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The Limits of Mixing: A Chocolate Chip Example

Posted by Dr. Ron Lasky on Thursday, May 30, 2013

Folks,

We tend to think of mixing as something that can completely even out those things being mixed.  As an example, let’s assume you are making chocolate chip cookies and would like to have 10 chocolate chips in each large cookie.  You make enough batter for 100 cookies and then mix in 1,000 chocolate chips.  After mixing for a long time you put 100 dollops of the batter on the baking pan and bake up the cookies.  Upon inspecting the cookies, to your dismay, you find that you have only 13 cookies with 10 chocolate chips.  More than 40 cookies have 30 percent more or 30 percent less than 10 chips.  Worse yet, 3 cookies have 4 or less chocolate chips and 7 have 16 or more.  See the graph below. You decide that you did not mix them enough, so you make another batch and mix for 4 hours.  The results are the same.

Statistics tells us why the above scenario is so.  In a case like this one, the number of chips in a cookie is described by the Poisson distribution.  The mean will be 10 chips, since we are using the Poisson distribution, the standard deviation will be the square root of the mean or 100.5=3.16, or about 3 chips.  One way to assure a more even distribution of chocolate would be to divide each chip into 10, so we would have 10,000 smaller chips in a batch.  On average each cookie would now have 100 chips and the standard deviation would be 10.  Plus and minus one standard deviation is about two thirds of the data, so two thirds of the cookies would have +/- 10% of the desired amount of chocolate, a much better result.  If we divided the chips into even smaller sizes, we would further tighten the distribution.

How does any of this relate to solder preforms or solder paste?  In the new world of lead-free solder pastes, where it is common to have 3 or 4 alloying elements, some in very small concentrations, it can be difficult to control the concentration of the alloying elements throughout a sample of the alloy.  The limits of mixing are just part of several processes that are required to assure that a modern lead-free solder has a consistent formulation.  These are some of the topics you should discuss with your solder supplier to assure that you get consistency in any solder alloy you purchase.  Asking to see assay analysis of a solder alloy is often a good idea, too.

Cheers,

Dr. Ron

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Leadframe Solderability Issues in Power Semiconductors

Posted by Dr. Andy Mackie on Friday, April 5, 2013

It is no secret that automotive semiconductor customers are becoming increasingly demanding. The "under the hood / bonnet" electronics environment is arguably one of the most thermally stressful environments on the planet. Electronics close to the engine block can experience extremes ranging from frigid winter cold to tropical heat, with the added heat source of the adjacent internal combustion engine.

The moisture sensitivity level (MSL) standard from JEDEC / IPC was developed to cover the moisture-absorption and "popcorning" effects of polymeric overmolded materials, but has been expanded in usage to cover a variety of different packaging situations and failure modes. The standard does allow for a certain amount of delamination, even under the MSL1 conditions usually required by automotive semiconductor customers. However, now "zero tolerance for delam" is the most common request from automotive design engineers. In order to meet this need, both overmolding materials manufacturers and leadframe suppliers have been working on how to drive to zero delamination. Leadframe manufacturers have developed a variety of approaches to their products that enhance the adhesion between the leadframe metal itself and the overmolding compound. Usually, this takes the form of physical and chemical texturing of the copper, using a process such as brown oxide formation.

It is no surprise that this need for adhesion enhancement (AE) drives leadframe treatments that are antithetical to the need for formation of void-free, high conductivity electrical connections between the die and the leadframe - basically, it messes with the solderability of the preform or solder paste. In order to get around this issue, leadframe manufacturers have increasingly moved to the use of spot-plating of silver onto copper, with thicknesses ranging from 2-9microns. Why is the silver so thick, in comparison to silver sputtering onto the die surface? Simply because copper diffuses very quickly into the silver, so a thicker silver layer leads to a longer shelf-life for the leadframe. Note also that plating does not have as good process control as sputtering, but it is a lot cheaper and faster.

You can see (below) a schematic of solder paste printed onto one of these leadframes.

 

 

 

 

 

 

 

 

 

 

 

 

An emerging failure mode is one of incomplete wetting onto the leadframe, leading to failures at the sites where solder has failed to flow over the silver plated area completely - "delamination sites" - (below). The flat, shiny, silver finish is not a suitable surface for overmolding compounds to bond to.

 

 

So why isn't the solder wetting well? The answer becomes clear pretty quickly when you do some back-of-the-envelope calculations of the expected final silver content of the finished joint. Let's assume some bondline thicknesses (BLT) is (25,75microns) of a solder containing 2.5%Ag (such as Indalloy 151 or 163) and the plating thickness is (3-9)microns. Typical plating thicknesses of 2-9microns may be seen, based on a recent customer survey), with a mean around 3microns.

So what is the silver content of the final joint, assuming all the silver is dissolved?

 

 

The calculations, therefore, show that it is from 6 to 27% silver. The 27% level is well beyond the solubility limit of silver in these types of solder, and in fact in most solders, at the expected soldering temperatures. The mechanism of non-wetting is clear: solder can no longer wet onto silver, once it has become filled with insoluble intermetallic particles.

The message to power semiconductor component suppliers is:

  • Maintain the silver thickness at a consistent, low level: set up tighter specifications on the silver spot-plating from your supplier.
  • Update your incoming quality control inspection so you can be sure you are getting what you paid for in terms of thickness of silver and consistency.
  • Manage leadframe inventory so you run leaner, so you do not run into leadframe lifetime issues with copper diffusing through the thin silver layer and oxidizing (solderability / voiding problems).

You do have an alternative (moving to an alternate solder type), but then you are into a lengthy requalification procedure.

As always, please contact me if you need assistance.

Cheers!  Andy

 

 

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What Is Indium?

Posted by Carol Gowans on Friday, March 15, 2013

Being the Indium Corporation, we know what indium is, where it comes from, and how to use it.  But sometimes we forget that not everyone is as immersed in indium as we are.

So what is indium?  Of course it is an element with an atomic number of 49, an atomic weight of 114.818amu, a relative density of 7.31g/cm3, and a melting point of 157°C.  I have known that for most of the 27 years I have worked at Indium Corporation, but what exactly does that mean?

Well, the atomic number is important because it is the number of protons in the nucleus - and this is what gives each element its physical characteristics.  It also places it in the periodic table (directly to the left of indium on the chart is cadmium which has an atomic number of 48 and to the right is tin, which has an atomic number of 50).  This puts indium in the group of metals known as "Other Metals", along with bismuth, tin, zinc, antimony, gallium, and germanium.  The atomic weight is a measurement of the total number of particles in the nucleus of the atom.  If you want to know more about protons, electrons, and neutrons, go to the Jefferson Lab site.

