Optical proximity correction

The conventional diffraction-limited resolution is given by the Rayleigh criterion as ${\displaystyle 0.61\lambda /NA,}$ where ${\displaystyle NA}$ is the numerical aperture and ${\displaystyle \lambda }$ is the wavelength of the illumination source. It is often common to compare the critical feature width to this value, by defining a parameter, ${\displaystyle k_{1},}$ such that feature width equals ${\displaystyle k_{1}\lambda /NA.}$ Nested features with ${\displaystyle k_{1}<1}$ benefit less from OPC than isolated features of the same size. The reason is the spatial frequency spectrum of nested features contains fewer components than isolated features. As the feature pitch decreases, more components are truncated by the numerical aperture, resulting in greater difficulty to affect the pattern in the desired fashion.

OPC applied to contact pattern. Due to the edge modification in the mask layout (top), the center contact in the right column is undersized in the wafer printed image (bottom).

The degree of coherence of the illumination source is determined by the ratio of its angular extent to the numerical aperture. This ratio is often called the partial coherence factor, or ${\displaystyle \sigma }$.[1] It also affects the pattern quality and hence the application of OPC. The coherence distance in the image plane is given roughly by ${\displaystyle 0.5\lambda /(\sigma NA).}$[2] Two image points separated by more than this distance will effectively be uncorrelated, allowing a simpler OPC application. This distance is in fact close to the Rayleigh criterion for values of ${\displaystyle \sigma }$ close to 1.

A related point is that the use of OPC does not change the illumination requirement. If off-axis illumination is required, OPC cannot be used to switch to on-axis illumination, because for on-axis illumination, imaging information is scattered outside the final aperture when off-axis illumination is needed, preventing any imaging.

Aberrations in optical projection systems deform wavefronts, or the spectrum or spread of illumination angles, which can affect the depth of focus. While the use of OPC can offer significant benefits to depth of focus, aberrations can more than offset these benefits.[3] Good depth of focus requires diffracted light traveling at comparable angles with the optical axis, and this requires the appropriate illumination angle.[4] Assuming the correct illumination angle, OPC can direct more diffracted light along the right angles for a given pitch, but without the correct illumination angle, such angles will not even arise.

As the ${\displaystyle k_{1}}$ factor has been steadily shrinking over the past technology generations, the anticipated requirement of moving to multiple exposure to generate circuit patterns becomes more real. This approach will affect the application of OPC, as one will need to take into account the sum of the image intensities from each exposure. This is the case for the complementary photomask technique,[5] where the images of an alternating-aperture phase-shifting mask and a conventional binary mask are added together.

In contrast to multiple exposure of the same photoresist film, multiple layer patterning entails repeated photoresist coating, deposition, and etching to pattern the same device layer. This gives an opportunity to use looser design rules to pattern the same layer. Depending on the lithography tool used to image at these looser design rules, the OPC will be different. Multiple-etch patterning may become a popular technique for future technology generations. A specific form of multiple-etch patterning, using sidewall sacrificial features, is currently the only demonstrated way of systematically patterning features less than 10 nm.[6] The minimum half-pitch corresponds to the deposited thickness of the sacrificial feature.

Today, OPC is rarely practiced without the use of commercial packages from electronic design automation (EDA) vendors. Advances in algorithms, modeling techniques and the use of large compute farms has enabled the most critical patterning layers to be corrected overnight, starting from the 130 nm design rules (when model based OPC was first used) [7] down to the most advanced design rules. The number of layers requiring sophisticated OPC has increased with advanced nodes, as previously non-critical layers now require compensation.

The use of OPC is not restricted to the low ${\displaystyle k_{1}}$ features which are commonly encountered today, but can be applied to any desired image correction scheme which can be modeled accurately. For example, proximity effect correction in electron beam lithography is included as an automated capability on commercial electron-beam lithography tools. Since many non-lithographic processes exhibit their own proximity effects, e.g., chemical-mechanical polishing or plasma etching, these effects can be mixed in with the original OPC.

Subresolution assist features (SRAFs)

Optical proximity correction of a main circuit and its assist features.

Assist feature OPC. The use of assist features match isolated feature images closer to dense feature images, but the assist features may themselves print accidentally.

Defocus effect on SRAFs. Defocus can still limit the benefits of assist features, by allowing their printing.

Subresolution assist features (SRAFs) are features which are separated from targeted features but assist in their printing, while not being printed themselves. Printing SRAFs are a critical yield detractor and require additional OPC models to determine and remove SRAFs where undesirable printing may occur.[8] SRAFs have more pronounced effects on the diffraction spectrum than targeted feature resizing and/or attachments. The requirement to not print constrains their use with low doses only. This could pose issues with stochastic effects.[9] Hence their main application is to improve depth of focus for isolated features (dense features do not leave enough room for SRAF placement). Since SRAFs redistribute energy toward higher spatial frequencies or diffraction orders, the depth of focus is more dependent on the illumination angle (center of spectrum of spatial frequencies or diffraction orders) as well as the pitch (separation of spatial frequences or diffraction orders). In particular, different SRAFs (position, shape, size) could result in different illumination specifications.[10][11] In fact, certain pitches forbid the use of SRAFs for specific illumination angles.[12] Since the pitch is usually predetermined, some illumination angles must be avoided even with the use of SRAF OPC. Generally, though, SRAFs cannot be a complete solution, and can only approach the dense case, not match it.[13]

• Computational lithography
• Phase-shift mask
• Inverse lithography

• Overview of OPC, with diagrams, by Frank Gennari