8 Basic block diagram of PID control [ 42 ] 2 3 Figure 2.9 Ultimate period (Pu) at which oscillations reach a constant amplitude [ 4 4 ] 2 5 Figure 2.10 LabVIEW front panel view for sheet resistivity measurement 2 6 Figure 2.11 Factor f (geometric factor) versus Q (resistance ratio) [ 31 ] 2 7 Figure 2.12 Profilometer measurement set - up to determine thickness of sample 2 8 Figure 2.13 Circuit paste thickness versus posi tion . ( Average thickness 36.34 m ) . .. . 3 0 Figure 2.14 Representation of traces of 3 horizontal scans (H) and 3 vertical scans (V) 3 0 Figure 2.15 4 - wire configuration used for contact resistivity measurement 3 2 Figure 2.16 LabVIEW front panel view for contact resistivity measurement 3 3 Figure 2.17 One of the IV Sweep for Heraeus sample 3 4 Figure 2.18 Resistance versus gap spacing for Heraeus sample at room temperature 3 4 Figure 2.19 Image of Heraeus Sample 3, Cont act 2 with 2.5X magnification 3 5 Figure 2.20 Signatone probing station & S - 725 micropositioner 3 7 Figure 2.21 Kurt J. Lesker AXXIS system used for sputter deposition . 39 viii Figure 3. 1 Sheet resistivity versus temperature for Heraeus sample 4 1 Figure 3.2 Sheet resistivity versus temperature for DAD87 sample 4 2 Figure 3.3 Sheet resistivity versus temperature for silver nickel sample 4 3 Figure 3.4 Sheet resistivity versus temperat ure for all samples 4 4 Figure 3.5 Sheet resistivity versus temperature for annealed samples 4 5 Figure 3.6 Resistance of contact 1, 2, 5 of DAD87 sample 47 Figure 3.7 Resistance of contact 1,3,4,5 of Heraeus sample 48 Figure 3.8 Resistance of silver nickel sample measured over the 4 cooling cycles 49 Figure 3.9 Contact resistivity versus temperature of all samples 5 0 Figure 3.10 SEM for reference sample (alumina substrate, deposition time 40 minutes) 5 3 Figure 3.11 SEM for reference sample (alumina substrate, deposition time 10 minutes) 5 3 Figure 3.12 The thickness of the sample (sapphire substate) 5 5 Figure 3.13 Resistivity vs temperature for reference s ample (annealed) ) . Bulk platinum: S. V - Platin. Met. Rev , vol. 48, no. 2, 2004 . . 5 6 Figure 3.14 Variation of resistivity vs temperature for various density values 5 7 Figure 3.15 Sheet resistivity vs temperature along with predicted error bars (errors< 5%) 59 ix KEY TO SYMBOLS AND ABBREVIATION S EESI Environmental and Energy Study Institute SOFC Solid oxide fuel cells LPG Liquid petroleum gas PEM Polymer electrolyte membrane PAFCs Phosphoric acid fuel cells MCFCs Molten carbonate fuel cells V Volt A Ampere CHP Combined heat power PID Proportional Integral Derivative RAB Reactive air brazing Ag Silver YSZ Yttrium Stabilized Zirconia Ag - Ni Silver - Nickel PaS pascal - second MPa megapascal C Celsius K Kelvin Cl Chlorine Na Sodium k cps Kilo centipoise x lb. Pound LSM Lanthanum strontium manganite LCM Lanthanum calcium manganite LSF Lanthanum strontium ferrite LSCF L anthanum strontium cobalt ferrite LSMF L anthanum strontium manganese ferrite PSM P raseodymium strontium manganite PSMF Praseodymium strontium manganese ferrite ASTM American Society for Testing and Materials TLM Transmission line method CTLM C ircular transfer length method RTD Resistance temperature detectors VI Voltage - Current K p Proportional gain K i Integral gain K d Derivative gain G u Ul timate gain P u Ultimate period , Resistance ratios resistivity 2D 2 Dimensional micrometer xi mg milligram SEM scanning electron microscopy 1 CHAPTER 1 INTRODUCTION, BACKGROUND, AND MOTIVATION 1.1 Rationale and Research objective - Heraclitus, could be the modern - day redefined slogan to narrate the the most crucial factor which not only fuels the modernization but is required for the most basic requirements . 80% of the total energy requirement of the world comes from using fossil fuels. [1] According to Environmental and Energy Study Institute (EESI) , 76% of the total greenhouse gas emission in US came from burning fossil fuels in 2016 [2] . With the temperature of the earth rising nearly twice the rate it was 50 years ago [3] , switching to efficient conventional sources of energy has hardly remained a choice anymore. Solid oxide fuel cell (SOFC) is a very promising energy conversion technology which converts chemical energy directly to electr ic al energy. It has high efficiency (around 60%) when used as a standalone and can go up to 80% by implementing cogeneration to serve thermal and electric loads [4] and high fuel flexibility (it can use methane, ethanol, propane, LPG, diesel, biofuels etc.) [5] [6] . The exhaust heat in SOFC s can be further used for co generation and is capable of powering from a few kilowatts for commercial and residential applications up to megawatt capacity to support electric power generations and industries [7] . Nernst observed electrical conduction in stabilized zirconia at high temperatures which led to his 2 patent that used zirconia filament for fabrication of the incandescent bulb [8] . Based on the theory put forth by Nernst et al. first contributed in commencing and operating the very first fuel cell [9] . They used oxides of materials such as lanthanum, yttrium, zirconium and cerium as electrolytes. Since then efforts have been taken to increase the conductivity and mechan ical strength of the electrolyte. In the late 1950s attempts were made to fabricate a fuel cell resistant to carbon monoxide and having a stable electrolyte [11] . Solid oxide fuel cells are composed of a solid oxide which acts as an electrolyte in contact with an anode (negative electrode) and a cathode (positive electrode). The fuel cells are characterized based o n the electrolyte and the fuel use d to generate energy , temperature range of the cells and the type of electrochemical rea ction taking place. Figure 1. 1 Basic operation of SOFC operating on H 2 fuel [10] The basic reactions taking place during the operation of SOFC s using H 2 fuel are as follows [11] . Reaction at anode: H 2 + O 2 - 2 O + 2e - Reaction at cathode: O 2 + 4e - 2 - 3 Overall Reaction: 2H 2 + O 2 2 O The fuel is oxidized at the anode into electrons and protons while the reduction of oxygen takes place at the cathode which ultimately reacts to form water. These reactions depend upon the electrons formed during oxidation which travel from the anode to the cathode forming an electri c circuit and generating electrical energy from the reaction . Solid oxide fuel cells are primarily used in combined heat power (CHP) applications which present the advantage of increased efficiency (up to 80 %) and power reliability. CHP has the capaci ty to provide high quality and un interrupted power supply to individual houses, residential complexes, hospitals and industries . They also have the advantage of being environmental friendly [7] . Solid oxide fuel cells are regarded as one of the most promising green technologies for power generation. However, operation of the fuel cells at high temperature s can be challenging due to problems such as (i) Electrode sintering (ii) Interfacial diffusion occurring between electrode and electrolyte (iii) Disparate thermal expansion coefficients resulting into mechanical stress (iv) Limitations on the choice of materials Moreover, circuit paste delamination and degradation under redox and thermal cycling are major problems which need to be overcome [12], [13] . Resolving these issue s will greatly boost SOFC performance and lifetime. Although the solid oxide fuel cells have high efficiency, they operate on a low open circuit voltage 4 (~1 V). By connecting several individual cells in series, a higher voltage level can be achieved . T hese cells are linked together using an appropriate ceramic or metallic interconnect. The metallic interconnects have several advantages over the ceramic interconnects such as lower fabrication and material cost , easy to shape, better thermal and electrica l conductivity . [13] [14] . However, the weak contact/adhesion as well as resistive scale formation between the metal ceramic interface can affect the overall SOFC performanc e. This setback can be rectified using a stable current collecting layer which improves the overall electrica l contact and minimizes the losses in the cell [15] . The pastes u sed for experimentation in this study are silver nickel, Heraeus and DAD87. The set - up and methodology to measure the sheet resistivity and contact resi stivity is studied. Surface treatments and environmental conditions might influence the properties and performance of solid oxide fuel cell circuit pastes. The electrical performance is compared before and after annealing to observe the effects on resistiv ity. The effect of high temperature on the electrical properties of the circuit pastes is observed. The temperature range for the test measurements is from room The ultimate goal of the project is to improv e performance and cost eff iciency of the solid oxide fuel cells through the use of circuit pastes. The main parameters identified to record and analyze the performance of the circuit pastes are as follows: 1) S heet resistivity 2) C ontact resistivity 5 3) A dhesion of the paste to the SOFC substrates Efforts are focused on improving the adhesion and mechanical strength of the silver pastes. The performance of the circuit paste has a profound effect on the efficiency and the performance to cost ratio of SOFCs. C ircuit pastes should exhi bit properties such as good