How does P²t stress relate to MOSFET safe operating area?

[likephysics]

Saw a calculation of stress in a datasheet (page14) here -
http://tinyurl.com/43465sv
(The device drives a Mosfet.)
How do you relate the P^2 t stress calculation in the datasheet to the Safe operating area curve in a Mosfet datasheet.
If the Stress is 20W^2 sec, then how do you interpret it? The Mosfet should be able to withstand 20watts for 1sec.
The watt square is confusing me. Why watt square*t? why not joules.

 

[likephysics]

Anyone?

 

[jsgruszynski]

The first section on the same page says what it is but you have to apply engineering knowledge to infer where it comes from.

The units come from two separate effects:

• P t which results in units of energy delivered as heat that modulates to heat transfer effectiveness - this is the "accumulated heat over time" or integrated heat effect
• P which is the instantaneous power delivered to the load and dissipated as heat

These combined as function: Damage(P_{short-circuit}, E_heat) which are modeled multiplicatively, hence P²t

This value is "essentially constant for intervals of less than 100ms for any given device type" so basically you have thermal equilibrium because you aren't generating heat fast enough to exceed the heat sink capacity of the package. Above that you start to have a positive feedback loop on heat that accelerates the effect of the short circuit power (P).