Numerical study of extreme-ultra-violet generated plasmas in hydrogen

Abstract

In this thesis, we present the development and study a numerical model of EUV-induced plasma. Understanding of behavior of low pressure low density plasmas is of industrial relevance, because of their potential use for on-line removal of different forms of contaminations from multilayer mirrors, which will help increase the throughput of EUV lithography. The model is 2D axially symmetric particle-in-cell code, hence it allows the full geometry of an axially symmetric chamber to be taken into account. Therefore, a quantitative connection between different experimental data, such as discharge characteristic measurements, and plasma parameters could be established. In order to ensure that the simulations could be relied on for quantitative comparisons, special attention was paid to validating the model. First, the mplementation of the model was tested using the accumulated large body of the swarm data to check the values of cross-sections (see chapter 2, section 2.8). In a second step (see chapter 5), direct simulation of the dynamics of a low-density plasma, ignited by an electron avalanche, in the presence of a diagnostic probe was used as both a validation step and as a first direct comparison between experiment and model. In this study, the plasma, the probe response to the plasma, and the probe’s influence on the plasma were all included in the model. Besides validation, the simulated plasma parameters were compared with that estimated from the probe IV curves using a variety of techniques. It was shown that different probe analysis techniques lead to significant under and over estimates of plasma densities. From these results, we suggested a useful criterion for estimating the error margin in experiments. The introduction of EUV radiation into the experimental chamber adds a new layer of unknown and/or poorly known parameters, such as the power spectral density and intensity. These new unknowns were treated, within limits, as free parameters that were varied to obtain close agreement between the numerical model and experimentally measured parameters. This approach was only possible because of the extensive testing and validation of the model, which allowed us to freeze the model state, and concentrate on the effects of added the parameters and new EUV plasma dynamics. The influence of different parameters on the ignition and dynamics of EUV induced plasmas was studied (see chapter 6). It was found that even low (i.e. 1%) transmission in the spectrum purity filters in vacuum-ultraviolet wavelength range can have a significant role for EUV-induced plasma formation. Finally, an experiment with carbon etching, due to EUV induced plasma was considered (see chapter 7). It was found that the predicted yield of carbon removal under EUV radiation in a hydrogen atmosphere corresponds well to etching experiments without EUV. This suggests that the underlying physical mechanism is the same in both cases, and that direct EUV processes play an insignificant role in carbon etching. The developed model is applicable to pulsed low pressure low density EUV generated plasmas. It has proven to be a convenient instrument to help experimentalists understand EUV plasma dynamics. Although the model can be extended in various ways, the most promising, from the perspective of understanding EUV plasma, is the extension of the model to a hybrid plasma model (see Chapter 8).