printability, high efficiency, reliability, durability and long - life even after exposure to high temperatures [16] [17] . The average efficiency of SOFCs is around 60%. The material s used as well as the processing method s ha ve an impact on the efficiency of SOFCs. The adhesive strength of the silver paste is getting more attention in the SOFC industry due to the impact it has on the lifetime of the cell. T here seems to be a strong connection between the circuit paste composition and its adhesion properti es [17] . Having high green strength avoids flaking and chipping of the paste even after aging. The silver should be able to main good adhesion with the substrate despite the amount of variation in it within permissible range. Along with good conductivity it should exhibit good stability in both reducing and o xidizing atmosphere and have a CTE (coefficient of thermal expansion) close to other SOFC components. Higher mechanical strength and strong adhesion even at higher temperatures, chemical compatibility, ease of fabrication and low cost are some of the other desirable properties along with high conductivity which help in boosting SOFC performance. The visco - elastic properties of the chosen pastes should be such that it exhibits good reproducibility over several months of shelf life retaining consistent thic kness over the printed area. It should not spread too much and should be able to maintain a well - defined edge [17] . After being screen printed on a SOFC substrate, a mesh like structure does not produce circuit pastes 6 with optimum performance. The pastes should be unvarying throughout the printed area and must be free of meshes or indentations. It should adhere to the substrate well and should not peel later. It should also have sufficient mechanical strength so as to endure the SOFC operations [16] . T he interactions of the components of the paste are complex and influence the printability. Thus, choosing the right material for the thick film becomes crucial for the SOFC operations. 1.2 Choice of substrate and silver inks C ommercially available thick film pastes used in solid oxide fuel cells includ e unfritted silver pastes, fritted circuit pastes, active metals and reactive air brazing alloys (RAB). The unfritted circuit pastes are composed of silver particles and organic particles whi ch can be exposed to a . If these circuit pastes are subjected to a Even after the effect of constrained sintering, t hese pastes are observed to remain porous which could result into higher resistivity of the material. Fritted Ag circuit pastes are made up of electrically inactive glass particles which will contribute to lower conductivity. Opposed to this, the silve r nickel circuit pastes are expected to be dense, they contain silver and nickel which are both conductive and have a larger electrically active contact area with the substrate. This leads us to believe that they would have lower resistivity. Transient por ous nickel interlayers have been seen to stimulate Ag wetting to SOFC substrates like YSZ [18] . Moreover, the circuit pastes are capable of being produced in an inert atmosphere which assure s high interface strength even under reduc tion by hydrogen. In conclusion, the Ag - Ni pastes are 7 believed to exhibit better adhesion, lower resistivity along with high oxygen and hydrogen permeability . Heraeus and DAD87 are the most commonly used current collecting silver pas tes used by the SOFC community [19 - 24] . The performance of c ommercially available pastes viz He raeus and DAD87 is tested and used as baseline for performance comparison of silver nickel pastes specifically prepared for this experimentation . DAD87 is a conductive material mainly composed of epoxy resin, silver and organic solvents . It is an adhesive with good electric conduction, heat resistance and low ionic impurity content. Some of the important properties of the DAD87 are summarized in table 1.2 as per stated in the analysis report presented by the manufacturer. (Shanghai Resea rch Institute of Synthetic Resins Co. Ltd) [25] . Table 1. 1 Important characteristics of DAD87 Property Value Appearance Silver white colored paste 20 ± 5 Specific Gravity 4.05 Silver Content (%) Shearing strength at room temperature (MPa) 8 Heraeus is a brand which specializes in high quality and high - performance silver metallization solutions. The paste which we have used is the Silver C8710 having the following properties specified by the manufactu rer (Heraeus Precious Metals NA) [26] . It is expected to give an even and dense film. Table 1. 2 Important characteristics of Heraeus C8710 Property Value Viscosity 293.7 kcps Solid Content (%) 81.38 % Initial Adhesion 6.82 lb. Aged Adhesion (72 hours at 150 2.47 lb. Lanthanum strontium manganite (LSM) with the compound formula La x Sr x MnO 3, is an excellent candidate for SOFC cathode material and would be the substrate under consideration for measurement of contact resist ivity . They are perovskite - structures which exhibit superior thermal expansion and are generally used when SOFC s are operated at a temperature a r ound 800ºC . Its structural compositi on is in the form ABO 3 where A can be represented by the lanthanum and strontium atoms and B can be represented by manganese atoms. [27] [28] . The perovskite - structured , ceramic electrode materials - lanthanum strontium ferrite (LSF), lanthanum strontium cobalt ferrite (LSCF), lanthanum strontium manganese ferrite (LSMF), praseodymium strontium manganite (PSM) and praseodymium strontium manganese ferrite 9 (PSMF) are some of the other material s which are generally used in the relatively operating temperature range of 600 to 800ºC [29] . 1.3 Evaluation of electrical performance of circ uit pastes on SOFC substrates The e xperimental work includes silver inks printed on non - conducting substrate alumina. The van der Pauw method is used to measure in - plane electrical sheet res istance which follows the ASTM standard. This involves the application of a current , and measur ement of a voltage using 4 contacts to measure sheet resist ivity of a small, flat sample with arbitrary shape and uniform thickness. Some of the requirements o f the van der Pauw test measurement are as follows: a) This test method requires the specimen to be homogeneous in thickness. b) The contacts should follow linear voltage - current characteristics at the measurement temperature. c) Current used for the measurement should be small to avoid resistive heating. d) Contacts should be adequately small in size compared to the sample [30] . e) The positions of the contacts positioned around the perimeter of the sample give measurements with better acc uracy [30] . f) The shape of the sample can be arbitrary but better results are obtained for samples which are symmetric in shape [31] . Samples are screen printed on a nonconductive alumina substrate for temperature dependent sheet resistance measurement. The geome tries which can be used for the method, the instruments used, 10 the procedure for the measurement, design of the test structure and the formula e used to calculate the final sheet resistivity are explained in the next chapter. The transmission line method ( TLM) and the circular transfer length method (CTLM) are two of the most popular methods to measure contact resistivity. The measurement of contact resist ivity will help us determine the quality of ohmic contacts which ultimately affect the performance of the SOFC. T he TLM method may cause error s due to the effect of current crowding which includes flow of current from one contact to the other [32] . CTLM is used to determine the contact resistivity using the four - probe design to compensat e for the losses due to the probes. The silver inks are tested on SOFC conducting substrate - LSM (lanthanum strontium manganite ). The structure that has been chosen to test the contact resist ivity consist of a circular contact having a ring - shaped gap o n the conductive substrate as proposed by Marlow and Das [33] . This method consists of passing a current of fixed magnitude through a center contact of radius r 0 , while mo nitoring the voltage drop between the center contact and the ground plane. This will result into a voltage drop across the contact and conducting substrate below. The magnitude of the voltage drop will depend o n the dimension of the gap spacing. The value of specific contact resistivity is calculated based on the resistance value measured as a function of the gap spacing. The non - linear curve between the total resistance and the gap - spacing can be transformed into a linear relation by using a correction fac tor [33] [34] . The procedure of the measurement, the design of the instrument, the mathematical equations to arrive at the specific contact resistivit y and the 11 probable errors which might take place in the measurement have been elaborated in the next chapter. Either 2 - wire or 4 - wire measurement s can be used while measuring the contact resistance. The 4 - wire measurement was found to be important for this work in order to achieve greater accuracy since the contact resistivities are relatively small . In the 4 - wire process , the test current is applied to the source leads and the sample under measurement . A voltmeter is used to measure the voltage between a second set of sense leads. The resistance is computed