Adaptive Transient Leakage-Aware Linearised Model for Thermal Analysis of 3-D ICs

Physics-based models for thermal simulation that
involve numerical solution of the heat equation are well placed to
accurately capture the heterogeneity of materials and structures
in modern 3-D integrated circuits (ICs). The introduction of nonlinear
effects such as leakage power significantly improves their
accuracy. However, this non-linearity increases considerably the
complexity and computational time of the analysis. In this paper,
we introduce a linearised thermal model by demonstrating that
the weak temperature dependence of the specific heat and the
thermal conductivity of IC related materials has only minor effect
to computed temperature profiles. Thus, these parameters can
be considered constant for the operating temperature ranges of
modern ICs. The non-linearity in leakage power is approximated
by a piecewise linear least square fit and the resulting model
is linearised by exact Newton’s method. The method is applied
to transient thermal analysis with adaptive time step selection,
where we demonstrate the importance of applying Newton
corrections to obtain the right time step size selection. The
resulting method is typically 2-3x faster than a full non-linear
method with a global relative error of less than 1%