The phase-shifting mask consists of a normal transmission mask that has been coated with a transparent layer patterned to ensure that the optical phases of nearest apertures are opposite. Destructive interference between waves from adjacent apertures cancels some diffraction effects and increases the spatial resolution with which such patterns can be projected. A simple theory predicts a near doubling of resolution for illumination with partial incoherence σ < 0.3, and substantial improvements in resolution for σ < 0.7. Initial results obtained with a phase-shifting mask patterned with typical device structures by electron-beam lithography and exposed using a Mann 4800 10× tool reveals a 40-percent increase in usuable resolution with some structures printed at a resolution of 1000 lines/mm. Phase-shifting mask structures can be used to facilitate proximity printing with larger gaps between mask and wafer. Theory indicates that the increase in resolution is accompanied by a minimal decrease in depth of focus. Thus the phase-shifting mask may be the most desirable device for enhancing optical lithography resolution in the VLSI/VHSIC era.

Improving resolution in photolithography with a phase-shifting mask

The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

On the diffraction theory of optical images

In this thesis, we first look at the Optical Proximity Correction (OPC) problem and define the goals, constraints, and techniques available. Then, a practical and general OPC framework is built up using concepts from linear systems, control theory, and computational geometry. A simulation-based, or model-based, OPC algorithm is developed which simulates the optics and processing steps of lithography for millions of locations. The key contributions to the OPC field made in this thesis work include: (1) formulation of OPC as a feedback control problem using an iterative solution, (2) an algorithm for edge movement during OPC with cost function criteria, (3) use of fast aerial image simulation for OPC, which truly enables full chip model-based OPC, and (4) the variable threshold resist (VTR) model for simplified prediction of CD based off aerial image.
A major contribution of this thesis is the development of a fast aerial image simulator which is tailored to the problem of OPC. In OPC applications, it is best to compute intensity at sparse points. Therefore, our fast aerial image simulator is tailored to computing intensity at sparse points, rather than on a regular dense grid. The starting point for the fast simulation is an established decomposition of the Hopkins partially coherent imaging equations, originally proposed by Gamo (14). Within this thesis, the decomposition is called the Sum of Coherent Systems (SOCS) structure. The numerical implementation of this decomposition using Singular Value Decomposition (SVD) is described in detail.
Another contribution of this thesis is the development of a variable threshold resist model (VTR). The model uses the aerial image peak intensity and image slope along a cutline to deduce the development point of the resist, and has two primary benefits: (1) it is fast, (2) it can be fit to empirical data.
We combine the fast aerial image simulator and the VTR model in an iterative feedback loop to formulate OPC as a feedback control problem. (Abstract shortened by UMI.)

/pdf/fast-optical-and-process-proximity-correction-algorithms-for-telex7u167.pdf

Fast optical and process proximity correction algorithms for integrated circuit manufacturing

In all imaging systems, the forward process introduces undesirable effects that cause the output signal to be a distorted version of the input. A typical example is of course the blur introduced by the aperture. When the input to such systems can be controlled, prewarping techniques can be employed which consist of systematically modifying the input such that it (at least approximately) cancels out (or compensates for) the process losses. In this paper, we focus on the optical proximity correction mask design problem for "optical microlithography," a process similar to photographic printing used for transferring binary circuit patterns onto silicon wafers. We consider the idealized case of an incoherent imaging system and solve an inverse problem which is an approximation of the real-world optical lithography problem. Our algorithm is based on pixel-based mask representation and uses a continuous function formulation. We also employ the regularization framework to control the tone and complexity of the synthesized masks. Finally, we discuss the extension of our framework to coherent and (the more practical) partially coherent imaging systems

