The change in mean temperature of the test line divided by the change in power dissipation in the line, as described in the following equation:
Rth = ΔT/ΔP (1)
where
Rth is the thermal resistance (ºC/W);
ΔT is the change in mean temperature (ºC);
ΔP is the change in power dissipation that caused the change in mean temperature (W).
NOTE 1 It is assumed that any electromigration damage that may occur during the isothermal test does not affect the thermal resistance of the line to the first order.
NOTE 2 The thermal resistance Rth is defined assuming temperature uniformity along the test line and the linear dependence of T on P: in a plot of T versus P, Rth is the slope of the straight line. Rth is dependent on the geometry of the test structure and on the thermal conductance of between the test line and the ambient. On the other hand, because the thermal conductance of the materials in the path of the heat flow from the test structure is temperature dependent, the T-versus-P relationship is not linear; i.e., the slope of this curve will gradually decrease with increasing power dissipation. In other words, Rth is temperature dependent. Therefore, over a limited range of temperatures (typically 50 °C), the T-versus-P relationship can still be considered linear,
T = T0 + Rth ×P. (2)
As a consequence, a best straight-line fit of equation (2), using some measured (T, P) data pairs in this limited temperature range, can be used to estimate the thermal resistance value, Rth , and the thermal resistance intercept, T0.