ITRS_modeling_lithography

Support from Modeling and Simulationis critical both to push the limits of traditional optical and extremeultraviolet (EUV) lithography and to assess new Next Generation Lithographytechnologies. Furthermore, an intimate link between equipment-scale and feature-scalesimulation is required for state-of-the-art lithography simulation. Equipmentscale effects often require modeling with random variables with user-defined oruser-measured probability distributions. While calculation of lithographicimage formation relies on well-established physical models, thephysical/chemical understanding of resist processes, particularly forchemically amplified resists, is far less advanced. Resist models are typicallysemi-empirical, and they require fitting and calibration with experimentaldata. 

The key requirements for simulationof optical imaging are accuracy, speed of computation, and the capability tomodel the effects of non-ideal masks, non-ideal lenses, multilayer resists andnon-planar substrates. With mask feature sizes at 4x reduction during imagingbecoming comparable with the wavelength, polarization effects and the exactmask topography need to be included. Problem-specific algorithms andimplementations are needed to deal with the “tricks” used when pushing opticallithography to the limits, such as off-axis illumination, complicated maskgeometries including phase-shifting, optical proximity correction (OPC), anddouble or even multiple exposure/patterning. Especially the latter techniquerequires the rigorous treatment of wafer topography in the simulation. Toolsmust be predictive and efficient enough to support source mask optimization(SMO) and inverse lithography (IL).

Non-idealities of the optical system usedare getting more and more critical and must be appropriately addressed insimulation. The influence of defects on the mask and on the wafer is becomingmore and more important and requires appropriate simulation capabilitiesespecially for the identification of “killer defects”. 

New techniques used in EUV or future nextgeneration lithography (NGL) techniques, such as replacement of lenses bymultilayer mirrors and the use of reflecting masks EUV lithography must beappropriately modeled and included in the simulation programs. Mask pattern generatorsand some NGL options - including proximity electron lithography and masklesslithography - involve imaging with electrons. Simulations of stochastic spacecharge effects, geometrical aberrations and electron optical lens designperformance using either magnetic or electrostatic lens elements are needed.Direct Self Assembly DSA which is being driven by ERM is another interestingnear-term option, which needs to be addressed by simulation. Support fromsimulation for narrowing down the options for future Next GenerationLithography has been and will continue to be important.

A specific challenge for lithographyModeling and Simulation is to accurately predict the behavior ofstate-of-the-art photoresists over a wide range of imaging and process conditions.For these, better physical/chemical models must be developed to predictthree-dimensional resist geometries after development and process windows,including effects such as Line-Edge Roughness (LER) and Line-Width Roughness(LWR). Better calibration techniques are required both for model developmentand for customizing models implemented in commercial tools to appropriatelydescribe the photoresists in question. Calibration obviously depends on thequality of input data, e.g., CD measurements. Therefore, it is necessary tobetter understand and estimate measurement errors. Systematic errors should bedealt with by models of the measurement tools, for example, CD-SEMs. With thegrowing importance of LWR and LER, lithography simulation needs to contributeto the assessment of their influence on device and interconnect performance(LER) and variability (LWR). Since here not the roughness of the resistpatterns is important but that of the etched structures, intimate coupling withetching simulation is indispensable. Simulations of etching are important tounderstand the relationship between 3D edge roughness and profiles in resistfeatures and the resulting roughness and profiles in etched gates, contacts ortrenches. Intimate links with etching simulation must also be established alsoto predict the geometry of non-ideal mask edges which are frequently result ofthe mask-making lithography steps. Generally, many challenges are associatedwith variability control, not just scaling. Variability control not only mustkeep up with dimensional scaling, but often needs to improve even faster. Tofurther extend optical lithography, new practices are required to bettercomprehend the increasing variation of critical dimensions as a fraction of thefeature size in the design process. These practices are usually referred to as“design for manufacturing” (DFM). DFM allow designers to account formanufacturing variations during circuit design optimization, enabling the ICfabrication process to be optimized to provide the highest performance at aminimal cost. Ultimately, the designer could optimize the circuit withknowledge of all physical variations in the fabrication process and theirstatistical distribution. Starting with optical proximity correction to put nominalimages on target, mask patterns are now designed to improve depth of focus,increase contrast, and reduce MEEF. The scope of computational lithography alsoincludes illuminator design, which has expanded as exposure systems with moreversatile illuminators have become available.

A specific requirement for lithographyModeling and Simulation is the need for very efficient simulation tools whichallow the simulation of large areas and/or the conduction of simulation studiesfor a multitude of variations of physical parameters or layouts to supportgrowing design for manufacturing (DFM) needs. In fact, lithographic simulationsof fullchip layouts are now needed to verify OPC and phase assignment data toavoid expensive masks being fabricated with errors or with corrections havingonly marginal performance. These simulations must be reasonably accurate andexecute at high speed to evaluate the entire layout in a reasonable amount oftime. Furthermore, simulation must contribute to the increased integration betweendesign, modeling, lithographic resolution enhancement techniques and extensivemetrology needed to maintain expected circuit performance.

Besides models ofimage formation and resist profile generation in the lithography process,mechanical models are also critical for designing lithography tools. Refinementand application of finite element methods is important for assuring exposuretools, masks and wafers remain stable enough to meet demanding overlaytolerances. Static and dynamic models of lens mounting stability, stagestability and also aspects of exposure tool hardware design are critical.Static and dynamic mechanical models are also critical for designing adequatemounting methods for masks and wafers to maintain desired position under high stageacceleration values and to maintain desired flatness. Equilibrium andnon-equilibrium models of thermal effects are also essential for exposure tooldesign, especially for modeling heating of the immersion fluid in immersionlithography and its effect on distortion and aberrations. Models of fluid flowfor immersion have also been essential in designing fluid delivery systems thatminimize immersion-specific defect formation. (Refer to the Lithography chapter.)