Application of a collisional radiative model to atomic hydrogen for diagnostic purposes

Abstract

Optical emission spectroscopy is one of the standard diagnostic methods to determine plasma parameters. In hydrogen plasmas often the intensity of the Balmer lines is recorded. To analyze such measurements population models for the hydrogen atom are needed. The flexible package Yacora is used to construct a new collisional radiative model for low pressure, low temperature hydrogen plasmas. This model includes six possible excitation channels: effective excitation of H, recombination of ${\mathrm{H}}^{+}$, dissociative excitation of ${\mathrm{H}}_2$, dissociative recombination of ${\mathrm{H}}_2^{+}$, dissociative recombination of ${\mathrm{H}}_3^{+}$ and mutual neutralization of ${\mathrm{H}}^{-}$ and ${\mathrm{H}}_x^{+}$. The model is applied to a uniform ECR plasma with high dissociation degree and low ionization degree, i.e. electron collision excitation from H is the dominant excitation channel. The cross sections for this channel taken from literature showed a non-physical discontinuity at electron energies close to the threshold energy. This discontinuity has been removed by using a smoothing procedure. For known plasma parameters the deviation between measured and calculated population densities decreases significantly by using the smoothed data. Furthermore, the agreement of the electron density deduced from the ratio ${\mathrm{H}}_{\beta }/{\mathrm{H}}_{\gamma }$ with results of other diagnostic methods is enhanced dramatically.

Introduction

Low pressure, low temperature plasmas are used in a wide range of technical and research applications [1]. Most of these plasmas contain a certain amount of hydrogen atoms produced by dissociation of ${\mathrm{H}}_2$ or other molecules, e.g. hydrocarbons or silanes.

The most important plasma parameters in these plasmas are temperature, density and velocity distribution functions of the particles. Plasma diagnostics which determines the plasma parameters is a key issue to improve the understanding of plasma processes [2], [3].

Plasma diagnostics usually is based on the measurement of externally accessible physical parameters of the plasma. For example a spectrometer can be used to record the intensity of a radiative transition. Models in which the plasma parameters are used as free parameters are applied to predict values of the measured parameter. A comparison of the results of measurement and calculation enables the determination of the plasma parameters.

For low pressure, low temperature plasmas, many different diagnostic methods are available [2], [3]. One of these methods is the optical emission spectroscopy (OES) [4], [5], [6], which is based on a very simple and robust experimental setup. One main advantage of this method is its non-invasive nature, i.e. the plasma is not affected by the measurements.

For the interpretation of spectroscopically measured intensities population models are needed. Such models calculate population densities of excited states in atoms, molecules or ions depending on the plasma parameters. For very high electron densities ($n_{\mathrm{e}}\gtrsim {10}^{24}{\mathrm{m}}^{-3}$ in hydrogen plasmas) the states thermalize and the local thermodynamic equilibrium (LTE) can be applied. For very low electron densities ($n_{\mathrm{e}}\lesssim {10}^{17}{\mathrm{m}}^{-3}$ in hydrogen plasmas) the corona equilibrium which balances electron collision excitation from the ground state with radiative transitions is valid. For intermediate electron densities the excitation and de-excitation processes for all states in the atom, molecule or ion have to be balanced by the population model [7]. Such models are called collisional radiative (CR) models [8], [9], [10]. For high and low electron densities CR models represent the LTE and corona equilibrium, respectively.

The first CR model for H was developed by Johnson and Hinnov [11]. Since then other CR models for the hydrogen atom have been presented [12], [13], the most prominent one is the ADAS package [13]. The typical application ranges of these models are recombining ($T_{\mathrm{e}}<1\mathrm{eV}$) or ionizing plasmas ($T_{\mathrm{e}}>10\mathrm{eV}$) which means that the population densities of exited states are determined mainly by recombination from ${\mathrm{H}}^{+}$ and electron collision excitation from H, respectively.

In typical process plasmas [14] and sources for positive [15] or negative hydrogen ions [16] the electron temperature is between these values. In this intermediate parameter range population processes from additional neutral particles (${\mathrm{H}}_2$) or ions (${\mathrm{H}}_2^{+}$, ${\mathrm{H}}^{-}$) can have an influence on the population of excited states. Additionally, the average energy of the plasma particles is either below or close to the threshold energy of some of the excitation processes. Thus, the corresponding cross sections and the energy distribution functions of the involved particles have to be known very accurately for low energies.

The flexible package Yacora was developed and used to construct a new CR model for hydrogen plasmas. This paper describes in more detail the application of the model to an uniform ECR plasma with electron temperatures in the parameter range between recombining and ionizing plasmas ($1\mathrm{eV}<T_{\mathrm{e}}<10\mathrm{eV}$), high dissociation degree and low ionization degree, i.e. electron collision excitation from H is the dominant excitation channel. This regime is outside the parameter ranges in which the previously existing CR models for H have been tested. Comparison of measured and calculated population densities enables the revision of the cross sections available in literature for collision excitation from the ground state of H at electron energies close to the threshold.