The standard way of treating temperature effects in semiconductor devices
and circuits is based on the assumption of a constant device temperature which
can be obtained by *a priori* assumptions on the dissipated power or by
measurements. However, in general this *a priori* assumed dissipated power is
not in accordance with the resulting dissipated power. Furthermore, devices
may be thermally coupled resulting in completely different temperatures than
would be expected from individual self-heating effects alone. This is of special
importance as many circuit layouts rely on this effect, e.g., current mirrors
and differential pairs [25]. Therefore, the temperature must not be
considered a constant parameter, but must be introduced as an additional
solution variable.

Thermal coupling can be modeled by a thermal circuit [25,45].
The topological equations describing a thermal circuit are similar in form to
Kirchhoff's equations and the branch relations map to familiar electrical
branch relations. The electrical compact models have been extended to provide
the device temperature as an external node. For distributed devices *MINIMOS-NT*
solves the lattice heat flow equation to account for self-heating effects.
This is of course far more accurate than assuming a spatially constant
temperature in the device and estimating the dissipated power by
Joule-heat terms alone as is done for the compact models. To provide a
connection to an external thermal circuit arbitrary thermal contacts can be
defined.

The thermal heat flow *P* between two points with
temperatures
and
is given by [51]

with

with

Equation (2.25) is equivalent to Ohm's law with replacing the node voltage and

1999-05-31