EUV lithography (EUVL) is a candidate technology for patterning of ever shrinking feature

sizes in integrated circuits. There are several challenges to high volume manufacturing

of devices using EUVL in a cost-effective manner, which include limited source power, mask

defects and non-idealities in the photoresist, the imaging medium. Focus of this thesis is on

photoresists. Specifically, influence of absorption shot noise on the final LER was studied

experimentally through comparative analysis of LER obtained with EUV (92 eV photons)

and 100 keV e-beam lithography. The key contribution here is that the lithography experiments

were performed with matched imaging conditions between EUV and e-beam, which

allowed for a fair comparison between the LER values measured using the two patterning

technologies. In scenarios where the e-beam spatial resolution was better than that for EUV,

the technique of gray-scale e-beam lithography was experimentally demonstrated to result in

closely matched image gradients between e-beam and EUV patterning. It was shown that the

measurable parameter known as the exposure latitude is a good parameter to test whether

the aerial images between two experiments have identical gradients for idential materials and

processing conditions.

With matched imaging conditions, resist materials and processing conditions, lithographic

data showed that the incident flux needed to pattern 50 nm half-pitch lines and

spaces for a leading chemically amplified resist was 10.7 photons/nm2 for 92 eV photons,

and 4.44 electrons/nm2 for 100 keV electrons. Measurements of absorption of 100 keV electrons

estimated through an EELS measurement with 120 keV beam showed that despite having

access to core levels in the material (e.g., 284 eV edge in carbon), these electrons mostly just

excite the energy levels less than 100 eV in the resist, with a mean deposited energy of 35 eV.

Results showed that the probability of an energy loss event in a 45 nm thick resist film with

100 keV electrons was 0.4, about 2.35x larger than that for EUV (0.17). By combining the

incident flux and the absorption probabilities, the absorption flux was found to be similar

between the two patterning technologies. A possible reason is that either the secondary

electron spectra created in the material through ionization events are similar for EUV and 100 keV e-beam exposures, or that there are only small differences which ultimately do not

matter from the standpoint of acid generation statistics. With matched imaging conditions

and matched absorption density, the mean LER for e-beam was found to be larger by about

1 nm.

Influence of various material contributors in determining the resist LER was also studied

from a modeling standpoint. Reaction/diffusion parameters in a stochastic resist model were

calibrated to resist contrast curve data and line/space patterns. With the best fit reaction

and diffusion parameters, the contributions of absorption shot noise, acid generation statistics

and the base counting statistics on the resist LER were determined. Shot noise was found

to account for 46% of the total LER, while the acid generation and base loading statistics

were found to account for 22% and 32% of the LER respectively.

Interactions of low energy electrons in EUV resists were studied from both experimental

and modeling standpoint. Low energy (< 92 eV) electrons are primarily responsible for

initiating chemistry that leads to image formation in EUV resists. Thus key to controlling

EUV exposure efficiency is understanding low energy electron radiation chemistry efficiency

as a function of electron energy. Thickness versus exposure dose measurements were made

with incident electron energies ranging between 29 eV and 91 eV. Thickness removed was

much larger than the average secondary electron range and was bake temperature dependent

and thus is a useful indicator of de-protection blur introduced by the bake process. The

dissolution volume per eV deposited energy was nearly similar for 29 eV to 91 eV energies,

although there is some indication that incident electrons with lower energies are slightly

more effective at causing chemistry. The volume removed per eV was about 0.1 nm3 per 1

nm2 area.

The well-known dielectric model for inelastic scattering was used to develop a stochastic

model for simulating trajectories traversed by secondary electrons in the resist. Electron

energy loss spectroscopy (EELS) was used to measure the dielectric function for a leading

chemically amplified resist. Analytical expressions for the Mermin dielectric functions which

account for energy and momentum transfer were then fit to the measurement to build a

complete dielectric model for the resist. Stochastic simulations were then performed with

the scattering parameters determined by the dielectric model to calculate energy deposition

and acid generation statistics. These results were used to quantify the net acid generation

blur, which was found to be between 1.8 nm and 2 nm from the point of origin of the electrons.

The radial distribution of acid generation sites was fit using a Rayleigh distribution and the

best fit sigma parameters in the distributions were found to range between 1.2 nm at 30 eV and

1.41 nm at 91 eV. The net acid yield calculated by the simulator was found to be 1.6 for an

80 eV electron.

