Electron Impact Ionization Cross-sections of CH3 and SiH3 Radicals Targets﻿

doi:10.21203/rs.3.rs-1980381/v1

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Electron Impact Ionization Cross-sections of CH₃ and SiH₃ Radicals Targets

https://doi.org/10.21203/rs.3.rs-1980381/v1

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Single differential cross sections as a function of secondary electron energy at fixed incident electron energies 100 and 200 eV for the targeted molecule CH₃ and SiH₃ have been evaluated by using a modified Jain-Khare semiempirical approach. The integral or total electron-impact ionization cross-sections and the averaged secondary electron energy from differential ionization cross sections are calculated for incident electron energy from ionization threshold to 5 keV regime. The temperature dependent ionization rate coefficient is also calculated using total ionization cross-sections and Maxwell-Boltzmann distribution of electron energy. The calculated values of total ionization cross sections corresponding to (e, 2e) processes for CH₃ and SiH₃ molecules are in good accord with available theoretical and experimental results.

Mass Spectrometry

Electron-impact ionization cross sections

Averaged energy

Rate coefficient

CH3

SiH3

The novelty of the modified Jain-Khare (JK) semiempirical approach received remarkable surveillance of the total ionization cross-sections (TICS) for their unique properties. The atomic and molecular electron impact ionization cross sections data are beneficial for the evaluation of radiation chemical data for fusion edge, low-temperature plasmas processing, gas discharges, planetary, interstellar, cometary atmosphere, radiation chemistry and mass spectrometry along with the chemical analysis [1–5]. In view of the various applications, the interaction of electrons with molecules and their radicals has remained a valuable field of interest for a long [6, 7].

The free radicals are highly reactive molecular species because of its unpaired electron that are of great importance to understanding mechanism in chemistry and the several astronomical objects [8]. Therewith, radicals play a significant role in molecular plasmas to deposition [9] using various methods. Methyl (CH₃) and silyl (SiH₃) radicals are an instance of free radicals and are shows relevance in various concerns. Methyl radical is the optimum transient hydrocarbon radical used in tropospheric chemistry. Methyl radical plays a vital role to understand atmospheric oxidation and plasmas based on hydrocarbons [10]. Methyl radicals are also found in the upper atmospheres of Saturn [11] and Neptune [12] along with interstellar clouds [13] because of the photolysis process. The silyl (SiH₃) radical is isovalent of methyl (transient free) radical [14]. It is also reported that silyl radicals control the growth of hydrogenated silicon films in the chemical vapor deposition (CVD) [15] and plasma-enhanced chemical vapor deposition (PECVD) technique [16].

In this work, we have used the modified JK semiempirical model [17, 18] to evaluate the secondary energy-dependent ionization cross sections (SDCS) for the CH₃ and SiH₃ free radicals at 100 and 200 eV corresponding to (e, 2e) ionization processes. The averaged secondary electron (SE) energies along with usable parameters in radiation dose monitoring and plasma simulation [19] are also evaluated. The value TICS are calculated from SDCS for a value of energy in the range of ionization threshold to 5 keV. We made a comparative study of TICS with available theoretical calculations with the Binary-Encountered-Dipole (BED)- Binary-Encounter-Bethe (BEB) model of Ali et al. [20], semiclassical Deutsch-Märk (DM) calculations by Deutsch et al. [21] and Spherical Complex Optical Potential (SCOP) method mentioned in Joshipura et al. [22] and experimentally probed by Tarnovsky et al. [23, 24] and Baiocchi et al. [25] reveals good agreement.

The comprehensive details of modified JK semiempirical formulation to evaluate differential and integral ionization cross sections of molecules due to electron impact are discussed in our previous articles [26–28]. In brief, (e, 2e) processes for the production of SE of energy (𝜖) by an incident electron energy (E), the differential ionization cross-section per energy is given by

$${\text{Q}}_{\text{i}}\left(\text{E},\in \right)=\frac{{4{\pi }\text{a}}_{0}^{2}\text{R}}{\text{E}}\left[\left(1-\frac{\text{ϵ}}{\left(\text{E}-{\text{I}}_{\text{i}}\right)}\right)\frac{\text{R}}{\text{W}}\frac{{\text{d}\text{f}}_{\text{i}}\left(\text{W},0\right)}{\text{d}\text{W}}\text{ln}\left[1+{\text{C}}_{\text{i}}\left(\text{E}-{\text{I}}_{\text{i}}\right)\right]+\frac{\text{R}}{\text{E}} {\text{S}}_{\text{i}}\frac{(\text{E}-{\text{I}}_{\text{i}})}{\left({\text{ϵ}}^{3}+{\text{ϵ}}_{0\text{i}}^{3}\right)}\left(\text{ϵ}-\frac{{\text{ϵ}}^{2}}{\left(\text{E}-\text{ϵ}\right)}+\frac{{\text{ϵ}}^{3}}{{(\text{E}-\text{ϵ})}^{2}}\right)\right]$$