The specific gravity or relative density of an element, which, in the case of indium, is 7.31g/cm3, depicts its relative density compared to water.  If the relative density of an element is less than one, then it will float in water.  If it is greater than 1 then it will sink.  If you compare indium's relative density to that of lead, which is 11.35, you will see that, if you had a piece of each material cut to the exact same dimensions, the lead would be heavier than the indium.

Between the atomic number and the specific gravity, I use the specific gravity more often.  It is used in a formula to find the weight of a solder part, or of a length of wire or ribbon.

So where does indium come from?  Since indium is an element, it comes from the earth's crust.  It is generally refined as a by-product of zinc ore mining.  There is an ongoing debate about the availability of indium.  But a lot of work is being done to create more efficient extraction methods and reclaim, particularly of ITO targets, to assure an adequate indium supply for existing and emerging technologies for decades to come.

Okay, now for the fun part. Where is indium used?  It would probably be shorter to say where it ISN'T used!  If you are involved in any of the following areas, you have a need for indium:

  • Cryogenic sealing
  • Hermetic sealing
  • Low temperature soldering for temperature sensitive devices
  • Step soldering
  • Solar panels (CIS & CIGS)
  • Coatings for displays and glass (ITO & IGZO)
  • Pb-free soldering
  • Fuses
  • CTE mismatch when bonding dissimilar materials
  • Thermal management

 

Indium is certainly one of the more versatile metals because it works and plays well with others.  Read more about indium:

Indium Solder and Sealing

Thermal Management

Heat Spring

Low Temperature Solder

We like new challenges and applications, so if we can help you (or you think you can stump us), email me at cgowans@indium.com.

 

 

 

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Has Lead-Free RoHS Compliant Assembly Reliability and Cost "Arrived?"

Posted by Dr. Ron Lasky on Monday, February 25, 2013

Folks,

I was at APEX 2013 San Diego this past week.  San Diego is a great venue for the show, but I always forget how cold it can be (55-65°F) this time of year.  The folks at iConnect 007 interviewed me at the show; the topic was lead-free reliability and has cost for consumer electronics been demonstrated.  You can see the interview here.

These are topics I think about often, so let’s discuss them a bit. First, let’s consider reliability.  RoHS was enacted on 01 July 2006, more than 6 ½ years ago.  Each year more than $1 trillion-worth of electronics are made, therefore, in this period of time, something over $3 trillion worth of consumer electronics have been manufactured.  There have been no “the sky is falling”-type of reliability issues in this time.  How can I say this?  Well, my office at the Thayer School of Engineering at Dartmouth is across the hall from the IT (information Technology) Dept.  They purchase all of the millions of dollars worth of PCs, printers, displays etc. that Thayer uses.  Several years ago (say early 2011) I stopped by when most of the department was in and cheerfully asked if the reliability of the equipment they purchase has gone down since lead-free assembly was enacted.  They asked me in unison, “What’s lead-free assembly.”  After I explained what lead-free assembly was, they confirmed that they have noticed no changes in reliability.  Since RoHS, my family has purchase about 100+ electronic devices, a few have had reliability problems, about as many as in the past.  Most were attributed to hard drive fails.  Of the scores of friends and colleagues I have, no one has ever commented that they have noticed an increase in electronics fails. So, my conclusion is that consumer product reliability is not "practically" worse if my family and  these many  other folks haven’t noticed it.

I have made an informal study of reliability data of lead-free vis-a-vis tin-lead solders published in papers.  A statement from Rockwell Collin’s JCAA/JGF-PP No Lead solder Project: -55C-125C Thermal Cycle Testing Final Report  sums up my overview conclusion nicely: “Test vehicles assembled with lead-free materials (notably tin-silver-copper) exhibited lower reliability under some test conditions.”  Nay sayers might be quick to suggest that this statement  says that lead-free is no good.  However, the statement could be reworded to say: “In considerably more than half of the test conditions, test vehicles assembled with lead-free materials had higher reliability." Counting the comparisons in the Rockwell Collins paper shows lead-free better in 51 cases, tin-lead better in 31 cases, and one draw.  However, it is disturbing that a small percentage of lead-free assembled test vehicles had much much worse reliability than tin-lead test vehicles.  This later information makes me believe that lead-free is not yet ready for mission-critical, high-reliability, long-life products.  These small numbers of much poorer reliability assemblies must be understood and corrected before lead-free is ready for mission-critical prime time.  The much shorter life cycle of today’s consumer electronics may also mask this concern.

What about cost?  I don’t at all want to minimize the expense that many went through to go lead-free and RoHS compliant.  In about 2007, one of our colleagues estimated that it cost the electronics industry $20 billion to become RoHS compliant.  I think this number is low, but, from a consumer’s perspective, there has been no cost hardship.  The price of a PC continued to go down during and after RoHS implementation, as shown in the figure below.  While performing my non-scientific survey of co-workers, family, and friends on reliability, I also asked about cost.  All agreed, electronics are cheaper than ever.

Challenges still exist, even in consumer electronics with the Head-in-Pillow, Graping, non wet opens, and other defects.  However, we can all purchase lead-free, RoHS compliant products at a reasonable cost and reliability.

 

Cheers,

Dr. Ron

The source for the image is :http://thomaslah.wordpress.com/2010/02/03/apple-and-intel-defying-gravity/

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Weibull Analysis III: Multiple Failure Modes

Posted by Dr. Ron Lasky on Monday, February 11, 2013

Folks,

Our discussion of Weibull Analysis continues.....Let’s say you have worked hard and assembled some SMT lead-free PCBs for thermal cycle testing.  You used the best lead-free solder paste, and some lead-free solder preforms as you assembled several through-hole components with the Pin-in Paste process.  You were a little concerned with the assembly process as the board was thermally and physically massive and the reflow process needed to be a bit above the recommended temperature and time.

The results of the thermal cycle testing are shown in Figure 1 below.  You dutifully report the characteristic life (or scale) as 2,387 cycles and the first fail at 300 cycles.  You were quite disappointed, as in the past similar, but slightly smaller boards, had a slightly higher scale, but more importantly, the first fail was about 1,000 cycles.  Anyway, you write you report up and file it away.

 

Figure 1. A Weibull Plot of the Thermal Cycle Data

Hold on!  The data are screaming at you the something is going on.  Look at the same data in Figure 2.  Note two distinct lines shown in green.  These two separate lines suggest very strongly that there are multiple failure modes.  The line furthest to the right is likely the typical failure mode observed in the past.  The line to the left is a new early failure mode.  It could be due to something like oxidized pads or some other phenomena not seen when testing similar but smaller boards.  Root cause failure analysis should be performed to try and understand to new failure mode.

