# High-Tolerance Grating Couplers for Vertical Backside Coupling
## 3 Results and Discussion
### Fabrication Tolerance  
In practice, the light alignment inaccuracy and the fabrication errors (etching depth error and etch groove width error of the GC) in the scheme may cause severe performance declines, especially a CE decrease. Those were simulated and are depicted in Figure 6, which considers the impact of structural variations in the grating period \(\Delta\Lambda\), individual sub-grating parameters \(\Delta\)P1-\(\Delta\)P4, and etching depth \(\Delta\)d on the CE at a wavelength of 1550 nm, as shown in Figure 6a. Figure 6d shows that within the range of \(\pm\)30 nm for grating period variations, the CE remained above 36%. Additionally, when the individual widths of the four sub-gratings varied, the CE stayed above 38% as shown in Figure 6c. This is attributed to the larger minimum feature size, allowing the GC to exhibit a high fabrication tolerance. Moreover, as shown in Figure 6b, the CE can be maintained well with an etch depth variation of \(\pm\)10 nm.  
Here, it is assumed that the chip was integrated on top of the optical fiber facet by using the method described in [7]. During the transfer, aligning the fiber's core from the backside with the GC may not be perfect, especially if performed manually. Therefore, optimization of the 3D GC structure was conducted to account for those possible misalignment issues. Figure 7a illustrates the impact of both x and z offsets (vertical and horizontal plane of the chip) between the fiber's core and the GC, on the CE at 1550 nm. Within the range of \(\pm\)3 \(\upmu\)m, for both x and y offset, the CE still exhibited performance above 30%. Additionally,  
Figure 6: **(a)** Schematic representation of fabrication error parameters considered in the analysis. **(b)** Fabrication tolerance to etching depth deviations (\(\Delta\)d). **(c)** Width deviation tolerance of each sub-grating in the focusing GC (\(\Delta\)P1-\(\Delta\)P4). **(d)** CE vs grating period size deviations. All figures are generated for an incident light at 1550 nm.  
after cleaving the fiber's tip to transfer the chip on it, surface roughness of fiber's facet can lead to an angular misalignment between fiber and chip. Therefore, as shown in Figure 7b, the impact on the CE of the angular misalignment between fiber and GC was investigated, where positive angular misalignment stands for a tilted fiber oriented towards the output waveguide of interest. It can be observed that within a range of \(\pm 5\) degrees, there was a minimal decrease in CE. The above observations demonstrate that our GC designed for perfectly vertical backside coupling has a good tolerance of misalignment, while also exhibiting high fabrication tolerance. Additionally, other fabrication errors such as sidewall roughness of the fabricated waveguides and grating grooves can affect the overall device performance, despite a lesser impact compared to the two errors already investigated. Indeed, because of the relatively big dimensions within the GCs (minimum feature size of 200 nm), as well as the use of a wide Si waveguide (600 nm) between them, the final PIC device was less sensitive to usual nanometer-scale roughness. On the other hand, the use of other materials such as SiNx (with a refractive index of 1.7-2.3) could also minimize those scattering losses as well as propagation losses, however, at a cost of a lesser CE [20].