Quantifying fabrication errors in meta-lenses by Monte Carlo simulations

Metasurfaces and metalenses have shown remarkable progress and performance in laboratory results in the past years. For metasurfaces to make the transition from laboratory to large scale adaptation, several challenges need to be overcome: high manufacturing yields must be shown to reach cost-effective fabrication, the robustness of metalenses to various imperfections should be demonstrated and integrated systems with metalenses need to be made with higher performance than conventional systems. Controlling the various types of unavoidable fabrication imperfections is critical for achieving these. In this paper we present Monte-Carlo simulations of metalenses with random fabrication defects as a tool to quantify the performance loss associated with different types of errors. We model changes in sidewall steepness, feature size and missing structures. We study these effects in a reference metalens consisting of SiliconNitride pillars on a glass substrate. The methods presented in this paper can be readily applied to other metalens and metasurface designs and are implemented in the PlanOpSim software package. We find that when the deviations in sidewall steepness are within a distribution with root mean square of 1.5° and changes in pillar shape have a root mean square no larger than 10nm the focusing efficiency of the metalens remains within 90% of its nominal value.