A Novel Method for Direct Solder Bump Pull Testing Using Lead-Free Solders

This thesis focuses on the design, fabrication, and evaluation of a new method for testing the adhesion strength of lead-free solders, named the Isotraction Bump Pull method (IBP). In order to develop a direct solder joint-strength testing method that did not require customization for different solder types, bump sizes, specific equipment, or trial-and-error, a combination of two widely used and accepted standards was created. First, solder bumps were made from three types of lead free solder were generated on untreated copper PCB substrates using an in-house fabricated solder bump-on-demand generator, Following this, the newly developed method made use of a polymer epoxy to encapsulate the solder bumps that could then be tested under tension using a high precision universal vertical load machine. The tests produced repeatable and predictable results for each of the three alloys tested that were in agreement with the relative behavior of the same alloys using other testing methods in the literature. The median peak stress at failure for the three solders tested were 2020.52 psi, 940.57 psi, and 2781.0 psi, and were within one standard deviation of the of all data collected for each solder. The assumptions in this work that brittle fracture occurred through the Intermetallic Compound layer (IMC) were validated with the use of Energy-Dispersive X-Ray Spectrometry and high magnification of the fractured surface of both newly exposed sides of the test specimens. Following this, an examination of the process to apply the results from the tensile tests into standard material science equations for the fracture of the systems


Introduction to a New
, (B) Hot Bump Pull [45], (C) Cold Bump Pull [45] .       [1] Unlike in welding, where similar alloys are joined together using a filler material with similar structural and thermal properties, soldering can join together similar or dissimilar alloys with a filler material with a lower melting temperature alloy. This means that in soldering, only the filler reaches a molten state, whereas in welding all objects present will be molten at one point during the process. This process creates both a mechanical bond between the objects, as well as a chemical one. The chemical bond is composed of Intermetallic compound (IMC), which is a brittle alloy of the solder and the objects it is connecting. Figure 2 depicts a comparison of soldering versus welding. To clarify, soldering is the same process as brazing. However, it occurs at lower temperature ranges, with a molten filler metal temperature cutoff for soldering up to 450°C, while brazing has a cutoff temperature above 450°C. Unlike in welding, where the weld is often stronger than the material around it, solder joints are often the point of failure in these systems. In years past, tin-lead alloys were used to solder electrical components together.
These alloys were desirable due to their high electrical conductivity, low melting temperature, high availability and relatively low costs. The lead helped to stabilize the tin and reduce the chance of the spontaneous formation of tin whiskers, which form beneath the surface of the solidified tin and can extend far beyond the intended connection, creating electrical shorts that can cause a system to fail.
However, health concerns arose from the issues surrounding the use and disposal of heavy metals such as lead. Thus, after the passing of the Lead Exposure Reduction Act in 1993 in the U.S., and the European Union's ban of lead in electronics becoming law in 2003, and going into effect in 2006, there has been a large push in industry to find suitable alternatives for tin-lead solders.
To-date, legislation has yet to be passed regarding the sale or production of consumer electronics containing lead in many of other major global economic powers, such as in the U.S., Japan, and China. Despite this however, many organizations, including Samsung, Apple, Google, and JEDEC (Joint Electron Device Engineering Council) have made efforts to move towards reducing or eliminating lead from the products and technologies they produce, support, or recommend.
To examine one aspect of the impact of this change, refer to the sales growth rate in the electronics industry of 3% in 2013 and the projected growth rates of 5% and 6% in 2014 and 2015 [2]. This, coupled with the positive trends in global sales growth rates in years past, give strong support to the projection that production and sales growth will continue. Due to the international nature of many of the products in the electronics industry, such as smartphones, televisions, digital media players and even automotive control systems, the option to have a lead-free zone surrounding the EU would not be economically feasible as it would create two separate marketplaces. This means that the discussion of the benefits of lead-free solder is no longer merely of academic or environmental interest, but also economical. Global smartphone sales alone, with more than 680 million units sold in 2012, experienced a one year growth rate exceeding 40% with more than 960 million units sold in 2013 [3]. In much the same way as California vehicular legislation can regulate national behavior due to automotive suppliers wishing to sell cars which are "50 State legal", so too has the EU legislation impacted the global electronics industry.
For this reason, extensive studies on the material properties of lead-free solders and fluxes have been performed [4][5][6][7][8][9][10][11]. These studies have a focused interest on ever smaller systems due to their reduced packaging size, the materials needed and general mobility. This market-pull for pocket-sized devices has made surface mount technology a major source of development and growth in the electronics industry [11][12][13][14][15][16][17]. As such, the need then for further understanding of this technology in an applied manor is deepened.
The study of solder for surface mount systems (SMDs) from a structural [11,18] or even material science [19] perspective is not a novel concept. Developing this further, in recent years there has been significant research looking into the concepts of grain development [8], crack growth and fracturing of solder [14,[19][20][21][22]. This work has made it possible for the development of numerous industry standards and best practice methods to become available [21,22].
It is the purpose of the current work described in this thesis, to experimentally study three lead-free soldering alternatives and compare those results to the material's microscopic structure to create a mathematical model which could aid future scientists and engineers in the selection of lead-free soldering alternatives in the future.

