Study of Tin Whisker Growth and their
Mechanical and Electrical Properties
Moheb Nayeri Hashemzadeh
LITH - IFM - EX - - 05 / 1499 - - SEMechanical and Electrical Properties
IFM, Link¨opings UniversitetMoheb Nayeri Hashemzadeh LITH - IFM - EX - - 05 / 1499 - - SE
Examensarbete: 20 p Level: D
Supervisor: Dr. Werner H¨ugel, Dr. Verena Kirchner
Robert Bosch GmbH-AE/QMM-S5 Examiner: Prof. Ulf Helmersson,
IFM, Link¨opings Universitet Link¨oping: September 2005
Department of Physics and Measurement Technology, IFM Link¨oping University
SE-581 83 Link¨oping
September 2005
x x LITH - IFM - EX - - 05 / 1499 - - SE
Study of Tin Whisker Growth and their Mechanical and Electrical Properties
Moheb Nayeri Hashemzadeh
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 prohib-ited 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 exten-sive 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. Tin whisker Nyckelord Keyword Sammanfattning Abstract F¨orfattare Author Titel Title
URL f¨or elektronisk version
ISRN NUMMER: Spr˚ak Language Svenska/Swedish Engelska/English Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats ¨ Ovrig rapport
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 materi-als (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 −60oC to 60 oC, humidity storage, high
temperature storage and room temperature storage. Some samples were also heat treated post plating, for 5 minutes at 180oC. Some of the samples were studied with help of Focused Ion Beam systems.
Results and Conclusions
Both calculations and tests showed that whiskers are highly resilient towards vi-brations 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 com-pound 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.
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 H¨ugel and Dr. Verena Kirchner, for the help and the support I have received with my work. Dr. Werner H¨ugel 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.
S¨ukr¨u Tavasligolu 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.
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
η0-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
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
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
Introduction
Whiskers are metal filaments that have been shown to grow spontaneously on met-als 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 fail-ures. The most famous failure probably is the lost of the satellite Galaxy IV in
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 regard-ing the soldered electronics, this excludregard-ing 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
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.
• 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.
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 prop-erties 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.
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].
sur-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 ob-served and the longest whiskers obob-served 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].
2.1.2
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 13.2oC. 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 Cu6Sn5 (η’-phase) forms spontaneously and for temperatures above 100oC 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 Thermal conductivity at 300 K, (κ300K), [m·KW ] 65 400
Specific heat capacity at constant pressure and 300 K, (Cp), [kg·KJ ] 230 385
Resistivity at 300 K, (ρ300K), [10−9 Ω · m] 110 17
Temperature coefficient, (α), [10−3 K−1] 4.63 4.33 Melting point at pressure 105 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].
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 = T S − 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
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 ∂t ∼ κβnD( b l2)( γb2 kBT ), (2.2)
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.
2.2.2
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 tem-peratures 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 re-covery 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 thin-ner 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 melt-ing points [1, 16]
• Cd, Tm = 594K
• Sn, Tm = 505K
• Zn, Tm = 693K
The range of the recrystallization temperatures of these metals contains room tem-peratures.
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 F = −{π 6(r ± √ r2− a2)3+π 2(r ± √ r2− a2)a2}E + 2π(r ±√r2− a2)rσ, (2.3)
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 the material as seen in figure 2.5 a). It is shown that for a < r = rc = 2σE 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 dt =
2Eb3 RkBT
D, (2.4)
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
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 ˚A3 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 equa-tions that depending on what kind of diffusion that is contributing to the whisker
growth limit whisker growth rate. The three diffusion types are: lattice diffusion, grain boundary diffusion or diffusion through dislocation pipes. The slowest diffu-sion type is lattice diffudiffu-sion and diffudiffu-sion 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
dt = kx σ RwT
Dx, (2.5)
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 dh2 dt = k2 σ − k3 Lw n , (2.6)
where k2 and n are both dependent on dislocation density and temperature but
in-dependent 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 dislo-cation 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
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 IMC that forms during room temperature is the η0-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 ∆t = 2 ln(b/a) σ0ΩsD kBT a2 , (2.9)
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.
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 neighbor-ing 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.
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,
VSn = 2.70 · 10−29 m3, for Cu it is VCu = 1.18 · 10−29 m3 and for the η0-phase
Vη0 = 1.78 · 10−29 m3. This results in
11 ∗ Vη0
6 ∗ VCu+ 5 ∗ VSn
≈ 95%.
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 ∗ Vη0
5 ∗ VSn
≈ 145%.
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
Sn + 1
2O2 → SnO, (2.10)
Sn + O2 → SnO2. (2.11)
The density for SnO is 6450 kg/m3 and for SnO
2 it is 6950 kg/m3 [17]. The
VSnO2 = 1.20 · 10
−29 m3. The volume change is:
2 · VSnO VSn ≈ 129%. (2.12) 3 · VSnO2 VSn ≈ 134%. (2.13)
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 232oC, and thus melting the plated Sn has
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].
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
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.
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
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
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 elec-tronic 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
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 sec-tion 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 reason-able 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 sec-tion 4.2.1.
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 pro-gram 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 electri-cal 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: K(T ) = LT
ρ(T ), (3.2)
where L = 2, 44 ∗ 10−8 [V2/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
dif-ferent 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
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 lit-erature, 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 ma-terials 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 180oC, 5 min
E-Cu58 Ni = 2 µm Bright Sn 3-5 µm
Ag = 0.15 µm Bright Sn 10-12 µm Ag = 2 µm
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, ta-ble A.4, page 69. The 12 different groups have been undergoing different com-binations 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 -60oC 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.
3.4.3
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
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.
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 con-tact 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
f = 1.88 2 8π√ρ √ Ed L2 . (4.1)
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
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
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
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]).
R = ρL
A (4.2)
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.
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
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 sys-tem 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-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 gen-eral 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 sec-tion 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 partic-ular 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
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, result-ing 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 dif-ferent 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
