Inspired by many success stories of machine learning (ML) in a broad range of artificial intelligence (AI) applications, both industrial and academic researchers are now actively developing ML solutions for challenging problems in computational lithography. In this work, we explore the possibility of utilizing ML software and hardware platforms for mask synthesis applications. Specifically, we demonstrate a standalone mask synthesis flow that runs entirely on the TensorFlow ML platform with a reinforcement learning (RL) approach and GPU acceleration. We will describe the architecture of our ML mask synthesis framework that comprises separable and interchangeable components including neural network (NN)-based 3D mask, imaging and resist models. We will discuss the readiness of these components and present the proof-of-concept evaluation results of the proposed ML mask synthesis framework.
Strong resist shrinkage effects have been widely observed in resist profiles after negative tone development (NTD) and therefore must be taken into account in computational lithography applications. However, existing lithography simulation tools, especially those designed for full-chip applications, lack resist shrinkage modeling capabilities because they are not needed until only recently when NTD processes begin to replace the conventional positive tone development (PTD) processes where resist shrinkage effects are negligible. In this work we describe the development of a physical resist shrinkage (PRS) model for full-chip lithography simulations and present its accuracy evaluation against experimental data.
Extreme ultraviolet lithography (EUVL) uses a 13.5nm exposure wavelength, all-reflective projection optics, and a reflective mask under an oblique illumination with a chief ray angle of about 6 degrees to print device patterns. This imaging configuration leads to many challenges related to 3D mask topography. In order to accurately predict and correct these problems, it is important to use a 3D mask model in full-chip EUVL applications such as optical proximity correction (OPC) and verifications. In this work, a fast approximate 3D mask model developed previously for full-chip deep ultraviolet (DUV) applications is extended and greatly enhanced for EUV applications and its accuracy is evaluated against a rigorous 3D mask model.
3D lithography simulations capable of modeling 3D effects in all lithographic processes are becoming critical in OPC
and verification applications as semiconductor feature sizes continue to shrink. These effects include mask topography,
resist profile and wafer topography. In this work we present an efficient computational framework for full-chip 3D
lithography simulations. Since fast modeling of mask topography effects has been studied for many years and is a
relatively mature area, we will only briefly review a full-chip 3D mask model, Tachyon M3D, to highlight the
importance and modeling requirements for accurate prediction of best focus variations among different device features
induced by mask topography. We will focus our discussions on a full-chip 3D resist model, Tachyon R3D, its derivation
and simplification from a full physical resist model. The resulting model form is fully compatible with the existing 2D
resist model with added capabilities for resist profile and top loss prediction. A benchmark against the full physical
model will be presented as well. We will also describe the development of a full-chip 3D wafer topography model,
Tachyon W3D, and the preliminary results against rigorous simulations.
Best focus variation among different device features is one of the limiting factors to process window in semiconductor
photolithography applications. Accurate prediction of best focus variation in full-chip optical proximity correction
(OPC) and verifications is important in order to detect and mitigate the problem in design and post-design stages. In this
work, the origin of best focus variation is first studied analytically by analyzing a simple but important imaging problem.
It shows that phase difference between diffraction orders causes best focus shift. Then a rigorous simulation of mask
diffraction further shows that the phase difference induced by 3D mask topography is non-zero and is a function of
pattern and angle of incidence onto the mask. As a result, 3D mask models that can take into account oblique incidence
effects are required in order to accurately predict best focus variations in full-chip applications. Tachyon M3D is a fast
3D mask model developed for full-chip OPC and verifications. Its accuracy in predicting best focus variation against
measured wafer data is evaluated in this work. The results show very good correlation between M3D simulations and
As the industry drives to lower k1 imaging we commonly accept the use of higher NA imaging and advanced
illumination conditions. The advent of this technology shift has given rise to very exotic pupil spread functions that
have some areas of high thermal energy density creating new modeling and control challenges. Modern scanners are
equipped with advanced lens manipulators that introduce controlled adjustments of the lens elements to counteract the
lens aberrations existing in the system. However, there are some specific non-correctable aberration modes that are
detrimental to important structures. In this paper, we introduce a methodology for minimizing the impact of aberrations
for specific designs at hand. We employ computational lithography to analyze the design being imaged, and then devise
a lens manipulator control scheme aimed at optimizing the aberration level for the specific design. The optimization
scheme does not minimize the overall aberration, but directs the aberration control to optimize the imaging performance,
such as CD control or process window, for the target design. Through computational lithography, we can identify the
aberration modes that are most detrimental to the design, and also correlations between imaging responses of
independent aberration modes. Then an optimization algorithm is applied to determine how to use the lens manipulators
to drive the aberrations modes to levels that are best for the specified imaging performance metric achievable with the
tool. We show an example where this method is applied to an aggressive memory device imaged with an advanced ArF
scanner. We demonstrate with both simulation and experimental data that this application specific tool optimization
successfully compensated for the thermal induced aberrations dynamically, improving the imaging performance
consistently through the lot.