from the measured voltage over the supplied current. This method is generally preferred for low resistance and micro - ammeter applications [35] . In the 2 - wire measurement , the same set of leads used to pass the current through the sample are used to measure the voltage. T hus, the voltage drop across the test leads also contributes to the measured value and leads to a resistance error in the measurement. While using the 4 - wire measurement, the current flowing through the sense leads is negligible due to the large input re lead resistances can be neglected. In addition to preventing the voltage drop across the measurement probes, it also helps to reduce the effect of resistance spreading occurring at every probe as well as contact resistance between the probes and the material under test [36] . As we are dealing with conductive substrates and films, the resistance is expected to be of lower values. The effect of annealing on the resistance of the circuit pastes is observed and studied. The co nclusive part of the thesis include s list of precautions that should be considered while performing low resistivity measurements. This gives an idea about the accuracy of the data collected and 12 discusses certain precautions that can be taken to reduce errors in the measurement . The first step includes th e proper calibration and analyzing the precision of the measurement instruments. Thermal emfs and device heating should be given special attention when it comes to low resistance measurements. This issue can be dealt with by making use of the zero feature on the instrument [35] or m easuring current versus voltage sweeps and using the slope for determining sample conductivity. Environmental and external factors also affect the measurement accuracy to a certain extent. Issues such as temperature variation, humidity, electrostatic fields, mechanical vibrations, contamination of the insulators have been discussed in detail in the later sections of the thesis. The Keithley handbook on low level measurements discusses these issues encountered in low level measurements . 1.4 Thesis Content In this thesis the sheet resistivity and contact resistivity of thick - film circuit pastes is computed and presented . Chapter 1 covers the operation and applications of solid oxide fuel cells. It defines the objective of the thesis wor k and expounds on the motivation to do so. It introduces us to the materials under analysis and experimental procedures chosen to perform the required measurements. In Chapter 2, the experimental procedures used in this thesis are described thoroughly. T he experimental set up, system design and the formulae are explained in detail. The PID control mechanism for stabilization of temperature is explained. 13 In Chapter 3 the measurement results are presented . The probable reasons and mechanisms behind the trends are discussed. The probable errors as well as ways to prevent to the errors in the measurement are analyzed . In Chapter 4, the conclusion of this thesis work is presented, and potential future work is suggeste d. 14 CHAPTER 2 EXPERIMENTAL PROCEDURE S This section explains how the samples have been prepared for the measurement of contact resistivity and sheet resistivity. It elaborates on system design, experimental methods as well as the mathematical aspect of the measurements under consideration. It gives details about some of the supplementary procedures that need to be conducted alongside the resistivity measurements. (Thickness measurement and gap spacing measurement) 2.1 Sample Preparation All the samples have been prepared by Genzhi Hu and Dr. Jason Nicholas using the method of screen printing. Screen printing is the second most popular technique to produce SOFC circuit pastes, the first being type - casting. Screen printing uses a powder, so lvent and binder to produce a slurry. This is also referred to as ink, which is generally of high density. A metal screen is placed over the substrate and the ink is placed between the edge of the sample and a squeegee [37] . A polymer coating on the screen prevents the ink from making contact to the sample except in the regions where the polymer coating has been removed. In this way, t he paste is applied to the substrate in selective areas . The effect of screen quality on the f inal print outcome and uniform transfer of paste is noteworthy and requires special attention [38] . The basic set up of the screen - printing process is shown in Figure 2.1. The film is generally dried and sintered after the printing process. 15 Figure 2. 1 Basic screen - printing process [38] The samples have been designed on AutoCAD and submitted to the manufacturer , Sefar Inc. , for fabrication of cus tomized screens. The substrate used is 96% pure alumina for measurement o f sheet resistivity. The Heraeus sample is placed into a drying oven at 80 °C for a duration of 10 minutes. This process is repeated for every layer printed. The sample is later placed in a carbon - gettered controlled atmosphere furnace. The furnace temperature is increased at a rate of 5°C/min un is then held cooling rate (5°C/min) is used to bring the sample back to the room temperature. 16 The procedure for producing DAD87 and the Heraeus samples is similar . The same substrate with the same dimensions is used to produ ce the sample. The paste is applied to the customized screen by a stirring rod which is later printed on to the substrate. After each layer is applied, the sample is placed in an air - drying oven at 80 °C for 10 minutes. However, the post - treatment on the D AD87 samples after the printing is slightly different than the Heraeus samples. For the DAD87 , the furnace is held at 250 °C for one hour and heated at a rate of 5 °C/min. The furnace is cooled at the same rate until it reaches room temperature. For fabri cation of silver - nickel samples a 99.8%+ Nickel powder was mixed with Heraeus V737 polymeric vehicle using a stainless - steel rod at a 2:1 weight ratio to produce nickel paste. The same procedure is repeated with the silver to produce silver paste. After ea ch layer is printed, the sample is placed in an air - drying oven for a duration of 10 minutes. 6 layers of silver and 3 layers of nickel are printed using this process . The samples are held at 850 °C for two hours in a carbon - gettered controlled atmosphere to sinter the nickel network. It is later brazed at 1050 Heating and cooling rate of 5 The method for preparing contact resistance samples and sheet resistance sample is ident ical , however the screen - printed pattern s are different . The structure of the sample used for the sheet resist ivity measurement is designed as per the ASTM standards [31] . The cir cular pattern suggested by Marlow and Das for contact resist ivity characterization was chosen for the measurements [33] . The pictures below illustrate the patterns for the test samples along with their dimensions. 17 Figure 2. 2 Pattern for test sample for measurement of sheet resistivity Figure 2. 3 Pattern for test sample for measurement of contact resistivity 18 2.2 Measurement of sheet resistivity Sheet resistance is a frequently used term to express the lateral resistance across a thin square of material i.e. resistance between opposite sides of a square [39] . It is commonly used to characterize materials made by semiconductor doping, metal deposition, screen printing and glass - coating . The sheet resistivity measurements are designe d according to the ASTM standards F76 - 08. [31] . The v an der Pauw method is one of the popular Kelvin techniques to measure resistivity which involves application of current and me asurement of voltage on the contacts placed on the circumference of arbitrary shaped sample having uniform thickness. This method is particularly used for samples with comparatively smaller area because the layout and positioning of the contacts is simplified in this case [36] . Using a 7002 Ke ithley switch system and Keithley 7012 - S 4 × 10 Matrix Card, 8 measurements configurations are achieved at each temperature step to obtain the resistivity measurements. Figure 2. 4 illustrates the configurations for application of current and measurement of v oltage to obtain the specific sheet resistance. Figure 2. 4 v an der Pauw resistivity measurement configurations [36] 19 2.2.1 Apparatus and system design The system design and the connection diagrams have been presented in this section. It is necessary that the sample should exhibit linear VI characteristics. This indicates that the minority carrier injection does not influence the measurement. The current used for the measureme nt should be as low as possible. This will reduce resistive heating and help achieve the desirable accuracy . The following apparatus is used in the measurement procedure: a) 2400 Keithley Series Sourcemeter is used to source current through the specimen with variation less than ± 0.5%. b) 2182 Keithley Nanovoltmeter is used measure the voltage between the contacts to an accuracy of ± 0.5 %. It also measures the resistance of the RTD which assists in measuring the temperature of the sample. c) Keithley 7002 switch system and Keithley 7012 - 2 4 × 10 Matrix Card is used to connect the contacts to the appropriate meters to form the correct configuration used for sheet resistance measurements. A total of 8 configurations are required to calculate the sheet resistivity illustrated in Figure 2. 