Inverse Conduction Heat Transfer and Kriging Interpolation Applied to Temperature Sensor Location in Microchips

[+] Author and Article Information
David Gonzalez Cuadrado

School of Mechanical Engineering,
Purdue University,
500 Allison Road,
West Lafayette, IN 47906
e-mails: dgcuadrado@purdue.edu;

Amy Marconnet

School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: amarconn@purdue.edu

Guillermo Paniagua

School of Mechanical Engineering,
Purdue University, 500 Allison Road,
West Lafayette, IN 47906
e-mail: gpaniagua@me.com

1Corresponding author.

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received September 27, 2017; final manuscript received December 28, 2017; published online March 2, 2018. Assoc. Editor: Sreekant Narumanchi.

J. Electron. Packag 140(1), 010905 (Mar 02, 2018) (8 pages) Paper No: EP-17-1099; doi: 10.1115/1.4039026 History: Received September 27, 2017; Revised December 28, 2017

Large thermal gradients represent major operational hazards in microprocessors; hence, there is a critical need to monitor possible hot spots both accurately and in real time. Thermal monitoring in microprocessors is typically performed using temperature sensors embedded in the electronic board. The location of the temperature sensors is primarily determined by the sensor space claim rather than the ideal location for thermal management. This paper presents an optimization methodology to determine the most beneficial locations for the temperature sensors inside of the microprocessors, based on input from high-resolution surface infrared thermography combined with inverse heat transfer solvers to predict hot spot locations. Specifically, the infrared image is used to obtain the temperature map over the processor surface, and subsequently delivers the input to a three-dimensional (3D) inverse heat conduction methodology, used to determine the temperature field within the processor. In this paper, simulated thermal maps are utilized to assess the accuracy of this method. The inverse methodology is based on a function specification method combined with a sequential regularization in order to increase accuracy in the results. Together with the number of sensors, the temperature field within the processor is then used to determine the optimal location of the temperature sensors using a genetic algorithm optimization combined with a Kriging interpolation. This combination of methodologies was validated against the finite element analysis of a chip incorporating heaters and temperature sensors. An uncertainty analysis of the inverse methodology and the Kriging interpolation was performed separately to assess the reliability of the procedure.

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Fig. 2

Sketch of the simulated microchip with the sources of heat flux and the temperature reading location

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Fig. 1

Schematic of the inverse 3D conduction methodology coupled with Kriging method optimization to obtain the optimal sensor location

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Fig. 4

Sketch of the reduced chip structure including the geometry of the real microchip with 100 heaters

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Fig. 5

Temperature distribution within the chip for the reduced chip and the simplified reduced chip model at t = 1.5 s and t = 5 s

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Fig. 6

(a) Imposed heat flux in the numerical experiment for the corner and center heaters and (b) temperature increase over time at the top surface in the corner and center locations of the microchip

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Fig. 7

Comparison between the imposed heat flux and the heat flux estimated with the inverse 3D methodology

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Fig. 8

Temperature maps in the plane where the temperature sensors should be located at t = 1.5 s and t = 2.7 s

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Fig. 9

Location of the optimal points inside of the microchip envelope for the case run with eight sensors

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Fig. 3

(top) Schematic of the complete experimental test fixture and (bottom) the comsol model used for the inverse method and Kriging model. (bottom inset) Approximate verification model to prove the simplified geometry.

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Fig. 10

Kriging interpolation results for the temperature maps using the optimal location for the sensors




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