Influence of electron recapture by the cathode upon the discharge characteristics in dc planar magnetrons

In dc magnetrons the electrons emitted from the cathode may return there due to the applied magnetic field. When that happens, they can be recaptured or reflected back into the discharge, depending on the value of the reflection coefficient (RC). A 2d3v (two-dimensional in coordinate and three-dimensional in velocity space) particle-in-cell–Monte Carlo model, including an external circuit, is developed to determine the role of the electron recapture in the discharge processes. The detailed discharge structure as a function of RC for two pressures (4 and $25\mathrm{mtorr}$) is studied. The importance of electron recapture is clearly manifested, especially at low pressures. The results indicate that the discharge characteristics are dramatically changed with varying RC between 0 and 1. Thus, the electron recapture at the cathode appears to be a significant mechanism in magnetron discharges and RC a very important parameter in their correct quantitative description that should be dealt with cautiously.

Figure 1

Scheme of the magnetron in the study with the magnetic field. The maximum strength of the magnetic field is $300\mathrm{G}$. The scheme is cylindrically symmetrical towards the axis $r=0$.

Figure 2

Cross sections for electron-Ar collisions.

Figure 3

Convergence of the cathode potential $U_0$ for $p=4\mathrm{mtorr}$ and $\mathrm{RC}=0.5$. The dashed line represents a simulation initiated with a homogeneous plasma density. The solid line corresponds to a simulation started with the converged data of a run with $\mathrm{RC}=0$. The transition occurs at $t=24.2\mu \mathrm{s}$.

Figure 4

Discharge characteristics: (a) electric potential at $p=4\mathrm{mtorr}$, (b) electron density at $p=4\mathrm{mtorr}$, (c) electric potential at $p=25\mathrm{mtorr}$, and (d) electron density at $p=25\mathrm{mtorr}$.

Figure 5

Erosion profile at $p=4\mathrm{mtorr}$ and $\mathrm{RC}=0.5$. The solid line represents the calculated results and open triangles the measured data.

Figure 6

Trajectory of a sample electron emitted from the cathode for (a) $\mathrm{RC}=0$ and (b) $\mathrm{RC}=1$.

Figure 7

Plasma potential $V$, normalized with respect to the cathode potential $U_0$, along $r=17.2\mathrm{mm}$ at $p=4\mathrm{mtorr}$ for different values of the reflection coefficient.

Figure 8

Electron energy probability function at $p=4\mathrm{mtorr}$ as a function of the reflection coefficient.

Figure 9

Ionization rate along $r=17.2\mathrm{mm}$ at $p=4\mathrm{mtorr}$ as a function of the reflection coefficient.

Figure 10

Electron density along $r=17.2\mathrm{mm}$ at $p=4\mathrm{mtorr}$ as a function of the reflection coefficient.

Figure 11

Ionization rate along $r=17.2\mathrm{mm}$ at $p=25\mathrm{mtorr}$ as a function of the reflection coefficient.

Figure 12

Cathode potential $U_0$ as a function of the reflection coefficient. Solid curve for $p=4\mathrm{mtorr}$, dashed curve for $p=25\mathrm{mtorr}$. Triangles represent the calculated values.

Figure 13

Discharge current $I_{\mathit{disch}}$ as a function of the reflection coefficient. Solid curve for $p=4\mathrm{mtorr}$, dashed curve for $p=25\mathrm{mtorr}$. Triangles represent calculated values.

Figure 14

Secondary-electron emission coefficient at $p=4\mathrm{mtorr}$ as a function of the reflection coefficient. Solid curve: as seen by the cathode (SEEC from ion beam data). Dashed curve: as seen by the discharge (effective SEEC). Triangles represent calculated values.

Figure 15

Time evolution of the cathode potential. Dotted curve: recapture treated probabilistically, as in Refs. 17, 18. Solid curve: recapture treated with a constant $\mathrm{RC}=0.39$.