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

24 2.3. Analytical thermal model
1. The region where power is dissipated is approximated by a simple geometry. Two
models have been adopted:
➤ THS model – an infinetly thin rectangle, Thin Heat Source model (Fig.
2.12b). This case is described in section 2.3.1.
➤ VHS model – a parallelepiped with finite thickness, Volume Heat Source
model (Fig. 2.12a). This case is described in section 2.3.2.
2. Power density is uniform within the heat source region and zero outside the
region.
3. Boundary Conditions are neglected in all directions except the top surface, where
adiabatic boundary condition is set. The image function method is used to solve
the steady-state heat-flow equation.
4. The geometry of the heat source is independent on bias conditions.
2.3.1. Case of rectangular heat source (THS)
Figure 2.13: Thermal model of an integrated device. The chip is a right parallelepiped
with a rectangular heat source of dimensions WL located at the depth zs from the
surface and centred around the point (xs, ys, zs).
To develop a solution as a first step adiabatic boundary condition at the top surface
is neglected. The temperature distribution in an infinite domain with a THS at a point
P=(x,y,z) is given by [35] :
θ(x, y, z) = qs
4πk [g(δx2, δy2, δz) − g(δx2, δy1, δz) − g(δx1, δy2, δz) + g(δx1, δy1, δz)]
(2.40)