Yaoming Shi

• BS Physics MS Physics PhD Physical Chemistry
• Shanghai Precision Measurement Semiconductor Technology Inc

The Riemann $\Xi(z)$ function (even in $z$) admits a Fourier transform of an even kernel $\Phi(t)=4e^{9t/2}\theta''(e^{2t})+6e^{5t/2}\theta'(e^{2t})$. Here $\theta(x):=\theta_3(0,ix)$ and $\theta_3(0,z)$ is a Jacobi theta function, a modular form of weight $\frac{1}{2}$. (A) We discover a family of functions $\{\Phi_n(t)\}_{n\geqslant 2}$ whose Fou...

An effective image based method to automatically measure the profile parameters (PPs), including the critical dimensions (CDs), the full height and other structural parameters, of the integrated circuit (IC) devices in batch is proposed. In this method, templates are used to indicate the patterns of interest and the regions of the desired PPs; patt...

Spectroscopic ellipsometry technology has extensive applications in semiconductor metrology. Compared with spectroscopic ellipsometry, the Mueller matrix ellipsometry can acquire more useful information about the sample. In this paper, we present the construction of Mueller measurement equipment for 300 mm integrated circuit production line applica...

Optical critical dimension (OCD) measurement has been widely demonstrated as an essential metrology method for monitoring advanced IC process in the technology node of 90 nm and beyond. However, the rapidly shrunk critical dimensions of the semiconductor devices and the increasing complexity of the manufacturing process bring more challenges to OCD...

Reducing leakage current and improving device's stability become important challenge for CMOS develop under the technology node of 22nm. FinFET has been attractive as the most potential device structure under 22nm. Unique FinFET device structure has the absolute advantage in restraining short channel effect. This paper presents an optical metrology...

In modern IC industry, optical critical dimension (OCD) technique has been more and more applied, as one of the most import process control tools. In this work, OCD spectroscopy metrology was used to measure the profiles of 2-D sigma-shaped Source/Drain structures at advanced node. Due to the complexity of the samples, eighteen parameters were inve...

Mask Fidelity plays a vital role in the lithography process of cutting-edge IC fabrication. The Fidelity of Mask is fundamental to the final performance of the lithography process in production. A contour is extracted from the CD-SEM image of the corresponding fabricated mask under evaluation with at best one pixel resolution. This contour is then...

The Riemann $\Xi(z)$ function admits a Fourier transform of a even kernel $\Phi(t)$. The latter is related to the derivatives of Jacobi theta function $\theta(z)$, a modular form of weight $1/2$. P\'olya noticed that when $t$ goes to infinity, $e^t$ goes to $e^t+ e^{-t}=2\cosh t$. He then approximated the kernel $\Phi(t)$ by $\Phi_{P}(t)$ that cont...

One embodiment relates to a method of model-based optical metrology. An area of a geometrical structure of dispersive materials on a substrate is illuminated with polarized incident electromagnetic radiation using an illuminator of a scatterometer apparatus. Spectral components of the incident electromagnetic radiation reflected from the area are m...

In this work, Optical Critical Dimension (OCD) spectroscopy was used to monitor the critical dimension for After-Etch Inspection (AEI) structures at sub 65 nm node, such as Poly Gate, Shallow Trench Isolation, Offset Spacer, and Oxide-Nitride Spacer. The dynamic repeatability of the measurement was obtained through a 10-cycle measurement process wi...

Since the measurement precision of OCD (Optical Critical Dimension) technology highly depends on the optical hardware configuration, spectra types, and inherently interactions between the incidence of light and various materials with various geometrical structures, here a method is introduced for seeking the most sensitive measurement configuration...

Optical critical dimension (OCD) measurement has been widely demonstrated as an essential metrology method for advanced IC process monitoring at 90 nm node and beyond. However, aggressive IC industry scaling requirements and sharply increased process control complexity motivated the development of metrology tools. Oxide - Nitride spacer etched poly...

This work studied the case that the illumination light spot size is larger than the grating region during optical critical dimension (OCD) measurement. The analysis is based on Mueller matrix formulism. The total Mueller matrix output is the combination of both the grating Mueller matrix contribution and the surrounding film Mueller matrix contribu...

In this work, optical critical dimension (OCD) spectroscopy was used to monitor the critical dimension for gate and STI AEI (After-Etch Inspection) structures. The reference measurements with CDSEM (CD Scanning Electron Microscope) and TEM (Transmission Electron Microscopy) were also carried out. The OCD results show high precision, high stability...

We consider FLRW cosmological models for perfect fluid (with rho as the energy density) in the frame work of the f(rho) modified theory of gravity [V. N. Tunyak, Russ. Phys. J. 21, 1221 (1978); J. R. Ray, L. L. Smalley, Phys. Rev. D. 26, 2615 (1982) ]. This theory, with total Lagrangian R-f(rho), can be considered as a cousin of the F(R) theory of...

The spectral sensitivities of scatterometry based on Mueller matrix formulism at the technology node of 65 nm and beyond were studied. The advantage of Mueller matrix based polarized light scattering technique over conventional ellipsometry technique in measuring patterned wafers was present. RCWA method was used to simulate the 2D gratings scatter...

