Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.

Low-Cost Micromechanically Tunable Optical Devices: Strained Resonator Engineering, Technological Implementation and Characterization

The rapid growth of the optical communication branches and the enormous demand for more bandwidth require novel networks such as dense wavelength division multiplexing (DWDM). These networks enable higher bitrate transmission using the existing optical fibers. Micromechanically tunable optical microcavity devices like VCSELs, Fabry-Pérot filters and photodetectors are core components of these novel DWDM systems. Several air-gap based tunable devices were successfully implemented in the last years. Even though these concepts are very promising, two main disadvantages are still remaining. On the one hand, the high fabrication and integration cost and on the other hand the undesired adverse buckling of the suspended membranes. This thesis addresses these two problems and consists of two main parts: • PECVD dielectric material investigation and stress control resulting in membranes shape engineering. • Implementation and characterization of novel tunable optical devices with tailored shapes of the suspended membranes. For this purposes, low-cost PECVD technology is investigated and developed in detail. The macro- and microstress of silicon nitride and silicon dioxide are controlled over a wide range. Furthermore, the effect of stress on the optical and mechanical properties of the suspended membranes and on the microcavities is evaluated. Various membrane shapes (concave, convex and planar) with several radii of curvature are fabricated. Using this resonator shape engineering, microcavity devices such as non tunable and tunable Fabry-Pérot filters, VCSELs and PIN photodetectors are succesfully implemented. The fabricated Fabry-Pérot filters cover a spectral range of over 200nm and show resonance linewidths down to 1.5nm. By varying the stress distribution across the vertical direction within a DBR, the shape and the radius of curvature of the top membrane are explicitely tailored. By adjusting the incoming light beam waist to the curvature, the fundamental resonant mode is supported and the higher order ones are suppressed. For instance, a tunable VCSEL with 26 nm tuning range, 400µW maximal output power, 47nm free spectral range and over 57dB side mode suppresion ratio (SMSR) is demonstrated. Other technologies, such as introducing light emitting organic materials in microcavities are also investigated.

Development of directly modulated high speed telecommunication lasers based on surface defined feedback gratings

High-speed semiconductor lasers are an integral part in the implemen- tation of high-bit-rate optical communications systems. They are com- pact, rugged, reliable, long-lived, and relatively inexpensive sources of coherent light. Due to the very low attenuation window that exists in the silica based optical fiber at 1.55 μm and the zero dispersion point at 1.3 μm, they have become the mainstay of optical fiber com- munication systems. For the fabrication of lasers with gratings such as, distributed bragg reflector or distributed feedback lasers, etching is the most critical step. Etching defines the lateral dimmensions of the structure which determines the performance of optoelectronic devices. In this thesis studies and experiments were carried out about the exist- ing etching processes for InP and a novel dry etching process was de- veloped. The newly developed process was based on Cl2/CH4/H2/Ar chemistry and resulted in very smooth surfaces and vertical side walls. With this process the grating definition was significantly improved as compared to other technological developments in the respective field. A surface defined grating definition approach is used in this thesis work which does not require any re-growth steps and makes the whole fabrication process simpler and cost effective. Moreover, this grating fabrication process is fully compatible with nano-imprint lithography and can be used for high throughput low-cost manufacturing. With usual etching techniques reported before it is not possible to etch very deep because of aspect ratio dependent etching phenomenon where with increasing etch depth the etch rate slows down resulting in non-vertical side walls and footing effects. Although with our de- veloped process quite vertical side walls were achieved but footing was still a problem. To overcome the challenges related to grating defini- tion and deep etching, a completely new three step gas chopping dry etching process was developed. This was the very first time that a time multiplexed etching process for an InP based material system was demonstrated. The developed gas chopping process showed extra ordinary results including high mask selectivity of 15, moderate etch- ing rate, very vertical side walls and a record high aspect ratio of 41. Both the developed etching processes are completely compatible with nano imprint lithography and can be used for low-cost high-throughput fabrication. A large number of broad area laser, ridge waveguide laser, distributed feedback laser, distributed bragg reflector laser and coupled cavity in- jection grating lasers were fabricated using the developed one step etch- ing process. Very extensive characterization was done to optimize all the important design and fabrication parameters. The devices devel- oped have shown excellent performance with a very high side mode suppression ratio of more than 52 dB, an output power of 17 mW per facet, high efficiency of 0.15 W/A, stable operation over temperature and injected currents and a threshold current as low as 30 mA for almost 1 mm long device. A record high modulation bandwidth of 15 GHz with electron-photon resonance and open eye diagrams for 10 Gbps data transmission were also shown.