This dissertation presents a full framework for modeling transmission effects due to three-dimensional mask topography in optical lithography from solving Maxwell's equations using rigorous simulation through fast-CAD for full chip level aerial image quality characterization in optical projection printing. As the semiconductor industry advances to the 22nm technology node where features are sub-wavelength, lithography imaging must be accurate to the nanometer. Non-ideal transmission caused by scattering off of mask edges has become an increasingly important source of inaccuracies in lithography modeling. Here mask edge effects are treated in two modules: modeling the near field scattering phenomena and then moving that information into fast-CAD first cut accurate simulation.

Phase errors induced by mask edges lead to an asymmetric behavior through focus, which when combined with polarization dependent effects lead to significant loss in the process window. Phase shifting masks, leveraging image benefits of 0 degree and 180 degree transmission, further complicate the interplay of partial signal delay and the resulting complex phase errors. It is shown that for even conservative imaging scenarios up to 40% of the focus latitude is lost.

Two methods for characterizing this scattering induced by mask edges are introduced.

The first is an experimental approach, which uses gratings to characterize the polarization dependent magnitude of these errors as might be utilized in an inexpensive mask monitoring apparatus. The second method examines the direct near field behavior with simulation, leading to more accurate phase information as well as guidelines for edge-to-edge cross-talk. A MoSi attenuating 180 degree phase shift mask was characterized in detail, with boundary layer values of about 20 nm (1/10 wavelengths) in mask dimensions even for high off-axis illumination. Non-attenuating chromeless masks and complicated mask stacks such as TaSiO2 showed significant electromagnetic errors as high as 1/4 wavelengths, suggesting that they are not viable for advanced lithography applications. Further, a study of a hypothetical thin phase shifting mask showed that the phase error effects is inherent to the use of neighboring phase wells, and cannot be remedied by material improvements.

The most significant contribution of this dissertation is the development of Source-Pupil Kernel Convolution with Pattern Matching (SP-KCPM) that connects the information gained from boundary layer modeling to fast-CAD pattern matching tools, achieving a 10^4 speedup compared to conventional imaging. SP-KCPM is built on a computational engine developed by Frank Gennari that optimizes the process of pixel based multiplication of a target pattern across large layouts. The degree of similarity is then used in SP-KCPM to estimate aerial image values. Full complex interactions are included, and along with a pupil-based framework enables more general imaging by including additional phenomena such as defocus, zernike aberrations, measured aberrations, and potentially resist and polarization effects without needing separate kernels or algebraic perturbations. Since the pupil calculation is generated automatically and can combine many effects, the need for deriving and confounding multiple physical phenomena has been eliminated. Proximity effects between features are also accounted for, removing the need for a prior image calculation or restrictions to a specific image contour. A new coherent source model combined with source splitting is used to generalize the aerial image quality assessment to distributed off-axis sources utilized in advanced resolution enhancement techniques.

This distributed source-pupil based convolution method has guaranteed impressive accuracy well beyond that historically reported for kernel convolution pattern matching methods at full chip speeds, thus enabling many new applications. Careful implementation considerations such as pattern size, gridding, normalization, and source clustering guided the development of a very accurate system. For various sources, dipole, annular, quad, and pixelated optimized sources, R^2 correlation is shown to be above 0.99. Additionally, effects of defocus, zernike aberrations, background aberrations, and asymmetric sources have all been shown to be accurate.

As an example of new applications, SP-KCPM was tested on highly pixelated sources used in source-mask-optimization, and accuracy of R^2 = 0.99 was achieved on general layouts by splitting the source into 12 regions. This capability is used to demonstrate the ability to make decisions between source distributions and mask blanks. Realtime tracking of mask changes facilitates further applicability in optical proximity correction is sufficiently fact for interoperability as part of an optimization scheme. Hotspot detection is used to quickly make decisions between sources or mask types by assessing the impact an optimized source solution over a larger non-optimized layout region. Real time tracking of mask changes opens the door for SP-KCPM to be used for optimization techniques and optical proximity correction (OPC). SP-KCPM is shown to be a general tool, useful wherever fast imaging is at a premium with applicability in many forms of optical imaging such as inspection and character recognition, in addition to standard projection printing.

Electronic monitoring utilizing process-specific Ring Oscillators (RO) is explored as a means of identifying, quantifying, and modeling sources of variation in circuit performance due to manufacturing and layout design parameters. This dissertation contains the first measured silicon results for the utilization of parameter-specific modification of ring oscillator layouts to electronically monitor particular process variation. Design and testing for this work were made possible through the Berkeley Wireless Research Center. The working circuits were fabricated by ST Micro in a 45 nm fabrication process that was under development.