REVIEW OF LITERATURE
In the world of electronics, solder serves a fundamental role connecting electronic components together. Forming both a structural and electrical connection between integrated circuits (ICs), printed circuit boards (PCBs), capacitors, resistors, and more, solder connects the various components that make up the hardware within such everyday devices as desktop and laptop computers, cell phones, wearables, watches and more. Soldering, shown in Figure 3, is the act of connecting metal objects together through the use of a filler metal. This process is accomplished in the same way as brazing, in which a filler metal with a lower melting temperature than the objects it is intended to connect is heated until it becomes a liquid. It is then applied at the junction of the other objects and allowed to cool. Common methods of soldering include through hole, surface mount, and wiring connections, and can be applied through various methods, such as wave soldering, pastes, drop deposition, and the classic use of an iron and solder wire. Soldering, like brazing, forms both a mechanical and chemical connection between the filler and non-melted metals. At the interface, the filler wets the other objects and an alloy layer is formed; this Intermetallic Compound, or IMC, as it is often referred to, shown in Figure 4, is a stoichiometric phase composed of the solder and the substrate to which it is connected [6]. IMCs are normally composed of covalently bonded atoms, are brittle and have a higher melting temperature than the solder which was used to form them. This is part of the reason why a discoloration is often left behind on the surface of a substrate after solder has been removed. Figure 4: IMC of solder and copper substrate (a) Sn-3.5Ag and (b) Sn-3.5Ag-0.3Cu [23] As lead-free solders gain a dominant market share over leaded solders worldwide due to environmental concerns and legislation, the need to create, test, and validate the properties of these new solder alloys has also risen. The requirements of lead-free solders are much the same as traditional leaded solders; they must have similar melting temperatures, strength and durability, ductility, thermal fatigue resistance, electrical resistance, should use the same manufacturing processes wherever possible, and allow for the continued miniaturization of the electronics industry. Other key variables, such as the operating constraints for the substrate materials used as a support structure for these devices, the operating temperature of the circuitry, the properties of the electronic components, and the solder material costs play large roles in solder selection as well.
In 1994 classify what one should look for in leaded solder replacements [6]. By looking at the key factors of the physical metallurgy, mechanical properties and oxidation and corrosion behavior, the work shed light onto some of the key factors that would be of great interest in future studies. At the time, lead had yet to be banned from use in electronic devices, but was no longer allowed in plumbing construction in many countries, and it was widely believed that similar legislation could pass as a blanket standard within these countries in the future. Thus, some lead-free solders were already in use, but only in a select few industries and the research into lead-free alternatives was limited. This early review of the key factors in selecting, developing and using lead-free solders highlights many of the criteria that would be tested in the twenty years that have followed.
Following this, extensive research has been performed into the optimum levels of other metals within the tin-based alloy mixtures of lead-free solders as well as investigating ways of optimizing and testing such properties as the IMC composition, size and wettability of assorted solders on varying substrates [4-11, 20, 24 -27].
Simultaneously to the work developing different compositions for solder alloys, much research has been done to test the wetting behavior of these new materials on assorted substrates, with a focus on the contact angle and formation of the IMC and comparing these results to those of leaded solders [24,[26][27][28][29][30][31][32]. The wettability of solder is the ease at which molten solder will form a connection to the substrate it is coming into contact with by dissolving a small layer of the substrate to create an IMC.
In solders, this behavior is often monitored by measuring the contact angle of cured solder on a substrate after the sample has been bisected and examined under a microscope. It can also be done using photos of the profile of a drop of any fluid, or a solidified solder bump on a substrate. This wetting process can be aided by using higher temperatures, with clean and non-oxidized substrates. Figure 5 depicts the process to measure the contact angle of a solidified solder bump. industry. There are, however, numerous possible issues that may arise from the use of tin, and the mitigation of these issues has also been studied at length [4][5][6][7][8][9][10][11].
Previously, lead could be used to help hinder some of these concerns, like the formation of tin whiskers or tin pest. However other elements would instead be needed to be used to help mitigate these issues in new solder alloys.
It is also important that one recognizes the reason why lead was used in the soldering process at all, due to the fact that its dangers have been well-known for decades. Lead, like tin, is abundant, inexpensive, has a low melting temperature and bonds well to other metals. There was also the possibility to create a eutectic mixture of tin and lead with desirable characteristics. The eutectic mixture is composed of 63% tin, 37% lead, and was one of the many common solders used by numerous industries to make connections. Eutectic alloys are mixtures of elements which have a homogeneous bulk that solidifies all molten content at the same time and temperature and have the lowest melting point for the alloy for any other ratio [25]. This eutectic behavior, in combination with higher cooling rates and low melting temperature, leads to smaller, more uniform grain structures and helps to mitigate the formation of dendrites within the cooled bulk. Ratios with higher lead content, such as 50/50 mixtures were also commonly used. A phase diagram is shown in Figure 6, and can be used to identify the solubility of one element in another as well as the behavior of the alloy through a range of temperatures from a solid to molten state. In non-eutectic structures, large dendrites resembling fern branches of the phase which has solidified first will be formed. Not only can these dendrites pose a risk as locations of possible weakness within the solder, but they can also create deficits of the element surrounding itself. In other words, a lead-rich dendrite would be surrounded by lead poor material after cooling. It is the goal of many lead-free solders which are used to replace leaded solders in a one-to-one fashion that they behave in such a manner as 63/37 ratio solder. Figure 6: Phase diagram of tin-lead solder [33] The formation of tin whiskers, shown in Figure 7, is the phenomenon in which thin, single crystal structures of pure tin spontaneously grow from the surface of solidified tin. These whiskers have been found to cause tremendous damage to essential electronics in many devices by causing shorts between connections and can grow in all open directions from the solidified tin [34,35].

