Beyond the Data Sheet: Demystifying Thermal Runaway

Nov 1, 2007 12:00 PM
By Roger Stout, Senior Research Scientist, ON Semiconductor, Technology Development, Advanced Packaging, Phoenix

Then, as if the terms weren't confusing enough, note that if the reverse voltage (V^R) on the device is constant with temperature, the device power as a function of temperature (being the product of the power-law current and a constant voltage) also follows a power law with the same power-law strength, as did the current.

Finally, even when the device terminal voltage is not constant with temperature (for instance, in power MOSFETs where on-resistance is a function of temperature — so at constant current, the voltage will change significantly with temperature), it is fairly likely that, at least over some reasonable range of temperatures and operating conditions, device power in a real application could be approximated by some sort of power law.

Therefore, in general, we'll henceforth be referring only to device power in the power law, and will be the power-law strength of the device power, as in:

Indeed, to obtain Fig. 3 and Fig. 4, the various power-law strengths and functions as described here were computed from data obtained on the device data sheets. In the case of Fig. 3, a MOSFET, the power-law strength came out to about 200°C (which is why the device lines were effectively straight over the plotted 125°C range). By contrast, for the power rectifier of Fig. 4, the power-law strength came out to only about 15°C, explaining the rapid curvature of the device lines over the same temperature range.

If it turns out there is strong nonlinearity (say, if λ is 30°C or lower), then you may find the following additional relationships useful in quantifying your runaway margin. Given θ_JX is the theta of your cooling system as experienced by the device of interest, the runaway junction temperature (point of tangency as shown in Fig. 2) is given by:

And as a result of the amazing mathematical properties of the exponential function, the T-intercept that goes with it, is a simple λ offset from the runaway temperature:

Obviously, the runaway temperature margin is the difference between your designed T-intercept (T_X) and the intercept given by Eq. 9 (T_Y). (One of your jobs as the designer is to decide how small a margin you're comfortable with.) In addition, the nondimensional quantity,

and the nondimentional temperature,

are useful for computing the two intersections between the device line and the nominal system line, which satisfy the nondimensionalized equation: kz = e^z.

If k > e, you'll have both the stable design point of the original system as well as the theoretical (but unstable) upper intersection. If k = e, you're already at perfect runaway. If k < e, there are no solutions, meaning your system design was bad at the outset and so you need a lower theta or a lower ambient just to get started.

The True Meaning of Theta and Ambient

By definition, the T-intercept of our system line is the zero-power device junction temperature. If our device of interest were the only heat source in the system, then and only then would this zero-power temperature be ambient. However, in most systems of interest, there are many interacting heat sources, each contributing to each other's background temperature. In other words, the T-intercept of our device of interest is neither more nor less than the temperature it reaches when it is turned off and the rest of the system is otherwise normally powered.

Similarly, as shown in Fig. 5, for the system line to mean anything, its slope must correspond to incremental changes in junction temperature for incremental changes in power dissipation. If the system is thermally linear (hence, the principle of linear superposition is applicable), then the slope of a device's system line will not change just because its background temperature (T-intercept) shifts right or left. What one must not do is compute θ_JA as the difference between actual operating temperature and the ambient temperature, divided by device power, while additional heat sources are active.

As other heat sources are turned on, the background temperature of each device rises. Each increase in this background temperature effectively moves the T-intercept of that device's system line to the right. If you have a device subject to thermal runaway and have computed the temperature margin relative to the ambient temperature, then each background temperature increase from every other heat source eats into this margin. In other words, a proper thermal runaway analysis also must comprehend all the thermal interactions between all your heat sources. Then your runaway margin is a real margin.

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