Papers by Andreas Erdmann
Proceedings of SPIE, Apr 28, 1999
In general, simulation requires a thorough understanding of the physics and/or chemistry of the p... more In general, simulation requires a thorough understanding of the physics and/or chemistry of the processes. This should lend itself of models which can be used to establish simulation software. In addition, for a simulation to be successful, a calibration of the model is needed. A good model using bad parameters returns bad results. In lithography simulation there are settings of parameters which are well known. Others are less known and may be hard to obtain. A typical example is the development parameters, or parameters describing the reaction mechanism for chemically amplified resist. To support the user of simulation software in the process of finding proper input parameters, the new software package FIRM has been developed and will be presented in this paper, together with applications. FIRM uses models for the optical or e-beam lithography, the same as SOLID-C and SELID, and determines any set of coefficients from given experimental observations. From an initial set of coefficients, it tries to fit calculations to observations. FIRM accepts various types of measurements, e.g. thickness tables of the resist or focus-exposure matrices. In addition, the user selects from a wide list of resist models the parameters to be refined. FIRM then tries to find correlation between the parameters and the differences between calculation and observation. In an iterative process 'best' parameters are determined. The validity of the algorithm is verified against well known test cases. Next, applications of FIRM to several new chemically amplified resists for DUV will be presented using different types of experimental input.
Proceedings of SPIE, Feb 3, 2010
In this paper a rigorous three dimensional EUV mask simulation model is presented. The mask near ... more In this paper a rigorous three dimensional EUV mask simulation model is presented. The mask near field is simulated with the Waveguide method which is similar to the RCWA approach. Additionally the method is extended by a so called decompositions technique. The mask image is computed by coupling the Waveguide method with a fully vectorial imaging simulation model based on an extended Abbe approach. The basic theory of the models is explained. The optimization and combination of both simulation approaches enables the simulation and analysis of larger EUV mask areas required for the analysis of complex three dimensional EUV mask structures as well as the very fast simulation of standard sized EUV mask areas required in the context of source mask optimizations. Corresponding simulation examples like a rigorous source mask optimization and a mask induced imaging artifact analysis of a larger mask area demonstrate the capabilities and the performance of the new simulation system.
Proceedings of SPIE, Aug 26, 2003
Because the capabilities for experimental studies are still limited, a predictive simulation of E... more Because the capabilities for experimental studies are still limited, a predictive simulation of EUV lithography is very important for a better understanding of the technology. One of the most critical issues in EUV lithography modeling is the description of the mask, especially including multilayer defects. A new model for the characterization of defects in the multilayer of an EUV reflective mask is presented. The mask is divided into an absorber part, which defines the features on the mask, and a multilayer part, which determines the reflectivity of the mask without absorber. Since the height of the mask features is large in comparison to the illumination wavelength, the computation of the absorber part is performed by a finite-difference time-domain (FDTD) method. Because of the limited range of illumination angles with a high reflectivity and the limited diffraction efficiency of the multilayer, the computation of the reflectivity of the defective multilayer is performed by the Fresnel-method. The defect topography is taken into account by means of correcting the phase and the angle of incidence. For the complete computation of the reflected light from the EUV mask a coupling of the two methods is realized. Thus, the model can be applied to two and three dimensional defects and masks. The impact of the defects on the mask reflectivity, the near field and the aerial image is analyzed. Typical mask structures, such as 2D-lines and 3D-dots with various defects, are investigated. First comparisons with another simulation model, the MMFE method, are presented.
Proceedings of SPIE, May 4, 2006
This paper presents an evaluation of the finite-difference time-domain method (FDTD) and of the w... more This paper presents an evaluation of the finite-difference time-domain method (FDTD) and of the waveguide method (WG) for the simulation of typical hyper NA imaging problems. In contrast to previous comparisons of rigorous mask modeling methods, which were restricted to the assessment of few near fields, diffraction efficiencies, or aerial images at fixed imaging configurations, we compare the methods in
The impact of polarization was observed in the extreme ultraviolet (EUV) imaging simulations for ... more The impact of polarization was observed in the extreme ultraviolet (EUV) imaging simulations for high NA lithography [3] [4] [5]. It is shown that polarized illumination can improve the local contrast of images or NILS (normalized intensity log slope). This work investigates the possibilities to polarize EUV light by optimized multilayers. The characterization and simulation of multilayer structures has been performed using Dr.LiTHO [10]. The most efficient multilayer polarizers operate close to Brewster angle, where the reflectivity for TM polarized light (RTM) is close to zero, according to Fresnel’s equations. A multiobjective optimization algorithm was used to identify the suitable multilayer configurations maximizing reflectivity of TE polarized light (RTE) and fraction of polarization. Fraction of polarization (FoP) was calculated as the ratio between (RTE-RTM)/(RTE+RTM) to obtain the suitable multilayer with variable thickness. The multilayer structure is optimized to have the highest reflectivity of TE polarized light and fraction of polarization at the Brewster angle. It was found that MoSi multilayer can achieve 99.9% fraction of polarization by optimizing the thickness of Si and Mo. In reality, a multilayer polarizer has to operate over certain ranges of incident angles and/or wavelength ranges. Multilayer is optimized for different ranges of wavelength (13 nm : 14 nm) and incidence angles (37° : 47°). Additional simulations investigate the impact of different options in the design of the multilayer (e.g., constant vs. variable bilayer thickness) and materials (e.g., RuSi vs. MoSi multilayers) on the achievable performance.
