**Touzelbaev, M.N., Miler, J.,** Yang, Y., Refai-Ahmed, G., and Goodson, K.E., 2013, “High-Efficiency Transient Temperature Calculations for Applications in Dynamic Thermal Management of Electronic Devices,”* Journal of Electronic Packaging*, Vol. 135, pp. 031001-1 to 031001-8.

### Abstract

PDFThe highly nonuniform transient power densities in modern semiconductor devices pres-ent difﬁcult performance and reliability challenges for circuit components, multiple levels of interconnections and packaging, and adversely impact overall power efﬁciencies. Run-time 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 time-dependent dissipation power. A device temperature is represented as output of an inﬁnite-impulse response (IIR) multistage digital ﬁlter, processing a stream of sampled power data; this method effectively calculates temperatures by a fast numerical convolu-tion of the sampled power with the modeled system’s impulse response. Parameters such as a steady-state thermal resistance or its extension to a transient regime, a thermal transfer function, are typically used with the assumption of a linearity and time-invariance (LTI) to form a basis for device thermal characterization. These modeling tools and the time-discretized estimates of dissipated power make digital ﬁltering a well-suited technique for a run-time temperature calculation. A recursive property of the pro-posed 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 time-constant spectrum of the device temperature response. We verify this network extraction procedure for a simple geometry with a closed-form 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 time-domain con-volution, 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 algo-rithms; in this work, however, use of z-transforms 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 man-agement algorithms for all high-power architectures and expand the application range to embedded platforms for use in a pervasive computing environment.