Using an emissive probe the distribution of plasma potential V p in the bulk plasma of a dc Magnetron discharge has been determined for a range of argon pressures (0.26, 0.53 and 0.78 Pa) and cathode voltages (between −236 and −338 V). The results reveal a large axial variation in the space potential in the confined plasma, with V p ∼ 25 V over a distance of 5 cm, from plasma to sheath-edge. By combining the derived electric field with the modelled magnetic field, the distribution of single-particle drifts have been found, namely the electron E ∧ B, ∇B and curvature drift speeds. The predicted E ∧ B drift speeds (with values up to about 1.5 × 10 5 m s −1 ) are typically two to three times higher than the ∇B and curvature drifts. The Hall current channel is a broad region extending from above the 'racetrack' down to a position close to the axis, 6 cm from the cathode. The calculated total Hall current is approximately five times the discharge current. Using a simple model of the discharge, in which there is no spatial variation in electron current density J e , the gyrofrequency to collision frequency ratio averaged over the plasma bulk is found to be ω/ν ≈ 7.7 ± 4.2. In an extension to the model, a possible distribution of electron current throughout the plasma is considered, which allows the determination of ω/ν locally in the bulk. Using this method, the maximum value of ω/ν is found to be about 25, however both models indicate that cross-field electron transport occurs more rapidly than from a classical prediction.
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The time-dependent plasma discharge ionization region model (IRM) has been under continuous development during the past seven years and used in several studies of the ionization region of high-power impulse magnetron sputtering (HiPIMS) discharges. In the present work, a complete description of the most recent version of the IRM is given, which includes improvements, such as allowing for returning of the working gas atoms from the target, a separate treatment of hot secondary electrons, addition of doubly charged metal ions, etc. To show the general applicability of the IRM, two different HiPIMS discharges are investigated. The first set concerns 400 µs long discharge pulses applied to an Al target in an Ar atmosphere at 1.8 Pa. The second set focuses on 100 µs long discharge pulses applied to a Ti target in an Ar atmosphere at 0.54 Pa, and explorers the effects when varying the magnetic field strength. The model results show that Al 2+-ions contribute negligibly to the production of secondary electrons, while Ti 2+-ions effectively contribute to the production of secondary electrons. Similarly, the model results show that for an argon discharge with Al target the contribution of Al +-ions to the discharge current is over 90 % at 800 V, while Al +-ions and Ar +-ions contribute roughly equally to the discharge current at 400 V. For high currents the discharge with Al target develops almost pure self-sputter recycling, while the discharge with Ti target exhibits close to a 50/50 combination of self-sputter recycling and working gas-recycling. For a Ti target, a self-sputter yield significantly below unity makes working gas-recycling necessary at high currents. In the discharge with Ti target the B-field was reduced in steps from the nominal value, which resulted in a corresponding stepwise increase in the discharge resistivity.
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