thermal via allocation for 3d ics considering temporally and spatially variant thermal power
All existing methods for thermal-via allocation are based on a steady-state thermal analysis and may lead to excessive number of thermal vias. This paper develops an accurate and efficient thermal-via allocation considering temporally and spatially variant thermal-power. The transient temperature is calculated using macromodel by a structured and parameterized model reduction , which generates temperature sensitivity with respect to thermal-via density. By defining a thermal-violation integral based on the transient temperature, a nonlinear optimization problem is formulated to allocate thermal-vias and minimize thermal violation integral. This optimization problem is transformed into a sequence of subproblems by Lagrangian relaxation, and each subproblem is solved by quadratic programming using sensitives from the macromodel. Experiments show that compared to the existing method using steady-state thermal analysis, our method is 126X faster to obtain the temperature profile, and reduces the number of thermal vias by 2.04X under the same temperature bound.
thermal management and simulation structured and parameterized macromodel sqp optimization