Study of Tin Whisker Growth and Their Mechanical and Electrical Properties Moheb Nayeri Hashemzadeh

Home , Whisker (metallurgy)

Examensarbete

Study of Tin Whisker Growth and their Mechanical and Electrical Properties Moheb Nayeri Hashemzadeh

LITH - IFM - EX - - 05 / 1499 - - SE

Study of Tin Whisker Growth and their Mechanical and Electrical Properties

IFM, Link¨opingsUniversitet

Moheb Nayeri Hashemzadeh

LITH - IFM - EX - - 05 / 1499 - - SE

Examensarbete: 20 p

Level: D

Supervisor: Dr. Werner Hügel, Dr. Verena Kirchner Robert Bosch GmbH-AE/QMM-S5 Examiner: Prof. Ulf Helmersson, IFM, LinköpingsUniversitet Linköping: September 2005

Avdelning, Institution Datum Division, Department Date Department of Physics and Measurement Technology, IFM Link¨oping University September 2005 SE-581 83 Link¨oping

Spr˚ak Rapporttyp Language Report category ISRN NUMMER: Svenska/Swedish Licentiatavhandling x Engelska/English x Examensarbete LITH - IFM - EX - - 05 / 1499 - - SE C-uppsats D-uppsats Ovrig¨ rapport

URL f¨orelektronisk version

Titel Study of Tin Whisker Growth and their Mechanical and Electrical Title Properties

F¨orfattare Moheb Nayeri Hashemzadeh Author

Sammanfattning Abstract The phenomenon of spontaneous growth of metallic ﬁlaments, known as whisker growth has been studied. Until now the problem that Sn whisker growth could cause in electronics by making shorts has been partially prohibited as Pb and Sn have been used together in solders and coating. Regulations restricting Pb use in electronics has made the need to understand Sn whisker growth more current. It is shown that whiskers are highly resilient towards vibrations and shocks. A Sn whisker is shown to withstand 55 mA. Results show that reﬂowing of the Sn plated surface does not prevent extensive whisker growth. Results show that intermetallic compound growth can not be the sole reason behind whisker growth. Nickel and silver underlayer have been shown not to prevent whisker growth, but perhaps restrain whisker growth. Heat treatment damped whisker growth considerably. It is judged that base material CuSn6 is less prone to show whisker growth than CuSn0.15 and E-Cu58.

Nyckelord Tin whisker Keyword Abstract

Purpose

The phenomenon of spontaneous growth of metallic ﬁlaments, known as whiskers, has been studied and compared with existing theories. Until now the problem that tin whisker growth could cause in electronics by making shorts has been partially prohibited as lead and tin have been used together in solders and coating. Due to a more environment aware society, where use of lead in solder and coating will be restricted, the need of understanding the phenomenon of tin whisker growth has become more current. A study of the mechanical and electrical durability of tin whiskers has also been carried out.

Procedure

Tin whiskers current carrying capacities was tested and based on the experimental results finite element method calculations were made in the Ansys program. Tin whiskers endurance against vibrations and shocks have been calculated and tested. Whisker growth on different metallic systems, undergoing different conditions have been observed. The metallic systems have been three different sorts of base materials (all consist mainly of copper) with a layer of dull or bright tin on it and in some cases nickel or silver underlayer between the base material and the tin layer. The test conditions the samples underwent with different combinations were: soldering simulation, temperature cycling between −60 oC to 60 oC, humidity storage, high temperature storage and room temperature storage. Some samples were also heat treated post plating, for 5 minutes at 180 oC. Some of the samples were studied with help of Focused Ion Beam systems.

Nayeri Hashemzadeh, 2005. 6 7

Results and Conclusions

Both calculations and tests showed that whiskers are highly resilient towards vibrations common in vehicles. Tests showed also that whiskers can withstand very high shocks, not breaking when subjected to shocks of 1000 m/s2 during 6 ms. Tests have shown whiskers withstanding currents up to 55 mA. The longer the whiskers the lower current carrying ability, while thicker whiskers can carry higher currents. The whisker that could withstand 55 mA was 120 µm long and had a diameter of 5.5 µm. Due to the shifting quality of the plating of the samples clear conclusions regarding storage conditions that are favorable for whisker growth can not be made. This points to the importance of process stability when plating, as to get homogenous plating quality. Results show that soldering simulation, which is melting the tin plated surface does not prevent extensive whisker growth. Results show that intermetallic compound growth can not be the sole reason for whisker growth. Nickel and silver underlayer have been shown not to prevent whisker growth, but perhaps restrain it. Heat treatment damped whisker growth considerably but did not prevent it. It is judged that base material CuSn6 is less prone to show whisker growth than CuSn0.15 and E-Cu58.

Keywords: Tin whisker Acknowledgements

I would like to thank Prof. Ulf Helmersson for his help and support, making it possible for me to do my master thesis in Germany at Robert Bosch GmbH, Reut- lingen.

I would like to thank both my supervisors at Robert Bosch GmbH, Dr. Werner Hügeland Dr. Verena Kirchner, for the help and the support I have received with my work. Dr. Werner Hügel had a great part in helping me in my work, from having ordered the samples that were studied during this work, to booking test sessions as well as helping with the theoretical part of the work. Dr. Verena Kirch- ner was very helpful in helping with practical issues and giving advise in theoretical matters as well as helping me write this report. I would also like to thank all the other people at Robert Bosch GmbH that were very forthcoming in helping me, specially following names come to mind, even though there were many more: Joachim Gugeler for the tests concerning mechanical durability. Thomas von Bargen for the FEM simulations. Markus Schill for the FIB sessions. SükrüTavasligolu for saving my computer several times. Markus Guber for providing time to discuss his results and views regarding whisker growth. Fabian Bez for helping me looking through some of the samples Pravin Sinha for helping me in searching for articles. David Nerz for his help with some of the samples. Nathalie Becker for her help in practical and scientific matters. Parviz Kamvar for his advices in scientific matters.

Moreover I would like to thank my brother Mohit Nayeri, for being supportive both on a scientiﬁc sense as well as on a personal level.

I would like to dedicate this work to my mother, Mary Berari.

Nayeri Hashemzadeh, 2005. 8 Frequently Used Abbreviations and Symbols

EDX Energy Dispersive X-ray spectroscope FEM Finite Element Method FIB Focused Ion Beam IMC Intermetallic Compound LM Light Microscope PSD Power Spectral Density RoHS Restriction of Hazardous Substances Directives SEM Scanning Electron Microscope 0 η -phase Cu6Sn5 Icrit The critical current at which the whiskers fuse Tm The melting point temperature Ag Silver Cu Copper Ni Nickel Pb Lead Sn Tin Zn Zink

Nayeri Hashemzadeh, 2005. 9 Contents

1 Introduction 12 1.1 Purpose ...... 14 1.2 Outline ...... 14

2 Theoretical Background 16 2.1 Fundamentals ...... 16 2.1.1 General Properties of Whiskers ...... 16 2.1.2 Cu-Sn Properties ...... 19 2.2 Tin Whisker Growth Models ...... 19 2.2.1 Surface Energy Eﬀects ...... 20 2.2.2 Stored Strain Energy ...... 22 2.2.3 Internal Mechanical Stresses ...... 25 2.3 Mitigation Strategies ...... 29

3 Procedure 31 3.1 Instruments Used ...... 31 3.1.1 Light Microscope ...... 31 3.1.2 Scanning Electron Microscope ...... 31 3.2 Measuring Mechanical Durability ...... 33 3.2.1 Stereo Microscope ...... 33 3.2.2 Vibration and Shock Table ...... 33 3.2.3 Vibration and Shock Tests ...... 33 3.3 Measuring Electrical Durability ...... 35 3.3.1 Microprobe ...... 35 3.3.2 Electrical Conductivity Tests ...... 36 3.3.3 Finite Element Method ...... 37 3.4 Studying Whisker Growth ...... 38 3.4.1 Focused Ion Beam ...... 38 3.4.2 Sample Speciﬁcs ...... 39 3.4.3 Sample Study ...... 40

Nayeri Hashemzadeh, 2005. 10 Contents 11

4 Results 42 4.1 Mechanical Durability ...... 42 4.1.1 Natural Frequency of Whiskers ...... 42 4.1.2 Results from Vibration Tests ...... 43 4.1.3 Results from Shock Tests ...... 44 4.2 Electrical Durability ...... 45 4.2.1 Electrical Conductivity of Whiskers ...... 45 4.2.2 FEM Calculations ...... 46 4.3 Whisker Growth Study ...... 47 4.3.1 FIB Results ...... 48

5 Discussion of the Results 56 5.1 Mechanical Properties ...... 56 5.2 Electrical Properties ...... 56 5.3 Tin Whisker Growth ...... 57 5.3.1 Heat Treatment ...... 57 5.3.2 Soldering Simulation ...... 57 5.3.3 Storage Conditions ...... 58 5.3.4 Base Material ...... 58 5.3.5 Underlayer ...... 59 5.3.6 Dull versus Bright Sn ...... 60 5.3.7 Tin Layer Thickness ...... 60 5.3.8 Conclusions on Whisker Growth Models ...... 61

6 Future Work 62

A Methods 67

B Results 70 B.1 Natural Frequency Calculations ...... 70 B.1.1 Connected at Both Ends ...... 73 Chapter 1

Introduction

Whiskers are metal filaments that have been shown to grow spontaneously on metals such as cadmium (Cd), zinc (Zn), aluminum (Al), silver (Ag), molybdenum (Mo), tungsten (W) and tin (Sn) [1, 2]. In everyday language the word whisker usually refers to cat bristle, which is quite describing for most whiskers, which grow straight and stiff, as can be seen in figure 1.1 a), however kinked whiskers, as e.g. shown in figure 1.1 b), are quite usual as well.

Figure 1.1: a) Most commonly whiskers grow quite straight out of the surface. This picture was taken with scanning electron microscopy. b) A kinked whisker in a M-form. This picture was taken by a focused ion beam microscopy.

The phenomenon of whisker growth was ﬁrst reported in 1946 by H. L. Cobb [3]. He made his observation of whisker growth on condensers which were electro- plated with Cd, some growing long enough to result in short between the condenser plates. However the knowledge about whiskers and thus recognizing the hazards with whiskers has been over and over forgotten, causing some serious component failures. The most famous failure probably is the lost of the satellite Galaxy IV in

Nayeri Hashemzadeh, 2005. 12 13

1998, the estimate worth of the satellite was 250 million dollar [4, 5]. There have been other serious failures reported due to whiskers in aircrafts, computer centers and medical devices [5]. Most whiskers do not grow more than a few hundred micrometers, but whiskers of lengths up to 5 mm have been observed in this work.

Figure 1.2: Cross section overview of a molded semiconductor component.

The plague of whiskers could soon become even more evident if the right counter measures are not taken. This is due to new regulations made by the European Union as to restrict or ban lead (Pb) use in electronics depending on what these applications will be used for. This regulations are summarized under the name of Restriction of Hazardous Substances Directives (RoHS) and are to be implemented across the European Union from July the 1st 2006. The regulations applied for the automotive industry go under the name of End of Life Vehicles and here the legislation states that there should not be more than 60 g lead per vehicle regarding the soldered electronics, this excluding the battery of the vehicle. If this limit is exceeded, the manufacturer must supply cost free recycling of the parts that cause the overstep. Until now most manufacturers have used a mixture of Sn-Pb alloys for soldering and coating their components. The Sn-Pb mixture makes the solder surface less prone to whisker growth [1, 6, 7]. With the general demand to decrease Pb use and particularly due to RoHS manufacturers must ﬁnd a replacement for Sn-Pb solders. Pure Sn is the favored candidate for galvanic plating purposes. Both because of the low costs involved in making the switch from Sn-Pb plating to Sn plating and because of tin’s desirable properties regarding solder ability, ductility, conductivity and corrosion resistance. This has created a great need to try to prevent or dimin- ish Sn whisker growth. If manufacturers want to be able to do so, the properties of whiskers have to be better understood. 1.1. Purpose 14

1.1 Purpose

The purpose of this thesis was to better understand the root cause of Sn whisker growth and try to understand how to prevent or restrain Sn whisker growth. This was set to be done by reviewing the theories that exist about this phenomenon as well as studying growth of whiskers on different sets of samples undergoing different conditions. Another side to the thesis was to test and calculate on Sn whiskers electrical and mechanical properties. More specific, testing how much current Sn whiskers are able to sustain and how much vibration and how high mechanical shocks whiskers can withstand.

1.2 Outline

The chapters are structured in the following manner:

• Chapter 2. In this chapter an overview of whisker properties, specially for Sn whiskers is given. Properties of Sn and Cu that will be important for this work are also listed. A review of some of the theories that exist regarding whisker growth is presented, with some calculations on these models. In the last section of the chapter some of the mitigation strategies that are suggested against whisker growth are described.

• Chapter 3. In the first part of this chapter the devices that were commonly used in different experiments are presented. The second part covers exper- iment specific devices, the samples as well as the methods that were used during the work.

• Chapter 4. In this chapter the results achieved are presented followed by some discussions about the results. In the first section of this chapter results regarding the mechanical durability of Sn whiskers are presented. In the second section of the chapter test results of the current carrying ability of Sn whiskers are presented, and then some finite element method calculations are presented. In the last section results from studying the growth of whiskers on different samples undergoing different test conditions are described.

• Chapter 5. In this chapter a more thorough discussion about the results is presented. Connection is made with results achieved in other studies as well as the theories that exist. 1.2. Outline 15

• Chapter 6. What will be the future of whisker growth research is discussed as well as the work that could follow the results of this master thesis. Chapter 2

Theoretical Background

2.1 Fundamentals

To be able to understand why whiskers grow, it is important to understand the properties of whiskers. Some models that have been proposed to explain the root cause of why whiskers grow can be neglected because of their inability to explain the properties that whiskers have shown. A review of some of the major theories regarding whisker growth will be given further on in this chapter. Some of these theories will seem to be less able to explain some of the results reported around whiskers, given in the two following sections and in section 2.3, which covers some of the mitigation strategies suggested in literature against Sn whisker growth. For this work properties of Sn whiskers are mostly important. Properties of Cu is interesting as well, both regarding the practical issues around this work as well as reviewing theories on Sn whisker growth.

