The accidental thermal engineer: Can we know Tj by looking at Tcase? (Part 3)

The accidental thermal engineer: Can we know Tj by looking at Tcase? (Part 3)

If you’ve spent some time in the world of power semiconductors, then it’s likely that you’ve come across the concept of “thermal resistance.” If you haven’t come across this before, or you need a refresher, then I’d recommend a look at the Wikipedia article or the JEDEC JESD51 series of standards, particularly JESD51-1, Section 2.

Thermal resistance can be thought of as a way to characterize the ease with which heat energy travels through a particular pathway. There are several ways of defining thermal resistance, and two of the most common are shown in Figure 1.

Figure 1 Thermal resistance defined in terms of temperature difference and heat flux (left) and material dimensions and properties (right).

Figure 1 Thermal resistance defined in terms of temperature difference and heat flux (left) and material dimensions and properties (right).

In Figure 1 (left) we are defining thermal resistance Rthx-y[1] simply in terms of the heat flow between two points at different temperatures, without knowing anything about how the heat flows between those two points. In Figure 1 (right), on the other hand, we define Rthx-y as a function of the dimensions and thermal conductivity of a block of material, with the assumption that heat flow is occurring through the mechanism of conduction only. Note that in the right-side definition, we could also define Rthx-y through a composite block of differing materials with different “k” values simply by adding the thermal resistances of the different layers together. Aha! So going back to our original question, would a knowledge of the thermal resistance from the die to the top of the case (Rthj-c) help us to determine Tj from Tcase? See Figure 2.

Figure 2 An idealised cross-section of an LFPAK MOSFET showing the location of Rthj-c.

Figure 2 An idealised cross-section of an LFPAK MOSFET showing the location of Rthj-c.

Rthj-c is the conduction-only thermal resistance from the die through the top clip and plastic to the top surface of the device case, although it is not one of our “standard” datasheet parameters.  So supposing our MOSFET supplier is kind enough to supply an Rthj-c number, and we also have the equation

equation 1

then we can find Tj from Tcase by a simple bit of algebra, can’t we? Sadly, the answer is “no” for two very good reasons:

First, re-arranging the above equation would give us

equation 2

We’ve been given Rthj-c, and we can measure Tcase, but what about the heat flux “q”? In other words, what proportion of the total die dissipation is travelling upwards through the Rthj-c route? As far as I know, it is impossible to measure this quantity under lab conditions. Attempts to estimate or calculate a value for q is likely to lead to wildly inaccurate answers for Tj. Although it superficially looks as if we can infer Tj from Tcase using this method, it is of little or no practical value.

Going back to the Figure 1 (left) definition of thermal resistance, the second reason why attempting to use thermal resistances in this way is flawed.  The concept of thermal resistance assumes the heat energy flows down a single, clearly defined path and the temperature at point “y” is only dependent on that of point “x” and the heat flow q. It does not consider any additional parallel paths from x to y – or that some of the heat energy emanating from x may not even reach y at all! In my previous post, I demonstrated that the proportion of heat energy reaching the top of the device case through the Rthj-c route is tiny. Furthermore, the device is surrounded by air that has been warmed by heat loss from the adjacent PCB surface.

The over-arching point I am trying to make is that thermal resistances are not intended to be used as design tools. In fact, JEDEC  makes this point very clearly in JESD51-2:

“…The intent of (thermal resistance) measurements is solely for a thermal performance comparison of one package to another in a standardized environment. This methodology is not meant to and will not predict the performance of a package in an application-specific environment.

In my next post, I’ll  explore a related theme: the usefulness (or otherwise) of the concept of “top-side cooling.” In the meantime, for an interesting and thought-provoking discussion of thermal resistance, you might like to read this article by my former colleague Clemens Lasance.

[1] Sometimes you may see Rth written as RΘ, mainly in American texts. The two are interchangeable, but I’ll be sticking with Rth.

Christopher Hill
Christopher Hill
With over 20 years experience as an applications engineer specialised in power MOSFETs, Chris has dealt with a multitude of power semiconductor design-in challenges. One of the recurring themes in these challenges has been ‘thermal’, and therefore he has spent much of his working life immersed in questions of a thermal nature. He has authored numerous conference papers, magazine articles and application notes on a variety of power semiconductor topics. In his free time he likes nothing better than plodding through muddy fields in the North of England.

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