Novel apodization and pellicle optical models for accurate optical proximity correction modeling at 45 and <inline-formula><math altimg="none" display="inline" overflow="scroll"><mrow><mn>32</mn><mspace width="0.3em" /><mi>nm</mi></mrow></math></inline-formula>

Abstract

An accurate optical model is the foundation of an accurate optical proximity correction ͑OPC͒ model, which has always been the key for successful implementation of model-based OPC. As critical dimension ͑CD͒ control requirements become severe at the 45-and 32-nm device generations, OPC model accuracy and hence optical model accuracy requirements become more stringent. In previous generations, certain optical effects could be safely ignored. For example, the transmission attenuation particularly at high spatial frequencies caused by lens apodization effects and organic pellicle films was ignored or not accurately modeled in conventional OPC simulators. These effects are now playing a more important role in OPC modeling as technology scales down. Our simulations indicate these effects can cause CD modeling errors of 5 nm or larger, at the 45-nm technology node and beyond. Therefore, they must be accurately modeled in OPC modeling. In our OPC modeling methodology, we propose two novel low-pass-filter models to capture the frequency-dependent transmission attenuation due to lens apodization and to pellicle films. These parameterized novel lowpass-filter models ensure that lens apodization and pellicle-film-induced transmission attenuation can be appropriately account for through regression during the experimental OPC model calibration stage in the case where no measured transmission data are available, thus enabling physics-centric OPC model building with considerably higher accuracy. We can then avoid overfitting the OPC model, which could cause instability in the OPC correction stage. The validity and efficiency of the proposed novel models are also verified using an industry-standard lithography simulator as well as an experimental OPC model calibration at the 45-nm technology node.