Figure 7:
Example of Tin Whiskers [34] Another major issue to mitigate while using tin, called tin pest, shown in Figure   8, takes place over time with a solid tin specimen, and is the process in which a decay of tin will occur at low temperatures. This degradation is a transformation of tin from beta form to white alpha form tin, were the solidified body will break down to a powder and could lead to eventual voids in the electronics, and ultimately mechanical failure [36]. One should note however, that tin pest is not the same as electromigration, where material in a conductor will change location due to the movements of ions caused by the flowing electrons within the body.  [36] In addition to generating increasingly complex alloys to achieve desirable solder behaviors like those discussed above, additional processes and elements have been added to substrates and components to achieve superior bonding [24,28,38].
Numerous studies have taken place to observe the reaction between assorted lead-free solders and different surface treatments [24,28,38]. Within these studies, the IMC, wetting behavior, mechanical strength, and other important bond criteria have been studied extensively. It is of special note, that these extra processes do not positively impact the soldering process in all ways. Black pad, for example, can occur when an Electroless Nickel/Immersion Gold (ENIG) coating is applied to the substrate [39][40][41].
ENIG coatings are applied to substrates to help mitigate the oxidation of the copper contacts, aid in the boding of aluminum wires, give a more uniform surface for soldered connections and have desirable wear characteristics. Black pad has a black appearance where the nickel has corroded, as can be seen in Figure 9, and is present at locations of weakness in the connection. This corrosion decreases the solderability of the joint and will often cause failures in use when the connection experiences stresses from thermal or mechanical changes. Figure 9: Example of black pad [31] Through the work of the above mentioned studies, industry suppliers and developers, numerous lead-free solder alternatives have been developed [38]. These solders are in turn, tested through a number of well described physical and simulated  [16,19,20].
The focus of many of these studies pertains to testing the accuracy of the results against experimental data to make recommendations to future users. This enables other researchers to create detailed simulations of some of the more recent advances in microelectronics packaging, like flip-chip assembly, shown in Figure 10. and melted on each contact while the IC is upside down and is separated by a small air gap. The solder volumes are often referred to as bumps, and can be applied through wave soldering, using pastes, or direct placement. The IC is then placed right side up onto the contacts of the PCB and heat is applied to liquefy the solder at the points of contact. This process is referred to as reflowing, and normally takes place in highly controlled ovens. One can then recognize the importance of the works mentioned above in simulating these assemblies, as the numerous contacts and surface area create a significantly more complex structure to simulate. Of note within these works is Darveaux's work to improve modeling of the initiations of cracks within solder, as well as the growth of cracks within solder once they form; Liu and Madeni's work towards discerning the fundamental properties of solders under normal usage conditions and Tamin's simulations of twisting forces on solder connections [16,18,19]. Darveaux's work in particular, is often referenced by other researchers.
The different behaviors and properties of lead-free solders under numerous thermal conditions have also been extensively experimentally studied [4,7,27,28,42]. Due to the fact that the operating temperature of many electronics can frequently be in excess of 60 degrees Celsius, which is above half the melting point of many of the solders used to hold them together, thermal issues causing creep, microstructure recrystallization, changes in plasticity and more can become significant problems [25].
This is clear when examining the ways in which solder fails, where failure in real world applications is often led by the formation of cracks [18,43]. It is because of this that it was also important to develop a phase diagram of Sn-Ag-Cu and other lead-free alloys replacing the well studied tin-lead solders in order to be able to predict the behavior of the new solder as their temperatures changed [7]. Additionally, there has also been work done using thermal cycling of the components, which allows for accelerated aging of solders to test their long-term properties. This accelerated aging, along with studies into the inconsistencies in thermal expansion between alloys and substrates, allows for a better understanding of the temperature driven creep and failure, mentioned above [25,27].
It is also necessary to describe some of the major changes that occur during solder aging under different thermal conditions, such as those described by . It is possible during the reflowing process or at the higher working temperatures of these alloys that the interior structure can change and that the physical properties of the material can be altered with age [44]. As the solder is heated to high temperatures, recrystallization can occur, wherein new grains will nucleate and grow, and will take the place of the smaller, disconnected grains. This leads to an increase in ductility of the material, but at a loss of strength and the hardness associated with it, and can be detrimental to the solder's performance later [44]. Additionally, the size of the IMC can grow during this period as well as during normal operations, as shown in Figure 11, and can take on a thickness similar to the IMC formed by other alloys. The growth of the IMC can also pose an issue to the strength of the connection, as it is traditionally more brittle than the metal that surrounds it and thus larger IMC layers can lead to a greater possible number of crack nucleation sites. Nishikawa found that the growth of the IMC is not limitless, however, and will peak after enough time has passed [44].
As electronics have become smaller, so too have the solder connections that bind them. The use of Ball Grid Arrays (BGAs) can help to accommodate this.
However, it is of great interest to many researchers to what limit this reduction is due, based on the reduced contact size causing a reduction in overall robustness of the system [14]. This decrease in size can also yield higher current densities, returning then, to the possible problem of electromigration mentioned above. One must then also anticipate changes to experimental results of these smaller systems based upon the age of the solder connections [23,42,44]. An example method of accelerated aging being used to test solder was performed by , where the solder is aged at higher temperatures in oil baths to create simulated older joints for testing. Other researchers have also used dry ovens to achieve similar results [44].
These tests are then often performed shortly after the solder has originally been placed, as well as throughout the simulated lifetime of the connection.
Building on the types of equipment usage expected of soldered connects, it is also important to experimentally study the behavior of solders under impact loading conditions. This is due to the fact that many electronics have the possibility of experiencing multiple impacts throughout their usage lifetime and this is one of the leading causes of failure of hand-held electronic devices [15]. To simulate this type of abuse, ball shear and impact tests have been developed [15,42]. These tests can be either direct solder shearing tests, or an impact to the components or devices. In   [15] Ou et al. used the justification for this test stating that solder ball shearing and pulling tests could not easily reproduce the jolt caused in accidental dropping of a device. One key conclusion from this work would at first appear counter to others: the impact toughness of the solders increased with age. This is then explained due to the softening of the solder over time and the increased size of the IMC, allowing the solder bumps to perform better than when they were first formed.
In addition to simulating the varying real-world usages of soldered connections between multiple components, as the tests performed using drop-impact assemblies do, it is also important to fully understand the strength and behavior of the solder joint connections under applied load conditions without additional components attached.
For this, numerous pull tests have been developed. However this work will focus mainly on the Hot Bump and Cold Bump Pull tests, (HBP, CBP), where solder bumps that have been connected to a substrate are pulled off vertically from the substrate.
These testing methods have been widely used with a large number of solder and substrate materials [11, 22, 23 37, 44, 45]. The HBP, shown in Figure 13 , is a method in which a hot pin is forced into the solidified solder bulk, causing the solder to become molten at the point of contact, the system is then allowed to cool, and finally the pin is pulled upward, causing the soldered connection to break away from the substrate. Figure 13: Hot Bump Pull (HBP) testing diagram [45] While this testing method has been found to be effective, there are concerns with its accuracy [45,44]. The main reasons for this are the recrystallization that occurs within the solder when the pin is applied, possible changes to the chemical composition of the solder from molecular exchange with the pin, and the formation of the IMC between the pin and the solder. It is also extremely important to clarify the anticipated results of these pull-off tests; using the work of Darveax and others, Zaal states that it should be possible to create one hundred percent brittle failure of the solder. This is due to the condition, where under lower strain rates the solder will fail in a ductile manor in the bulk of the body, but under high rates of strain the junction will fail in a brittle manor at the IMC. An example of this transition of the tensile strength and failure modes can be seen in Figure 14. Figure 14: Solder tensile strength and ductility changing with strain rates [20] In their study, Zaal et al. and others have sought to validate the results of their work by demonstrating that the solder bumps would fail in a ductile manner when pulled at lower strain rates, and would fail in a brittle manner at the IMC with higher strain rates. To do so, values for the system extension rates were used based on the JEDEC standard, which is self-described to be a 'low speed testing procedure', with values up to 0.3 millimeters per second. Thus by beginning with a low extension rate and increasing towards the 0.3 millimeters per second limit, these studies were able to transition from ductile failure of the solder bulk to failure of the IMC. In this way, it was stated that a bias in the testing procedure could be identified, and if a solder bump could fail both in a ductile and brittle manner, that the test itself was not impacting the mode of failure. Examples of the differences between these two failure modes are shown in Figure 15. Figure 15: Examples of ductile and brittle solder failures [22] To avoid many of the complications caused from using HBP, many researchers have instead opted to use the Cold Bump Pull (CBP) method, as shown in Figure 16. In the CBP method the solder bump is instead gripped by a mechanical tweezing system, squeezed to achieve a mechanical grip, and then forcibly removed.
This method has also been used extensively with relatively consistent results [20,23,45].  [45] One of the key issues with the CBP testing method however, as discussed by , is that a number of other variables arise from the use of tweezers to test solder [20]. The added variables pertain to the application of force from the tweezers. The closing speed, pressure, jaw size, and jaw height relative to the PCB and center of the solder all pose significant challenges in achieving reliable and repeatable results. Both Zaal and Gerbracht discuss this method at length, however the JEDEC B115A standard which is used to control these tests is relatively limited in these regards [13,20,21]. Zaal then performed a number of experiments to determine the effect of jaw closing speeds, pressures and biases caused from the use of this system.
As Figure 17 illustrates, the application of the tweezers causes a distortion of the solder bump in order to achieve a mechanical grip of the solder. This distortion, driven by the closing of the jaws, can happen at speeds exceeding 25 ms closing time and can cause strain rates of 10 -1 s [20]. Figure 17: Distortion of solder bump due to jaw closing for CBP testing [20] As mentioned earlier, the distortion of the solder bump can create cracks within the solder, which can then cause the solder to bias brittle failure during testing. to compare testing methods using various solder alloys [4-11, 13, 15, 16, 19, 20]. One of the main issues with these current testing methods is the need for specific manufacturers' equipment or a large number of test-specific independent variables.
These independent variables include, but are not limited to, the physical properties of the tweezers or hot metal pin, or other test-specific peripheral equipment being used, and must first be addressed before testing and analysis of the solders can begin. It was the goal of this research to produce a direct solder joint-strength testing method that does not require customization for different solder types, does not create a bias towards a specific failure mode due to the method of testing, requires no brandspecific machinery, requires no specific preparation of the PCB surface, and works to eliminate the variables produced in other testing methods that one must first "optimize" through trial-and-error before beginning testing.
In order to accomplish this goal, an examination of the current testing methods and standards was conducted in the literature review. These include such methods as shearing tests, the Hot Bump Pull (HBP) and Cold Bump Pull (CBP) methods, as well as indirect tensile methods like the JEITA EIAJ ED-4701, all shown in Figure 18. Examining these current testing methods led to the generation of a list of variables that each method would need to establish as a baseline before the results of one research group with a given alloy could be compared to the results for different alloys from other research groups. For the HBP method, for example, these variables include the pin size, composition, temperature and depth-of-pin penetration; for the CBP method one must consider jaw size, clamping speed, force and depth, jaw height and pulling speed. It was the aim of the research described in this work to combine the processes of these various testing methods to eliminate all trial-and-error, as well as to remove the failure mode bias that many testing methods can produce when performed incorrectly [20,21].
In order to achieve these aims, a combination of the Hot Bump Pull and Cold Bump Pull methods was developed. This new method, illustrated in Figure 19, uses an external solder gripping system which was inspired by the CBP method, but in place of using stiff mechanical jaws to deform the bottom curvature of the solder bumps to achieve a mechanical grip upon application of an upward force, grip on the bump is achieved by surrounding the bump with a stiff epoxy, creating a uniform traction. The epoxy envelopes the entire bottom curvature of the bump without causing any plastic deformation to the sample prior to testing. A load is then applied through a pin located above the solder bump as one would find with the HBP. To achieve this, a stainless steel screw is inserted head first into the epoxy directly above the solder bump during the epoxy curing process to function as the pin. Once the system has cured, the screw is installed in a tensile loading machine and is pulled away from the PCB upon which the solder is connected. The tension applied to the stainless steel screw is transferred into the epoxy, which then applies uniform tractions to the entire solder bump. with a hot pin via the HBP method. In order to use this new IBP method, the following steps were taken: solder joints were made on untreated pieces of PCB that were as delivered from the manufacturer, the solder was encapsulated using the casting method mentioned above, then the samples underwent tensile loading, where the applied load and extension were monitored and recorded. Following this, the results from these tensile tests were analyzed, and lastly, a group of untested samples were cut in half and examined using optical microscopy to observe the internal structure of the bumps. This final step allowed for an examination of the alloy grain structure, the grain boundary curvatures within the bump, and the evaluation of the IMC layer, which was formed between the alloy and PCB substrate surface. This is a key advantage of the testing method, as the IBP does not cause deformation or recrystallization of the solder bump prior to testing, unlike the HBP and CBP methods.
The primary advantage that the IBP process yields is therefore a more accurate representation of the bump microstructure precisely as it was created and tested.
Conversely, the CBP and HBP methods require microscopy after bump generation, as well as after the test-specific processes were conducted, to gain a full understanding of the bump characteristics prior to, and during testing. Additionally, the IBP method does not cause a change in the bumps between the stages of generation and testing that could yield a bias in the tests. Examples of these biases in other popular testing methods are the micro-cracks which can form within the bump during CBP prior to testing, creating a bias towards brittle failure before testing begins, and with the system recrystallization and the generation of a second IMC layer that must be formed, and acts as a site of failure in the HBP method.