The design was based on a process design kit provided by ST Micro. The lithography simulation was carried out using generic models in Mentor Graphics Calibre. Five systematic process effects were considered: etch, focus, misalignment, and capping layer and Shallow Trench Isolation (STI) stress. In all cases, inverter layouts were modified in order to increase sensitivity to a particular parameter within design rule constraints. For monitoring etch, the presence or absence of adjacent dummy gates and pre-correction for residual lithographic effects were used. For monitoring gate focus, spillover functions and Pattern Matching were used as an initial guide to place added surroundings to the gate; this was followed by systematic optimization via Mentor Graphics Calibre simulations. A focus sensitivity of 1.5 times that of a dense gate was achieved. For monitoring gate-to-active misalignment, a set of 5 pre-programmed offsets on an `H-shaped diffusion' was designed. The RO frequency versus offset relationship in design showed a parabolic shape with a speed up of 3.2% for 15nm misalignment. The capping layer and lateral STI stress monitors were designed based on changes in the lateral size of the source and drain, including those of asymmetrical source/drain areas.

Seventeen chips were received, packaged, and automatically tested. The measured range of the across-wafer variation was 11.1% for control-case RO with minimum sized gate area. For a given monitor on a typical chip, the variation among the 36 RO instantiations normalized to its mean is 0.2-0.3 %, with the larger value occurring for the smaller gate areas. When these values were multiplied by the square root of the product of 36 instances time 26 transistors per RO, the average threshold slope (AVT) of 2.3mV/um was obtained in an equivalent Pelgrom model.

The measured RO frequency sensitivity to gate focus monitors shows that they are about 4% slower than the control ROs. This decrease is attributed to parasitic effects as well as the non-uniform `hour-glass' shape produced at the top and bottom of the gate from the horizontal extensions used to increase focus sensitivity. The pre-programmed gate-to-active misalignment monitors show a 2-4 nm overlay error for 17 chips. The fact that the experimental measurements are less sensitive than predicted during the design stage is in part attributed to the fact that the wafer was run under unusually good control without any programmed treatments such as defocus. This observation is supported by the fact that the measured range of RO frequency was typically centered and 1/6-1/4th of the SS-FF guard band. The unanticipated requirement to apply strong OPC techniques with scatter-bars to the monitor designs in order to guarantee that they would not impact product yield also resulted in considerable sensitivity loss.

The Nitride Contact Etch Stop Liner (CESL) strain-induced monitors show a ring oscillator frequency increase of 5.3% and 13.9% for 1.8X and long length source/drain diffusion (LOD) respectively as compared to minimum LOD, after the normalization of raw data to simulation data so as to correct for parasitic effects. This increase is due to increased CESL-induced strain for large LOD. For the same LOD, asymmetrical designs show a 3% ring oscillator frequency increase for larger source LOD than that of larger drain LOD, indicating transistor injection velocity as well as mobility is important.

The random variation of RO circuit performance for a given layout monitor within a chip is examined for 3 sources of variations: changes in gate length (L), gate oxide thickness (Tox), and channel doping (Nch). The strategy here is to make a linear approximation of the measured RO frequency sensitivity to these 3 parameters under 5 distinct combinations of operating voltages and temperatures using the 45nm PDK BSIM4/PSP models. The strategy is implemented using least mean square (LMS) analysis. For all of the blocks, the LMS results indicate that the source of random within-chip variation is dominated by random dopant fluctuations in comparison with changes in L and Tox.

This dissertation extends fast-CAD kernel convolution methods for the identification of unintended effects in optical lithography, including OPC-induced sensitivities, high-NA and polarization vector effects. A more accurate through-focus physical model is incorporated, and the application of layout decomposition guidance for double patterning is demonstrated. All layout regions react differently to lithographic processes such as aberrations, and the vulnerabilities are non-intuitive and hard to capture with design rules. The pattern matcher is a fast tool, developed by Gennari and Neureuther, for quickly scanning layouts to find vulnerabilities to unintended effects of lithographic processes. Kernel convolutions are performed between Maximum Lateral Test Patterns (MLTPs) and mask layouts, and are over a factor of 10⁴ times faster than rigorous simulation. Challenges faced in pattern matching extensions include MLTP derivation, edge movement prediction, defocus accuracy improvement, and integration of image effect estimation into real-time guidance for layout decomposition.

As motivation for why variability and yield are important, a study is presented in which a probabilistic distribution of transistor Critical Dimensions (CD) is generated given a focus-exposure joint distribution. An interpolation model is used to generate CD response surfaces, producing a fast method for the analysis of average CD variation for each transistor, the spread of individual variations, the OPC performance, the Across Chip Linewidth Variation (ACLV), and yield distribution. This study motivates the importance of understanding the variability in a layout; the remainder of the dissertation demonstrates how pattern matching can provide a fast approximation to variability due to lithographic effects.

