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±3.8 and -63±12.4 MPa, respectively. Corresponding plane-strain moduli are 134.4±3.9 and 142±2.6 GPa, respectively