Measurements of the electron energy distribution function in molecular gases in a shielded inductively coupled plasma

Abstract

A cylindrical Langmuir probe has been used to measure the electron energy distribution function (EEDF) in atomic and molecular gases in a shielded inductively coupled plasma. We report the EEDFs in these gases as a function of pressure. While the electron properties in a discharge depend on the product of the neutral number density (N0) and the effective discharge dimension (deff) for a given gas, this dependence is different for different gases. We find that pressure is a convenient parameter for comparison of the EEDFs in these gases. The EEDFs in inert (Ar, Kr, Xe) and molecular gases (H2,N2,O2,H2O,CO2,CF4) in the low pressure limit (below 1 mTorr) show a “three-temperature” structure. Since this wide range of gases display similar EEDF shape, we propose this structure to be common to all gas discharges in this limit. The EEDF in all of the gases shows a two-temperature structure with apparent tail depletion at 3 mTorr. The similarity of the EEDFs in all of the above gases is probably due to nonlocality of the electrons at these low pressures. The molecular gases exhibit a nearly Maxwellian EEDF between about 10 and 30 mTorr, while the EEDF in argon is non-Maxwellian in this range. At pressures above 30 mTorr, the EEDFs in molecular gases show deviations from a Maxwellian distribution, reflecting the electron-neutral collision cross sections of each gas. The EEDFs in molecular gases at 100 mTorr show significant deviations from a Maxwellian distribution. We find that the EEDF in molecular gases can be approximated by a Maxwellian distribution over a fairly large pressure range of 3–50 mTorr for the purposes of modeling these discharges.

Measurement and modeling of time- and spatial-resolved wafer surface temperature in inductively coupled plasmas

“…The minimal rf modulation allows measurement of electron energy probability function using the second derivative method. [13][14][15][16] The electron saturation regime in which the I-V characteristic is obtained does not significantly perturb the plasma as shown by the small energy difference ͑less than 1 eV͒ between the peak and zero crossing of the second derivative of the probe current. 14,16 The electron temperature is defined as 2 / 3 of the average electron energy.…”

“…The electron temperature variation from r =0 to r = 7.5 cm, 2.5 cm above the wafer surface, is within 5% for the conditions investigated so spatial gradients in T e can be neglected. We note that for the plasmas investigated, the measured electron energy distribution is not far from a Maxwellian distribution 14,15,21 and this estimation of the floating potential is reasonably accurate-probably to within 1 -2 V. The ion-electron recombination energy is set to be equal to the Ar ionization energy, 15.8 eV.…”

“…[13][14][15][16] The electron saturation regime in which the I-V characteristic is obtained does not significantly perturb the plasma as shown by the small energy difference ͑less than 1 eV͒ between the peak and zero crossing of the second derivative of the probe current. 14,16 The electron temperature is defined as 2 / 3 of the average electron energy. We note that it is possible to obtain the positive ion flux using the Langmuir probe by biasing the probe into the ion saturation regime; we do not operate the probe to obtain the ion saturation current.…”

“…Great care has to be taken, including probe design and probe operating, to ensure reliable measurements obtained by the probe. [14][15][16] The probe can access radial positions from r =0 to r = 7.5 cm, at a height of 2.5 cm above the wafer surface. Because of the presence of the Faraday shield, the rf modulation of the plasma potential is minimized and is well below 150 mV.…”

Numerical study of the effect of gas flow in low pressure inductively coupled Ar/N2 plasmas

“…The coupled calculation is examined by COMSOL Multiphysics 4.2, a finite element analysis simulation software, which includes plasma module and computational fluid dynamics (CFD) module with an unitized graphical user interface (GUI). Figure 1 shows the model geometry used in this work, which has been described in earlier publications [12,15]. The calculations are performed for the case of an Ar/N 2 ICP plasma operating at the rf frequency of 13.56 MHz and the total gas pressure of 20 mTorr with the gas flows of 5-700 sccm.…”