Mechanical properties of thin films from the load deflection of long clamped plates

A plane-strain load-deflection model for long plates clamped to a rigid support is developed. The analytical model describes the nonlinear deflection of plates with compressive or tensile residual stress and finite flexural rigidity under uniform load. It allows for the extraction of the residual stress and plane-strain modulus of single-layered thin films. Properties of compressively and weakly prestressed materials are extracted with an accuracy achieved previously only with tensile samples. Two approximations of the exact model are derived. The first reduces the plates to membranes by neglecting their flexural rigidity. Considerable errors result from this simplification. The second approximation provides an exact expression for the linear plate response. Using the model, mechanical properties were extracted from two plasma-enhanced chemical-vapor deposition (PECVD) silicon nitride films with weakly tensile and compressive prestress, respectively. Measured residual stresses are 1.3/spl plusmn/3.8 and -63/spl plusmn/12.4 MPa, respectively. Corresponding plane-strain moduli are 134.4/spl plusmn/3.9 and 142/spl plusmn/2.6 GPa, respectively.

[1]  G. Johnson,et al.  Mechanical Characterization of Thin Films Using Full-Field Measurement of Diaphragm Deflection , 1993 .

[2]  H. Baltes,et al.  Industrial fabrication technology for CMOS infrared sensor arrays , 1997, Proceedings of International Solid State Sensors and Actuators Conference (Transducers '97).

[4]  Joost J. Vlassak,et al.  Re-Examining the Bulge Test: Methods for Improving Accuracy and Reliability , 1991 .

[5]  O. Tabata,et al.  Mechanical property measurements of thin films using load-deflection of composite rectangular membranes , 1989 .

[6]  D. Maier-Schneider,et al.  Elastic properties and microstructure of LPCVD polysilicon films , 1996 .

[7]  D. Harding,et al.  Temperature Dependence of the Intrinsic Stress and Biaxial Modulus of Plasma Deposited Silicon Nitride and Silicon Oxynitride Films , 1994 .

[8]  S. Timoshenko.  Theory of Elastic Stability , 1936 .

[9]  S. Senturia,et al.  Verification of FEM analysis of load-deflection methods for measuring mechanical properties of thin films , 1990, IEEE 4th Technical Digest on Solid-State Sensor and Actuator Workshop.

[10]  J. Taylor,et al.  Correlation between Processing, Composition, and Mechanical Properties of PECVD-SiN, Thin Films , 1990 .

[11]  J. Maibach,et al.  A new analytical solution for the load-deflection of square membranes , 1995 .

[12]  R. Howe,et al.  Microfabricated structures for the in situ measurement of residual stress, Young’s modulus, and ultimate strain of thin films , 1987 .

[13]  J. Söderkvist,et al.  Characteristics of quasi-buckling , 1993 .

[14]  M. Stadtmüeller.  Mechanical Stress of CVD‐Dielectrics , 1992 .

[15]  Mark G. Allen,et al.  Calibrated measurements of elastic limit, modulus, and the residual stress of thin films using micromachined suspended structures , 1988, IEEE Technical Digest on Solid-State Sensor and Actuator Workshop.

[16]  J. Maibach,et al.  Computer-aided characterization of the elastic properties of thin films , 1992 .

[17]  Michael Curt Elwenspoek,et al.  Membranes fabricated with a deep single corrugation for package stress reduction and residual stress relief , 1993 .

[18]  R. Mountain,et al.  A technique for the determination of stress in thin films , 1983 .

[19]  W.H. Ko,et al.  A study on silicon-diaphragm buckling , 1990, IEEE 4th Technical Digest on Solid-State Sensor and Actuator Workshop.

[20]  B. J. Daniels,et al.  Accuracy and Reliability of Bulge Test Experiments , 1993 .

[21]  T. H. T. Wu,et al.  STRESS IN PSG AND NITRIDE FILMS AS RELATED TO FILM PROPERTIES AND ANNEALING , 1992 .

[22]  Miko Elwenspoek,et al.  Buckled membranes for microstructures , 1994, Proceedings IEEE Micro Electro Mechanical Systems An Investigation of Micro Structures, Sensors, Actuators, Machines and Robotic Systems.

[23]  Joost J. Vlassak,et al.  A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films , 1992 .

[24]  Bumkyoo Choi,et al.  Improved analysis of microbeams under mechanical and electrostatic loads , 1997 .

[25]  O. Tabata,et al.  Control of internal stress and Young's modulus of Si3N4 and polycrystalline silicon thin films using the ion implantation technique , 1990 .

[26]  Joost J. Vlassak,et al.  Measuring the Mechanical Properties of Thin Metal Films by Means of Bulge Testing of Micromachined Windows , 1994 .

[27]  The In-Situ Measurement of Biaxial Modulus and Residual Stress of Multi-Layer Polymeric Thin Films , 1990 .

[28]  M. Elwenspoek,et al.  Deflection and maximum load of microfiltration membrane sieves made with silicon micromachining , 1997 .

[29]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[30]  H. Baltes,et al.  A Novel Method to Measure Poisson's Ratio of Thin Films , 1997 .