Application specific aberration as a result of localized heating of lens elements during exposure has become more
significant in recent years due to increasing low k1 applications. Modern scanners are equipped with sophisticated lens
manipulators that are optimized and controlled by scanner software in real time to reduce this aberration. Advanced lens
control options can even optimize lens manipulators to achieve better process window and overlay performance for a
given application. This is accomplished by including litho metrics as part of the lens optimization process. Litho metrics
refer to any lithographic properties of interest (i.e., CD variation, image shift, etc...) that are sensitive to lens aberrations.
But, there are challenges that prevent effective use of litho metrics in practice. There are often a large number of critical
device features that need monitoring and the associated litho metrics (e.g., CD) generally show strong non-linear
response to Zernikes. These issues greatly complicate the lens control algorithm, making real-time lens optimization
difficult. We have developed a computational method to address these issues. It transforms the complex physical litho
metrics into a compact set of linearized "virtual" litho metrics, ranked by their importance to process window. These
new litho metrics can be readily used by the existing scanner software for lens optimization. Both simulations and
experiments showed that the litho metrics generated by this method improved aberration control.
Optical lithography has had great success in recent history in utilizing the most advanced optical technology to create
NA=1.35 immersion lenses. These lenses have aberration levels at or below the 5m level. Much of this is due to
advancements in lens design, materials, and aspheric polishing techniques. Now that the lenses are nearly "perfect",
more attention is being given to the illuminator and its performance. This paper examines the fundamental metrics that
are used to analyze the illumination source shape as it pertains to the optical proximity effect (OPE). It is found that the
more traditional metric of partial coherence, σ, is often not sufficient to explain through pitch CD performance. Metrics
are introduced to compare multiple sources and compared to their correlation to OPE with respect to a reference. A new
parametric model for annular illumination is introduced and shown to correlate within an RMS=0.03nm of the OPE data.
The accuracy of a fast 3D thick mask model is evaluated for 6% AttPSM having sub-resolution assist features (SRAF).
The main features and SRAFs are designed to print 40nm lines or spaces on wafer (k1~0.28) through pitch from 100nm
to 500nm. The resulting optimum SRAF sizes vary from 10nm to 48nm depending on the main feature pitch, mask tone
and illuminator shape. The model accuracy is evaluated on both main feature CDs and SRAF side lobe intensities by
comparing with a rigorous model. The fast 3D model shows improvements in both areas over thin mask model,
particularly in SRAF printability prediction.
A new framework has been developed to model 3D thick mask effects for full-chip OPC and verifications. In addition to
electromagnetic (EM) scattering effects, the new model also takes into account the non-Hopkins oblique incidence
effects commonly found in real lithography systems but missing in prior arts. Evaluations against rigorous simulations
and experimental data showed the new model provides improved accuracy, compared to both the thin-mask model and
the thick-mask model based on Hopkins treatment of oblique incidence.
Model based OPC is critical for mask design employing current design rules. Models based on the aerial image assume resist response will generally follow behavior predicted by diffractive optics, however, some classes of resist introduce non-optical resist response. It is critical to understand the proximity behavior of these resists in order to accurately manufacture lithographic masks. In this paper, we present modeling and experimental results for a class of resist systems exhibiting a strong non-optical resist response; reversed bias in nested versus isolated space pattern dimension. The behavior is ascribed to a secondary source of proximity originating from heat absorbed during PEB within the exposed region, which produces a non-uniform, pattern dependent, effective PEB temperature. A continuum PEB model employing a combined mass and energy balance is developed as well as experimental methods to determine the parameters in the model. The resulting calibrated model reproduces the degree of proximity bias measured with SEM for a variety of process conditions. Both proximity correction and characterization of k1 performance for the resist system are discussed.