We find a Lax pair for the geometrically exact discrete Hamiltonian equations for the discrete elastic rod. This is paper III of a series.

In previous work, the dynamics of the elastic rod was recast in a Lax pair formulation, with fiducial arc length s and time t as continuous independent variables. However, the solution of these equations cannot apply directly to a system where the fiducial arc length s is a discrete variable. In this paper, we show how to discretize the continuous...

We introduce a spectral parameter into the geometrically exact Hamiltonian equations for the elastic rod in a way that creates a Lax pair. This assures integrability and permits application of the inverse scattering transform solution method. If the method can be carried through, the solution of the original problem is recovered by setting the spec...

The mechanical properties of a deoxyribonucleic acid (DNA) molecule can be likened to those of a homogeneous elastic rod with a circular cross-section (isotropic). DNA in the eukaryotic cell undergoes a myriad of positional and structural changes during the course of a cell cycle. Our long-term objective is the development of a mathematical represe...

We have developed a new statistical mechanical theory for wormlike chains and elastic rods which will account for deformations of bending, twisting, shear, and axial extension/stretching. We have derived a Fokker–Planck equation for Green’s function. We have also obtained an exact expression for the mean square end-to-end distance. Our new theoreti...

The processes of transcription and replication are catalysed by processive enzyme complexes which move translationally along the DNA helix, unwinding the DNA helix ahead of the complex and reforming a duplex helix behind the complex (Gamper and Hearst 1982; Cook et al. 1994). These processes are known to torsionally stress DNA.

We have derived a generalized one-dimensional time-independent nonlinear Schrödinger equation for the stationary state configurations of supercoiled DNA, based on an elastic rod model which includes deformations of bending, twisting, shear, and extension. Closed-form solutions for the axis of DNA have been obtained in terms of elliptic functions an...

We have derived a time‐independent, one‐dimensional nonlinear Schrödinger equation for the stationary state configurations of supercoiled DNA. The effect of DNA self‐contact has been included analytically. For the cases of non‐self‐contact and periodic boundary conditions, closed‐form solutions have been obtained which describe the stationary state...

We show that no experiment involving parity can measure the left–right coherence of a state ‖ψ〉=aL‖L〉+eiφaR‖R〉 if sin φ is zero and ‖L〉 and ‖R〉 are real mirror images of one another. We then exhibit a number of experiments in elastic linear light scattering which provide all‐or‐none measurements of left–right coherence.

The coupled-dipole approximation has been used to model polarized light-scattering data obtained from the sperm of the octopus Eledone cirrhosa. Mueller scattering-matrix elements (which describe how a sample alters the intensity and degree of polarization of scattered light) were measured as a function of angle. The sample was modeled as a helical...

We consider processes quadratic in incident intensity, in which two identical photons are annihilated simultaneously. We construct a formalism for these processes that is maximally analogous to the Stokes-Mueller formalism for linear processes. The two-photon properties of the incident beam require nine Stokes-like parameters for their description;...

A two-frequency beam from a Zeeman laser scatters elastically from an isotropic medium, such as randomly oriented viruses or other particles suspended in water. The Zeeman effect splits the laser line by 250 kHz, and beats can be seen electronically in the signal from a phototube that views the scattered light. There are independently rotatable hal...

We present a new method of analyzing the polarization dependence of nonlinear light scattering (2 in, 1 out), which generalizes the 4×4 Mueller matrix used in linear scattering. We apply it to the case of an isotropic ensemble of anistropic scatterers, obtaining a “super-Mueller matrix” of dimension 4×4×4. Limiting ourselves to coplanar scattering,...

We present a closed-form solution to the problem of elastic light scattering by a randomly oriented ensemble of cylinders of finite length. All the Mueller scattering matrix elements are calculated, so the solution is complete in the sense that all possible polarization effects are treated. The cylinders are assumed to be made of an isotropic mater...

Typescript. Thesis (Ph. D.)--Wayne State University, 1993. Includes bibliographical references (leaves 208-213). ALSO AVAILABLE IN MICROFORM.

We present a central multipole calculation of the effect of a static magnetic field on nonresonant elastic scattering by an isotropic solution of molecules that are small compared to wavelength. Results are presented as perturbations to the observable Mueller scattering matrix. It is particularly interesting that perturbations appear in the six ret...

We consider the scattering of light from a molecule or a cluster. The scattering may be elastic or inelastic, but we limit ourselves to the special case of transitions from initial states having total angular momentum number J=0 to final states also having J=0. In practice, this covers elastic scattering from clusters as the rotational temperature...

In Part I of this paper, we started from a dipole array model of elastic light scattering, and found the longwave asymptotic formulas for all 16 elements of the orientation averaged Mueller scattering matrix. However, the Perrin symmetry of the scattering matrix was not obvious from the formulas obtained in Part I. In this paper, Part II, we carry...

Starting from a dipole array theory of elastic light scattering by particles of arbitrary shape and composition, we develop long-wave asymptotic formulas for all sixteen elements of the Mueller scattering matrix, valid after orientation averaging. The six dipole elements have long been known to be asymptotically proportional to k4 where k is the wa...