Plasma deposition in an ideal showerhead reactor: a two-dimensional analytical solution

Abstract

The interplay of gas flow and depletion by plasma dissociation determines the spatial distribution of species and the deposition uniformity in a plasma source. Many plasma reactors use a gas showerhead and the design of the flow dynamics is a critical aspect of the reactor performance. In this paper, plasma deposition is considered as chemically reacting gas flow in an ideal showerhead reactor. The gas fluid flow is described by finite-gap stagnation-point creeping flow. The distribution of neutral species across the electrode gap is determined by diffusion equations, whereas their lateral transport is purely convective. Parameters relevant to large-area radio-frequency plasma deposition are particularly suitable for a complete analytical solution of the multi-component transport. A representative reaction scheme for hydrogen/silane plasma deposition is used for an analytical example from first principles which shows good agreement with numerical simulation. For a laterally uniform plasma, apart from edge effects, the deposition uniformity is limited only by the lateral uniformity of the pressure: if the electrode gap is very small in a large-area reactor, the pressure and deposition rate will be non-uniform even for a uniform showerhead. The deposition mass flux is self-consistently accounted for by the Stefan velocity for arbitrary levels of gas concentration and depletion, and its influence on streamlines and fluid velocity is shown.

Enhancement of Cleanliness and Deposition Rate by Understanding the Multiple Roles of the Showerhead Electrode in a Capacitively Coupled Plasma Reactor

“…Howling et al used an SiH 4 /H 2 mixture to calculate the Peclet number (Pe = d ū/D, where d is the characteristic length, ū is the characteristic velocity, and D is the diffusion coefficient) in their CCP process conditions. Taking the binary diffusion coefficient for SiH 4 and H 2 at 100 Pa and 473 K to be 0.14 m 2 s −1 , the Pe was calculated as only 0.03 [8]. As our process conditions are similar to those of Howling et al, we confidently assumed that our gas transport phenomena are also observed under conditions of rapid diffusion.…”

“…Therefore, chip manufacturers have continuously targeted high production efficiency [3][4][5]. Towards this objective, showerhead-type capacitively coupled plasma (CCP) PECVD reactors operated in the torr regime are often considered the best configuration for performing challenging processes [6][7][8]. This is because these reactors have the ability to deposit films with specified properties and with high uniformity.…”

Industrial plasmas in academia

“…A significant problem in deposition reactors is the gas supply and the pumping of the plasma reactor [13]. This problem will be treated here in more detail.…”

Two-dimensional particle-in-cell simulation of electron heating effect in multiple hollow cathode trenches with curved boundary

“…From the perspective of the fluid pipe, to obtain a uniform fluid distribution without converting to turbulence in the chamber, the diffuser structure of the showerhead is more advantageous than the orifice structure. Therefore, the HC structure was tested experimentally and simulated for various trench structures [12,13]. In addition, simulations were performed on the repetitive form of the trenches, which can be applied to the showerhead structure.…”