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 <i>k<sub>1</sub></i> 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 (AIMS<sup>TM</sup>) 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 AIMS<sup>TM</sup> 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.