Development of the Isotraction Bump Pull (IBP) Solder Testing Method
Once the concept for a new testing method had been identified, it was important to determine the number of variables present, and thus the appropriate number of experiments that must be performed to determine the behavior of the test itself, as well as various lead-free solders that could be examined using this method. To do this analysis, the Buckingham Pi Theorem was used [46]. This is a method that creates dimensionless groups of the variables of a system that allow for comparison and evaluation of changing variables and their relative importance in affecting an outcome.
Five key parameters were identified for these experiments and are listed in Table 1 as either a variable, controlled variable or fixed parameter. These parameters are then combined into dimensionless groups based on the base units that they contain. For this study the base units of F, L and t were used for force, length and time, respectively.
These base units are generic units, and take the place of more specific terms, thus acceleration written as ft/s 2 or m/s 2 would both be distilled into L/t 2 . In order to determine the number of Pi groups to derive from this list, the following equation is used:

Equation 1
Where p is the number of dimensionless groups, n is the number of dimensional parameters, and k is the number of physical dimensions, force (F), length (L) and time (t). Given as there are five parameters and three physical dimensions for the pull-off tests, there are then two Pi groups that are formed, shown below. In addition to the dimensionless groups formed above for the tensile experiments, the same process was conducted for the interior structure of the solder bumps which was to be evaluated in parallel with the tensile testing.

