Thermal via allocation for 3D ICs considering temporally and spatially variant thermal power

ABSTRACT

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.

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INDEX TERMS

Primary Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.2 Design Aids

General Terms:
Algorithms, Design

Keywords:
SQP optimization, structured and parameterized macromodel, thermal management and simulation