2.1.1 General Properties of Whiskers In 1952 Herring and Galt published a report showing the elastic and plastic properties of Sn whiskers to be near what would be expected of perfect single crystals [8]. This has led to the conclusion that whiskers are nearby perfect crystals. They thus also conﬁrmed the theoretical calculations on the strength of perfect crystals [9]. Bulk materials show much less strength than perfect single crystals due to high numbers of dislocations and grains. Sheng et al. published 2002 Sn whiskers studies done with Focused Ion Beam systems (FIB) showing that whiskers contain many defects, which they thought were mainly dislocations [10]. Dunn published in 1986 results about the Young’s modulus of whiskers varying depending on which direction the whisker grow [11]. The values ranged between 8 to 85 GPa. Dunn wrote about the diﬃculty of measuring the diameter and the imperfection of assuming that the whiskers are cylindrical in the calculations.

Nayeri Hashemzadeh, 2005. 16 2.1. Fundamentals 17

Figure 2.1: The picture shows a whisker with an irregular cross section.

Figure 2.2: In picture a) a whisker growing from a nodule can be seen. b) A whisker surrounded by eruptions or ﬂowers as they also are called. Both phenomena appear on bright tin.

There is also one report from Kehrer and Kadereit in 1970 which claims whiskers to be hollow [12], but this has neither been reported by other groups nor observed during this work. The shape of a whisker can vary from quite cylindrical to a more irregular form as can be seen in figure 2.1. The striation seen on the side of the whisker shown in figure 2.1, gives the impression that the whisker is being ”pressed” out of the surface. Whiskers have usually a very homogeneous diameter from tip to toe. In 1953 Koonce and Arnold showed that the growth of whiskers occur by continuous addi- tion of material to the root of the whisker, which can be observed by the fact that the shape of the tip of the whisker does not change during the growth [13]. This finding ruled out the earliest theory regarding how whiskers grow put forward by Peach in 1952 [14]. Whiskers can grow directly from the surface or grow from outgrowths on the sur- 2.1. Fundamentals 18 face known as nodules which can be seen in figure 2.2 a). In figure 2.2 b) a whisker can be seen surrounded by eruptions or flowers as they also are called. The last two phenomena appear when Sn whiskers are growing on bright tin. Bright Sn is achieved by adding organic soluble to the galvanic bath. The grain structure in bright Sn is smaller than in dull Sn. It has been reported that the whiskers seem to have a period of a constant growth until the growth rate suddenly decreases greatly [15]. The growth rates that have been reported vary, but lie usually somewhere between 100 µm to 1 mm per year [15]. During this work whisker diameters between 1 µm to 6 µm have been observed and the longest whiskers observed were up to 5 mm, but for most whiskers the length seem not to surpass more than a few 100 µm.

Figure 2.3: Phase diagram of the Cu-Sn systems. At room temperature the intermetallic that forms is the η’-phase [18]. 2.2. Tin Whisker Growth Models 19

2.1.2 Cu-Sn Properties Tin has two allotropes at normal pressure, α-Sn and β-Sn [16]. Grey Sn as α-Sn is usually referred to, is an intrinsic semiconductor and is stable at temperatures below 13.2 oC. For this work only the metal form of Sn, that is β-Sn or white Sn, which is stable for temperatures above 13.2 oC, is interesting. White Sn has a body centered tetragonal crystal structure with the lattice constants of a = b = 0.58318 nm and c = 0.31819 nm [17]. The molar weight of Sn is 118.71 g. The density for β-Sn is 7310 kg/m3. Copper has a face centered cubic structure with lattice constants a = b = c = 0.36149 nm and a molar weight of 63.546 g resulting in a density of 8920 kg/m3. The phase diagram for the intermetallic compound (IMC) that forms between Cu and Sn is shown in picture 2.3. For this work only phases which are stable at temperatures below the Sn melting point are interesting. At room temperature o Cu6Sn5 (η’-phase) forms spontaneously and for temperatures above 100 C there will also be formation of Cu3Sn (-phase) at the expense of the η’-phase [19]. The η’-phase has the density of 8270 kg/m3. In table 2.1 some of the electrical and mechanical properties of Sn and Cu, which have been used for the calculations of the durability of whiskers, can be found.

2.2 Tin Whisker Growth Models

As mentioned in chapter 1, the first reported observation of whiskers was on elec- troplated Cd in 1946 by Cobb [3], causing shorts on condensers. Eventually these problems lead Bell Telephone to change to pure tin electroplating in 1948, just to find pretty soon that pure Sn showed the same type of problems. Consequently the first report on Sn whisker growth came from Bell Laboratories in 1951 [20]. Since then most of the articles produced around the whisker growth phenom-

Tin Copper W Thermal conductivity at 300 K, (κ300K ), [ m·K ] 65 400 J Speciﬁc heat capacity at constant pressure and 300 K, (Cp), [ kg·K ] 230 385 −9 Resistivity at 300 K, (ρ300K ), [10 Ω · m] 110 17 Temperature coeﬃcient, (α), [10−3 K−1] 4.63 4.33 5 Melting point at pressure 10 Pa, (Tm), [K] 505 1356 Young’s modulus, (E), [109 P a] 55 120 Shear modulus [109 P a] 21 46 Poisson ratio, (v) 0.36 0.34

Table 2.1: The properties of (bulk) Sn and Cu that are important for this work are put together [16, 17]. 2.2. Tin Whisker Growth Models 20 enon have focused mostly on Sn whiskers. Some of the theories existing regarding whisker growth are speciﬁcally made for Cu-Sn systems, e.g. the theory that will be covered in section 2.2.3.

There are basically three different theories on why whiskers grow, i.e. what is the driving force behind whisker growth. Within these theories there are different suggestions about how whiskers grow, i.e. what are the mechanisms of whisker growth. The driving forces for whisker growth can be classified into the following classes 1. Surface energy effects [21, 22]

2. Stored strain energy [23, 24, 25]

3. Internal mechanical stresses [10, 26, 27] The three models above are listed in chronological order. First theory states that a local negative surface tension is the reason why whiskers grow. The stored strain energy theory involves an abnormal recrystallization process. The third theory about internal mechanical stresses states that formation of intermetallic between the base material and the tin layer causes stress in the tin.

2.2.1 Surface Energy Eﬀects Both J. D. Eshelby and F. C. Frank suggested independently in 1953 that a local negative surface tension is the driving force for whisker growth [21, 22]. The energy required to form a fresh surface comes from the surface being attacked by the atmosphere resulting in a negative surface tension, γ. The simple thermodynamic equation for surfaces is given by

U = TS − pV + µN + γA, (2.1) where U is the energy of the system, T is the temperature, S is the conventional entropy, p is the pressure, V is the volume, µ is the chemical potential, N is the number of particles and A denotes the surface area [28]. In most cases γ is positive which means in order to minimize the energy of the system, the surface has to be as small as possible. A local negative surface tension hence provides the needed driving force for a whisker to grow. The authors suggested two different dislocation mechanisms to feed the whisker with the needed building material. Eshelby suggested that a Frank-Read source below a hump that is created by the negative surface tension emits the dislocation loops that make the whisker grow [21]. The dislocation loop provided with the right amount of stress first expand to 2.2. Tin Whisker Growth Models 21 the radius of the whisker and then glide vertically, depositing one atomic layer at the base of the hump, causing a whisker to grow. By making some assumptions, Eshelby reaches the following expression for the growth rate of the whisker: ∂h b γb2 ∼ κβnD( 2 )( ), (2.2) ∂t l kBT where h is the length of the whisker, κ is a factor depending on the detailed stress distribution, β is the fraction of the number of lattice sites per loop which can emit or absorb vacancies, n is the number of loops in transit between source and surface at one time, b is the Burgers vector, l is the length of the Frank-Read source, D is the self-diffusion coefficient of the material and kB and T are the Boltzmann constant and the temperature. The result from calculations with this model where the length of the Frank-Read source and the size of the κβn factor is varied is shown in figure 2.4.

Figure 2.4: In the Eshelby whisker growth model, the whisker growth rate is dependent on the length of the Frank-Read source and a κβn factor as given in equation 2.2. Eshelby suggest in his paper that the κβn factor is between 100 to 1000. A Frank-Read source usually has the equivalent length of a few hundred lattice constants.

Eshelby suggested that the γb2 should be around 1 eV. The self-diﬀusion of Sn at room temperature is 2 · 10−22 [29]. Even though a negative surface tension with the suggested dislocation mechanisms has not been discredited, it has to be stated that the theory is not referred to very often. 2.2. Tin Whisker Growth Models 22

2.2.2 Stored Strain Energy Ellis et al. suggested in 1958 that an abnormal form of recrystallization process is the reason behind the whisker growth [23]. Recrystallization theory states that lattice defects and grain boundaries rearrange in the bulk material at certain temperatures to minimize their energy. This is due to shear strain stored in the bulk material resulting from plastic deformation in the material as it is formed [30]. The recrystallization process is ordered in three principal stages:

• Recovery

• Recrystallization

• Grain growth

In the recovery stage, the dislocation density is diminished and energy is released. This process starts as soon as the Sn layer is plated. In the second stage, that is recrystallization, new grains are formed. This stage can run parallel to the recovery stage. Grain growth takes place in highly mismatched sites in relation to surrounding material. In the last stage the grain boundaries are rearranged to decrease the grain boundary area. The number of grains decreases as well. It is suggested that this stage would be inhibited when whiskers grow. Grain boundaries lie usually perpendicular to the surface to decrease the curvature of the surface and hence are quite immobile. This eﬀect is more apparent in thinner ﬁlms where pinned grain boundaries at the surface can make all of the grain boundary area immobile. Therefore it is possible that at certain conditions growth of whiskers is more favorable to release the shear strain that is not released through the normal procedure of this last stage. Boguslavsky and Bush suggest that there should be preferred orientation of the grains that grow whiskers towards both the free surface and neighboring grains [25]. Another fact that makes recrystallization to an eligible candidate to promote whisker growth is that recrystallization takes place for temperatures around 0.3- 0.7 Tm, where Tm is the melting point of the metal. The metals that have shown whisker growth at room temperature at normal conditions have the following melting points [1, 16]

• Cd, Tm = 594K

• Sn, Tm = 505K

• Zn, Tm = 693K The range of the recrystallization temperatures of these metals contains room temperatures. 2.2. Tin Whisker Growth Models 23

Furuta and Hamamura [24] did some further development of the theory of El- lis et al. [23] to explain growth of kinked whiskers and they proposed an equation to determine the growth rate. The growth of the kinked whiskers was explained by boundary-slip, due to uneven stress, caused in the grains from which kinked whiskers grow.

Figure 2.5: Schematic view of the nucleating crystal suggested by Furuta and Hamamura [24]. a is the radius of the nucleating crystal at the intersection with the free surface and r is the radius of the spherical nucleating crystal. a) shows a cross section of the nucleating surface and b) shows the top view of the nucleating crystal.

The equation is based on some assumptions about the form of the grain that grows the whisker. Figure 2.5 shows a simpliﬁed model of the nucleating crystal, where the intersection of the nucleating crystal with the surface is assumed as a circle with radius a and the nucleating crystal is spherical with radius r. The change in the free energy F for the subsequent growth of the nucleating crystal is expressed by π √ π √ √ F = −{ (r ± r2 − a2)3 + (r ± r2 − a2)a2}E + 2π(r ± r2 − a2)rσ, (2.3) 6 2 where E is the strain energy in the unit volume of the parent material and σ is the boundary energy per unit area. The plus sign is valid if the boundary center is within the material (that is r is within the material) and minus if it is outside 2σ the material as seen in ﬁgure 2.5 a). It is shown that for a < r = rc = E whisker growth will occur, while otherwise normal recrystallization will pursue. Using this expression, pressure inside of the nucleating crystal is calculated and with that following expression for the whisker growth rate is achieved:

dh 2Eb3 = D, (2.4) dt RkBT where R is the average distance from the grain boundary to the inside of the grain, b is the atomic spacing in the material, kB is the Boltzmann constant, T 2.2. Tin Whisker Growth Models 24 is the temperature, and D is the self-diﬀusion coeﬃcient of the material. Furuta and Hamamura used following number for their calculation of Sn whisker growth: E = 0.2J/cm3, D = 10−16 m2/s , T = 300K, R = 100 A˚ and b3 = 30 A˚3 the growth rate is about 3 A/s˚ or around 1 mm/year.

Figure 2.6: This is a schematic view of Lindborg’s whisker growth model [35]. In a) and b) the line that is marked as 1 is a Bardeen-Herring dislocation loop which is expanding. In c) the loop has reached its full size and starts to glide to the surface. A second loop has started to expand labeled as line 2. In d) the ﬁst loop has reached where the whisker brakes the surface, pushing the whisker one atomic layer [33].

Boguslavsky and Bush [25] suggest in turn that how the whiskers grow is through the two stage model that Lindborg suggested in 1975 [33]. In this model a Bardeen- Herring source generates the dislocation loops that by gliding reaches where the whisker brakes the surface, making the whisker grow by one atomic layer. Linds- borg’s work concentrates on how whiskers grow, even though he seem to be dubious about the role of stored strain energy [33]. Galyon has in his compilation work of articles relating to tin whisker growth, Annotated Tin Whisker Bibliography, mis- takenly considered that Lindborg means with this mechanisms that the whiskers grow at the tip [2]. In reality Lindborg writes in his article When the loop reaches the surface the whisker is pushed up one atomic step in the direction of the Burgers vector of the loop. [33] The first stage of the Lindborg model includes expansion of the dislocation loop to the size of the whisker cross section. Lindborg suggests three different equations that depending on what kind of diffusion that is contributing to the whisker 2.2. Tin Whisker Growth Models 25 growth limit whisker growth rate. The three diffusion types are: lattice diffusion, grain boundary diffusion or diffusion through dislocation pipes. The slowest diffusion type is lattice diffusion and diffusion through dislocation pipes is the fastest one. Dislocation pipes are description of dislocations where the boundary of the dislocations is described as a ”pipe” with a certain radius [34]. Equation 2.5 is the general form of the Lindsborg’s three whisker growth rate limiting equations:

dhx σ = kx Dx, (2.5) dt RwT where kx depends on the diffusion source and different material properties, Rw is the whisker radius, σ is the stress in the direction of the Burgers vector of the loop, T is the temperature and Dx denotes the type of diffusion that is in effect. The second stage is the gliding of the loop in direction of its Burgers vector, i.e. the direction of the growth of the whisker. The growth rate for the whisker is given by n dh2 k3 = k2 σ − , (2.6) dt Lw where k2 and n are both dependent on dislocation density and temperature but independent of stress, k3 is dependent on the Burgers vector and the stress and Lw is the space between dislocations. n varies between 10 to 20, making the equation 2.6 highly stress dependent. This means that for high stress situation the first stage, that is generation of the dislocation loops would not keep up, and the whisker growth rate would then be governed by equation 2.5 where the stress dependence is linear. It is also pointed out in Boguslavsky’s and Bush’s work [25] that dislocation distance, Lw, is larger in low angle grain boundaries giving a higher growth rate. At the same time they state that high angle grain boundaries, where the lattice mismatch is usually greater, provides for a faster grain boundary diffusion, which would make them more favorable to provide the Sn that is needed for the whisker. They thus conclude that a balanced mix of low angle grain boundaries and high angle boundaries would provide the best settings for whisker growth. As it was pointed out earlier, Lindborg did not favor the stored strain energy model, while he in a article that was published 1975 could not show that micros- train was an important factor for Zn whisker growth [35]. Rather he found that internal compressive macrostress was the driving force behind zinc whisker growth. Concluding that the stored strain energy is negligible.

