Investigating the Performance of Directional Boundary Layer Modelthrough Staged Modeling Method

摘要

Generally speaking, the models used in the optical proximity effect correction (OPC) can be divided into three parts, mask part, optic part, and resist part. For the excellent quality of the OPC model, each part has to be described by the first principles. However, OPC model can't take the all of the principles since it should cover the full chip level calculation during the correction. Moreover, the calculation has to be done iteratively during the correction until the cost function we want to minimize converges. Normally the optic part in OPC model is described with the sum of coherent system (SOCSt11) method. Thanks to this method we can calculate the aerial image so fast without the significant loss of accuracy. As for the resist part, the first principle is too complex to implement in detail, so it is normally expressed in a simple way, such as the approximation of the first principles, and the linear combinations of factors which is highly correlated with the chemistries in the resist. The quality of this kind of the resist model depends on how well we train the model through fitting to the empirical data. The most popular way of making the mask function is based on the Kirchhoff s thin mask approximation. This method works well when the feature size on the mask is sufficiently large, but as the line width of the semiconductor circuit becomes smaller, this method causes significant error due to the mask topography effect. To consider the mask topography effect accurately, we have to use rigorous methods of calculating the mask function, such as finite difference time domain (FDTD[21) and rigorous coupled-wave analysis (RCWAE31). But these methods are too time-consuming to be used as a part of the OPC model. Until now many alternatives have been suggested as the efficient way of considering the mask topography effect. Among them we focused on the boundary layer model (BLM) in this paper. We mainly investigated the way of optimization of the parameters for the BLM since the feasibility of the BLM has been investigated in many papers[41[51[61. Instead of fitting the parameters to the wafer critical dimensions (CD) directly, we tried to use the aerial image (AI) from the rigorous simulator with the electromagnetic field (EMF) solver. Usually that kind of method is known as the staged modeling method. To see the advantages of this method we conducted several experiments and observed the results comparing the method of fitting to the wafer CD directly. Through the tests we could observe some remarkable results and confirmed that the staged modeling had better performance in many ways.