 

Figure 2. A Weibull Plot of the Thermal Cycle Data with Multiple Failure Modes Noted

Now for a human interest note:

One of the rewarding aspects of being a professor at Dartmouth is the outstanding nature of many of the students.  They are not just good academically, but often are talented artistically, athletically, etc.  This point was brought home to me recently.  In a class I teach, ENGS 1: The Technology of Everyday Things, we were recently discussing the conservation of angular momentum (CoAM).  One of the most striking ways to demonstrate CoAM is an ice skater’s spin.  I went on the internet and could not find a good video of a spin.  I then remembered that one of my former students, Julia Zaskorski was on Dartmouth’s figure skating team.  I asked her if she had a video she could share.  It appears below.  She is a materials science and physics major.  Who knows, maybe we will see her at APEX or SMTAI in a few years. 

Here is a little bio in her own words:

               My name is Julia Zaskorski, and I’m a junior from Wellesley College taking part in the 12 College Exchange Program at Dartmouth.  At Wellesley I am majoring in physics with the intent to pursue mechanical engineering.  Despite Wellesley’s relationship with nearby MIT, Wellesley does not have its own engineering program, so I sought out the more self-contained curriculum and atmosphere at the Thayer School of Engineering.  In addition to the draw of the Thayer School, the Dartmouth Figure Skating team was also a hugely motivating factor for my exchange, as Wellesley does not have a team, let alone a rink.  I have known the coach of the Dartmouth team for several years now, and to finally see my name on the roster for the team is a dream come true.  The engineers, as well as the winter activities here in Hanover, pulled my heart to Dartmouth long before I’d ever set foot on campus. 

  Cheers,

  Dr .Ron                           

 

 

 

 

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Weibull Analysis II: The Curse of the Early First Failure

Posted by Dr. Ron Lasky on Tuesday, January 22, 2013

Folks,

In continuing our discussion on Weibull Analysis, let’s assume we assembled some SMT and through-hole PCBs with lead-free solder paste.  On this board are also some bottom-side terminated (BTC) components (often called QFNs), that are also assembled with solder preforms.  A stress test is performed to test the BTCs.  In such a test, the first fail in Weibull analysis is the most important data point.  No matter the results of remainder of the data, these later fails cannot undo the effect of a very early first fail. 

To understand this concept, let’s look at the Weibull chart below.  In many high reliability applications, there may be a requirement that some small percentage of the components under test have at least some minimum reliability.

 

Figure 1.  Weibull Analysis with an Early Fail.

As an example, let’s say that 1% of the components cannot have less than 500 cycles of life.  By looking at Figure 1, we see that 1% have less than 150 cycles of life (see arrow.)  This one early outlier dramatically affects the Weibull Analysis.

However, if that outlier was removed, as seen in Figure 2, the data suggest that 1% of the components will have a life of 900 cycles.  We can see the dramatic effect the first fail has on this result.  Note that the first fail does not affect the “scale” or characteristic life much (2647 vs 2682).  Hence, the characteristic life, is not a robust metric to use in a high reliability environment.  However, the shape or slope is dramatically affected by the early fail as it changes from 2.22 to 4.23 when the early fail is “censored.” 

Figure 2. Weibull Analysis with the Early Fail Removed (Censored).

Why might an outlier like this exist?  Almost certainly there is something unusual about the early fail.  It might be something like an oxidized pad preventing good wetting of the solder.  Perhaps something like this failure mode might be discovered in root cause failure analysis.  However, I am typically opposed to censoring data, even with supportive failure analysis.  I think the test should be done over.  It is often too easy to talk yourself into accepting inconclusive failure analysis.

What is your opinion?

Cheers,

Dr. Ron

 

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Interpreting Weibull Plots: I

Posted by Dr. Ron Lasky on Tuesday, January 15, 2013

Folks,

A while ago I discussed the Weibull Distribution and its importance in electronics reliability analysis.  This distribution has been used to evaluate the life of solder joints whether formed in SMT, wave, or even using solder preforms. In the next few posts, I would like to discuss how to interpret Weibull plots.

Let’s consider two Weibull plots from thermal cycle testing of lead-free solder joints as seen below in Figure 1.

Figure 1.  A Weibull Plot of Thermal Cycle Data for Alloy 2 and Alloy 4.

Both alloys have almost exactly the same scale, or characteristic life. You will remember that characteristic life is the number of cycles at which 63% of the test subjects fail.  For Alloy 2 it is 2,593 cycles and for Alloy 4 it is slightly better at 2,629 cycles.  However, these two alloys performed dramatically differently.  The most striking difference is in their “spread.”  We see this much greater spread for Alloy 4, when we plot a fit to the data as a normal distribution, as in Figure 2 below.

Figure 2. The Best Fit Normal Distribution Plot for Alloy 2 and Alloy 4.

In the Weibull plot, the data for Alloy 2 has a very steep slope or shape factor, this indicates a tight distribution.  A tight distribution is desirable as it facilitates more accurate prediction of thermal cycle life.  Alloy 2 is clearly superior.  So, in a Weibull distribution, not only is a large scale factor or characteristic life desired, but so is a steep slope or larger shape factor.

Next time we will talk about outliers.

Cheers,

Dr. Ron

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Time Required for Refrigerated Flux and Solder Paste to Reach Room Temperature

Posted by Brandon Judd on Friday, December 21, 2012

One question that I often hear from customers is; “Once out of the refrigerator, how long do I have to wait to allow my solder paste and/or flux to reach room temperature in order to use it?”

It is indeed very important for solder pastes and fluxes to be at ambient temperature (approximately 23oC) in order for them to exhibit optimal performance, as the rheology of these materials will differ in a refrigerated state. Additionally, "cool" materials condense atmospheric moisture onto their surfaces (like a glass of cold water in the humid summer air). This condensed moisture is an unwanted ingredient in high quality soldering.

In order to quantify the amount of time necessary for these materials to reach room temperature, we refrigerated both solder paste and flux in 6oz cartridges.  We then recorded the time it took to reach room temperature by placing thermocouple leads in the center of the materials through small holes that were drilled in the containers.

The following is a graph of the time versus temperature of warming both paste and flux:

For the testing above, the ambient temperature was approximately 22-24oC.  The flux required approximately 2.5 hours to reach room temperature, whereas the solder paste required approximately 2 hours.  It would be expected that the solder paste would reach room temperature faster than flux alone, as the metal content of the paste increases the thermal conductivity of the material. 

