Simulation Of Profile Evolution Research Articles

Plasma–surface kinetics and simulation of feature profile evolution in Cl2+HBr etching of polysilicon

The etching of polysilicon by low energy Cl2+HBr plasma beam was studied, and the etching yield as a function of composition, ion impingement energy and ion incident angle was measured. The etching yield by HBr plasma beam is slightly lower than Cl2 plasma beam. The angular dependence of etching yield by both Cl2 and HBr beam strongly suggests the mechanism of ion induced chemical etching, with highest etching yield at normal incident angle. For Cl2 beam, the etching yield almost keeps constant until the off-normal incident angle of ions increased to 45°, while for HBr beam, the etching yield starts dropping even with small off-normal angle. The angular dependence of etching yield by Cl2+HBr plasma at different composition exhibits similar trend as pure HBr. Using x-ray photoelectron spectroscopy, the coverage of Cl and Br on polysilicon surfaces after etching in Cl2+HBr plasmas was measured. The Cl coverage after etching with pure Cl2 plasma beam is about 1.4 times higher than the Br coverage after etching with pure HBr plasma beam, due to the larger size of Br atom. The instantaneous sputtering yields of polysilicon by Ar+ ions after Cl2 and HBr plasma etching are similar, indicating that the lower Br coverage is not responsible for the lower etching rate in HBr plasma. The effect of the angular dependent etching yield difference between Cl2 and HBr on feature profile evolution, as identified with Monte Carlo simulation, might contribute to the more anisotropic etching in HBr plasma.

Etching of polysilicon in inductively coupled Cl2 and HBr discharges. II. Simulation of profile evolution using cellular representation of feature composition and Monte Carlo computation of flux and surface kinetics

A Monte Carlo simulator was developed to simulate the profile evolution during the Cl etching of patterned polysilicon in high density plasma etchers. The simulator used Monte Carlo techniques to compute the transport and surface kinetics combined with a cellular representation of the feature. The Monte Carlo algorithm permitted the incorporation of all the dominant physical and chemical mechanisms of the etching process such as angle-dependent ion-enhanced etching, physical sputtering, ion scattering, surface recombination, plasma deposition, sidewall passivation, and line-of-sight redeposition without encountering numerical difficulties. The technique allows for the modification of surface kinetics rates based on the surface composition. Simultaneous composition-dependent etching and deposition could be handled easily. A modification of the cellular representation of the feature (similar to a string-and-node algorithm) was developed to determine neutral species interactions with the surface enabling accurate simulation of deposition processes. A surface normal calculation algorithm involving least-squares fitting of the surface was developed to handle specular ion scattering. A generalizable structure allowing the incorporation of all chemical and physical processes was developed to handle the compositional, energy, and angular dependent surface processes. Test cases were run to quantify the accuracy of the combined Monte Carlo and cellular algorithms.

Etching of polysilicon in inductively coupled Cl2 and HBr discharges. III. Photoresist mask faceting, sidewall deposition, and microtrenching

The etching artifacts observed during the high density Cl2 plasma etching of photoresist-masked polysilicon [A. P. Mahorowala and H. H. Sawin, J. Vac. Sci. Technol. B 20, 1055 (2002)] were analyzed using a 212-dimensional Monte Carlo profile evolution simulator [A. P. Mahorowala and H. H. Sawin, J. Vac. Sci. Technol. B 20, 1064 (2002)]. A set of profile evolution simulations for the Cl etching of photoresist-masked polysilicon features, including plasma deposition of two representative etching byproducts (C and SiCl2) were performed. The extent of deposition and the formation of facets, straight sidewalls, and microtrenches were strongly affected by the competing etching and deposition. The simulations suggested that the top facet angle was controlled by the surface composition at the top of the photoresist lines and the angular dependence for etching of the deposited material; the facet being less steep when there was more deposition of Si-based byproducts. The lower facet angle and the polysilicon sidewall profile were governed by the feature aspect ratio, the sticking probabilities, and fluxes of the depositing material and the depositing material etching angular dependence. Feature bottom microtrenching was strongly linked to sidewall curvature, i.e., bowing. Microtrenching was found to begin when the sidewalls bowed sufficiently. Scattering of the ions from the curved sidewalls exhibited a focusing effect on the directional ions concentrating them at a point near the sidewall, thereby causing the microtrenching.

