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Why does corner rounding occur? How can we compensate for corner rounding?
Line-End Treatments Multiple Treatments Combining Vertex Treatment with Fracture Features... What is Vertex Treatment? What Are the Typical Challenges? The challenges faced by photomask makers and wafer lithographers today are quite similar in many respects to those faced by the industry ten years ago. However, with shrinking geometries the challenges have intensified. It has been known for a very long time that, although design features tend to be sharply rectilinear, photomask corners and their corresponding wafer images are not square. "Corner rounding," as it is typically called, has been observed for many years. Until relatively recently, however, the rounding was insignificant relative to the size of the overall geometries. With today's design rules in the sub-half micron range in production devices, corner rounding is no longer an insignificant challenge. Corner rounding and its cousin, line-end shortening, have become problems that require addressing. Both problems can result in degraded device performance, reduced reliability, and in some cases lost yield. They can also cause some problems in mask inspection resulting in "false defects."
Why does corner rounding occur? There are several factors which can cause corner rounding on the photomask and similar factors in wafer exposure and processing. On photomasks, corner rounding and line-end shortening have been attributed to the limitations of the exposure tool, to electron-beam proximity effects, to physical effects observed in mask development and etch. It is important to simply understand that each of these effects tend to result in rounding at both interior and exterior corners. All electron-beam and laser mask exposure tools employ some sort of flying elliptical spot of a finite diameter. While the spot size tends to be small relative to the size of the feature being written, some degree of corner rounding is likely to happen due to the elliptical nature of the exposure tool's beam spot. Not much can be done with the data to make the exposing spot more square, however, solutions exist to compensate for the rounding effect. The electron-beam proximity effect is also a well known physical characteristic of e-beam exposure tools and photomask materials. The e-beam proximity effect can be briefly described as a neighborhood dose effect. Electrons have a tendency to scatter at material interfaces. If we were to examine a cross-section of a photomask, for instance, we'd see several material layers including resist, an anti-reflective layer, chrome, and quartz. At each material transition both forward and backward scattering may occur. The magnitude of the scattering is related to the injection energy of the electron source and the molecular weight of the materials. There are two components to dose, forward scatter electrons and backward scatter electrons. If we were to trace the electrons through the materials and calculate the effect their paths have on the exposure imparted to the resist (see CATS' SCELETON™ module), we would be able to determine the proximity function which results from both forward and backward scatter of electrons. A typical proximity function may look similar to the following graph:
 Figure: Typical Proximity Function Notice that there is a finite range to both the forward and backward scatter components to the exposure. It is the backward scatter component that plays a role in corner rounding. Examine the following diagram:
 The square in this diagram represents a square feature in the design to be exposed on a photomask. The tiny circle represents the point of incidence of the electron beam while the larger circle represents the back scatter range. It can be said that at point #1 in the diagram, all points within the larger circle contribute some dose to the center point since that point is within the back scatter range of all points within the larger circle. At point #2, only 1/2 as much "neighborhood" is contributing back scatter dose to the point, while at point #3 only 1/4 the back scatter dose is observed. So, while the forward scatter dose is essentially the same for all three points, the back scatter component of the dose is clearly the most in the center of the figure (where the figure is essentially infinitely large relative to the back scatter range) and the least at a corner. The e-beam proximity effect clearly is one component in corner-rounding. How can we compensate for corner rounding effects in data preparation? Regardless of the various causes of corner rounding, the general solution is to add more dose at exterior corners and subtract some dose at interior corners. One technique available in CATS to accomplish this is the addition of "serif" features to exterior corners and/or the subtraction of serif features at interior corners. While this does not systematically take into account the complexities of the e-beam proximity function, it does provide a fast and efficient tool for the selective modification of shapes to compensate for an observable phenomenon. What are the Capabilities of CATS' Vertex Treatment? The Vertex Treatment option in CATS provides the ability to: describe a vertex describe a treatment A vertex is described as either an interior corner, an exterior corner, or an end-of-line. Additionally, the vertex is described by the attributes of its adjacent edges.  Once a vertex is defined, an associated treatment serif may also be defined. The serif is described by its shape, by its long and short dimensions and by its long- and short-dimension offsets. A serif description is associated with each type of vertex to be treated. Up to three vertex/serif definitions may be described at one time. Inner & Outer Vertex Treatments Let's look at some simple examples. In the first example, let's add a 1/2 micron square serif centered on the outer corner of the design shape.  Square Outer Vertex Treatment Let's look at a similar example where the data is the same and the shape is the same but the serif is inset into the figure by .15 µm:  Offset Square Outer Vertex Treatment Note that the serif is still 0.5 µm on a side but it is inset into the vertex to create a smaller extension of the exterior vertex. How would this technique apply to interior vertices? Let's look at a 0.5 µm serif centered on an interior corner:  Square Inner Vertex Treatment And let's look at an outset serif on an interior corner:  Offset Square Inner Vertex Treatment The user may also choose non-rectangular shapes for inner and outer vertex treatments. Diamond-shaped and tringular-shaped serifs may be generated in both square and rectangular ("stretched") aspect ratios. Let's look at some examples:
Now that we've examined both outer and inner vertices, let's take a look at some of the possible line-end treatments. A line-end may be treated as two exterior corners such that serifs are placed on the corners, or it may be treated with one of two unique line-end treatments: extension or hammerhead. A line-end treatment using .5 µm square serif features centered at the corners of the line-end would be as follows: 
Centered Square Line-End Treatment The placement of these serifs may be offset either into or away from the line-end corners. The serifs placed here may also be given long and short dimensions so that they may extend the end of the line as in the following example. 
Centered Rectangular One of the special line-end treatments is an "extension." The amount of the extension may be defined as well as any desired offset. 
Extension Line-End Treatment The other special line-end treatment is a "hammerhead." Both the extension and the protrusion amounts may be specified as well as offset values. 
Offset Hammerhead CATS can use three vertex rules in any given fracture. This allows the simultaneous treatment of outer, inner and line-ends in a single pass. It also means that the user could perform three different line-end treatments in a single pass, or three different corner treatments in a single pass. Let's look at a couple of examples here. In the first example we'll illustrate single-pass treatment of inner corner, outer corner and line-ends.
 Let's look at another example. Notice here that we've performed the following treatments:
The types of treatments that will be selected depend on the goal of the treatment. If the goal is to reduce mask corner rounding and line end shortening then the serif treatments will be moderate and the features will not be apparent on the mask. However, if the goal of the treatment is to produce improved wafer images, then the serif features will be visible on the photomask. In a final example, a pattern is treated and sleeved in a single fracture step. In this example, the outer corners are treated with a .5 µm square serif, the inner corners are treated with a .3 µm square serif and the treated pattern is sleeved. The resulting pattern is composed of a bulk region whose resolution is 0.25 µm and a sleeve region whose resolution is 0.05 µm. Sleeving is a method of dividing a pattern into a bulk region and a sleeve region for improved line-edge quality and faster write times.
CATS' Vertex Treatment option provides the user with the ability to simultaneously and independently treat inner vertices, outer vertices, and line-ends to compensate for typical corner rounding and line-end shortening effects on the photomask and/or wafer. The process adds negligible overhead to the fracture process and is seamlessly integrated with CATS' standard fracture capabilities. For more demanding devices, Vertex Treatment may be used in conjunction with Photolynx® (optical proximity correction) to provide less rigorous treatments for less critical layers. |
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