Solder Bump Generation
While many possible methods for the generation of solder bumps exist, for instance the use of solder pastes and resists, hand soldering, soldering masks and large scale industrial soldering methods; a solder bump-on-demand generator was used for this work. The system was fabricated based on the designs of numerous researchers, such as Amirzadeh, Cheng, Chandra, Jivraj and Li, with slight alterations [47][48][49][50][51]. At its core, the system uses the application of positive pressure pulses of nitrogen gas to drive small volumes of molten material from a crucible onto a substrate positioned below. A photo of this system can be seen in Figure 20: Desktop Solder Bump-On-Demand Generator Setup. One of the key advantages of this method over the others mentioned above is that it allows for a higher degree of accuracy than hand-soldering, but does not require the same level of peripheral equipment that other large scale methods do. For example, the crucible used for this work was found to produce samples with an accuracy of + 20 mg, or 13% of the 150 mg average mass, but was self-contained and required no large-scale industrial equipment to operate.  In addition to the main body and bottom plate, a second circular plate was attached at the top of the crucible main body and a brass quarter-inch plumbing tfitting was attached to a through-hole in the center. This t-fitting was used to supply nitrogen gas into the cavity of the crucible above the molten alloy and create high pressure pulses inside the system, as well as to allow for the gas to be subsequently vented after each bump had been generated. Once the system had been assembled, the crucible was encased in a six-inch ring of mineral wool insulation inside a steel shell and heated to a temperature of 340 °C using cartridge heaters (McMaster Carr, Part# 3618K403), a K-type thermocouple (McMaster Carr, Part# 9251T93) on the exterior surface of the crucible wall and a temperature controller (Omron, E5EC, Japan). An on/off control sequence was used for this control, and allowed the temperature of the crucible to fluctuate by + 5°C. The body of the crucible was supported on a steel plate, which was in turn supported by a set of four threaded rods and could be leveled above the surface which held the PCB substrate.
The process under which solder bumps were generated is shown in Figure 22.
Under normal operating conditions, the solder was held in place in the body of the crucible due to capillary action. When a signal was sent from the control system, a pulse of nitrogen gas entered the crucible; this increased pressure would cause a small volume of the molten solder to descend through a 0.04'' diameter hole in the sapphire nozzle, down and away from the main body of the solder towards the PCB substrate positioned below the system. The nitrogen was then vented from the top of the system into the environment. In Figure 22, panels c and d, this venting would then cause a pressure drop inside the crucible and the main volume of the descending solder to return towards the bulk. During this return process, a small volume of the solder would destabilize from the returning volume and fall away, assuming a nearly spherical form. This volume of molten solder then impacted the PCB below the crucible and a solder-PCB contact joint was formed.  Additionally, the substrate that was used in this study was a commonly used and available material referred to as FR-4 PBC (McMaster Carr, Part# 8521K35), composed of a multilayer fiberglass wafer with a single copper foil top surface. The substrate pieces were cut into one-inch by one-inch squares using a sheet metal shear, and were used as-manufactured. There was no cleaning process, deoxidizing or fluxing process used, and each substrate piece was processed by hand. To ensure proper soldering, the substrates were placed onto a hotplate (Fisher Scientific Isotemp, Pittsburg, PA) at a temperature of 200°C directly before testing, at a distance one-half inch below the crucible nozzle. During this process, the substrate pieces would reach a temperature of approximately 180°C before the solder impacted them.

Solder Bump-Epoxy Encapsulation
Once the solder bump samples were generated, they were encapsulated in a steel reinforced epoxy (JB Weld, Sulphur Springs, TX). This was accomplished using two custom-made casting mold assemblies, shown in Figures 24 and 25, composed of aluminum centering base plates, split Teflon (PTFE) molding cups, PVC support washers, aluminum lower pressure plates and a top pressure plate. Each casting mold assembly was capable of producing six samples at a time, thus twelve samples could be produced simultaneously with the two assemblies. Teflon was selected for the mold forms due to its long chain non-polar molecular structure, to which the epoxy will not readily bond [54]. Additionally, to ensure that the epoxy did not bond to the copper-faced PCB, a Teflon spray was applied to the surface of the PCB after the bump had been deposited. This was done using a thin applicator dipped into the Teflon spray and did not come into contact with the solder bump. The split casting molds were fabricated in-house from a one-inch outer diameter and half inch inner diameter Teflon tubing. Twelve total one-inch tall molds were produced, which were subsequently cut in half vertically; this allowed for the mold to be split apart and removed easily after the epoxy had cured.
To create the pull-off samples, the solder samples were held in place using an aluminum base plate with milled reliefs for one inch squares of the PCB. The Teflon molds were then placed surrounding each sample, and two PVC washer plates were used to hold the molds in place. Epoxy was piped into each mold prior to the attachment of a top plate, through the use of a heavy duty plastic food storage bag, similar to an icing bag. Lastly, the systems were placed under compression using twoinch long stainless steel screws passing through the aluminum base plates up through polycarbonate top plates. In addition to the six holes used to clamp them in place, these top plates had holes drilled at the corresponding centers of each of the six molds for that assembly, and allowed for the stainless steel screws that functioned as the pulloff pins to be passed through them and held in place during the curing process.
Additionally, the top plates were used to ensure that the Teflon molds were held closed during the curing process. The top plate was then bolted into place and the epoxy was allowed to cure for eighteen hours, per the epoxy manufacturer's recommendation.
Once the epoxy had fully cured, the molds were disassembled and the samples removed. Flashing from the epoxy at the seam of the Teflon molds was removed and all samples were subsequently labeled using the format: Alloy-Production Run, Mold, Position. As there were three lead-free solder alloys tested, SnAg, SAC 305 and SnCu, and an example of this notation would be SnAg 216. All of the SnCu samples that were tested in this study can be seen in Figure 26. This system was used to ensure that in addition to the ability to gather bulk information on the performance of a given alloy in this test, that one could ensure that the solder bump-epoxy assembly fabrication process produced consistent results in each of the twelve production locations and that no bias was being created in the tests due to fabrication errors.

