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Measuring Stress in Thin-Film - Substrate Systems Featuring Spatial Nonuniformities of Film Thickness and/or Misfit Strain


Brown, Michal Amaris (2007) Measuring Stress in Thin-Film - Substrate Systems Featuring Spatial Nonuniformities of Film Thickness and/or Misfit Strain. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/9GD9-A088.


It is very important to be able to accurately determine the film stress distribution in a thin film structure, since stress can lead directly to failure and as such is intimately related to reliability and process yield. The most common way of inferring film stress caused by a given process is by measuring system curvature before and after the process; the change in curvature is directly related to the stress caused by that process, usually through the Stoney formula. This formula was derived based on a number of restrictive assumptions. Two of these are the assumptions of a spatially uniform film thickness and a spatially uniform misfit strain; taken together, these assumptions imply constant curvature and film stress over the entire wafer. In practice, these conditions are rarely met, and yet the Stoney formula is still the film stress measurement standard.

Recently, extensions to this formula were derived which allow for spatial non-uniformities in film thickness and misfit strain. The resulting Stoney-like relations which relate film stress and wafer curvature, known as the HR relations, require knowledge of not only the curvature at a single point, but also full-field curvature information. In this work, the HR relations are verified by comparison with X-ray microdiffraction. Two independent XRD measurements are used; one measures substrate curvature and the other determines film stress. Since these measurements are independent, the substrate curvature data are used as an input to the Stoney and HR stress/curvature relations. The resulting film stresses are then compared with XRD film stress data. From this, it is established that the HR relations result in substantially more accurate film stress predictions than does the Stoney analysis.

Next, a full-field curvature measurement technique, Coherent Gradient Sensing, is introduced as an ideally suited measurement tool for inferring film stress through the HR analysis. CGS measurements are taken of several progressively more interesting test wafers and the curvature is used through the HR relations to determine film stress.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:curvature measurement; full-field measurement; stress; stress-curvature relations
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Materials Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Rosakis, Ares J.
Thesis Committee:
  • Rosakis, Ares J. (chair)
  • Streit, Dwight
  • Ravichandran, Guruswami
  • Bhattacharya, Kaushik
  • Johnson, William Lewis
Defense Date:25 May 2007
Non-Caltech Author Email:michalamaris (AT)
Record Number:CaltechETD:etd-06042007-171342
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2451
Deposited By: Imported from ETD-db
Deposited On:05 Jun 2007
Last Modified:16 Mar 2020 21:13

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