4. d) The s ystem uses Omega iSeries CNi32 temperature controller to control and read the temperature of the furnace. The controller makes use of PID control for temperature regulation. . 20 Figure 2. 5 Switching diagram for Keithley 7002 switch system Figure 2.6 shows the entire set - up to complete both the sheet resistivity measurements. It consists of sample stage on to which a sample under measurement is mounted. It is enclosed by a furnace which use s a temperature controller operating on PID based control to regulate the temperature. A thermostat is attached to the furnace to detect the sample temperature at any given time during the measurement. Additionally, a switch system, N anovoltmeter, S ourceme ter can be been seen in the picture. A computer (with LabVIEW functionality) is necessary for data collection and processing. . 21 Figure 2. 6 Resistivity measurement set - up 2.2.2 Temperature stabilization As per the ASTM standard the control and measurement of the temperature of the sample under [31] . T he PID control has been deployed for temperature control and regulation. An important term associated with the PID control is the process variable which is the difference in the setpoint temperature and the current temperature. Based on this 22 difference, it makes a change in the successiv e values such that the process value reaches as close to the desired setpoint as possible . The three components of the PID control are listed below along with their corrective action [40] . Proportional - Makes a correction based on current error i.e. difference betw een the set point and process variable. The speed of response can be improved by increasing the proportional gain. System will become unstable if optimum value for the gain is not chosen [41] . Using the proportional gain alone in the system results into steady state error between the process variable and the set point. Figure 2. 7 Response of a PID controller [41] Integral - Makes a correction based on the integration of the error with respect to time. It is mainly used to decrease the steady state error. The proportional combined with integral control is the most popular control used in industrie s [42 ] . Derivative - Makes a correction based on the derivative of the error with respect to time. It is used when the rate of change of process variable is high. 23 . Figure 2. 8 Basic block diagram of PID control [42] The three gain variables Kp, Ki, Kd corresponding to proportional, integral and derivative control i.e. the process variable should be as close to the set point as possible . National Instruments explains the steps carried out for tuning the PID by means of trial and error in one of their articles [43] . a) Initially the proportional gain is taken into account , keeping the values of integral gain and derivative gain equal to zero. The proportional gain is increased until the response to any disturbance is a steady oscillation. Care must be taken that the value of Kp is not too high to cause instability. 24 b) Once the value of proportional gain has been chosen, the integral gain Ki is selected to eliminate the steady state error. Choosing the integral gain is a tradeoff between minimizing the steady state error and reducing the overshoot. c) Increase value of Kd until t he oscillations in the system are minimized. Derivative action can allow you to have greater values of Kp and Ki whilst maintaining the loop stability . This giv es you a faster response and a better loop performance. The disadvantage of using the derivativ e control is that the system becomes highly sensitive to noise after including the derivative control. Ziegler Nichols Method: Ziegler Nichols Methods is a commonly used technique to tune PID controllers. John A. Shaw explains in his book the following s teps followed to tune the PID using the closed loop method [44] . The integral and derivative control are set to zero and only proportional control is set at first. The proportional control is gradually increased until the oscillations start. The proportional gain is increased until the oscillations reach a constant ampl itude. The gain at which this event occurs is called as the ultimate gain (Gu) and the period of the oscillations is the ultimate period (Pu). Figure 2.9 illustrates the ultimate period in the oscillations. The gains used to tune the PID are calculated bas ed on a fixed formula using the ultimate gain and the ultimate period. 25 Figure 2. 9 Ultimate period (Pu) at which oscillations reach a constant amplitude [44] Table 2. 1 Calculation of PID gain values using the ultimate gain and ultimate period [44] . Control KP Ki Kd P 0.5 Gu PI 0.45 Gu PID 0.6 Gu 2.2.3 Process and Methodology Place the specimen on the sample stage after making appropriate connections on the sample . Silver paste is used to attach the test leads to the contacts. Switch on the temperature controller and give it time to stabilize. The temperature controller should be properly tuned using the PID control. Keithley 7002 switch system should be programmed such as to achieve required sequence of contac t pairs for resistivity measurement. 2400 Keithley Series S ourcemeter to source current between required contact pairs and 2182 Keithley multimeter to measure potential difference between the contacts should be warmed up for at least 2 hours before the mea surement to make 26 sure the instrument is stabilized. Input values of current (0.05 ampere used for this experiment), been depicted in the figure below . F igure 2. 10 LabVIEW front panel view for sheet resistivity measurement 2.2.4 Calculations The formulae to calculate the ultimate sheet resistivity as per the recommendations of the ASTM standards are as follows [31] . 1) Resistance ratio and = the potential difference measured between contacts 3 and 4 when current enters contact 1 and exists contact 2. 27 2) Calculate relationship between factor f and Q where and are the geometric factors which are a function of resistance ratios and . The correction factor takes into account the current crowing taking place near the contacts. Figure 2. 11 Factor f (geometric factor) versus Q (resistance ratio) [31] 3) Calculate resistivity If is not within 10% of , the sample is not homogeneous, and a more uniform sample is necessary for the experiment . 4) The average resistivity is calculated as 28 Units: Voltage (V) - Volt, Thickness (t) - cm, Current (I) - Ampere, Resistivity ( , ) · cm, Temperature - 2.2.5 Profilometer for thickness measurement The thickness of the sample is necessary to calculate sheet resistivity of the sample. The NanoMap 500 LS is used for measuring the thickness of the sample. Figure 2. 12 Profilometer measurement set - up to determine thickness of sample The procedure to carry out the profilometer measurements is as follows: 29 1) The NanoMap Software is used to collect the data. Load the sample on the center stage. Auto load the probe tip aft er making sure the sample is placed below the z stage. 2) Adjust the tip location by adjusting the X and the Y co - ordinates of the probe tip. 3) The following parameter s are selected in the thickness measurement of the sheet resistivity samples: Mode: Long Scan 2D Vertical Range: 500 Scan Distance: 10000 Scan Speed: 100 Sample Frequency: 50 Points/Scan: 5000 Data Resolution: 2.00 # Lines: 1000 Contact Force: 5.00 mg 4) Run the program to get a graph on the signal screen. Set the markers after the measurement is complete to get the thickness measurement. Take multiple readings at different co - ordinates to get an estimate of the thickness variation. 30 Figure 2. 13 Circuit paste thickness versus position (Average thickness 36.34 m) 6 measurements are taken for the samples - 3 horizontal lines scans (H) and 3 vertical lines scans (V), as shown in the picture below. Average of the 6 readings is then taken to get the final thickness value . Figure 2. 14 Representation of traces of 3 horizontal scans (H) and 3 vertical scans (V) 31 2 .3 Measurement of contact resistivity Experimental investigation of contact resistivity of circuit pastes screen printed over SOFC substrate LSM is presented. According to Christine et al. the best choice of ink for contact resistivity is contingent on the material used f or substrate and its roughness and cannot be recommended in general [45] . J. H. Klootwijk and C. E. Timmering demonstrate the advantage of circular transfer length method (CTLM) over linear transfer length method (TLM) [32] . The TLM method may cause errors due to the effect of current crowding which causes flow of current from one contact to the other [32] . The 4 - wire method is used to avoid the effect of test lead resistances as recommended in the Keithley Low Level Measurement Handbook [35] . . 2.3.1 Apparatus and System Design The apparatus used for the measurement of contact resistivity is similar to that used for sheet resistivity. The switching diagram of the system using the Keithley 7002 switch system and 7012 - S 4× 10 Matrix Card is illustrated in Figure 2.1 5 . Additionall y , the following apparatus is involved in the measurement of contact resistivity on the same set - up illustrated in Figure 2.6. a) 2400 Keithley Series Sourcemeter is used to source current through the specimen. b) 2182 Keithley Nanovoltmeter is used to measure the voltage between the contacts as well as resistance of the RTD to compute the sample temperature. c) Keithley 7002 switch system and Keithley 7012 - S 4× 10 Matrix Card is used to connect the contacts to appropr iate meters to form the correct configuration used for contact resistance measurements . 