Paper PS2-WeM1
Self-Consistent Modeling of Capacitive Coupling in Inductively Coupled Plasmas

Wednesday, November 12, 2014, 8:00 am, Room 308

Plasma etching of microelectronic structures at advanced technological nodes (< 1x nm) places great emphasis on process uniformity.[1] Antenna designs have become more complicated in industrial inductively coupled plasma (ICP) tools to improve uniformity.[2] The antenna region in ICPs also contain auxiliary systems for gas flow, temperature control, etc. which influence the antenna electrical characteristics. Plasma equipment models typically employed to investigate ICP sources have used a circuit model to compute voltage and current along the coils to capture the antenna-plasma coupling self-consistently.[3,4] However, the approach is limited to simple coil structures which is not necessarily the case for next-generation ICP tools. For example, Applied Materials’ AdvantEdge chamber utilizes a two-coil structure fed through the same power supply.[5]

In this work, we discuss results from a two-dimensional plasma equipment model, HPEM[6], which has been modified to compute the voltage and current (amplitude and phase) in the coils by solving the equivalent circuit of the coils and the plasma in the frequency domain. The plasma is treated as the secondary coil of an air-core transformer. The amplitude of the driving voltage is adjusted in the circuit model such that the sum of inductive, capacitive and resistive powers is maintained constant. Capacitive coupling is calculated by including the voltage on the coils in the Poisson’s equation. The coil currents from the circuit model are used as driving terms in the solution of the wave equation and to compute resistive losses in the coils.

Results will be discussed for an Ar/Cl₂ plasma and the consequences of varying electronegativity of the feedstock gas mixture, varying current ratios between the two-coils and the phase of current between the coils on capacitive coupling will be assessed over a pressure range of 5 – 150 mTorr. We found that inductive component of the power coupled increases with pressure from 5 to 30 mTorr as the increase in electron density supersedes the rise in collision frequency. While, power is dominantly coupled inductively for electropositive gas mixture, the pressure at which transition to capacitive mode occurs decreases as electronegativity increases.

[1] K. Ahmed and K. Scheugraf, IEEE Spectrum 48 (11), 50 (2011).

[2] Ch. Hollenstein, et al., Plasma Sources Sci. Technol. 22, 055021 (2013).

[3] M.J. Kushner, et al., J. Appl. Phys. 80, 1337 (1996).

[4] T. Panagopoulos, et al., J. Appl. Phys. 91, 2687 (2002).

[5] A. Agarwal, et al., Trans. Plasma Sci. 39, 2516 (2011).