AVS2010 Session PS1-ThA: Plasma Modeling

Beam-surface interaction between fluorocarbon ions (mainly CF3+) or hydrogen ions (H+) with a polymethyl methacrylate (PMMA) surface has been examined at the atomic level with the use of molecular dynamics (MD) numerical simulations. The work is motivated by the desire to control line edge roughness (LER) or line width roughness (LWR) observed after plasma etching processes, which is incurred by deterioration of photoresist polymers exposed to reactive plasmas. Molecular structures of commercially available photoresist polymers are complex in general and typically not disclosed in the public domain, so we use PMMA in this work as a model polymer in a hope that, combining this study with other previous studies on plasma-polymer interaction based on other simple organic polymers, an insight into the mechanism of photoresist deterioration due to plasma exposure will be gained. For example, PMMA contains ester bonds (R-COO-R’) and their interactions with plasmas are a subject of this study. In this presentation, we shall focus on two specific issues. One is to evaluate sputtering yields of PMMA by Ar+ or CF3+ ion injections with various injection energies. With Ar+ injection simulations, we shall clarify the nature of physical sputtering of PMMA whereas, with CF3+ injection simulations, we hope to understand the modification mechanism of a polymer mask during oxide etching processes. Our MD simulation results have so far indicated that there is a strong dependence of sputtering yields on the direction of polymer chains against the incoming beam angle at the atomic level. The other issue is solidification of polymer by hydrogen plasma exposure, which may be used to cure polymers after the mask formation process by photolithography. In the simulations, hydrogen beams are injected into PMMA and we have observed increase of the relative carbon density in the polymer due to hydrogen abstraction reactions.

A set of quantum electron scattering calculations are performed on SiBr and SiBr₂ using the electron-molecule code Quantemol-N [3]. The resulting cross-sections are used to complete a set of gas-phase reactions contributing to the etch process. Etch-profile simulations are then performed using the Monte Carlo Feature Profile Model code (MCFPM) [4]. Here we use incident species fluxes derived from simulations of Ar/HBr/O₂ plasmas. Results are presented which include an analysis of the contribution of the etch products SiBr and SiBr₂.

[1] J. M. Lane, F. P. Klemens, K. H. A. Bogart, M. V. Malyshev, and J. T. C. Lee, J. Vac. Sci. Technol. A 18, 188 (1999)

[2] S. A. Vitale, H. Chae, H. H. Sawin, J. Vac. Sci. Technol. A, 19, 2197 (2001)

[3] J. Tennyson, D. B. Brown , J. J. Munro , I. Rozum , H. N. Varambhia and N. Vinci, J. Phys.: Conf. Ser., 86, 012001 (2007)

[4] R. J. Hoekstra, M. J. Grapperhaus, and M. J. Kushner, J. Vac. Sci. Technol. A 15, 1913 (1997)

Plasma etching of high aspect ratio (HAR) features is extremely challenging as it places great emphasis on uniformity of just about every characteristic of the plasma: density, fluxes, fields, energy and angular distributions to mention a few. At large aspect ratios, even minor variations in the bulk plasma can translate into huge deviations on the feature scale. One important plasma characteristic that influences etch properties is the ion temperature. Small variations in ion temperature can lead to non-uniform or tapered etch profiles since even marginally cold ions when accelerated through the sheath (having large voltage drops for HAR process) can deviate significantly from the normal leading to offset of the bottom of the feature compared to the top.

In this work, a 2/3 dimensional plasma equipment model (CRTRS) [1] has been used to assess the consequences of ion and neutral temperature on etching processes. CRTRS previously only included continuity and momentum equations for charged species. The model has been improved to include solution of the energy equations for all heavy neutral and charged species to obtain the ion and neutral temperatures. The model results have been validated using experimental data from laser induced fluorescence measurements.[2] In this talk, results of this validation exercise will be discussed. We found that while ion temperatures peak in the sheath region near the electrodes under the influence of high electric fields, neutral radicals’ temperature peak predominantly in the bulk via collisions with ions (for example, charge exchange reactions). Consequently, inclusion of Franck-Condon heating sources is important for low fragmenting gas mixtures such as pure Ar compared to, for example, N₂ to accurately predict neutral temperatures.

The validated model is then applied to a typical high-power HAR etch process. Modeling results are used to understand the impact of gas and ion temperatures on electron heating and power deposition mechanisms, ion energy and angular distributions, plasma uniformity and neutral radical composition. Plasma characteristics are investigated for etch-relevant feed gas mixtures over a wide range of pressures (20 – 100 mT).

¹ A. Agarwal, P.J. Stout, S. Rauf and K. Collins, 56^th AVS Symposium 2009.

² G.A. Hebner and A.M. Paterson, Plasma Sources Sci. Technol. 19, 015020 (2010).

As high aspect ratio (HAR) etch requirements have grown more stringent, the strategies used to deliver an appropriate combination of species to the wafer have evolved considerably. One common approach is to use a capacitively coupled plasma (CCP) reactor with a combination of generator frequencies and complex feed gas mixtures. The use of multiple frequencies allows for generation of a large plasma density using a high frequency source while biasing the wafer substrate at low frequency to control the flux and energy of impinging ions. Complex feed gases provide etch precursors from which to make volatile products as well as passivating species to protect certain features (e.g. sidewalls). Such a large parameter space of frequencies, powers, pressures, and feed gases to employ, however, has made modeling an increasingly attractive option to gain insight and understanding, both during engineering design and process development. Here, we use a plasma model to investigate the impact of frequency mixture in low pressure capacitively coupled discharges.

