Intense boundary emission destroys normal radio-frequency plasma sheath

The plasma sheath is the non-neutral space charge region that isolates bulk plasma from a boundary. Radio-frequency (RF) sheaths are formed when applying RF voltage to electrodes. Generally, applied bias is mainly consumed by a RF sheath, which shields an external field. Here we report evidence that an intense boundary emission destroys a normal RF sheath and establishes a type of RF plasma where external bias is consumed by bulk plasma instead of a sheath. Ions are naturally confined while plasma electrons are unobstructed, generating a strong RF current in the entire plasma, combined with a unique particle and energy balance. The proposed model offers the possibility for ion erosion mitigation of a plasma-facing component. It also inspires techniques for reaction rate control in plasma processing and wave mode conversion.

Figure 1

Simulation results of RF plasma with and without boundary emission. In (a) potentials of normal CCP are compared to a condition with surface emission of ${10}^{21}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$, which is around twice the initial plasma electron flux. Applied bias is consumed by bulk plasma, and two small sheaths opposite to normal RF sheaths appear at both ends. In (b) the total currents of RF discharge with and without strong boundary emission are compared. They have a phase difference of nearly 0.5π and the boundary emission enlarges the total current by more than one order of magnitude. The external source is $V_{\mathrm{RF}}\cos \left(\omega t\right)$. (c) The transition from a normal RF plasma (CCP) to inverted RF plasma when increasing ${\mathrm{\Gamma }}_{\mathrm{em}}$. Mean sheath potential and mean electric field of the left wall are recorded with different boundary emissions. For convention, mean sheath potential in CCP is chosen as positive, which becomes negative after ${\langle {\mathrm{\Gamma }}_{\mathrm{ep}}-{\mathrm{\Gamma }}_{\mathrm{em}}\rangle }_T<0$ (marked as the mode transition). The sign of the wall electric field is also inverted after mode transition.

Figure 2

(a), (b) $J_c$ and $J_d$ in a sheath of CCP and IRP. $J_d\gg J_c$ in a RF sheath of CCP and $J_c\gg J_d$ in inverted RF sheath. (c), (d) Normalized ion and electron velocity distribution functions when $\omega t=0.5\pi$ for CCP (left panel) and IRP (right panel). Velocity space is normalized to $v_{\mathrm{Tep}}=\sqrt{\frac{T_{\mathrm{ep}}}{m_e}}$ and $c_s=\sqrt{\frac{T_{\mathrm{ep}}}{m_i}}$. (c) Left panel shows that ions are accelerated towards the boundary in CCP and a presheath exists which ensures a minimum velocity when ions enter the sheath. Right panel shows that there is no presheath in IRP and ions are repelled back to plasma by an inverse sheath barrier. The size of a RF sheath in CCP is greater than in IRP. (d) Left panel shows that plasma electrons are repelled in CCP, while right panel shows that in IRP plasma electrons are unimpeded and part of the emitted electrons are repelled back to the surface, forming an intense electron concentration near the surface.

Figure 3

Schematic of the adopted theoretical model for inverted RF plasma. $\overline{{\phi }_{\mathrm{inv}}}$ is mean potential of plasma center relative to wall, ${\phi }_{\mathrm{inv}}\left(\omega t\right)$ is real-time wall potential relative to sheath edge, and $E_{\mathrm{tran}}\left(\omega t\right)x_s\left(\omega t\right)$ is sheath edge potential relative to the plasma center. Two limiting cases dictated by Eq. (3.5a) are plotted plus normal situations between two limits. Dashed pink curve represents limit of Eq. (3.5a) when no external source is given, which is reduced to a floating inverse sheath. Two dotted blue curves represent the limit of Eq. (3.5b) with an infinite external source, where the mean inverse sheath barrier is eliminated and bulk plasma is directly linked with the boundary without a sheath in a half period. Note that the black dash-dotted line is only an approximation of an inverse sheath edge; actually the position of sheath edge $\left(\omega t\right)$ is time-dependent, the same as in CCP.

Figure 4

Results given by theory. (a) The same parameters as in the simulation are used to calculated space potential in IRP at $\omega t=0,0.5\pi ,\pi$. (b) $\frac{{\phi }_{\mathrm{inv}}\left(\omega t\right)}{\overline{{\phi }_{\mathrm{inv}}}}$ at different $V_{\mathrm{RF}}$, unit V. $V_{\mathrm{RF}}=0$ gives a floating inverse sheath [Eq. (3.5a)], sheath potential is sinusoidal for small $V_{\mathrm{RF}}$, for large $V_{\mathrm{RF}}$ it is rectified in a half period [Eq. (3.5b)]. (c) $\overline{{\phi }_{\mathrm{inv}}}$ with different ${\mathrm{\Gamma }}_{\mathrm{em}}$ and $V_{\mathrm{RF}}$. The minimum ${\mathrm{\Gamma }}_{\mathrm{em}}$ to invoke IRP increases with $V_{\mathrm{RF}}$, and $\overline{{\phi }_{\mathrm{inv}}}$ increases with ${\mathrm{\Gamma }}_{\mathrm{em}}$.

Figure 5

Time evolution of mode transition. Initially ${\mathrm{\Gamma }}_{\mathrm{em}}=5\times {10}^{19}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$ is given until a stable normal RF sheath is formed. ${\mathrm{\Gamma }}_{\mathrm{em}}$ is suddenly changed to ${\mathrm{\Gamma }}_{\mathrm{em}}=5\times {10}^{20}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$ to initiate the transition. Space potentials within decades of periods during transition are recorded; a straight black curve (front) is applied potential profile in vacuum serving as reference. All data are taken at $\omega t=0$. (a) Inverted RF plasma mode is switched on, no presheath exists in steady state, and inverse sheath barriers are clearly seen. The bulk plasma is poorly shielded by sheaths and an applied field is unimpeded in plasma. (b) Inverted RF plasma mode is switched off, RF sheath is space-charge limited, ions are unconfined, Bohm criterion is valid, and bulk plasma is well isolated from the boundary with a weak transiting field in plasma bulk.