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

When thermal runaway is a possibility, what you want to quantify during the design phase is the margin by which runaway can be avoided. Fig. 2 illustrates this concept: If the system line shifts to the right, there comes a point at which the system and device lines are exactly tangent (where their slopes are equal, in fact). Note that if the system line stays properly located, even a local device temperature perturbation this far to the right will not actually experience runaway, because there is still considerable cooling margin at that point. But, if the system line actually shifts that far to the right, thermal runaway will indeed occur.

The Power-Law Device Model

Before proceeding, we should head off some unfortunate possible confusion between the power a device dissipates (that is, the terminal voltage multiplied by current passing through the device), and the power in the mathematical term power law, which refers to a quantity being raised to a power. If the base quantity happens to be the base of the natural logarithms (e), the power law becomes more specifically the exponential law.

A classic example of a power-law device is a reverse-biased diode, for which there's a rule of thumb that says the leakage current goes up by a factor of 2 for every 10°C increase in temperature. The following equation expresses this directly:

With a little algebraic slight of hand, any power law can be turned into an exponential law. Thus, the next equations say the same thing as Eq. 1:

where I_O is the device current at a temperature of 0°C and is the power-law strength that can be derived from the leakage current at any two temperatures at which leakage current happens to be known. (Although you probably won't find I_O on a data sheet, you can deduce it from any other current and temperature, once λ is known.)

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