State-of-the-art EUV exposure systems utilize EUV radiation around 13.52 nm with a full band spec... more State-of-the-art EUV exposure systems utilize EUV radiation around 13.52 nm with a full band spectrum extend- ing from 13.2 nm to 13.8 nm. The variation of the wavelength in this range modifies the diffraction angles with an impact on the image blur and non-telecentricity effects. Dispersion of the materials on the EUV mirrors and on the 3D mask introduce an additional sensitivity of the imaging characteristics to the exposure wavelength. We employed the simulation models of the Fraunhofer IISB lithography simulator Dr.LiTHO in combination with measured optical material data from PTB to quantify the resulting image impact and to differentiate between the identified contributors to polychromatic imaging effects.
The basic limitations of optical lithography are characterized by the minimum resolvable feature ... more The basic limitations of optical lithography are characterized by the minimum resolvable feature size dmin = k1λ/NA and the depth of focus dfoc = k2λ/NA2, where λ is the wave- length of light and NA the numerical aperture of the projection system. The parameters k1 and k2 depend on the imaging technology. Typical production values are k1 ≥ 0.7 and 1 ≤ k2 ≤ 2. The upper formulas are commonly used for the evaluation of the imaging process in air. The projection of the image into optically linear resists only scales these formulas according to its refractive index.
Proceedings of SPIE, Dec 18, 2012
Projection lithography at wavelengths in the extreme ultraviolet spectral range between 5 and 20 ... more Projection lithography at wavelengths in the extreme ultraviolet spectral range between 5 and 20 nm (EUV-lithography) employs reflective optical components including masks. This article applies rigorous electromagnetic field (EMF) simulation in combination with accurate projection image modeling to explore the impact of typical mask geometry parameters on the characteristics of lithographic processes. This includes telecentricity and shadowing effects resulting from the off-axis illumination in EUV systems and mask induced aberration{like effects. The importance of these effects for several alternative mask concepts including attenuated and alternating phase shift masks is investigated.
Understanding, characterization and management of 3D mask effects, including non-telecentricity, ... more Understanding, characterization and management of 3D mask effects, including non-telecentricity, contrast fading and best focus shifts, become increasingly important for the performance optimization of future extreme ultraviolet (EUV) projection systems and mask designs. Novel imaging configuration and central obscuration in high NA EUV projection systems introduce additional imaging effects. A simplified coherent imaging model, rigorous mask diffraction simulations, images for individual source areas and a hybrid mask model are employed to analyze the root causes of observed imaging artifacts. Based on this, several image enhancement strategies including modifications of mask and source are devised and investigated for lines/spaces.
Proceedings of SPIE, Apr 1, 2013
ABSTRACT
SPIE eBooks, Feb 23, 2021
In the previous chapters we described light and photoresist properties by continuous variables. L... more In the previous chapters we described light and photoresist properties by continuous variables. Lithography in the range of a few tens of nanometers and below exhibits several effects and observations that cannot be explained by such a continuous description. Instead, the discrete nature of energy (light) and matter (photoresist) and the randomness of related events have to be recognized to understand stochastic phenomena such as the roughness of printed feature edges, small local variations of size and placement of nominally identical features, and rare non-systematic printing errors. This chapter provides an introduction to stochastic effects in advanced lithography. An overview of the important discrete variables and processes, resulting lithographic phenomena, modeling approaches, and observed dependencies is presented. We will explain how to comprehend the statement of Chris Mack [1] that stochastic effects define the ultimate limits of lithography. The last section discusses several proposed mitigation strategies, especially the development and application of novel photoresist materials, to push this limit as far as possible. Numerous references for an in-depth study of this topic are provided.
