Measurement of Local Thermal Deformations in Heterogeneous Microstructures via SEM Imaging with Digital Image Correlation

Abstract

It is challenging to measure accurately and with high spatial resolution the local thermal strains in heterogeneous microstructures due of the complex nature of the thermal deformations and local boundary conditions. In the enclosed study, a digital image correlation (DIC) based, thermal strain mapping technique is described that is able to probe thermal deformations with sub-micron spatial resolution and sub-nanometer displacement accuracy for both homogeneous and heterogeneous materials, including cross-sections of IC packages. The full-field thermal deformation maps of different materials within a nanostructured IC chip cross-section are established from room temperature up to 160 °C, uncovering the heterogeneous nature of the specimen while accurately measuring the highly non-uniform displacement and strain fields across the multiple material constituents. As described in this work, the DIC-enabled technique is capable of high resolution mapping of local thermo-mechanical deformations in heterogeneous materials, providing a methodology that can improve our understanding of complex material systems under controlled thermal-environmental conditions.

Appendix A

Procedure for Patterning with Gold Nanoparticles

In our studies, the AuNPs are produced using the following procedure, which is a slight modification of the process outlined by Kammers and Daly [31, 32]. First, gold (III) chloride trihydrate (HAuCl4•3H2O) and trisodium citrate dihydrate (C6H5Na3O7•2H2O) purchased from Sigma Aldrich are used to make stock solutions of 10 mM HAuCl4 and 38.8 mM Na3-citrate. Appendix Figure 14 shows a schematic of the process to synthesize AuNPs. Here, 400 mL of 1 mM HAuCl4 (diluted from 10 mM stock solution) is added to a beaker and brought to a boil while stirred with a magnetic stirring rod. Between 6.5 and 40 mL of 38.8 mM Na3-citrate is then added to the boiling solution to produce AuNPs with diameters of 136 nm, 48 nm, 32 nm and 15 nm, respectively. The authors produced smaller particles with the addition of more Na3-citrate, achieving a minimum particle size of 7 nm in the patterning experiments. The final particle size to be deposited is chosen according to the SEM magnification and spatial resolution that is needed for a given experiment. Generally speaking, a minimum of 3x3 pixels should be used to resolve each one gold particle in the final image to obtain accurate mapping using DIC. It is noted that, when viewing the resulting dispersion of discrete gold nanoparticles via colloidal suspension in transparent media by using white light illumination, the color of the scattered light depends upon the size of the suspended particles. The scattered colors in the bottles and the relative diameters of the gold nano-particles are shown in Appendix Figure 15 to illustrate this effect. After synthesis, the AuNPs are stored in dark glass bottles to protect them from UV rays that would reduce any remaining HAuCl4 until use. Our studies used the gold colloidal solutions within 1 week in all cases. Though longer storage time may also be acceptable, we have no data to confirm this.

Fig. 14

Schematic for process used to synthesize gold nanoparticles

Fig. 15

Wavelength of light absorbed by the nano-particle solution is a function of particle size; small particle solutions appear red and larger particle solutions are lavender in color

To attach the AuNPs to a heterogeneous material surface, the specimen surface is first coated with a nano-layer of material to obtain a uniform material surface for consistent patterning. Once the nano-layer of deposited, the nano-layer surface is treated with organosilane molecules that possess a pendant functional group with a strong affinity for gold. In this work, the specimen that possesses reactive oxide/hydroxyl groups on their surface are immersed in (3-mercaptopropyl) methyldimethoxysilane (MPMDMS) to bond the silane molecules.

The specimen is then rinsed with deionized water, placed in fresh acetone, and agitated in an ultrasonic cleaner to remove residual contaminants; if left on the surface, the contaminants will darken the solution and affect the production of AuNPs. Once initial cleaning is completed, the specimen is transferred to amethanol bath and agitated in an ultrasonic cleaner for approximately 5 min. After the methanol cleaning is complete, the specimen is rinsed in deionized water, dried with compressed air, and stored in a sealed, container that is cleaned using acetone, then ethanol and finally deionized water. When ready to complete the process, the specimen is placed in boiling water for ~2 min to create a thick pseudo-boehmite layer and maximize the number of hydroxyl groups on the specimen surface in order to achieve dense AuNP surface coverage that is needed for local mapping throughout the region of interest. The specimens is then rinsed with deionized water and gently dried with compressed air. It is emphasized that the surface treatment described above should be performed immediately prior to patterning to ensure there is no degradation of the prepared surface. If patterning is immediately performed after air drying, all of our experiments show that this will result in a reproducible, hydrophilic surface for pattern application.

The specimens are silanized by soaking in vials filled with one part APTMS or MPMDMS to four parts methanol for 24 h as soon after hydroxylation as possible. In our studies, the entire specimen is immersed in the solution, but only those surfaces to be patterned have to be immersed. After soaking each specimen, the specimen is removed and immediately immersed in a beaker filled with 100 mL of methanol. The methanol is stirred with a magnetic stirrer such that it flows over the surface of the specimens for 30 min. The specimen is then transferred to a beaker of fresh methanol and rinsed for an additional 30 min. Following the methanol rinse, the specimens are rinsed with deionized water and placed in a vial that is subsequently filled with AuNPs of the desired diameter. As noted earlier, if darkening of the AuNP solution is observed when the specimen is placed in the solution, this is an indication of contamination that will induce AuNP aggregation or flocculation. In such case, the specimen should be immediately removed from the solution, thoroughly cleaned again using methanol and deionized water. Once this is done, the specimen can then be placed into a new vial to which the AuNP solution is added. The specimen should be soaked in the solution for a time that ranges between 24 h and 5 days, with larger particle sizes requiring less soaking time.