**1. Introduction**

Photons of the soft X-ray spectral region (≈ 0.1–10 nm) have very small absorption lengths in all kinds of material due to the strong interaction with matter [1]. This fact together with the short wavelength qualifies this radiation as a tool for structuring and the analysis with nanometer resolution. An important application is the next-generation lithography that further reduces the achievable feature size in computer chip production [2, 3]. Surface analysis becomes extremely precise by means of reflectometry and scatterometry [4–6] and also the binding state of molecules can be studied by spectral investigations [7–9]. Microscopy with radiation at wavelengths in the water window (*λ* = 2.3–4.4 nm) allows highly resolved direct

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

imaging of samples in aqueous environments [10–12]. Mostly, these applications are realiz‐ ed at large-scale facilities, such as synchrotron sources or free-electron lasers. However, the demand for beam time is always too large to be satisfied by these institutions, and thus, people endeavor to transfer experiments to their laboratories. This constitutes the need of compact beam sources as can be realized by the principle of laser-produced plasmas (LPP) that is the subject of this chapter.

In order to classify and compare the radiation of different soft X-ray beam sources, the brilliance *Br* is a commonly used quantity that is the number of photons within a narrow spectral range Δ*λ*/*λ* emitted into a solid angle *Ω* from an area *A* within the time scale *τ* (typically the wavelength range Δ*λ* is defined to be 0.1% of the central wavelength *λ*) [1]:

$$Br = \frac{N\_{ph}}{\pi \cdot A \cdot \Omega \cdot \Delta\lambda / \ \lambda} . \tag{1}$$

The value of *Br* is given in the unit 1/(s·mm2 ·mrad2 · 0.1%BW) with 0.1%BW indicating the bandwidth of 0.1%. A distinction is made between the peak brilliance, where *τ* denotes the pulse duration, and the average brilliance, where *τ* is the inverse of the repetition rate.

In comparison to synchrotrons and free-electron lasers, the brilliance of laser-produced plasma sources is several orders of magnitude lower. However, there are strategies to increase their brilliance which involve, e.g., higher power densities of the generating laser pulse. On the other hand, the density of the target material has a strong impact on the achievable number of soft X-ray photons too, whereas basically the source brilliance scales with the density. Thus, the brightest plasmas can be achieved with solids. Respective target materials are deposited on rotating cylinders [13] or quickly moving tapes [14], which provide repetition rates of up to 1 kHz. Prominent elements are gold or tin for the production of radiation at a wavelength of 13.5 nm, which is applied in EUV lithography [15]. Furthermore, there are sources employing cold gases in a solid phase, such as an argon filament that emits soft X-rays in the wavelength range 2–5 nm [16]. Achievable plasma sizes with solid targets are comparably small and on the order of several tens of μm (full-widths at half-maximum, FWHM).

A plasma of similar brilliance and extent is obtained with liquid targets, e.g., xenon [17], methanol [18], or tin [15]. A fluid jet [19] provides high target densities but might lead to size and brightness fluctuations. Going one step further to individual microscopic droplets [20], the advantage is the mass limitation such that the entire target material is converted into a highly ionized plasma state, supporting source stability. However, the drawback of solid and liquid target concepts is the inevitable production of fast particles and ions with kinetic energies of up to several hundred keV [21], which severely damage optics in the beam path. There are mitigation strategies to slow down the debris material such as repeller fields [22] or localized gas jet shields [23], but still the collector optics has a limited lifetime [2]. Contrarily, gaseous targets are almost free from debris [24]. Short gas pulses with durations of μs to ms are expanded from a pressure of several 10 bar into vacuum by a piezomechanical or electro‐ magnetic nozzle, resulting in a supersonic jet. Different target gases feature individual spectra of the resulting radiation, ranging from emitters with characteristic spectral lines (low atomic number, e.g., nitrogen) to broadband emitters (high atomic number, e.g., xenon) [25]. However, here, the conversion efficiency from laser energy into soft X-ray energy is comparably low due to the low density of the target material. Furthermore, achievable plasma sizes of several 100 μm are large. For metrology or scientific applications, though, these sources are very attractive due to their high cleanliness and versatility [8, 26].

In this study, a brilliance enhancement of laser-produced plasmas is demonstrated for gaseous jet targets, making use of supersonic effects. First, the theoretical background is provided to describe the physical properties of laser-produced plasmas as well as the gas dynamics of the related jet target. Experimental techniques are introduced that are employed to characterize the plasma and the gas jet. The effect of supersonic shocks within the target gas is investigated in both ways, theoretically and experimentally, revealing a significant brilliance enhancement for plasmas generated in respective shock regions. This chapter is based on a previous publication by Mey et al. [25] and has been revised and extended partly.