Of course, your particular conditions (refrigerator temperature, container size and shape, ambient temperature, etc.) will make your situation somewhat different.

For questions regarding the proper handling and storage procedures for solder materials, please contact Askus@indium.com.

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Where is Tin Silver Solder, Now That You Need It?

Posted by Carol Gowans on Friday, November 16, 2012

Over the years, solder alloy choices have been pretty stable.  In the last century, SN63 and SN62 could be found at any company making any kind of electronic device, and both alloys were the backbone of every company making solders.

But, when lead was identified as causing health issues, it was legislated out of everything from paint to gasoline to electronics, including solders.  In 2003, RoHS (Restriction of Hazardous Substances) was passed in Europe to restrict the use of lead (as well as mercury, cadmium, hexavalent chromium, and polybrominated diphenyl ethers: PBDE) in electronics and electronic equipment.

The electronics industry is now focused on SAC alloys (so named because they contain Sn, Ag, and Cu).  But, there is also SnAg, which was used in the lead era when a higher melting point was required.  The addition of the copper (in SAC) offers the benefit of improving wetting and potentially reducing the silver content from a non-copper alloy like 96.5Sn 3.5Ag. 

But, there are many applications where SnAg works well. Changing from it would require customer and/or government approval, and that involves a lot of extra money and time. This lead-free alloy works well in the assembly of a variety of medical devices that use non-traditional metallizations and fluxes.  The Cu addition (in a SAC alloy) probably would not improve the results enough to warrant the cost of requalifying an existing medical device through government agencies, so they stay with what works. 

So, if you are using 96.5Sn 3.5Ag (or 96Sn 4Ag), don't be afraid to stick with it.  Indium Corporation offers both of these solder alloys (and over 250 other alloys) in a variety of forms: preforms, wire, paste, and ribbon.   And, if you want to look at the SAC alloy family to see if it works better in your application, we will help you with that, too.  Just contact our Application Engineering Staff for help.

Carol

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Can Your Mortality Be Modelled with The Weibull Distribution?

Posted by Dr. Ron Lasky on Monday, October 29, 2012

Folks,

In the last posting, we saw how Weibull analysis helped us to determine that SACM lead-free solder (SAC105 with about 0.1% manganese) has comparable (actually better) thermal cycle performance versus SAC305 solder.  Software like Minitab will give us even more detailed information about the performance of the solder joints in stress testing as we see in Figure 1, above.

 

 

 

In addition to the Weibull plot, we also have the Probability Density Function (PDF), the Survival Function and the Hazard Function.  The PDF tells us when it is most likely that a test board will fail in a test population, as shown by the inserted red line.  We see that it is a little less than 2,000 cycles.  The Survival Function shows the percent of surviving test boards.  We observe that the expected life (the 50% point) is quite close to the maximum of the PDF.  The Hazard Function tells us the rate at which the test boards are dropping out.  It increases with time, but there are few boars left so the PDF drops down at the end of the test, even though the fall out rate is the highest.

 

 

 

 

It is interesting (and perhaps appropriate as Halloween approaches) to consider if human mortality follows a Weibull distribution.  I used some data for the Centers for Disease Control  that are a little over ten years old, for males in the US.  So, the mean life expectancy is a little low at 72 years.  (I was a little lazy, the old data were a little easier to work with than new data, some conversions are needed to make it work.) The data appear above in Figure 2. 

 

As you can see, just like a solder joint, your life expectancy can be modeled quite well by the Weibull distribution.

Cheers,

Dr. Ron

 

 

 

 

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Electronics Failure Analysis for Pb- and Pb-Free Solder Joints

Posted by Dr. Ron Lasky on Monday, October 8, 2012

Folks,

 

The Weibull distribution is arguably the most important distribution in failure analysis of leaded and lead-free solder joints.  It is the first thought of someone trying to model thermal cycle, drop shock, or other failure modes associated with through-hole and SMT assembly.

The Likelihood of Getting Heads in 60 Coin Tosses is Described by The Binomial Distribution

 

The Weibull distribution was invented by Waloddi Weibull in 1931.  This invention fact was recounted by Dr. Robert Abernethy in his famous textbook on Weibull analysis, The New Weibull Handbook. This statement may not seem unusual, until we ponder that all common distributions in statistics were discovered, not invented.  The three most common statistical distributions are the Normal, Poisson, and Binomial distributions. As an example of a discovered statistical distribution, let’s consider the Binomial distribution.  This distribution describes, among other things, the odds in flipping a coin.  If you flip a fair coin 60 times, you are most likely to obtain 30 heads (H) and 30 tails (T), but getting 29 H and 31 T or 32 H and 28 T would not be all that uncommon.  Mathematical analysis shows that the curve below results.  If a coin flipping experiment is performed many times, this curve will faithfully predict the results.  The curve is not invented it is discovered from the deep theoretical underpinnings of the Binomial Distribution.

 

 

Waloddi Weibull 1887-1979

 

 

 

 

The fact that the Weibull distribution was invented suggests that Weibull selected it because it fit many types of failure data.  He defined cumulative Weibull distribution is defined as:

 

Where eta is the characteristic life or the scale function and beta is the slope, were as F(t) is the cumulative fraction of failures.  Weibull proposed this function because for beta less than 1, F(t) describes “infant” mortality fails.  In this situation the failure rate is decreasing with time. For beta greater than 1, it describes “wear out” failures, where the failure rate is increasing with time.  In electronics, we typically try to weed out infant mortality by using “burn in.” For beta equal to 1, the failure rate is constant.  These three scenarios are shown in the figure below.

So typically, in electronics failure analysis, we are plotting failure data versus time to determine beta and eta, typically with software like Minitab®.

In the next posting we will analyze some failure data to determine eta and beta and discuss their significance.

Weibull himself was a curious character and much of the available information on him is chronicled by Abernethy. 

For sure Weibull was a vigorous man.  His second wife was almost 50 years his junior and he fathered a daughter at about 80 years of age!

Cheers,

Dr. Ron

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Statistically Significant vs Practically Significant Results in SMT Assembly

Posted by Dr. Ron Lasky on Monday, September 17, 2012

Folks,

Everyday, we are exposed to the results of surveys and polls.  A typical example might be that President Obama is leading Mitt Romney in a poll by 48% to 45%, but the results are not statistically significant.  A reasonable question might be, “What does it mean to be statistically significant ?”  