MLTPs, derived as the inverse Fourier Transform of the Zernike polynomials, are the theoretically most sensitive patterns to lens aberrations. As well as being used as input to the pattern matcher, MLTPs can also be etched onto a mask to function as aberration monitors. However, MLTPs are inherently very costly and unfriendly for mask manufacturing, due to round edges and touching phases. Both a mask-friendly handmade pattern and an automated method of monitor modification are presented. The handmade pattern retains 68% of its sensitivity to defocus and orthogonality to other aberrations, and the automatically generated pattern passes all DRC checks with only minimal modifications.

Use of the pattern matcher on pre-OPC layouts admits the identification of problematic hot-spots earlier in the design flow. Several studies are presented on the effects of different OPC algorithms on match factors. In most cases, match factors do not vary significantly between the pre-OPC layout and the post-OPC layout, and the pre-OPC match factor is a good indicator for the sensitivity of the post-OPC layout area. However, in some circumstances, especially when SRAFs are present, the pre- and post-OPC match factors can vary by a larger amount. It is shown that defocus and proximity sensitivities occur in different locations on a layout, and if OPC targets the best-case simulation, then it is possible for OPC to worsen sensitivities to aberrations. As a consequence, pattern matching should be used on post-OPC layouts to check for any created sensitivities.

Extensions of the pattern matcher are presented for high-NA and polarization vulnerabilities. This involves the generation of three to five match patterns for either on-axis or off-axis illumination, with a vulnerability score being calculated as a weighted sum of the match factors. The patterns are tested against simulation, and found to be good predictors of vulnerability to high-NA and polarization vector effects. High-NA and polarization vector effects are significant, causing intensity changes of 40% or 10% respectively for the on-axis case, and 8% for the off-axis case.

The accuracy of the pattern matcher is evaluated, and improved. A method for predicting edge movement through coma, rather than just change in intensity, takes the image slope into account and improves the R² from 0.73 to 0.95. A major contribution of this dissertation is the improvement of the pattern matching model for defocus. A quadratic model for defocus is presented, using both the Optical Path Difference (OPD) and OPD², rather than just the linear term. OPD² expands to yield two new patterns, Z₀ and Z₈, to be used in addition with Z₃, which is derived from the OPD term. Using the three match patterns, prediction of the change in intensity through focus improves from completely non-predictive to an R² value of 0.92. Results show that the Z₃, pattern and a combined Z₀ and Z₈, pattern predict change in intensity through defocus at line ends with an R² of 0.96, indicating that two match factors with algebraic weighting factors are likely possible. These results are of great importance, as defocus is not a small aberration, reaching typical values of nearly one Rayleigh unit, and the ability to find defocus-induced hot-spots is of practical interest.

Double patterning is identified as an emerging technique that benefits from the application of pattern matching. In double patterning, a layout is split into two masks, each mask being exposed separately, effectively doubling the pitch. A process flow is presented showing that pattern matching can add value both within the double patterning decomposition algorithm, and also on the post-decomposition layout. Pattern matching is tested on post-decomposition layouts, showing that in one particular case using complementary dipole illumination, the match factors for coma are increased significantly on the post-decomposition layout. In another case for annular illumination, introducing an extra split is shown to reduce the variability through coma, and reduces the match factor by 55%. Furthermore, when splitting an H-structure, a number of different splits are scanned by the pattern matcher, and the split with the lowest intensity change through defocus (which was two thirds smaller than the largest change) is correctly identified. These examples show that the pattern matcher is an appropriate tool for double patterning, that can quickly provide a measure of intensity change through defocus during the layout decomposition process.

This dissertation describes the development and application of a new simulator, RADICAL, which can accurately simulate the electromagnetic interaction in extreme ultraviolet (EUV) lithography at a wavelength of 13.5nm between the mask absorber features and a buried multilayer defect three orders of magnitude faster than rigorous methods. RADICAL achieves this performance by using simulation and modeling methods designed specifically for the individual EUV mask components simulated. The nonplanar nature of a multilayer coated buried defect can be simulated using a ray tracing method developed by Michael Lam, or the faster advanced single surface approximation (SSA) for shorter defects with more uniform layers below the mask surface, and the absorber is modeled using a propagated thin mask model which efficiently accounts for the thickness of the absorber material. The multilayer and absorber simulation results are linked by a Fourier transform which converts the electric field output by one simulator into a set of plane waves for the next.

