Driven continuously by Moore’s Law, semiconductor manufacturing technology is rapidly evolving along a dual-track technological path that combines “feature size scaling” and “three-dimensional heterogeneous integration”. As the core building blocks of integrated circuits, functional thin films’ interfacial properties and mechanical behaviors are directly related to the reliability and performance of devices. Currently, mainstream thin film deposition technologies represented by physical vapor deposition (PVD), chemical vapor deposition (CVD), and atomic layer deposition (ALD) have been able to achieve the preparation of thin films with nanoscale precision. However, in thin film systems formed under thermodynamic non-equilibrium states, there is a common problem of the dynamic evolution of intrinsic stress. This phenomenon stems from the intrinsic stress generated by lattice mismatch during the thin film deposition process, which is superimposed with the thermal stress caused by differences in thermal expansion coefficients of heterogeneous materials in the service environment, as well as combined mechanical loads such as tension, compression, and bending. The coupled effect of multiple stresses is highly likely to induce serious consequences such as interfacial delamination, lattice distortion, and even structural failure of devices. Therefore, conducting research on the generation mechanism of wafer thin film stress and establishing a unified curvature radius-stress characterization model for wafer thin films is of great engineering value for optimizing the process flow and improving device yield.

In order to monitor the evolution law of the stress during the growth process of the wafer thin film in real time, we conduct research on the stress testing theory of the wafer thin film. Firstly, through multi-physical field coupling modeling and simulation, the generation mechanism of the thin film stress and its spatial gradient distribution law are revealed. Secondly, a curvature radius-stress characterization model based on the stress testing theory and the least-squares method is proposed. This model optimizes the calculation process of the curvature radius by using the method of least-squares fitting of a circle, improving the repeatability and accuracy of the curvature radius. Finally, based on this model, a contact stress testing system with multi-parameter coordination is established. By precisely controlling key parameters such as elastic modulus, Poisson’s ratio, substrate curvature radius, thin film thickness, and substrate thickness, a quantitative conversion mechanism between curvature and stress is established.

The static thermal load simulation reveals the phenomenon of stress concentration at the SiO?/Si interface. Results of the simulation show that the thermal displacement field exhibited significant axial gradient characteristics, and the displacement distribution presents a concentric circular ring topological structure. The maximum stress value is controlled at approximately 300 MPa. It is worth noting that material differences will cause nonlinear changes in temperature. In addition, extreme value regions of the stress are mainly distributed at the edge of the SiO? thin film, which is consistent with the gradient distribution law of the Stoney’s formula (Fig. 1). Then, compared with the traditional characterization model, a curvature radius-stress characterization model based on the stress testing theory and the least-squares method is proposed, and a contact stress testing system is established (Fig. 4). Two characterization models are used to conduct stress analysis on the data of stress calibrators with stresses of 40, 150, and 300 MPa respectively. These results show that when the stress is 40 MPa, the difference between these two characterization models is small (n-order polynomial method: 0.18?0.42 MPa; least-squares method: 0.19?0.40 MPa). However, when the stress increases to 150 MPa and above, the convergence of the least-squares method is significantly better than that of the n-order polynomial method (for example, when the stress is 300 MPa, the repeatability of the least-squares method is 0.16 MPa, which is 46.7% lower than 0.30 MPa of the n-order polynomial method) (Table 2). These research results indicate that the characterization model based on the least-squares method has stronger robustness in high-stress fields (≥150 MPa), and its optimized measurement repeatability can meet the accuracy requirements for thin film stress monitoring in semiconductor manufacturing processes.

Through finite element analysis method for modeling and simulation, the generation mechanism of the wafer thin film stress and its spatial gradient distribution law are revealed. A curvature radius-stress characterization model based on the stress testing theory and the least-squares method is proposed. This model optimizes the calculation process of the curvature radius by using the method of least-squares circle fitting, improving the repeatability and accuracy of the wafer thin film stress. The experimental data show that the test repeatability of this model is better than that of the traditional polynomial method. In addition, based on this model, a contact stress testing system with multi-parameter coordination is established. By precisely controlling key parameters such as elastic modulus, Poisson’s ratio, substrate curvature radius, thin film thickness, and substrate thickness, a quantitative conversion mechanism between curvature and stress is established to meet the accuracy requirements for thin film stress monitoring in semiconductor manufacturing processes.