Etching of polysilicon in inductively coupled Cl2 and HBr discharges. IV. Calculation of feature charging in profile evolution

The ability to simulate feature charging was added to the Monte Carlo profile evolution simulator described in the companion article of this series [A. P. Mahorowala and H. H. Sawin, J. Vac. Sci. Technol. B 20, 1077 (2002)]. Two electrical assumptions were compared: (1) a perfect insulating feature and (2) a resistive feature. The potential profiles for the entire feature were generated and the ion and electron fluxes were computed along the feature surface. The resistive feature representation enabled the incorporation of bulk conduction and surface leakage that is not possible when using the insulator approximation. For highly resistive surfaces, the solutions for the two assumptions were shown to converge. With the insulator approximation, the potential profiles were calculated by determining the accumulated charge on the feature surface and solving Poisson’s equation over the entire simulation domain. Calculation of the potential profiles with the resistive feature approximation involved the determination of the steady-state current to the feature surface and solution of the current continuity in a resistive feature. Both solutions required the solution of Laplace’s equation with differing boundary conditions. The resistive feature approximation was used to study the role surface and bulk conductivities have on the potential profiles. It was shown for submicron features that the conductivities of most bulk materials could be approximated as perfectly insulating or conducting; however, surface leakage and passivation films could lead to circumstances where realistic conductivities are needed to obtain the correct solution. The charging of features was shown to scale inversely with the feature size. Therefore, charging is more significant in larger features. The materials properties of most materials lead to the conclusion that for current paths on the order of 0.25 μm, bulk materials can be treated as either perfect insulators of conductors. However, surface leakage or ultraviolet radiation may also make bulk oxide significantly conductive. Therefore, modeling it as a resistive material is required. Finally, the deposition of thin insulating layers on conductive materials could easily lead to feature charging.

Level set approach to simulation of feature profile evolution in a high-density plasma-etching system

The simulation of feature profile evolution in high-density plasma-etching processes has been carried out using a level-set technique. The main feature of this work is the inclusion of sheath dynamics, angular distribution of ions and reemission of neutrals in the trench, etch kinetics, and a level set equation for tracking a moving front of the feature profile. Sheath dynamics showed that the damped potential was somewhat shifted to the right and smaller than the applied potential. Etch profile simulations were performed for etching of silicon in inductively coupled plasmas of Cl2 and CF4 under various conditions. In dry etching of Si with CF4 discharges, polymer deposition was dominant at pCFx>10 mTorr, while surface fluorination (or ion-enhanced etching) was a main mechanism at pCFx<10 mTorr. The predicted etch profiles showed a slight bowing on the sidewalls and substantial tapering near the bottom, depending on the plasma parameters.

Numerical simulations of glacial-valley longitudinal profile evolution: Comment and Reply

Numerical simulations are useful where field evidence is impossible, as in astronomy. In geomorphology numerical simulations are also used, but a model's assumptions can be verified with field evidence. [MacGregor et al. (2000)][1] present six assumptions that follow [Davis' (1906) glacial-landscape

SiO 2 and Si etching in fluorocarbon plasmas: Coupling of a surface model with a profile evolution simulator

A surface model for Si and SiO 2 etching in fluorocarbon plasmas has been developed as a part of a complete plasma simulator including plasma physics, plasma chemistry, surface chemistry and a topography profile evolution simulator. It can predict the transition from etching to deposition region, which depends on F and CF x radical concentration, ion flux to the surface and ion energy. The coupling of the surface model with the profile simulator can predict the RIE lag during etching of features with different aspect ratios.

