Subsections

• 9.4.1 Cross Section
• 9.4.2 Strain Curve
• 9.4.3 Practical Example

9.4 Investigation of Fabricated Cantilevers

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.

9.4.1 Cross Section

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$_2$-layer on it. Above the SiO$_2$-layer the picture shows the bottom part of the deposited poly-SiGe film. This multilayer film has a germanium concentration $x$ between 62 and 65% in the layers. The Young modulus for silicon germanium $E_{SiGe}=E_{Si}(1-x)+E_{Ge} x$ varies only between 146 and 148GPa under the assumption that $E_{Si}$ is 173GPa and $E_{Ge}$ 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 10$\mu$m) is deposited. PECVD films grow very fast, namely at 120-130nm/min, while LPCVD films have only a deposition rate between 16-19nm/min [138].

Figure 9.7: Cross section of the poly-SiGe multilayer. Courtesy of IMEC/Gregory van Barel.

9.4.2 Strain Curve

The developed methodology to treat thin film stress is applied to the experimental setting presented in [147]. In this experiment a 10$\mu$m thick SiGe film was deposited on a SiO$_2$ 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 1$\mu$m. 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$_2$ 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 [136], 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 1.3$\times$10$^{-3}$ 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.

Figure 9.8: Strain versus thickness in the SiGe multilayer thin film.

The large compressive strain at the bottom of the SiGe film explains the very large deflections for thin cantilevers. At first the neutral bending line which is located midway, is moving with the cantilever thickness, and secondly the stiffness is decreased for thinner cantilevers. This strain curve was used to simulate the deflections for various thicknesses for the 1mm long cantilever structure as shown in Fig. 9.4. As demonstrated in Fig. 9.9, the simulated cantilever deflections show good agreement with the experimentally determined deflections.

Figure 9.9: Measured and simulated cantilever deflections for different thicknesses.

9.4.3 Practical Example

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$_2$ 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.

Figure 9.10: Array of unreleased cantilevers. Courtesy of IMEC/Gregory van Barel.

In Fig. 9.10 the selected structure is marked with a yellow rectangle. This cantilever is 900 $\mu$m long, 50 $\mu$m wide, and 6 $\mu$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 $\times$220)$\mu$m. The strain curve (see Fig. 9.8) loads the deflection problem. The simulated deflection at the end of the 900 $\mu$m long and 6 $\mu$m thick cantilever is 44.6 $\mu$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.

Figure 9.11: Initial structure with unreleased cantilever.

Figure 9.12: Cantilever structure after simulated deflection.

Figure 9.13: Cut of the deflected cantilever structure.