Molecular Beam Epitaxial Growth of III-V Semiconductor Nanostructures on Silicon Substrates

The main focus and concerns of this PhD thesis is the growth of III-V semiconductor nanostructures (Quantum dots (QDs) and quantum dashes) on silicon substrates using molecular beam epitaxy (MBE) technique. The investigation of influence of the major growth parameters on their basic properties (density, geometry, composition, size etc.) and the systematic characterization of their structural and optical properties are the core of the research work. The monolithic integration of III-V optoelectronic devices with silicon electronic circuits could bring enormous prospect for the existing semiconductor technology. Our challenging approach is to combine the superior passive optical properties of silicon with the superior optical emission properties of III-V material by reducing the amount of III-V materials to the very limit of the active region. Different heteroepitaxial integration approaches have been investigated to overcome the materials issues between III-V and Si. However, this include the self-assembled growth of InAs and InGaAs QDs in silicon and GaAx matrices directly on flat silicon substrate, sitecontrolled growth of (GaAs/In0,15Ga0,85As/GaAs) QDs on pre-patterned Si substrate and the direct growth of GaP on Si using migration enhanced epitaxy (MEE) and MBE growth modes. An efficient ex-situ-buffered HF (BHF) and in-situ surface cleaning sequence based on atomic hydrogen (AH) cleaning at 500 °C combined with thermal oxide desorption within a temperature range of 700-900 °C has been established. The removal of oxide desorption was confirmed by semicircular streaky reflection high energy electron diffraction (RHEED) patterns indicating a 2D smooth surface construction prior to the MBE growth. The evolution of size, density and shape of the QDs are ex-situ characterized by atomic-force microscopy (AFM) and transmission electron microscopy (TEM). The InAs QDs density is strongly increased from 108 to 1011 cm-2 at V/III ratios in the range of 15-35 (beam equivalent pressure values). InAs QD formations are not observed at temperatures of 500 °C and above. Growth experiments on (111) substrates show orientation dependent QD formation behaviour. A significant shape and size transition with elongated InAs quantum dots and dashes has been observed on (111) orientation and at higher Indium-growth rate of 0.3 ML/s. The 2D strain mapping derived from high-resolution TEM of InAs QDs embedded in silicon matrix confirmed semi-coherent and fully relaxed QDs embedded in defectfree silicon matrix. The strain relaxation is released by dislocation loops exclusively localized along the InAs/Si interfaces and partial dislocations with stacking faults inside the InAs clusters. The site controlled growth of GaAs/In0,15Ga0,85As/GaAs nanostructures has been demonstrated for the first time with 1 μm spacing and very low nominal deposition thicknesses, directly on pre-patterned Si without the use of SiO2 mask. Thin planar GaP layer was successfully grown through migration enhanced epitaxy (MEE) to initiate a planar GaP wetting layer at the polar/non-polar interface, which work as a virtual GaP substrate, for the GaP-MBE subsequently growth on the GaP-MEE layer with total thickness of 50 nm. The best root mean square (RMS) roughness value was as good as 1.3 nm. However, these results are highly encouraging for the realization of III-V optical devices on silicon for potential applications.

