High Efficiency Transient Temperature Calculations for Applications in Dynamic Thermal Management of Electronic Devices

Abstract

The highly nonuniform transient power densities in modern semiconductor devices present difficult performance and reliability challenges for circuit components, multiple levels of interconnections and packaging, and adversely impact overall power efficiencies. Runtime temperature calculations would be beneficial to architectures with dynamic thermal management, which control hotspots by effectively optimizing regional power densities. Unfortunately, existing algorithms remain computationally prohibitive for integration within such systems. This work addresses these shortcomings by formulating an efficient method for fast calculations of temperature response in semiconductor devices under a timedependent dissipation power. A device temperature is represented as output of an infiniteimpulse response (IIR) multistage digital filter, processing a stream of sampled power data; this method effectively calculates temperatures by a fast numerical convolution of the sampled power with the modeled system's impulse response. Parameters such as a steadystate thermal resistance or its extension to a transient regime, a thermal transfer function, are typically used with the assumption of a linearity and timeinvariance (LTI) to form a basis for device thermal characterization. These modeling tools and the timediscretized estimates of dissipated power make digital filtering a wellsuited technique for a runtime temperature calculation. A recursive property of the proposed algorithm allows a highly efficient use of an available computational resource; also, the impact of all of the input power trace is retained when calculating a temperature trace. A network identification by deconvolution (NID) method is used to extract a timeconstant spectrum of the device temperature response. We verify this network extraction procedure for a simple geometry with a closedform solution. In the proposed technique, the amount of microprocessor clock cycles needed for each temperature evaluation remains fixed, which results in a linear relationship between the overall computation time and the number of temperature evaluations. This is in contrast to timedomain convolution, where the number of clock cycles needed for each evaluation increases as the time window expands. The linear dependence is similar to techniques based on FFT algorithms; in this work, however, use of ztransforms significantly decreases the amount of computations needed per temperature evaluation, in addition to much reduced memory requirements. Together, these two features result in vast improvements in computational throughput and allow implementations of sophisticated runtime dynamic thermal management algorithms for all highpower architectures and expand the application range to embedded platforms for use in a pervasive computing environment.