Stability analysis of reactive sputtering process with variable sticking coefficients Chuan Li * , Jang-Hsing Hsieh School of MPE, Nanyang Technological University, Singapore 639798, Singapore Abstract In reactive sputtering, the introduction of reactive gas would create a hysteresis transition from metal to compound mode in both the target and the substrate. The hysteresis transition is characterized by a sudden change in partial pressure, sputtering rate and fraction of compound formation, etc. Therefore, the stability is an important issue of process control. In this paper, a mathematical model with variable sticking coefficients based on surface kinetics is introduced to study the process stability. The variable sticking coefficient represents different mechanisms for surface reactions from the type of Langmuir to precursors. To facilitate the analysis, several nondimensional parameters are introduced and used for formulation. Results show that, when the chemical reaction on a substrate is moderate, a higher sputtering yield of the compound leads to a more stable steady-state at lower inflow rates. However, when the ratio of sputtering yield (compound/metal) is zero, there is no hysteresis transition because of the deposition of pure metal (single phase) on the substrate. For different sticking mechanisms, the precursor type is found to make the surface easier to saturate with compound due to its higher default sticking coefficient and the lower pressure and inflow rate for the hysteresis transition. D 2004 Elsevier B.V. All rights reserved. Keywords: Reactive sputtering; Langmuir kinetics; Sticking coefficient; Stability; Hysteresis 1. Introduction Reactive sputtering is a very important PVD process in thin film deposition particularly for producing complex compound films such as oxides, nitrides or carbides. Due to tremendous applications of these films, the process is extensively used in manufacturing the semiconductor and display devices [1–3]. Numerous studies [4–7] have shown that the hysteresis transition between the metallic and compound modes at the target surface is one characteristic feature of the reactive sputtering process. This hysteresis behavior is due to the introduction of reactive gas and commonly described by an abrupt change in deposition rate, film composition, partial pressure of the reactive gas and cathode voltage [6–10]. The first trial to model this phenomenon was originally proposed by Berg et al. [11– 13]. In their studies, a mass balance for the reactive gas in the chamber including absorption and sputtering at the surfaces of target and substrate was considered at first. The deposition rate and film compositions were then calculated as a function of inflow rate of reactive gas. This model successfully depicts the hysteresis transition by some simple but sound physical effects. However, one assumption of constant sticking coefficients made for the surface reactions with reactive gas typically leads to an underestimate of real situations. It is therefore necessary to investigate the issue based upon the theory of surface kinetics for chemical reactions. A variable sticking coefficient as a function of compound fraction is then proposed and discussed thoroughly. In this study, we first establish formulae for reactive sputtering based on Berg’s model and then recast the non- linear ordinary differential equations in terms of several nondimensional parameters. The steady-state solutions are then solved in details with the variable sticking coefficients. Finally, the influence of different sticking mechanisms on the steady-state solutions is carefully examined. 0040-6090/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2004.08.050 * Corresponding author. E-mail address: mcli@ntu.edu.sg (C. Li). Thin Solid Films 475 (2005) 102 – 108 www.elsevier.com/locate/tsf