To determine statistical significance, typically, the statistician will use the criteria that if there is only a 5 percent or less chance that the conclusion would be wrong, it is considered statistically significant.  So, when another poll would state that President Obama leads by 49% to 44% and it is statistically significant, there is, statistically, less than a 5 % chance that the conclusion is wrong.  The 5 % criteria is not cast in concrete. Sometimes 10%, 1%, or even 0.1% might be used.  However, tradition has given us 5% as the default value for “statistically significance.”  It is also helpful to understand that, the more data points in the sample, the more likely the results will be statistically significant.

But if some data are statistically significant, is it always "practically" significant?  As an example, let’s say that you really like chocolate.  Your favorite brand is in a taste test and it scores 9.6 out of 10, whereas a new chocolate scores 9.7/10 and the results are statistically significant.  On the downside, the new chocolate costs 5 times as much.  Is it worth the extra money to convert to the new chocolate? In this case, we have to ask, is the difference practically significant.  The answer is, in all likelihood, no.  Such a difference as 0.1 point out of 10 is very small, and taste is also subjective.  Here, the result might not be practically significant.  The subjectiveness of a taste test may mean that you either can’t tell the difference or that you still like your favorite chocolate the best.

Let’s consider another less subjective example.  Suppose that, in a certain application, solder voiding  is a critical concern.  So, you measure the voiding of two solder pastes.  After collecting hundreds of data points, you find that the average voiding of one solder paste is 8% and that of the other is 7%.  Analysis with Mintab® software tells you that the difference is statistically significant.  But is the difference practically significant?  Probably not. 

How do you determine practical significance? Typically it would be by experimentation or in some cases by experience.  In our example of solder voiding, suppose experiments showed that, as long as the voiding average is below 30%, there will be no concerns.  In light of this, engineering may have set a specification that voiding must not be greater than 25% on average.  (All of this discussion assumes that the spread or standard deviation of the data is not large, but this subject is the topic of another discussion.)  So, in this case, the difference between 7 and 8 percent voiding may be statistically significant, but not practically significant.  So, a prudent engineer may select the 8% paste if it had other desirable features, such as better response to pause, or resistance to graping, or improved head-in-pillow defect.

So always ask yourself, is the difference both statistical and practical.

The image shows solder joint graping, which is often more of a concern than voiding.

Cheers,

Dr. Ron

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No-Clean Solder Paste for Clip-bonding Die-Attach

Posted by Dr. Andy Mackie on Thursday, September 13, 2012

I’m just back from Malaysia, where I visited one of our larger customers who has been using our high-lead (high-Pb) dispensable NC-SMQ75 solder paste for many years. No surprises there, but what many people don’t realize is that the NC-SMQ75 solder paste can be used as a no-clean material in many power die-attach applications. I [ACM] spoke to my friend SzePei Lim [SPL], our Area Technical Manager, based in Kuala Lumpur, about the revolutionary NC-SMQ75 paste:

[ACM] Please tell me about NC-SMQ75. What makes it a unique material?

[SPL] Indium's NC-SMQ75 no-clean die-attach solder paste is one of an emerging class of materials from Indium Corporation based on “ULR” (ultra-low residue) fluxes: these have residue levels of 4% or less after  reflow. NC-SMQ75 leaves only about 4%, by weight, of flux: therefore around 0.4%, by weight, of a 90%w/w metal solder paste. This is the lowest residue solder paste we know of that is widely used in the power semiconductor assembly industry. NC-SMQ75 no-clean solder paste is our best seller in the die-attach application on leadframes for power devices, such as clip-on-leadframe and leadframe-based clip-bonded stacked die. It can be applied by either dispensing or printing, and can be reflowed under either a forming gas or a nitrogen environment.

[ACM] What does “no-clean” mean in high-temperature power semiconductor die-attach applications? They are very different from standard no-clean solder paste usages.

[SPL] There are some big differences: the current flow in power semiconductors is vertical (from top to bottom or vice versa), rather than between adjacent conductors, like in surface mount technology (SMT), plus the package is overmolded with a solid-filled epoxy-based material.

A high voltage and thin die therefore combine to give a significant field strength across the die. A ULR flux with benign, hard residues and low resistivity (good electrical properties) is, therefore, critical. This type of residue also allows for good bonding to the overmolding compound, to prevent delamination during thermal cycling and MSL testing. Customers using this paste in no-clean applications report that, once the reflow profile has been optimized to minimize both voiding and residue levels, the final overmolded component is suitable for use in many different type of application, including automotive.

[ACM] Is there a tradeoff between a ULR no-clean solder paste and reduced voiding?

[SPL] A customer has to be careful to optimize their reflow profile to minimize voiding. That is true for the ULR pastes as well as other types. However, NC-SMQ75 has repeatedly proven itself to be able to reflow with less than 5% total voids in many smaller die applications, especially those less than 10 x 10mm.

[ACM] Solder pastes typically “spit” badly when reflowed, leaving undesirable flux spatter on wirebonding pads. Is it possible to use this as a no-clean paste even in a wirebonded application?

[SPL] Yes. Perhaps surprisingly, these ultra low residue characteristics enable NC-SMQ75 to be used as a true no-clean solder paste, even in the power die-attach application where subsequent steps include  wire-bonding. We have experience with several customers, where the design and placement of the paste deposit can be optimized to minimize the issue of flux spitting onto wirebond pads. And we can provide guidance where needed. This usually works best in applications where there are fewer than 5 wirebond pads per component. 

[ACM] Are there any special precautions that need to be taken when evaluating the NC-SMQ75 for no-clean power applications?

[SPL] Power semiconductor device types are undergoing rapid evolution, as the electrical demands of the devices drive customers away from thin wirebonds towards more robust copper-clip-based applications. Die are also becoming thinner: down to 50 microns, in some cases. As with all applications where there is no single set of applicable industry standard test methods, large-scale testing of multiple batches of components and paste batches is recommended, to establish sufficient data to allow clear decisions to be made on the usefulness of the solder paste in the final assembly process.

Occasional incompatibility with a specific type of semiconductor die may be seen, but it is something that we know about as a rare issue. Indium Corporation technical personnel can assist during the evaluation process, to guide customers on what to look out for. Additionally, I, and several of my colleagues, have extensive experience using NC-SMQ75 in no-clean die-attach applications. The compatibility of the final reflowed flux residue with different types of overmolding compounds is usually very good, with the Sumitomo G700 series appearing to be one of the best types, although Hitachi, Panasonic, and others may also be suitable.

Customers using a standard convection oven modified for high-temp applications need to ensure the N2  flow rate is stable and that there is a controlled, low-ppm oxygen level throughout the oven.

