Dr. Zhengrong Zhu Profile

Dr. Zhengrong Zhu

at Carnegie Mellon Univ

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Publications (7)

Proceedings Article | 28 May 2004 Paper

Propagation of EM waves in axial symmetric structures and its implication for 3D rigorous lithography process simulation

Zhengrong Zhu, Andrzej Strojwas

Proceedings Volume 5377, (2004) https://doi.org/10.1117/12.535648

KEYWORDS: Waveguides, Dielectrics, Computer simulations, Scattering, Lithography, Wave propagation, Radio propagation, Optical lithography, Electromagnetic scattering, Diffraction

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Amid the different approaches to rigorously model the scattering of electromagnetic waves in sub-wavelength photolithography process, waveguide methods have been proven to be accurate and efficient. While totally different from the time domain methods such as FEM and TDFD, waveguide methods simultaneously compute diffraction of the incident plane waves with different incidence angles by a periodical dielectric structure. EM modes inside dielectric layers are solved for by decoupling the eigen-system and the electromagnetic field boundary conditions between each two adjacent layers are applied to stitch the modes and obtain the full scattering matrix. It is clear that the number of orders of the plane waves under consideration directly affects the accuracy of a waveguide simulator. However, in a 3-D simulation, simulation time and memory usage increase drastically with the increase of the number of orders. These limitations prevent waveguide methods from being applied to large layout patterns that require higher simulation orders. Since many cases under study in lithography process optimization and layout printability analysis are actually axial-symmetric about both x and y axes, it is possible to use this symmetry to simplify the calculation. Based on our definitions of the four fundamental groups of symmetric and anti-symmetric functions and the operations between these symmetric groups, we have made some fundamental discoveries of the waveguide propagating behaviors inside symmetric dielectric structures. In this paper, we will describe our new rigorous theory to decompose the propagating waves in a symmetric layer into four symmetric and anti-symmetric transmitting plane wave groups. Each group can be directly stitched to the next layer without losing symmetry or anti-symmetry. Furthermore, any form of incident waves can be reorganized into the above four plane wave groups, so can the reflective and refraction fields. We have shown that by using this field decomposition technique, we can compute scattering of the four smaller diffraction mode groups separately and the computational complexity will be greatly reduced as compared with the full mode simulation. We have developed a new version of the 3-D simulator, METRO, which incorporated this new method and achieved very high computational efficiency. For example, a 33 by 33-order, double precision simulation will only require 300M bytes memory and take less than 15 minutes without any loss of accuracy on a 1G processor compared with 1.7G memory usage and 10 hours simulating time on the same processor without symmetric simplification.

Proceedings Article | 28 May 2004 Paper

A superfast 3D lithography simulator and its application for ULSI printability analysis

Zhengrong Zhu, Andrzej Strojwas

Proceedings Volume 5377, (2004) https://doi.org/10.1117/12.535682

KEYWORDS: Lithography, Computer simulations, Photoresist materials, Light scattering, Calibration, Scattering, Waveguides, Dielectrics, Metals, Diffraction

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Printability challenges are already one of the key limits of new technology generations and the situation will become even worse with the delay in the introduction of 157nm lithography. To optimize the set-up of RET and verify their efficiency within a photo process window, it has become necessary to run detailed lithography simulations. While some 1-D test patterns can be simulated using the 2-D software tools, patterns such as line-ends, corners and metal islands should be evaluated by 3-dimensional simulators. Such a simulator can be calibrated using a small number of in-line measurements and then employed to analyze the “difficult to print patterns”. However, until recently the computational efficiency of such a 3-D tools has not been sufficient for practical applications. Since a lot of features under study are axial-symmetric, symmetry of the 3-D structures can be used to reduce computational complexity. To address this issue, we have developed a method to simulate three-dimensional axial-symmetrical structures. This method is based on the observation that scattering in and out of axial symmetrical structure can be classified into four kinds of scattering waves and each kind of scattering wave can be computed separately. Based on this observation, we have greatly reduced the run time and memory usage of the rigorous waveguide method without any loss of accuracy. According to our experiments, memory usage was reduced to one-forth and run time was shortened to 3~5% of the original simulation. (20-30 times speed up) In this paper, we will discuss applications of the new symmetrical simulator METROPOLE-3D to lithography simulation and layout analysis. We will discuss the fast calibration of METROPOLE-3D simulator. The simulated CD data was compared with experimental FEM wafer data to calibrate the parameters used in PEB and photoresist development. We are now able to analyze a lot of axial symmetrical dense and isolated 2-D structures with unprecedented speed. In this paper, wee will present a full lithography analysis example from a real product manufactured in the state-of-the-art lithography process.