Introduction to Tensile Testing with the IBP Method
Once the lead-free solder samples had been produced and encapsulated in epoxy, they could then undergo tensile testing. This was done using an Instron 3345 Single Column universal testing machine. However, any high-accuracy tensile testing system could be used. Due to the IBP method functioning as a hybrid of the HBP and CBP solder testing methods, it was a goal of this study to develop a method that could conform to the mechanical limitations of the machines used for these tests, thus the tests were performed at a constant displacement rate of 0.3 mm/s, per the recommendations of the CBP method.

Tensile Testing of IBP Samples
In order to apply load to the samples tested in this study, custom load fixtures  The bottom of the system was fixed in place on the Instron machine and the top fixture was pulled upwards during testing. In order to accomplish this, the stainless steel screw embedded in the epoxy was threaded into the top fixture. The top assembly was then lowered into position with the bottom fixture and a square steel plate, referred to as the top plate was bolted into place on the bottom plate, which was in turn fixed to the bottom of the Instron. A hole was drilled into the center of the top plate which allowed for the epoxy to pass through it, but held the PCB in place while the stainless steel screw was pulled upwards during testing.
To perform these tests, each sample was individually loaded into the fixture system, then positioned and clamped in place. The results were monitored using the Instron Merlin computer software (Instron, Norwood, MA), and the system displacement and load were monitored and recorded for future analysis. Twenty-four samples of both SnAg and SnCu were tested in this manor, as well as thirty-six SAC 305 samples. The reason for the sample size increase for SAC 305 was due to difficulty in achieving consistent results, and so additional tests were conducted to produce a larger set of viable data. Once each lead-free solder alloy had been tested, the results were then imported individually into a Microsoft Excel file, and then processed simultaneously with a custom MATLAB (Mathworks, Inc., Natick, MA) script. In addition to interpretation and comparison of the pull-off test data, this script was used to calculate the Young's Modulus of the alloys, ensure that unsuccessful tests were identified, and was used for the statistical analysis that followed. An additional MATLAB script was created to determine the area of the IMC of each sample after testing and was used to convert the measured loads on the system in pound force to the stress values of lb f /in 2 , knowing the areas.

Accuracy of the Load Results at Low Loads
The Instron 3345 used in this study is rated to have a load accuracy of + 0.5% down to one-one hundredth of the load cell capacity. For these experiments a 5000 newton (N) load cell was used, which would then hold that level of accuracy above a value of 50N, or 11.24 lb f . Due to the process of the experiments in which load was increased through the specimen from a beginning value of zero through the critical load of the solder-PCB contact joints, it was then important to determine the accuracy of the Instron at low loads with the custom jaw setup used. This was accomplished using the setup shown in Figure 28. The results of these tests showed that at loads less than 1 lb f with the fixture system used for the entire study, that the error ranged from 0.7% to 0.9 %, and was in excess of the 0.5%, but for loads above 1.1 lb f the errors of the results from the Instron machine were less than the 0.5% rating. Due to this behavior, the results from the experiments that follow do not use loads of less than 1.1 lb f for the statistical analysis performed in Chapter 4.
In addition to this evaluation of the load cell accuracy, if the results of raw data are considered, one can see in Figure 29 that at lower loads the system produces data which can be considered to be inaccurate. During standard testing, there is a period of time in which the system is allowed to ascend freely. This is made possible by the oversized gap between the two steel plates that are used to hold the PCB in place during testing and was necessary to the assembly to ensure that the system was not under tension prior to the controlled start of the experiment. After the experiment had started and the PCB ascended and eventually made contact, the load perceived by the load cell underwent a sudden rise, despite experiencing a constant system displacement rate. After the completion of this low load evaluation study, values that were below the threshold of 1.1 lb f were removed to normalize the data and remove the variance of distance covered before each individual PCB made contact with the top plate. The displacement for all systems was then normalized at a value of zero when each system rose above the 1.1 lb f threshold.

Identification of Different Result Types
There were two types of test results from the pull-off process described above: unsuccessful tests due to epoxy-solder interface failure and successful pull-off tests.
These two types of test results can be easily identified from their plots or physical differences, shown in Figure 30, where the data in blue is a SnAg solder bump that experienced a failure of the epoxy-solder interface, and the green line represents a successful test of a SnCu sample.  The distinction between these results can be described as the following: unsuccessful tests were those in which the epoxy has failed due to plastic deformation at the epoxy-solder interface during testing and the bumps were not removed from the PCB as a result. The successful tests were all of those in which the bumps separated from the PCB with a brittle failure of the IMC. Due to the relatively high speed at which these tests were performed, per the CBP method guidelines, there were no ductile failures of the solder bumps. These types of tests would have resulted in failure of the solder bulk during testing, rather than a failure of the IMC.

Identification of the Intermetallic Compound (IMC) Area
Upon the completion of the pull-off tensile tests, the tensile loads in pound-force applied to all samples were converted to stress values of pound-force per square-inch, or psi based on the area of the contact. This was done to allow for comparisons to solder alloy data from other sources using conventional pull-off testing methods, as well as to allow for a normalization of the results for all solder bumps tested in this study. This was done by using the cross-sectional area of the IMC layer, through which all loads were applied and where fracture occurred. Figure 32 shows the newly exposed faces created by the fracture of the sample, as an example of a solder bump post-tensile test. In order to accurately analyze the size of the IMC for each solder bump tested, a single photo of the full grouping of PCB squares was taken for each alloy. These photos, like the one shown in Figure 33, captured each square with the same scale.
Following this, each PCB square was isolated and analyzed in MATLAB using a custom image processing script. In order to analyze the size of each IMC area, the photos of each sample's PCB were processed individually. Shown in Figure 34, each PCB square was converted to a grey-scale image, and the contrast was increased to make identification of the IMC from the copper substrate easier for the program to distinguish. The image was converted to black and white, and the "islands" inside the IMC area were removed and the centroid of the IMC was identified with a red dot. Once these steps had been taken, the size of the IMC was stored by the program as a number of pixels. This pixel count was then converted to a square area using the scale in the original PCB grouping image and a final area in square inches was calculated. While it would have been possible to assess the size of the IMCs using the bottom face of the solder bumps, the high level of contrast of the IMC and copper substrate yielded a more repeatable process than using the solder face. The calculated area of each sample's IMC was then used to calculate the stress each system was exposed to during testing from the measured forces.

