The main purpose of cantilever simulation is to predict the deflection for different geometries (e.g. length and thickness), mechanical boundary conditions, and deposition process parameters. In the following, fabricated cantilevers with a cross section as described in Section 9.4.1 are investigated.
The cross section of the investigated cantilever structures is shown in Fig. 9.7. At the lower part of this SEM picture one can see the silicon substrate with a 250nm thick sacrificial SiO-layer on it. Above the SiO-layer the picture shows the bottom part of the deposited poly-SiGe film. This multilayer film has a germanium concentration between 62 and 65% in the layers. The Young modulus for silicon germanium varies only between 146 and 148GPa under the assumption that is 173GPa and is 132 GPa, respectively.
The multilayer SiGe film is deposited in three steps:
1) At first a PECVD seedlayer with 95 nm thickness is deposited as nucleation layer for the following LPCVD layer, because the nucleation on the substrate with LPCVD needs much more time. 2) Then a 370nm thick LPCVD layer is deposited in order to help crystallizing the top PECVD layer. Crystalline material has much more the desired properties than an amorphous one.
3) In the last step a PECVD layer with the desired film thickness (for example 10m) is deposited. PECVD films grow very fast, namely at 120-130nm/min, while LPCVD films have only a deposition rate between 16-19nm/min .
The developed methodology to treat thin film stress is applied to the experimental setting presented in . In this experiment a 10m thick SiGe film was deposited on a SiO sacrificial layer, as described above. After removal of this sacrificial layer, the deflection of the free 1mm long cantilever was measured at different thicknesses from 10 down to 1m. The smaller thicknesses were made by thinning. It was observed that the deflection increases exponentially with reduced thickness.
The intrinsic strain curve for this SiGe multilayer film (see Fig. 9.8), which is qualitatively predicted by the found methodology, was calibrated according to the measurement results. Since the SiO layer is amorphous, no misfit stress can arise here. It is worth mentioning that intrinsic compressive strain which loads a mechanical problem, must have a positive sign, because compressive materials want to expand. Compressive strain has only the same negative sign as stress, if a material is compressed by external forces.
The highest intrinsic compressive strain value with 0.08 is at the bottom of the SiGe film. This can be explained with a compressive stress exhibition of the individual islands which first form on the sacrificial layer , and with the insertion of excess atoms. Thermal stress can also be compressive.
Within the next 800nm of the film the strain plunges down to a minimum of 1.310 because of the tensile stress source in the deposited material, namely the coalescence of grain boundaries, the grain growth, and the excess vacancy annihilation. In the rest of the film there is a slow increase of the compressive part.
For this phenomenon it is assumed that the grains tend to grow isotropically, but due to their neighbors they are prevented to extend in the plane and they are forced to grow into the height instead, which leads to compressive stress.
As practical example for the simulation procedure a fabricated cantilever as shown in Fig. 9.10 is used. In this SEM picture which shows an array of unreleased cantilevers with different lengths, the surrounded SiO is already removed so that the side walls of the cantilevers lie free. The etching process was stopped before the sacrificial layer is removed and, therefore, the SiGe cantilevers are still fixed. The light material which separates and frames the cantilevers is also SiGe with the same composition as for the cantilevers.
In Fig. 9.10 the selected structure is marked with a yellow rectangle. This cantilever is 900 m long, 50 m wide, and 6 m thick. The multilayer cross section of this SiGe cantilever is the same as displayed in Fig. 9.7 and described in Section 9.4.1.
Fig. 9.11 shows the initial structure for the simulation with FEDOS, where the silicon substrate is green, the SiGe frame is blue, and the cantilever is red. The dimensions of the simulated geometry are identical with the yellow framed structure in Fig. 9.10. The structure has a floor space of (1120 220)m. The strain curve (see Fig. 9.8) loads the deflection problem. The simulated deflection at the end of the 900 m long and 6 m thick cantilever is 44.6 m. The structure after simulation with the deflected cantilever is displayed in Fig. 9.12. A cut of this deflected cantilever structure is shown in Fig. 9.13.