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Technical Brief

A New Analytical Method for Calculating Maximum Junction Temperature of Packaged Devices Incorporating the Temperature Distribution at the Base of the Substrate

[+] Author and Article Information
J. H. L. Ling

Department of Mechanical Engineering,
National University of Singapore,
117576, Singapore
e-mail: g0900551@nus.edu.sg

A. A. O. Tay

Department of Mechanical Engineering,
National University of Singapore,
117576, Singapore
e-mail: mpetayao@nus.edu.sg

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received December 8, 2013; final manuscript received July 23, 2014; published online October 6, 2014. Assoc. Editor: Mehmet Arik.

J. Electron. Packag 137(1), 014502 (Oct 06, 2014) (6 pages) Paper No: EP-13-1133; doi: 10.1115/1.4028120 History: Received December 08, 2013; Revised July 23, 2014

All current analytical methods for calculating junction temperature of field effect transistor (FET) and monolithic microwave integrated circuits (MMIC) devices have assumed a constant uniform temperature at the base of the substrate. In a packaged device, however, where the substrate is attached to a carrier, finite element thermal analyses have shown that the temperature distribution along the base of the substrate is not uniform but has a bell-shaped distribution. Consequently, current analytical methods which attempt to predict the junction temperature of a packaged MMIC device by assuming a constant uniform temperature at the base of the substrate have been found to be inaccurate. In this paper, it is found that the temperature distribution along the base of a substrate can be well approximated by a Lorentz distribution which can be determined from a few basic parameters of the device such as the gate length, gate pitch, number of gates, and length of substrate. By incorporating this Lorentz temperature distribution at the base of the substrate with a new closed-form solution for the three-dimensional temperature distribution within the substrate, a new analytical method is developed for accurately calculating the junction temperature of MMIC devices. The accuracy of this new method has been verified with junction temperatures of MMIC devices measured using thermoreflectance thermography (TRT) as well as those calculated using finite element analysis (FEA).

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Figures

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Fig. 1

Substrate subjected to an embedded localized constant heat source of finite length Wg, and a constant substrate base temperature. The remaining surfaces are assumed adiabatic.

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Fig. 2

Line heat source of finite length l in a semi-infinite solid

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Fig. 3

Schematic cross section of a PA MMIC package and the thermal resistance network

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Fig. 4

Details of the 3D finite element mesh: (a) in the carrier and jig and (b) around the gates

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Fig. 5

A typical temperature distribution at the base of a substrate of a packaged PA MMIC computed from FEA and fitted with a Lorentz function

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Fig. 6

Values of TL for varying ls and λ, with b = 100 μm

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Fig. 7

Determination of w from thickness of substrate, b, length of heat source, ls, and angle β

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Fig. 8

Effect of ls and β on To,max for λ = 0.5 W/mm

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Fig. 9

Effect of ls and β on To,max for λ = 1.0 W/mm

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Fig. 10

Effect of ls and β on To,max for λ = 1.5 W/mm

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Fig. 11

Effect of ls and β on To,max for λ = 2.0 W/mm

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Fig. 12

Variation of βo with ls

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Fig. 13

Comparison between present analytical method, Darwish et al. [12], FEA, and TRT-measured temperatures for the PA MMIC

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