A Comparison of X-Ray Microdiffraction and Coherent Gradient Sensing in Measuring Discontinuous Curvatures in Thin Film: Substrate Systems

[+] Author and Article Information
Michal A. Brown

Department of Materials Science, California Institute of Technology, M/C 205-45, Pasadena, CA 91125mabrown@Caltech.edu

Tae-Soon Park

 Oraxion Diagnostics, 3077 Skyway Court, Fremont, CA 94539

Ares Rosakis

Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125

Ersan Ustundag

Department of Materials Science and Engineering, Iowa State University, 2220 Hoover Hall, Ames, IA 50011

Young Huang

Department of Mechanical Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

Nobumichi Tamura, Bryan Valek

Advanced Light Source, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720

J. Appl. Mech 73(5), 723-729 (Oct 14, 2005) (7 pages) doi:10.1115/1.2150500 History: Received March 18, 2005; Revised October 14, 2005

The coherent gradient sensor (CGS) is a shearing interferometer which has been proposed for the rapid, full-field measurement of deformation states (slopes and curvatures) in thin film-wafer substrate systems, and for the subsequent inference of stresses in the thin films. This approach needs to be verified using a more well-established but time-consuming grain orientation and stress measurement tool, X-ray microdiffraction (XRD). Both CGS and XRD are used to measure the deformation state of the same W film/Si wafer at room temperature. CGS provides a global, wafer-level measurement of slopes while XRD provides a local micromeasurement of lattice rotations. An extreme case of a circular Si wafer with a circular W film island in its center is used because of the presence of discontinuous system curvatures across the wafer. The results are also compared with a theoretical model based on elastic plate analysis of the axisymmetric biomaterial film-substrate system. Slope and curvature measurements by XRD and by CGS compare very well with each other and with theory. The favorable comparison demonstrates that wafer-level CGS metrology provides a quick and accurate alternative to other measurements. It also demonstrates the accuracy of plate theory in modeling thin film-substrate systems, even in the presence of curvature discontinuities

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Schematic of the CGS setup in reflection mode (a) and its working principle (b)

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Figure 2

(a) Laue pattern from the single crystal Si wafer. (b) Definition of coordinate system and the projection angle α; slope in xzplane=tan(α).

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Figure 3

The microdiffraction setup at the Advanced Light Source. The incoming X-ray beam is reflected from the sample surface and captured by the detector.

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Figure 4

Sample schematic

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Figure 5

Theoretical prediction of surface (a) curvature and (b) slope across the diameter of a radially symmetric circular wafer with a circular film island in the center. The assumed film stress is −2GPa.

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Figure 6

CGS slope measurements in the x and y directions. Horizontal, ∂f∕∂x: (a) wafer image and (b) horizontal slope map. Vertical, ∂f∕∂y: (c) wafer image and (d) vertical slope map.

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Figure 7

Wafer topography, through integration of x and y slope maps: (a) full-field map; (b) radial cut through y=0

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Figure 8

CGS curvature maps in the x,y and twist directions: (a) horizontal map, κxx=∂2f∕∂x2, (b) vertical map, κyy=∂2f∕∂y2, (c) twist map, κxy=∂2f∕∂x∂y, (d) principal curvature, κmax=κrr

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Figure 9

(a) Horizontal interferogram and slope maps: (b) with filtering and smoothing and (c) with no smoothing (raw data)

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Figure 10

Data were extracted from CGS slope maps across the sample diameter (a) and compared with XRD (b)

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Figure 11

Comparison of (a) XRD and (b) CGS data with theoretical predictions, using film stress as the fitting parameter



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