# Spectroscopic Studies of Laser-Based Far-Ultraviolet Plasma Light Source
## 4 Results and Discussion  
Under the LTE hypothesis, the radiation of thermal light sources is governed by the fundamental laws of thermodynamics. Their intensity and spectral distribution, which depend on temperature, can be determined with the [PERSON]'s law of absorption-emission and [PERSON]'s equation, respectively, [23]. For a truly black-body over the wavelength range from zero to infinity, the radiation power emitted by the surface is given by the Stefan-Boltzmann's law. When the temperature of a black-body radiator increases, the overall radiated energy increases and the peak of the radiation curve moves to shorter wavelengths according to the Wien's displacement law. In this framework, the peak of the radiation curve (i.e., \(\lambda_{W}\) [nm] \(\mathrm{T_{bb}}\)[eV] \(\approx\) 250, where \(\lambda_{W}\) and \(\mathrm{T_{bb}}\) are the peak of black-body radiation curve and its temperature, respectively) varies in the wavelength range of \(\approx\)170-120 nm for a black-body temperature (i.e., the radiation temperature) of \(\approx\)1.5-2 eV, respectively. Typical radiation-hydrodynamic calculations for the laser irradiance relevant to the LPP EUV/XR source experiments (not shown here) show that a maximum of the local radiation temperature in the plasma core is much less than local electron temperature. Thus, to produce an efficient pulsed plasma FUV light source, it is expected that the electron temperature should be higher than \(\mathrm{T_{bb}}\). On the other hand, the measured plasma threshold fluences (\(\mathrm{F_{th}}\)) for the various metal targets in the air at atmospheric pressure are reported to be in the region of 0.9 \(\leq\mathrm{F_{th}}\leq\) 8.5 J cm\({}^{-2}\) for a Q-switched 1.0 \(\upmu\)m, ns Nd:YAG solid-state laser [24]. For example, the measured \(\mathrm{F_{th}}\) is \(\approx\)0.9, 3, and 8.5 J cm\({}^{-2}\) for the zinc (Zn), molybdenum (Mo) and tungsten (W) metal targets, respectively. Therefore, the necessary plasma threshold laser irradiances for 10 ns, 60 ns, and 100 ns FWHM pulses are approximately in the range of \(\approx\)(0.9-9) \(\times\) 10\({}^{8}\), (0.2-2) \(\times\) 10\({}^{8}\), and (0.1-0.9) \(\times\) 10\({}^{8}\) W cm\({}^{-2}\) for Zn, Mo and W metal targets, respectively. Note that the plasma threshold fluence is defined using the emission of a given spectral resonance lines of neutral element, e.g., the strong radiation originated from transitions among 3d\({}^{10}\)4s4p-3d\({}^{10}\)4s4d of Zn I in the wavelength region of 320-340 nm [22]. Our calculations show, using the FAC code, low-ionized charge states, e.g., Zn III-Zn IV radiate strongly over the wavelength region of 120-170 nm. Thus, a somewhat higher laser fluence (or irradiance) than \(\mathrm{F_{th}}\) is needed to produce an efficient FUV plasma light source. Figure 2: **(a)**: Calculated spectral emissivity and opacity coefficients versus the wavelength at \(\rho\approx 10^{-4}\) g cm\({}^{-3}\) and kT \(\approx\) 5 eV; **(b)**: the calculated spectral radiance for an artificial homogeneous Si plasma at \(\rho\approx 10^{-4}\) (blue shaded area) and \(\approx\) 4\(\times\)10\({}^{-4}\) g cm\({}^{-3}\) (dark solid line), kT \(\approx\) 5 eV, and d \(\approx\) 350 \(\upmu\)m. The black-body emission curve versus the wavelength at the same temperature is also shown. The spectral contributions of the main individual Si ions (i.e., Si III and Si IV) are also presented. Note that the ordinates of **(a,b)** are not in the same scale. The spectral features of various gases, liquid metal droplets [20] (not shown here), and metal targets were generated by a 1.0 \(\upmu\)m fiber laser with 60-100 ns FWHM and 2-20 kHz repetition rates at a low laser irradiance region of \(\approx\)10\({}^{6}\) to 5 \(\times\) 10\({}^{9}\) W cm\({}^{-2}\).