We report on the computational modeling of gas break down and evolution of plasma in an all-dielectric resonator structure. Two cylindrical dielectric resonators (DR) of diameter 25 mm with material relative permittivity of 172.5 separated by a 1 mm gap are observed to resonate in a strong constructive interference mode (CIM) at 1.47 GHz. The electric fields in the gap between the DRs are amplified to about 30 times the incident wave strength which leads to gas breakdown in argon at 10 Torr. The species densities in the bulk of plasma rise primarily due to the wave power addition into the plasma. As the species densities rise above 1017 m−3, the bulk plasma acts as a lossy material and the wave experiences significant damping through collisional losses. As plasma densities in the bulk rise to around 1018 m−3, the wave is damped significantly in the bulk, and a surface plasmon polariton (SPP) wave mode develops at the interface of plasma sheath and the DR surfaces. These surface waves are initiated due to a thin negative permittivity region of the plasma in the vicinity of the DR surface. The quasi-steady state operation of the resonator system depends on the propagation of the damped CIM in the bulk regions of the plasma, the SPP waves in the sheath region and the slower ambipolar diffusion process in plasma. Gas temperature rise in plasma is found to be small throughout the time scales considered and electrostatic fields are found to play an equally important role for large plasma densities in the sheath regions.

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Quantitatively accurate, physics-based, computational modeling of etching and lithography processes is essential for modern semiconductor manufacturing. This paper presents lithography and etch models for a trilayer process in a back end of the line manufacturing vehicle. These models are calibrated and verified against top-down scanning electron microscope (SEM) and cross-sectional SEM measurements. Calibration errors are within 2 nm, while the maximum verification error is less than 3 nm. A fluorocarbon plasma etch of the spin-on-glass (SOG) layer accounts for most of the etch bias present in the process. The tapered profile in the SOG etch step is generated due to the polymerization process by fluorocarbon radicals generated in the plasma. The model predicts a strong correlation between the etch bias in the SOG etch step and the neutral-to-ion flux ratio in the plasma. The second etch step of the flow, which etches the spin-on-carbon (SOC) layer using an H2/N2 plasma, results in a negative etch bias (increase in CDs) for all measured features. The ratio of hydrogen to nitrogen radical fluxes effectively controls the etch bias in this step, with the model predicting an increase in the etch bias from negative to positive values as the H-to-N ratio decreases. The model also indicates an aspect ratio dependent etch rate in the SOG and SOC etch steps, as seen in the etch front evolution in a three-dimensional test feature. The third and final step of the process, SiO2-etch, generates an insignificant etch bias in all the test structures. Finally, the accuracy of the etch simulations is shown to be dependent on the accuracy of the incoming photoresist shapes. Models that consider only the top-down SEM measurement as input and do not account for an accurate photoresist profile, suffered significant errors in the post-etch CD predictions.

The critical dimensions of advanced semiconductor manufacturing processes have decreased to a few tens of nanometers while the aspect ratios have increased beyond 100. The performance of plasma etch patterning processes as well as the cost and time of the development cycle are critical to the success of ramping a new technology node toward profitable high-volume manufacturing. In this paper, a computational patterning software, ProETCH®, has been developed with rigorous physics and advanced algorithms for modeling the etch patterning process, with the featured capabilities in calibrating the reaction mechanisms and optimizing the etch process. A shallow trench isolation etch process using self-aligned double patterning was investigated. A reaction mechanism of silicon etch by Ar/Cl2 plasma was developed to address the surface reactions, and a plasma hypermodel was introduced to correlate process operating conditions to plasma parameters at the wafer surface. The parameters of the reaction mechanism and the plasma hypermodel were calibrated with experimental data obtained from cross-sectional scanning electron microscope (XSEM) images. The calibrated model is used to identify the different fundamental pathways that contribute to the observed profile metrics in XSEMs. The model was then used for process development and optimization by solving the forward and inverse problems. In the forward problem, the model is used to predict the etching profile at different process conditions. Predictions for both interpolation conditions (process parameters within the range used for developing the model) and extrapolation conditions (process parameters outside of the range used for developing the model) agree well with the experimental data with the root mean square error less than 4 nm (1 nm resolution used for the mesh). In the inverse problem, the developed model is used to search for process conditions (e.g., values of bias power and pressure), which could result in desirable profiles. The solutions to the inverse problem demonstrate a degeneracy in process space of the etching process for a given target profile.

Understanding the origins and propagation of defects and hotspots in patterning processes used for semiconductor fabrication is of paramount importance in managing yield. In this paper, results from physics-based simulators to model lithography and dry etch processes are presented and compared to experimental results. These models are used to study different types of hotspots and defects observed in a litho-etch-litho-etch (LELE) multipatterning process. At each pass of the LELE flow, patterns are printed into a SiO2 collecting layer using a trilayer film stack comprised of a negative tone photoresist layer, a spin-on-glass layer (SOG), and a spin-on-carbon layer (SOC). After both passes of the LELE process, the patterns in the SiO2 collecting layer will be transferred to a TiN hardmask prior to final etch into an underlying dielectric. The SOG and SiO2 layers are etched using fluorocarbon plasma, while the SOC layer is etched with an H2/N2 plasma generated in a capacitively coupled plasma source. A pinching hotspot is observed during the single litho-etch pass in a region where two features are placed very close and the image contrast is low. However, for some lithography process conditions, this hotspot is rectified by subsequent etch steps and does not always transfer as a defect into the SiO2 layer. The quenching of the hotspot occurs primarily during the etching of the SOC layer due to the aspect ratio-dependent etching (ARDE) effect. A bridging hotspot is also observed at lithography during the single litho-etch pass at high exposure doses. This hotspot, on the other hand, is exacerbated by the etch steps because of the ARDE effect. Hotspots are also identified that originate from overlay errors between photomasks exposed during first and second passes of the LELE process. The etch bias generated during etching of the SOG layer is crucial to ensure that the overlay-related hotspot does not translate to the SiO2 layer. The extent of etch bias in the SOG etch step is critical and can be tuned by adjusting the neutral to ion flux ratio during that etch step. Increasing the flux ratio improves the process window for the overlay defect; however, when the ratio is higher than approximately 20% of the nominal value, a different defect type is formed in the SOG layer due to the inverse ARDE effect that propagates downstream to the SiO2 layer.