2.2.3 Internal Mechanical Stresses A theory about whisker growth in dependence on internal mechanical stresses was put forward by K. N. Tu in 1994 [26]. In this paper Tu discussed whisker growth 2.2. Tin Whisker Growth Models 26 on Cu-Sn systems, which is the materials most important for this thesis. The basic idea is that whiskers grow because of stresses that are caused due to formation of intermetallic compound (IMC) between copper and tin. It was shown by Tu in 1973 that the reaction of Cu with Sn seems to have an effect on whisker growth [19]. It can be seen in the phase diagram for Cu-Sn system in figure 2.3 that the 0 IMC that forms during room temperature is the η -phase, Cu6Sn5. Tu suggested that an uneven IMC growth taking place at the η0-phase/Sn interface and mostly in the grain boundaries of the Sn results in a compressive stress in the Sn film which leads to whisker growth. He writes the following in his paper:

At room temperature we can assume that there is no diffusion of Sn into Cu since Sn diffuses substitutionally in Cu and the diffusivity is negligible. [26]

This conclusion is based on the work of Butrymowicz et al. [36]. Also in this model weak spots at the surface are assumed, where the tension that otherwise is build up is released in form of whiskers. Tu suggested that these spots are where the surface oxide is broken. As long as the stress is maintained in Sn by the chemical reaction the whisker growth is sustained. For kinked whiskers Tu suggested that the surface oxide on one side of the whisker ”heals”, resulting in kinking the whisker until the oxide is cracked again. Tu calculated the rate of chemical reaction and the rate of the whisker growth. Gibbs free-energy change for the reaction is

dG = −SdT + V dp − Cdξ, (2.7) where G is Gibbs free energy and ξ is a reaction variable for the extent of the reaction. C is the chemical aﬃnity which is

C = µη0 − 6µCu − 5µSn, (2.8)

µ is here the chemical potential. From this a chemical driving force is calculated and by making some assumptions and solving a diﬀerential equation Tu reaches the following formula for the growth rate of the whisker

∆h 2 σ0ΩsD = 2 , (2.9) ∆t ln(b/a) kBT a where 2b is the distance between two neighboring whiskers, a is the radius of the whisker, σ0 is the stress at a distance of b from the whisker (this has been used as boundary condition when solving the diﬀerential equation), Ω is the atomic volume, s is the step height between the base atoms and D is the grain boundary diﬀusivity of Sn at room temperature. 2.2. Tin Whisker Growth Models 27

Figure 2.7: This picture is taken from Tu’s paper in 1994. It is a sketch of the top view of whiskers growing. In this model the whiskers would have a diameter of 2a and a spacing of 2b [26].

Figure 2.8 shows calculations made on this equation where parameter a which is the radius of the whisker and b which is half of the distance to the nearest neighboring whisker is varied. Otherwise same values that was used by Tu in his 1994 paper is used [26], σ0Ω = 0, 01eV , kBT = 0, 025eV at room temperature, s = 0, 3nm and the grain boundary diﬀusivity of Sn at room temperature, D = 10−12m2/s. As graph 2.8 shows the growth rate increases as the a and b come closer in value

Figure 2.8: This graph shows the whisker growth rate according to equation 2.9, based on Tu’s model [26]. The whisker radius a and the spacing between each whisker 2b is varied. to each other due to the ln(b/a) in the denominator. 2.2. Tin Whisker Growth Models 28

Volume Change An important part of Tu’s suggested mechanism for whisker growth is the volume lost caused by the creation of Cu6Sn5. By using the density of the material or the shape of the unit cell, the volume/atom for the Cu, Sn and Cu6Sn5 can be calculated. The density for Cu is 8920 kg/m3, the density for Sn is 7310 kg/m3 and the density for η0-pahse is 8280 kg/m3 [16, 37]. The atomic volume for Sn is around, −29 3 −29 3 0 VSn = 2.70 · 10 m , for Cu it is VCu = 1.18 · 10 m and for the η -phase −29 3 Vη0 = 1.78 · 10 m . This results in

11 ∗ V 0 η ≈ 95%. 6 ∗ VCu + 5 ∗ VSn Meaning a decrease in the total volume. However if it is considered that the growth of the η0-phase would almost only occur in the η0-phase/Sn interface and that the volume change would only be on the cost of the Sn ﬁlm the result is changed to

11 ∗ V 0 η ≈ 145%. 5 ∗ VSn This calculation shows that the growth of IMC in the Cu-Sn interface would cause stress if the IMC boundary does not move deeper into the Cu substrate. Based on this calculation it is easy to calculate how much η0-phase is needed to provide the material needed for a Sn whisker, assuming that all of the η0-phase growth would translate to Sn being pressed out as whiskers. An uneven growth of IMC amounting to 0.1 µm η0-phase on an area of 100 µm times 100 µm would result in an about 140 µm long whisker with a diameter of 2 µm. This simple example is only to visualize roughly how little IMC growth of η0-phase would be needed to provide the Sn for the whisker.

Barsoum et al. published in 2004 an article where they proposed it is the reaction of oxygen with the metal that causes whiskers to grow [27]. In this model diﬀusion of oxygen into the metal and the following reaction with the metal gives a volume expansion that would cause stress, which would be relieved in the same way as in Tu’s model [26]. For Sn the possible reactions with O2 are 1 Sn + O → SnO, (2.10) 2 2 Sn + O2 → SnO2. (2.11)

3 3 The density for SnO is 6450 kg/m and for SnO2 it is 6950 kg/m [17]. The −29 3 average atomic volume for SnO is VSnO = 1.73 · 10 m and for SnO2 it is 2.3. Mitigation Strategies 29

−29 3 VSnO2 = 1.20 · 10 m . The volume change is: 2 · V SnO ≈ 129%. (2.12) VSn 3 · V SnO2 ≈ 134%. (2.13) VSn It has to be pointed out that Barsoum et al. reached their conclusions after having coated some samples with polymer coating and keeping some samples in the free for just three months. It has been reported that conformal coating as it is called could retards whisker growth but does not prevent it [38]. Also Guber has shown in his master thesis in 2004 that there is no relation between thickness of the surface oxide and whisker growth [39].

2.3 Mitigation Strategies

Through the years different methods, besides mixing tin with lead, have been suggested as mitigation strategies. Results concerning these strategies have been different and some times even contradicting each other. The strategies most current for this work are: 1. Variation of the tin plating thickness. Already in 1963 it was shown that by varying the Sn layer thickness whisker growth could be restrained [40]. Different intervals of Sn layer thickness have been suggested, within which there will be whisker growth, while outside there is no whisker growth. Arnold suggested in 1966 such an interval to be for 0.5 µm > Sn layer thickness > 8 µm. [41]. 2. Use of different base material. It has long been known that different base materials have shown different aptitude towards whisker growth [40]. For instance there seems to be no growth of whiskers when tin is deposited on base material FeNi43 [42]. 3. Use of an underlayer between the base material and the Sn layer. Use of an underlayer, also known as barrier layer, between the base material and the tin layer is another way to try to control whisker growth. Nickel is the underlayer most reported on as used between Sn and Cu, with some claims of total prevention of whisker growth while others report only damping of whisker growth [5, 43, 44]. 4. Reflowing the Sn surface. Reflowing the Sn surface, that is exceeding the melting point of Sn, which is 232 oC, and thus melting the plated Sn has also been reported as a way to reduce whisker growth [43]. 2.3. Mitigation Strategies 30

5. Annealing of the Sn layer after plating. Annealing, that is heating under the melting point of the Sn, is reported to drastically reduce whisker growth [45]. There are two theories on why this is achieved. One is that annealing leads to a fast and even growth of IMC in Cu-Sn systems [26]. The other explanation is that annealing releases the stored energy [25]. Chapter 3

Procedure

3.1 Instruments Used

In the ﬁrst section of this chapter the instruments that were used in more than one type of tests are presented. Following this section each type of tests and the corresponding instruments and samples are presented.

3.1.1 Light Microscope Two types of light microscopes were used during the work.

Model and Manufacturer Magniﬁcation Light microscope 1: Ergolux from Leitz 50 – 500 Light microscope 2: Axioskop 2 MAT from Zeiss 25 – 1000 The ﬁrst light microscope (LM 1), was a simpler model which was not connected to a computer with a camera. Light microscope 2 (LM 2), which was more frequently used, was connected to a camera of model Axiocam HRC with the computer software MaGraBo. This gave the possibility to measure and take picture from the samples.

3.1.2 Scanning Electron Microscope A scanning electron microscope (SEM) of model 1450 VP from LEO was used. Detailed information about how SEM functions can be found on internet or in literature, e.g. Flewitt and Wild’s Physical Methods for Materials Characterisation [46]. In this model a tungsten ﬁlament is used to generate the electrons that bombard the surface. The secondary electrons with their low energy are detected, giving a good resolution of the surface. There is also the possibility to use a ﬁlter to detect

Nayeri Hashemzadeh, 2005. 31 3.1. Instruments Used 32 the backscattered electrons that have a higher energy, to get a better contrast between the different materials on the surface. The electrons can be accelerated to an energy of 50 keV . The apparatus is said to be able to theoretically to give 800 000 times magnification, but in reality the quality of the pictures limits the magnification to 10 000 times. The resolution is 20 nm.

Energy Dispersive X-ray spectroscope The 1450 VP is equipped with an Energy Dispersive X-ray spectroscope (EDX). Information about how EDX functions can be found on internet or in literature, e.g. Flewitt and Wild’s Physical Methods for Materials Characterization [46]. With this EDX, one could detect elements as light as Boron.

Figure 3.1: The depth for which EDX gives information about is roughly obtained by this diagram which is given in the manual of the EDX that was used. By using the density of the elements that are near to surface one can estimate the penetration depth. In this work mostly an electron beam energy of 30 keV was used. Sn has the density of 7.31 g/cm3, resulting in a penetration depth of 2.5 µm.

The penetration depth of the analysis is dependent on the materials that are 3.2. Measuring Mechanical Durability 33 investigated and the kinetic energy of the electrons in the beam. Figure 3.1 shows how this information can be obtained. Roughly one can say that elements that make up less then 1% of the weight of the composition will not be noticed in the EDX diagram.

3.2 Measuring Mechanical Durability

3.2.1 Stereo Microscope Stereo Microscope of Wild Peerbrugg was used with the camera Axiocam MRC5, together with the computer software MaGarBo. Stereo microscope was used for looking at samples that were hard to look at with ordinary light microscope due to their dimensions. Here the highest resolution that can be achieved is 50 times. It is however not possible to measure lengths with this microscope.

3.2.2 Vibration and Shock Table To test the vibration endurance of the whiskers two vibration tables were used.

Vibration table 1: RMS, SW1507 Accelerometer: Enevco SN 40021, Sensitiveness: 1.041 [mV/(m/s2] Vibration table 2: RMS, SW8130 Accelerometer: Enevco SN 40021, Sensitiveness: 1.041 [mV/(m/s2] The two tables have diﬀerent weights, table 2 being the heavier one. This does not inﬂuence the result of the vibration tests. The vibrations are produced for a combination of all directions and they reach up to 4500 Hz, depending on how high is the power spectral density (PSD [(m/s2)2/Hz)]). The PSD describes the relation between the acceleration and the frequency produced. This is measured by the accelerometer and registered in a computer. For the mechanical shock resilience test table 2 was used because it can produce higher shocks.

3.2.3 Vibration and Shock Tests Experiments were carried out to test the resilience of whiskers against vibrations and shocks. Two diﬀerent types of samples were used in these tests. Sample 1, shown in ﬁgure 3.2, showed growth of two large whiskers which were studied by the stereo microscope. One whisker had grown a distance of 800 µm, from one pin to the other creating a short and the other whisker was about 350 µm 3.2. Measuring Mechanical Durability 34

Figure 3.2: This sample, noted as sample 1, was used as to test whiskers endurance against vibrations and shocks. The sample is a sensor with pins that are coated with bright Sn. It can more clearly be seen in b) that a long whisker has grown from one pin to another, causing a short. long.

Figure 3.3: This sample, noted as sample 2, was used to test whisker endurance against vibrations. On this sample growth of many whiskers was observed. The whiskers growing out from the edge of the sample were counted and measured for each pin to see if vibration would make the amount of whiskers less.

Sample 2, shown in ﬁgure 3.3, had many whiskers on it. The whiskers on the edges of each pin which were longer than 30 µm were counted and measured with light microscope 2 (see section 3.1.1). All together about 1000 whiskers were noted on the edges of the sample. First vibration tests were done with duration of 5 minutes on vibration table 1 (see section 3.2.2, page 33). The vibration generated were random and as follows: • 0.1 (m/s2)2/Hz, 0.2 (m/s2)2/Hz and 0.3 (m/s2)2/Hz, frequencies: 10-4500 Hz

• 0.4 (m/s2)2/Hz, frequencies: 10-3970 Hz (limit of vibration table) 3.3. Measuring Electrical Durability 35

For each PSD of 0.1, 0.2, 0.3 and 0.4 (m/s2)2/Hz the subsequent frequencies were used on the samples.

Figure 3.4: Proﬁle of vibration tests according to ISO 16750-3 standard, which is the hardest type of vibration test for electronic devices used in vehicles. The random vibration has the proﬁle of what would be generated by roughness in the roads, while the sine vibrations simulate the motion of the cylinders.

