Andreas Erdmann

Topography effects and wave aberrations in advanced PSM-technology

Both mask design and quality of the projection optics have a large impact on the performance of a phase shift mask (PSM). Topographic features on the reticle such as etched trenches in alternating PSM produce a spectrum of the diffracted light which differs from that one of an infinitely thin amplitude/phase object, as it is assumed in standard imaging algorithms. Many authors have investigated the consequences of this phenomenon with respect to aberration free imaging. However, the diffraction of light from topographic features implies also a modified interaction between the mask and wave aberrations of the projector. Rigorous simulation of the light diffraction from the mask is combined with standard lithography imaging algorithms to explore the interaction of topography effects and wave aberrations. For example, the nominal shift of a phase edge in the final resist profile can result both from topography effects and/or from odd-order wave aberrations such as tilt and coma. The sensitivity of typical lithographic parameters with respect to topography parameters and typical wave aberrations is investigated. PSM are also used for the monitoring of aberrations. Neglecting the topography of these phase objects may result in a misinterpretation of aberration phenomena. Consequences of rigorous diffraction defects for the design and interpretation of phase objects in aberration monitors will be discussed.

Toward automatic mask and source optimization for optical lithography

The application of resolution enhancement techniques pushes optical projection lithography close to its theoretical limit with a k1-factor of 0.25. For the imaging close to this limit the interaction between the mask and the shape of the illumination aperture gains increasing importance. By jointly optimizing the mask and the source low k1 images can be printed with process latitudes not achievable otherwise. This paper proposes a new optimization procedure for mask and source geometries in optical projection lithography. A general merit function is introduced, that evaluates the imaging performance of specific patterns over a certain focus range. It also takes certain technological aspects, that are defined by the manufacturability and inspectability criteria for the mask, into account. Automatic optimization of the mask and illumination parameters with a genetic algorithm identifies optimum imaging conditions without any additional a-priori knowledge about lithographic processes. Several examples demonstrate the potential of the proposed concept.

Dr.LiTHO : A Development and Research Lithography Simulator

This paper introduces Dr.LiTHO, a research and development oriented lithography simulation environment developed at Fraunhofer IISB to flexibly integrate our simulation models into one coherent platform. We propose a light-weight approach to a lithography simulation environment: The use of a scripting (batch) language as an integration platform. Out of the great variety of different scripting languages, Python proved superior in many ways: It exhibits a good-natured learning-curve, it is efficient, available on virtually any platform, and provides sophisticated integration mechanisms for existing programs. In this paper, we will describe the steps, required to provide Python bindings for existing programs and to finally generate an integrated simulation environment. In addition, we will give a short introduction into selected software design demands associated with the development of such a framework. We will especially focus on testing and (both technical and user-oriented) documentation issues. Dr.LiTHO Python files contain not only all simulation parameter settings but also the simulation flow, providing maximum flexibility. In addition to relatively simple batch jobs, repetitive tasks can be pooled in libraries. And as Python is a full-blown programming language, users can add virtually any functionality, which is especially useful in the scope of simulation studies or optimization tasks, that often require masses of evaluations. Furthermore, we will give a short overview of the numerous existing Python packages. Several examples demonstrate the feasibility and productiveness of integrating Python packages into custom Dr.LiTHO scripts.

Comparison of simulation approaches for chemically amplified resists

Lithography simulators have become a standard tool in industrial and governmental research and development departments. IN contrast to the modeling approaches for the optical system and for the lithographic performance of i- line resists, there is still no consensus on the modeling of chemically amplified resist (CAR). Existing models differ in the description of the kinetics and the diffusion phenomena during post exposure bake and in the specification of the development rate. A modeling approach was established, that combines the light induced generation of photoacid, in- and out-diffusion of acid or base components, a generalized deprotection kinetics, Fickian and non-Fickian diffusion of resist components and an arbitrary development rate model. Existing models such as the effective acid model and a standard deprotection model for CAR can be considered as special cases of the implemented model. To evaluate the importance of certain options of the model and of the model parameters we have evaluated the performance of the model by comparing simulated CD data and resists profiles with experimental data.

Rigorous diffraction analysis for future mask technology

Advanced lithographic techniques such as phase shift masks (PSM) and optical proximity correction (OPC) result in a more complex mask design and technology. With shrinking feature sizes, the topography of the mask becomes more and more important. We compare diffraction spectra, aerial images and resist profiles, which result for rigorous simulations were performed with a time-domain finite- difference algorithm. Consequences with respect to process linearity, mask error factor, printability of small assist features in OPC and phase defects in PSM will be discussed.