Proceedings of SPIE, Aug 2, 2016
Numbers in the index correspond to the last two digits of the six-digit citation identifier (CID)... more Numbers in the index correspond to the last two digits of the six-digit citation identifier (CID) article numbering system used in Proceedings of SPIE. The first four digits reflect the volume number. Base 36 numbering is employed for the last two digits and indicates the order of articles within the volume. Numbers start with 00
Proceedings of SPIE, Sep 22, 2011
Proceedings of SPIE, Mar 13, 2009
ABSTRACT As the technology marches towards the 32nm node and beyond in semiconductor manufacturin... more ABSTRACT As the technology marches towards the 32nm node and beyond in semiconductor manufacturing, double patterning and double exposure techniques are currently regarded as the potential candidates to produce lines and spaces (L&amp;S) and contact holes (C/H), respectively. In this paper, the Waveguide method, a rigorous electromagnetic field (EMF) solver, is employed to investigate the impact of wafer topographies on two specific double patterning techniques. At first, the topography effects induced by the first patterning on the second lithography process in a lithography-etch-lithography-etch (LELE) process are demonstrated. A new methodology of the bottom anti-reflective coating (BARC) optimization is proposed to reduce the impact of wafer topography on resist profiles. Additionally, an optical proximity correction (OPC) of the second lithography mask is demonstrated to compensate the wafer topography induced asymmetric deformations of line ends. Rigorous EMF simulations of lithographic exposures are also applied to investigate wafer topography effects in a freezing process. The difference between the optical properties of the frozen (first) resist and the second resist potentially causes linewidth variations. Quantitative criteria for tolerable refractive index and extinction differences between the two resist materials are given. The described studies can be used for the optimizations of topographic waferstacks, the OPC of the second litho mask, and for the development of resist materials with appropriate optical properties.
Proceedings of SPIE, Mar 31, 2014
ABSTRACT We propose a framework for the rigorous simulation of the combined lithography/directed ... more ABSTRACT We propose a framework for the rigorous simulation of the combined lithography/directed self-assembly (DSA) of block copolymers process. As an example, the rectification of a contact hole through grapho-epitaxy DSA is presented. The proposed modeling strategy, using a full-fledged lithography simulation and a coarse-grained polymer model in conjunction with a particle-based Monte-Carlo simulator, provides direct insight into various aspects of the pattern and defect formation. We accordingly characterize and quantify the combined process performance and its determining factors. Appropriate metrics and representations for the common process windows are derived.
Proceedings of SPIE, Mar 31, 2014
An in situ aberration measurement method using a two dimensional (2D) phase-shift ring mask has b... more An in situ aberration measurement method using a two dimensional (2D) phase-shift ring mask has been proposed for lithographic projection lenses, which is more accurate and faster than AMAI-PCA method. The defocus of the aerial image of the 2D measurement mask is the main source of the measurement error of this method. In this paper, a defocus measurement method for the aberration measurement method is proposed, in which the residual of the principal component analysis process is used as the criterion. After the defocus is accurately measured, the most suitable linear relationship model, which plays a very important role in the aberration measurement method, can be determined. Simulations with the lithography simulator Dr. LiTHO demonstrated that the accuracy of the defocus measurement method is approximately 1nm. The aberration measurement method can detect 12 Zernike aberrations (Z5~Z16) with maximum systematic error of approximately 1mλ, when the suitable linear relationship model is used.
Proceedings of SPIE, Oct 6, 2011
The impact of edge profile roughness of the absorber lines on an optical photomask has been studi... more The impact of edge profile roughness of the absorber lines on an optical photomask has been studied by means of rigorous EMF simulation for the mask diffraction spectrum and subsequent imaging. Roughness has been modeled using two different approaches, a sinusoidal description and an algorithm known from literature based on Fourier transformation. The latter one allows one to arbitrarily create rough profiles and surfaces based on the three morphological parameters standard deviation σ, roughness exponent α, and correlation length ξ. A software interface for use of the generated profiles with the waveguide EMF solver of the Dr.LiTHO lithography simulation suite has been implemented. It was shown by means of image analysis and study of the resulting process windows that mask roughness is partially transferred to the aerial image. Isolated and dense features behave differently, leading i.a. to an iso-dense bias different to that of ideal lines. Process windows shift or even shrink in the presence of roughness, due to a certain smearing of the curves reducing the overall window. Tapered sidewalls can add to these effects in the same order of magnitude.
Proceedings of SPIE, Mar 11, 2010
ABSTRACT This paper aims at identifying appropriate bottom anti-reflective coatings (BARCs) for d... more ABSTRACT This paper aims at identifying appropriate bottom anti-reflective coatings (BARCs) for double patterning techniques such as Litho-Freeze-Litho-Etch (LFLE). A short introduction into the employed optimization methodology, including variables, figures of merit, models and optimization algorithms is given. A study on the impact of a refractive index modulation caused by the first lithographic step is presented. Several optimization surveys taking the index modulation into account are set forth, and the results are discussed. In addition to optimization procedures aiming at optimizing one litho step at a time, a co-optimization study for both litho steps is proposed. Finally, two multi-objective optimization procedures that allow for a post-optimization exploration and selection of optimum solutions are presented. Numerous solutions are discussed in terms of their anti-reflectance behavior and their manufacturing feasibility.
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Papers by Andreas Erdmann