Optical Microscopy
In addition to the tensile tests performed on the solder bump samples, five samples of each alloy were also examined using optical microcopy. This was accomplished through the use of a diamond embedded wafering blade on a low-speed specimen saw (Buehler 11-1180, Road Lake Bluff, Illinois) to vertically cut the specimens in half. Once the samples were bisected, they were mounted into clear epoxy pucks, like the one shown in Figure 35, and polished to remove the tooling marks from the bisection process. This was accomplished using a rotary polishing wheel and a wet sanding process with a progression from 400 grit sanding paper to 1200 grit paper, then 3.0 μm and finally 0.5 μm aluminum oxide polishing compounds on rotating felt pads. The samples were then chemically etched using an etching solution of 2% NaCl 5% HCl, 93% Methanol for thirty seconds each, per the notation of the 8th Edition of the Metals Handbook [55]. Once this process had been completed, the samples were analyzed using a lower power (Leica, Stereo Zoom 4, Wetzlar, Germany) and high power optical microscope (Nikon, Optihot-100, Tokyo, Japan). The purpose of this analysis was to determine the number of grains per solder sample, the size of the grains, the solder contact angle with the PCB and the characteristics of the IMC at the joint contact.

Scanning Electron Microscopy
In addition to optical microscopy, a scanning electron microscope was used to take high magnification images of the post-fracture surfaces and to perform a process called Energy-Dispersive X-Ray Spectrometry, or EDS. Samples were mounted on a sample holder, as shown in Figure 36,  More importantly to this aspect of the study however, this process was performed to confirm the assumption that the fracture of these systems occurred through the IMC and not at an interface between the IMC and the solder. To evaluate the results of the EDS, one would take each newly exposed face, position multiple points of evaluation along said face, and examine the EDS spectrum plot that was then produced. This plot shows the number of hits that are produced as electrons are emitted at different energy levels. Each element has different characteristics under this process, and so the presence of individual elements and their relative quantities in an area may be identified. An example of this process can be seen in Figure 38.

Tensile Tests
During the course of this study, three lead-free solders were tested using the IBP testing method. These alloys, Sn 96.5 Ag 3.5 , Sn 99.3 Cu 0.7 , and Sn 96.5 Ag 3.0 Cu 0.5 , referred to as SnAg, SnCu as SAC305, were tested as solder bumps on a consumer-available FR4 PCB substrate, and were soldered using a solder bump-on-demand generator fabricated in-house. The bumps underwent a novel tensile testing procedure to evaluate both the viability of this new testing method, as well as to compare the results of each solder to the others. The tests were performed in conformance with the testing parameters of the CBP method and produced brittle fractures of the IMC, which had been generated during the soldering process at the interface of the solder and substrate.
Twenty four samples each of SnAg and SnCu were tested in this study, as well as thirty six samples of SAC305. Due to the adherence to the testing parameters of the CBP method, all successful tests that were performed in this study generated brittle failure of the IMC. The distinction between 'successful' and 'unsuccessful' tests was as follows: all successful tests were those which produced a failure of the soldered joint; unsuccessful tests were those that did not produce a failure of the joint, and could not be tested further. The only circumstance under which this would occur was when the epoxy used to encapsulate the bumps would plastically deform to the point that the solder would no longer be supported and would slip from its hold. For the 84 tests conducted in this study, unsuccessful tests occurred a total of 5 times, accounting for 5.9% of the total tests. Of the SnAg samples tested, this occurred for 1 test, or 4.2% of the sample group, for SAC305, 1 of the 36, or 2.8% of the set was not successfully tested. Lastly, there were 3 unsuccessful for SnCu, which represents 12.5% of the final alloy set. Through examination of the ring formed in epoxy cylinders used to support the solder during testing, it was noted that each of the unsuccessfully tested samples contained trapped air pockets at the interface between the solder and the epoxy which functioned as a void in the supporting ring. Refer to Figure 39 for greater detail. It is proposed that these voids decreased the overall strength of the epoxy to the extent that it could not perform its task as desired. All unsuccessfully tested samples contained at least one such void. Additionally it is proposed that unsuccessful tests occurred more often for SnCu than the other two alloys due to the higher loads necessary for failure that this alloy required, thus exposing these systems to higher peak stress values. Of the successful tests, there were then three sub-sections of the tested population. Low peak value samples, high peak value samples, and testing samples which produced bond failure between the wafer substrate and the copper foil of the FR4 PCB. While it is was possible to create a threshold to separate the first two sub-groups of this set to decrease the spread in the final testing values, this was seen as an evaluation of the soldering process rather than the solders or testing methods, which were the main focus of this study. Therefore a threshold value was not established.
For the third subset of the successfully tested sample group, those which caused pad failure of the PCB, the data was still used for comparison of the average peak stress to failure due to the fact that if a soldered contact fails through the IMC or at the PCB, either circumstance will result in a failure of the system. If the system transitions from a failure at the IMC to a failure instead at the PCB, the new testing method is still valid. However, it shows the mechanical strength of the solder and IMC no longer are the weak links in the system chain, yet the testing method itself is still valid. For these specific tests, if the area of the IMC was easily identified for the stress calculations, an average value for the IMC area for the entire alloy-specific data set was used.
At the conclusion of the testing sequence, a plot containing all of the test results for each alloy was produced, like the one shown in Figure 40 A. In this plot, one can see both successful and unsuccessful tests that were produced from this sample set. A further clarification of the distinct form of these plots can be seen in Figure 40 B. One should note in these plots that there are distinct first and second peak values of these tests, as is pointed out in Figure 40 B. The first peak occurs due to the increasing curvature of the PCB not being matched by the matching opposing face of the epoxy which was cast upon it; as the PCB curvature increases there is a suction between the PCB and epoxy that is overcome and the sudden and sharp drop in load can be observed. A residual layer of the Teflon release agent is present between these faces and creates an airtight seal which the increasing curvature of the PCB breaks.
Unsuccessful tests, like the example in Figure 40 B, are easily identified by the curved shape of their testing results, which is caused by the plastic deformation of the epoxy that surrounds the lower curvature of the solder bump.   were in agreement with trends identified in the literature [44,45]. The raw data for each solder was normally distributed and the mean and median values for each solder were calculated within one standard deviation of the mean of each original data set. By using the box plot to examine the median values of the data, it is clear the two bimetallic alloys performed with superior mean peak testing values, and of those two, that SnCu was the leading alloy. In addition to the mean and median peak values for the SAC305 solder being lower than the two other solders tests, it also had the largest amount of deviation, while the SnCu solder had both the highest mean and median values and the lowest deviation.