Validity of the Hopkins approximation in simulations of hyper-NA (NA>1) line-space structures for an attenuated PSM mask

In our previous work we have shown that as the NA of a lithographic projection system increases some of the simulation assumptions that are traditionally made - such as the so-called Hopkins assumption, i.e. the assumption that diffraction at the mask is independent of the angle of incidence of the illuminating light waves - break down, at least in some cases. Reliable simulation results will then only be obtained if this Hopkins assumption is eliminated, i.e. when the diffraction effect is reevaluated for each incident direction. The differences in the results between two such simulations, one using the Hopkins approach, the other with this assumption removed, have been demonstrated to be very significant in some case, but today there is no clear understanding when the removal of the Hopkins assumption is essential: a systematic study is not available. As simulations without the Hopkins approximation are significantly more time consuming than simulations done under the Hopkins assumption, a better understanding of which model can or must be used under which circumstances, would be of significant practical importance. The aim of this paper is to provide such a more systematic study for the case of 6% attenuated PSM with line/space structures targeting at a 45 nm resist linewidth for a variety of pitches, for a NA = 1.2 water immersion system. Standard lithographic metrics such as process windows will be used to compare the two simulation approaches. All this work will be done taking the mask topography and optical material parameters into account. As the polarization state of the mask-illumination will also greatly affect the imaging quality at hyper-NA, we will compare the results for different polarization states and illumination modes.

Fast near field simulation of optical and EUV masks using the waveguide method

A new and optimized waveguide based electromagnetic field solver for optical and EUV mask simulations is presented. After an introduction of the waveguide method, the convergence and speed optimization and the adaptation of the method to optical and EUV lithography mask simulations are presented. Additionally a model for the simulation of EUV multilayer defects and an optimized decomposition technique for three dimensional waveguide simulations enabling very fast computations as well as large mask area simulations is presented. Subsequently the capabilities of the new electromagnetic field solver are demonstrated exemplarily based on state-of-the-art optical and EUV masks.

Rigorous mask modeling using waveguide and FDTD methods: an assessment for typical hyper-NA imaging problems

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 terms of CPU-time and memory requirements, their capability to predict parameter dependencies and more global lithographic process characteristics such as process windows and through-pitch behavior.

Mask modeling in the low k1 and ultrahigh NA regime : Phase and polarization effects

This paper reviews state of the art mask modeling for optical lithography. Rigorous electromagnetic field (EMF) simu-lation of light diffraction from optical masks is compared to the traditional assumption of an infinitely thin mask, the so called Kirchhoff approach. Rigorous EMF simulation will be employed to analyze mask polarization phenomena which become important in the ultrahigh NA regime. Several important lithographic phenomena, which can be explained only with rigorous EMF simulation, are discussed. This includes the printability of small assist features, intensity imbalanc-ing for alternating PSM, and process window deformations. The paper concludes with a discussion on material issues and algorithmic extensions which will be necessary for an accurate modeling of future mask technology.

Efficient simulation of light diffraction from three-dimensional EUV masks using field decomposition techniques

As the opportunities for experimental studies are still limited, a predictive simulation os EUV lithography is very important for a better understanding of the technology. One of the most critical issues in modeling of EUV lithography is the description of the mask. Typical absorber heights in the range between 80 and 100nm are more than 5 times larger than the wavelength of the used EUV radiation. Therefore, it is virtually impossible to perform parameter studies for 3D EUV masks, such as arrays of contacts or posts, with nowadays standard computers by straightforward application of finite-difference time-domain (FDTD) algorithms, which are used for the rigorous electromagnetic field simulatin of optical masks. This paper discusses the application of field decompsition techniques for an efficient simulation of 3D EUV-masks with FDTD algorithms. Comparisons with full 3D simulations are used to evaluate the accuracy and the performance of the proposed approach. The application of the new QUASI 3D rigorous electromagnetic field simulation for EUV masks reduces memory requirements and computing time by a factor of at least 100. The implemented simulation appraohc is applied for a first exploration of mask induced imaging artifacts such as placement errors, telecentricity errors, Bossung asymmetries, and focus shifts for 3D EUV masks.