As a new form of projection lithography technology, EUV is fundamentally different than current technologies and therefore requires new methods for mask analysis, inspection and compensation. At the 13.5nm wavelength, all materials have a refractive index of around unity and are absorptive. This means that EUV masks must be reflective multilayers. Understanding the electromagnetic response of these new masks, specifically the effects of multilayer defects requires new simulation methods, such as RADICAL.

The accuracy and speed of RADICAL has been verified by comparisons with rigorous finite difference time domain (FDTD) simulations, rigorous waveguide method simulations, and actinic inspection experiments provided by Lawrence Berkeley National Laboratory (LBNL) and Intel. RADICAL matches the critical dimension (CD) predicted by FDTD within 1nm for defects up to 2.5nm tall on the multilayer surface. It matches actinic inspection results, within the error of the experiment, for defects up to 6.5nm tall on the surface. This accuracy is acceptable because the EUV defects expected in production lithography are expected be 2nm tall or less. RADICAL is typically about 1,000 times faster than FDTD for a single simulation of a two-dimensional absorber pattern. But, RADICAL's modular design allows the re-use of multilayer simulation results so subsequent simulations of different patterns over the same defect geometry take a small fraction of the time of the first simulation.

RADICAL has been applied to many important issues in EUV lithography. It was used to advance the understanding of isolated defects by showing that they are primarily phase defects, because they cause an inversion in aerial image intensity through focus, but cannot simply be modeled by a thin mask defect with a uniform phase. This means EUV buried defects must be treated differently than the phase defects encountered in conventional optical lithography masks.

Experimental images of isolated defects were used to extract large aberrations from the state of the art Actinic Inspection Tool (AIT) at LBNL. This novel method for aberration extraction required only the comparison of the center intensity of an isolated defect image through focus between RADICAL and the AIT images. This work resulted in a deeper understanding of the AIT tool, which led to improvements of the tool by the team at LBNL, which have benefited the entire industry.

The critical issue of the printability of buried defects near features and its dependence on illumination in future production tools is addressed by a thorough investigation of the resulting aerial images and CD change for defects near 22nm and 16nm features. The effect of the position, size and shape of the defect is explored. The printability of a buried defect is very dependent on its position relative to the absorber features and the worst case position depends on the defect size. Also, defects only a few nanometers tall that are covered by the absorber can still cause an unacceptable CD change. The effects of illumination are also investigated to show that the improved image slope produced by advanced off-axis illuminations reduces the printability of buried defects in focus, but through focus the area affected by a buried defect is much larger for dipole and annular illuminations than it is for tophat.

The final topic of this dissertation is defect compensation. Two methods are proposed to reduce the effects of a buried defect by adjusting the absorber pattern. The first employs pre-calculated design curves to prescribe absorber modifications based only on the CD change caused by the defect. This method successfully compensates for the defect in focus, but the defect still causes a CD change through focus. To reduce the effect of the defect through focus, absorber is used to cover the defect and block the out of phase light from the defect. This covering produces some improvement in through focus printability and works best for defects which have a narrower surface geometry after smoothing.

We present a selection of topics relating to modeling, designing, and measuring EUV (Extreme Ultraviolet) photomasks, with implications for high-volume nanofabrication of integrated circuits. These EUV photomasks must be accurately designed, but rigorously modeling large domains is extremely computationally intensive; we introduce an approximateFresnel Double Scattering model which is 10,000x faster. This approximation can predict the trend of phase vs pitch, which is critical to designing EUV phase shift masks (PSMs). We also explore novel mask architectures to improve efficiency and contrast, such as an etched multilayer PSM (up to 6x throughput but restrictive applicability), aperiodic multilayers (up to +22% throughput and more general applicability), and multilayers with minimal propagation distance at certain angles (lower throughput but higher contrast with minimized 3D effects). Finally we explore computational metrology with EUV reflectometry, scatterometry, and imaging for probing the phase and amplitude response of an EUV mask, with experimental demonstrations at the Advanced Light Source synchrotron. We perform reflectometry experiments on 3 masks with different architectures to infer approximately 25 physical film parameters each. Another reflectometry application to contamination monitoring achieved single-picometer precision for thickness (3σ < 6pm) and sub-degree precision for phase (3σ < 0.2deg). We compare two implementations of phase scatterometry, either applying nonlinear optimization with approximate scattering, or linearizing the rigorous scattering relationship between intensity and phase; linearization is shown to generally be more accurate, but both methods have similar precision. We apply novel software and hardware for phase imaging, using PhaseLift convex phase retrieval, combined with a set of custom Zernike Phase Contrast (ZPC) zone plates. We perform hyperspectral ZPC phase imaging on 3 masks, where we see promising agreement with reflectometry in the trend of phase vs wavelength.