Also test with duration of 22 hours were done on table 2 (see section 3.2.2). This test is according to ISO 16750-3 standards and is the hardest type of test for electronic devices used in vehicles. The proﬁle of this standard is shown in picture 3.4.

The parameters for the shock tests done on vibration table 2 were as following: • 100 shocks with 500 m/s2, duration 6 ms. • 100 shocks with 1000 m/s2, duration 6 ms.

3.3 Measuring Electrical Durability

3.3.1 Microprobe Microprobe was used to measure the current carrying capacity of the whisker. The device used is a Programmable Power Supply HM7044 and this device is from 3.3. Measuring Electrical Durability 36

HAMEG Instruments. A voltage was applied in the tests and the current was measured and plotted with a PC. It is possible to set a compliance current that is the limit to how high the generated current can be. The highest allowed current for the device was 0.1 A. The Microprobe is equipped with a microscope that gives magniﬁcation of up to 500 times.

3.3.2 Electrical Conductivity Tests The conductive properties of the whiskers were tested with the microprobe. Fig- ure 3.5 shows the sample on which the whiskers that were tested were found.

Figure 3.5: Whiskers grown on devices like this were used to test the conductivity of the whiskers. Whiskers in the range of 100 to 200 µm could be found on these samples. This device is plated with bright Sn on Cu.

These samples showed good propensity to grow whiskers with a length up to 200 µm. Whiskers were first selected with the light microscope. The selected whiskers were studied closer in the SEM to get more information about the length and the diameter. A voltage interval was applied on the sample to measure the current going through the whiskers. The voltage interval and the compliance current was varied (see section 3.3.1). In the beginning a fine needle was used, with a tip diameter of about 10 µm, which was brought to contact with the whiskers, using the microscope of the Microprobe to realize a good contact. Many measurements were done, but results or reasonable results were achieved scarcely. This was contributed by us in beginning to bad contact. As to achieve better contact, conducting glue was applied on the fine needle. The conducting glue contains silver to make it conductive. With the help of the glue more reasonable results were achieved. Still many times even though contact was clearly realized, no results were achieved. This will be further discussed in section 4.2.1. 3.3. Measuring Electrical Durability 37

Test have also been carried out by using a Cu pin coated with Sn, instead of a needle. No contact glue was used in these tests.

3.3.3 Finite Element Method

Finite Element Method (FEM) was used to simulate the critical current, Icrit, at which whiskers are fused. The program Ansys was used to make the simulations. FEM is used for solving complicated physical problems by dividing the physical model into simpler elements with homogeneous boundary conditions. The program solves the partial differential equation for each element and puts the results together to determine the reaction of the whole geometry. The simulation was done for a cylindrical whisker in contact with two pins of Cu, perpendicular to the surface of both of the pins. The environment was taken to be vacuum for simplification. The whisker was divided in 200 elements and the pins were divided in 300 elements each making the total amount of elements in the model to be 800. Simulations were done with more elements, showing that adding more elements to the model did not change the result considerably, but made the simulations slower. Besides the thermodynamic heat transfer equations used in the program some other relations were specified. This was the temperature dependence of electrical resistivity ρ(T ) which gives also the temperature dependence of the thermal conductivity through the Widemann-Franz law [16]:

ρ(T ) = ρ300K ∗ (1 + α(T − 300)). (3.1) where ρ300K is the electrical resistivity at 300 K, T is temperature and α is the temperature coefficient. Values of ρ300K and α can be found in table 2.1, page 19. The Widemann-Franz law for metals is: LT K(T ) = , (3.2) ρ(T ) where L = 2, 44 ∗ 10−8 [V 2/K2] is the Lorenz number and K(T ) is the thermal conductivity. Results from experiments were used to make a fit between Icrit measured for different diameters and lengths of whiskers and the highest temperature achieved in the simulated whisker. In this way a fusing temperature for the simulations was defined which differs from the melting temperature given in literature for Sn. 3.4. Studying Whisker Growth 38

3.4 Studying Whisker Growth

3.4.1 Focused Ion Beam The Focused Ion Beam (FIB) system used was from Fei, model FIB 200. Detailed information about how FIB systems function can be found on internet or in literature, e.g. Flewitt and Wild’s Physical Methods for Materials Characterisation [46]. This FIB uses Ga+ ions to bombard the samples. The secondary electrons are detected to get a picture. The ions are accelerated by 30 kV and the current used to get a picture of the sample lies between 4 pA to 70 pA. Magniﬁcation of about 100 000 times can be achieved. For this work the magniﬁcations of up to 50 000 times have been used. The pictures taken have been taken from an angle of π/4 radians to the surface of the sample.√ This means that in the vertical direction the shapes of the sample appear 1/ 2 shorter than they are. One can also make cuts on the sample by using higher ion currents. The currents used to make a cut on the sample, that is to gradually etch away the surface materials are between 6300 pA to 11 500 pA. Cuts on dimensions as little as 0.5 µm can be made. Before making a cut a layer of platinum (Pt) was deposited in FIB, as to protect the surface. This is made by releasing a gas containing Pt atoms over the surface of the sample. By shooting a current of 350 pA to 1000 pA the bonds between the Pt atoms are broken and the Pt is precisely deposited.

Figure 3.6: Schematic of the cross section of the samples studied.

Base Material Underlayer Sn Layer Heat Treatment CuSn0.15 - Dull Sn 3-5 µm - CuSn6 Ni = 0.15 µm Dull Sn 10-12 µm 180 oC, 5 min E-Cu58 Ni = 2 µm Bright Sn 3-5 µm Ag = 0.15 µm Bright Sn 10-12 µm Ag = 2 µm

Table 3.1: The parameters that were combined for the 48 diﬀerent types of samples. 3.4. Studying Whisker Growth 39

3.4.2 Sample Specifics 576 samples were prepared in the end of June 2004 to investigate whisker growth. The 576 samples were of 48 different types, i.e. they were arranged in 12 different groups undergoing different test conditions. The 48 different types of samples had different nominal layer systems and post plating treatments. A schematic of the cross section of the samples showing the layer systems can be seen in figure 3.6. The list of the 48 types of samples that were ordered can be found in the appendix, table A.3, in page 68. Table 3.1 shows an overview of the parameters that were changed for the different samples. More information about the plating process can be found in the appendix, table A.4, page 69. The 12 different groups have been undergoing different combinations of conditions as can be seen in the appendix, table A.1, page 67. The conditions are the following:

• Soldering simulation: Reﬂowing the Sn plated surface, i.e. heating up the surface to 260 oC, which is above the Sn melting point

• Temperature Cycling: 500 cycles between -60 oC to 60 oC

• High Temperature Storage: 50 oC

• Room Temperature Storage: 22 oC

• Humidity: 1000 h storage under humid conditions, 85 % relative humidity and at 50 oC

Figure 3.7 shows a schematic overview of how the samples were delivered to us, where the dashed lines present how we divided each delivered part into three samples.

Figure 3.7: A schematic of the coated parts the way they were delivered. The dimension of the part is 3 × 1 cm. The dashed line presents how each part was divided into three samples. The hole on the upper part is made for the bath process to dip it into the galvanic bath. 3.4. Studying Whisker Growth 40

3.4.3 Sample Study After a storage of about six months the samples were thoroughly examined, mainly with the help of LM 2 ( see section 3.1.1), to detect whisker growth. A grading system was made to judge the level of whisker growth, as can be seen in table 3.2.

1 No whiskers could be observed 2 Hillocks or very small whiskers observed 3 Whiskers were observed, few and short 4 Whiskers were observed to grow with high density or being very long 5 Many long whiskers were observed

Table 3.2: The grading system that was used to judge whisker growth on the samples.

The whiskers found were measured and the longest whisker was noted in a table that will be discussed further more in the results section. It has to be noted that the measured length of the whiskers is only the length of the projection of the whisker in the horizontal plane and therefore depends highly on how the whisker grows out of the surface. It was discovered that whisker growth on the samples was rather inhomogeneous. Therefore grades with mixed number were also used to mark that fact. After optical investigation of all of the samples, some samples were chosen for a closer study with FIB system. One or two FIB cuts were made on the samples to study the whisker- and layer cross sections. First a layer of Pt was deposited with a current of 350 pA in the FIB system. The dimensions of the layer varied regarding how deep the cut was meant to be, but usually it was around 30µm × 7µm with a thickness of about 1 µm. The depth of the cuts were usually around 15 µm. The cuts were done in a first step by a current of 11 500 pA, which gives a faster cut but a more rough one. To make the cross section finer, a current of 6 500 pA was used. Pictures were taken by a current of 4 pA or 11 pA in. To measure the average IMC and Sn thickness from the pictures taken with the FIB, the thickness of each layer was measured on 20 places, equidistant from each other. As explained before, the pictures taken by FIB were taken under an angle√ of π/4 rad from the surface, so the measured thickness were multiplied with 2. These samples were further studied by help of the SEM and EDX. This as to get information on the density of whisker growth in the surroundings of the FIB cut, as well as the material composition of the surface around the FIB cut. Measurement of whisker density was done in SEM on some of the samples that were studied in FIB as to see how much whisker growth there was in the near vicinity of the cut. This was done was by centering the SEM picture on the FIB cut with a magnification of 150 times, resulting in an area of about 760 µm times 3.4. Studying Whisker Growth 41

420 µm visible in the monitor. The whiskers that were seen in this area were measured. Out of this a whisker volume per area could be calculated. EDX analysis was done in the same way, with a magniﬁcation of 500 times and work distance of roughly 20 mm with a fairly sharp contrast to get a measurement of the composition of the surface material. The information depth of these measurements are roughly 2 µm. Chapter 4

Results

4.1 Mechanical Durability

Whiskers can cause shorts in electronics. This can happen principally in three ways: • a whisker can grow from one electrical contact to another

• two whiskers can grow on two diﬀerent electrical contacts, and come in contact with each other

• a whisker could break and fall oﬀ, making a short somewhere else on the circuit board. Vibrations with frequencies around the natural frequency of the whisker may cause a whisker to break. Calculations on the natural frequency of whiskers and tests on whiskers resilience against vibrations and shocks will be presented.

4.1.1 Natural Frequency of Whiskers The natural frequencies of whiskers can be calculated with the Euler-Bernoulli Beam theory. These calculations can be found in Appendix B, page 70. For a cylindrical whisker that grows perpendicular to the surface with one end free the natural frequency equation is √ 1.882 Ed f = √ . (4.1) 8π ρ L2 Here f is the natural frequency , d the diameter , L the length, E the Young’s modulus of the whisker and ρ is the density of the whisker. Figure 4.1 shows calculations that were made on this model with help of Matlab, and plotted by

Nayeri Hashemzadeh, 2005. 42 4.1. Mechanical Durability 43 using the program Origin. A more precise table can be found in the appendix, table B.1, page 74.

Figure 4.1: Calculations made on the natural frequency of a cylindrical whisker. The length and the elasticity modulus are varied, while the diameter is set to, d = 2 µm. The frequency f ∝ d.

Whisker Length Natural Freqeuncy Natural Frequency [µm] free at one end [Hz] connected at both ends [Hz] 800 (Sample 1) 460-1490 3250-10600 350 (Sample 1) 2390-7790 - 30-200 (Sample 2) 7320-≈ 5 ∗ 105 -

Table 4.1: Natural frequency range for the group of the whiskers that were tested with an estimated diameter of 2 µm. Only the whisker of size 800 µm is connected at both ends.

If the whisker has grown to connect perpendicular to another electrical contact and both ends are set to be equal, the natural frequency is then 6.36 times bigger than the frequency resulting from equation 4.1. These calculations can also be found in the appendix B.1.1.

4.1.2 Results from Vibration Tests Tests were carried out as described in section 3.2. As can be seen in figure 3.2 the whisker of a length of 800 µm found on sample 1 is in contact with the other 4.1. Mechanical Durability 44 pin, thus the natural frequency would change as discussed previously. Table 4.1 shows the range the natural frequency of these whiskers should lie according to the calculations made. As described in section 3.2 in the first set of tests that had duration of 5 minutes, the samples were tested for frequencies up to 4500 Hz. As can be seen in table 4.1 frequencies as high as 4500 Hz could contain the natural frequency of the whiskers of the sample 1, i.e. if the Young’s modulus of the two whisker would be small enough. Nevertheless none of the two whiskers on the first sample broke off after the first set of tests. Neither did the number of whiskers on sample 2 decrease after these tests, which is consistent with the fact that the natural frequency of the whiskers on sample 2 were not reached. The second test with a duration of 22 hours and conditions according to the hardest standard vibration test done for electronics used in automotive industry with the highest frequency of 2000 Hz was done on sample 1. None of the two whiskers broke off after this test either, ruling out the necessity of doing this test for the second sample.

4.1.3 Results from Shock Tests Shock tests were performed on sample 1 with 100 shocks, each with a duration of 6 ms and accelerations of 500 and 1000 m/s2. None of the whiskers broke. This is in good accordance with tests performed by Dunn in 1988 [11]. He reported that whiskers with lengths up to 1 mm withstood shock loads up to 2000 g, g being the gravitation constant of the earth.

Figure 4.2: The expected resistance of a whisker with dependence of its length, calculated using the equation 4.2. The diameter of 2.5 µm is used here because it was the diameter most common for the whiskers that were tested. 4.2. Electrical Durability 45

4.2 Electrical Durability

Tests were performed to investigate how much electrical current whiskers can carry. Based on the results achieved FEM was used in Ansys program to simulate the critical current at which whiskers fuse.

4.2.1 Electrical Conductivity of Whiskers As described in section 3.3 it was difficult to achieve results measuring the electrical conductivity of the whiskers. This difficulties are presumably caused by a non conductive surface oxide. The variation of the resistance in different measurements for the same whisker is also contributed to the surface oxide. The resistance of the test setup was measured by bringing the needle or the pin directly in contact with the surface of the sample. This measured resistance is in series with the resistance of the whisker. The lowest achieved resistance of the test setup was 0.1 Ω which is subtracted from the results. The expected resistance of the whiskers can be calculated using the resistivity of Sn, (ρ = 110 · 10−9Ωm [16]). L R = ρ (4.2) A Here L is the length of the whisker, and A is the cross section area. In figure 4.2 the expected resistance for a whisker with a diameter of 2.5 µm in dependence on its length is shown.

