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

14 2.2. Chip thermal model - mathematical considerations
The linearity is assumed, however in a final solution, by applying the Kirchhoff
transform, the nonlinear solution can be received.
For bipolar devices, the heat generation occurs in BC-SCR 1 region. (Fig. 2.1). A
Figure 2.2: Assumptions for constructing the thermal domain for VHS and THS models.
heat is located underneath the emitter window (n region). As an immediate consequence,
the heat source can be approximated as a rectangular parallelepiped volume
centred at a depth zs. In a more simple approximation, the heat source is treated as
an infinetly thin rectangle. In both cases the power density is assumed to be uniform.
Therefore, two cases will be considered:
(a) Volume Heat Source (VHS). (b) Thin Heat Source (THS).
Figure 2.3: BC-SCR region can be approximated by Volume or Thin Heat Sources.
➤ Volume Heat Source (VHS), where the power density g inside the parallelepiped
is defined as:
g(x, y, z) = P
[W/cm 3 ] (2.4)
VHS
where P is a power density and VHS = H · W · L. W is the BC-SCR width, L is
the length and H thickness.
➤ Thin Heat Source (THS), where the power density g is defined by Eq. 2.5
g(x, y, z) = q · δ(z − zs) [W/cm 3 ] (2.5)
where q = P/W L represents the power density per unit area.
1 Base-Collector Space-Charge Region