# Presentation: 047796

## Strains in Polycrystalline Thin Films  G. S. Cargill III, Lehigh Univ., and A. M. Maniatty, RPI – MET DMR-0312189

- Synchrotron x-ray sources and microbeam focusing allow orientation and strain measurements to be made over micron size areas on a grain-by-grain basis.

- Maps of a 5μm  5μm area of the film taken at 20 minute intervals after heating to 300°C and cooling to room temperature show grain orientations. Grain orientations and deviatoric strains were determined for each measurement location.

- From the x-ray experiments, average perpendicular deviatoric strains for grains of different orientations were determined as a function of time. The strain decreases over time, but relaxation occurs at different rates and to different extents for different families of grains.

- Measurements on a 2μm-thick Al-4 wt % Cu film illustrate the complexity masked by the traditional strain measurements but revealed in grain-by-grain strain measurements.

- Notice the wide distribution of strain magnitudes, indicated by the vertical bars as RMS deviations from the average, and likewise, for each orientation family. A goal of this research is to determine the microstructural features responsible for differences in local behavior.

- Finite element simulation of a polycrystalline film using an elasto-viscoplastic crystal model that accounts for grain orientation, grain size, and film thickness effects predicts well the

- average perpendicular deviatoric strain after cooling to room temperature, and also predicts grain to grain variability (as shown in the histogram). However,  the measured variability is higher than that predicted.

**Notes:**
Stresses and strains in thin polycrystalline metal films,  usually due to differences in thermal expansion between the films and their substrates, have traditionally been determined from optical measurements of substrate curvatures and from x-ray diffraction measurements of average lattice parameters over square millimeter areas of the films.  

Synchrotron x-ray sources and microbeam focusing optics now allow orientation and strain measurements to be made over micron size areas on a grain-by-grain basis. The instrument used for our measurements, on the UNICAT beam line at APS/ANL, is illustrated in the top left figure.  Understanding local grain orientation and strain behavior provides a critical link between microscopic and macroscopic properties of polycrystalline solids, including aluminum and copper thin films used in microelectronic devices. This information is important for developing and testing models for strain relaxation in these materials and for improving reliability and lifetimes of integrated circuits and microelectronic mechanical devices which contain metal films.  

X-ray microbeam diffraction measurements on a aluminum-on-glass sample illustrate the complexity that is masked by the traditional strain measurements but is revealed in grain-by-grain strain measurements may play important roles in stress relaxation and device reliability.   This sample consists of a 2μm-thick Al - 4 wt % Cu film and  a 150Å-thick Cr film, to improve adhesion, on a potash soda zinc glass  substrate.  The top right figure shows the grain maps of a 5μm  5μm area of the film taken at 20 minute intervals after heating to 300°C and cooling to room temperature.  The maps were constructed from a mesh of diffraction measurements with a 0.5 μm  0.7μm x-ray microbeam.  Grain orientations and deviatoric strains were determined for each measurement location.  Different colors represent different grain orientations with respect to the film plane.  

The bottom right figure shows average perpendicular deviatoric strains for grains of different orientations, and for all grains regardless of orientation, for the same thirteen data sets shown in the top right figure.  The horizontal axis represents time during the measurements, running from right to left.  The overall average perpendicular deviatoric strain decreases over the 450 minutes required for these measurements, from -1.610-3  to -0.2 10-3.  The relaxation occurs at different rates and to different extents for different families of grains, (111), (100), and (110).  Most notable, however, is the wide distribution of strain magnitudes, indicated by the vertical bars as RMS deviations from the averages.  Similarly wide distributions are seen for each of the orientation families.  Residual strains and strain relaxation rates for individual grains vary widely.  A goal of this research is to determine the microstructural features responsible for these differences in local behavior.

The bottom left figure shows results of a finite element simulation, carried out at RPI, for a model polycrystalline film, using grain sizes and orientations like those in the actual film used in the x-ray experiments, using model parameters obtained from other literature data for mechanical behavior of copper.   This simulation predicts the same magnitude of residual strain as seen experimentally for cooling an initially strain-free film from 300°C to room temperature.  The simulation shows some grain to grain variability, indicated by the width of the histogram plot, but less variability than seen experimentally.   We are in a good position now to do some additional simulations.

Publications appearing in 2004 based on this work:
L. E. Moyer, G. S. Cargill III, B. C. Larson, W. Yang, G. E. Ice, "X-ray Microbeam Diffraction Measurements in Polycrystalline Aluminum and Copper Thin Films," MRS Symp. Proc. 795, U1.7.1 (2004).
G. S. Cargill III, “White Beam X-ray Microdiffraction Analysis of Polycrystalline Thin Films,” Microsc. Microanal. 10 (Suppl 2), 1024-1025 (2004).

Invited talks given in 2004 based on this work:
G. S. Cargill III, “Electromigration-induced Stress and Composition Changes from Real-time X-ray Microdiffraction and Microfluorescence,” CHESS Journal Club, Cornell University, January 16, 2004.
G. S. Cargill III, ““Electromigration-induced Stress and Composition Changes from Real-time X-ray Microdiffraction and Microfluorescence,” APS Lunch Seminar, Argonne National Laboratory, July 2, 2004.

## Strains in Polycrystalline Thin Films G. S. Cargill III, Lehigh Univ., and A. M. Maniatty, RPI – MET DMR-0312189

- Experiments were carried out by Lehigh graduate students Laura Moyer and Gan Wang.  Dr. Moyer completed her PhD in August 2005 and is now employed by Alcoa Inc. During summer 2005, Mr. Wang  participated in a Southeastern Univ. Research Assoc. sponsored project with Dr. B. C. Larson at ORNL. Hongquing Zhang completed his first year in the group as a graduate student, and Jen Deng completed her first year in the group as an undergraduate work study student.

- Dr. Cargill (far right) with Lehigh University students (from left) Hongquing Zhang, Jen Deng, Laura Moyer, and Gan Wang.

**Broader Impacts:**

- Top, Linda Ge and Dr. Maniatty.
- Bottom, Chia-Ju Yang and Nicole Bieber.

- Simulation work has been carried out at Rensselaer by graduate students Chia-Ju Yang and Linda Ge.  Dr. Yang finished his PhD in August 2004 and is currently employed at CCI America, Inc.  Nicole Bieber, a high school student, visited Maniatty’s group in Summer 2005.