Length [µm] 60 115 240 115 70 170 105 80 140 55 200 Diamter [µm] 2.5 2.5 2.5 2.5 2.8 2.5 1.6 1.9 5.5 1.6 3.3 Resistance [Ω] 0.4 0.7 6.7 6 3 14 23 14 34 30 30 Resistivity [10−9Ωm] 17 30 140 260 260 400 440 480 580 1100 1200

Table 4.2: In this table the lowest measured resistance for diﬀerent whiskers are presented.

Table 4.2 shows the results of the resistivity and resistance of some of the whiskers tested. In most cases the measured resistivity was higher than ρ = 110 · 10−9Ωm, but there is also cases where the resistivity is lower than expected for Sn. Due to difficulties mentioned not many graph where one actually can see at which current the whiskers get fused were achieved, figure 4.3 shows such a graph. Table 4.3 shows the fusing currents for investigated whiskers. The highest current carried by a whisker was 55 mA as seen in figure 4.4. This whisker had a diameter of about 5.5 µm and a length of about 120 µm. Try to do tests with higher compliance currents than 55 mA eventually rendered in the fusing of the whisker. The values in table 4.3 shows the fusing currents achieved in the tests. 4.2. Electrical Durability 46

Figure 4.3: This graph shows the electrical current in dependence on the applied voltage for a whisker, withstanding currents of up to 17 mA before fusing. The whisker had a length of 140 µm and a diameter of 3,7 µm.

4.2.2 FEM Calculations Table 4.3 shows the temperatures achieved in the FEM calculations for respective whisker and its critical current. Calculations were done for whiskers with diameter of 2.5 µm, where there was more results and the simulation fusing temperatures were more consistent. The mean value of the simulated fusing temperatures for whiskers with a diameter of 2.5 µm in table 4.3 gives the fusing temperature of 382.5 K for the FEM model. Despite the simpliﬁcation of the geometry, the diﬀerence in conditions and the

Length [µm] Diameter [µm] Icrit [mA] FEM simulated fusing temperature [K] 240 2.5 11 378.7 150 2.5 15 351.6 140 2.5 21 409.4 120 2.5 23 390.4 140 5.5 32 305.6 120 5.5 55 315.4 140 3.7 17 308.6 110 2.1 20 431.3

Table 4.3: Summary of the critical currents (Icrit) at which the whiskers got shorter or got fused in the tests. FEM simulations were made for these Icrit, resulting in the temperatures given in the outer right column. 4.3. Whisker Growth Study 47

Figure 4.4: This graph shows the highest current carried by a whisker. The whisker in question had a length of about 120 µm and a diameter of 5.5 µm. The peculiar form of the graph could be due to deformations taking place at the tip as the current is getting near 55 mA. lack of a bigger experimental data basis to build the model on, some conclusions from the simulated results can be made. It can be seen in the figure 4.5 a stark increase in Icrit as the length decreases, this is because the two pins would more effectively divert the heat from the whisker. It can also be seen that Icrit(L) seems to converge towards a certain value as the length increases, in this case towards 1.5 mA. This is presumably because the pins are less effective heatsinks for long whiskers.

4.3 Whisker Growth Study

As described in section 3.4.2 there were 576 samples that had undergone different conditions or had different sample specifics. These samples were carefully studied with light microscope 2 (see section 3.1.1). Each sample was graded with the system explained on page 40. The results of this work can be found in the appendix, table B.2 and table B.3. As can be seen in these tables, the results from group 7xx are incomplete, this due to an unfortunate accident which mixed up the samples in that group. Some of the samples were graded with more than one number, for example 1-5, meaning that some areas of the 1 by 1 cm sample showed no growth of whiskers while other areas showed lots of long whiskers. The target of these investigations was to identify which type of samples show whisker growth and which conditions promote or prohibit whisker growth. Look- 4.3. Whisker Growth Study 48

Figure 4.5: FEM simulation for the critical current (Icrit) at which the whisker will fuse in dependence of the whiskers length. The whiskers are set to have a diameter of 2.5 µm. ing at the results in table B.2 and table B.3, and comparing the 12 sample groups (the conditions the groups had undergone can be found in table A.1) it is difficult to identify conditions that promote whisker growth. There are groups that in general show more whiskers than other groups, but it is hard to single out conditions that would be behind these differences. Results from some of the samples contradict reports on whisker growth from other researchers. Specifically samples with Ni underlayer, that as discussed in section 2.3, page 29, were reported to restrain whisker growth. Some of the reasons behind the whisker growth seen on these samples will be shown in following section.

4.3.1 FIB Results FIB cuts were made to study the cross section of some of the samples. In particular inhomogeneous samples and those with underlayer that had shown whisker growth. The first sample looked at with the help of FIB systemes was sample 634. This sample is graded as 1-5 meaning that it shows great local variation of whisker growth. Two FIB cuts were made on sample 634, one cut on an area with many whiskers and one FIB cut on an area with no whiskers. Pictures from the cuts made are shown in figure 4.6 a) and b) respectively. One can see that there is clear differences between the cross sections of the two cuts. In figure 4.6 a) one sees that the Sn thickness is quite thin (about 1 µm) and that there is a lot of IMC, which probably is Cu6Sn5. It is also hard to recognize that there is any coherent Ni layer. EDX analysis over the cut showed no traces of Ni. In figure 4.6 b) one 4.3. Whisker Growth Study 49

Figure 4.6: a) and b) show FIB cuts on sample 634, c) shows the nominal conﬁguration of sample 634. a) is from an area with growth of many long whiskers while b) is made on an area with no whisker growth. In ﬁgure a) the whisker itself is shown with a thicker base due to the platinum sputtered on the spot that was intended to be cut by the FIB. can see that the Sn layer is much thicker, with a thickness of about 8 µm. It is also possible that there is thin coherent layer of Ni, which has limited the growth of IMC which is much less apparent in comparison.

Other FIB cuts from samples that have shown great variation of whisker growth, have given similar results, i.e. great differences in Sn and underlayer thicknesses. This means that the nominal layer thicknesses on these samples are not reliable. This applies in particular for samples with a hole. As explained in section 3.4.2, page 39, one of three samples had a hole. This is due to the fact that the parts were hung from the holes as they were dipped in the galvanic bath solution, resulting in different parameters for the areas near the hole. This is noted in table B.2, page 75 and table B.3, page 76, with L noting a sample with a hole, and KL notes a sample without a hole. These differences makes it difficult to compare the storage conditions of the different groups. It is however interesting to be able to see with help of FIB cuts how differences in layer thicknesses on a sample of size 1 times 1 cm effect whisker growth. Some of the interesting FIB pictures taken will be shown below

No Use of Underlayer The sample showing locally the highest whisker densities, with the longest whiskers was sample 640. Pictures from the two FIB cuts made on sample 640 can be seen in ﬁgure 4.7. Sample 640 had a hole and as can be seen there is great variation between the Sn layer thicknesses. The area which showed a lot of whiskers had a 4.3. Whisker Growth Study 50

Figure 4.7: Sample 640 had a hole, showing great local variation in whisker growth. In a) it can be seen that the Sn thickness is much less than the nominal value given in c). The area where the cut was done, showed many long whiskers, longest around 250 µm. Figure b) is from a place with no whiskers. combined Sn and IMC thickness of about 1.5 µm. The place with no whiskers had a combined Sn and IMC thickness of about 13 µm.

Figure 4.8: a) shows the FIB cut from sample 813 and b) from sample 1113. Sample speciﬁcs for both of the samples can be seen in c). Both of the samples were without a hole. The cross sections of the two samples seem quite similar. Sample 813 was graded as 3, showing small whiskers. No whiskers were detected on sample 1113 in the light microscope.

FIB cuts were also made on samples 813 and 1113, making it possible to compare the diﬀerence between 813 graded as a 3 and 1113 graded as 1. Both samples had no hole. Figure 4.8 a) and b) show the result. Cross sections of both samples are similar. Taking a look at the storage conditions the two samples have undergone, the diﬀerence between the two samples is that samples 8xx have undergone temperature cycling. Both have been kept for 1000 h at 85 % relative humidity and 50 oC and then stored at room temperature for the rest of the six months. This indicates that temperature cycling encourages whisker growth. 4.3. Whisker Growth Study 51

Figure 4.9: Sample 801 was graded as a 1 meaning no whiskers were observed on the sample. The speciﬁcs of sample 801 can be seen in b).

To be able to judge the inﬂuence of the base material FIB cuts were made on another sample in the 8xx group. Sample 801 has nominally been plated with 3-5 µm dull Sn on the base material CuSn6. Figure 4.9 shows the FIB cut from sample 801, which was graded as 1. In comparison with the cross sections showed in ﬁgure 4.8, 801’s cross section seems quite similar. No whiskers were detected on samples of type x01, indicating that whisker growth is inhibited or retarded on base material CuSn6. Samples from types of x43, which are plated with 3-5 µm bright Sn over CuSn6 did not show that much whisker growth either. Samples plated with 3-5 µm dull or bright Sn with no underlayer on the other two base materials (CuSn0.15 and E-Cu58) showed in general growth of many whiskers.

Figure 4.10: FIB cuts from sample 211 can be seen in a) and b). The nominal value of the Ni underlayer and Sn layer can be seen in c). In a) the cut from the area with many long whiskers is seen. One can see that there is still some small amount of Sn, while most have reacted to become intermetallic compound, probably both Cu6Sn5 and Ni3Sn4. In b), from the area with no whisker growth, there seem to not be any unreacted Sn. 4.3. Whisker Growth Study 52

Figure 4.11: In a) the EDX analysis over the FIB cut where there was a lot of whiskers on sample 211. b) is from the place with no whiskers. As can be seen the presence of Ni is more evident on the EDX analysis taken from the place with substantial whisker growth. The cross section of the two FIB cuts can be seen in ﬁgure 4.10.

There has however been extensive whisker growth observed on some samples with base material CuSn6, e.g. sample 211, which nominally has 2 µm Ni underlayer and 3-5 µm dull Sn and has been studied with FIB cuts as shown in following section.

Ni Underlayer Some samples with holes with nominal Ni underlayer showed extensive whisker growth. Sample 211, which has a hole, was graded as 1-4 with the biggest whisker being at least 120 µm. As mentioned the base material for 211 is CuSn6, a base material which has not shown that much whisker growth. Figure 4.10 shows the two cross sections done on the sample 211, a) from the area with high whisker density and b) from the place with no whiskers. In b) there seems to be no unreacted Sn left and the layer that probably is the Ni layer (and not IMC) seems coherent, otherwise there is not much difference between the two cross sections. EDX analysis made from the area of the cuts show some difference as seen in figure 4.11 a) and b). Presence of Ni is more evident in the EDX analysis taken from the area of the cuts over the place with a lot of whiskers. This indicates that at least there is more Ni in the top layer for the whisker dense place. FIB cuts were also made on samples 138 and 335 which showed inhomogeneous whisker growth. They have a nominal Ni layer thickness of 2 µm. The Ni layer observable on these samples were less than that. It is however difficult to see clearly were Ni layer ends and were IMC begins. Table 4.4 is a summary of the measured Sn and IMC thickness of these samples. For samples without hole (presumably with more reliable layer thicknesses) and Ni underlayer there are only three samples showing whisker growth. These samples 4.3. Whisker Growth Study 53

Figure 4.12: The nominal values for samples 833, shown in a) and sample 1033 shown in b) can be seen in c). Sample 1033 showed more and longer whiskers than sample 833. are 821, 833 and 1033 with 0.2 µm Ni layer. FIB cuts were made on all these samples. The FIB cut showed that the Sn layer thickness on all these samples is about 3 µm, which is according to the nominal values. Figure 4.12 shows the FIB cuts on samples 833 and 1033. Samples 821 and 833 were graded as 2-3, meaning that not many whiskers were detected on the two samples. Sample 1033 was however graded as 4, with some whiskers longer than 80 µm. The diﬀerence between samples 821 and 833 and sample 1033 is that there is more IMC on 1033 than the other two.

Ag Underlayer Only two samples without hole and with Ag underlayer showed whisker growth. Figure 4.13 shows the FIB cuts made on these two samples, sample 1032 and 1120. The cross sections of the samples agree with the nominal layer thickness of both of the samples (2 µm Ag underlayer and 10-12 µm dull Sn layer). Sample 1032 has the base material E-Cu58 and sample 1120 has base material CuSn0.15. It has to be noted that both samples showed little amount of whisker growth, the longest whiskers noted had length of about 20 µm. It is however interesting to see that

138 211 335 No whisker Whisker No whisker Whisker No whisker Whisker Sn thickness [ µm ] 4.24 0.21 0 0.16 0 0.08 IMC thickness [ µm ] 2.12 2.77 1.65 1.65 1.82 1.68 Sn and IMC thickness [ µm ] 6.36 2.98 1.65 1.81 1.82 1.76

Table 4.4: Samples 138, 211 and 335 had a nominal Ni layer thickness of 2 µm. The Sn and IMC thicknesses are measuered from the FIB cuts made on these samples. 4.3. Whisker Growth Study 54

Figure 4.13: The two pictures show FIB cut from samples 1032 and 1120. Both sample 1032, shown in a) and sample 1120 shown in b) had the nominal values of 10-12 µm dull Sn plated on 2 µm Ag underlayer, which is in accordance with the thicknesses seen in the ﬁgure. there can be whisker growth despite a 2 µm Ag underlayer.

Sample Whisker volume Sn thickness IMC Sn+IMC IMC/(Sn+IMC) per area [nm] [µm] [µm] [µm] 138 0 4.24 2.12 6.36 0.33 211 0 0 1.65 1.65 1.00 335 0 0 1.82 1.82 1.00 801 0 1.09 1.01 2.10 0.48 640 0 11.57 1.04 12.61 0.08 1113 0.246 1.19 1.44 2.63 0.55 211 0.653 0.16 1.65 1.81 0.91 138 0.893 0.21 2.77 2.98 0.93 833 2.40 2.47 0.33 2.80 0.12 821 4.33 2.35 0.33 2.68 0.12 335 4.69 0.08 1.68 1.76 0.95 813 7.65 1.01 1.77 2.78 0.64 640 21.2 0.42 1.07 1.49 0.72

Table 4.5: Whiskers around the FIB cuts were measuered and based on those measurements the whisker volume per unit length was calculated. Also from the pictures taken in the FIB system the thicknesses of the Sn layer and the IMC layer were measured.