Numerical simulations of glacial-valley longitudinal profile evolution

Research Article| November 01, 2000 Numerical simulations of glacial-valley longitudinal profile evolution K.R. MacGregor; K.R. MacGregor 1Department of Earth Sciences and Center for the Study of Imaging and Dynamics of the Earth, University of California, Santa Cruz, California 95064, USA Search for other works by this author on: GSW Google Scholar R.S. Anderson; R.S. Anderson 1Department of Earth Sciences and Center for the Study of Imaging and Dynamics of the Earth, University of California, Santa Cruz, California 95064, USA Search for other works by this author on: GSW Google Scholar S.P. Anderson; S.P. Anderson 1Department of Earth Sciences and Center for the Study of Imaging and Dynamics of the Earth, University of California, Santa Cruz, California 95064, USA Search for other works by this author on: GSW Google Scholar E.D. Waddington E.D. Waddington 2Geophysics Program, University of Washington, Seattle, Washington 98195, USA Search for other works by this author on: GSW Google Scholar Author and Article Information K.R. MacGregor 1Department of Earth Sciences and Center for the Study of Imaging and Dynamics of the Earth, University of California, Santa Cruz, California 95064, USA R.S. Anderson 1Department of Earth Sciences and Center for the Study of Imaging and Dynamics of the Earth, University of California, Santa Cruz, California 95064, USA S.P. Anderson 1Department of Earth Sciences and Center for the Study of Imaging and Dynamics of the Earth, University of California, Santa Cruz, California 95064, USA E.D. Waddington 2Geophysics Program, University of Washington, Seattle, Washington 98195, USA Publisher: Geological Society of America Received: 04 May 2000 Revision Received: 17 Aug 2000 Accepted: 25 Aug 2000 First Online: 02 Jun 2017 Online ISSN: 1943-2682 Print ISSN: 0091-7613 Geological Society of America Geology (2000) 28 (11): 1031–1034. https://doi.org/10.1130/0091-7613(2000)28<1031:NSOGLP>2.0.CO;2 Article history Received: 04 May 2000 Revision Received: 17 Aug 2000 Accepted: 25 Aug 2000 First Online: 02 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation K.R. MacGregor, R.S. Anderson, S.P. Anderson, E.D. Waddington; Numerical simulations of glacial-valley longitudinal profile evolution. Geology 2000;; 28 (11): 1031–1034. doi: https://doi.org/10.1130/0091-7613(2000)28<1031:NSOGLP>2.0.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract Glaciers shape alpine landscapes. They broaden valley bottoms, enhance local valley relief, generate multiple steps, overdeepen valley floors, and cause tributary valleys to hang. These distinctive glacial signatures result from 104–105 yr of erosion, during which swings in climate drive advances and retreats of alpine glaciers. We use a numerical model of glacial erosion to explore the development of the longitudinal profiles of glaciated valleys. The model is driven by the past 400 k.y. of variable climate. Because both sliding speed, which dictates abrasion rate, and water-pressure fluctuations, which strongly modulate quarrying rate, should peak at the equilibrium-line altitude (ELA), we expect the locus of most rapid erosion to follow the transient ELA. Simulations of a single glacial valley show rapid flattening of the longitudinal profile. Inclusion of a tributary glacier creates a step immediately downvalley of the tributary junction that persists over multiple glaciations and commonly leaves the tributary valley hanging. Steps and overdeepenings result from an increase in ice discharge immediately below the tributary junction, which is accommodated primarily by increased ice thickness and hence sliding rate. The size of the step increases with the ratio of tributary to trunk ice discharge, while the height of a hanging valley reflects the difference in the time-integrated ice discharge in tributary and trunk valleys and therefore increases as the discharge ratio decreases. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Hardmask charging during Cl2 plasma etching of silicon

Feature profile evolution simulations of plasma etching rely to first order on the accurate prediction of ion fluxes to all points on the evolving surface. Previous experimental and theoretical work strongly suggests that dielectric charging effects play a key role in a type of anomolous feature evolution known as “notchings.” This involves charging of newly exposed gate dielectric material, subsequent ion trajectory bending, and notch formation due to localized ion flux enhancement. Few researchers, however, have considered charging of masking dielectrics (e.g., SiO2 hardmasks) and its associated effects on feature evolution, even though such charging is likely to occur in modern high-density plasma etching systems. In this article, we develop a combined reactor- and feature-scale model of Cl2 plasma etching of crystalline silicon, allowing for the possibility of hardmask charging and ion trajectory deflection. We show via comparison of simulation results to cross-sectional scanning electron micrographs of silicon trenches that these charging effects can explain the formation of wide, “triangular,” microtrenches seen when etching silicon at 2 mTorr pressure and low rf-bias power. Furthermore, the model correctly predicts the disappearance of these microtrenches when the rf-bias power is raised.

