BackgroundPredictive estimates of the final process outcome(s) of multistep, coupled processes can be difficult to make based on data measured at the various process steps. Self-aligned quadruple patterning (SAQP) is an example of such a process where the prediction of pitch-walk is desired at the various process steps.AimsBe able to both predict pitch-walk values and the uncertainty in the predicted values at SAQP process steps based on optical critical dimension (OCD) spectroscopy outputs (dimensions, angles, thicknesses, and so on) of mandrel, spacer, and other SAQP features.ApproachTrain a neural network using OCD-modeled values of an SAQP process to be able to predict SAQP pitch-walk at early process steps. Use Bayesian dropout approximation (BDA), a methodology using Bayesian inference with stochastic neural networks, to estimate uncertainty in the predicted SAQP pitch-walk.ResultsAble to predict pitch-walk values, and the uncertainty in the predictions, of the final SAQP structure after the deposition of the first spacer. The pitch-walk predictions become more accurate as OCD information from the bottom mandrel RIE and bottom spacer are added as inputs to the BDA network.ConclusionsIn contrast to a single output value that traditional neural networks would predict, BDA makes an estimated distribution of predictions, where the BDA network gives both a most likely value as well as a distribution of potential values. While this paper shows the power of BDA to predict SAQP pitch walk, it is expected that BDA will be a valuable tool to analyze many data sets in semiconductor manufacturing to help improve yield and performance.
Predictive modeling of the pitch-walk variance from multistep coupled processes, such as SAQP using experimental metrology observables, has the potential to give both deep understanding and a control mechanism for pitch-walk variance. In this study, with the Bayesian dropout approximation, a methodology using Bayesian inference via use of stochastic neural networks was employed to both model and predict the SAQP pitch-walk variance distribution. Bayesian neural networks were implemented as variational ensembles of networks with hidden layers, where the neural net training uses conventional dropout, while the forward solves employ a dropout Bayesian vector methodology previously developed by Gal and Ghahramani.1, 2 An important distinction here is that the forward propagations effectively sample the network to make a prediction, resulting in a distribution of outputs achieving the best model, not just a single expectation value. A complete dataset of fin module OCD metrology measurements per chip at top mandrel, bottom mandrel, and final fin reveal were used. Since the measured dataset was limited to small number chip locations, data augmentation with the highly efficient method of the volume of simplex was used to generate 30K samples. The synthetic data and the experimental data were used for neural network calibration and validation, respectively.
The utilization of EUV pellicles as protective layers for EUV masks requires the use of refractory materials that can tolerate large temperature excursions due to the non-negligible absorption of EUV radiation during exposure. Additionally, the mechanical stress induced on the EUV pellicle by the thermal load is dependent on the thermal expansion of the material which can be responsible for transient wrinkling. In this study, an ultrathin (20 nm), free-standing membrane based on silicon nitride is utilized as a learning vehicle to understand the material requirements of EUV pellicles under dynamic exposure conditions that are typical of commercial EUV scanners. First, the nanoscale radiative properties (emissivity) and thermo-mechanical failure temperature of the dielectric film under vacuum conditions are experimentally investigated utilizing a pulsed ArF (193 nm) probing laser. The silicon nitride membrane is found to be marginally compatible with an equivalent 80W EUV source power under steady state illumination conditions. Next, the thermal behavior of the EUV pellicle under dynamic exposure conditions is simulated using a finite element solver. The transient temperature profile and stress distribution across the membrane under stationary state conditions are extracted for an equivalent 60W EUV power source and the pellicle wrinkling due to heating and consequent impact on CD uniformity is estimated. The present work provides a generalized methodology to anticipate the thermal response of a EUV pellicle under realistic exposure conditions.
KEYWORDS: Process modeling, Monte Carlo methods, Interfaces, Physical vapor deposition, Systems modeling, 3D modeling, Particles, Deposition processes, Thin films, Numerical analysis
We have created a finite-element based, multiple-material,
levelset-based code to implicitly represent and track evolving
islands and grains. With this method, the code can track island
growth in three dimensions through nucleation to coalescence into a
grain structure. We discuss the numerical methods, capabilities,
and limitations of the code, and then examine the microstructures
that result from different models of growth based on starting
structures derived from atomistic Monte Carlo simulations. We show
simulation results from a kinetically limited process (electroless
deposition), a transport-limited process (physical vapor
deposition), and a process neither transport nor kinetically
limited (physical vapor deposition with orientation
dependent sticking factors).
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