Micro-electromechanical Structural Design and Optimization of Vertical Cavity Photonic Devices with Wide Continuous Tunin

Abstract

This dissertation covers the design and optimisation aspects of microelectromechanical tunable vertical cavity devices using the finite element method (FEM). The main emphasis 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 continuous tuning. A multi-membrane InP0/air Fabry-P ́ erot optical filter is presented and comprehensively analysed. In this work, a systematic structural design procedure which provides clear guidelines in the design process is proposed. An accurate analytical electromechanical model for the devices has been derived. This can be an invaluable tool in providing a quick insight at beginning of design phase. With the use of the FEM program, the effect of the non-linear stress stiffening has been widely investigated and its effect on the extension of the mechanical travel range of the device actuation demonstrated. It was also interesting to deduce from the calculations that regardless of the device structural configuration, normalised deflection-voltage characteristic profile remains invariable. The distortion of the actuated membrane is known to have often severe consequences on the performance of MOEMS devices. This work shows how the choice of structural design dimensions affect the membrane distortion. One difficulty encountered in the FEM mathematical model calculations of these devices with 3D models is the huge demand on the computing resources where 3D models are concerned. In this work a very accurate 2D software method based on the FEMLAB software that is faster and requires much less computing resources was implemented. This tool has been applied in the design and design optimisation of various features of the investigated devices. Further, it has been used in investigating the effects of 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 reliable way. For calculations that could not be carried out with the 2D approximation software tool, the standard FEM setups built into FEMLAB were applied. Calculations involving micromachined structures with in-plane residual stress that results in changed rigidity and out-of-plane deformations required a modification of the standard methods to incorporate stress. This enabled the exploration of the nature and effect of residual biaxial and gradient stress in the devices and a more accurate prediction of the tuning behaviour of devices with residual stress as seen when compared with measurements.