Proceedings Article | 17 December 2003 Paper

METROPOLE-3D: a three-dimensional electromagnetic field simulator for EUV masks under oblique illumination

Zhengrong Zhu, Kevin Lucas, Jonathan Cobb, Scott Hector, Andrzej Strojwas

Proceedings Volume 5256, (2003) https://doi.org/10.1117/12.518544

KEYWORDS: Extreme ultraviolet, Photomasks, Waveguides, Light scattering, Electromagnetism, Scattering, Reflectivity, Diffraction, Lithographic illumination, Electromagnetic scattering

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Proceedings Article | 16 June 2003 Paper

Rigorous EUV mask simulator using 2D and 3D waveguide methods

Zhengrong Zhu, Kevin Lucas, Jonathan Cobb, Scott Hector, Andrzej Strojwas

Proceedings Volume 5037, (2003) https://doi.org/10.1117/12.484963

KEYWORDS: Extreme ultraviolet, Photomasks, Waveguides, Extreme ultraviolet lithography, Reflectivity, 3D modeling, Lithography, Computer simulations, Dielectrics, Diffraction

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Proceedings Article | 16 July 2002 Paper

Three-dimensional modeling of wafer inspection schemes for sub-70-nm lithography

Zhengrong Zhu, Aaron Swecker, Andrzej Strojwas

Proceedings Volume 4689, (2002) https://doi.org/10.1117/12.473455

KEYWORDS: Wafer inspection, 3D modeling, Lithography, Semiconducting wafers, Dielectrics, Computer simulations, Inspection, Optical lithography, Reflectivity, Electromagnetism

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The production of 70nm devices is projected for the year 2008. With this projection, optical lithography will become more challenging since as the device size goes down, the potential for introducing killer defects also increases dramatically. Wafer inspection will play a key role in controlling the defect mechanisms and keeping an acceptable yield for next generation VLSI manufacturing. Metrology tools for the new generation lithography will have the following features. First, the projection and collection lenses will have higher numerical apertures (NA) to obtain high-resolution images. Typically, the NA will be as high as 0.9. Second, the wavelength used for wafer inspection will be much smaller so that common wafer materials will become highly absorptive. Last, with the increased number of process steps, wafer inspection will need to provide information for more critical processes. Based on these features, accurate modeling of the next generation wafer inspection schemes is needed to aid in the characterization and optimization of the inspection tools. The simulation tool must be able to simulate inspection systems with high NA lens, DUV wavelengths, and highly absorptive wafer materials accurately and quickly. At Carnegie Mellon University, a simulator called METRO-3D was developed into a defect inspection simulator for DUV lithography processes. This simulator is able to successfully model various types of defect mechanisms. However, it has experienced occasional numerical instabilities, with discontinuous dielectric structures composed of highly absorptive materials. In order to provide a tool to simulate the wafer inspection scheme of SUB-70NM NODE LITHOGRAPHY, we have incorporated a new algorithm to model the wafer inspection system more accurately and robustly. Numerical experiments shows that the algorithm is capable of simulating topographies with discontinuous dielectric functions, yielding stable results even when the material is highly absorptive. To verify the accuracy of the simulator, several simulations were compared with both analytical models and results form other existing simulators. The results show good matches between METRO-3D and these well-established results. Finally, we performed simulations on industrial data and the results exemplified the ability of METRO-3D to model complex 3-D structures. In this paper we will present is efficient and stable EM solver and the results of the simulator applied to various sub-70nm node wafer inspection schemes.

Proceedings Article | 12 July 2002 Paper

Infrastructure for model-based OPC development in the deep submicron era

Zhengrong Zhu, Dennis Ciplickas, Andrzej Strojwas

Proceedings Volume 4692, (2002) https://doi.org/10.1117/12.475678

KEYWORDS: Calibration, Optical proximity correction, Photoresist materials, Lithography, 3D modeling, Semiconducting wafers, Computer simulations, Etching, Data modeling, Photoresist developing

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Proceedings Article | 16 June 1998 Paper

Experimental analysis of vibration confinement to enhance conventional active vibration control

William Clark, Zhengrong Zhu

Proceedings Volume 3326, (1998) https://doi.org/10.1117/12.310659

KEYWORDS: Vibration control, Active vibration control, Actuators, Sensors, Optical simulations, Control systems, Feedback control, Systems modeling, Mechanical engineering, Mathematical modeling

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