Measuring thermal resistance

In the course of all the dumb things I do with electronics, I have often been forced to ask if some on-hand adhesive would be adequate for mounting heat sinks.  Often this is a matter of ad-hoc retrofitting rather than better design practice.  An example might be putting small milled heat sinks on a Raspberry Pi or replacing a small GPU heat sink with a trashy integral fan.  Maybe I need an insulating washer for a Multwatt-15 package, and all I have is mica for a TO-220.  Will an aluminized mylar antistatic bag work well enough?

"Don't worry, this is just temporary" --me, ca. 2009

Beyond that, what about more typical design guidelines?  Figures for typical case-sink thermal resistance for a common TO-220 package vary widely.  Whose numbers should I have confidence in using -- or should I just assume the worst numbers I can find?  That hardly seems better than guessing.

Asking the internet for the thermal properties of anything other than a legitimate TIM is pretty much futile.  Even those figures listed for half of the common materials at the bottom of the market are probably questionable anyway.  Is that $0.99 white goo from ebay really 1.5 W/mK?  After stumbling on enough clickbait advertisements non-quantitative or questionable computer cooling articles or product reviews wherein heat flows are measured in minutes of videogame, I figured I might as well just do it myself.  That's not to say my efforts were all that accurate.  Consider this more as an inexpensive method in development than a set of authoritative results.

So how to measure thermal resistance of a TIM?  There are a number of ways. A smart way might be like the above image.  Say we use heated and chilled volumes of water pumped through heat exchangers.  If we can measure the inlet and outlet temperatures on the heat exchangers, as well as the volume flow rates on either side, we can quantify the heat flow that actually passes through the thermal interface.  Sure, heat is being being lost in the hoses and into the air, but so long as we know the temperature differentials and the mass flow rates (implied by volumetric flow), we can eliminate those unknowns.  This could be a static configuration, or maybe we could switch the inlet from chilled to heated and extract the thermal resistance from the transient response.

That's a really cool idea, but I don't have a bunch of flow meters and pumps and I don't feel like putting that together just to test some goo once in a while.  Certainly, there are a lot of other methods that are all documented and standardized.  It seems that in most cases though, fabrication of either heaters, sensors, or interface surfaces becomes difficult, expensive, or at least tedious.  I don't want to have to hand-finish any more surfaces than necessary. 

Let's try something that's cheaper lazier simpler.  Consider the above diagram involving an electric heater and a heat sink.  In this configuration, it's simple enough to find the input heat flow, but how can the flux through the interface be quantified if the cold side is just a heat sink and ambient losses are unknown?  My primary assumption is this: if the stray losses on the heater can be made negligible, then the input power is approximately equal to the heat flux through the TIM.  Then, for the fixture area:

Maybe that's a bit too hopefully simplistic.  Maybe we can try to come up with an approximate loss ratio by using a simulation model.  Or better yet, if we can run the heater in the absence of the heat sink, we can get a rough figure for the heater-ambient thermal resistance, i.e. the resistance of the stray loss path.  If that information were available, the resistance of the conduction path then becomes:

By the time the numbers congeal in my mind, I already have visions of an assembly method.  Before we bother getting out of the chair, let's see if any of this seems reasonable.  With a few minutes of effort in FEMM, I threw together a questionable simulation of such a fixture.  The primary flaw is the fact that I didn't model any sort of convection transfer at the solid-air boundaries.  I just set a fixed boundary temperature at the extremities of the heat sink. It'll be close enough.  There are only a few things I want to know here:

• What is the temperature gradient like around the interface?  
• Will sensor placement be critical? 
• Is the flux density uniform across the interface plane?
• What's a ballpark figure for the stray losses from the heater?

Along with the goofy boundary condition selection, the axisymmetric model often forces approximations of shapes that aren't cylinders coaxial to the z-axis.  The heater resistors are modeled as a single cylinder with a geometry that approximates the degree to which cross-bored holes will occlude the cross-sectional area of the heater bar.

