# EUV-Induced Plasma: A Peculiar Phenomenon of a Modern Lithographic Technology
## 1 Introduction  
_EUV-Induced Plasma and Its Relation to Photolithography_  
Photolithography is one of the key steps in the production process of semiconductor structures, i.e., computer chips, on the nanoscale. In these systems, a pattern on a so-called reticle is imaged in a repetitive way on each single microchip by an optical system, which decreases the image on a spatial scale by a factor of 4. To the end of fulfilling the ever-lasting drive for shrinking the dimensions of the features on such chips, the following two well-known equations for the system's resolution or critical dimension (CD):  
\[\mathrm{CD}\ =\ \frac{k_{1}\lambda}{\mathrm{NA}} \tag{1}\]  
and the depth of focus (DOF)\[\text{DOF}\ =\ \pm\frac{k_{2}\lambda}{\left(NA\right)^{2}} \tag{2}\]  
are crucial [1]. In these equations, \(k_{1}\) and \(k_{2}\) are process dependent constants, \(\lambda\) is the wavelength of the light used, and \(\text{NA}\ =\ n\sin\alpha\) is the numerical aperture of the used lens with \(n\) and \(\alpha\) the refractive index of the medium surrounding the lens and the acceptance angle of the lens, respectively. Decreasing the feature size on a chip requires increasing NA and/or conducting the photolithographic process at a smaller wavelength. In the past, the wavelength of the light used has been scaled down from 436 nm (g-line) to 365 nm (i-line) to 248 nm (KrF) to 193 nm (ArF). The most advanced deep Ultraviolet (DUV) machines that are currently in the field employ \"immersion lithography\"--introduced in 1987 [2]--where the lens is immersed in a medium with a higher refractive index (e.g., in water with \(n\) = 1.43). This has led to an increase of NA up to 1.35. The shift from the 22 nm to the 14 nm node was achieved with double patterning lithography based on 193 nm DUV systems [3]. Photolithography using Extreme Ultraviolet (EUV) photons with wavelengths of 13.5 nm (and energies of 92 eV) has been introduced with the eye on achieving significant cost reduction (per produced chip) and downscaling of the feature size even more [4]. Several types of EUV sources have been, or are, under development for the production of the high flux of needed EUV photons. Besides the relatively low power xenon-based EUV sources [5], types of high power EUV sources include EUV sources that are based on laser produced plasmas (LPP) from tin droplets [6; 7; 8] and EUV sources that are based on laser-assisted discharge produced plasmas (DPP) in tin vapor [9]. Lithography tools ideally operate under vacuum conditions since EUV photons are effectively absorbed by almost any medium. However, for technical reasons, modern lithographic tools using EUV light operate in 1-10 Pa hydrogen background gas [3]. Inherently, everywhere, such photons travel through the background gas, neutral gas particles are photo-ionized, and plasma is created. These so-called EUV-induced plasmas are highly transient in time and they initially contain highly energetic electrons (76 eV) that thermalize on time scales of 100 ns--10 \(\upmu\)m, depending on the system's conditions. Especially, in the early stages of the afterglow of such pulsed plasma, the highly energetic electrons may create additional plasma species due to consecutive electron impact ionization of gas neutrals, while ionic compounds are accelerated towards plasma-facing surfaces--EUV-induced plasmas interact with the machine by means of, for instance, initiating plasma-enhanced chemistry, ion bombardment of delicate plasma-exposed surfaces, and enabling contamination transport to positions in the machine where harm is most dominantly felt. It is not only to fulfill scientific curiosity with respect to this peculiar type of plasma, but also for its practical implications towards EUV lithography (EUVL) that research groups all over the world have started considerable research efforts.