Aerial image measurement system (AIMSTM) has been widely used for wafer level inspection of mask defects. Reported inspection flows include die-to-die (D2D) and die-to-database (D2DB) methods. For patterns that do not repeat in another die, only the D2DB approach is applicable. The D2DB method requires accurate simulation of AIMS measurements for a mask pattern. An optical vectorial model is needed to depict the mask diffraction effect in this simulation. To accurately simulate the imaging results, a rigorous electro-magnetic field (EMF) model is essential to correctly take account of the EMF scattering induced by the mask topography, which is usually called the mask 3D effect.
In this study, the mask 3D model we use is rigorous coupled-wave analysis (RCWA), which calculates the diffraction fields from a single plane wave incidence. A hybrid Hopkins-Abbe method with RCWA is used to calculate the EMF diffraction at a desired accuracy level while keeping the computation time practical. We will compare the speed of the hybrid Hopkins-Abbe method to the rigorous Abbe method.
The matching between simulation and experiment is more challenging for AIMS than CD-SEM because its measurements provide full intensity information. Parameters in the mask 3D model such as film stack thickness or film optical properties, is optimized during the fitting process. We will report the fitting results of AIMS images for twodimensional structures with various pitches. By accurately simulating the AIMS measurements, it provides a necessary tool to perform the mask inspection using the D2DB approach and to accurately predict the mask defects.
KEYWORDS: Lithography, Visual process modeling, Data modeling, Calibration, Diffusion, 3D modeling, Scanning electron microscopy, Optical proximity correction, Semiconducting wafers, 3D image processing
A traditional approach to construct a fast lithographic model is to match wafer top-down SEM images, contours and/or gauge CDs with a TCC model plus some simple resist representation. This modeling method has been proven and is extensively used for OPC modeling. As the technology moves forward, this traditional approach has become insufficient in regard to lithography weak point detection, etching bias prediction, etc. The drawback of this approach is from metrology and simulation. First, top-down SEM is only good for acquiring planar CD information. Some 3D metrology such as cross-section SEM or AFM is necessary to obtain the true resist profile. Second, the TCC modeling approach is only suitable for planar image simulation. In order to model the resist profile, full 3D image simulation is needed. Even though there are many rigorous simulators capable of catching the resist profile very well, none of them is feasible for full-chip application due to the tremendous consumption of computational resource. The authors have proposed a quasi-3D image simulation method in the previous study , which is suitable for full-chip simulation with the consideration of sidewall angles, to improve the model accuracy of planar models. In this paper, the quasi-3D image simulation is extended to directly model the resist profile with AFM and/or cross-section SEM data. Resist weak points detected by the model generated with this 3D approach are verified on the wafer.
Traditionally, an optical proximity correction model is to evaluate the resist image at a specific depth within the photoresist and then extract the resist contours from the image. Calibration is generally implemented by comparing resist contours with the critical dimensions (CD). The wafer CD is usually collected by a scanning electron microscope (SEM), which evaluates the CD based on some criterion that is a function of gray level, differential signal, threshold or other parameters set by the SEM. However, the criterion does not reveal which depth the CD is obtained at. This depth inconsistency between modeling and SEM makes the model calibration difficult for low k1 images. In this paper, the vertical resist profile is obtained by modifying the model from planar (2D) to quasi-3D approach and comparing the CD from this new model with SEM CD. For this quasi-3D model, the photoresist diffusion along the depth of the resist is considered and the 3D photoresist contours are evaluated. The performance of this new model is studied and is better than the 2D model.
Calibration of mask images on wafer becomes more important as features shrink. Two major types of metrology have
been commonly adopted. One is to measure the mask image with scanning electron microscope (SEM) to obtain the
contours on mask and then simulate the wafer image with optical simulator. The other is to use an optical imaging tool
Aerial Image Measurement System (AIMSTM) to emulate the image on wafer. However, the SEM method is indirect. It
just gathers planar contours on a mask with no consideration of optical characteristics such as 3D topography structures.
