Objective Excimer lasers are widely used in industrial, medical, and scientific fields because of their short wavelength, high power, and narrow line width. Especially rare gas halogen excimer laser, because of its high peak output power, high single pulse energy, and ultraviolet wavelength, has become the main laser source in the semiconductor lithography industry. Its energy is one of the three key parameters (energy, linewidth, and wavelength) of excimer laser for photolithography, which directly determines the processing accuracy, yield, and key dimensions of semiconductor lithography. When studying the energy of an excimer laser, the closer the model approaches the actual law of light output energy, the more conducive to the study. The output energy model of an excimer laser is the basis for studying and controlling the energy characteristics of the laser. Discharge process of excimer laser is a complex nonlinear process, which leads to the accuracy of laser discharge energy model based on discharge dynamics is difficult to meet the needs of simulation research and control algorithm design. In this paper, the method based on deep learning was applied to identify the energy mode of excimer laser to avoid the inaccuracy of theoretical modeling.
Methods The development of deep learning theory has become more and more complete. It has become a tool and has been widely applied. Among them, recurrent neural network (RNN) is an important branch in the field of deep learning. It has been widely used in language recognition, machine translation, text analysis and other fields. In recent years, circulating neural networks abroad, especially its variant gate recurrent unit (GRU), has been applied to model recognition, trend prediction and other fields. In this paper, the gated recurrent unit network was used to identify the discharge energy model of the excimer laser. Firstly, based on the characteristics of the excimer laser energy, the discharge voltage and discharge interval were selected as the input of the established gating recurrent unit network. Then, according to the characteristics of the gated recurrent unit network and the excimer laser energy, a neural network suitable for energy model identification of excimer laser was established. When using the GRU network to identify the laser light energy model, a burst pulse energy sequence was used as a time sequence. Finally, the back propagation through time (BPTT) was used to train the established GRU network.
Results and Discussions Using GRU to learn the energy model of excimer laser requires a lot of data. The data was taken from a KrF excimer laser that produces laser of 248 nm, which worked at a repetition frequency of 4 kHz. Since the wavelength of the excimer laser also affects the energy data, in the course of the experiment, the wavelength was controlled at 248.327 nm using feedback technology. Energy data of the laser was collected under discharge high voltages of 1400 V, 1450 V, 1550 V, and 1600 V, respectively. In order to make full use of the data, at each training, the data under different discharge voltages was randomly selected to train GRU. The termination condition was set as 100000 trainings or the maximum error less than 0.15 mJ. The maximum error of model under each high voltage was less than 0.15 mJ (Fig. 6). Since the energy center value was 10 mJ, the relative error was less than 1.5%. The change of the maximum error in the training process indicates that the GRU neural network converges during the training process (Fig. 7). The data outside the training set was used to validate the model. The model obtained by training was used to calculate the laser light energy when the high voltage was 1550 V, and the comparison between the obtained energy value and the energy value collected on the actual laser after processing (1) is shown in Fig.8. The energy obtained through the GRU neural network has a good coincidence with the energy of the actual pulse. Another verification data set was collected at laser working with repetition frequency of 1, 2, 3, and 4 kHz. The maximum error between the model data and the actual laser data was less than 0.13 mJ under different repetition frequencies, that is, the relative error was less than 1.5% (Fig. 10).
Conclusions The energy model of excimer laser is a complex nonlinear model, which is difficult to get an accurate model from the theory. However, the actual research and application work need an accurate laser output energy model. In this paper, through the method of deep learning, GRU neural network was to identify the energy model. The verification results show that the maximum error between the pulse energy generated by the laser energy model identified by GRU neural network and the actual energy was less than 1.5%. The maximum error 1.5% is less than 2.74% of the required energy stability in dose control, which meets the simulation requirements of the model control effect. This method can accurately identify the laser energy model. Using the identified model can be more convenient for the simulation of energy control algorithm, so as to improve the energy stability control and dose accuracy control of excimer laser.