Where, i symbolize the formation of i^th type cations and the first and second parts deal with the Bethe and Möller cross-sections. The symbols a₀, R, 𝜖_0i, I_i, $\frac{{df}_{i}\left(W,0\right)}{dW}$, C_i and S_i represents the first Bohr radius, Rydberg’s constant, energy parameter, ionization threshold, oscillator strengths, collisional parameter and the number of electrons participating in collisional processes respectively [26].

The averaged SE energy <𝜖> are evaluated with the help of the energy-dependent cross sections Q_i (E, 𝜖) i.e. an important parameter to explore plasma physics related calculations [19]. The averaged SE energy <𝜖> is defined as

$$<\in > =\frac{{\int }_{0}^{\left(E-{I}_{i}\right)}W{Q}_{i}(E,\in )d\in }{{\int }_{0}^{\left(E-{I}_{i}\right)}{Q}_{i}\left(E,\in \right)d\in }$$

Where, energy loss (W) is the sum of ionization threshold (I_i) and the SE energy (𝜖), Mathematically, W = I_i + 𝜖.

The TICS is given by

$${\text{Q}}_{\text{i}}^{\text{T}}\left(\text{E}\right)={\int }_{0}^{(\text{E}-{\text{I}}_{\text{i}})}{ \text{Q}}_{\text{i}}\left(\text{E},\in \right)dϵ$$

In the present model, the ionization threshold and the dipole oscillator strengths $\frac{{df}_{i}\left(W,0\right)}{dW}$ are the major input parameter which has one to one mapping with the photoionization cross-sections Q_i^ph(in mega barn) as [29]

$${Q}_{i}^{ph}\left(Mb\right)=109.75 \frac{{df}_{i}\left(W,0\right)}{dW}\left({eV}^{-1}\right)$$

For individual atoms C, H and Si, the photoionization cross sections (PICS) are derived from experimental measurement [30]. The PICS for C and Si atoms are calculated from the Hartee-Slater central field calculations by Railman et al. [31] along with the work of Sakamoto et al. [32] and Berkowitz et al. [33] for H atom, from ionization threshold to 50 keV. For W > 50 eV, the PICS are extrapolated using Thomas-Reike-Kuhn (TRK) model with ⁓0.1% accuracy [34].

The collisional parameter C_i is a very sensitive parameter, that depends on the type of the molecular ions species, energy and the energy parameters 𝜖_0i [17, 18, 26, 27]. The ionization threshold I_i or appearance energies [35], C_i and 𝜖_oi are tabulated in Table 1.

Table 1

Table for ionization potential I_i, Collision parameter C_i, and energy parameter 𝜖_0i for CH₃ and SiH₃ radicals.
Molecules	I_i [35]	C_i	𝜖_0i
CH₃	9.84	0.034	60
SiH₃	8.14	0.075	35

In view of various applications in plasma processes, we have calculated the ionizations rate coefficients by using present calculated TICS which is based on Maxwell distribution law [36, 37] given as

$${\text{R}}_{\text{i}}=\underset{-{\infty }}{\overset{+{\infty }}{\int }}4{\pi }{\left(\frac{1}{2{\pi }\text{m}{K}_{B}\text{T}}\right)}^{\frac{3}{2}}{m}_{e} exp\left(\frac{-\text{E}}{{K}_{B}\text{T} }\right){\text{Q}}_{\text{i}}\left(\text{E}\right) \text{E}\text{d}\text{E}$$

The factor R_i is the function of energy and temperature. Where, ${K}_{B}$, m_e and T are Boltzmann coefficient, mass of electron and temperature, respectively.

The modified JK semiempirical approach briefly described above [26] is used to calculate the SDCS and TICS for the considered targets CH₃ and SiH₃ radicals. The SE energy-dependent differential cross sections at 100 and 200 eV incident electron energies (Fig. 1). In the literature both experimental and theoretical data are not available for comparison with our results for (e, 2e) differential cross-sections.

