Fracture Properties of LPCVD Silicon Nitride and Thermally Grown Silicon Oxide Thin Films From the Load-Deflection of Long $\hbox{Si}_{3}\hbox{N}_{4}$ and $\hbox{SiO}_{2}/\hbox{Si}_{3}\hbox{N}_{4}$ Diaphragms

The bulge test is successfully extended to the determination of the fracture properties of silicon nitride and oxide thin films. This is achieved by using long diaphragms made of silicon nitride single layers and oxide/nitride bilayers, and applying a comprehensive mechanical model that describes the mechanical response of the diaphragms under uniform differential pressure. The model is valid for thin films with arbitrary z-dependent plane-strain modulus and prestress, where z denotes the coordinate perpendicular to the diaphragm. It takes into account the bending rigidity and stretching stiffness of the layered materials and the compliance of the supporting edges. This enables the accurate computation of the load-deflection response and stress distribution throughout the composite diaphragm as a function of the load, in particular at the critical pressure leading to the fracture of the diaphragms. The method is applied to diaphragms made of single layers of 300-nm-thick silicon nitride deposited by low- pressure chemical vapor deposition and composite diaphragms of silicon nitride grown on top of thermal silicon oxide films produced by wet thermal oxidation at 950degC and 1050degC with target thicknesses of 500, 750, and 1000 nm. All films characterized have an amorphous structure. Plane-strain moduli E
_ps
and prestress levels sigma
₀
of 304.8 plusmn 12.2 GPa and 1132.3 plusmn 34.4 MPa, respectively, are extracted for Si
₃
N
₄
, whereas E
_ps
= 49.1 plusmn 7.4 GPa and sigma
₀
= -258.6 plusmn 23.1 MPa are obtained for SiO
₂
films. The fracture data are analyzed using the standardized form of the Weibull distribution. The Si
₃
N
₄
films present relatively high values of maximum stress at fracture and Weibull moduli, i.e., sigma
_max
= 7.89 plusmn 0.23 GPa and m = 50.0 plusmn 3.6, respectively, when compared to the thermal oxides (sigma
_max
= 0.890 plusmn 0.07 GPa and m = 12.1 plusmn 0.5 for 507-nm-thick 950degC layers). A marginal decrease of sigma
_max
with thickness is observed for SiO
₂
, with no significant differences between the films grown at 950degC and 1050degC. Weibull moduli of oxide thin films are found to lie between 4.5 plusmn 1.2 and 19.8 plusmn 4.2, depending on the oxidation temperature and film thickness.