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Research Papers

Application of Kriging and Radial Basis Function for Reliability Optimization in Power Modules

[+] Author and Article Information
Pushparajah Rajaguru

e-mail: p.r.rajaguru@gre.ac.uk

Chris Bailey

Computational Mechanics and Reliability Group,
University of Greenwich,
SE10 9LS London, UK

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the Journal of Electronic Packaging. Manuscript received March 27, 2012; final manuscript received March 18, 2013; published online April 12, 2013. Assoc. Editor: Shidong Li.

J. Electron. Packag 135(2), 021009 (Apr 12, 2013) (13 pages) Paper No: EP-12-1043; doi: 10.1115/1.4024056 History: Received March 27, 2012; Revised March 18, 2013

This paper discusses the design for reliability of a wire bond structure in a power electronic module based on computational approach that integrates methods for high fidelity analysis, reduced order modeling, numerical risk analysis, and optimization. This methodology is demonstrated on a wire bond structure in a power electronic module with the aim of reducing the chance of failure due to the wire bond lift off in a power electronic module. In particular, wire bond reliability of the power module related to the thermal fatigue material degradation of aluminum wire is one of the main concerns. Understanding the performance, reliability, and robustness of wire bond is a key factor for the future development and success of the power electronic module technology. The main focus in this study is on the application of reduced order modeling techniques and the development of the associated models for fast design evaluation and analysis. The discussion is on methods for approximate response surface modeling based on interpolation techniques using Kriging and radial basis functions. The reduced order modeling approach uses prediction data for the electrothermomechanical behavior of the power module wire bond design obtained through nonlinear transient finite element simulations, in particular, for the fatigue lifetime of the aluminum wire attached to the silicon chip and the warpage (displacement) of the wire in the module. These reduced order models are used for the analysis of the effect of design uncertainties on the reliability of these advanced electronics modules. To assess the effect of uncertain design data, different methods for estimating the variation of reliability-related metrics of the wire bond model are researched and tested. Sample-based methods, such as full-scale Monte Carlo and Latin hypercube, and analytical approximate methods, such as first order second moment (FOSM) and point estimation method (PEM), are investigated, and their accuracy is compared. The optimization modeling analyzes the probabilistic nature of the reliability problem of the aluminum wire bond structures under investigation. Optimization tasks with design uncertainty are identified and solved using a particle swarm optimization algorithm. The probabilistic optimization deals with two different characteristic performance metrics of the design, the electrothermomechanical fatigue reliability of the aluminum wire attached to the chip and the thermally induced warpage of the wire in the module structure. The objective in this analysis is to ensure that the design has the required reliability and meets a number of additional requirements.

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References

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Figures

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Fig. 1

Cross-sectional view of power module, courtesy of Ref. [2]

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Fig. 2

Framework of numerical design procedures

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Fig. 3

The dimensions of the wire bond model, courtesy of Ref. [21] and the resulted FEA computer model

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Fig. 4

Wire loop ratio (left figure) with extreme values of 10% (middle figure) and 80% (right figure)

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Fig. 5

Plastic strain of sliced part of the aluminum wire with 17.5 micron thickness in the Al plate Al wire interface

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Fig. 6

Warpage (out of plane) of the aluminum wire and ramped load current of the model for every 60 seconds

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Fig. 7

95% Prediction interval of Gaussian distribution

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Fig. 8

Bandwidth for warpage Kriging model design variables at the nominal design of the wire bond structure

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Fig. 9

Distribution of Kriging plastic strain (left) and Kriging warpage (right) obtained by various distribution estimation methods at the nominal design of wire bond model

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Fig. 10

Distribution of radial basis plastic strain (left) and radial basis warpage (right) obtained by various distribution estimation methods at the nominal design of wire bond model

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Fig. 11

Distribution of plastic strain of aluminum wire under specified lower limit for reliability with lower specification limit (LSL) = 9 × 10–3 and LSL = 7.5 × 10–3 for nominal design values

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Fig. 12

The values of objective function (radial basis ROM for warpage (μm) and constraint function (radial basis ROM for plastic strain ( × 10–3)) against optimization iterations

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Fig. 13

The values of objective function (Kriging ROM for warpage (μm)) and constraint function (Kriging ROM for plastic strain ( × 10–3)) against optimization iterations

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