Effect of surface kinetics on the step coverage during chemical vapor deposition

Profile evolution simulations during chemical vapor deposition based on a 2D continuum model reveal that the type of surface kinetics plays an important role in determining step coverage of films deposited in high aspect ratio trenches and vias. Linear surface kinetics, resulting from an adsorption rate limited process, is found to cause difficulty in bringing about conformal step coverage in deep narrow trenches without reducing the growth rate considerably. Under such condition, void-free filling cannot be achieved while maintaining a growth rate acceptable to integrated circuit (IC) manufacturing. The numerical study also suggests that the high tendency of the precursor for chemical equilibrium on a surface, resulting in nonlinear kinetics by a surface reaction limited process, is crucial to achieve a uniform step coverage as typically observed in SiO2 deposition from tetraethylorthosilicate (TEOS).

Three-dimensional spatiokinetic distributions of sputtered and scattered products of Ar/sup +/ and Cu/sup +/ impacts onto the Cu surface: molecular dynamics simulations

Energy and angular distributions of reflections and sputtered atoms are essential inputs for feature profile evolution simulations. Molecular dynamics simulations are used to compute the three-dimensional energy and angular distributions for reflected and sputtered products when both Ar/sup +/ and Cu/sup +/ ions bombard a copper surface. We term these "spatiokinetic" distribution functions (SKDF's). We show by example that SKDF's for reflected Ar/sup +/ ions focus as the incident angle /spl theta//sub i/ (normal=0/spl deg/) is increased from 60-75/spl deg/ and broaden as the incident energy E/sub i/ is increased from 55-175 eV. We show that the SKDF's for glancing-angle reflected Cu/sup +/ ions focus when E/sub i/ is increased from 55-175 eV. We show that the SKDF's for copper atoms sputtered by 175 eV Ar/sup +/ are insensitive to /spl theta//sub i/;. We report total sputter yields for Ar/sup +/ and Cu/sup +/ ions at 55 and 175 eV for incident angles between 0/spl deg/ and 85/spl deg/, and sticking probabilities for Cu/sup +/ ions for these energies and angles. Comparison to representative experimental results (Doughty et al., 1997) is given.

Pattern-Dependent Charging and the Role of Electron Tunneling

We review the prevailing causes of and remedies for profile distortion (notching) resulting from pattern-dependent charging during etching in high density plasmas. A new mechanism for notch reduction, based on electron tunneling through thin gate oxides, is explained through detailed modeling and simulations of charging and profile evolution in polysilicon gate definition. Tunneling currents from the substrate decrease surface charging potentials–responsible for ion deflection–at the bottom of high aspect ratio trenches. The exponential dependence of electron tunneling on the oxide electric field predicts an abrupt transition from severe notching to virtually no notching as the gate oxide thickness is decreased, which has been seen in experiments.

The Role of the Substrate on Pattern‐Dependent Charging

Monte Carlo simulations of charging and profile evolution during plasma etching reveal that the substrate can mediate current imbalance across the wafer. This function couples patterned areas, where the electron shading effect dominates, to substrate areas directly exposed to the plasma. When a net positive current flows through the pattern features to the substrate, increasing the exposed area decreases the substrate potential, thereby causing notching at the connected feature sidewalls to worsen, in agreement with experimental observations.

Ion mass effect in plasma-induced charging

Simulations of charging and profile evolution during etching of high aspect ratio polysilicon gates in typical high-density plasmas containing heavy ions (e.g., BCl3+, Cl2+), predict a reduction in charging and notching when lighter ions (e.g., He+) are added. The reduction occurs because of the influence of the ion mass on the ratio R of the ion sheath transit time to the rf period, which determines the spread in the ion energy distribution at the wafer. The effect is most pronounced when R⩽0.1–0.2 for light ions and, simultaneously, R⩾0.6 for heavy ions; then, more light ions arrive at the patterned structure with low energies, where they help decrease localized charging. When the rf bias frequency is reduced so that R⩽0.3 for all ions, the effect disappears.

On the Origin of Charging Damage during Etching of Antenna Structures

Monte Carlo simulations of charging and profile evolution in patterned antenna structures during etching in high‐density plasmas reveal a rapid change in the potential of the lines at end point, which causes a surge in electron tunneling through thin gate oxides and possibly charging damage. The condition of the substrate (grounded vs. floating) determines the magnitude of the surge and whether it will be followed by a steady‐state current until all lines of the pattern become disconnected. A reduction in damage is possible by controlling the substrate condition, which may be assessed through notching experiments.

