# EUV-Induced Plasma: A Peculiar Phenomenon of a Modern Lithographic Technology
## 2 EUV-Induced Plasma
### Scaling Laws  
Most of the reported experiments have been conducted in conditions that, in one way or another, deviate from the conditions that are expected in current and future EUVL tools. However, from both experiments and numerical work, the scaling laws with respect to several parameters, such as EUV spectrum, gas pressure, pulse energy, repetition rate, and gas type, can be derived and are as follows. * Influence of EUV spectrum  
The spectrum of the light that is used to irradiate the system under investigation is of utmost importance. Where during normal operation the normal-incidence multi-layer mirrors in the lithography tool inherently narrow down the spectrum to a range that closely centered around 13.5 nm, experiments have also been conducted for wider spectral ranges. For instance, it was shown by the MCRS experiments that the density of an EUV-induced plasma in 10\({}^{-4}\) mbar residual background gas keeps increasing significantly, even after the main in-band EUV radiation has fully vanished in the absence of a spectral purity filter (SPF) [51]. This effect was explained by out-of-band radiation that was emitted by the EUV source later in time. The fact that the contribution of out-of-band radiation to the total emission of the EUV source is relatively low, is more than compensated by the higher total ionization cross section at lower photon energies. For instance, the total ionization cross section of \(2.5\times 10^{-21}\) m\({}^{2}\) is almost one order higher than the value of \(2.5\times 10^{-22}\) m\({}^{2}\) at 92 eV for N\({}_{2}\) molecules (making up \(\sim\)80% of the molecules) that are just above the ionization threshold (15.6 eV) [62]. An extensive study regarding the influence of the EUV spectrum on the creation of EUV-induced plasmas in hydrogen was published in Ref. [35]. In that publication, both the used spectral purity filter (no-filter, normal SPF, and aluminum filter) and source type (Xe-based EUV source versus Sn-based EUV source) demonstrated a significant effect on the plasma formation. * Gas pressure scaling  
Within the experimental range investigated [17], it has been demonstrated that the maximum obtained density of the bulk plasma scales quadratically with the pressure of the background gas. As mentioned before, the initial electrons are created by photoionization. From Equations (6)-(8), it can be understood that this process linearly scales with the H\({}_{2}\) density, i.e., pressure. These initial electrons can subsequently ionize H\({}_{2}\) by electron impact ionization, which scales with the electron density (linearly dependent on pressure) and the gas pressure (see Equations (10)-(12)). Hence, the electron density that was caused by electron impact ionization quadratically scales with pressure. This means that the pressure dependence of the total electron density has both a linear and a quadratic term, which only holds for the maximum obtained electron density in the investigated range. The electrons that were created by photoionization are only able to cause three electron impact ionization events due to the limited amount of energy (76 eV) and the lack of electron heating mechanisms. This means that the quadratic scaling will not hold for higher pressures or long time scales, since no more additional electrons will be created after a few collisions (the electrons have cooled down too much). In this regime, the density scales linearly with pressure, since every photoionization event creates in the end (via electron impact ionization) four electrons. * Pulse energy scaling  
It has been demonstrated that the maximum reached bulk plasma density just after the gas is irradiated with EUV photons is in the order of \(\sim\)10\({}^{15}\) m\({}^{-3}\) within the experimental range investigated [16; 17; 34]. This density scales linearly with pulse energy. * Source repetition rate scaling  
Most of the experiments up to now have been conducted while using an EUV source with a relatively low repetition rate of 500 Hz.