Hence, the image on wafer is not predicted precisely. Though the AIMSTM method can be used to directly measure the
intensity at the near field of a mask but the image measured this way is not quite the same as that on the wafer due to
reflections and refractions in the films on wafer.
Here, a new approach is proposed to emulate the image on wafer more precisely. The behavior of plane waves with
different oblique angles is well known inside and between planar film stacks. In an optical microscope imaging system,
plane waves can be extracted from the pupil plane with a coherent point source of illumination. Once plane waves with a
specific coherent illumination are analyzed, the partially coherent component of waves could be reconstructed with a
proper transfer function, which includes lens aberration, polarization, reflection and refraction in films. It is a new
method that we can transfer near light field of a mask into an image on wafer without the disadvantages of indirect SEM
measurement such as neglecting effects of mask topography, reflections and refractions in the wafer film stacks.
Furthermore, with this precise latent image, a separated resist model also becomes more achievable.
Typical OPC models focus on predicting wafer contour or CD; therefore, the modeling approach emphasizes careful
determination of feature and edge locations in the photo-resist (PR) as well as the exposure threshold, so that the 'cut'
model image matches the wafer SEM contours or cut-line CDs most closely. This is an exquisite approach with regard to
the contour-based OPC, for the model is calibrated directly from wafer CDs. However, for other applications such as
hotspot detection or assist feature (AF) printing prediction that might occur at the top or the bottom of the PR, the typical
OPC model approach may not be accurate enough. Usually, these kinds of phenomenon can only be properly described
by rigorous simulation, which is very time-consuming and hence not suitable for OPC.
In this paper, the approach of building the OPC model with multiple image depths will be discussed. This approach
references the images at the bottom and/or the top of the PR. This way, the behavior of the images which are not shown
at the normal image depth can be predicted more accurately without distorting the optical model. This compromised
OPC modeling approach is beneficial for runtime reduction compared to the rigorous simulation, and for better accuracy
compared to conventional model. The applications for AF printing and hotspot predictions using the multiple image
depth approach will be demonstrated.
It is believed that smaller correction segments could achieve better pattern fidelity, however, some unstable OPC results
which are beyond the capability of common OPC correction schemes were found once the segment length is less than a
certain threshold. The dilemma between offering more degree-of-freedom by decreasing the correction segment length at
the cost of longer correction time and the instability induced by the reduced segment length challenges every OPC
In this paper, 2 indices are introduced; the segmentation index is proposed to determine a reasonable minimum segment
length while the stability index can be used to examine whether the correction system is a stiff convergence problem. A
compromised correction algorithm is also proposed to consider the OPC accuracy, stability and runtime simultaneously.
The correction results and the runtime are analyzed.
Design rules and the design rule check (DRC) utility are conventional approaches to design for manufacturability
(DFM). The DRC utility is based on unsophisticated rules to check the design layout in a simple environment. As the
design dimension shrinks drastically, the introduction of a more powerful DFM utility with model-based layout
patterning check (LPC) becomes mandatory for designers to filter process weak-points before taping out layouts. In this
paper, a system of integrated hotspot scores consisting of three lithography sensitive indexes is proposed to assist
designers to circumvent risky layout patterns in lithography. With the hotspot fixing guideline and the hotspot severity
classification deduced from the scoring system provided in this paper, designers can deliver much more manufacturable
As the patterning of IC manufacturing shrinks to the 32-nm node and beyond, high-NA and immersion lithography are
required for pushing resolution to its physical limit. To achieve good OPC performance, various physical effects such as
polarization, mask topography, and mask pellicle have to be considered to improve the model accuracy.
The attenuation and the phase variation of TE and TM wave components induced by the pellicle would impact optical
qualities in terms of resolution, distortion, defocus shift, and high-order aberrations. In this paper, the OPC model
considering pellicle effects is investigated with Jones pupil. The CD variation induced by the pellicle effect can be
predicted accurately. Therefore, the improvement on model accuracy for 32-nm node is demonstrated.