[ACM] I understand that there are new, lower voiding, ultralow residue, no-clean pastes being developed for power semiconductor devices: is that true?

[SPL] Yes, our US- and China-based research and development teams, led by Dr Ning-Cheng Lee, are developing even more solder pastes for no-clean die-attach in this market. Some of these may also be applicable for our new HTPbF (high-temperature lead-free) drop-in die-attach paste, the BiAgX material, but that is still a few months away from implementation.

SzePei, thank you for teaching us. Many thanks for your gift of mooncake last month, and please enjoy your Zhongqiu celebration! 

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A Penny per Gram

Posted by Dr. Ron Lasky on Monday, August 13, 2012

Folks,

It has been a while, let's look in on Patty......

 

Patty had to admit that she was very fortunate.  She had yet to turn 30 and she was a Senior Vice President at ACME.  There was even a small article about her in Fortune magazine.  But she had to admit that, at some level, she was bored.  She missed the action of being out on the line and solving problems. 

With these thoughts she headed toward the lunch room.  She had avoided eating lunch with the execs and still ate lunch with the young engineers that were her age. No one thought it strange.  Pete was occasionally the old timer in the group, as he was approaching 45 years old. 

As she sat at lunch with her friends, Patty also had to admit that she was jealous of all of the group's talk about solving technical problems.  She was now responsible for corporate strategies and seldom got her “hands dirty.”  So she missed the technical challenges on the shop floor. 

 

After lunch she stopped Pete.

“Hey, Pete, could you stop by my office?” Patty asked.

“Kiddo, for you anything….even that,” he answered and they both chuckled.

As Pete sat down in Patty’s office, she asked him, “How do you like your new job?”

“What’s not to like? Twice as much money and working with you!” Pete answered.

“But don’t you miss ... ,” Patty stopped and struggled to gain her composure.

Peter helped her, “Working on the shop floor solving process problems?”

“Yes, so much so that I could almost cry,” Pete finished.

They were silent for awhile.

Then Pete suggested, “Why don’t I see if I can find us a problem.”

Patty smiled. Pete was always well connected.

 

 

A few days passed and Patty had just about forgotten about their meeting.  There was a knock on her door and Pete stuck his head in.

“Hey kiddo, we have an assignment,” Pete shouted cheerfully.

Patty perked right up.

“What’s the scoop?” she asked.

“You know the new program that rewards cost savings?” Pete asked.

“Sure, I think it is a great idea,” Patty responded.

“There is a conflict in our plant in Santa Clara. Management wants to give a $10,000 reward and the senior purchase manager is blocking it,” Pete elaborated.

“Why?’ Patty asked.

“The engineer deserving of the reward purchased a solder paste that improved uptime,” Pete said.

“Sounds great, what is the issue?" Patty asked. "Let me guess. The better solder paste costs more?” she asked.

“Yep!” Pete responded, “One penny per gram.”

“Mike Madigan wants someone to negotiate the situation. Why not us?” Pete asked.

Patty quickly sent Mike an email offering to help.  He gave her the go ahead shortly thereafter.

In a matter of days the arrangements were made and Patty and Pete were on a jet from Boston’s Logan airport to San Jose, California. 

Their flight had taken off and they were enjoying a snack, when Pete commented, “Let’s hope we don’t find someone there like the guy who wanted to assemble the boards without the boards,” Pete chuckled.

At this comment, Patty almost choked on her sparkling water.  About four years ago, when Patty was just starting out, they were working on a critical project.  The manager in charge wanted the boards to be assembled on a certain date.  Unfortunately, the PWBs did not arrive on time, even though all other components, connectors, and the other hardware where ready.  The manager, in frustration, came out to the line on the scheduled start date and was furious that the boards were not being assembled.

The manager asked the lead engineer, “Why aren’t the boards being assembled?”

The lead engineer responded, “The PWBs did not arrive from the vendor.”

To this the manager responded, “Aren’t you going to assemble them anyway?” (See note below.*)

This was their favorite story about the occasional comedy in electronics assembly.

It seemed like no time at all and Patty and Pete were sitting in the conference room that had been reserved for the meeting.  They introduced themselves to a young engineer who was sitting in the room waiting for the meeting to start. His name was Dave Ferris.

“So Dave, you are the cause of this meeting, eh?” Pete teased.

“I guess so. I can’t believe how hard it is to sell productivity here.  The amount of time the new solder paste saves enables us to produce 1,000 more units per year on each line. And these boards are super expensive, with high margins.   Admittedly the solder paste costs $0.01 more per gram, but the additional profit is over $800,000 per year for each of our three lines,” Dave Ferris explained.

“How did you perform the calculations,” Patty asked.

“I went to a workshop run by this quirky, cheerful guy everyone calls ‘The Professor.’ He was amazing,” Ferris replied.

Pete and Patty both chuckled.

“We know The Professor well,” they chimed in unison.

“We assume you used “ProfitPro™ for the calculations?” Pete asked.

“Yes,” Dave responded with a surprise in his voice that they would know about such things.

Will Patty and Pete save the day?  Will Dave get his award?  Stay tuned to see.

Cheers,

Dr. Ron

*As hard as it is to believe, the story about building the boards without the PWBs is true.  Thanks to ITM.

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Cleaning No-Clean Solder Paste Residues in SMT Assembly

Posted by Dr. Ron Lasky on Monday, July 2, 2012

Folks,

There is a lot of interest in cleaning PCBs that have been assembled with no-clean solder pastes. 

Recently I discussed the topic with my good friend Mike Bixenman of Kyzen.

Dr. Ron (DR)

Mike, many of the best performing lead-free and lead containing solder pastes today are no-cleans.  They have been designed to solve assembly problems like graping and the head-in-pillow defect.  For the vast majority of applications, the small amount of residue left by a no-clean is not a problem.  However, some assemblers want the performance of no-cleans, but need to clean the no-clean residue as they have extreme reliability or cosmetic requirements.  Are there cleaning solutions for these situations?

Mike Bixenman (MB)

Absolutely!

DR

Can you tell use a little bit about these cleaning solutions?

MB

Several factors come into consideration when engineering electronics assembly cleaning agents. Design factors include the soil make-up, heat exposure, Z-axis clearance under bottom termination components, material compatibility, and cleaning equipment. Typical process goals require that all flux be removed in one cleaning cycle, shiny solder joints (no chemical attack to the alloy), fast production speed, no material effect to labels and other materials of construction, long chemistry bath life, and low operating concentrations.  

