Micro-electromechanical Structural Design andOptimization of Vertical Cavity Photonic Devices with Wide Continuous Tuning

Abstract

This dissertation covers the design and optimisation aspects of microelectromechanicaltunable vertical cavity devices using the finite element method (FEM). The main empha-sis of the work was on the electromechanical structural design and optimisation of mul-tiple air-gap tunable DBR-based vertical cavity photonic devices with wide continuoustuning. A multi-membrane InP/air Fabry-P ́erot optical filter is presented and comprehen-sively analysed. In this work, a systematic structural design procedure which providesclear guidelines in the design process is proposed. An accurate analytical electromechan-ical model for the devices has been derived. This can be an invaluable tool in providing aquick insight at beginning of design phase. With the use of the FEM program, the effect ofthe non-linear stress stiffening has been widely investigated and its effect on the extensionof the mechanical travel range of the device actuation demonstrated. It was also interest-ing to deduce from the calculations that regardless of the device structural configuration,normalised deflection-voltage characteristic profile remains invariable. The distortion ofthe actuated membrane is known to have often severe consequences on the performance ofMOEMS devices. This work shows how the choice of structural design dimensions affectthe membrane distortion. One difficulty encountered in the FEM mathematical model cal-culations of these devices with 3D models is the huge demand on the computing resourceswhere 3D models are concerned. In this work a very accurate 2D software method basedon the FEMLAB software that is faster and requires much less computing resources wasimplemented. This tool has been applied in the design and design optimisation of variousfeatures of the investigated devices. Further, it has been used in investigating the effectsof scaling of the tunable devices. In a situation where a desire exists to tailor-scale adevice such that the resulting device replicates the tuning characteristics of the original,it is hereby demonstrated that this can be achieved in a simple, predictable and reliableway. For calculations that could not be carried out with the 2D approximation softwaretool, the standard FEM setups built into FEMLAB were applied. Calculations involvingmicromachined structures with in-plane residual stress that results in changed rigidity and out-of-plane deformations required a modification of the standard methods to incorporatestress. This enabled the exploration of the nature and effect of residual biaxial and gradi-ent stress in the devices and a more accurate prediction of the tuning behaviour of deviceswith residual stress as seen when compared with measurements.