# Intermetallic Growth Rate is Strongly Temperature Dependent

Folks,

In a previous post, I discussed that, contrary to popular belief, intermetallic compounds (IMCs) formed in soldering processes are not necessarily brittle. I reviewed some literature that indicated that failure modes are usually at interfaces between the IMCs themselves, the IMCs and the copper or solder and often in the bulk solder itself. The perspective that IMC growth may not significantly affect reliability is also supported by work performed by Lee, et al. Figure 1, from Lee’s paper, shows that aging for 250 hrs at 150°C does not significantly affect characteristic life in thermal cycle testing.

Figure 1. Aging for up to 250 hours at 150°C did not significantly affect characteristic life in thermal cycle testing in Lee’s referenced paper.

However, it would be prudent to minimize the thickness of IMCs. So this raises the question: how quickly do IMCs grow at any given temperature? Work performed by Siewert, et al[i] holds the answer. In this paper, Siewert supported past work that the thickness of IMCs grows as X=(kt)0.5 and added new data to support modeling using this equation. In this equation, X is IMC growth distance, k is a constant dependent on temperature, and t is the time. One might expect that X is strongly dependent on temperature (T) and it is. Using data from Siewert’s paper, I was able to generate values of k as a function of T and plot them in an Arrhenius plot. See Figure 2.

Figure 2. An Arrhenius plot for k.

I next used Figure 2 to obtain a value of k at 70°C and plotted the IMC growth X in microns as a function of time in hours. The result is in Figure 3.

Figure 3. IMC grow as a function of time at 70°C.

Note that about 40 years are required to obtain a little over 10 microns of growth. Figure 4 shows the results for IMC growth at 200°C. In this case, only 100 hours are required to obtain about 10 microns of growth. So going from 70 to 200°C produces an acceleration factor of over 30,000 in the effective IMC growth rate to 10 microns.

Figure 4. IMC growth as a function of time at 200°C.

These are theoretical calculations from data collected at different temperatures. Let’s see if the formulas work in real life. In another paper [ii]by Ma, et al. his team aged some solder joints at 125°C for 120 hours. The equations used above would predict IMC growth of 2.2 microns under these conditions. From Figure 5, we see about 2 microns of growth consistent with the calculation estimate.

Figure 5. Images from Ma’s paper of IMC growth at 125°C for 120 hours.

So although IMCs are not that brittle, it is wise to limit their growth. Hence, limiting exposure to very high temperature aging is wise, but certainly minimizing solder rework is advisable, as the molten solder enables very fast IMC growth.

Cheers,

Dr. Ron

[i] Siewert, T. A., et al, Formation and Growth of IMs at the Interface Between Lead Free Solders and Copper Interfaces, IPC Apex, 1994.

[ii] X. Ma, et al Materials Letters 57 (2003) 3361-3365.

# How to Land That Job in an Interview

Folks,

It’s a stressful time when you are interviewing for a job. As a former manager at IBM, Universal Instruments, and Cookson Electronics, I have interviewed more than 300 people for jobs. I’ve also interviewed for a few myself. As a result of these experiences, years ago some management friends and I collaborated on some of the best job interviewing tips.

Having taught about 3,000 students at Dartmouth over the last 15 years, I typically give a lecture on the last day of class entitled, “Tips for Success and How to Interview for a Job.” These Powerpoint slides have some of the ideas gleaned from what I learned above.

Some years ago I was interviewing for a job and the interviewing manager asked me, “Why should I give you this job?”

I answered without hesitation, “Because I led a team of engineers that contributed to the design and build this optoelectronic transceiver module.”

As I handed the optoelectronic transceiver module to the manager to look at, the non-verbal vibrations I received from him where very positive.

A few weeks after I got the job, he told me that handing him the hardware that I worked on was what sealed the deal.

Most of us recognize that an artist or writer should have a portfolio when they go on job interviews, but don’t appreciate that an engineer should have one too, even if like mine, it had only one item. I share this strategy with my current students and on a regular basis they tell me how this approach led to them getting a job.