Cleaning solutions vary depending on the cleaning equipment. For solvent systems, a solvent cleaning agent is needed - with properties that allow for non-flammability, constant boiling mixture, and being environmentally-friendly to workers and the environment. For solvent cleaning agents that are rinsed with water, the cleaning agent requires a solvent mixture that can be rinsed with water while matching up to the soil and cleaning equipment. For aqueous cleaning agents, the cleaning agent is engineered with properties that provide solvency for the soil, polarity for inducing a dipole and/ or to oxidize and reduce the soil, low surface tension to reduce the wetting angle, buffers to stabilize pH, defoaming to reduce the tendency to foam at high pressures, and inhibitors to widen the passivation range on metallic alloys.

The property most critical is the nature of the soil. As soldering temperatures rise and the time exposed to higher temperatures increase, solder paste material supplies must improve the oxygen barrier and prevent flux burn out. This requires higher molecular weight compositions that may change the nature of the soil and the cleaning solution needed to remove the soil. Other factors such as processing conditions and how these conditions can change the soil’s cleaning properties must be considered. For example, excessive exposure to heat may polymerize the flux residue rending the soil uncleanable. To better understand and plan for these factors, solubility testing and matching the cleaning agent to the soil assist formulators in designing cleaning agents that are effective on a wide range of soldering material residues.

DR

What type of equipment is typically needed?

MB

Two key factors must be matched to clean:

1: Potential energy of the cleaning agent for the soil and

2: Kinetic energy of cleaning machine for delivering the cleaning agent to the soil necessary to create a flow channel needed to rapidly displace the soil.  

The cleaning machine requires energy to deliver the cleaning fluid across a distance and create enough force to deflect fluids under the Z-Axis. The capillary attraction for moving the cleaning fluid into an out of tight gaps is created by fluid flow, spray impingement pressure and surface tension effects. When cleaning under tight standoffs, cleaning agents that wet (form small droplets) improves capillary action, penetration and wetting of the residue. The solubility rate is dependent on the soil, temperature effects and concentration of the cleaning agent needed to dissolve the soil. Hard soils clean at a slower rate and remove the soil in a concentric (tunneling effect) manner. Soft soils clean at a fast rate and remove the soil in a channeling (multiple tunnels) effect.

The Z-Axis gap height has a direct correlation to the energy required to penetrate and remove the soil under components, time required to clean the soil and wash temperature. The irony is that lower Z-axis gaps increase capillary action of the flux for underfilling the bottom side of the component. When this occurs, flux residue dams up and closes any flow channels under the component. Research findings indicate that high pressure coherent spray jets are needed since energy drop is less and defective energy is higher. The wash time needed to clean under a 1-2 mil gap as compared to a 4-6 mil gap can range from 4-8 times longer. Higher wash temperatures increase the softening effect and aid in penetrating and removing the soil. The net effect is that, as components decrease in size, the Z-Axis gap height reduces and the cleaning factors needed to clean the soil increase. These effects favor spray-in-air cleaning equipment over immersion cleaning equipment.

DR

How are the results of cleaning assessed, so that we know that the boards are truly clean?

MB

The first level that we judge cleaning performance by is the visual presence of the residue post cleaning. Most cleaning processes have no problem with removing surface residue from the assembly. The issue is the residue under the bottom side of the component. This complicates the issue since the residue under a specific component is where most failures occur. These site-specific failures may reduce the confidence in existing IPC standards that correlate anion and cation ionic residues over the entire board surface area. So, when designing the cleaning process, we use test cards with bottom termination components and judge cleaning performance by the level of flux residue remaining under those components. To achieve this value, all components are removed and the surface area of the residue under components is graded and statistically analyzed.

Let me finish by adding that highly dense interconnects assembled onto circuit boards is advancing at a rapid pace. Traditional SMT component spacing between conductors was larger. No-clean post soldering residues posed minimal risks to reliability. The information age has spoiled us in expecting higher functionality in smaller spaces. As assembles reduce in size and increase the levels of functionality, cleaning becomes more important.  I hope that the cleaning factors discussed in this interview provide insight into cleaning process design considerations that may be of help.

DR

Mike, thanks.  Who should folks contact if they would like more information on cleaning boards assembled with no-clean solder pastes.

MB

Thanks for letting me share with your readers.   I would be glad to help anyone with the cleaning challenges they face.  Contact me at mikeb@kyzen.com.

Cheers,

Dr. Ron 

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Solder Coating Thickness for Tabbing Ribbon

Posted by Jim Hisert on Thursday, June 21, 2012

While it is important to have at least 10µm of solder on each side of a tabbing ribbon to form a proper solder joint during cell interconnection, more is not always better. What we have found is that thicker solder coatings may provide adequate and consistent solder joints, but at a reduced bond strength.

The test was performed on c-Si cells, with an industry leading flux, and 3 sets of tabbing ribbon with different solder coating thicknesses. The tabbing ribbon was made from the same ribbon stock to minimize any variation between test subjects. The samples were prepared on a Komax X-series tabber/stringer, and the tabbed cells were allowed to rest at ambient conditions for >48 hours after soldering to relieve stresses. Next, the tabbing bonds on each cell were peel tested at 90°F using a XYZTEC Condor 150-3. Average (not peak) bond force values across the cell were recorded. 

We are happy to apply custom solder coating thickness to tabbing ribbon for you.

I hope this helps you make a good decision when you are specifying material.

Shoot me an email!

~Jim

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Lead-Free Electronics Assembly Using the SMT Process - at PCM

Posted by Dr. Ron Lasky on Wednesday, May 30, 2012
Folks,
 
Struggling to find a good, royalty-free, video of electronics assembly, my Dartmouth ENGM 185 class on manufacturing processes decided to make our own.  I think its is pretty good considering our limited budget ( $0).
 

 
It was filmed at PCM in Springfield, VT. The young woman in the video is my ENGS 3 student from last summer, Ruthie Welch.  The entire ENGM 185 class participated in the production.
 
PCM's Assembly process uses lead-free solder paste.
 
Cheers,
 
Dr. Ron

 

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India WEEE/RoHS Is Here! Compliments Of The Government of India, Ministry of Environment & Forests

Posted by Liyakathali Koorithodi on Tuesday, May 29, 2012

Indian electronics manufacturers and solder users. This info is for you.

After many years of discussion and policy making, the Indian Government rolled out its WEEE/RoHS directive, effective 01 May 2012. This directive is known as e-waste (Management and Handling) Rules 2011 thru the vide number S.O No. 1035 (E) by The Government of India, Ministry of Environment & Forests. (for Hindi version click here).