Density Check Whisker density check was done on some of the samples that were studied with FIB. The whisker densities of these samples are compared to the Sn and IMC layer thicknesses of the samples in table 4.5. There is little correlation to be noted between whisker growth and the other parameters listed in the table. It can be seen 4.3. Whisker Growth Study 55 that samples showing inhomogeneous whisker growth have either a much thicker Sn layer where there is no whisker growth compared with where there is whiskers, or they do not have any unreacted Sn layer where there is no whisker growth. Chapter 5

Discussion of the Results

In this chapter the experimental ﬁndings will be reviewed and compared with the theoretical models and existing research.

5.1 Mechanical Properties

The calculations and the results achieved shows that Sn whiskers have high resilience against vibration and mechanical shock. The risk of whiskers breaking off and causing a short somewhere else on the electronic board can however not be ruled out based on our tests or calculations. It is probable that longer and thinner whiskers than those tested are more likely to break off for vibrations and shocks that were tested. In our tests random vibrations were applied on the samples, which could mean that the natural frequency of the whisker could be in the test frequency range but not sustained long enough to make the whisker to break off. However, considering the second test with a duration of 22 hours, it is not likely that this was the case. This would mean that either the Young’s modulus made the natural frequency of the whiskers tested to be outside the tested frequency range or whiskers are not damaged by vibrations in the range of their natural frequency.

5.2 Electrical Properties

It can be seen in table 4.2 that the resistivity of the different whiskers differ up to a factor of 100. This is thought to depend mostly on a thin isolating layer of oxide surrounding the whisker. Another factor for the huge difference in the results is the difference in the contact resistance. Two of the resistivity measured are lower than the resistivity given for β-Sn in the literature. This could be perhaps because whiskers are single crystals and therefore

Nayeri Hashemzadeh, 2005. 56 5.3. Tin Whisker Growth 57 have lower resistivity. The highest current measured to be tolerated by a whisker was 55 mA. This value is higher than what has been reported from other authors, e.g. Dunn 1988 [11]. The peculiar graph shown in figure 4.4, where the measured current first goes up to 54 mA, than decreases to about 45 mA and thereafter goes to peak at 55 mA (the compliance current) is probably due to start of changes in the whisker, e.g. melting of the tip of the whisker. The FEM simulation of the critical current for different lengths of whiskers of with a diameter 2.5 µm was based on a small experimental data base. The simulation of fusing temperature could become considerably better with a bigger experimental data base. The simplification of the environment of the whisker to be vacuum is presumably more important when the whisker is longer, resulting in a lower critical current. However, the results give a good indication of the currents a whisker can tolerate, as well as how current carrying capacity depends on the length.

5.3 Tin Whisker Growth

The plating of the samples revealed to be inhomogeneous, especially in the regions of the holes. Therefore the ﬁnding of clear correlations is very diﬃcult. There are however some clear conclusions which can be drawn from the investigation of all the samples with the light microscope. The results of this investigation is found in table B.2 and table B.3. One clear result is that it is important to be able to control the plating parameters to get a homogenous plating.

5.3.1 Heat Treatment One of the results worth noting in table B.2, page 75 and table B.3, page 76, is that samples that have been heat treated can grow whiskers, however the whisker growth observed was limited. Samples that had undergone heat treatment were kept at 180 oC for 5 minutes, which is a known mitigation practice (see section 2.3). Out of the 66 heat treated samples, 4 showed whisker growth after six month. The longest whisker measured (on sample 628) was around 25 µm. This indicates that heat treatment restrains whisker growth.

5.3.2 Soldering Simulation It can be seen from the light microscope investigation that reflow of the Sn plated surface as a mitigation strategy (see section 2.3) is not effective. Groups 0xx to 5xx underwent all soldering simulation (see table A.1, page 67), which is reflow of the Sn plated surface (that is heating the surface above the Sn melting point). As 5.3. Tin Whisker Growth 58 can be seen in table B.2 and table B.3 there is extensive whisker growth on some of these samples.

5.3.3 Storage Conditions It is difficult to draw any clear conclusion from the storage conditions due to the uneven plating quality of the samples. The following conclusions are based on the FIB studies and due to the small quantity perhaps immature. FIB cuts made on samples 813 and 1113 (see figure 4.8, page 50) show that both samples had equivalent Sn layer thicknesses. Sample 813 showed whisker growth while no whisker growth was observed on sample 1113 in the light microscope. A reason behind this difference is perhaps that the 8xx group have undergone temperature cycling as opposed to the 11xx group (see the appendix A and table A.1). Figure 4.12 on page 53 show the FIB cuts on the samples 833 and 1033, which show equivalent Sn layer thicknesses. It is however impossible to judge if the nominal 0.2 µm Ni layer of the samples are equivalent. More whisker growth and longer whiskers were observed on sample 1033. There is more IMC growth on sample 1033 than 833 according the pictures from the FIB system. If the Ni layer thicknesses of both samples are assumed to be equal, the more extensive whisker growth of sample 1033 could be contributed to the difference in storage conditions. Group 10xx has been stored at 50 oC while the group 8xx has been stored at room temperature. Group 8xx has also undergone temperature cycling, which group 10xx has not (see table A.1, page 67).

5.3.4 Base Material Looking at the three diﬀerent base materials (see appendix A, table A.2, page 67 for composition of the three base materials) samples with base material CuSn6 showed less whisker growth than samples with the two other base materials. A comparison of the observed whisker growth can be seen in table 5.1.

Samples with Whiskers Base Material No Hole All CuSn6 4/107 20/176 CuSn0,15 11/112 40/176 E-Cu58 10/111 40/176

Table 5.1: An overview is given of how many samples that showed whiskers in relation to the base materials and if the samples had holes on them or not.

Looking at the samples without hole only four samples showed growth of whiskers 5.3. Tin Whisker Growth 59 on samples with base material CuSn6. The whiskers observed on three of the four samples were smaller than 10 µm. The forth sample, sample 444, which was graded as 1-4 (a grading that indicates uneven plating) showed whiskers as long as 100 µm. Another aspect of samples with base material CuSn6 is that beside sample 442 which had a hole, no whiskers were found on samples with the nominal 3-5 µm Sn layer and no underlayer. This was studied with a FIB cut made on sample 801 (see figure 4.9, page 51), which showed a 1 µm thick IMC layer and 1 µm Sn layer. This is equivalent to the IMC and Sn layer seen in the FIB cuts made on sample 813 (see figure 4.8, page 50). The Tu model which assumes the IMC growth as the reason behind whisker growth (see section 2.2.3) can not be confirmed with these results [26]. There are however samples with base material CuSn6 showing growth of very long whiskers, up to 120 µm. These samples have however a hole on them, which suggest uneven plating. A conclusion out of these results could be that the range of Sn thickness which within the whisker growth occurs on base material CuSn6 is more narrow, with the upper limit of the Sn thickness being quite low (with regards from FIB cuts made on sample 801 lower than 2 µm).

5.3.5 Underlayer Use of Ni or Ag underlayer seems to have a damping effect on whisker growth. However some of the longest whiskers that were found where on samples which nominally had a Ni underlayer. Results from FIB cuts made on samples with whisker growth showed that the Ni layer thickness on these samples were under the nominal values. Three of the samples with Ni underlayer and no hole showed whisker growth, and all these samples had nominally 0.2 µm Ni underlayer. This could suggest that an intact 2 µm thick Ni underlayer prevents whisker growth. The few whiskers found on samples with Ag underlayer were all quite small. Judg- ing from the cross section pictures taken from these samples the layer thicknesses are according the nominal value. There is no IMC visible, which is another argu- ment against the model of Tu that assumes growth of IMC as the reason behind whisker growth [26]. Looking at the FIB cuts made on samples with Ag underlayer that showed whisker growth (see figure 4.13 a) and b) ) there is some interesting note to take. Even though the Sn layer is very thick on these samples, there is mostly no more than one grain in the vertical direction. The picture taken from cross sections with thick Sn layer and no whisker growth however show several grains in the vertical direction as can be seen in figure 4.6 b) and figure 4.7 b). This is in accordance with the stored strain energy theory (see section 2.2.2, page 22) where the normal recrystallization process is assumed to be inhibited due to grain boundary 5.3. Tin Whisker Growth 60

Figure 5.1: a) Illustration of figure 4.13 a) and b), where there is only one grain in the vertical direction for the samples with Ag underlayer that showed whisker growth. b) illustrates figures 4.6 b) and 4.7 b) which are pictures taken from places with no whisker growth. In these pictures one can observe several grains in the vertical direction. immobility. The boundaries would be pinned to there position, perpendicular to the surface. Thereof thicker layers of Sn with more than one grain in the vertical direction would be less likely to show whisker growth. This is illustrated in figure 5.1.

5.3.6 Dull versus Bright Sn The presented results do not indicate that bright Sn is more prone to whisker growth than dull Sn. The longest whiskers were however observed on samples with bright Sn. The mechanisms for whisker growth on bright Sn and dull Sn seem to differ on some manners. The grains of bright Sn are usually too small in their normal size to support a whisker, therefore whiskers on bright Sn seem to mostly grow from a nodule or with following flower eruptions as can be seen in figure 2.2 and figure 4.7. This growth mechanism demands a more complex explanation for whisker growth on bright Sn than dull Sn.

5.3.7 Tin Layer Thickness Table 4.5 is a trial to find a relation between Sn layer thickness and IMC growth with whisker growth. The information about the IMC and Sn thickness was taken from the FIB cuts. Another problem that should be noted is that some of the samples had Ni underlayer and some of the IMC formed would be between Sn and Ni. The differences between bright and dull Sn has not been taken in consideration either. With all these objections it is interesting to see that there is very little con- 5.3. Tin Whisker Growth 61 nection between the parameters put up and whisker growth. What can be seen is that samples showing inhomogeneous whisker growth, have either a much thicker Sn layer on the areas where there is no whisker growth compared with where there is whiskers, or they do not have any unreacted Sn layer on the areas where there is no whisker growth. This indicates that whisker growth in relation with the Sn layer thickness occurs within an interval as written in section 2.3. These intervals seem to depend strongly on the base material, underlayer, the storage conditions and type of Sn (dull or bright Sn). At the same time a limit is maybe a to definite answer to a problem which is more complex than that.

5.3.8 Conclusions on Whisker Growth Models Whisker growth as a result of surface energy effects (see section 2.2.1) seem to lack in ability to explain why whisker growth differs for Sn plated on different base materials as well as the role of the Sn layer thickness on whisker growth. The success of different mitigation strategies, e.g. annealing or use of underlayer is not treated in the proposed models either. Tu’s model where whisker growth is explained due to internal mechanical stress caused by growth of the IMC Cu6Sn5 (see section 2.2.3) is incompatible with some of the findings done in this work. These findings are lack of clear correlation between IMC thickness and whisker growth and that whisker growth was observed on samples with Ag underlayer despite lack of IMC. Stored strain energy where an abnormal recrystallization process is behind whisker growth (see chapter 2.2.2) seems not to be contradicted by this work. However, reasons behind why whisker growth would differ on different base material or with use of underlayer are not treated in the literature that was studied [24, 25]. Chapter 6

Future Work

For the electronic industry there is still a lot of work to be done to be able to rely on Sn coatings. Due to the urgent necessity of attending to the Sn whisker growth problem, work on whisker growth will have to go in two directions. One is to understand in detail the complex mechanisms of whisker growth. The other is to decide on which remedies that can restrain whisker growth. Solutions that provide enough security against failures while not adding to much new costs and steps to the production. Remedies on this problem will perhaps come before the whisker growth mechanisms are fully understood. This could be achieved by changing parameters such as base material, underlayer, Sn layer thickness as well as experimenting on the preparation conditions, from changing the galvanic bath properties to post treatment after the plating. When it comes to the work that has been done in this thesis, it will be interesting to follow up on the samples that were studied to see how they have evolved. It would also be interesting to investigate the actual layer thicknesses and perhaps this way being able to decide more accurate the parameters that will restrain whisker growth.

Nayeri Hashemzadeh, 2005. 62 Bibliography

[1] B. D. Dunn, Whisker Formation on Electronic Materials, Circuit World, 2, 4, pp. 32-40, (1976).

[2] G. T. Galyon, Annotated Tin Whisker Bibliography, NEMI Tin Whisker Modeling Project, (July 2003).

[3] H. L. Cobb, Cadmium Whiskers, The Monthly Review of the American Electroplaters Society, 33, pp. 28-30, (1946).

[4] I. Amato, Tin Whiskers: The Next Y2K Problem?, Available on: http://www.fortune.com/fortune/thisjustin/0,15704,1012859,00.html, Fortune Magazine, (Jan, 2005).

[5] J. A. Brusse, G. J. Ewell, J. P. Siplon, Tin Whiskers: Attributes and Mitiga- tion, 22nd Capacitor and Resistor Technology Symposium, pp. 67-80, (2002).

[6] B. D. Dunn, Metallurgy and Reliability in Spacecraft Electronics, Metals and Materials, 34, pp. 32-40, (1975).

[7] K. M. Cunningham, M. P. Donahue, Tin Whiskers: Mechanism of Growth and Prevention, 4th International SAMPE Electronics Conference,pp. 569- 575, (1990).

[8] C. Herring, J. K. Galt, Elastic and Plastic Properties of Very Small Metal Specimens, Letters to the Editor, pp. 1060-1061, (1952).

[9] C. Kittel, Introduction to Solid State Physics, Seventh Edition, pp. 587-607, (1996).

[10] G. T. T. Sheng, C. F. Hu, W. J. Choi, K. N. Tu, Y. Y. Bong, L. Nguyen, Tin Whiskers Studied by Focused Ion Beam Imaging and Transmission Electron Microscopy, Journal of Applied Physics, 92, 1, pp. 64-69, (2002).

[11] B. D. Dunn, Mechanical and Electrical Characteristics of Tin Whiskers with Special Reference to Spacecraft Systems, European Space Agency, (1988).

Nayeri Hashemzadeh, 2005. 63 Bibliography 64

[12] H. P. Kehrer, H. G. Kadereit, Tracer Experiments on the Growth of Tin Whiskers, Appleid Physics Letters, 16, 11, pp. 411-412, (1970).

[13] S. E. Koonce, S. M. Arnold, Growth of Metal Whiskers, Letters to the Editor, pp. 365-366, (1952).

[14] M. O. Peach, Mechanism of Growth of Whiskers on Cadmium, Letters to the Editor, pp. 1401-1403, (1952).

[15] R. M. Fisher, L. S. Darken, K. G. Carroll, Accelerated Growth of Thin Whiskers, Acta Metallurgica, 2, (1954).

