Eur. Phys. J. D 60, 309–316 (2010) DOI: 10.1140/epjd/e2010-00192-6 Regular Article T HE EUROPEAN P HYSICAL JOURNAL D Extreme-ultraviolet emissivity from Xe 8+ to Xe 12+ by using a detailed line-by-line method J. Zeng a , C. Gao, and J. Yuan Department of Physics, College of Science, National University of Defense Technology, Changsha Hunan 410073, P.R. China Received 17 December 2009 / Received in final form 4 May 2010 Published online 27 July 2010 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2010 Abstract. A theoretical model has been developed to calculate the emissivity of low density xenon plas- mas (from Xe 8+ to Xe 12+ ) by employing a detailed line accounting formalism. A complete set of atomic data such as transition probabilities for electric (magnetic) dipole and quadruple E1, E2, M1 and M2 and electron impact excitation collision strength, which is accurate to fine-structure level, was calculated using a full configuration interaction formalism and was used to solve the rate equation which determines the population of different levels. Detailed results are given for pure Xe 10+ ion, which is essential for extreme-ultraviolet emission at 13.5 nm, and for low density plasmas (the electron density was taken to be 10 12 cm -3 ) at temperatures of 30, 45, 55, 65 and 75 eV. The fraction of different ionization stages was obtained by a completely coupled rate equation from neutral atom to Xe 20+ by using a detailed configu- ration accounting method. The results show that the emissivity of the dipole forbidden lines of transition array 4s 2 4p 6 4d 7 5s → 4s 2 4p 6 4d 8 of Xe 10+ is very sensitive to the temperature, which should be a useful tool to diagnose the temperature in EBIT plasmas. 1 Introduction The search for optimum radiation source emitting at 13.5 nm for extreme ultraviolet (EUV) lithography is one of the most important subjects in the microelectronics in- dustry [1]. Xenon is a popular material which can be used for EUV sources due to its inherent cleanliness and moder- ate conversion efficiency. Experimental research was car- ried out to investigate the emission properties of xenon plasmas [2–6], which showed that emission lines around 13.5 nm is mainly contributed by Xe 10+ . Combining with theoretical analysis, researchers identified that the lines around 13.5 nm are almost entirely made up of the main 4p 6 4d 7 5p → 4p 6 4d 8 Xe 10+ transition. Some of the exper- imental data such as energy levels and ionization poten- tials of different ionization stages of xenon are compiled by Saloman [7]. The experiments mentioned above [2–6] were per- formed with either laser-or gas discharge-produced plas- mas with medium or high density. For such medium or high density plasmas, it is difficult to extract detailed in- formation on atomic data of respective Xe ions due to the large number of satellite lines and/or to the limited instrumental resolution power. In order to reduce the in- fluence of too many unresolved lines, one effective method is to further decrease the density of plasmas, resulting in fewer highly excited states and, in addition, some degree of ion stage differentiation, to gain information on emission a e-mail: jiaolongzeng@hotmail.com lines of individual ion stages. Fahy et al. [8] recorded EUV spectra in the wavelength region 10–14 nm from Xe plas- mas with electron densities in range of 10 13 –10 14 cm -3 or even lower than this value at the electron beam ion trap (EBIT) of NIST [9]. Later, they [10] extended their obser- vation to the 4.5–20 nm wavelength region, with electron beam energy being varied from 180 eV to 8 keV. Radia- tion from charge states of Xe 6+ to Xe 43+ was observed. Trabert et al. [11] reported wavelengths of prominent lines arising from Li-, Be-, B-, Na-, and Mg-like ions in the 4–20 nm wavelength region using superEBIT. Biedermann et al. [12] investigated emission spectra from Xe 17+ –Xe 25+ in the spectral range between 9 and 25 nm using Berlin EBIT. Various theoretical models were developed to interpret the experimental results. Sasaki et al. [13] theoretically investigated the EUV emission spectra of Xe plasma by using an unresolved transition array (UTA) model, where populations of different charge states were obtained using the WHIAM collisional-radiative (CR) model [14]. Pop- ulations of excited states were approximated to be in lo- cal thermodynamic equilibrium (LTE). Krucken et al. [15] calculated emission spectra in the optically thin limit for Xe 8+ –Xe 12+ at an electron density of 10 17 cm -3 and an electron temperature of 32 eV based on the CR model. For EBIT plasmas, most theoretical researches used sta- tistical approaches. Fahy et al. [8,10] calculated the wave- lengths and transition probabilities for a range of charge states in xenon (Xe 8+ –Xe 17+ ) using the Cowan suite of codes, which were used to aid experimental analysis. In