Here is an email from a student who graduated more than 10 years ago, relating to a new job she just landed:

“I just wanted to thank you for a job interviewing tip from back when I was in school.  You suggested that we bring an example of something that we’ve worked on.  I’ve done that all these years, and I have to say, I’m pretty sure it’s gotten me several job offers!  I know at least one of my current employers’ interviewers definitely appreciated it.  Anyway, so thank you!”

So, hopefully you have a job you love and never have to interview again, but if you do, take something that you worked on as a “show and tell.” It also helps in that it focuses the interview on something you know about and will look good discussing.

BTW, if you would like a copy of my Powerpoint presentation mentioned above, send me a note (rlasky@indium.com) and I will send you a copy.

Cheers,

Dr. Ron

# Intermetallics and Kirkendall Voids Continue to Grow at Room Temperature

Folks,

In my last post, I discussed intermetallic compounds (IMCs) and what I referred to as the “miracle of soldering.” I also mentioned that research focused on the brittle nature of IMCs suggests that failures in stress tests are more likely due to failures between the interfaces of the IMCs and the solder, the IMCs and the copper, or the IMCs (Cu6Sn5 with Cu3Sn) themselves and are not related to any perceived brittle nature of the IMCs.

Another weakening mechanism in soldering and thermal aging of solder joints is Kirkendall voids. Kirkendall voids form when one metal diffuses more rapidly into another metal than vice versa. A copper-tin interface displays such a mechanism. Copper diffuses into the tin more rapidly than the tin into the copper. This mechanism can result in actual voids in the copper at the metal interface. See the image below. In addition to causing a possible weakness at the interface, the excess copper that diffuses into the tin creates compressive stresses than can result in tin whiskers.

Kirkendall voids

IMCs and Kirkendall voids are formed quite quickly at soldering temperatures. However, even at room temperature IMCs and Kirkendall voids continue to grow, albeit at a much reduced rate. The reason for this continued growth is that on the absolute temperature or Kelvin scale, room temperature is a considerable fraction of the melting temperature of solders. As an example, the melting temperature of SAC is about 219°C, this temperature is equal to 492K (219+273), whereas room temperature is 295°K, so room temperature is 60% of the way to the melting point of SAC solder (295/492 = 0.60). Compare this situation to steel, which melts at about 1480°C. The steel would be red hot at 60% (780°C) of its melting point on the absolute scale. So, since room temperature is 60% of the way to melting, the IMC and Kirkendall forming processes don’t stop at room temperature. Hence, IMCs and Kirkendall voids continue to grow, as do related effects such as tin whiskers.

Stay tuned. Next time we will discuss IMC growth rates and resulting effects in stress testing as we wrap up this series on IMCs.

Cheers,

Dr. Ron

# Copper-Tin Intermetallics: The Miracle of Soldering

Most articles discussing the copper-tin intermetallics that form during soldering refer to them as a necessary evil. The evil being the perception that intermetallics are brittle and can lead to failures in thermal cycling or drop shock.

I view the situation differently. From my perspective, the formation of copper-tin intermetallics is the miracle of soldering. Look at it this way, to assemble electronics, bonding copper to copper (the leads on the components to the pads on the PWB) in the presence of polymers (the PWB epoxies and the component cases) is required. These polymer materials can only take about 250°C for a few minutes. Copper melts at 1083°C, so bonding copper to copper in the presence of polymers would appear to be quite a challenge. Enter tin-based solder.

Lead-free (tin-based) solder, say SAC305, melts at about 219°C. So, with a peak temperature of about 245°C, in the reflow oven, solder can be melted and form an electrical and mechanical bond with the copper in the leads and pads. At 245°C, the many polymer materials are unharmed for the 90 seconds or so that soldering requires at this temperature.

But, what about the material properties of the intermetallics that are formed? Aren’t they too brittle? Lee et al* performed analyses that suggest that the intermetallics formed in soldering are not brittle. Their work also suggests that the failure modes are not in the intermetallics, but in the interfaces between the intermetallics and the solder, copper, or the different intermetallic compounds, Cu3Sn and Cu6Sn5. These two intermetallic compounds are shown in the figure below.