[16] C. Nordling, J. Osterman,¨ Physics Handbook for Science and Engineering, Studentlitteratur, (1999).

[17] http://www.webelements.com, (Jan, 2005).

[18] T. B. Massalski, Binary Alloy Phase Diagrams, pp. 964-965.

[19] K. N. Tu, Interdiﬀusion and Reaction in Bimetallic Cu-Sn Thin Films, Acta Metallurgica, 21, pp. 347-354, (1973).

[20] G. T. Galyon, A History of Tin Whisker Theory: 1946 to 2004, IBM eSG Group, (2004).

[21] J. D. Eshelby, A Tentative Theory of Metallic Whisker Growth, Journal of Applied Physics, pp.755-756, (1953).

[22] F. C. Frank, On Tin Whiskers, Philosophical Magazine, 44, pp. 854-860, (1953).

[23] W. C. Ellis, D. F. Gibbons, R. C. Treuting, Growth of Metal Whiskers From the Solid, John Wiley& Sons, pp. 102-120, (1958).

[24] N. Furuta, K. Hamamura, Growth Mechanism of Proper Tin- Whisker, Japanese Journal of Applied Physics, 8, 12, pp. 1404-1410, (1969).

[25] I. Boguslavsky, P. Bush, Recrystallization Principles Applied to Whisker Growth in Tin, APEX Conference, (2003).

[26] K. N. Tu, Irreversible Process of Spontaneous Whisker Growth in Bimetallic Cu-Sn Thin Film Reactions, Physical Review B, 49, 3, pp. 2030-2034, (1994).

[27] M. W. Barsoum, E. N. Hoﬀman,l R. D. Doherty, S. Gupta, A. Zavalian- gos, Driving force and Mechanism for Spontaneous Metal Whisker Forma- tion, Physical Review Letters, 93, 20, (2004). Bibliography 65

[28] A. Zangwill, Pysics at Surfaces, Cambridge University Press, (2001).

[29] B. F. Dyson, T. R. Anthony, D. Turnbull, Interstitial Diﬀusion of Copper in Tin, Journal of Applied Physics, 38, 8, p. 3408, (1967).

[30] D. Hull, D. J. Bacon, Introduction to Dislocations, Pergamon Press, 3rd Edition, (1984).

[31] C. M. Rice, D. S. Eppelsheimer, M. B. McNeil, Surface Tension of Solid Tin, Journal of Applied Physics, 37, 13, pp. 4766-4768, (1966).

[32] T. J. Whalen, S. M. Kaufman, Comment on ”Surface Tension of Solid Tin” by Rice, Eppelsheimer, and McNeil, Journal of Applied Physics, 38, 8, pp. 3408-3409, (1967).

[33] U. Lindborg, A Model for the Spontaneous Growth of Zinc, Cadmium and Tin Whiskers, Acta Metallurgica, 24, pp. 181-186, (1976).

[34] P. Shewmon, Diﬀusion in Solids, The Minerals, Metals & Materials Society, Second Edition, (1989).

[35] U. Lindborg, Observations on the Growth of Whisker Crystals From Zn Elec- torplate, Metallurgical Transactions, 6A, 8, pp. 1581-1586, (1975).

[36] D. B. Butrymowicz, J. R. Manning, M. E. Read, Diﬀusion Rate and Mass Transport Phenomena for Copper Systems, Natl. Bur. Stand (U.S.), (1977).

[37] R. J. Fields, S. R. Low, Physical and Mechanical Properties of Inter- metallic Compound Commonly Found in Solder Joints, Available on: http://www.metallurgy.nist.gov/mechanical properties/solder paper.html, (Mars, 2005).

[38] J. S. Kadesch, J. Brusse, The Continuing Dangers of Tin Whiskers and Attempts to Control them with Conformal Coating, Avail- able on: http://nepp.nasa.gov/docuploads/95565195-0E5A-40D8- 98D88425FF668F68/JayBrusseRevision2.pdf, (Mars, 2005).

[39] M. Guber, Whiskerbildung im System Kupfer-Zinn, Max-Planck Institut f¨ur Metallforschnung Stuttgart, (2004).

[40] V. K. Glazunova, An Investigation of teh Conditions of Spontaneous Growth of Filiform Crystals on Electrolytic Coatings, translated from Zhurnal Prik- ladnoi Khimii, 36, 3, pp. 543-550, (1963). Bibliography 66

[41] S. M. Arnold, Repressing the Growth of Tin Whiskers, Plating, 53, 1, pp. 96-99, (1966).

[42] R. Schetty, Minimization of Tin Whisker Formation for Lead-Free Electronics Finishing, Circuit World, pp. 17-20, (2000).

[43] B. D. Dunn, A Laboratory Study of Tin Whisker Growth, European Space Agency, (1987).

[44] C. Xu, Y. Zhang, C. Fan, A. Vysotskaya, J. Abys, Understanding Whisker Phenomenon-Mechanisms Study, Lucent Technologies, (2002).

[45] N. A. J. Sabbagh, H. J. McQueen, Tin Whiskers: Causes and Remedies, Metal Finishing, pp. 27-32, (1975).

[46] P. E. J. Flewitt, R. K. Wild, Physical Methods for Materials Characterisation, Institute of Physics Publishing, (2002). Appendix A

Methods

Tests Soldering Simulation Temperature Cycling Humidity High Temperature Room Temperature 0xx x x x 1xx x x x x 2xx x x x x 3xx x x x 4xx x x x 5xx x x x 6xx x x 7xx x x x 8xx x x x 9xx x x 10xx x x 11xx x x Temperature Cycling: 500TC -60◦C/+60◦C Humidity: 1000h 50◦C/85%rH High Temperature: 50◦C Room Temperature: 22◦C / 50%rH Soldering Simulation: 3x260◦C

Table A.1: Summary of test and storage conditions for each sample group. Each group contained 48 diﬀerent types of samples as can be seen in table A.3.

Base Material Composition 6 % Sn CuSn6 Rest Cu 0,1% Sn CuSn0,15 Rest Cu 0,005-0,04% O 99,9% Cu E-Cu58 Rest Various

Table A.2: The composition of the three diﬀerent base materials that were used.

Nayeri Hashemzadeh, 2005. 67 68

Number Bath Type Ag-layer Ni-layer Base Tin thickness Heat Treatment Parts Date Sample [µm] [µm] material 3-5 µm 10-12 µm without 5’,180oC Quantity processed 1 Dull tin - CuSn6 X X 8 24-Jun 2 Dull tin - CuSn6 X X 8 24-Jun 3 Dull tin - CuSn6 X X 8 24-Jun 4 Dull tin - CuSn6 X X 8 24-Jun 5 Dull tin 0.15 CuSn6 X X 8 22-Jun 6 Dull tin 0.15 CuSn6 X X 8 22-Jun 7 Dull tin 2 CuSn6 X X 8 22-Jun 8 Dull tin 2 CuSn6 X X 8 22-Jun 9 Dull tin 0.15 CuSn6 X X 8 24-Jun 10 Dull tin 0.15 CuSn6 X X 8 23-Jun 11 Dull tin 2 CuSn6 X X 8 23-Jun 12 Dull tin 2 CuSn6 X X 8 23-Jun 13 Dull tin - CuSn0,15 X X 8 24-Jun 14 Dull tin - CuSn0,15 X X 8 24-Jun 15 Dull tin - CuSn0,15 X X 8 24-Jun 16 Dull tin - CuSn0,15 X X 8 24-Jun 17 Dull tin 0.15 CuSn0,15 X X 8 22-Jun 18 Dull tin 0.15 CuSn0,15 X X 8 22-Jun 19 Dull tin 2 CuSn0,15 X X 8 22-Jun 20 Dull tin 2 CuSn0,15 X X 8 22-Jun 21 Dull tin 0.15 CuSn0,15 X X 8 24-Jun 22 Dull tin 0.15 CuSn0,15 X X 8 23-Jun 23 Dull tin 2 CuSn0,15 X X 8 23-Jun 24 Dull tin 2 CuSn0,15 X X 8 23-Jun 25 Dull tin - E-Cu58 X X 8 24-Jun 26 Dull tin - E-Cu58 X X 8 24-Jun 27 Dull tin - E-Cu58 X X 8 22-Jun 28 Dull tin - E-Cu58 X X 8 24-Jun 29 Dull tin 0.15 E-Cu58 X X 8 23-Jun 30 Dull tin 0.15 E-Cu58 X X 8 23-Jun 31 Dull tin 2 E-Cu58 X X 8 22-Jun 32 Dull tin 2 E-Cu58 X X 8 22-Jun 33 Dull tin 0.15 E-Cu58 X X 8 24-Jun 34 Dull tin 0.15 E-Cu58 X X 8 23-Jun 35 Dull tin 2 E-Cu58 X X 8 23-Jun 36 Dull tin 2 E-Cu58 X X 8 21-Jun 37 Bright tin 2 E-Cu58 X 8 28-Jun 38 Bright tin 2 E-Cu58 X 8 25-Jun 39 Bright tin E-Cu58 X 8 29-Jun 40 Bright tin E-Cu58 X 8 28-Jun 41 Bright tin 2 CuSn6 X 8 28-Jun 42 Bright tin 2 CuSn6 X 8 25-Jun 43 Bright tin CuSn6 X 8 29-Jun 44 Bright tin CuSn6 X 8 28-Jun 45 Bright tin 2 CuSn0,15 X 8 28-Jun 46 Bright tin 2 CuSn0,15 X 8 25-Jun 47 Bright tin CuSn0,15 X 8 29-Jun 48 Bright tin CuSn0,15 X 8 28-Jun

Table A.3: Summary of the plating parameters for each of the 48 types of samples. 69

Process Step Time Temp. Current/ Thickness and Voltage/CD Other Data Alkaline soak 30 sec. 60 oC NA Electro-Clean 60 sec. 65 oC 8.0 V Cleaner 5 sec. 25 oC. NA Neutralization Activation 30 sec. 25 oC NA

0.15 and 2 µm as required Nickel Plating 120 sec. 55 oC 5 A/dm2 (see test matrix)

0.15 and 2 Silver barrier 10 sec. 25 oC at 5 A/dm2 µm as layer plating 154 sec. required (see matrix)

3-5 µm and Tin Plating-1 140 sec. 45 oC 20 A/dm2 10-12 µm (dull tin) 32 sec. as requiered (see matrix)

3-5 µm and Tin Plating-2 165. Sec 40 oC 20 A/dm2 10-12 µm (bright tin) as requiered 48 sec. (see matrix)

Rinse 5 sec. 25 oC NA Post- 10 sec. 25 oC NA Treatment-1 Rinse 10 sec. 60 oC NA Post- 10 sec. 25 oC NA Treatment-2 Rinse 10 sec. 25 oC NA Followede by hot air dry

Table A.4: Plating protocol for the samples used to study whisker growth under diﬀerent storage conditions. Appendix B

Results

B.1 Natural Frequency Calculations

For the calculation of the natural frequency the whisker is assumed to grow straight and perpendicular to the surface as can be seen in ﬁgure B.1.

Figure B.1: Schematic for the calculation of whisker’s natural frequency.

Euler-Bernoulli’s beam theory was used to calculate the natural frequency whiskers. The equation given in the Euler-Bernoulli’s beam theory is d4W (x, t) EI + mW¨ (x, t) = q(x, t), (B.1) dx4 where E is the Young’s modulus or elasticity modulus, I is the area moment of the inertia, W is the displacement of each point in the beam, m is the mass distribution/unit length and q(x, t) is the external load on the whisker. For this problem q(x, t) = 0, because no external force on the whisker is supposed. d4W (x, t) EI + mW¨ (x, t) = 0. (B.2) dx4

Nayeri Hashemzadeh, 2005. 70 B.1. Natural Frequency Calculations 71

E, I and m are taken as constants regarding x and time. To solve this equation W (x, t) is assumed to be separable, i.e. that the function W (x, t) is made of two independent functions. W (x, t) = X(x)T (t). (B.3) The following four boundary conditions can be formulated W (0, t) = 0, (B.4) ∂W (0, t) = 0, (B.5) ∂x ∂2W (L, t) = 0, (B.6) ∂x2 ∂3W (L, t) = 0. (B.7) ∂x3 Boundary conditions B.4 and B.5 result from the fact that the displacment W (x, t) is unchanged for x = 0. Boundary condition B.6 comes from the fact that the shear stress V is zero in the end of the whisker/beam. The following relation is given, ∂2W (x, t) V = −EI . ∂x2 Boundary condition B.7 comes from the fact that the torque is ∂3W (x, t) M = −EI , ∂x3 and M is zero at the end of the beam. Using equation B.3 in equation B.2 gives T 00 EI XIV = − = −λ, (B.8) T m X T 00 + λT = 0, ⇒ IV mλ (B.9) X − EI X = 0. With λ > 0 the following result is achieved for the equation of B.9.

T (t) = C0 cos(ωt) X(x) = C1 cosh(ηx) + C2 cos(ηx) + C3 sinh(ηx) + C4 sin(ηx)

2 mω2 For simplicity ω = λ and η = EI . With C0 6= 0 the following relations are given due to boundary conditions 1 to 4.

