85.40.Hp Lithography, masks and pattern transfer; Micro- and nano-electromechanical systems (MEMS/NEMS) and devices, see 85.85.+j
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We have fabricated circular silicon nitride drums of varying diameter (20 μm to 1 mm) and thickness (15 nm–75 nm) using electron beam lithography and measured the dissipation (Q−1) of these amorphous silicon nitride resonators using optical interferometric detection. We observe that the dissipation is strongly dependent on mode type for relatively large, thick membranes as predicted by the current models of dissipation due to clamping loss. However, this dependence is drastically reduced for smaller or thinner resonators, with thinner resonators showing higher quality factors, for low order modes. Highest quality factors that can be reached for these thin resonators seems be limited by an intrinsic mechanism and scales linearly with the diameter of the membrane. Our results are promising for mass sensing and optomechanical applications where low mass and high Qs are desirable.
As semiconductor lithography marches towards the era of sub 45nm feature size, many novel technologies are proposed to prolong the lifetime of photolithography, such as advanced resolution enhancement techniques (RETs), extreme ultraviolet (EUV) lithography, and double patterning/exposure techniques. The increasingly stringent process conditions, the immaturity of facilities, processes, and materials, and the dramatically rising expenses in cost and time for all the promising novel lithography technologies have put indispensable demands on the physical modeling and simulation of the lithography process. In particular, the interaction of light with sub-wavelength features on the lithographic masks and wafers is found to have more and more pronounced impact on the lithographic performance. This impact cannot be simply ignored as it is in many current simulations. Therefore, rigorous electromagnetic field (EMF) solvers become indispensable for the simulation of novel lithography technologies. However, the choice of the EMF solvers is greatly limited due to the requirement on its speed, accuracy, efficiency, and flexibility. In this thesis, the Fraunhofer IISB developed Waveguide Method is presented as the rigorous EMF solver for the simulation of novel lithography technologies. New modeling approaches, extensions, and optimizations are proposed and developed to enhance the performance of the Waveguide Method, and to enable new applications such as rigorous exposure simulation in double patterning/exposure techniques. An important new model, namely the Waveguide decomposition method (WDM), reduces the computational complexity of the diffraction of a 3D mask to that of several 2D masks. WDM is demonstrated to have superior simulation speedup with sufficient accuracy. It allows rapid simulation of large 3D mask areas (> 10 μm×10 μm at a wavelength of 193 nm, or > 50λ × 50λ) and extremely fast computation of standard sized masks (< 1 μm × 1 μm at a wavelength of 193 nm, or < 5λ × 5λ). The speedup of WDM can be further scaled up by distributed computation with excellent parallelization efficiency. Another important and originative model, namely WaferWaveguide, tailors theWaveguide Method for the rigorous EMF simulation of topographic (non-planar) wafers in many emerging double patterning/exposure techniques. A flexible layer-based description approach is developed to model diverse wafer topographies. Extensions and optimizations to reduce the computation load and to enable dynamic exposure simulation in case of bleachable resists are developed and featured. A parallelization of the Wafer-Waveguide Method is also presented to speed up the computation. Applications employing the proposed Waveguide Method, WDM, and WaferWaveguide are exemplified. The rigorous EMF effects in advanced phase-shift masks are demonstrated. EUV mask induced aberrations and the resulting imaging artifacts are investigated. The printability of EUV multilayer defects is analyzed with respect to the defect parameters and other process conditions. Several emerging double patterning / exposure techniques are explored. The impact of wafer topography on the final lithographic performance is evaluated. The simulation results can be used to instruct the control of critical parameters in these processes to avoid detrimental wafer topography effects. An example exploiting simulations to predict the best process condition in a double exposure scheme is also given.
The reduction of semiconductor device dimensions necessitates, amongst other things, a reduction in linewidth fluctuation of the individual device components. The achievement of specified tolerances for future technology is an as yet unsolved problem for mass manufacture. The impact of many process and material parameters on resulting linewidth fluctuation is known experimentally, but no models yet exist that allow a sufficiently accurate prediction of linewidth fluctuation. In this thesis, new models for the mesoscopic (i.e., discrete and stochastic) simulation of photoresist patterning in optical lithography have been developed and implemented. It has been proven that modeling of the Poisson distributed num ber of photons (so called "shot noise") is unnecessary. This implies, contrary to common believe in literature, that the average number of photons absorbed during photoresist exposure has no direct impact on linewidth fluctuation. The new photoresist post-exposure bake simulation algorithm reduces the required computing time and memory resources when compared with the standard approach for mesoscopic simulation of reaction and diffusion processes. The new algorithm for the subsequent photoresist development simulation combines an overlap-free description of the photoresist polymers with calibrated development rates. This enables quantitative match of the average profile linewidth predicted by mesoscopic models with established macroscopic models and experimental data for the first time. Profile data obtained from mesoscopic simu lations requires additional post-processing in order to carry out an automated evaluation. An efficient algorithm has been developed for the unambiguous determination of the surface position of the developed photoresist. The new models have been used to analyze the impact of process and photoresist material properties on linewidth fluctuation. Comparisons with experimental data from literature show a very good agreement.