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Study on Estimation Method for Maximum Temperature of Multi-layered Micro-probe by Joule-Heating

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Abstract

In this study, a method which would improve reliability of coated vertical type micro-probe under Joule heating is described. The method is to decouple the mechanical and electrical characteristics of a probe. That is, the method is to coat a metal with good electrical characteristics on a core metal with a good mechanical characteristics by electroplating. For various configurations of cross-sectional area of probe, FE analysis are performed, and a fabricated vertical micro-probe is tested to improve the accuracy of FE analysis. By increasing the coating thickness of a metal (gold, Au) with good electrical characteristics by electroplating while keeping a total cross-sectional area of a probe constant, the maximum temperature of probe continues to decrease as the cross-sectional area of core metal (nickel, Ni) with the good mechanical characteristics is reduced. A simple formula to predict the maximum temperature of probe depending on the coating thickness based on the results of FE analysis is proposed. The formula describe that the maximum temperature of the probe by Joule heating is a function of the ratio of the conductivity of the coating metal to the core metal and the ratio of the cross-sectional area of the coating metal to the total cross-sectional area of the probe.

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Abbreviations

\(\dot{Q}_{Joule}\) :

Joule heat generation rate

\(\dot{Q}_{cond}\) :

Conductive heat transfer rate

\(\dot{Q}_{conv}\) :

Convective heat transfer rate

\(I\) :

Electrical current

\(R\) :

Total electrical resistance of the probe

\(R_{coating}\) :

Resistance of coating

\(R_{core}\) :

Resistance of core

\(\rho\) :

Electrical resistivity

\(\rho_{coating}\) :

Electrical resistivity of coating

\(\rho_{core}\) :

Electrical resistivity of core

\(A\) :

Total cross-sectional area

\(A_{coating}\) :

Cross-sectional area of coating

\(A_{core}\) :

Cross-sectional area of core

\(l_{c}\) :

Characteristic length of the probe

\(r\) :

Area fraction of coating

\(k\) :

Thermal conductivity

\(k_{coating}\) :

Thermal conductivity of coating

\(k_{core}\) :

Thermal conductivity of core

\(T_{0}\) :

Temperature of the upper and lower ends of probe

\(T_{max}\) :

Maximum temperature of probe

\(\uplambda\) :

Ratio of thermal conductivity of core to that of coating

\(C^{*}\) :

Calibration parameter for maximum temperature estimation equation

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Acknowledgements

This research was supported by Kyungsung University Research Grants in 2018

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Authors and Affiliations

  1. Department of Mechanical Engineering, Korea University, 145, Anam-ro, Sungbuk-Ku, Seoul, 02841, Republic of Korea

    Hyun-Woo Jung & Yun-Jae Kim

  2. Department of Mechanical and Automotive Engineering, Kyungsung University, 309, Suyeong-ro, Nam-gu, Busan, 48434, Republic of Korea

    Jun-Hyub Park

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  1. Hyun-Woo Jung
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Correspondence to Jun-Hyub Park.

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Jung, HW., Kim, YJ. & Park, JH. Study on Estimation Method for Maximum Temperature of Multi-layered Micro-probe by Joule-Heating. Int. J. Precis. Eng. Manuf. 21, 1955–1964 (2020). https://doi.org/10.1007/s12541-020-00392-y

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