B.4 ⇔ C1 cosh(η · 0) + C2 cos(η · 0) + C3 sinh(η · 0) + C4 sin(η · 0) = 0, B.5 ⇔ C1 sinh(η · 0) − C2 sin(η · 0) + C3 cosh(η · 0) + C4 cos(η · 0) = 0, B.6 ⇔ C1 cosh(η · L) − C2 cos(η · L) + C3 sinh(η · L) − C4 sin(η · L) = 0, B.7 ⇔ C1 sinh(η · L) + C2 sin(η · L) + C3 cosh(η · L) − C4 cos(η · L) = 0. B.1. Natural Frequency Calculations 72

Boundary conditions B.4 and B.5 result in C2 = −C1 and C4 = −C3. Boundary conditions B.6 and B.7 result in the following equation matrix. cosh(η · L) + cos(η · L) sinh(η · L) + sin(η · L) C 0 1 = . sinh(η · L) − sin(η · L) cosh(η · L) + cos(η · L) C3 0 For this equation system to have a non trivial solution the determinant of it should be equal to zero. That is

cosh(η · L) + cos(η · L) sinh(η · L) + sin(η · L) = 0. sinh(η · L) − sin(η · L) cosh(η · L) + cos(η · L) This gives cosh(η · L) cos(η · L) + 1 = 0. (B.10) This equation gives the natural frequency of the whisker/beam. ω substituted back instead of η into equation (B.10) gives: m √ m √ cosh(( )1/4L ω) cos(( )1/4L ω) + 1 = 0. EI EI This equation can be solved numerically, e.g. by using Matlab. Figure B.2 shows m 1/4 √ how this function looks like up to the ﬁrst mode. Here x = ( EI ) L ω. This

Figure B.2: Plot over equation B.10, where first zero occurs for x = 1.88. function has infinite amount of zeros, due to the cos in the function. Only the first zero point is interesting due to the high natural frequencies of the whiskers. The first zero for the function is for x = 1.88. This gives ω 1 EI 1.88 f = = ( )1/2( )2 (B.11) 2π 2π m L B.1. Natural Frequency Calculations 73

The area moment of the inertia is calculated in the following way ZZ I = y2dydz (B.12)

πd4 The area moment of the inertia for a cylinder is I = 64 , where d is the diameter d 2 of the whisker. The mass per unit length of the whiskers, m = πρ( 2 ) · 1, where 1 is the unit length and ρ is the density of the whisker. Putting these substitutions into equation B.11 result in v u πd4 1 uE · ( ) 1.88 f = t 64 ( )2 (B.13) 2π πρd2 L ( 4 ) √ 1.882 Ed ⇔ f = √ (B.14) 8π ρ L2

B.1.1 Connected at Both Ends For a whisker that is connected at both ends the boundary conditions are diﬀer- ent. Presuming that the connections at both ends are equal, following boundary conditions are valid

W (0, t) = 0, (B.15) ∂W (0, t) = 0, (B.16) ∂x W (L, t) = 0, (B.17) ∂W (L, t) = 0. (B.18) ∂x Following the same procedure as the case with one end free the following equation is achieved cosh(η · L) cos(η · L) − 1 = 0. (B.19) The ﬁrst solution of equation B.19 is η · L = 4.73 instead of 1.88 for the one end free case. Comparing equation B.11 the natural frequency of whiskers connected 4.73 2 at both ends is 1.88 = 6.36 times higher. B.1. Natural Frequency Calculations 74

L [mm] \ E [Gpa] 8 25.325 40.725 54.2 69.6 85 0.05 117080 208310 264160 304740 345330 381630 0.1 29270 52077 66039 76185 86333 95407 0.2 7317 13019 16510 19046 21583 23852 0.3 3252 5786 7338 8465 9593 10601 0.4 1829 3255 4127 4762 5396 5963 0.5 1171 2083 2642 3047 3453 3816 0.6 813 1447 1834 2116 2398 2650 0.7 597 1063 1348 1555 1762 1947 0.8 457 814 1032 1190 1349 1491 0.9 361 643 815 941 1066 1178 1 293 521 660 762 863 954 1.2 203 362 459 529 600 663 1.4 149 266 337 389 440 487 1.6 114 203 258 298 337 373 1.8 90 161 204 235 266 294 2 73 130 165 190 216 239

Table B.1: Some of the values that were generated with Matlab for a whisker with one free end and a diameter of 2 µm are represented here. L is the length of the whisker and E is the Young’s modulus range for whiskers found by Dunn in 1988 [11]. B.1. Natural Frequency Calculations 75

”+” 0 100 200 300 400 500 1 1–2, L 1; KL 1; KL 2; K 1–2; KL 1; L 2 1, L 1; KL 2; KL 1; L 1; KL 1; KL 3 1, L 1–2; KL 2; KL 2; KL 1; L 1–2; KL 4 1, L 2; L 2; KL 2; KL (6 µm) 1–2; KL 1; L 5 1, KL 1–2; KL 2; KL 1; L 1–2; KL 1; KL 6 1, L 1; L 2; KL 1–2; ; KL 1; KL 1; KL 7 1, Kl 2; L 1; KL 1–2; KL 1; L 1; KL 8 1, L 1; KL 2; KL 1–2; KL 1–2; KL 1; L 9 (65 µm) 3–4, L 1; KL 1; KL (10µm) 2–3; L 1; KL 1; KL 10 1, Kl 1–2; L 1; KL 1; L 1–2; KL 1; KL 11 1, Kl 1; KL (120µm) 1-4; L (20 µm) 3–4; L 1; KL 1; KL 12 1, L 2 ;L 1; KL 1–2; L 1; KL 2; KL 13 (10 µm) 3, L (12 µm) 2–3; KL 1–2; KL (10 µm) 2–3; L (7 µm) 2; KL (20µm) 2-3; KL 14 1, KL 1; L 1; KL 1; L 1; KL 1; KL 15 1, KL 1; L 1; KL (10 µm) 3; L 1; KL 1; KL 16 1, KL 1; L 1; KL 2; L 1–2; KL 1; KL 17 1, KL ;L 1; KL 1–2; L 1–2; KL 1; KL 18 1, KL 1–2; L 2; KL 2, L 1; KL 1–2; KL 19 1, L 1; KL 1; KL 1; l 1; KL 1; KL 20 1, KL 1; KL 1; L 2, l 1; KL 1; KL 21 1, KL 1; L 1–2; KL 1–2, KL 1–2; KL (5µm) 2; L 22 (55 µm) 3–4, L 1–2; KL 1; KL (15 µm) 3–4; L 1–2; KL 1; KL 23 1, KL (3 µm) 1–3; L 1; KL (45 µm) 3–4; L 1; KL 1; KL 24 1, L 1–2; KL 2; KL 2; L 1–2; KL 1; KL 25 (50 µm) 4, KL 2–3; L (30 µm) 3; KL (10 µm) 3; L (15 µm) 2; KL 1; KL 26 1, KL 1; L 1; KL 1–2; L 1; KL 1; KL 27 1, L 1–2; KL 1; KL 2; L 1; KL 1; KL 28 1, L 1; KL 1; KL 1–2; L 1; KL 1; KL 29 1, L 1–2; KL 1; KL 2; L 1; KL 1; KL 30 1; KL ;L 2; KL 1–2; L 1; KL 1; KL 31 1, KL (8 µm) 1–3; L 1; KL 1–2; L 1; KL 1; KL 32 1; KL 1–2; L 1 ; KL 1; L 1; KL 1; KL 33 1; KL (5 µm) 1–3; L 1; KL (15 µm) 3; L 1; KL 1; KL 34 1; KL (15µm) 3–4; L 1; KL (35 µm) 4; L 1; KL 1; KL 35 1; KL (35 µm) 1–4; L 2-3; KL (110 µm) 1–5; L 1; KL 1; KL 36 1; KL 1; L 1; KL 1–2; L 1–2; KL 1; KL 37 1 ; KL (40µm) 1–4; L 1; KL (15 µm) 3; L 1–2; KL 1; KL 38 1; KL (30 µm) 1–4, L 1; KL (30 µm) 1–4; L 1–2; KL 2; KL 39 1; KL 1; L 1; KL (80 µm) 4; L (7 µm) 2; KL 1; KL 40 1; KL (50 µm) 2–3; L 1–2; KL 1; L 1; KL 1; KL 41 1; KL 1; L 1; KL (50 µm) 4; L (5µm) 1–2; KL 1; KL 42 1; KL 1; L 1; KL 1–2; KL (80 µm) 1–4; L 1; KL 43 1; L 1; KL 1; KL 1–2; L 1; KL 1; KL 44 1; KL 1; L 1;KL 1–2; KL (100 µm) 1–4; KL 1; KL 45 1; KL (140 µm) 1–4; L 1; KL (190 µm) 5; L 1; KL 1; KL 46 1; L 1–2; KL 1; KL 1–2; L 1–2; KL 1; KL 47 1; KL 1–2; KL 1; L 1–2; L (50 µm) 1–3; KL 1; KL 48 1; KL (35 µm) 1–3; L 1; KL (70µm) 2–3; L 1–2; KL 1; KL

Table B.2: Results from studying whisker growth on diﬀerent sets of samples undergoing diﬀerent storage conditions. In table A.3 and table A.1 sample properties and treatment conditions for each sample can be found. The grading system is explained in table 3.2 on page 40. The samples graded with two numbers show inhomogenous whisker growth. The longest whiskers measured on the sample are noted in paranthesis next to the grades. Samples with a hole are indicated with L and those without with KL. B.1. Natural Frequency Calculations 76

”+” 600 700 800 900 1000 1100 1 1, L 1 1; KL 2; L 1; KL 1–2; KL 2 1, L 1 1; KL 2; L 1; KL 1–2; KL 3 1, L 1–2 1; KL 2; L 2; KL 1; KL 4 1, L 1–2 1; KL 2; L 2; KL 1; KL 5 1, L 1 1; KL 2; L 1; KL 1; KL 6 1, L 1; KL (15 µm) 2–3; L 2; KL 1; KL 7 1, L 1 1; KL 1–2; L 1; KL 1; KL 8 1, L 1–3 1; KL (15 µm) 3; L 2; KL (5 µm) 2; KL 9 (10 µm) 2–3, L 1–2; KL 1; L 1; KL 1; KL 10 (50 µm) 3–4, L 1; KL (10 µm) 2–3; L 1; KL 1; KL 11 1–2, L 1–2; KL 1; L 1; KL 1–2; KL 12 (7 µm) 1–3, L 1–2; KL 1; L 1; KL 1–2; KL 13 (30 µm) 4, L (20µm) 3; KL (15 µm) 3; L (10 µm) 3; KL 1; KL 14 2, L 1; KL 1; L 1; KL 1; KL 15 (30 µm) 2–3, L 1; KL 2; L 2; KL (5 µm) 1–2; KL 16 1, L 1–2; KL 2–3; L 2; KL 1; KL 17 1, L 1; KL 1; L 1; KL 1; KL 18 (20 µm) 2–3, L 1; KL (30 µm) 3; L 1; KL 1; KL 19 1, L 1; KL 2; L 1; KL 1; KL 20 (30 µm) 3, L 1; KL (15 µm) 2–3; L 2; KL (9 µm) 2; KL 21 (30 µm) 3–4, L (30µm) 2–3; KL (40 µm) 3–4; L 2; KL 1; KL 22 (50 µm) 3–4, L 1; KL (10 µm) 2–3; L 1; KL 1–2; KL 23 (10 µm) 2–3; L 1–2; KL (15 µm) 3; L 1; KL 1; KL 24 (40 µm) 2–3; L 1; KL 2–3; L 1; KL 1; KL 25 (25 µm) 2–3; L (6µm) 2; KL (15 µm) 3–4; L 2; KL 2; KL 26 1–2; L (5µm) 2; KL 1; L 1; KL 1; KL 27 (10 µm) 2–3; L 1; KL 2; L 1; KL 1; KL 28 (25 µm) 2–3; L 1; KL 2–3; L 1; KL 1–2; KL 29 1; L 1–2; KL 1; L 2; KL 1; KL 30 (30 µm) 2–3; L 1–2; KL (35 µm) 2–3; L 1; KL 1; KL 31 (20 µm) 2–3; L 1–2; KL 1; L 1; KL 1; KL 32 1–2; L 1–2; KL 2; L (22 µm) 2–3; KL 1–2; KL 33 (110 µm) 4; L (15µm) 2–3; KL (40 µm) 4; L (80 µm) 4; KL 1; KL 34 (130 µm) 1–5; L 1; KL (40 µm) 3; L 2; KL 1; KL 35 (25 µm) 1–3; L 1; KL 2; L 1; KL 1; KL 36 2; L 1–2; KL 1; L 2; KL 1; KL 37 1; L 1; KL 1; L 1–2; KL 1; KL 38 1–2; L 1; KL 1; L 1; KL 1; KL 39 (25 µm) 3; L 1–2; KL (130 µm) 1–5; L (50 µm) 3; KL (60 µm) 2–3; KL 40 (250 µm) 1–5; L 1–2; KL (110 µm)1–5; L 1; KL 1–2; KL 41 1; L 1; KL 1; L 1; KL 1; KL 42 1; L ; KL 2; L 1; KL 1; KL 43 (25 µm) 2–3; L 1–2; KL 1; L 1; KL 1; KL 44 (25 µm) 2–3; L 1; KL 1; L 1; KL 1–2; KL 45 1; L 1; KL 1; L 1; KL 1; KL 46 1; L 1; KL 1; L 1; KL 1; KL 47 (60 µm) 2–3; L (50µm) 1–3; KL 2; L 1–2; KL (40 µm) 2–3; KL 48 (215 µm) 1–5; L 1; KL (110 µm) 1–5; L 1; KL 1–2; KL

Table B.3: See explenations for table B.2. Copyright The publishers will keep this document online on the Internet - or its possible replacement - for a period of 25 years from the date of publication barring excep- tional circumstances. The online availability of the document implies a permanent permission for anyone to read, to download, to print out single copies for your own use and to use it unchanged for any non-commercial research and educational purpose. Subsequent transfers of copyright cannot revoke this permission. All other uses of the document are conditional on the consent of the copyright owner. The publisher has taken technical and administrative measures to assure authenticity, security and accessibility. According to intellectual property law the author has the right to be mentioned when his/her work is accessed as described above and to be protected against infringement. For additional information about the Link¨oping University Electronic Press and its procedures for publication and for assurance of document integrity, please refer to its WWW home page: http://www.ep.liu.se/

Upphovsrätt Detta dokument h˚allstillgängligt p˚aInternet - eller dess framtida ersättare - under 25 ˚arfr˚an publiceringsdatum under förutsättningatt inga extraordinära omständigheter uppst˚ar. Tillg˚angtill dokumentet innebärtillst˚andför var och en att läsa,ladda ner, skriva ut enstaka kopior förenskilt bruk och att använda det oförändrat för ickekommersiell forskning och förundervisning. Overföringav¨ upphovsrätten vid en senare tidpunkt kan inte upphäva detta tillst˚and.All annan användningav dokumentet kräver upphovsmannens medgivande. Föratt garan- tera äktheten, säkerheten och tillgängligheten finns det lösningar av teknisk och administrativ art. Upphovsmannens ideella rättinnefattar rättatt bli nämnd som upphovsman i den omfattning som god sed kräver vid användning av dokumentet p˚aovan beskrivna sätt samt skydd mot att dokumentet ändras eller presenteras i s˚adan form eller i s˚adant sammanhang som är kränkande förupphovsmannens litterära eller konstnärliga anseende eller egenart. Förytterligare information om Linköping University Electronic Press se förlagets hemsida http://www.ep.liu.se/ c 2005, Moheb Nayeri Hashemzadeh

Nayeri Hashemzadeh, 2005. 77