In the JK formulation (Eq. 1), the first part is called the Bethe term providing the growing contribution of the dipole-allowed interaction whereas the second part is the Möllar term which is indicative of non-dipolar and indicative of electron exchange in the process. The cross-sections are uniform in nature about W/2 or (∈+I)/2, where incident and ejected SE of (e, 2e) processes carries equal energies.

Figure 2, shows the integral or TICS for CH₃ and SiH₃ radicals in the incident electron energies from ionization threshold to 5 keV and we made a comparative study with available theoretical and experimental results.

CH₃

The present results for methyl radical are in satisfactory agreement from ionization threshold to 200 eV in line with SCOP model used by Joshipura et al. [22] and a slight deviation of about 12% exists above the 200 eV. On the other hand, our results are underestimated by ⁓2.5% lesser than the BED-BEB estimations by Ali et al. [20] for energies range 40–250 eV and 22% deviation shown from 12 eV to 33 eV with the DM calculations by Deutsch et al. [21]. Experimentally, Tarnovsky et al. [23] calculated absolute TICS using the fast-neutral beam technique from ionization threshold to 200 eV with the uncertainties of ± 15%. Baiocchi et al. [25] using crossed electron beam technique with a combined error limit of ± 30% is obtained for cross-sections. From 20eV to 200 eV, our results lie within experimental error bars.

SiH₃

Experimental data lie within the quoted experimental error of ± 15% with Tarnovsky et al. [24]. From threshold to 44 eV, our results are overestimated by 6% with the theoretical estimations made by Joshipura et al. using SCOP model [22] and, from 44 eV to 3000 eV, the present data set is underestimated by 14% with the same. In a comparison of our results with BED-BEB observations by Ali et al. [20] are deviated 5.6% and above 14% in energy range from the threshold to 55 eV.

The above calculations also satisfy access, consistency, and reliability checks [4, 38] viz. (i) the confined area in figures (1) for SE energy-dependent cross sections for these targets corroborate TICS at 100 eV and 200 eV. (ii) in the low energy regime, our current calculations of TICS adhere to the Wannier threshold law [38].

Using Eq. (2), the averaged SE energy <𝜖> as the function of incident electron energy, evaluated by differential cross sections for CH₃ and SiH₃ radicals ranging from ionization threshold to 5 keV shown in Fig. 3. As the ionization potential for the considered targets are nearly equal so that the present results for the targets are nearly equal at a given energies and half at (I_i+ 𝜖).

An attempt has also been made to evaluate the ionization rate coefficients, an important parameter in plasma study. The molecular rate coefficients are calculated using our current estimations of (e, 2e) TICS and Maxwell-Boltzman distribution for electrons. The values are depicted in the Fig. 4. These calculations are evocative, since no data is available for comparison.

The modified JK semiempirical approach has been employed to calculate differential and TICS for CH₃ and SiH₃ radicals. The modified JK semiempirical formulation is based on Bethe and Möller cross-sections in respect of the optical oscillator strength was our major input data. The applied JK semi-empirical formulation is very helpful in the calculation of integral or differential cross-sections at low energies. Inspite of the non-availability of the experimental or theoretical data for differential cross sections data and the rate coefficients for the considered targets, the calculated TICS from differential cross sections in the incident electron energy range ionization threshold to 5 KeV are in line with available experimental and theoretical data which assured our methodologies for further investigation on other free radicals and it may also facilitate the atomic and molecular data sets for modelling codes and various applications. Furthermore, undoubtedly for the sake of authenticity of the present results, we require more experimental measurements for differential and integral ionization cross sections.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Electron Impact Ionization Cross-sections of CH₃ and SiH₃ Radicals Targets

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Version 1

Abstract

Figures

1. Introductions

2. Theoretical Methodology And Input Data

3. Results And Discussion

4. Conclusions

Declarations

References

Status:

Version 1

Electron Impact Ionization Cross-sections of CH3 and SiH3 Radicals Targets﻿

Status:

Version 1

Abstract

Figures

1. Introductions

2. Theoretical Methodology And Input Data

3. Results And Discussion

4. Conclusions

Declarations

References

Status:

Version 1

Electron Impact Ionization Cross-sections of CH₃ and SiH₃ Radicals Targets