# Fabrication Tolerances' Impact on an ODAC-Based PAM-4 Transmitter
## 3 Results and Discussion  
The graphs of the SER versus chip iteration when \(\sigma_{n}\) = 0 and when \(\sigma_{n}\) = 2% are presented in Figure 8a,b. With the light control as expected, the total 1000 iterated PICs passed the SER threshold, as shown in Figure 8a. When \(\sigma_{n}\) is increased to 2%, only 3 chips out of the 1000 mimed was seen to have failed while the rest passed the SER threshold we set, which implies a high tolerance due to decreased deviation from the coupling condition.  
For further analysis of the results when \(\sigma_{n}\) = 2%, the PAM-4 amplitude levels of one PIC from the failed and passed categories are extracted and simulated to obtain the PAM-4 eye diagrams of the failed and passed PICs, as shown in Figure 8c,d. From the eye diagram of the failed PICs in Figure 8c, it can be observed that the amplitude levels of the signal are not equidistant, which results in error detection. Unlike the passed PIC with the eye diagram in Figure 8d, an improved equidistant signal level is observed and as such, detection is accomplished with less error at the receiver.  
Moreover, by increasing the impact of \(\sigma_{n}\) from 6% to 12%, it is observed that the overlapping levels 10 and 01 increase. As a result of this, the numbers of failed PICs increase, which implies a low yield. Looking at the result of \(\sigma_{n}\) = 12% in Figure 9b, for instance, close to 50% of the PICs failed due to the high spread of levels 01 and 10, as clearly shown in the histogram in Figure 5d, which translates to a high loss in the production scenario.  
Figure 7: Procedure for data extraction from the programmable device and offline processing for error analysis.  
In addition, the graph in Figure 10 summarizes the percentage of failed and passed chips against all instances of \(\sigma_{n}\) we have tested, which simplified our findings. The number of failed and passed PICs in each \(\sigma_{n}\) we have simulated, as plotted in Figures 8 and 9, are obtained and estimated as a percentage of the total 1000 runs per \(\sigma_{n}\). The linear behaviour of the number of both passed and failed chips in the figure can explain what would be expected in a fabrication scenario and this serves as a predictive template to analyse any passive device. Furthermore, the graph also reveals that such an oDAC-based PAM-4 transmitter is sensitive to component deviations resulting from passive variations. In comparison to the related works in [13; 16], we have used the SER as a performance metric in this work, which translates to the linear behaviour in correlation with the passive variance. The median of the wavelength deviation in correlation with the distance between identical PIC devices within a wafer has been used in [13], which shows a linear relationship. These findings can also be compared with those in the work in [16], where an OSNR is used as a performance metric for wavelength mismatch. In the work, the waveguide width/thickness also exhibits a linear relationship with the wavelength shift slop, leading to variations in the output signal OSNR performance.  
Figure 8: SER versus the number of PIC mimed at \(\sigma_{n}=\) (**a**) 0%, (**b**) 2%, and eye diagram of one selected PIC from failed and passed categories when \(\sigma_{n}=\) 2%. (**c**) Failed PIC. (**d**) Passed PIC.