Full field measurements of curvature using coherent gradient sensing: application to thin film characterization A.J. Rosakis a , R.P. Singh a, *, Y. Tsuji b , E. Kolawa b,c , N.R. Moore Jr. c a Department of Aeronautics, California Institute of Technology, Pasadena, CA 91125, USA b Department of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA c Jet Propulsion Laboratory, Pasadena, CA 91109,USA Received 11 August 1997; accepted 2 January 1998 Abstract This paper introduces coherent gradient sensing (CGS) as an optical, full-field, real-time, non-intrusive and non-contact technique for measurement of curvature and curvature changes in thin film and micro-mechanical structures. The technique is applied to determine components of the curvature tensor field in multilayered thin films deposited on silicon wafers. Curvature field measurements using CGS are compared with average curvatures obtained using high-resolution X-ray diffraction. Finally, examples are presented to demonstrate the capability of CGS in measuring curvature in a variety of thin film and micro-mechanical structures.  1998 Elsevier Science S.A. All rights reserved Keywords: Stress; Surface defects; Surface morphology; X-ray diffraction 1. Introduction As the electronics industry pushes for smaller and smaller dimensions of metal interconnections and for more com- plex multilayered structures, the mechanical properties and stresses of thin films used for these interconnections becomes crucial to the lifetimes of ultra large scale inte- grated circuits [1,2]. However, the difficulty in measuring the mechanical properties and stresses of interconnections increases as their size decreases [3]. Currently, the major concern for the interconnection materials is residual stresses present in these materials as a result of the fabrication pro- cess and additional stresses resulting from thermal cycling [4–6]. Typically, integrated circuit metallization consists of many layers deposited onto a silicon substrate, very often at elevated temperatures. The layers exhibit different mechanical, physical and thermal properties leading to high stresses in interconnection structures. These stresses cause stress induced voiding [7–21], are directly related to electromigration [22–29] and may cause cracking of the substrate [3]. All of which are leading failure mechan- isms in integrated circuits. An understanding of stresses, their distribution, and origins is a crucial step in improving reliability of integrated circuits. Currently used experimental techniques for measuring stresses are based either on direct measurements of strains in the films using X-ray diffraction [30,31] or on the mea- surements of substrate curvature or deflection [32]. Curva- ture and curvature change measurements are typically related to the stress state in the layered structures by means of theoretical analyses based either on approximate plate theories [33,34] or more recently on exact continuum mechanics formulation [35,36]. The X-ray diffraction technique typically employed for polycrystalline materials involves measuring d-spacings of a single reflection for several orientations of the sample [30]. This determines strains along different directions of the sample. The technique is non-destructive, does not require special sample configurations and it permits a mea- surements of all the components of stress in the film. How- ever, it is limited to crystalline materials, e.g. stresses in passivation layers cannot be measured, and is difficult to Thin Solid Films 325 (1998) 42–54 0040-6090/98/$19.00  1998 Elsevier Science S.A. All rights reserved PII S0040-6090(98)00432-5 * Corresponding author. Tel.: +1 818 3954527; fax: +1 818 4492677; e-mail: raman@atlantis.caltech.edu