cent Technologies, Inc.
2471 East Bayshore Road, Suite 600, CA 94301, USA
Phone: +1-650-433-1025 FAX:+ 1-650-960-3954 e-mail: leo@luminescent.com
ABSTRACT
In this paper, we first give an overview of Inverse Lithography Technology (ILT) based on Level Set Methods (LSM),
followed by showing the applications of ILT in the advanced lithography process for different devices, such as DRAM,
SRAM, FLASH, random logic, and imaging devices. ILT can not only correct the main patterns, but also insert SRAFs
automatically using model based mathematically methods. The process of SRAF generation in ILT is unified with the
process of inversion. With the help of ILT, SRAFs can be inserted at whatever source parameters, for whatever target
patterns, and whenever they are physically needed. Therefore it is a relatively simple task for ILT to take into account of
SRAF during technology evaluation. We will show results of optical condition selection taking into consideration of
SRAF insertion, which demonstrate the adaptive nature of ILT SRAF capability. We show wafer verifications collected
at multiple advanced semiconductor manufacturing companies at 45nm node in comparison with their current OPC
solution. Final wafer results show ILTs ability in many aspects improve pattern fidelity, enlarge process window, and
remarkably control the line-ends shortening.
Keywords: Inverse Lithography Technology (ILT), OPC, RET, Lithography, SRAF, SRAM, 45nm Technology
1.

INTRODUCTION
Increasingly, for semiconductor manufacturers moving to advanced nodes 90nm, 65, 45, and below the greatest
challenge is lithography. This is because lithography is fundamentally constrained by basic principles of optical physics.
At 65 nm and below, a line is less than a third of the effective wavelength of 193nm; optical diffraction and interference
are becoming fundamental obstacles, not just second order effects.
It has long been known that the best lithography that is theoretically possible can be achieved by considering the design
of photomasks as an inverse problem -- and then solving the inverse problem to find the optimal photomask for a given
process, using a rigorous mathematical approach. Inverse lithography technologies (ILT) have been explored for many
years[1-8]. Although these early approaches to ILT often resulted in superb lithography, they were generally impractical
in a production environment. Run-times were many orders of magnitude too slow, and the resulting masks were often
too complex to manufacture.
By ILT we mean the following: given the known forward transformation of a lithography process, ILT mathematically
dtermines the optimized mask which produces the desired wafer target with the best pattern fidelity and/or largest
process window. The forward transformation is modeled accurately, which may take into account all of the elements of
the transformation from mask to wafer: for example, the electromagnetics of the 3D mask, the optics of illumination and
the lens, the behavior of the photoresist, the dose, focus conditions, aberrations, etc. However, the strict inverse problem
is ill-posed; because the forward operator is many-to-one (that is, many different masks will yield identical on-wafer
results), and the function has no well-defined inverse. Moreover, for typical target patterns (e.g., a drawn layout with
Manhattan geometry and sharp corners), there does not exist any mask function which will produce the exact drawn
wafer target. These issues are addressed by recasting the inverse problem as an optimization problem.
2.

ILT USING LEVEL SET METHODS (LSM) OVERVIEW




Our approach to ILT is based on a branch of mathematics invented by Stan Osher at UCLA. Commonly known as
Level-Set Methods[9], these techniques have been applied to the solution of inverse problems in a wide range of
engineering disciplines such as image processing and fluid dynamics. In our formulation, the design intent target and
simulated wafer contour are represented in 2D pixilated arrays (2D gray scale image). The post correction mask is
represented as 2D level-set function, and mask transmission as 2D, potentially complex, array (Figure 1). The above
formulation of the problem has a variety of advantageous properties. For example, the level-set representation allows for
contours to merge, break, appear, or disappear, in a consistent, mathematical representation. Various functions (for
example, the wafer image) can be determined as closed form expressions. The mask function itself is an element of a
Hilbert-space which is much larger than the two-dimensional space of the photomask, which allows for more global
solutions to be found.
Design GDS
target
Cost func
down
(EPE,PW,
MEEF)
Level Sets
evolve with
gradient
Represent in
pixel image
Represent in
Level-Sets
curve
-able to
calculate
gradient

