Development of a New Electro-thermal Simulation Tool for RF circuits

26 2.4. Compact Thermal Model
Figure 2.14: Thermal model of an integrated device with a volume heat source. The
heat source is modelled as an embedded parallelepiped of dimensions WLH centred
around the point (xS, yS, zS).
As for the THS, let us define the function λ:
θ(x, y, z) = λ(δx1, δx2, δy1, δy2, δz1, δz2) (2.47)
and δx1 = x − x1, δx2 = x − x2, δy1 = y − y1,δy2 = y − y2, δz1 = z − z1, δz2 = z − z2
where x1, y1, x2, y2, z1, z2, are coordinates of the volume heat source.
The solution for semi-infinite domain is given by the superposition of the contributions
of the real and image sources:
θ0(x, y, z) = λ(x − x1, x − x2, y − y1, y − y2, z + z1, z + z2)+
2.4.
Compact Thermal Model
λ(x − x1, x − x2, y − y1, y − y2, z − z1, z − z2)
(2.48)
An approach to the thermal analysis depends strongly on a kind of issue, which has to be
solved. In the previous sections, the analytical thermal model has been described. The
heat was exchanged through only one bottom boundary, with a constant temperature
(isothermal boundary condition). Here, only one parameter (thermal resistance value)
was necessary.
The thermal problem can be solved using more physically related quantity called
thermal resistance Rth or thermal impedance Zth. It is a simple approach, that can be
easily implemented into electrical simulator. In this case, the heat flow is represented
as a current, and a temperature is represented as a voltage. However, if the heat flow is