Mask Design for Optical Microlithography—An Inverse Imaging Problem

Multiple paths exists to provide lithography solutions pursuant to Moore's Law for next 3-5 generations of
technology, yet each of those paths inevitably leads to solutions eventually requiring patterning at k1 < 0.30
and below. In this article, we explore double exposure single development lithography for k1 ≥ 0.25 (using
conventional resist) and k1 < 0.25 (using new out-of-sight out-of-mind materials). For the case of k1 ≥ 0.25, we
propose a novel double exposure inverse lithography technique (ILT) to split the pattern. Our algorithm is based
on our earlier proposed single exposure ILT framework, and works by decomposing the aerial image (instead of
the target pattern) into two parts. It also resolves the phase conflicts automatically as part of the decomposition,
and the combined aerial image obtained using the estimated masks has a superior contrast.
For the case of k1 < 0.25, we focus on analyzing the use of various dual patterning techniques enabled by the
use of hypothetic materials with properties that allow for the violation of the linear superposition of intensities
from the two exposures. We investigate the possible use of two materials: contrast enhancement layer (CEL) and
two-photon absorption resists. We propose a mathematical model for CEL, define its characteristic properties,
and derive fundamental bounds on the improvement in image log-slope. Simulation results demonstrate that
double exposure single development lithography using CEL enables printing 80nm gratings using dry lithography.
We also combine ILT, CEL, and DEL to synthesize 2-D patterns with k1 = 0.185. Finally, we discuss the viability
of two-photon absorption resists for double exposure lithography.

ILT for double exposure lithography with conventional and novel materials

we apply combinatorial optimization techniques to binary mask design for optical lithography. The mask is optimized in such a way as to pre-compensate the distortions due to diffraction of the optical system. Mean squared error (MSE) criterion is used to formulate the problem as a binary linear programming (LP) one which is then solved via branch and bound and simplex algorithms. Variation of the optimal mask as a function of the optical system bandwidth is discussed. Examples involving corners squares bars and crosses are presented. 1.

Optimal binary image design for optical lithography

A number of pre-distorted mask design techniques for binary and phase-shifting masks are proposed. This approach is based on modeling the imaging mechanism of a stepper by the Hopkins equations and taking advantage of the photoresist nonlinear characteristics. Optimization techniques such as the branch and bound algorithm and simulated annealing algorithm are used to systematically design pre-distorted masks under incoherent and partially coherent illumination. Computer simulations are used to show that contour shapes of our designed mask patterns are sharper than those of conventional masks. The designed phase- shifting masks are shown to result in higher contrast as well as sharper contours than binary masks.

Binary and phase-shifting image design for optical lithography

An optimization based algorithm for designing phase-shifting masks is proposed. The approach is an extension of the previous work in the sense that the intensity image is optimized at a number of optical planes rather than just the focus plane. In addition, the algorithm can be used to design masks with shifted focus plane and/or extended depth of focus. The concept of a dual mask is introduced, and its consequences for practical phase-shifting mask design are shown. The proposed design techniques are applied to single line phase connectors, cross phase connectors, contact holes and bright lines. Simulation and experimental results verify the capability of the design technique for extending depth of focus and shift the focus plane. >

https://ieeexplore.ieee.org/iel3/66/5468/00210654.pdf

Systematic design of phase-shifting masks with extended depth of focus and/or shifted focus plane

We propose a new approach to systematic phase shift mask design. In doing so, we constrain the complexity of the mask at a pre-specified level by limiting the number of `features' on the mask. We then optimize the location, size, and phase of the features so as to achieve a desired intensity pattern on the wafer. The main advantage of this object-oriented approach over our previous pixel-based solution is that it results in substantially larger assisting phase shift features, and is therefore easier to fabricate. Our approach can also be used to design masks with proper bias and/or extension of the depth of focus. We show examples of contact hole, bright line, and chromeless line-space mask designs.

/pdf/computer-aided-phase-shift-mask-design-with-reduced-55m57u41a6.pdf

Computer-aided phase-shift mask design with reduced complexity

We propose an optimization based algorithm for designing phase-shifting masks. Our approach is an extension of our previous work [1, 2, 3] in the sense that the intensity image is optimized at a number of optical planes rather than just the focus plane. In addition, our algorithm can be used to design masks with shifted focus plane and/or extended depth of focus. We also propose the concept of “dual mask” and show its consequences to practical phase-shifting mask design. Finally, we show examples of our proposed design techniques for single line phase connectors, cross phase connectors, contact holes and bright lines. Simulation and experimental results verify the capability of our design technique to extend depth of focus and shift the focus plane.

Yong Liu

Papers

Optimal binary image design for optical lithography

Binary and phase-shifting image design for optical lithography

Systematic design of phase-shifting masks with extended depth of focus and/or shifted focus plane

Computer-aided phase-shift mask design with reduced complexity

Systematic design of phase-shifting masks with extended depth of focus and/or shifted focus plane