# EUV-Induced Plasma: A Peculiar Phenomenon of a Modern Lithographic Technology
## 2 EUV-Induced Plasma
### Dynamics of EUV-Induced Plasmas  
Figure 8 depicts the typical evolution of the density \(\overline{n}_{e}\) of free electrons in a resonant cavity that was obtained from MCRS measurements before, during, and after a low pressure (1-10 Pa) H\({}_{2}\) gas was irradiated with a pulse of EUV radiation [17]. \(\overline{n}_{e}\) is locally weighted with the square of the (microwave) electric field and volume averaged. \(\overline{n}_{e}\) is plotted in normalized values, since absolute values strongly vary with experimental parameters, such as gas pressure, pulse energy, and gas type. Absolute values that are below \(10^{17}\) m\({}^{-3}\) are typical densities expected for these kinds of plasma. Phenomenologically, the basic plasma processes can be split up into three different consecutive phases in time (see Figure 8). In Phase I, \(\overline{n}_{e}\) strongly increases upon irradiating the gas with EUV photons. In Phase II, there is no EUV-irradiation and \(\overline{n}_{e}\) decreases at a rate that is faster than exponential. In the last phase--Phase III--an exponential decay rate of the plasma sets in. Below, Phases I-III will briefly be discussed in consecutive order. Photoionization  
From Figure 8 it can be observed that, free electrons are created in Phase I, upon EUV-irradiation of the H\({}_{2}\) background gas. The three dominant photon-induced processes are single photoionization (Equation (6)), dissociative photoionization (Equation (7)), and double photoionization (Equation (8)). \[\mathrm{H}_{2}+h\
u\rightarrow\mathrm{e}+\mathrm{H}_{2}^{+} \tag{6}\]  
\[\mathrm{H}_{2}+h\
u\rightarrow\mathrm{e}+\mathrm{H}_{2}^{+*}\rightarrow \mathrm{e}+\mathrm{H}^{(*)}+\mathrm{H}^{+} \tag{7}\]  
\[\mathrm{H}_{2}+h\
u\rightarrow\mathrm{2e}+\mathrm{H}_{2}^{2+}\rightarrow \mathrm{2e}+2\mathrm{H}^{+} \tag{8}\]  
The cross sections for the reactions in Equations (6)-(8) are given in Figure 9 as a function of the photon energy in the range 20-120 eV. At photon energies of 92 eV (i.e., 13.5 nm), which is relevant for EUVL, contributions from single photoionization (roughly 80%) mainly dominate the total photoionization cross section \(\sigma_{\mathrm{pi}}=6.5\times 10^{-24}\) m\({}^{2}\). Figure 8: Typical electron density \(\overline{n}_{e}\) in an EUV-induced plasma in H\({}_{2}\) averaged over the measurement geometry. The figure inset is a zoom in up to 1 μs along with the temporally resolved EUV intensity with which the gas is irradiated. The consecutively occurring phases I, II, and III are discussed in the text below. Figure produced using data from [24]. In general, the photon energy in lithography systems considerably exceeds the ionization energy of the used gas; e.g., 15.4 eV for the transition from the ground state of hydrogen (\(H_{2}\), \(X^{1}\Sigma_{g}^{+}\)) to the stable ionic ground state (H\({}_{2}^{+}\), 1\(so_{s}\)). This excess energy is mainly transferred to the ejected electron, which then has an energy of 76.6 eV, while the created H\({}_{2}^{+}\) ion remains relatively 'cold' at room temperature. Equation (7) shows that H\({}^{+}\) ions are created through dissociation of an electronically excited H\({}_{2}\)\({}^{*}\) state with an atomic H radical as a second reaction product. The excess energy of this reaction is evenly distributed over the ionic and radical compounds since the ion and radical have similar masses (each about 8 eV [56]). The same principle accounts for Equation (8), where H\({}_{2}\)\({}^{2+}\) is highly unstable by definition. Upon dissociation of this compound, 18.8 eV is evenly distributed over the two resulting H\({}^{+}\) ions [57]. Overall, due to photoionization events, during EUV-irradiation, initial plasma is created that also contains H\({}^{+}\) and H\({}_{2}\)\({}^{+}\) and radicals, besides electrons (both fast and slow). Additionally, on small time scales (\(\sim\)200 ns) H\({}_{2}\)\({}^{+}\) and H\({}_{2}\) may react as [58]:  
\[\mathrm{H}_{2}^{+}+\mathrm{H}_{2}\rightarrow\mathrm{H}_{3}^{+}+\mathrm{H} \tag{9}\]  
to form H\({}_{3}\)\({}^{+}\) ions.