Copper tin intermetallics from Roubaud et al, “Impact of IM Growth on the Mech. Strength of Pb-Free Assemblies,” APEX 2001.

It has long been assumed that the thicker the intermetallics, the greater the risk of failure due to the intermetallic thickness. Lee’s work would appear to bring this concern into question.

Stay tuned for a continued discussion on intermetallics and their effect on reliability.

*Lee, C. C. et al, “Are Intermetallics Really Brittle,” IEEE Electronics Components and Technology Conference, 2007, pp. 648.

Cheers,
Dr. Ron

# Calculating Confidence Intervals on Cpks

Let’s look in on Patty, it’s been awhile.

Patty was looking forward to sleeping in.  Normally she was up very early, sometimes before 5:30 am, after usually getting to bed too late, so she was looking forward to an alarm set at 7:45 am. The kids were off from school and Rob was taking them skiing, so all agreed a 7:45 am wake up time was reasonable.  Since she had no early meetings, her scheduled 9 am arrival at her Ivy University office was also in the cards.

Patty was sleeping soundly when she heard her seven-year old twin sons shouting, “Mom! Dad! Come quickly.”   At the same time, their two-year old beagle, Duchess, started barking.

Her heart pounding, Patty raced to the racket now being produced by this energetic trio.  As she arrived she saw her sons and Duchess looking out of their back window to see a beautiful female deer eating from their bird feeder, just 30 feet away. The entire family was involved in a bird counting exercise and had noticed, several times, that the bird feeder was “wiped out” overnight. This mystery was now solved.

The entire family agreed that it was hard to be angry at the doe, as deer are such beautiful creatures.

Figure 1.  A Female Deer at the Bird Feeder at Patty’s House

It was 6:15 am and it didn’t seem to make sense to go back to bed.  So, Patty stayed up and was off to Ivy U in less than 30 minutes.

Patty had a rather light week as she had guest speakers for her two lectures.  However, she was sitting in for one of the engineering school’s senior professors later in the day.  This fellow prof had asked her to sub for him as he was called to an emergency meeting overseas.  Her topic was manufacturing processes; one with which she felt very comfortable.  But, she had to admit to being a bit nervous sitting in for one of Ivy U’s most famous professors.

As was her usual practice, Patty checked her email first.  After going through the first 5 or 6, she saw an email with the subject header, “Ivy U Professor Wins Prestigious Queen Elizabeth Prize for Engineering.”  As she opened the article, she was stunned as she saw a photo of the professor for whom she was substituting later in the day.  The article went on to explain that this prize was like the “Nobel Prize” for engineering.

As she finished her emails she was relishing the thought of having a less hectic day and week ahead.  Maybe she would even have time to read the Wall Street Journal during a relaxing lunch.  Suddenly, her phone rang, startling her a little.  She picked up the receiver to hear a familiar voice.

Madigan was CEO of ACME at large electronics assembly contractor. Patty worked at ACME before becoming a professor at Ivy U. Her husband, Rob, and sidekick, Pete, were also ACME employees, but were now all at Ivy U.  Pete was a research assistant and Rob was just becoming a research professor.  Although they all enjoyed their time at ACME, they were much happier at Ivy U.  All three had a part-time consulting contract with ACME and Madigan was typically their main contact at their former employer.

“Mike! What’s up?” Patty said cheerfully.

“We are evaluating a new solder paste and I’m concerned we might make a mistake if we switch,” Mike responded.

“Well, we agreed that consistency in the transfer efficiency (TE) of the stencil printed deposits was the most important criteria,” Madigan began.

“That sounds reasonable as most of our past work has shown that a consistent TE is a strong determinant of high first-pass yields,” Patty responded.

“Right! But the difference between the pastes is only two percent. The old paste has a Cpk of 0.98 and the new paste 1.00,” Mike went on.

“I sense there is more to the story,” Patty suggested.

“Yeah. The new paste has a poorer response to pause,” Madigan said.

“Yikes!” Patty almost shouted.

Patty had shown, time and time again, that poor response-to-pause in the stencil printing process can hurt productivity and lower profitability considerably.

“My sense is the two percent difference in Cpk, might not be significant,” Mike suggested.