This directive has 6 chapters covering electrical and electronics waste handling, responsibilities, recycling, etc. It also restricts the usage of certain hazardous substances in electrical and electronics equipment. This section is very similar to the European Union’s RoHS directive; but there is a two year time period to achieve this. So the India RoHS will be in force starting 01.May.2014 (this date applicable only to restriction of using hazardous substance mentioned in e-waste rule, 2011).

As with other RoHS directives, the Indian e-waste rules 2011 also come with an exemption list.

This directive compels consumers (including government departments) to strictly follow the ‘e-waste rule’ during their purchase and usage of electrical electronics equipment.

While industry has yet to discuss this rule in particular, the European Union’s WEEE/RoHS has been driving the Indian electronics industry for the last few years - and most of the manufacturers are complying with RoHS. This will have a big impact on local electronics manufacturers and governmental companies. From a lead-free solder alloy perspective, there will be big impact on knowledge transfer, training, and so on for local manufactures.

There are still many questions, like how this will be implemented, who will be responsible, how this will be rolled out to stakeholders, and more.

Indium Corporation would like to know what you think about this. We are happy to help customers and governmental agencies roll out this directive by providing technical information and other knowledge - sharing our support.

Please feel free to contact me with questions.

Liya

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The Miracle of Soldering

Posted by Dr. Ron Lasky on Monday, April 30, 2012

Folks,

Pity the copper age smelter of 3000BC.  He had to get his wood fire to 1085°C to smelt or melt copper, sometimes he couldn’t get that high a temperature.  Even when he was successful, his copper didn’t flow well and was soft. 

Bronze StrengthBut the winds of change were occurring about that time, news of tin was in the air.  When tin is mixed with about 90% copper, the melting temperature of the resulting bronze plummets to 850°C, this temperature drop, of over 200°C, is a big deal.  Not only did the lower temperature make it easier to melt the bronze, the bronze would flow better in molds.  In addition, the strength and hardness of bronze is many times that of copper.  From the figure above, you can see that a 10% addition of tin to copper produces a bronze that has 3 times the yield strength.  The Bronze Age had begun. Can you imagine the joy of the early metal smiths as they transitioned from copper to bronze, not only was bronze harder and stronger, but it was much easier to process and required less precious wood in the furnaces.  On the downside, tin was then, and still is, rarer than copper, so the cost of bronze is higher than copper alone.  Poor man’s bronze is brass (copper and zinc).  Since zinc is cheaper than copper, brass is less expensive, but from the chart (left), the materials properties are typically weaker than bronze.

Because of its greater strength and hardness, bronze was an important material for war.  If you had equal fighting ability to your enemy and he had a bronze sword and shield to your copper weapons you would lose every time.  So bronze smelting and manufacturing was likely an early military secret.

An equally important benefit of tin, is that when tin was alloyed with lead, a very low melting material was created that would bond to bronze and other metals.  Soldering  was invented.  Those of us that use solder everyday often don’t recognize the miracle of soldering.  When we solder electronic components to a PWB we are essentially bonding copper to copper (which melts at 1085°C) at a temperature of less than 250°C.  We do this metallurgical bonding in the presence of thermally delicate plastic.  So without solder, we would not have the electronics industry as it is exists today.

Tin does all of the “work” in soldering.  It is tin that forms the intermetallics Cu6Sn5 and Cu3Sn with copper. The other solder alloying elements such as lead, silver, and copper play important roles in wetting, spreading, and the ultimate strength of the bond, but only tin metallurgically interacts with the copper.

So when you pick up your mobile phone, type on your computer, or watch TV today, remember - without the “Miracle of Soldering” you wouldn’t be able to!

Cheers,

Dr. Ron

 

The Image is from Askeland's The Science and Engineering of Materials.

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Tin Wiskers, Solder Alloy Density, Safety: Sharing a Few Comments

Posted by Dr. Ron Lasky on Monday, April 16, 2012

Folks,

Some time ago I wrote a post, “In Search of Tin Whiskers,”  Michael responds below.  He makes some good points.

Dr. Ron, I'm responding to your  blog regarding tin whiskers. I actually have a failure analysis report I did a couple of years ago in which failure of our product was due to this issue and occurred on a part that came into RoHS compliance only 3 months prior.
 

I'm not sure that your question of identifying whisker issues in product that proper steps have been taken to mitigate the problem is a constructive one. The fact is that many of the component manufacturers from overseas jumped into compliance without any thought or regard to this issue thereby flooding the industry with components such as plagued my company. We have not had this issue since we've specified an alternate finish.

These whiskers are so delicate that most problems disappear when the technician starts to work on the failed unit and the problem never re-appears so it is written off as an anomaly, loose/bad connection and not investigated any further. It was only my own curiosity as to the number of "no problem found" failures of our keypads we had suddenly encountered that caused me to dig deeper and when I looked into the connector I was amazed at the crystal city staring back at me. I couldn't believe what I was seeing after all of these years.

After seeing this problem first hand I became, and am, quite convinced that there were and are people who will be losing life, limb, and property because this forced compliance with its risk was not given proper worldwide attention.

Michael.

A popular topic Re my blog is solder density calculations. Rhonda writes……

Hi Dr. Lasky,
I am a precious metals recycler and would very much appreciate your verifying the validity of an equation that approximates the Karat Value of various alloys of gold based on S.G. which I will call density or "D," and the Karat Value is "K." The equation is seems to hold relatively true even when the exact composition of the alloy is unknown, although the percent of error obviously will increase as density decreases. I would also appreciate not only verification but also more specific information on percent of error for densities below about 14 or 15 g/cc. Here is the equation:

K = 0.0089D^3 - 0.550D^2 + 12.5299D - 77.06

Thank you so much for whatever assistance you can provide.

Rhonda

These types of equations can only work for one alloying metal with the gold.  This one is only for copper.  It is also calibrated in Rhonda’s favor as it reads the karat level about 10% low.   I was able to determine this by using the Excel Solder Density worksheet that I developed. If the alloy was gold and lead, a 50% by weight gold (12 karat) would show as 15.7 karat with this equation and Rhonda would lose her shirt.

 

 

In response to my blog post on copper as the precursor to civilization, Harvey writes about pollution from early mining operations…..

Also interesting, early copper mining and processing led to the first examples of human induced environmental damage. There are documented sites in the Alps where copper processing by prehistoric peoples has left areas treeless to this day, due to heavy metal contamination.

Harvey

Mining and smelting were very tough businesses in ancient days.  In addition to pollution, many workers died from toxic fumes.

Dr. Ron

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