32 d) Omega iSeries CNi32 is utilized for temperature control. The controller makes use of PID control for temperature regulation. Figure 2. 15 4 - wire configuration used for contact resist ivity measurement 2.3.2 Process and Methodology Place the specimen on the sample stage and connect wires at appropriate points on the sample. Switch on the temperature controller (Omega iSeries CNi32) and give it time to stabilize. The temperature controller should be properly tuned using the PID control as described in the previous section. K eithley 7002 switch system should be programmed such as to achieve required sequence of contact pairs for resistivity measurement. 2400 Keithley Series Sourcemeter is used to source current between required contact pairs and 2182 Keithley multimeter is us ed to measure potential difference between the contacts . These instruments should be warmed up for at least 2 hours and given time to stabilize before starting the measurement . Input values of current, gap spacings in the program and all the other details which have been depicted in the figur e . The Lei c a MZ8 33 microscope and J - Image software has been used to measure the gap spacing between the inner circle and the outer ring . These details have been elaborated in the later sections of the chapter. Figure 2. 16 LabVIEW front panel view for contact resistivity measurement 2.3.3 Calculations The circular transfer length method (CTLM) consists of the following steps to get the contact resistivity [32] . 1) IV sweep yielding resistance value for each gap spacing at every temperature step Room temperature to with step size of approximately 34 Figure 2. 17 One of the IV Sweep for Heraeus sample 2) Plotting resistance versus gap spacing at every temperature step Figure 2. 18 Resistance versus gap spacing for Heraeus sample at room temperature 35 Calculate resistance by Y intercept value and multiple by area to get resistivity ( · for each temperature step. The Y intercept value is twice the value of the contact resistance and corresponds to a gap spacing of zero . 3) Measured non - linear curve transformed into a linear relationship using a correction factor c = ln Where R 1 is the radius of inner circular contact and s is the gap spacing . The correction factor is divided by the experimental CTML data to avoid underestimation of the contact resistance. 2.3.4 Measurement of gap - spacing It is necessary to know the gap - spacing between the inner - circle and the outer ring to calculate the final contact resistivity. A software called J - Image is used in measuring the gap spacing. The following steps are used to determine the gap spacing usin g the software. a) Take snapshots of the sample using the microscope. The Lei c a MZ8 microscope is used for this purpose. Note down the magnification at which the image is captured. Figure 2. 19 Image of Heraeus Sample 3, Contact 2 with 2.5X magnification 36 b) Spatial Calibration is used in setting the scale. Spatial calibration uses a single image of known dimension and appl ies the scale to measure unknown values. This procedure needs to be repeated when images of different magnifications are taken. c) After the scale is set, open the image in Image J and draw a line over the distance which needs to be measured . d) 10 readings are taken at different angles and positions. These readings are averaged to get the gap measurement. T able 2. 2 Reading s for gap spacing on J - Image ( Heraeus s ample 2 , gap spacing 1 ) (The unit for length is µm) C1 Area Mean Min Max Angle Length 1 629.004 42.536 28.763 66.235 - 90 181.821 2 559.115 44.164 35.141 59.693 91.245 158.857 3 535.818 43.907 31.945 67.865 0 153.116 4 465.929 42.94 23.438 69.496 0 133.966 5 477.577 43.087 24.773 104.723 55.125 137.501 6 500.874 44.809 30.251 104.679 - 123.311 142.819 7 407.688 45.922 26.584 74.096 - 43.781 115.035 8 512.522 51.302 33.665 89.44 141.766 145.562 9 663.949 44.109 28.851 118.834 - 23.334 191.237 10 524.17 44.096 29.346 113.757 37.405 148.896 Average 150.881 37 2.3.5 Measurement of contact resistivity at room temperature using four probe s The measurement apparatus consists of a Signatone probing station, Signatone S - 725 micropositioner and Keithley 2400 to measure resistivity. The micropositioner uses tungsten carbide probes which have nickel plated steel base and are held by the magnets. A microscope is used to make sure the connections are secure and not overlapping or touching each o ther. The measurement of contact resist ivity is taken at room temperature and compare d with the experimental values . Figure 2. 20 Signatone probing station & S - 725 micr o positioner 38 Procedure: 1) Measure the resistance of a surface mount resistor of a known value to check the accuracy and reliability of the system. 2) After the system gives satisfactory results, mount the sample on the sample stage. Adjust the knobs on the probe such that 2 of the probes touch the central circle and the other 2 probes touch the ground plane. 3) Set the Keithley 2400 Source m eter on s ense 4 - wire mode and a uto source mode. Repeat step 2 and 3 for each gap spacing. Calculate the contact resistivity by taking resist ance measurements at each gap spacing and the gap measurement data. In the next chapter the results of the contact and the sheet resistivity are discussed. The probable errors in the system and the measurement instrument are analyzed to create error bars for the measured data. The methods and precautions to minimize the errors are reviewed. 2.3.6 Preparation of reference sample A reference sample was produced using the method of plasma sputtering. This method includes a solid target bombarded with energetic ions which causes atoms to be ejected which are then deposited on the substrate in form of a thin film. The Kurt Lesk e r AXISS system was used to deposit a thin film of platinum ove r multiple substrate s . The resistance of this sample was measured on the assembled system and the values were compared against the known resistivity values of platinum . This helps us to verify the accuracy of our system and gives us confidence in measu red values. 39 Figure 2. 21 Kurt J. Lesker AX X I S system used for s putter deposition. 40 CHAPTER 3 RESULTS AND DISCUSSION Sheet resistivity measurements with 3 types of pastes and the effects of the temperature are shown . The contact resistivity between the circuit paste and SOFC conductive subst r ate LSM is presented. The contact resistivity is calculated based on the variation of resistance as a function of gap spacing . The values for the 3 pastes are compared before and after annealing. The possible error sources are documented and the precautions to reduce these errors have been discussed in this chapter. 3.1 Sheet resistivity results Sheet resistivity of 3 types of pastes (Heraeus, DAD87 and silver nickel) are tested on alumina substrate. The effect of annealing on the resistivity of sample is observed. The specific sheet resistance is compared with the resistivity of silver and nick el. 3.1.1 Sheet resistivity of Heraeus paste screen printed on alumina The sheet resistivity is computed for a sample which has 2 layers of Heraeus C8710 screen - printed on non - conductive substrate alumina. As seen from Figure 3.1 the resistivity is incr easing as the temperature increases. The sample exhibits positive temperature coefficient which is seen in most of conductors caused by a reduction in mobility within increased phonon scattering as temperature increases . The resistivity decreases after ann ealing due to an increase in sample density . The data is compared for the temperature rise cycle (room temperature to 450 as well as the cooling 41 down cycle ( 450 . The results for both the cycles are comparable a nd reproducible. Figure 3. 1 S heet resistivity versus temperature for Heraeus sample Heraeus - 2 layers of Heraeus C8710 screen printed on alumina The measurements are taken before and cau ses the sheet resistivity to decrease around 45 - 50 % of the value . The resistivity values of the annealed sample r · · cm as the temperature is varied (room Sahu et al. discusses that annealing might promote densification of the Ag layers up to a certain annealing temperature which we attribute to the decrease in effective sheet resistance [46] . 42 3.1.2 Sheet resistivity of DAD87 paste screen printed on alumina Figure 3. 2 Sheet r esistivity versus temperature for DAD87 sample DAD87 - 2 layers of DAD87 screen printed on alumina. causes the sheet resistivity in DAD87 to decrease to a larger extent ( 90 % lower than the value obtained before annealing) compared to the Heraeus samples (45 - 50% decrease) . The resistivity of the annealed DAD87 sample varies from · · cm as a function of temperature. The sample is seen to exhibit a negative tempe rature coefficient of resistance before annealing and a positive temperature coefficient post - annealing. 43 3.1.3 Sheet resistivity of silver nickel paste screen printed on alumina Figure 3. 