“Mike, I think you are on to something. What printing specs were you using and how many samples did you test?” Patty asked.

“The lower TE spec was 50% and the upper 150%. We tested 1,000 prints,” Madigan answered.

“Let me do some homework and I’ll get back to you,” Patty said.

“One problem. Can you get back by 3 pm today? The new solder paste supplier is coming for a meeting at 4PM and is pressing us,” Mike pleaded.

“OK. Will do,” Patty said, sighing a bit.

“There goes my somewhat relaxing day,” she thought.

It was a good thing she had already prepared her lecture and that it was scheduled for 4:30PM.

For several hours Patty thought and searched through some textbooks on statistical process control.  Finally, she came upon the solution to the problem in Montgomery’s Introduction to Statistical Quality Control.

“Perfect!” she thought.

She did finish early enough that she could read the WSJ over lunch, marveling, as always, that she was the only person her age that enjoyed reading a real newspaper.

She called Madigan at 3 pm.

“Mike, I think I have your answer.  I found a formula to calculate the confidence intervals of Cpks,” Patty started.

“The Cpk 95% confidence interval on the new paste is 0.95 to 1.05, however the old paste is 0.93 to 1.03,” Patty began.

“So, even I can sense that they aren’t different,” Mike commented.

“Yes, since the confidence intervals overlap, they are not statistically different,” Patty agreed.

Figure 2. The Confidence Interval of the Cpk on the New Paste is 0.95 to 1.05.

They chatted for a while and Madigan asked if Patty could join the first 20 minutes of the meeting by teleconference.  It was a bit close to her lecture start time, but she agreed.

Patty had met Madigan’s son at West Point when she visited there to be an evaluator for a workshop two years ago.  She decided to ask how he was doing.

“Thanks for asking. He is now a Firstie and was in the running for First Captain, but he just missed it.  It’s a good thing he takes after his mom,” Madigan proudly responded.

“Wow! That’s great,” Patty replied.

“I have to admit though, my wife and I are a bit nervous. He has chosen armor as his branch and there is a good chance he will see combat sometime in his career,” Madigan responded with a bit of concern in his voice .

They chatted for a while more and Patty was touched to see so much humanity in Mike Madigan.  He seemed much changed from his gruffness of earlier years.

Cheers,

Dr. Ron

As always, some of this story is based on true events

# Cpk is Still King in Evaluating an SMT Solder Paste Printing Process

Folks,

If you think about it, to evaluate any process you typically want to know its precision and accuracy. Look at the dart players in the Figure 1 below. The yellow player has good precision, but his accuracy is off. The green player has such poor precision, it is hard to tell if his accuracy is good. The yellow player will typically be easier to correct, as she just needs to change her aiming point.

Figure 1. The yellow player has greater precision. She only needs to change her aiming point.

Recently I was asked to evaluate several solder pastes to determine which printed better. We used transfer efficiency (the volume of the stencil printed solder paste “brick” divided by the stencil aperture volume) as the evaluation metric, expressed in percent. So 100% would be the target. The lower specification limit we choose was 50% and the upper specification at 150%.

Figure 2. Data from Pastes A and B.

A good result would be an average of 100% with a “tight” distribution. The “tightness” of the distribution being determined by the standard deviation. Figure 2 shows data from two pastes. Note that Paste A has an average of 100% and a standard deviation of 16.67%, whereas Paste B has an average of 80% and a standard deviation of 30%. Clearly, Paste A is superior to Paste B in both accuracy and precision. But what is the best way to express this difference? Is there one metric that will do it? Cpk is the answer.

Cpk is one metric that is sensitive to both the accuracy and precision. Cpk is defined as:

Where x is the average and S is the standard deviation.

Using these equations, we see that the Cpk of Paste A is 1.0, whereas the Cpk of Paste B is 0.333. Note that Paste B has a significant number of data points (about 17%) outside of the specification limits, however, Paste A has almost no data points out of specification.
So when evaluating most processes, Cpk tells it all!

Cheers,
Dr. Ron

# Area Ratios for Elongated “D” Apertures

Folks,

Ismail writes: Dr. Ron, I know that the area ratio for circular and square stencil apertures is 4d/t.  What is it for an elongated “D” aperture?

