The Meaning of "Good Enough"

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In my previous article I claimed that all the blocks I tested were ‘good enough’ and did not require further lapping. After this was published, it occurred to me that I had written a meaningless statement. I had not qualified what ‘good enough’ was.

In legalese ‘Good enough’ translates into:

“Surface figure and finish of a quality level sufficient so as not to significantly impact heat transfer between the bulk mass of the microchip and the bulk mass of the heat transfer device”.

This too is a vague and unqualified statement. In this case the problematic terms are ‘Quality’, ‘Sufficient’, and ‘Significant’. This article is mainly concerned with ‘Sufficient’. In order to define ‘Sufficient’, I will need to define ‘Significant’. The definition of ‘Quality’ is well beyond the scope of this article. For our purposes ‘Quality’ is synonymous with precision.

According to Arctic Silver, their ‘Arctic Silver 5’ compound transfers 350,000 watts of energy per square meter per degree Celsius across a 0.025 mm thick layer. For sake of simplicity I will assume a 1 cm² heat transfer area or 1/10,000 of the area quoted. This translates as 35 watts per degree Celsius, or in the terms used on this site to test waterblocks, 0.0286 C/W for a 1 cm² die (if you find an error in my math [a likely possibility] please e-mail me).

To complicate matters, a larger area will be able to transfer more energy. Fortunately the relationship between area and heat transfer is linear – this is to say a 2cm² transfer surface will have a C/W of 0.0143.

Now for the fun part. The error most machining and lapping processes produce on the base plate of a heatsink or waterblock is generally a smooth curve. This means that a larger contact plate will have larger gap between the transfer surfaces. Increasing the size of the contact surface increases the transfer area but it also increases the thickness of the layer of thermal paste.

To a heatsink manufacturer this means the surface tolerances they must achieve increases with the size of the die or IHS they are trying to cool.

This also places a restriction on how I should test the flatness of a heat transfer surface. For my test to be accurate and provide the manufacturer with some measure of justice, I should restrict my tests to the ‘Critical Zone’. The critical zone is the area of the base plate that comes in contact with the chip transfer surface.

As an example I will use the stock heatsink that came with my Athlon XP 2500+. On first glance it appears to have been lapped by hand with a belt sander at roughly 100 grit. Measured from the outermost edge to the outermost edge, there is ½ mm of error peak to valley (highest measured point to lowest measured point). If I restrict my test to 5 mm in from the outermost edge the reading dramatically improves to 14/100 mm. Restricting the test even further to the inner most 25mm of the block (the same zone tested in my previous article), the surface precision improves to 6/100 mm. When I restrict the test to the area AMD intended me to use, the measured error drops to 1/100 mm.

What then constitutes a surface of sufficient quality?

A sufficiently flat surface is one that is not a significant impediment to heat transfer. Any number I give you must be in some way arbitrary. A flatter surface will transfer heat better no matter how slight the improvement. And, as I have made mention repeatedly before, it is impossible to make a perfect surface. The pertinent question is when to stop.

In the last three paragraphs of a previous article, I discussed what constitutes a good surface finish. I believe this can provide a reasonable guideline for surface figure. As a rule of thumb, I suggest that if the figure of your base plate is within the roughness of the surface finish, you will no be able to achieve an appreciable gain in thermal transfer.

Consider it this way: on the base plate and the microchip surface, you have X thickness thermal compound in the surface roughness pits. In this case even a perfect surface will have 2x of thermal compound between the surfaces. Roughly half of this volume though will be copper, so as a rough estimate (given the variance between surface finishing systems, this is all we can hope for) there will always be at least X thickness of thermal compound between the surfaces.

If the deviation of the surface from perfect is less than X, then you can make no meaningful improvement to thermal transfer. Granted, this rule is still somewhat arbitrary but at this point it would be impractical to make any improvement to thermal transfer between surfaces.

Two final notes:

First, the value X, maximum allowable surface error, in the previous paragraph is a special case where both base plate and chip have the same surface roughness. Given that the two thermal transfer surfaces could have different surface finishes, the real value for X is:

{[X1 (the root mean square surface roughness for the base plate)] +[X2 (the RMS roughness for the chip surface)]}/2

Second, all the waterblocks I tested in the previous article met this criterion.

Ian Anderson

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