Three-dimensional integration is a very likely alternative to proceed with more-than-Moore device integration. The variety of advantages granted by the technology works as a stimulus for the industry to move in this direction. Furthermore, the technology is rather compatible with current processing techniques, reducing the cost for initial production. However, the implementation of 3D technology is not straightforward, especially for the manufacture of reliable devices.
Mass production of highly integrated devices is not yet a reality, but for some market niches 3D integration with through silicon vias is already in production. A great deal of effort has been placed on the further development of this technology. However, several different aspects must be properly addressed, such as yield, thermal management, mechanical stability, testing, and design, before mass production becomes a reality.
This work provides a theoretical contribution to surpass the mechanical challenges of fabrication and operation of TSVs. The stress in TSVs was investigated in depth under different scenarios. It is not always possible to understand experimentally the mechanical behavior of TSVs. Therefore, simulation and analysis techniques must be used in parallel to support and explain the observed behavior. The simulations were kept as close as possible to realistic conditions, and experimental data was used extensively when available. A high degree of caution must be followed, in spite of the past successes of various simulation techniques, because it is not uncommon for some detail to be overlooked during modeling.
The FEM was mainly implemented to approach the problems and develop models addressed here. Within FEM, a series of techniques were developed to enable or to improve the analysis. Initially, the stress generation for a TSV was studied and an analytic description for the stress was developed. It compares nicely to FEM results for stresses around the middle of the via. Furthermore, the analytical solution can also serve the purpose of a safe lower bound estimate for the stress in the via top and bottom. The combination of stress fields of a group of TSVs were also investigated and a methodology to improve the placement of TSVs was presented. The objective was to find the best TSV layout which will reduce the overall stress in the silicon surrounding the TSV structures.
In addition, the TSV was analyzed locally. Previous experimental data pointed out a stress reduction along the TSV’s sidewall, where Bosch scallops were present. A simulation scheme was created considering an approximation for the scallop form. The geometry of the scallops were identified as the most likely cause for this stress reduction. Furthermore, the effects of the scallop geometry for the stress along the via was investigated. So far, it is well known that the stress depends on the scallops’ shape, and a careful description of the scallops’ geometry is needed. A better approach is to use topography simulations of the Bosch process, but simulation time is the main restriction for this approach.
Within the scope of local stress effects, the impact of wafer handling on the TSV was investigated. The forced “unbow” of wafers was simulated during a mechanical chuck down. This type of simulation has structures with a large aspect ratio and large variation in length scales. A wafer diameter is usually in the range of hundreds of millimeters, while the biggest dimension of a TSV is less than a tenth of a millimeter. To address properly such a situation, a hierarchical scheme was proposed. The results showed that unfilled TSVs are more susceptible to mechanical instability in this situation. The metal in filled TSVs provides a good protection against movements which have a direct impact at the bottom of the TSV.
In the sequence, strain relaxation in the metal layers during thermal cycling was presented as the last of the local stress investigations. Experimental measurements of stress in full-plate samples during thermal cycles were used to characterize the plastic behavior of the metal films of a TSV. The challenge here was to obtain a model which could be used to predict the stress inside the TSV. A previous model, low temperature dislocation glide, was used to explain the stress measurements. However, the model depends on parameters which are not readily available. Moreover, due to the particularities of the model, traditional fitting techniques are of no use. The problem was overcome by applying a meta-heuristic search algorithm know as Genetic Algorithm. The procedure was restrained, as much as possible, to produce physically meaningful results. A very good match with experimental data was obtained. Subsequently, a scheme to couple the thermo-elastic FEM simulations with the calibrated model was developed. Hence, a full simulation of a TSV considering the scallops could be carried out to study the stress inside the TSV. The results revealed a particular evolution for the stress inside the via. The top and the middle of the via show different behaviors, the middle being the most dangerous region. There, the stress increases during heating and can reach values up to 10% larger than the initial stress.
Finally, the discussion moved down along the length scale in order to study mechanical stress during thin film deposition. The residual stress creation was studied, considering the microstructural evolution of the metal during growth. The coalescence was assumed as the only mechanism for generating stress during growth. Several models were discussed to compute the stress which is generated by the encounter of two islands. However, the stress due to coalescence is not a product of only one island encounter, instead it is the result of the impingement of islands with different sizes. Therefore, a statistical approach was proposed, in which the size distribution of the islands in a film was taken into consideration for the final stress of the film. As a result, the methodology provided an estimate for the residual stress due to coalescence in addition to the confidence interval for the stress variation.
This work has provided an assortment of simulation techniques for analysis of the mechanical stress in TSVs. Each technique was created to address a specific circumstance during the via processing or operation. Naturally, further improvement is required and some issues are already known. The first one is the improvement of the scallop description. Some unpublished results have shown that the description of the scallops by Bézier curves is not the best approach, mainly because of the peaks created at the scallop intersections. A connection between scallops made by a soft curve could improve the results. Regarding strain relaxation, it is known that the coupled scheme does not work for nonlinear variations of temperature. Modifications in the strain relaxation model are necessary in order to consider these problems. Finally, the estimate for residual stress must include other stress sources. In fact, it is surprising that it was possible to obtain a simulated value so close to the observed values by only considering the coalescence and thermal effects. Furthermore, improvements to the VW simulation are also needed, for instance, one should consider non-instantaneous nucleation of islands. The quality of the solution produced by the simulations depends greatly on the quality of the input data. This is especially true for microstructure simulations, where the availability of material parameters is very limited.