The area ratio of a stencil aperture is the area of the aperture opening divided by the area of the side walls.  It is interesting, as Ismail points out, that the area ratio of a circular aperture is the same as that of a square aperture.  A little 10th-grade geometry will point this fact out.  It ends up that the area ratio of an elongated “D” is a little more complex.  All of these aperture shapes and that for a rectangle aperture are shown in Figure 1.   The area ratio formulas are at the bottom of the figure.

Figure 1. The area ratio for several shaped apertures. The elongated “D” aperture is third from the left.

A rule of thumb that still seems to hold is that the area ratio should be 0.66 or greater for the best printing result.  It is possible to do somewhat better (i.e with an area ratio less than 0.66) with a superior solder paste and/or some of the new stencil nano-coatings.

The derivation of the area ratio for the elongated “D” is in Figure 2.

Figure 2.  The derivation of the area ratio for an elongated D shaped aperture.

Cheers,

Dr. Ron

# Alloy Metal Weight Fraction Calculation

“Dear Dr. Ron,

I see that you have developed software to calculate the density of an alloy if given the weight fractions of the constituent metals. Is it possible to find the weight fractions of the metals in an alloy given the alloy’s density? Thank you!”
Unfortunately, finding the weight fractions of the metals in an alloy from the alloy’s density can only be accomplished with a two metal alloy. First we must use the equation:

Equation 1

Where x is the weight fraction of metal A and the rhos are the associated densities.  All that has to be done is to solve for x.  The solution is worked out below in Figure 2, the final result is:

Equation 2

As an example, let’s say you have a gold-copper alloy with a density of 18.42 g/cc.  The density of gold (metal A) is 19.32 g/cc and that of copper (metal B) is 8.92 g/cc.   Substituting these values into equation 2 gives the weight fraction of gold as 0.958.  Hence the weight fraction of copper is 1-0.958 = 0.042.

I have developed an Excel-based software tool to perform these calculations. An image of it is shown in Figure 1.  If you would like a copy of this tool send me a note.

Figure 1.  A screen shot of the alloy metal weight fraction calculator.

Figure 2. The derivation of the weight fraction formula.

Cheers,

Dr. Ron

# Solder Alloy Density Equation: Why What Most People Think is Right is Wrong

Folks,

It’s hard to believe but I have been blogging for over 10 years. In all of this time, with the hundreds of posts I have made, the most popular topic by far has been calculating density in a metal alloy. One of the reasons for this popularity has been the belief that the density of an alloy is determined by the equation

Eq. 1

Where x is the mass fraction of metal 1, y the mass fraction of metal two, ? (rho) the respective densities and ?t the total or alloy density. I have shown in the past that the correct formula to calculate the alloy’s density is:

Eq. 2

This formula is derived below again.

People continue to ask why equation number 1 is not correct, so I have posted an explanation that has been modestly helpful.  I have thought of an example that shows that Eq. 1 cannot be correct and have now derived an equation in the form of Eq. 1 that uses volume fractions instead of mass fractions.  This derivation is also below and the equation is:

Eq. 3

However, Eq. 3 is not very useful as the volume fraction of each metal is not as readily available as the mass fraction, which is easily measured with a scale.

Now, to give an example that shows that Eq. 1 is unreasonable, let’s consider a thought experiment that will help us conclude that Eq. 1 can be way off. Consider a cubic meter of air in a container 1 meter on a side at room temperature. The cubic meter of air will weigh 1.225 kg. (The fact air weighs this much surprises many people.) Inside the container is 1.225 kg of a fine gold powder. We blow the gold powder into the air and it covers all of the inside with an equal concentration. The powder is so fine that it will remain suspended for a short time. So we will consider this an alloy of gold and air.  The mass fractions x and y are equal at 0.50.  So if Eq. 1 were to hold true the density of the “alloy” would be:

Eq. 4

Figure 1. The gold dust and air density experiment.