3 S heet resistivity versus temperature for silver nickel sample Figure 3.3 shows that the a nnealed silver nickel samples has higher resistivity compared to the reading taken before annealing and ranges between 3.5 · · cm as the temperature is increased from room temperature until 450 . We attribute this to the formation of nickel oxide in the paste at the higher temperatures . However, the strength and adhesion of the sample to the subst r ate improves significantly after a nnealing /densif ication . It is noteworthy to evaluate the overall performance modification of the fuel cell after oxidation equating the effects of both decrease in resistivity as well as improvement of adhesion of the circuit paste to the substrate. This w ould be further investigated by considering the contact resistivity of silver nickel paste screen printed on conductive LSM substrate. 44 3.1 .4 Summary of sheet resistance samples Figure 3. 4 Sheet r esistivity versus temperature for all samples Silver* - , vol. 8, 1147 1298, 1979 [47] Nickel** - Data from CRC Handbook of Chemistry and Physics Figure 3. 4 summarizes the sheet resistance of 3 types of ink s Heraeus, DAD87 and silver - nickel on alumina. It compares the resistivity of these samples before and after annealing. The figure shows that annealing reduces the resistivity for Heraeus and DAD87 samples . This effect is more dominant f or the DAD87 sample than the Heraeus sample. The reason for decrease in resistivity might be due to increase in crystallization of Ag layer happening due to annealing. The denser 45 sintered network exhibits lower resistivity due to increase in number of conduction pathways. Organic residues act as electrical barriers which might be responsible for decrease in conductivity of the samples. Desorption of these residues during the annealing proc ess facilitates better electrical performance [48] . A lthough a nnealing causes increase in resistivity in silver nickel samples it improves it s strength . The data has been compared with the resistivity of pure silver and pure nickel. The resistivity of the annealed inks has been found lower than the nickel resistivity but close to (slightly higher) pure silver. Figure 3.5 specifically shows the annealed data plots for easy visualization and comparison of the resistivity values. Figure 3. 5 Sheet resistivity versus temperature for annealed samples 46 3.2 Contact resistivity results Contact resistance is the contribution to the total resistance occurring as a result of contacting/touching interfaces [49] . One of the dominant components in the resistance of the SOFC is the contact resistivity between the interconnect material and the cathode. I t is imperative to focus o n decreasing the conta ct resist ivity in order to enhance the overall performance of SOFC stack cell. I t is essential that the samples are well sintered (at near full density ) in order to help accomplish this . 3.2.1 DAD87 screen printed on LSM The DAD87 ink was screen printed on LSM substrate in the pattern depicted in Figure 2.3 . As seen from Figure 3. 6 , with increasing temperature the resistance rises from room temperature until ~50 le explanation to this behavior was presence of moisture or oxygen vacancies. To test this theory the same sample was tested in vacuum. le in vacuum. It was later considere d that the rise in resistance over the initial temperature points might be due to the ferromagnetic - paramagnetic transitions at Curie temperature which depends on the composition of LSM (La x Sr x MnO 3 ) [50] . LSM with x=0.2 is used in this case. Hassini et al. x = 0.2 which is close to the values measured [51] . 47 Figure 3. 6 Resistanc e of contact 1, 2, 5 of DAD87 sample 3.2.2 Heraeus screen printed on LSM Rise is resistance as the temperature increases for the Heraeus samples . The resistance values are seen to decrease as the temperature increases C. The resist ance values for individual gap spacing was found to be lower for the Heraeus contac ts than the DAD87 and the silver nickel samples. 48 Figure 3. 7 Resistance of contact 1,3,4,5 o f Heraeus sample 3.2.3 Silver nickel screen printed on LSM The sample was test ed for 4 cycles (Heating - 6 6 together consist ed of 1 cycle). The resistance was observed to reduce with each cycle. The difference was prominent for the first cycle and was seen to reduce for the later cycles. The grap h below shows the comparison of the resistance values for contact 4 of the samples taken over the period of 4 cooling cycles. ( 6 The resistance decreases as much as 50% over the course of 4 cycles. This shows that the sample is sintered well towards the later cycles and gives lower resistance compared to the earlier cycles. The resistance does not decrease further after being subjected to 4 cycles. 49 Figure 3. 8 R esistance of silver nickel sample measured over the 4 cooling cycles As discussed previously, the resistance was impacted due to oxidation of metallic components should be accounted fo r as this resistance might dominate the circuit paste resistance in some cases. This is especially true if the oxidation causes cracking in either the subst r ate or the oxide layer or/and cause s porosity to reduce the overall conductivity [52] . In conclusion, it is important to choose circuit paste material with low resistivity as well as slow oxide scale developing rate. As seen in the graph, the resistance of the circuit paste does not increase with rise in temperature nor with progressions of subsequent cycles. This gives us a confidence that integration of nickel does not impact the SOFC conduction negativel y. 50 3.2.4 C ontact resistivity (Heraeus, DAD87, silver nickel screen printed on LSM) Figure 3. 9 C ontact resistivity versus temperature of all samples The resistivity of DAD87 is the highest among 3 and is around · cm 2 at room temperature. It increases further · cm 2 - magnetic paramagnetic transition · cm 2 at This followed by the contact resisti vity of silver nickel samples. The showed a rise in resistivity till · cm 2 . The resistivity decreased further thereafter and reached a lowest of 60 · cm 2 at The Heraeus sample has the least resistivity among the 3 samples. and a fter this temperature, the values are comparable for both Hera eu s and silver nickel inks. W illiam et al. have evaluated the contact resistance of Fe - Cr alloys with variation in chromium 51 content for construction of interconnect materials used with different types of perovskite type contact materials [53] . Materials 1.4742, alloy 446, 1.4509 are ferrite steels with variation in Cr, Mn, Ti, Al, Ni, Si. The details of the chemical comp osition, experimentation, methodology can be found in the literature . It has been further stated that integration of contact layers (JS - 1, JS - 2, JS - 3 - consisting of La - based perovskites) reduces the contact resistance significantly by compensating geometr ical irregularities of the cathode and/or interconnect materials). The contact resistivity of the semi - conductor alloys with the integration of contact layers is around · cm 2 . H. Schmidt et al. discusses the development of an intermediate layer to ma intain the electrical contact between the metallic plate and screen - printed electrode [54] . The influence of the material used in the contact layer on the contact resistance between the cathode and the metallic plate has been studied. For measurement of contact resistance, scr een - printing pastes were deposited on metallic bipolar plate. The contact material under investigation were - LaCoO 3 , La 0.8 Sr 0.2 CoO 3 , La 0.8 Sr 0.2 MnO 3 . It has been stated that considering the total electric losses in the SOFC the contact resistance in the sym · cm 2 . This gives us some confidence in the silver - nickel film fabricated, as the contact resistance measured is below this value. T he values of contact resistance with the LaCoO 3 subst r ate is a round · cm 2 plotted as a function of time. The resistance reduces almost to half with the La 0.8 Sr 0.2 MnO 3 subst r ate varying in the range 10 0 - · cm 2 plotted against time. This value lies between 10 - · cm 2 for the La 0.8 Sr 0.2 CoO 3 substrate. The contact layer prepared by the reaction sprayed powder showed the least resistanc of · cm 2 which stayed contact with time. Chuan et al. measured the contact resistivity of LSM based current collector and the cathode for SOFCs. This value was close · cm 2 [15] . Dey et al. studied the variation of contact 52 resistivity as a variation of temperature and contact pressure. The lowest contact resistivity of 48 · cm 2 at the anode side is observed at a compression load of 0.074 MPa and at an operating temperature of 800 · cm 2 at 800 ° C at a compression load of 0.064 MPa [55] . 3.3 Resistivity of reference sample Reference samples were fabricated using the method of magnetron sputtering of platinum . The resistivity of these samples was measured on the high temperature resistance measurement system. These values were compared against the known values to evaluate measurement errors in the systems. Precise measurement of the thickness was necessary to accurately calculate the resistivity of the reference sample in order to access the precision of the measuring instrument . The first set of reference samples was made by depositing platinum on alumina s ubstrate s by dc magnetron sputtering at 200 W for a duration of 10 minutes. Another set of the reference sample was made by depositing the platinum for 40 minutes. T he thickness of the sample was not measured accurately by the profilometer because of the s ubstrate variations as well as the sample being not thick enough. The thickness of these samples was later measured using SEM . The SEM imaging was done by Genzhi and Dr. Nicholas. Even after using the SEM, the thickness of the sample could not be accurate ly computed as the substrate was not smooth enough. 