Evaluation of Thin Film Residual Stress through the Theoretical Analysis of Nanoindentation Curve

나노 압입곡선의 이론적 분석을 통한 박막의 잔류응력 평가

  • 이윤희 (서울대학교 대학원 재료공학부) ;
  • 장재일 ((주) 프론틱스 연구개발부) ;
  • 권동일 (서울대학교 재료공학부)
  • Published : 2002.07.01


Residual stress is a dominant obstacle to efficient production and safe usage of device by deteriorating the mechanical strength and failure properties. Therefore, we proposed a new thin film stress-analyzing technique using a nanoindentation method. For this aim, the shape change in the indentation load-depth curve during the stress-relief in film was theoretically modeled. The change in indentation depth by load-controlled stress relaxation process was related to the increase or decrease in the applied load using the elastic flat punch theory. Finally, the residual stress in thin film was calculated from the changed applied load based on the equivalent stress interaction model. The evaluated stresses for diamond-like carbon films from this nanoindentation analysis were consistent with the results from the conventional curvature method.


Nanoindentation Technique;Thin Film Residual Stress;Indentation Load-Depth Curve;Contact Morphology;Load Controlled-Stress Relaxation


  1. Noyan, I. C. and Cohen, J. B., 1987, Residual Stresses, Springer-Verlag, New York
  2. Karlsson, L., Hultman, L. and Sundgren, J.-E., 2000, 'Influence of Residual Stresses on the Mechanical Properties of TiCxN1-x (x=O, 0.15, 0.45) Thin Films Deposited by Arc Evaporation,' Thin Solid Films, Vol. 371, pp. 167-177
  3. Uhlmann, E. and Klein, K., 2000, 'Stress Design in Hard Coatings,' Surface and Coatings Technology, Vol. 131, pp. 448-451
  4. Fang, W. and Lo, C.- Y., 2000, 'On the Thermal Expansion Coefficients of Thin Films,' Sensors and Actuators, Vol. 84, pp. 310-314
  5. Ruud, C. O., DiMascio, P. S. and Yavelak, J. J., 1985, 'Comparison of Three Residual-stress Measurement Methods on a Mild Steel,' Experimental Mechanics, Vol. 25, pp. 338-343
  6. Joo, J. W. and Park, C. K., 1998, 'Determination of Non-uniform Residual Stress by the Hole Drilling Method,' Trans KSME A, Vol. 22, pp. 268-277
  7. Perry, A. J., Sue, J. A. and Martin, P. J., 1996, 'Practical Measurement of the Residual Stress in Coatings,' Surface and Coatings Technology, Vol. 81, pp. 17-28
  8. Lee, O. S. and Read, D. T., 1995, 'Micro-strain Distribution around a Crack Tip by Electron Meam Moire Method,' KSME International Journal, Vol. 9, pp. 298-311
  9. Bergman, L. and Nernanich, R. J., 1995, 'Raman and Photoluminescence Analysis of Stress State and Impurity Distribution in Diamond Thin Films,' J. Appl. Phys., Vol. 78, pp. 6709-6719
  10. Doerner, M. F. and Nix, W. D., 1986, 'A Method for Interpreting the Data from Depth-sensing Indentation Instruments,' J. Mater. Res., Vol. 1, pp. 601-609
  11. Pharr, G. M. and Oliver, W. C.. 1992, 'Measurement of Thin Film Mechanical Properties Using Nanoindentation,' MRS bulletin, July, pp. 28-33
  12. Sines, G. and Carlson, R., 1952, 'Hardness Measurements for Determination of Residual Stresses,' ASTM Bulletin, February, pp. 35-37
  13. Underwood, J. H., 1973, 'Residual-stress Measurement Using Surface Displacements around an Indentation,' Experimental Mechanics, Vol. 13, pp. 373-380
  14. LaFontaine, W. R., Paszkiet, C. A., Korhonen, M. A. and Li, Che-Yu, 1991, 'Residual Stress Measurements of Thin Aluminum Metallizations by Continuous Indentation and X-ray Stress Measurement Techniques,' J. Mater. Res., Vol. 6, pp. 2084-2090
  15. Tsui, T. Y., Oliver, W. C. and Pharr, G. M., 1996, 'Influences of Stress on the Measurement of Mechanical Properties Using Nanoindentation: Part Ⅰ. Experimental Studies in an Aluminum Alloy,' J. Mater. Res., Vol. 11, pp. 752-759
  16. Bolshakov, A., Oliver, W. C. and Pharr, G. M., 1996, 'Influences of Stress on the Measurement of Mechanical Properties Using Nanoindentation: PartⅡ. Finite Element Simulations,' J. Mater. Res., Vol. 11, pp. 760-768
  17. Suresh, S. and Giannakopoulos, A. E., 1998, 'A New Method for Estimating Residual Stresses by Instrumented Sharp Indentation,' Acta Mater., Vol. 46, pp. 5755-5767
  18. Tsui, T. Y. and Pharr, G. M., 1999, 'Substrate Effects on Nanoindentation Mechanical Property Measurement of Soft Films on Hard Substrates,' J. Mater. Res., Vol. 14, pp. 292-301
  19. Thomsen, N. B., Fischer-Cripps, A. C. and Swain, M. Y, 1998, 'Crack Formation Mechanisms during Micro and Macro Indentation of Diamond-like Carbon Coatings on Elastic-plastic Substrates,' Thin Solid Films, Vol. 332, pp. 180-184