The weight of the 1 cubic meter container would now be 9650.6 kg/m3 * 1 meter3 = 9650.6 kg!  Whereas we know it to be 1.225 kg + 1.225 kg = 2.45 kg. Eq. 2 or 3 will provide the correct answer.

The correct derivations are below:

Eq. 5

Cheers,

Dr. Ron

# Full Autonomous Autos: Decades Away and In Need of Unprecendented Reliability

Folks,

Since writing my last blog post, there continues an unending litany of articles about the imminent arrival of the self-driving car. I stand by my position that a fully functional self-driving car is decades away. Let me discuss why.

As of August 28, 2014, according to Computer World Google’s self-driving cars were in fact unable to use about 99% of US roads.[51] As of the same date, the latest prototype had not been tested in heavy rain or snow due to safety concerns.[52] Because the cars rely primarily on pre-programmed route data, they do not obey temporary traffic lights and, in some situations, revert to a slower “extra cautious” mode in complex unmapped intersections. The vehicle has difficulty identifying when objects, such as trash and light debris, are harmless, causing the vehicle to veer unnecessarily. Additionally, the LIDAR technology cannot spot some potholes or discern when humans, such as a police officer, are signaling the car to stop.[53] Google projects having these issues fixed by 2020.[54]

Ford claims it will have self-driving cars deployed by 2020. However, a quote by Jim McBride, Ford technical lead, sheds some light:

“Q: What are the big technical challenges you are facing?

“A: When you do a program like this, which is specifically aimed at what people like to call ‘level four’ or fully autonomous, there are a large number of scenarios that you have to be able to test for. Part of the challenge is to understand what we don’t know. Think through your entire lifetime of driving experiences and I’m sure there are a few bizarre things that have happened. They don’t happen very frequently but they do.”

Level four is indeed impressive, but it is not full autonomous as described by SAE:

SAE automated vehicle classifications:

Level 0: Automated system has no vehicle control, but may issue warnings.

Level 1: Driver must be ready to take control at any time. Automated system may include features such as Adaptive Cruise Control (ACC), Parking Assistance with automated steering, and Lane Keeping Assistance (LKA) Type II in any combination.

Level 2: The driver is obliged to detect objects and events and respond if the automated system fails to respond properly. The automated system executes accelerating, braking, and steering. The automated system can deactivate immediately upon takeover by the driver.

Level 3: Within known, limited environments (such as freeways), the driver can safely turn their attention away from driving tasks.

Level 4: The automated system can control the vehicle in all but a few environments such as severe weather. The driver must enable the automated system only when it is safe to do so. When enabled, driver attention is not required.

Level 5: Other than setting the destination and starting the system, no human intervention is required. The automatic system can drive to any location where it is legal to drive.”

The difference between level 4 and 5 is enormous.  Just a few days ago I drove a level 2 Volvo SC90. It was a lot of fun. It had autonomous steering and acceleration/breaking. It worked very well, but it needed the lane markers, a not insignificant requirement.

Level 4 could not take you on a trip from my house, in Woodstock, VT, to a meeting in downtown Boston. To start, some of the trip is on roads without lane markers. Let’s also assume that there is construction with hand written signs directing the cars to a detour. There is also a traffic cop who signals you to stop and roll down the window to listen to instructions, a huge pot hole that has a hand-made warning sign is in downtown Boston, etc. None of these challenges would be unusual for a human, but a challenge for Level 4 autonomy.

Ford’s self-driving car has the equivalent of 5 laptop computers.

Singapore has implemented what appears to be level 3 vehicles, but there is a human backup and the route is specially selected.

All of this is exciting news.  But getting a vehicle that can handle 99% of human driving tasks with 99.99% reliability (let’s call it Phase I) will be easier that getting the last 1% with 99.99999% reliability (Phase II).  I agree that Phase I may be only years away, but Phase II is decades away.  Without Phase II, the driverless car that has no steering wheel or gas pedal is not achievable.

How does all of this affect us in electronics assembly?   It will be an interesting adventure to work with the auto industry on the extreme reliability required.  My guess is that this reliability need will be a dominant theme in the future.

Note: Probably the best article on this topic was in the June 2016 issue of Scientific American.

Cheers,

Dr. Ron