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 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

The direct problem of optical microlithography is to simulate printing features on the wafer under the given mask, imaging system, and process characteristics. The goal of inverse problems is to find the best mask, imaging system, or process to print the given wafer features. In this study, we proposed the strict formalization and fast solution methods of inverse mask problems. We stated inverse mask problems (or "layout inversion" problems) as nonlinear, constrained minimization problems over a domain of mask pixels. We considered linear, quadratic, and nonlinear formulations of the objective function. The linear problem is solved by an enhanced version of the Nashold projections. The quadratic problem is addressed by eigenvalue decompositions and quadratic programming methods. The general nonlinear formulation is solved by the local variations and gradient descent methods. We showed that the gradient of the objective function can be calculated analytically through convolutions. This is an important practical result because it enables layout inversion on a large scale in order of M log M operations for M pixels.

Fast pixel-based mask optimization for inverse lithography

The present invention provides a system and method of modifying the mask layout shapes of an integrated circuit layout design to compensate for reticle field location-specific systematic CD variations resulting from mask writing process variations, lens imperfections in lithographic patterning, and photoresist process variations Called PLC (Process-optimized Layout Compensation), each set of compensation rules according to the present invention is specifically tailored for a particular mask-writer-patterning-tools-and-resist-process combination, and are performed on a reticle-wide basis Furthermore, for each geometric shape in the mask layout, the amount of modification is determined based on a categorization of the type of the shape, the specific location in the reticle field the particular shape falls in, its context (ie, surrounding patterns, orientation, etc), as well as certain photoresist parameters to be used in the patterning process

System and method for reducing patterning variability in integrated circuit manufacturing through mask layout corrections

The application of resolution enhancement techniques pushes optical projection lithography close to its theoretical limit with a k1-factor of 0.25. For the imaging close to this limit the interaction between the mask and the shape of the illumination aperture gains increasing importance. By jointly optimizing the mask and the source low k1 images can be printed with process latitudes not achievable otherwise. This paper proposes a new optimization procedure for mask and source geometries in optical projection lithography. A general merit function is introduced, that evaluates the imaging performance of specific patterns over a certain focus range. It also takes certain technological aspects, that are defined by the manufacturability and inspectability criteria for the mask, into account. Automatic optimization of the mask and illumination parameters with a genetic algorithm identifies optimum imaging conditions without any additional a-priori knowledge about lithographic processes. Several examples demonstrate the potential of the proposed concept.

Toward automatic mask and source optimization for optical lithography

Lithography simulators have become a standard tool in industrial and governmental research and development departments. In contrast to the modeling approaches for the optical system and for the lithographic performance of i-line resists, there is still no consensus on the modeling of chemically amplified resists (CAR). Existing models differ in the description of the kinetics and the diffusion phenomena during post exposure bake (PEB) and in the specification of the development rate. A modeling approach was established, that combines the light induced generation of photoacid, in- and outdiffusion of acid or base components, a generalized deprotection kinetics, Fickian and non-Fickian diffusion of resist components and an arbitrary development rate model. Existing models such as the effective acid model and a standard deprotection model for CAR can be considered as special cases of the implemented model. To evaluate the importance of certain options of the model and of the model parameters we have evaluated the performance of the model by comparing simulated CD data and resist profiles with experimental data.

Comparison of simulation approaches for chemically amplified resists

Post exposure bake (PEB) models in the lithography simulator SOLID-C have been extended in order to improve the description of kinetic and diffusion phenomena in chemically amplified resists. We have implemented several new models and options which take into account effects such as the diffusion of quencher base, different approaches to model the neutralization between photogenerated acid and a quencher base, spontaneous loss of quencher, and arbitrary dependencies of the diffusion coefficients on acid or inhibitor, respectively. In this study, the impact of these new model options on critical phenomena like iso-dense bias, linearity and line end shortening are examined. The simulations were performed for a calibrated KrF/ArF resist models.

New models for the simulation of post-exposure bake of chemically amplifed resists

In this paper we examine new models and the indispensability of model parameters of chemically amplified resists (CAR) for their usage in predictive process simulation. Based on a careful exploration of different modeling options we calibrate the model parameters with different experimental data. Furthermore, we investigate different modeling approaches: (1) Mode of coupling between diffusion and kinetic reactions, sequence of quencher base events (Hinsberg model); (2) Mode of diffusion: Fickian and linear diffusion model; (3) Development rate model: Performance of the Enhanced Notch model. The resulting models are evaluated with respect to their performance by comparing with experimental line-width for semidense (1-2, 1-1.6, 1-1.4, 1-1.2) and dense features, the bias between different features and full resist profiles. The investigations are applied to the Shipley resist UVTM 113. Finally, a parameter extraction procedure for chemically amplified resists is proposed.

New methods to calibrate simulation parameters for chemically amplified resists

This article proposes a new optimization procedure for mask and illumination geometries in optical projection lithography. A general merit function is introduced that evaluates the imaging performance of arbitrary line patterns over a certain focus range. It also takes into account certain technological aspects that are defined by the manufacturability and inspectability of the mask. Automatic optimization of the mask and illumination parameters with a genetic algorithm identifies optimum imaging conditions without any additional a-priori knowledge about lithographic processes. Several examples demonstrate the potential of the proposed concept.

Bernd Tollkuehn

Papers

Toward automatic mask and source optimization for optical lithography

Comparison of simulation approaches for chemically amplified resists

New models for the simulation of post-exposure bake of chemically amplifed resists

New methods to calibrate simulation parameters for chemically amplified resists

Mask and source optimization for lithographic imaging systems