In our 2/3-dimensional fluid plasma model, charged species densities are computed by solving continuity equations for all species coupled with the full momentum equation (ions) or the drift-diffusion approximation (electrons). These equations, combined with the Poisson equation, which governs the electrostatic fields, are solved implicitly in time. The electron temperature is determined by solving the electron energy equation. The model also includes the full set of Maxwell equations in their potential formulation, Kirchhoff equations for the external circuit, and continuity equations for neutral species, along with non-uniform mesh generation to better resolve regions of interest. Ion energy and angular distributions are computed using a Monte Carlo-based particle simulation, which uses the spatially and temporally-resolved species densities, species fluxes, and electric fields from the plasma model as inputs.

As the downscaling of integrated circuit devices continues, minute variations in the feature profiles from processing techniques such as plasma etching significantly affect device performance . Thus, there is a need to predict the surface response during etching of a variety of materials, such as complex oxides. To accurately represent the kinetics involved, experiments are conducted in this work in an inductively coupled plasma (ICP) reactor equipped with a quadrupole mass spectrometer (QMS) for analyzing etch products and a quartz crystal microbalance (QCM) for measuring the etch rate in situ. This reactor is connected to a UHV transfer tube which allows the surface composition to be studied via x-ray photoelectron spectroscopy (XPS) without exposure to ambient conditions. The materials system studied include Hf-based high-k materials and YMnO₃, a multiferroic oxide, etched in Cl₂/BCl₃ plasmas. A surface site-based phenomenological model¹ that was previously developed for binary and ternary oxides is shown to be applicable to the prediction of how these complex oxides were etched. To use this model in a cell based Monte Carlo simulator to predict feature profile evolution, a translated mixed layer (TML) kinetics model² is utilized to describe the surface reactions such as ion impingement, neutral adsorption, physical sputtering and chemically enhanced ion etching. Reaction parameters that cannot be measured directly are extracted by comparing the model to etch yield data and validated against the phenomenological model. Ion incident angle dependence and an elliptical energy deposition model were used to capture the effects of surface morphology on the profile evolution under the bombardment of energetic and directional ions. Simulated profiles are compared to cross-sectional SEM images of the patterned material systems and display reasonable agreement.

Very small microplasma-based propulsion is gaining importance as a viable propulsion concept for small satellites that weigh less than 100 kg. These devices involve complex multiple physical phenomena associated with high-density plasma discharge in small volumes and coupling of plasma phenomena with high-speed viscous dominated flows. Specific requirements of minimal wall erosion and wall heat transfer are also driving oscillatory dielectric-barrier microdischarge designs, which introduced additional physics complexity associated pulsed microplasmas. We present computational modeling studies of microplasma propulsion devices. The model describes the plasma dynamics, gas-phase chemical kinetics, neutral dynamics, and coupling of plasma phenomena with high-speed flow for both DC and pulsed mode microdischarges. Unique computational challenges associated with this problem are described and solutions to these challenges as addressed in our model are presented. Results show the dominant mechanism for thruster performance improvement is the gas heating in the microplasma. The gas heating is primarily a result of near-wall ion Joule heating in the case of DC discharges and is also accompanied by significant wall heat loss. The use of dielectric-barrier microdischarge configuration accompanied by oscillatory excitation is shown to mitigate wall heat loss while sustaining off-wall gas heating.

Reliable and predictive feature profile evolution simulation is an extremely important topic for nanotechnology and semiconductor industry. If successfully solved, it will allow significant saving of time and resources presently spent on numerous design experiments directed on finding proper chemistries and conditions in a multi-parameter space of search for advanced etching or deposition. FPS-3D is a Monte Carlo code, where launched particles corresponding to the specified fluxes, each particle typically consisting of many gas molecules, or ions, or electrons, interacts with solid materials of the target. A cellular model is used for presenting solid materials. Each cell is a complex object consisting of the body of the cell and its surface layer, and is typically includes many molecules. All material properties and all reaction mechanisms are specified in the chemistry file. The output of gas and ion reactions is characterized in terms of probabilities and yields. The incoming fluxes could be specified via two different options. One option is to use the flux file, where all the data for fluxes of each gaseous species is provided for each energy-angular bin. This file is typically generated by a plasma simulation code (for example, such as HPEM [1], which we are currently using). A second option is to generate fluxes of species according to a few parameters specified in the input file. The second option is especially convenient for considering interactions of particle beams with solid materials. Upon collision of a flux particle with the target, the code determines a particular cell where the reaction occurs. The result of such an interaction could be a removal of some of molecules from the cell, or deposition of similar or different molecules to the cell, or both. The code considers low-energy gaseous species very differently from the high-energy species. The low-energy species are interacting only with the surface layer of the cell by mainly depositing or altering molecules in the surface layer, although spontaneous etching from the surface layer is taken into account as well. The energetic species, on the other hand, could do much more. They could also lead to removal of molecules from the surface layer and from the body of the cell with the yield corresponding to their energy and angle of incidence. Such yields could be larger than one for higher energies. This report will present technical details of FPS-3D and give a few examples of its operation in 2D and 3D. The author is thankful to Drs. S.-Y. Kang of TEL TDC and P. Miller of HFS for valuable discussions.

[1] M.J. Grapperhaus, M.J. Kushner, J. Appl. Phys. 81, 669 (1997).