A "reference cell" for generating radio-frequency (rf) glow discharges in gases at a frequency of 13.56 MHz is described. The reference cell provides an experimental platform for comparing plasma measurements carried out in a common reactor geometry by different experimental groups, thereby enhancing the transfer of knowledge and insight gained in rf discharge studies. The results of performing ostensibly identical measurements on six of these cells in five different laboratories are analyzed and discussed. Measurements were made of plasma voltage and current characteristics for discharges in pure argon at specified values of applied voltages, gas pressures, and gas flow rates. Data are presented on relevant electrical quantities derived from Fourier analysis of the voltage and current wave forms. Amplitudes, phase shifts, self-bias voltages, and power dissipation were measured. Each of the cells was characterized in terms of its measured internal reactive components. Comparing results from different cells provides an indication of the degree of precision needed to define the electrical configuration and operating parameters in order to achieve identical performance at various laboratories. The results show, for example, that the external circuit, including the reactive components of the rf power source, can significantly influence the discharge. Results obtained in reference cells with identical rf power sources demonstrate that considerable progress has been made in developing a phenomenological understanding of the conditions needed to obtain reproducible discharge conditions in independent reference cells.
A new algorithm that determines the evolution of a surface eroding under reactive-ion etching is presented. The surface motion is governed by both the Hamilton-Jacobi equation and the entropy condition for a given etch rate. The trajectories of "shocks" and "rarefaction waves" are then directly tracked, and thus this method may be regarded as a generalization of the method of characteristics. This allows slope discontinuities to be accurately calculated without artificial diffusion. The algorithm is compared with "geometric" surface evolution methods, such as the line-segment method.
An exact solution to the problem of collisionless, space-charge-limited flow of cold ions across a one-dimensional (planar) dc plasma sheath of negligible electron density is derived for general values of the presheath ion velocity v0 and electric field E0. For a given ion current density J and sheath thickness d, the exact solution reduces to the classical Child–Langmuir model in the case that v0=0 and E0=0. When either v0 or E0 is sufficiently large, however, the exact solution may differ appreciably from the Child–Langmuir law. The existence of a closed-form expression for the spatial variation of the sheath potential is shown to be contingent upon the satisfaction of a simple inequality relating v0 and E0 to J. When v0 obeys the Bohm criterion and the magnitude of E0 suggests that the Bohm energy is acquired over a distance not less than one Debye length, this inequality is indeed satisfied.
Application of the method of characteristics to the general case of ion or plasma etching is reviewed, yielding a topography evolution algorithm which is simultaneously accurate, flexible, and efficient. The behavior of initial slope discontinuities is computed by mapping the characteristic locus in the region of the discontinuity and removing any closed loops which appear in the locus. The new method is shown to produce profiles which satisfy the required entropy and jump conditions for any given variation of etching rate with surface slope, while allowing the use of longer integration time steps than conventional methods. Previously published "string" algorithms [W. G. Oldham, S. N. Nandgaonkar, A. R. Neureuther, and M. O'Toole, IEEE Trans. Electron Devices ED-26, 717 (1979); C. H. Ting, J. Vac. Sci. Technol. 16, 1767 (1979)] are compared to the new method, and are shown to be capable of generating correct profiles only under limited conditions, i.e., for specific etching behaviors or if slope discontinuities are artificially removed.
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