1.55 µm High-Speed QDs Lasers for Optical Telecommunication Applications

In this work investigation of the QDs formation and the fabrication of QD based semiconductor lasers for telecom applications are presented. InAs QDs grown on AlGaInAs lattice matched to InP substrates are used to fabricate lasers operating at 1.55 µm, which is the central wavelength for far distance data transmission. This wavelength is used due to its minimum attenuation in standard glass fibers. The incorporation of QDs in this material system is more complicated in comparison to InAs QDs in the GaAs system. Due to smaller lattice mismatch the formation of circular QDs, elongated QDs and quantum wires is possible. The influence of the different growth conditions, such as the growth temperature, beam equivalent pressure, amount of deposited material on the formation of the QDs is investigated. It was already demonstrated that the formation process of QDs can be changed by the arsenic species. The formation of more round shaped QDs was observed during the growth of QDs with As2, while for As4 dash-like QDs. In this work only As2 was used for the QD growth. Different growth parameters were investigated to optimize the optical properties, like photoluminescence linewidth, and to implement those QD ensembles into laser structures as active medium. By the implementation of those QDs into laser structures a full width at half maximum (FWHM) of 30 meV was achieved. Another part of the research includes the investigation of the influence of the layer design of lasers on its lasing properties. QD lasers were demonstrated with a modal gain of more than 10 cm-1 per QD layer. Another achievement is the large signal modulation with a maximum data rate of 15 Gbit/s. The implementation of optimized QDs in the laser structure allows to increase the modal gain up to 12 cm-1 per QD layer. A reduction of the waveguide layer thickness leads to a shorter transport time of the carriers into the active region and as a result a data rate up to 22 Gbit/s was achieved, which is so far the highest digital modulation rate obtained with any 1.55 µm QD laser. The implementation of etch stop layers into the laser structure provide the possibility to fabricate feedback gratings with well defined geometries for the realization of DFB lasers. These DFB lasers were fabricated by using a combination of dry and wet etching. Single mode operation at 1.55 µm with a high side mode suppression ratio of 50 dB was achieved.

Optical Antennas for Biosensing Applications

The aim of the thesis is to theoretically investigate optical/plasmonic antennas for biosensing applications. The full 3-D numerical electromagnetic simulations have been performed by using finite integration technique (FIT). The electromagnetic properties of surface plasmon polaritons (SPPs) and the localized surface plasmons (LSPs) based devices are studied for sensing purpose. The surface plasmon resonance (SPR) biosensors offer high refractive index sensitivity at a fixed wavelength but are not enough for the detection of low concentrations of molecules. It has been demonstrated that the sensitivity of SPR sensors can be increased by employing the transverse magneto-optic Kerr effect (TMOKE) in combination with SPPs. The sensor based on the phenomena of TMOKE and SPPs are known as magneto-optic SPR (MOSPR) sensors. The optimized MOSPR sensor is analyzed which provides 8 times higher sensitivity than the SPR sensor, which will be able to detect lower concentration of molecules. But, the range of the refractive index detection is limited, due to the rapid decay of the amplitude of the MOSPR-signal with the increase of the refractive indices. Whereas, LSPs based sensors can detect lower concentrations of molecules, but their sensitivity is small at a fixed wavelength. Therefore, another device configuration known as perfect plasmonic absorber (PPA) is investigated which is based on the phenomena of metal-insulator-metal (MIM) waveguide. The PPA consists of a periodic array of gold nanoparticles and a thick gold film separated by a dielectric spacer. The electromagnetic modes of the PPA system are analyzed for sensing purpose. The second order mode of the PPA at a fixed wavelength has been proposed for the first time for biosensing applications. The PPA based sensor combines the properties of the LSPR sensor and the SPR sensor, for example, it illustrates increment in sensitivity of the LSPR sensor comparable to the SPR and can detect lower concentration of molecules due to the presence of nanoparticles.