A methodology is presented to virtually predict etch profiles on flexible substrates across multi-dimensional process spaces using a minimal number of calibration experiments. Simulations and predictions of the physics and chemical kinetics of plasma etch on flexible substrates are performed using the commercial software SandBox StudioTM. The evolution of a trench profile is computed using surface kinetics models and the level set method. Local etch rates include visibility effects to account for partial shielding of the etch as the pattern is developed and the effects of redeposition. The results of the experiments are then used to update the calibrated model parameters. If the process objectives (e.g., sidewall angle, trench critical dimensions, and across the web uniformity) are not achieved, then a new set of experiments is suggested by the methodology. The process is repeated until the optimal process conditions are identified. The methodology is validated by experiments on etching line-space patterns of polysilicon films on polymer substrates. Results with reactive ion etching with either CF<sub>4</sub> and HBr are shown and the optimal etch recipes (power, etch time and gas flow rates) determined. It is found that this coupled simulation-experiment approach is much more efficient than full factorial experimental design at predicting process outcomes. The methodology presented requires 66% fewer experiments reducing the cost of development by a factor of three.
Uniformity of critical dimensions (CDs) across a wafer is an increasing challenge as both CDs and tolerances shrink. Plasma etch uniformity is achieved in part through reactor design and in part through the operating conditions or process recipe of the reactor. The identification of a recipe for a specific etch process is time consuming and expensive, requiring extensive experiments and metrology. Here we present two modules in SandBox StudioTM, SB-Bayesian and SBNeuralNet, to accelerate the prediction and optimization of etch recipes for across the wafer uniformity. A model of etch rates across the wafer is created that accounts for injector locations, gas flow rates and distribution and plasma powers. Synthetic experiments on etching line-space patterns on 300 mm wafers are performed and the CDs and their variations are computed at several hundred site locations. SB-Bayesian requires many fewer experiments to be calibrated and achieve an excellent qualitative match with the experimental data. SB-NeuralNet achieves comparable levels of accuracy to SBBayesian at predicting average CDs and uniformity, but it does not perform as well at predicting trends across the wafer. It is shown that neural nets require a prohibitive amount of experimental data to successfully predict wafer patterns. SBBayesian and SB-NeuralNet were used to create detailed process maps across the parameters space of interest to identify optimal recipes to achieve required CDs and tolerances. Both modules can predict optimal recipe conditions for achieving identified target CD and uniformity metrics. Using these tools, etch recipes for across the wafer uniformity are rapidly optimized at lower cost.
A two-dimensional, cellular automata model for atomic layer etching (ALE) is presented and used to predict the etch rate and the evolution of the roughness of various surfaces as a function of the efficiencies or probabilities of the adsorption and removal steps in the ALE process. The atoms of the material to be etched are initially placed in a two-dimensional array several layers thick. The etch follows the two step process of ALE. First, the initial reaction step (e.g., Cl reacting with Si) is assumed to occur at 100% efficiency activating the exposed, surface atoms; that is, all exposed atoms react with the etching gas. The second reaction step (e.g., Ar ion bombardment or sputtering) occurs with efficiencies that are assumed to vary depending on the exposure of the surface atoms relative to their neighbors and on the strength of bombardment. For sufficiently high bombardment or sputtering, atoms below the activated surface atoms can also be removed, which gives etch rates greater than one layer per ALE cycle. The bounds on the efficiencies of the second removal step are extracted from experimental measurements and fully detailed molecular dynamics simulations from the literature. A trade-off is observed between etch rate and surface roughness as the Ar ion bombardment is increased.
Predicting the etch and deposition profiles created using plasma processes is challenging due to the complexity of plasma discharges and plasma-surface interactions. Volume-averaged global models allow for efficient prediction of important processing parameters and provide a means to quickly determine the effect of a variety of process inputs on the plasma discharge. However, global models are limited based on simplifying assumptions to describe the chemical reaction network. Here a database of 128 reactions is compiled and their corresponding rate constants collected from 24 sources for an Ar/CF<sub>4</sub> plasma using the platform RODEo (Recipe Optimization for Deposition and Etching). Six different reaction sets were tested which employed anywhere from 12 to all 128 reactions to evaluate the impact of the reaction database on particle species densities and electron temperature. Because many the reactions used in our database had conflicting rate constants as reported in literature, we also present a method to deal with those uncertainties when constructing the model which includes weighting each reaction rate and filtering outliers. By analyzing the link between a reaction’s rate constant and its impact on the predicted plasma densities and electron temperatures, we determine the conditions at which a reaction is deemed necessary to the plasma model. The results of this study provide a foundation for determining which minimal set of reactions must be included in the reaction set of the plasma model.
