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Adaptive Power Blurring Techniques to Calculate IC Temperature Profile under Large Temperature Variations

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Power Blurring (PB) methods enable calculation of IC temperature profiles from the power dissipation map with calculation speeds hundreds of times faster than finite element methods (FEM). Both static [1,2] and transient distributions can be obtained [3]. Extensions to 3D chips [4] and to the inverse problem, i.e. estimating the power map from the temperature field [5], are available. So far however, the temperature dependence of the material parameters has been neglected. Temperature rises of 40-50°C on the chip will reduce the thermal conductivity of the silicon by 10-20%. This could affect the hot spot temperature by 5-7°C. In this work, we extend the PB approach to account for this effect. We propose two Adaptive Power Blurring (APB) methods based on iterative procedures. In both methods, the PB method provides an initial temperature distribution guess using room temperature Si thermal conductivity. Subsequent iterations take into account the preliminary temperature profile in the chip. The key difference between the two APB methods is the way the thermal masks are selected from a look-up table. The first variant uses one single mask based on the average temperature increase in the silicon, while the second approach employs a different mask for each point to account for the spatial variation of the temperature and according non-uniform thermal conductivity. In either case, the new estimate of temperature profile is acquired from convolution of the thermal masks and the IC Power map. These schemes are then applied iteratively until a final, self-consistent solution is reached. Good convergence is achieved only in 2-3 iterations in both methods. We will demonstrate that these APB methods substantially improve the accuracy under high temperature rise regime, in particular at hot spots, while still being much faster than traditional FEM computations.
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... The PB technique is based on the superposition principle, which requires linearity of the heat conduction equation. An adaptive PB technique is developed in [26], which can solve nonlinear problems, e.g., when the thermal conductivity of the silicon is modified based on the local temperature of the chip, using two or three iterations. Excellent agreements with self-consistent finite-element simulations have been obtained. ...
... Three orders of magnitude improvement in runtime as well as six orders of magnitude speedup are obtained by their PB method in comparison with solving the thermal network of the chip directly. Acquiring temperature profiles of power electronic transistor arrays [25], solving nonlinear problems (calculating temperature profiles in ICs considering temperature dependence of material properties of the chip) using only two or three iterations [26], and solving the inverse problem (i.e., obtaining heat dissipated in ICs from their temperature profiles) [27] are some other examples, which are illustrative of versatility of the PB technique. ...
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Fast Computation of Temperature Profile of VLSI ICs with High Spatial Resolution" Semiconductor Thermal Measurement, Modeling, and Management Symposium (Semi-Therm 24)
  • J H Park
  • X Wang
  • A Shakouri
  • S M Kang
J.H. Park, X. Wang, A. Shakouri, S.M. Kang, "Fast Computation of Temperature Profile of VLSI ICs with High Spatial Resolution" Semiconductor Thermal Measurement, Modeling, and Management Symposium (Semi-Therm 24), pp. 50-55, 2008.