53 Figure 3. 10 SEM for reference sample (alumina substrate, deposition time 40 minutes) Figure 3. 11 SEM for reference sample ( alumina substrate, deposition time 1 0 minute s) 54 It can be seen from Figure 3. 1 0 and 3.1 1 that the bright silver/white layer which is the platinum layer is not evenly deposited on the alumina substrate. This makes it difficult to measure the effective thickness of the sample to calculate the specific resistance. The irregular deposition thickn ess of the metal might affect the electrical behavior of the sample against a layer which is deposited regularly. Choosing aluminum nitride and sapphire as the substrates made it easier to compute the thickness of the sample s as these substrates are much smoother compared to the alumina substrates. A deposition time of 40 minutes was chosen to deposit platinum on the 2 substrates . Figure 3.1 2 shows the thickness plot of the reference sample platinum deposited on a sapphire substrate by plasma sputteri ng for a duration of 40 minutes. The flat portion of the graph represents the subst r ate and the elevated po rtion of the graph resembles the platinum deposited. Thus, it is possible to calculate the total thickness of the platinum that has been deposited. T he raw data collected by the profilometer has been analyzed and processed in origin prior to evaluating the thickness. 55 Figure 3. 12 The thickness of the sample ( sapphire substate) The resistivity of the reference sample is measure d by using the v an der Pauw method (previously used to measure the sheet resistance). The approximate error in the measured values can be computed by comparing the values against known values of platinum resistivity [56] . Figure 3.1 3 shows the resistivity of 2 reference sample (deposition time 40 minut es) plotted as a function of temperature. The sample has been subjected to a rise in temperature - room temperature to 6 and then allowed to cool back again to room temperature. The data plotted in Figure 3.1 3 has been collected while the sample was allowed to cool back. The resistivity data interpreted from has also been plotted. The difference is resistivity b etween the data plots - Westwood, reference sample and the bulk resistivity values is attributed to difference in densities of the sample s . 56 Figure 3. 13 Resistivity vs temperature for reference sample (annealed) . Bulk platinum : S. V - Platin. Met. Rev , vol. 48, no. 2, 2004 Westwood reported the effect of sputtering deposition pressure on resistivity and density of platinum film s [57] . The density of the films decreased linearly from bulk value to 60% of the bulk value as the pressure increased from 10 to 150 mTorr. This caused the resistivity to increase from twice the bulk value to ten times the bulk value. There was no change in impurity content at increased pressure. Thus, the change is resistivity was attributed to voids in grain boundaries and within the lattice occurring due to porosity in the films. According to Westwood, the pores located in between platinum decrease the effective c onduction path thickness and contribute to increased resistivity. Similar to the process used for this thesis, Westwood determined the resistivity from 57 four - point probe measurement and thickness measurement to determine the sheet resist ivity . The resistivity behavior of the fabricated reference sample - platinum sputtered film agrees with · with 96.94% of theoretical density and agrees well with values reported by other. The fit predicts the density of the reference sample to 20.8 g/cm 3. · error 1.2%) [57] . This indicates that platinum film in the reference sample is not completely dense (bulk density) and its resistivity would be further reduced when brought close to fully dense state and more closely agree with the literature values o f resistivity of bulk platinum. Figure 3. 14 Variation of resistivity vs temperature for various density values Figure 3.1 4 shows the variation of resistivity as a function of temperature. The variation of 58 resistivity with temperature is plotted for different values of density interpreted study . The graph is plotted n dens ity of sample as suggested by Westwood [57] . The interpreted data is close to the measured resistivity of the reference sample . The reference sample predicts the density of the reference sample to be 20.8 g/cm 3 . The density of the reference sample is calculated based of on the relationship established between resistivity (at room temperature) and density of sample put forth by Westwood . Agustsson et al. demonstrates the electrical resistance of the platinum films as a function of nominal thickness taken at 5 different growth temperature [58] . The resistance is high at first due to discontinuous film. Higher growth temperature result in lower film resistivity at room temperature. This effect is attributed to the in - plane grain size a nd increase in coalescence thickness . Thomas shows that the argon pressure (10 - 200 mTorr) has effect on the density of the films [59] . Our fit predicts the density of the reference sample to 20.8 g/cm 3 . This value matches exactly with the density crossover value calculated by Thomas. This indicates that platinum film in the reference sample is not completely dense (bulk density of platinum is 21.45 g/cm 3 ) and its resistivity would be further reduced when broug ht close to fully dense state and more closely agree with the literature values of resistivity of bulk platinum. 59 3.4 Probable errors in the measuring instrument Many factors contribute to the net error occurring in the measurement. One of the importa nt factors which affect the resistivity of the samples is the imprecision in calculating the average thickness of the samples. Other than this the accuracy of meters which have been used in the measurement system play a significant role in determining the correctness of the data. Figure 3. 15 Sheet resistivity vs temperature along with predicted error bars (errors< 5%) The experimental determination of the transport properties of a material requires some significant departures from the ideal model. An error of 1.2% has been calculated on the basis of the value reported by Westwood [57] . The percentage error might vary depending on the error in the 60 th ickness determination of each sample. Taking into consideration all the factor s an error of less than 5% could be predicted for the measurement. Some of the error sources which cause this error and might influence the measurement are discussed in this sec tion. The probable error sources are studied from the low level measurement handbook by Keithley [35] . 1) Current offsets: An input offset current which might be present in the meter adds currents to every measurement. Bias currents of active measu rement circuits and leakage current through insulators within the instrument are some of the causes of the offset current. This current can be nullified by using the null or zero feature on the instrument. 2) Triboelectric effects (charges produced by frict ion of conductor and insulators) and piezoelectric effects (charges generated due to mechanical stress inflicted on insulating materials ) also contribute to the offset currents circulating in the test system. Voltmeter offset: A sensitive voltmeter (Nanov oltmeter) is chosen to provide measurement of low resistance . It offers low voltage noise and drift as well as small input resistance. Certain offsets which come inherently with the voltmeter can be compensated by using the null feature on the instrument. Thermal emfs, radio - frequency interference, magnetic field interference, ground loops and voltmeter internal amplification offsets are some of the sources of offset voltages in the system. 61 3) Thermal emfs: Thermal emfs are formed when two dissimilar met als are joined to form a thermocouple producing error voltage which depends on the temperature gradient. These voltages are usually s . E T = Q AB (T 1 T 2 ) E T = Thermally generated emf Q AB T 1 T 2 or K) Offset voltages are taken care by shorting the tests leads toge ther and using the null feature on the instrument. Constructing circuits made of the same material as much as possible for the system, minimizing temperature gradients within the circuit, placing all junctions in close proximity, allowing test equipment to warm up sufficiently are some of the precautions that are taken to reduce thermal emfs. Considering the slow furnace temperature changes, the temperature near the sample is continuously measured and the reference temperature for the resistance measureme nt is updated by taking into consideration the sample temperature instead of the overall furnace temperature. The thermoelectric effect can be compensated for by using the relative feature to null the offset current occurring due to thermal emfs. 62 4) Point defects and structure of sample The v an d er Pauw method for measurement of sheet resistivity requires contact s of sufficiently small size positioned around the periphery of the sample. The effect of contact placement on the accuracy increases as the conta ct are shifted near the center of the sample [30] . The test method assumes that the sample is homogeneous [31] . V ariation in thickness of the sample as well as errors in evaluating the exact thickness of the sample will contribute to errors in the sheet resistivity measurement [34] . The thickness of the sample influences the accuracy of the mea surement to a larger extend when the aspect ratio (t/L) is greater than 50%. The error is around 3% when the value is less than 50%. The inaccurate determination and variation in gap spacing will lead to incorrect calculation of correction factor and con tact resistance [33] . The inner circles should be uniform, and its dimension must be accurately computed to maximize accuracy while calculating the specific contact resistance. The CTLM method assume s that there is no conduction in the substrate in the vertical direction. Smaller the sample size, higher the chances of this phenomenon occurring which might result into deviation from the actual values [60] . 