Accurate simulation of today's devices needs to account for real device geometry
complexities after the lithography and etching processes, especially when the channel
length shrinks to 65-nm and below. The device performance is believed to be quite
different from what designers expect in the conventional IC design flow. The
traditional design lacks consideration of the photolithography effects and pattern
geometrical operations from the manufacturing side. In to order obtain more accurate
prediction on circuits, an efficient approach to estimate nonrectangular MOSFET
devices is proposed. In addition, an electrical hotspot criterion is also proposed to
investigate and verify the manufacturability of devices during patterning processes.
This electrical rule criterion will be performed after the regular Design Rule Check
(DRC) or Design for Manufacturing (DFM) rule check. Photolithography and
industrial-strength SPICE model are taken into consideration to further correlate the
process variation. As a result, the correlation between process-windows and driving
current variation of devices will be discussed explicitly in this paper.
Optical proximity correction is the technique of pre-distorting mask layouts so that the printed patterns are as close to the desired shapes as possible. For model-based optical proximity correction, a lithographic model to predict the edge position (contour) of patterns on the wafer after lithographic processing is needed. Generally, segmentation of edges is performed prior to the correction. Pattern edges are dissected into several small segments with corresponding target points. During the correction, the edges are moved back and forth from the initial drawn position, assisted by the lithographic model, to finally settle on the proper positions. When the correction converges, the intensity predicted by the model in every target points hits the model-specific threshold value. Several iterations are required to achieve the convergence and the computation time increases with the increase of the required iterations. An artificial neural network is an information-processing paradigm inspired by biological nervous systems, such as how the brain processes information. It is composed of a large number of highly interconnected processing elements (neurons) working in unison to solve specific problems. A neural network can be a powerful data-modeling tool that is able to capture and represent complex input/output relationships. The network can accurately predict the behavior of a system via the learning procedure. A radial basis function network, a variant of artificial neural network, is an efficient function approximator. In this paper, a radial basis function network was used to build a mapping from the segment characteristics to the edge shift from the drawn position. This network can provide a good initial guess for each segment that OPC has carried out. The good initial guess reduces the required iterations. Consequently, cycle time can be shortened effectively. The optimization of the radial basis function network for this system was practiced by genetic algorithm, which is an artificially intelligent optimization method with a high probability to obtain global optimization. From preliminary results, the required iterations were reduced from 5 to 2 for a simple dumbbell-shape layout.
Optical proximity correction (OPC) is usually used to pre-distort mask layouts to make the printed patterns as close to the desired shapes as possible. For model-based OPC, a lithographic model to predict critical dimensions after lithographic processing is needed. The model is usually obtained via a regression of parameters based on experimental data containing optical proximity effects. When the parameters involve a mix of the continuous (optical and resist models) and the discrete (kernel numbers) sets, the traditional numerical optimization method may have difficulty handling model fitting. In this study, an artificial-intelligent optimization method was used to regress the parameters of the lithographic models for OPC. The implemented phenomenological models were constant-threshold models that combine diffused aerial image models with loading effects. Optical kernels decomposed from Hopkin’s equation were used to calculate aerial images on the wafer. Similarly, the numbers of optical kernels were treated as regression parameters. This way, good regression results were obtained with different sets of optical proximity effect data.
There have been several kinds of resist model proposed for optical proximity correction. The simplest one is the constant threshold resist model. By this method, only area with intensity above a certain threshold value would be developed. Unfortunately, the constant threshold resist model is too simplified to accurately describe the entire resist processes. To solve this problem, variable threshold resist models were proposed thereafter. The printed resist edge is characterized in terms of the aerial image properties, such as intensity, intensity slope and so forth. More parameters and freedoms are required to describe the complicated chemical reactions of the resist during exposure and development processes. However, the computation time for OPC would increase significantly due to the supplementary calculation of the extra aerial image properties. In this paper, the dual model of constant threshold was proposed to enhance the accuracy of constant threshold resist models. Two constant threshold resist models were determined by model fitting process based on different types of pattern structures. During the correction, one-dimensional and two-dimensional edges are identified first and different constant-threshold models were applied for simulation. Good corrections on both of the one-dimensional line/space widths and two-dimensional line-ends could be achieved. The simulation results were also compared with experimental data.