J. Plasma Physics (2013), vol. 79, part 5, pp. 509–512. c  Cambridge University Press 2013 doi:10.1017/S0022377812001183 509 Numerical analysis of monoenergetic electrons energy eﬀect on dynamic potential proﬁle of plasma sheath M. SHARIFIAN Physics Department, Faculty of Science, Yazd University, P. O. Box 89195-741, Yazd, Iran (mehdi.shariﬁan@yazduni.ac.ir) (Received 30 November 2012; revised 30 November 2012; accepted 7 December 2012; ﬁrst published online 10 January 2013) Abstract. The dynamic behavior of the electric potential distribution of a plasma sheath region in the presence of monoenergetic electrons with two diﬀerent values of energy, larger (fast electrons) and smaller (slow electrons) than the cathode potential energy, is examined numerically by the ﬁnite diﬀerence method. Exploring and comparing the plots of numerical computation results shows that the time evolution of the non-monotonic potential distribution heavily depends on the energy of monoenergetic electrons. 1. Introduction The study of sheath formation at the boundary of the plasma is of great practical importance. In plasma immersion ion implantation (PIII) (M¨ andl et al. 1997; Sheridan et al. 1998; Zeng et al. 1999; Qi et al. 2000; Bilek 2001; Yukimura 2001; Mukherjee et al. 2002; Kwok et al. 2003; Lacoste and Pelletier 2003; Masamune and Yukimura 2003; Ma et al. 2003; Rauschenbach and M¨ andl 2003; Tian et al. 2004, 2005, 2009; Meige et al. 2005; Sakudo et al. 2006; Ghomi et al. 2007, 2009; Huang et al. 2007; Li and Wang 2007; Mukherjee et al. 2007; Ghomi and Ghasemkhani 2009; Lejars et al. 2010; Li et al. 2010, 2012; Zhu et al. 2011), a plasma- containing species to be implanted into a substrate is generated by an external plasma source or by the neg- ative bias applied to the substrate (Conrad et al. 1987; Meige et al. 2005). After the negative bias is applied, electrons are repelled away from the surface leaving heavy ions forming an ion matrix sheath. These positive ions will subsequently be accelerated by the electric ﬁeld inside the ion sheath and implanted to the substrate surface (Lieberman and Lichtenberg 1994; Chu et al. 1996). When a low-pressure gas discharge is conﬁned in a solid vessel, there is the possibility of particle emission from the walls. In particular, when the wall is bombarded from the plasma by ions, electrons, meta- stables, neutrals, and photons, it can readily release ener- getic (non-Maxwellian) electrons. The nature of the space charged region that may form at the boundary of the plasma can be modiﬁed signiﬁcantly by the pres- ence of this group of electrons. Although these electrons may be generated by secondary emis- sion from the conﬁning structure, the exact nature of the source is not important for this analysis, provided that they are approximately energetic (Ingram and Braithwaite 1990; Demidov et al. 2005; Gyergyek et al. 2010). In plasma with non-Maxwellian electrons, a non- monotonic distribution of the potential can be formed inside the ion sheath with the potential larger than the biased electrode potential. It is supposed that the initial conditions of a sheath formation transient process determine the type of the steady-state potential distri- bution being formed. However, the steady-state model is not able to predict what kind of solution, monotonic or non-monotonic, is realized in the experiment. It is understood that in order to answer this question, a time-dependent model should be developed (Gurovich et al. 2006). A collisionless and time-dependent sheath model has been used to examine how the non-monotonic potential distribution can be formed inside the sheath due to the presence of non-Maxwellian electrons in the plasma. The appearance of a non-monotonic proﬁle of the potential in front of cathode depends on the density of the energetic electrons and time. In addition, it was found that this dependency on the fast electrons density is stronger than dependency on time (Shariﬁan and Shokri 2007). To the best of our knowledge, no analysis has been done on the eﬀect of the energetic electrons energy on the ion sheath dynamics. Present work will examine the eﬀect of energy of these energetic electrons on the ion sheath potential distribution dynamics. Here the applied dynamic model is exactly the same as the one used in our previous paper (Shariﬁan and Shokri 2007) and shares the same simpliﬁcation: the density of two groups of energetic electrons has been assumed to be constant inside the sheath (Gurovich et al. 2006). This work has been organized in four sections, in- cluding the Introduction as Sec 1. In Sec. 2, we present the equations that model the ion sheath dynamics in the presence of energetic electrons. Numerical results of the model are studied in Sec. 3. Finally, in Sec. 4, conclusions are presented.