Investigating the Efficiency of Using U-Net, Erf-Net and DeepLabV3 Architectures in Inverse Lithography-based 90-nm Photomask Generation

Photolithography plays a significant role in modern microchip manufacturing processes. The choice of lithography technique depends on the size of the smallest chip element and production volume. With the node of 180 nm or less (90, 65, 32 nm) the wave nature of the 193-nm source used in exposure brings about optical proximity effects [1]. These effects of effects can distort the microchip geometry and reduce the yield [2]. The major pattern irregularities are line end shortening, rounded corners, spurious inter-feature bridges, narrower or wider line widths, etc. [3]. Modern photolithography technologies involve a number of resolution enhancement methods enabling the correction of optical proximity effects [4]. Some of these methods introduce calculated changes to the photomask geometry to compensate for errors caused by diffraction effects. Two methods can be used to correct the optical proximity effects for the 90-nm and 180-nm nodes. The first method is optical proximity correction (OPC), which is based on either rule-based approach [5] or a model-based approach [6]. The second method, inverse lithography technology (ILT), enables the optimization of the shapes of the openings in photomasks [7]. The use of ILT requires considerable computational resources and takes much time. The more photomasks are used to manufacture a microchip and the smaller the feature size is, the more time and computation power are required [8]. Transition to a finer node leads to both an increase in the number of photomasks per chip and an increase in the computation time per single layer [9].

The use of machine learning-based methods of artificial intellect [10] and neural networks [11] can help without possibly to reduce the consumption of time and computational resources in OPC and ILT. Some research teams work on uniting machine learning-based-OPC approach and EDA technical solutions to speed up the computation of photomask sets [12]. The use of machine learning and neural networks in computational lithography is considered in [13]. Earlier we investigated the efficiency of using different machine learning (ML) algorithms in the OPC technique [14]. The present paper focuses on the use of artificial neural nets for the computation of a photomask corresponding to that calculated by ILT.

The use of generative adversarial networks (GAN) for calculating photomasks is one of the possible solutions. The approach can be used either by itself [15] or in combination with a conventional method [16] which quickens the learning and increases the computation accuracy. Another solution involves specialized convolutional neural networks [17, 18] which are modified standard CNNs [19] or newly developed CNNS [20].

In our research, we deal with a 90 nm chip fabrication process. The OPC techniques we have to hand correspond to lithography equipment parameters and resist properties, which restrict the use of other machine learning models and neural networks. For this reason, we have generated original data sets using Calibre Workbench. The objective of the research is to determine the efficiency of available CNNs in terms of computation time and accuracy. U-net [21], Erfnet [22] and DeepLab3+ [23] are used in the comparison.

The models were typically trained 30 epochs until overtraining; each epoch took about 2 min. The results averaged over ten training processes are given in Table 1.

It is seen from Table 1 that all networks demonstrate similar quality indexes (they are the same to two places of decimal). Given the large number of runs, we can conclude that the neural networks have the same computation accuracy. It should be noted that the Unet structure demonstrates the least computation time: it is twice as shorter as ErfNet time and four times as shorter as DeepLabV3+. It allows us to conclude that the Unet structure is the fastest framework.

For comparison, the computation of a single element using conventional methods with Calibre EDA takes about 1 s.

As can be seen from Table 1, on the dataset without MRC, IoU achieves 0.9894, i.e. the conventional ILT methods and neural net-based training gave almost the same results (the difference is about 1%). In this case, the accuracy of the correction becomes a decisive factor. To measure it EPE metric is used.

The EPE-based evaluation of our model is shown in Fig. 4. The EPE histograms of the neural network and the original ILT model are used as a quality measure.

It is seen from Fig. 4 that the EPE distribution of the neural network is closer to zero. It means the neural network gives better results than the original ILT algorithm. Besides, the ILT algorithm-based computation of one pattern takes about a second, while the neural network takes 7 ms, i.e., the network works two orders of magnitude faster.

Unfortunately, we cannot achieve the same results on the dataset with MRC. For this dataset the IoU metrics is only about 0.92 (see Table 1). Moreover, as seen in Fig. 5, the neural net-generated outputs have noticeably rounded corners. Typical to all three networks, this effect can be regarded as their main drawback.

Similar to other inverse problems, the inverse lithography is a class of problems where the use of neural networks looks most natural. The solution generated by a neural network can be easily tested by a direct numerical modeling. Unlike the iterative process of solving inverse problems, this sort of modeling doesn’t take much time.

With the first data set the non-MRC ILT method demonstrated that the neural network works faster and gives more accurate results than standard algorithms employed in the industry. On the validation sample of 300 pattern couples the Unet-based neural network showed better results than the original inverse lithography model, the single-pattern computation time having decreased by about 100 times. Thus, we can conclude that the approach offers an acceptable level of efficiency.

Given the second data set, the MRC-assisted ILT algorithm demonstrates insufficient accuracy of networks (about 92% in terms of the IOU measure). In this case the main drawback is the presence of blurred edges in the output patterns, especially; the blurriness is especially dramatic near the pattern angles. The approach needs further investigations to cope with the drawback. Since the extensive way of increasing the number of model layers (the use of ErfNet) and the total number of parameters and layers (the use of DeepLabV3+) proved ineffective, we regard the use of new learning methods and other convolution layers as next steps towards good results.