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RESEARCH PAPERS

# Determination of Strain Gradient Plasticity Length Scale for Microelectronics Solder Alloys

[+] Author and Article Information
Juan Gomez

Cemal Basaran

Electronic Packaging Laboratory, University at Buffalo, State University of New York, 212 Ketter Hall, Buffalo, NY 14260cjb@buffalo.edu

J. Electron. Packag 129(2), 120-128 (Oct 04, 2006) (9 pages) doi:10.1115/1.2721082 History: Received June 16, 2005; Revised October 04, 2006

## Abstract

Strain gradient plasticity theories that have emerged during recent years to provide an explanation for size dependent behavior exhibited by some materials have also created a need for additional material parameters. In this study on $Pb∕Sn$ solder alloys’ material length scale, which is needed for use in strain gradient plasticity type constitutive models, is determined. The value of length scale is in agreement with values available in literature for different materials like copper, nickel, and aluminum.

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## Figures

Figure 1

Scanning electron microscope picture showing the location of 100–200nm depth nanoindentation batch to determine reliability of the results and the end polished surface of the specimen

Figure 2

Nanoindentation at 200nm depth to determine reliability of results

Figure 3

Hardness versus depth of indentation and normalized hardness square versus inverse of indentation depth for Specimen 1-Solder 1 batch test Number 2. The data below 300nm have been neglected due to uncertainties in the contact surface.

Figure 4

Hardness versus depth of indentation and normalized hardness square versus inverse of indentation depth for Specimen 1-Solder 3 batch test Number 2. The data below 300nm have been neglected due to uncertainties in the contact surface.

Figure 5

Hardness versus depth of indentation and normalized hardness square versus inverse of indentation depth for Specimen 1-Solder 7 batch test Number 1. The data below 300nm have been neglected due to uncertainties in the contact surface.

Figure 6

Hardness versus depth of indentation and normalized hardness square versus inverse of indentation depth for Specimen 1-Solder 1 batch test Number 1. The data below 300nm have been neglected due to uncertainties in the contact surface.

Figure 7

Hardness versus depth of indentation and normalized hardness square versus inverse of indentation depth for Specimen 1-Solder 4 batch test Number 1. The data below 300nm have been neglected due to uncertainties in the contact surface.

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