These quick checks suggest that for a relatively small heater power (23W), only a modest amount of insulation should be required to keep losses quite low (1-5%), even when jacket temperatures are at ambient.  So long as attention is paid to geometry, sensor placement shouldn't be terribly critical either.  Let's cobble together some rickety bullshit!

Heater bar, resistors, thermal overload, spring, scrap aluminum

Milled CPU heat sink

Heater bar and spring guide in insulator case (nested peanut butter jars)

The assembly is fairly self-explanatory.  The heater bar is machined from aluminum; the heat sink is fabricated by modifying a CPU heat sink.  The frame is assembled from scrap aluminum.  The heater has an integral spring and the compression screw uses a stop so that pressures are repeatable.

The resistor leads are insulated with wire insulation trimmings.  The resistors are bonded to the heater bar using STARS-922 "heat sink plaster".  This is a semi-setting heat sink compound.  It congeals within a few minutes, but doesn't form a tough film like an RTV silicone would.  This makes it easier to replace parts if necessary.  At the time, I was not sure of the properties of this material, but I wanted to be able to press the resistors out if necessary.  Besides, experimentally determining unknown properties was kind of the whole point behind building the fixture, wasn't it?

WOULD YOU LOOK AT ALL THAT STUFF

Once things are together, there are a couple things we can try to test.  The generic ebay thermocouples can be characterized to eliminate any static offsets they might cause.  The heater losses can also be checked to some degree.  If the exposed face of the heater is insulated, the bar can be gradually brought up to a nominal operating temperature to find its resistance to ambient.  Combining this figure with preliminary TIM tests suggest that stray losses are well within 3%.  For a good thermal contact such as a metal-filled grease, stray losses should constitute only about 1-2% of the input power.  It's nice when simulations jive.  With thermal resistance of the loss path known, the more accurate method for calculating interface resistance can be used.

We can also try to figure out the spring constant and set the stop at a reasonable interface pressure.  Due to a mismeasurement, I ended up adjusting this in the middle of things; not everything is measured at the same pressure.  For the most part though, the differences are negligible.  As a reference, typical TO-220 mounting forces from Philips suggest a pressure range of about 80-600 kPa. I'm testing at the low end, but I'd have to use different springs and brackets to go much higher. 

I've tested a few things so far, and the results are fairly expected.  When translated to suit transistor packages, the resistance figures seem appropriate.  What's interesting (and disconcerting) is that the areal resistance (K*m^2/W) doesn't quite jive with any of the specifications for the products used.  Of course, they're generic ebay grease, so I'd sooner accept the experimental result.  The kapton tape is the film alone with its adhesive removed.  The grease used with the insulator films is the ZP brand white grease.  Permatex Ultra Grey has the highest filler content and density of any of Permatex's RTV gasket products (afaik).  The orange high-temperature product is one of the lowest-solids materials they offer. 

I could've made a table, but nnnnope

Thermal resistances when translated to common semiconductor packages

I'd like to try to work out some volumetric conductivity (W/(m*k)) figures, but I've had difficulty getting repeatable results.  I need to come up with a better method of determining or enforcing TIM film thickness.  I'm not that terribly concerned with volumetric conductivity, though.  For most electronics applications, I feel that it makes more sense to leave the otherwise unknown film thickness buried in the metric. 

I'd like to try testing a bunch of other things, but these are just the common sorts that I had on hand.  If anyone wants me to test something, let me know.  Hah! Just kidding.  I know nobody will ever read this.  In case you don't exist, here are some perishable links to the materials used:

• STARS-922 Heat sink plaster
• ZP white grease
• HY610 grease
• Plain silicone grease
• Permatex Ultra Grey
• Permatex High-Temp

It should be noted that some materials like the metal-filled greases and acetoxy-cure RTV silicones have electrically important properties that bear consideration.  Some day I might show my method for testing that.  I also hope to have some of the mechanical properties of the STARS-922 tested soon as well.