The design and optimization of highly nonlinear and complex processes like plasma etching is challenging and timeconsuming. Significant effort has been devoted to creating plasma profile simulators to facilitate the development of etch recipes. Nevertheless, these simulators are often difficult to use in practice due to the large number of unknown parameters in the plasma discharge and surface kinetics of the etch material, the dependency of the etch rate on the evolving front profile, and the disparate length scales of the system. Here, we expand on the development of a previously published, data informed, Bayesian approach embodied in the platform RODEo (<strong>R</strong>ecipe <strong>O</strong>ptimization for <strong>D</strong>eposition and <strong>E</strong>tching). RODEo is used to predict etch rates and etch profiles over a range of powers, pressures, gas flow rates, and gas mixing ratios of an CF4/Ar gas chemistry. Three examples are shown: (1) etch rate predictions of an unknown material “X” using simulated experiments for a CF<sub>4</sub>/Ar chemistry, (2) etch rate predictions of SiO<sub>2</sub> in a Plasma-Therm 790 RIE reactor for a CF<sub>4</sub>/Ar chemistry, and (3) profile prediction using level set methods.
Next generation semiconductor technologies like high density memory storage require precise 2D and 3D nanopatterns. Plasma etching processes are essential to achieving the nanoscale precision required for these structures. Current plasma process development methods rely primarily on iterative trial and error or factorial design of experiment (DOE) to define the plasma process space. Here we evaluate the efficacy of the software tool Recipe Optimization for Deposition and Etching (RODEo) against standard industry methods at determining the process parameters of a high density O<sub>2</sub> plasma system with three case studies. In the first case study, we demonstrate that RODEo is able to predict etch rates more accurately than a regression model based on a full factorial design while using 40% fewer experiments. In the second case study, we demonstrate that RODEo performs significantly better than a full factorial DOE at identifying optimal process conditions to maximize anisotropy. In the third case study we experimentally show how RODEo maximizes etch rates while using half the experiments of a full factorial DOE method. With enhanced process predictions and more accurate maps of the process space, RODEo reduces the number of experiments required to develop and optimize plasma processes.
A fast and inexpensive scheme for etch rate prediction using flexible continuum models and Bayesian statistics is demonstrated. Bulk etch rates of MgO are predicted using a steady-state model with volume-averaged plasma parameters and classical Langmuir surface kinetics. Plasma particle and surface kinetics are modeled within a global plasma framework using single component Metropolis Hastings methods and limited data. The accuracy of these predictions is evaluated with synthetic and experimental etch rate data for magnesium oxide in an ICP-RIE system. This approach is compared and superior to factorial models generated from JMP, a software package frequently employed for recipe creation and optimization.
Polymer shrinkage from curing in nanoimprint lithography (NIL) strongly affects the ultimate shapes of two- and three-dimensional structures produced following etching. We computationally study the curing step in the NIL process and predict the shape changes caused by polymer shrinkage. The shape changes are predicted for crosses, diamonds with sharp and rounded tips, and multitiered structures that are applicable for multibit memory devices and dual damascene processes. The shape changes from curing are shown to be governed by the shrinkage coefficient of the polymer resist, its Poisson’s ratio, and the geometric aspect ratios of the shapes. Finite element simulations demonstrate that shape change due to polymer densification is equal to the average volumetric contraction of the resist material, but shrinkage is not isotropic and vertical displacement dominates. The thickness of the residual layer does not impact the final profile of the imprinted shapes considered. Further analysis shows that diamonds with sharp tips stay sharp while the tips of rounded diamonds get sharper. Additionally, shape changes for multitiered structures are not uniformly distributed among the tiers. Using etch simulations, we demonstrate the significant impact of polymer shrinkage on the final feature profile.
Nanosculpting, the fabrication of two- and three-dimensional shapes at the nanoscale, enables applications in
photonics, metamaterials, multi-bit magnetic memory, and bio-nanoparticles. A promising high resolution and high
throughput method for nanosculpting is nanoimprint lithography (NIL). A key requirement to achieving
manufacturing viability of nanosculptures in NIL is maintaining image fidelity through each step of the imprinting
process. In particular, polymer densification during UV curing can distort the imprinted image. Here we study the
shape changes introduced by polymer densification and develop a forward method for predicting changes in
nanoscale geometries from UV curing. We show that shape changes by polymer densification are governed by the
Poisson’s ratio, the shrinkage coefficient of the polymer resist, and the geometric aspect ratios of the nanosculpted
shape. We also show that the size of the residual layer does not impact the final profile of the imprinted shape.