# EUV-Induced Plasma: A Peculiar Phenomenon of a Modern Lithographic Technology
## 2 EUV-Induced Plasma
### Recent Experimental Work on EUV-Induced Bulk Plasmas
The side walls of the measurement chamber are made of a mesh for visibility and the top and bottom lids contain concentric holes for entrance and exit of the EUV beam. At indicates the used gate width of the camera. Intensities are normalized for each image individually. Figure produced using data from [26]. [PERSON] et al. came to a similar conclusion by experimental work that was analyzed while using different probe theories and compared to numerical simulations [12; 22]. Microwave Cavity Resonance Spectroscopy (MCRS)  
[PERSON] and [PERSON] first proposed the utilization of the interaction between microwaves and plasma to probe electrons [37; 38; 39]. Later, this principle has been used in many studies, for instance to the end of measuring the density of free electrons in low pressure radiofrequency driven gas discharges [40]. In concert with laser-induced photodetachment, MCRS has even appeared as a feasible diagnostic to measure the density of negative ions in for instance etching [41; 42; 43] and in powder forming plasmas [44; 45; 46; 47; 48]. Recently, MCRS has even been applied as an electron diagnostic in plasmas at atmospheric pressure [49]. In MCRS-based diagnostics, the plasma under study is enclosed by a (cylindrical) resonant cavity. By sending in low power microwave radiation--for instance by means of an antenna through one of the side walls--a resonant mode might be excited at certain frequencies. These resonant frequencies are determined by I) the geometry of the plasma enclosing cavity (which is ideally fixed during experiment) and II) the permittivity \(\varepsilon\) of the medium inside the cavity volume. It is the change of \(\varepsilon\) due to the presence of free electrons in the cavity volume that is key to this diagnostic. Hence, by measuring the difference \(\Delta\omega~{}=~{}\omega-\omega_{0}\) between the resonant frequency \(\omega\) of a plasma-filled cavity and the resonant frequency \(\omega_{0}\) of an empty cavity, the density \(n_{e}\) of free electrons can be computed from [11]:  
\[\overline{n_{e}}~{}=~{}\frac{2m_{e}\varepsilon_{0}\omega^{2}}{e^{2}}\frac{ \Delta\omega}{\omega_{0}} \tag{4}\]  
where \(e\) and \(m_{e}\) are the charge and mass of an electron, respectively, and \(\varepsilon_{0}\) is the permittivity of vacuum. In practice, MCRS has been applied to EUV-induced plasmas by sending a pulsed EUV beam through a cavity that contained holes in its top and bottom cavity lids for this purpose (see Figure 5) [11; 17; 18; 34; 35; 50]. Microwave (MW) antennas that are inserted through the cavity wall are used to send in microwave radiation and to record the cavity's response (either in transmission or reflection mode). More experimental details can be found in the above referenced literature. Figure 5: Microwave Cavity Resonance Spectroscopy (MCRS) configuration for probing free electrons in an EUV-induced plasma. The pulsed beam of EUV light is directed through a resonant cavity. It should be noted that the bar on \(\overline{n_{e}}\) in Equation (4) indicates that this value is cavity-volume averaged and is weighted with the squared electric field distribution \(E^{2}(\overrightarrow{r})\) of the resonant mode inside the cavity:  
\[\overline{n_{e}}\ =\ \frac{\iint n_{e}(\overrightarrow{r})E^{2}(\overrightarrow{r })d^{3}\overrightarrow{r}}{\iint E^{2}(\overrightarrow{r})d^{3} \overrightarrow{r}} \tag{5}\]  
This means that electrons that were present in the cavity volume are probed to the highest extent at positions, where the used resonant mode has its maximum field strength (e.g., on the cavity's axis when the TM\({}_{010}\) mode (see Figure 6a) is used and roughly at half the cavity's radius when the TM\({}_{110}\) mode (see Figure 6b) is used). Despite the fact that MCRS is a strong diagnostic that has delivered valuable information and understanding regarding EUV-induced plasmas, its volume-averaged nature has always been considered to be disadvantageous, since local plasma physical effects could--in this configuration--not be resolved.