Design target
ILT mask with
SRAF
Forward
model

Figure 1. The level-set representation of mask problem and the flow of using Level Set Methods to solve the lithography
inverse problem.
A lithography forward model, which simulates the mask effects, scanner optics, resist development, and even etching
and SEM bias, are created and used in ILT. Such forward model is similar to models used in OPC and lithography
simulators. Therefore, once a mask pattern is given, a forward simulation can be run to compute the aerial and latent
image, and resist model convert the latent image into printed resist image.
We define a merit function, also called a cost function, energy function, or Hamiltonian (by analogy to quantum
mechanics). This function is indicative of the quality of the solution, or the goodness of the mask. In a simple case, the
Hamiltonian could be the absolute value of the difference between the wafer image and the target pattern, integrated over
the area of the mask. In practice, a number of additional elements may be included in the Hamiltonian. For example, the
wafer pattern at various conditions throughout the process window (i.e., over or under exposed and/or plus/minus focus),
the normalized image log slope (NILS) of the image, the robustness against Mask Error Enhancement Factor (MEEF), or
other factors as deemed appropriate. The actual functional form may be different from the form as described above as
well. Elements that are not directly related to lithography may be included; for example, simple masks may be preferred
over complex masks, and terms to this effect may be included in the Hamiltonian as well. What is essential is that the
Hamiltonian is a functional of the mask function, and minimizing Hamiltonian allows us to find the optimal mask,
according to the criteria we have chosen. Represent mask pattern, wafer contours and target in level set allows us to
compute the gradient of the Hamiltonian with respect to the mask patterns, and this enables us to use modern
minimization algorithms to solve the lithography inverse problem in a fast and efficient way in order to be used in full
chip correction.



Another important aspect of the minimization problem comes in the form of constraints. A variety of constraints are
imposed by the realities of mask manufacturing; for example, two disjoint chrome regions must be separated by a
minimum distance, and a chrome line must have a minimum width. We address these constraints by defining a sub-space
of the full Hilbert space of mask functions, and restricting our solution to this sub-space.
A key distinctive feature of ILT is the absence of pattern-dependent heuristics, and the ability to broadly explore wide
areas of solution space. This lead to an very important features in RET - sub-resolution assist features (SRAFs), which
are mask features that do not print on the wafer which are detached from the edges of the main mask patterns, and yet
manipulate the light reaching the wafer so as to accentuate the wafer image. In the past, these were placed empirically,
with great care, and frozen in place during the computation of the rest of the mask. In contrast, ILT can determine
optimal SRAFs simultaneously with the rest of the mask. The absence of segmentation scripts is a significant advantage
because it usually requires significant engineering resources to write such scripts for different patterns on different
design layers.
2.1

Model-Based SRAF in ILT Using LSM
SRAF is commonly used in RET. There are three major problems in the current SRAF generation: 1) SRAF placements
are primarily rule-based, and the rules are created using simple regular patterns, such as lines/spaces, or contacts with
different pitches. Such rule might not be applicable or accurate for complicated geometries in a real design; 2) SRAF
generation and OPC are two separate processes first the SRAFs are generated and then OPC is run. This can be time
consuming. 3) OPC only applies to main pattern. SRAFs usually are not optimized during OPC. 4) Side lobes that could
print are difficult to detect and fix.
In ILT, SRAFs are automatically generated during the inversion calculation, and they are optimized simultaneously with
the main features. Therefore, the SRAF generation becomes a straight forward, single-step process. Since every pixel is
considered in the computation in the pixel-based ILT implementation, the issue of side-lobe-printing which has been a
problem for edge-based OPC due to its edge-sampling-based approach can be effectively eliminated (Figure 2).
Rule-based SRAF
ILT

(a) (b)
Figure 2. An