Electron irradiance of conductive sidewalls: A determining factor for pattern-dependent charging

Numerical simulations of charging and profile evolution during gate electrode overetching in high density plasmas have been performed to investigate the effect of long conductive sidewalls on profile distortion (notching). The results reveal that the angle of electron irradiance of the conductive portion of the sidewalls affects profoundly the charging potential of the gates. Larger angles, obtained for thinner masks and/or thicker polysilicon, result in reduced gate potentials which, through their influence on the local ion dynamics, cause more severe notching at all lines of the microstructure.

On the origin of the notching effect during etching in uniform high density plasmas

We present a two-dimensional Monte Carlo simulation of profile evolution during the overetching step of polysilicon-on-insulator structures, which considers explicitly (a) electric field effects during the charging transient, (b) etching reactions of energetic ions impinging on the poly-Si, and (c) forward inelastic scattering effects. Realistic energy and angular distributions for ions and electrons are used in trajectory calculations through local electric fields near and in the microstructure. Transient charging of exposed insulator surfaces is found to profoundly affect local sidewall etching (notching). Ion scattering contributions are small but important in matching experimental notch profiles. The model is validated by capturing quantitatively the notch characteristics and also the effects of the line connectivity and open area width on the notch depth, which have been observed experimentally by Nozawa et al. [Jpn. J. Appl. Phys. 34, 2107 (1995)]. Elucidation of the mechanisms responsible for the effect facilitates the prediction of ways to minimize or eliminate notching.

Adatom mobility for the solid-on-solid model

The relaxation of a crystal surface through surface diffusion is studied within the solid-on-solid model. Two types of (conserved) dynamics are considered. ForArrhenius dynamics we show that the relevant transport coefficient, the adatom mobility, has a simple analytic form: It is independent of orientation, and depends exponentially on the inverse temperature, for any surface dimensionalityd. Together with the expression for the orientation-dependent stiffness this completely determines the macroscopic evolution equation for the surface. The predictions of the macroscopic theory are checked against simulations of profile evolution and roughening ind=1. For one-dimensionalMetropolis dynamics we provide an upper bound on the adatom mobility and obtain numerical estimates of its actual value, which indicate a nontrivial orientation dependence in this case. An alternative derivation of the macroscopic dynamics directly from the master equation is presented and discussed in relation to previous approximate work.

Study of silicon etching in CF4/O2 plasmas to establish surface re-emission as the dominant transport mechanism

This article describes an investigation of the etching of polysilicon in a CF4/O2 plasma. The ‘‘undercut’’ observed in etch profiles is related to the surface transport of reaction precursors. The possible mechanisms for this transport include surface re-emission and surface diffusion of the precursors. Simulations of profile evolution, conducted with both mechanisms, are compared with experimental results. The surface reemission simulations are found to predict experimental profile evolution accurately, whereas surface diffusion simulations require unphysical values for the surface diffusion length. Novel test structures have been fabricated and etched under the same conditions as used for trench etching. Surface re-emission simulations accurately predict the etch rate deep inside the shadowed cavity of different structures. On the other hand, simulations assuming surface diffusion to be dominant do not capture even the qualitative trends in test structure etching. This is strong evidence that surface re-emission is the dominant mechanism for transport of etch precursors in CF4/O2 plasmas.

Simulation of profile evolution in silicon reactive ion etching with re-emission and surface diffusion

This article describes a model that simulates etching profiles in reactive ion etching. In particular, models are developed to explain the significant lateral etch rate that is observed in many etch profiles. The total etch rate is considered to consist of two superimposed components: an ion-assisted rate and a purely ‘‘chemical’’ etch rate, the latter rate being due to etching by radicals in the absence of ion bombardment. The transport of radicals to the evolving interface is studied for two different transport mechanisms: re-emission from the surface and diffusion along the surface. For the case of transport by surface re-emission, a reactive sticking coefficient is defined for the radicals, and a formulation is developed to simulate etching for any value (between zero and unity) that this sticking coefficient may assume. When the sticking coefficient approaches either zero or unity, the method of characteristics is shown to be useful for profile simulation. Transport of radicals by surface diffusion is also investigated, and it is shown that the important dimensionless parameter governing profile evolution is the Damkohler number. The two models are compared to experiments performed on the etching of silicon in a SF6 plasma, and the surface re-emission model is shown to accurately predict the development of etching profiles.