This paper discusses the CD Bossung tilt phenomena in low-k1 lithography using interference harmonics and rigorous
EM spectrum analysis. Interference harmonics analysis is introduced to explain the interaction of diffraction orders in the
focal region leading to this abnormal CD behavior. This method decomposes the vector image formula into a
superposition of cosine components to describe the interference of diffraction orders. The symmetry properties of
components of an optical projection system were investigated to find out three potential sources for the asymmetric
Bossung behavior, namely mask 3D (M3D) effect, lens aberration, and wafer reflectivity. Under good lens aberration
and substrate reflectivity controls, the M3D effect accounts for most of the CD Bossung tilt. A rigorous EM mask
spectral analysis was performed to reveal the impact of mask topography on the near-field intensity of mask transmission
and the far-field image formation. From the analysis, the asymmetric phase distribution in the mask spectrum is the root
cause for CD Bossung tilt. Using both the interference harmonics and the rigorous EM spectrum analysis, the effect of
various resolution enhancement techniques (RET) to the Bossung tilt is also studied to find the best RET combination for
M3D immunity. In addition, a pupil optimization algorithm based on these two analyses is proposed to generate the
phase compensation map for M3D effect counteraction.
KEYWORDS: Electron beam lithography, Monte Carlo methods, Line edge roughness, Computer simulations, Critical dimension metrology, Transistors, Optical simulations, Diffusion, Optimization (mathematics), Point spread functions
Low-energy electron beam lithography is one of the promising next-generation lithography technology solutions for the 21-nm half-pitch node and beyond because of fewer proximity effects, higher resist sensitivity, and less substrate damage compared with high-energy electron beam lithography. To achieve high-throughput manufacturing, low-energy electron beam lithography systems with writing parameters of larger beam size, larger grid size, and lower dosage are preferred. However, electron shot noise can significantly increase critical dimension deviation and line edge roughness. Its influence on patterning prediction accuracy becomes nonnegligible. To effectively maximize throughput while meeting patterning fidelity requirements according to the International Technology Roadmap for Semiconductors, a new method is proposed in this work that utilizes a new patterning prediction algorithm to rigorously characterize the patterning variability caused by the shot noise and a mathematical optimization algorithm to determine optimal writing parameters. The new patterning prediction algorithm can achieve a proper trade-off between computational effort and patterning prediction accuracy. Effectiveness of the new method is demonstrated on a static random-access memory circuit. The corresponding electrical performance is analyzed by using a gate-slicing technique and publicly available transistor models. Numerical results show that a significant improvement in the static noise margin can be achieved.
KEYWORDS: Calibration, Line edge roughness, Scatterometry, Point spread functions, Process modeling, Scanning electron microscopy, Metrology, Scattering, Semiconducting wafers, Cadmium
Scatterometry has been proven to be effective in critical dimension (CD) and sidewall angle (SWA) measurements with
good precision and accuracy. In order to study the effectiveness of scatterometry measurement of line edge roughness
(LER), calibration samples with known LER have to be fabricated precisely. The relationship between ITRS LER
specifications and the feature dimension design of the LER calibration samples is discussed. Electron-beam-direct-write
lithography (EBDWL) has been widely used in nanoscale fabrication and is a natural selection for fabricating the
designed calibration samples. With the increasingly demanding requirement of lithography resolution in ITRS, the
corresponding LER feature of calibration samples becomes more and more challenging to fabricate, even for EBDWL.
Proximity effects in EBDWL due to electron scattering can cause significant distortion of fabricated patterns from
designed layouts. Model-based proximity effect correction (MBPEC) is an enhancement method for EBDWL to
precisely define fine resist features. The effectiveness of MBPEC depends on the availability of accurate electron-beam
proximity effect models, which are usually described by point spread functions (PSFs). In this work, a PSF in a double-
Gaussian function form at a 50 kV accelerating voltage, an effective beam size, and a development threshold energy
level of the resist are calibrated with EBDWL exposure tests. Preliminary MBPEC results indicate its effectiveness in
calibration sample fabrication.
Electron-beam-direct-write lithography has been considered a candidate next-generation technique for achieving high resolution. An accurate point spread function (PSF) is essential for reliable patterning prediction and proximity-effects correction. It can be derived via an effective parametric PSF calibration methodology, typically involving the fitting of the absorbed energy distribution (AED) from an electron-scattering simulation. However, the existing parametric PSF calibration methodology does not employ a systematic approach to obtain a new PSF form that is both compact and accurate when conventional PSF forms are not satisfactory. Only the AED fitting quality (rather than its patterning-prediction quality) is considered during the conventional calibration methodology. It also lacks a process to consider whether the predicted deviation (as simulated using the chosen PSF form) is satisfactory. This paper proposes a new parametric PSF calibration methodology to systematically obtain a PSF form consisting of the smallest number of terms, with a better combination of basis functions and that optimizes pattern accuracy. The effectiveness of using the new methodology is demonstrated in terms of fitting accuracy, patterning-prediction accuracy, and patterning sensitivity.
KEYWORDS: Sensors, Monte Carlo methods, Electron beams, Signal detection, Lithography, Electron beam lithography, Detector arrays, Optical simulations, Semiconducting wafers, Silicon
Multiple-electron-beam-direct-write lithography is one of the promising candidates for next-generation lithography
because of its high resolution and ability of maskless operation. In order to achieve the throughput requirement for highvolume
manufacturing, miniaturized electro-optics elements are utilized in order to drive massively parallel beams
simultaneously. Electron beam drift problems can become quite serious in multiple-beam systems. Periodic recalibration
with reference markers on the wafer has been utilized in single-beam systems to achieve beam placement accuracy. This
technique becomes impractical with multiple beams. In this work, architecture of a two dimensional beam position
monitor system for multiple-electron-beam lithography is proposed. It consists of an array of miniaturized electron
detectors placed above the wafer to detect backscattered electrons. The relation between beam drift and distribution of
backscattered-electron trajectories is simulated by an in-house Monte Carlo electron-scattering simulator. Simulation
results indicate that electron beam drift may be effectively estimated from output signals of detector array with some
array signal processing to account for cross-coupling effects between beams.
KEYWORDS: Monte Carlo methods, Scattering, Electron beam lithography, Silicon, Data modeling, Polymethylmethacrylate, Laser scattering, Direct write lithography, Computer simulations, Backscatter
Accelerating voltage as low as 5 kV for operation of the electron-beam micro-columns as well as solving the
throughput problem is being considered for high-throughput direct-write lithography for the 22-nm half-pitch node and
beyond. The development of efficient proximity effect correction (PEC) techniques at low-voltage is essential to the
overall technology. For realization of this approach, a thorough understanding of electron scattering in solids, as well as
precise data for fitting energy intensity distribution in the resist are needed. Although electron scattering has been
intensively studied, we found that the conventional gradient based curve-fitting algorithms, merit functions, and
performance index (PI) of the quality of the fit were not a well posed procedure from simulation results. Therefore, we
proposed a new fitting procedure adopting a direct search fitting algorithm with a novel merit function. This procedure
can effectively mitigate the difficulty of conventional gradient based curve-fitting algorithm. It is less sensitive to the
choice of the trial parameters. It also avoids numerical problems and reduces fitting errors. We also proposed a new PI to
better describe the quality of the fit than the conventional chi-square PI. An interesting result from applying the proposed
procedure showed that the expression of absorbed electron energy density in 5keV cannot be well represented by
conventional multi-Gaussian models. Preliminary simulation shows that a combination of a single Gaussian and double
exponential functions can better represent low-voltage electron scattering.
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