Actinometry of Low Density Hydrogen Plasma

Optical Emission Spectroscopy (OES) attains a crucial stance in the measurement of ground electronic state species concentrations and temperatures of plasma. It adheres to a principle of non-perturbation as scaled with other techniques of plasma diagnostics which makes it crucial to the field.

The following repository contains a baseline code for computation of data following optical emission spectroscopy for low density hydrogen plasmas using data assumptions for spectral lines of Hydrogen in $H-\alpha$ at $656.46$ nm and Argon used as actinometer at $811.50$ nm. It follows in multiple data points for whom due references have been added wherever required.

Description

Measurements made by OES require careful interpretation. For instance, OES provides measurements of species in electronic excited states which participates only in a minor proportion to the plasma or plasma/surface chemistry and which are at a concentration levels of less than $10^{-4}$ with respect to species in the electronic ground state.

The actinometric method proceeds with trace amounts of the actinometer particles added to the gas under study. For the actinometer, a chemically inert element whose characteristics (emission spectrum, electron excitation cross sections, coefficients of collisional and radiative quenching of excited states, etc.) are well known is used.

For density measurements of hydrogen atoms via actinometry, an admixture of argon atoms is usually used.

Getting Started

Theory: Formulas Involved

The emission intensity of $H-\alpha$ line is given by:

$$ I_{H-\alpha} = K(\nu_{H_{\alpha}}) A_{32} \nu_{H_{\alpha}} \nu_{emiss} \displaystyle \frac{ [H(n=1)] k^{H_{\alpha}}{e} n{e} + k_{diss} [H_{2}] n_{e} }{ [H] k_{Q H_{\alpha}/H} + [H_{2}] k_{Q H_{\alpha}/H_{2}} + k_{R} }$$

where,

$A_{ij}$ is the Einstein Coefficient (obtained from NIST database),

$k_{R} = (A_{32} + A_{31}) = 9.8 \times 10^{7} s^{-1}$,

$K(\nu_{H_{\alpha}})$ is the constant taking into account the optical device response,

$k_{Q H_{\alpha}/H}$, $k_{Q H_{\alpha}/H_{2}}$ represent the quenching rate constants of $H-\alpha$ by the $H_{2}$ molecules and the H atoms

The emission intensity of $Ar$ line is given by:

$$ I_{Ar} = K(\nu_{Ar}) A_{44} \nu_{Ar} \nu_{emiss} \displaystyle \frac{ [Ar(3p)] k^{Ar}{e} n{e}}{ [H] k_{Q Ar/H} + [H_{2}] k_{Q Ar/H_{2}} + k_{R Ar} }$$

where,

$A_{44}$ is the Einstein Coefficient for spontaeneous transition,

$k_{R Ar} = A_{44}$,

$k_{Q Ar/H}$ , $k_{Q Ar/H_{2}}$ represent the quenching rate constants of $Ar$ by the $H_{2}$ molecules and the H atoms

Thus, the ratio of emission intensities result in:

$$ \frac{ [H (n = 1)] }{ [Ar (3p)] } = F \frac{ k^{Ar}{e} }{ k^{H\alpha}{e} } Q_{T} \frac{I_{H\alpha}}{I_{Ar}}$$

where $F$ is the optical device factor:

$$ F = \frac{ K( \nu_{Ar} ) \displaystyle \left( \frac{\nu_{Ar} A_{44}}{k_{R.Ar}} \right) }{ K( \nu_{H_{\alpha}} ) \displaystyle \left( \frac{\nu_{H_{\alpha}} A_{32}}{A_{32} + A_{31}} \right) } $$

here,

$\nu_{Ar} = \displaystyle \frac{c}{\lambda_{Ar}}$;

$\nu_{H_{\alpha}} = \displaystyle \frac{c}{\lambda_{H_{\alpha}}}$

while $Q_{T}$ is the factor representing all quenching:

$$ Q_{T} = Q_{H_{2}} = \frac{ \left( 1 + 0.132 x_{H_{2}} \sigma_{H_{2}}^{H\alpha} PT^{-\frac{1}{2}} \right) } {\left( 1 + 0.162 x_{H_{2}} \sigma_{H_{2}}^{Ar} PT^{-\frac{1}{2}} \right) } $$

Code execution: Dependencies

• The computations relevant to the code require simple python compilers to execute the .ipnyb files. It may run remotely on virtually any OS and distro given the prior ability to engage in said format. This was originally written in Jupyter Notebook.
• Code 1: A technical code with no User-friendly interface where all required values are plugged into the code itself.
• Code 2: A more prompted and easier code with Dialog prompts to enter data.

Additionally, the code is primitive in the sense that it does not utilize object oriented programming and is a single hit and run for one data set. To compute simultaeneous data sets the code has to be re-pasted into another cell block and executed.

Installation (Jupyter Notebook)

For proper usage, you can find the installation documentation for the Jupyter platform, on ReadTheDocs. The documentation for advanced usage of Jupyter notebook can be found here.

For a local installation, make sure you have pip installed and run:

pip install notebook

Usage - Running Jupyter notebook

Running in a local installation

Launch with:

jupyter notebook

Running in a remote installation

You need some configuration before starting Jupyter notebook remotely. See Running a notebook server.

Authors

Shakil Imtiaz, BSc Physics (Hons)

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References

1. Gicquel, A., Chenevier, M., Hassouni, K., Tserepi, A., & Dubus, M. (1998). Validation of actinometry for estimating relative hydrogen atom densities and electron energy evolution in plasma assisted diamond deposition reactors. Journal of Applied Physics, 83(12), 7504–7521. https://doi.org/10.1063/1.367514
2. Rousseau, A., Granier, A., Gousset, G., & Leprince, P. (1994). Microwave discharge in H2: Influence of h-atom density on the power balance. Journal of Physics D: Applied Physics, 27(7), 1412–1422. https://doi.org/10.1088/0022-3727/27/7/012
3. Dyatko, N. A., Kashko, D. A., Pal’, A. F., Serov, A. O., Suetin, N. v., & Filippov, A. v. (1998). Actinometric method for measuring hydrogen-atom density in a glow discharge plasma. Plasma Physics Reports, 24(12), 1041–1050.
4. Turner, M. M., & Daniels, S. (n.d.). Actinometry - Use of Particle in Cell code to generate improved rate constants for determination of absolute O. 1–12.
5. Mukherjee, A., Sharma, N., Chakraborty, M., & Saha, P. K. (2022). A study on the influence of external magnetic field on Nitrogen RF discharge using Langmuir probe and OES methods. Physica Scripta, 97(5). https://doi.org/10.1088/1402-4896/ac6079