Optical Microscopy
In conjunction with the tensile tests that were conducted for this study, five randomly selected solder bumps from each solder alloy were selected for optical microscopy. These samples were prepared using the method described in Chapter 4, and examples of the final results can be seen in Figure 42. respectively. It was originally proposed that an increased contact angle would yield stronger adhesion to the solder bump by the epoxy, and that these values could be used to evaluate the behavior of one solder versus another. However, as the angles are so similar, no such distinction can be made.

Scanning Electron Microscopy (SEM)
Once the optical microscopy process had been completed, a scanning electron microscope was used for further visual and chemical analysis of the newly exposed faces created on the PCB and solder pieces of the broken test samples. Examples of the surface topography can be seen in Figure 43. One should note the presence of complementary patterns in these images, as the newly exposed faces of both the PCB and solder bump are the near opposite of each other. The EDS tests that were performed using these samples were conducted using four points of reference on each newly exposed face. The results from this were then displayed in individual plots and recorded. The final results for these tests were then compared to ensure that the same elements were present on both sides of the newly exposed faces. An example of this process can be seen in Figure 44. Although the plots are not a perfect match for one another, the correlation between the paired points was seen to be strong enough to confirm the original assumption that the fracture occurs through the IMC layer and not at the interface of the IMC and the solder, or the interface of the IMC and the copper substrate. This strong correlation of surface chemistry was present for all three alloys tested.  shown to produce similar statistical clustering of results with relative ease, and could be adapted to numerous types of tensile testing machines from other manufacturers.
For the three solders tested in this work, SnAg, SAC305 and SnCu, The median peak stress at failure for the three solders tested were 2020.52 psi, 940.57 psi, and 2781.0 psi, and were within one standard deviation of the of all data collected for each solder.
Optical and Scanning Electron Microscopy were successfully utilized in this study to observe the interior macro and micro structure of lead-free solder bumps. Use of the SEM to perform EDS on fractured samples was also used to validate the supposition that the fracture which occurred during tensile testing, took place through the IMC layer formed.
By performing high magnification examination of the newly exposed faces after fracture on the surfaces of the PCB and solder bump, visual confirmation was made that the fracture which occurred in this study was brittle. Additionally, by examining the results of the EDS raw data performed on both the PCB and bump faces, it was shown that the same materials were present in the same relative concentrations.
Furthermore this process showed for the SnAg tests that material present in the PCB but not originally found in the solder, namely copper, could be found in fractured surface of the solder bumps, meaning that an exchange of elements had occurred and that this exchange continued in the bump direction above the point of fracture.
Lastly, while the IMC thickness is too small to be analyzed as a homogeneous Mode I failure, if a fracture analysis were pursued, it must be performed for a Mixed Mode I/II interface fracture using a complex variable method. resulting in the magnitude of the stress intensity factor for the interface. The energy release rate may then be used to determine the magnitude of the stress intensity factor for the interface.

Future Work
Moving forward with this work, there are a number of small changes that may yield improvements on the system and procedures created in this study. These changes pertain to the crucible fabrication, substrate usage, casting method and tensile testing apparatus. Additionally, an expansion of the testing procedure with additional solders would also be beneficial in demonstrating the flexibility of the testing method. Lastly, this method could be adapted for use with other adhesion testing conditions, such as the adhesion strength of concrete to rebar, and the testing of adhesives.

Crucible Design Changes
In order to improve the deposition of solder onto the PCB substrate, simple and effective changes to the crucible are proposed. By changing the material of the crucible itself, from stainless steel with a relatively low level of thermal conduction to more conductive aluminum body with a stainless steel internal sleeve, one may be able to more quickly heat and cool the system for filling and changing solders during testing, and ensure a more even distribution of temperature throughout the entire system. This may also allow for faster fabrication of the crucible itself as aluminum has higher machining rates than stainless steel. Additionally, by reducing the internal size of the crucible to a standard drill size, the machining process would also be accelerated as only a drilling process, with a boring process no longer required.

Substrate Usage Changes
In order to produce more consistent bonding of the solder to the substrate, two changes to the system are proposed. The first is the addition of flux to the soldering process. Originally flux was not used in this study to reduce the number of variables involved in the testing procedure. However, if one were seeking only to test the tensile testing method itself, flux would not increase the level of complexity of this system and may aid in producing yet more consistent results with a potentially smaller standard deviation. The second system change would be the addition of solder resists on the surface of the PCB surrounding the targeted area where the soldered joint is to be made. This may allow for more control over the bonding area and may ensure that the IMC is formed only at the area of intent.

Tensile Testing Apparatus
In order to minimize the degree of deflection present in the tensile testing apparatus, minor design changes are proposed to the testing apparatus. Under the current design, there is a gap of twice the PCB thickness between the bottom and top support plates of the bottom half of the custom fixture. While this design was intended to ensure that the specimens were not under tension prior to testing, this allowed for two negative effects to take place. The first was a varied period of 'float' displacement at the beginning of each test where the sample would need to rise vertically and make contact before any relative load was observed, and that the PCB was then able to flex significantly after contact was made due to the large cavity in which it was held. By making the gap between these two plates smaller it may have minimized both of these effects. Additionally, the load cell that was used was appropriate for loads up to 5000 newtons, while the greatest load in this study was less than 445N, the use of a lower maximum load cell may have eliminated the need to remove data below the 1.1 lb f threshold discussed in Chapter 3.

Further Development of Casting Molds and Process
One of the greatest difficulties in this study was ensuring that the cast epoxy cylinders surrounding the solder bumps were made consistently and with as little use pre-fabricated polymers or heat activated powders to completely replace the epoxy. This type of change would allow higher accuracy materials to be utilized and could help to avoid inconsistencies caused from manual mixing.

URI ESEM Laboratory
Spectrum Report Friday, June 19, 2015 File