5) Effect of lead resistance When dealing with low resistance measurement s , the resistance of the test leads can significantly affect the accuracy of the measureme nt. The test current causes a small but significant voltage drop across the lead resistances. This is added to the sample resistance and has been found to result into a considerable error for these samples. To alleviate this error, a 4 - wire method is use d for contact resistivity measurement. In this technique, two wires are 63 used for current supply through the sample and two separate wires are used to measure the resulting voltage. The current leads still have a voltage drop across them equal to the curre nt times the lead resistance . H owever , the two voltage sense leads have negligible current flow . Th us , the voltage is measured at the sample and voltage errors caused by lead resistanc es can be neglected. The v an der Pauw method uses a 4 - point measurement as well - 2 adjacent contacts used to force current and the other set of adjacent contacts used to measure voltage. The method is designed such that it can be applied to any sample with an arbitrary geometric shape as long as it is homogeneous and uniform in thickness. 6 ) External factors Several external factors such as vibrations, contamination, humidity, magnetic and electrostatic fields, power line transients, insulator deformation, ground loops, stored charges, electrochemical effects etc. can affect the accuracy of measurement. Some of the important factors which would alter the precision of the test equipment under consideration are discussed. a) Electrostatic interference This occurs when a charged object or electrostatic voltage source is in close proximity of the test circuit. Resultant unwanted charges and noise currents might cause fluctuations in the measurements. 64 This effect can be minimized or avoided by keeping the sensitive parts of the system away from charged objects and mechanical vibrations. Metal enclosures with a grounded metal shield will divert the noise currents from the test conductors and reduce the effects of noise coupling [35] . b) Noise The major sources of noise in a measuring system are i) noises present in th e measuring instrument ii) connections made in the system iii) external disturbances iv) noise in voltage and current sources. The effects of noise can be mitigated by reducing the bandwidth , using low - pass filter, shielding, using zero - checks in measuring instruments, proper grounding etc. [35] . c) Moisture and Humidity Excess humidity can affect insulation resistance and interact with contaminant s resulting into offset currents in the circuit. This might also cause conductive paths allowing small magnitude of current to flow in un intended paths. In such cases the resistance measured might be smaller than the actual value [61] . To minimize the effects of moisture and humidity, it is important to make sure that the test components are clean and free of dust and oils. If the measurement results are inconsistent, moving the test system to air - conditioned environment is likely to modera te the effect of moisture on the system [62] . The sample is tested in vacuum and compared with the results measured in air to analyze the effect of moisture on the resistance of the sample. The results 65 were comparable, and moisture d id not play a significant role in affecting the test measurement s in this case. d) Ground loops Ground loops occur when more than one equipment in the system is connected to a common ground causing large noise current to flow in the systems causing unexpected voltage drops. The error caused by ground loops are negligible as the meter has isolated LO terminals. An effective and safe way to eliminate this phenomenon is to install ground isolators and ground all equipment at one single good earthing point. Adding separate ground connections to the floating devices and/or avoiding sensitive instruments to share the ground used by high power machinery lower th e occurrence of ground loops [63] . e) Electromagnetic interference EMI create s electrical noise that can affect measure ment equipment and processes. Some of the common sources of EMI are switching dc power supplies, variable frequency drives, inductive loads, electrostatic discharges, high voltage arcing etc. Keeping system away from interference sources, proper shielding , external filtering and grounding are the most effective ways to mitigate the effect of induced magnetic voltages [64] . 66 3. 5 Tensile test results Genzhi Hu and Professor Nicholas carried out the tensile tests on 3 types of inks - Heraeus, DAD87 and silver nickel. Multiple layers of silver ink are screen printed on an alumina bar which is attached to an alumina subst r ate via super glue. Another alumina bar is attached to th e substrate and both the alumina bars are sandwiched between the previous and a new alumina substrate which is attached at the second end of the two alumina bars. The load is placed in a load grip and the load at which the sample fractures is recorded. The load is applied at a rate of ~37.5µm/min until the sample shows sign of damage. T he tensile test results showed that the oxidized silver nickel samples showed the most strength among the chosen samples. This was followed by the densified silver nickel sam ples. The Heraeus and the DAD87 had significantly lower strength compared to the silver nickel samples. 67 CHAPTER 4 CONCLUSIONS AND FUTURE SCOPE The electrical performance (sheet and contact resistivity) of 3 inks namely - Heraeus, DAD87, Ag - Ni is stu died. The van der Pauw method has been used to measure the sheet resistivity and the CTLM method is utilized to compute the contact resistivity. · cm to 5 This is followed by the DAD87 · · cm It can be seen from the sheet resistivity data that t he performance of the DAD87 pastes can be greatly impr oved by annealing the sample ( resistivity value is 90 % lower than the value obtained before annealing) . Comparing the thickness measurements of DAD87 sample before and after annealing, the thickness is reduced around 30 % after annealing, which might sugg est density change /sintering effect which is influencing the resistivity. This is applicable to the Heraeus sample as well but to a much smaller extent (45 - 50% decrease) . The silver nickel sheet resistivity increases after annealing and is in range of · · cm This might be due to scale formation after oxidization of the sample at high temperature. However, the strength and adhesion of the Ag - Ni sample improves significantly after annealing/ sintering . The Ag - Ni circuit pastes show better adhesion to the substrate than the Heraeus and the DAD87 sample. The contact · cm 2 at room · cm 2 - magnetic paramagnetic 68 transition temperature) , it starts to reduce as the temperature increases and reaches a value of · cm 2 silver nickel samples · cm 2 . The resistivity decreased further thereafter and reached a lowest value · cm 2 This differen both Herae u s and silver nickel inks. According to H. Schmidt, after taking into account the total electric losses in the SOFC the contact resistance in the symmetrical test configuration should not exceed 20 000 µ · cm 2 [54] . The contact resistivity measured for the silver nickel samples is well below this value. Genzhi Hu and Jason Nicholas carried out the tensile tests on 3 types of inks. The tensile test results using this method showed that the oxidized silver nickel samples showed the most strength among the 3 samples. The Heraeus and the DAD87 had significantly lower strength compared to the silver nickel samples . The current collecting layer improves the overall electrical contact which minimizes the losses in the cell [15] . The oxidation of the nickel content does not increase the contact resistivity significantly but improves the overall electrical contact which leads to superior SOFC performance. The next step of the project would be to test the density of the sample before and after annealing. The error occurring in the measurement system could be calculated more efficiently by determining the density of the sample. A stainless - steel reference sample following the NIST 69 standard would allow us to calculate the error percentage with improved precision . 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