_{1}

^{*}

Partial single and double differential cross sections with their sums through direct and dissociative ionization of PF
_{3} have been evaluated at fixed electron energies 100 and 200 eV, by using modified Jain-Khare semi-empirical approach. To the best of my knowledge no other data of differential cross sections are available for the comparison. I have also calculated integral ionization cross sections with their ionization rate coefficients by using M-B distribution. No other data of partial ionization cross section are available till now. The sum/or total of evaluated partial cross sections reveal good agreement with available theoretical data.

Electron-molecule collision cross sections from very low energy up to threshold play a pivotal role in determining electron transport properties and electron energy distribution of a swarm of electrons drifting through various gases. Per-fluorinated compounds (PFC) are widely used in electrical industries, plasma-assisted fabrication of microcircuits, surface hardening, agriculture, and medicinal fields. PF_{3} is also a potential reagent for the gas- phase synthesis in microelectronic doping [_{3}, both evaluated by M. Vinodkumar et al. [

This letter reports the results of the single differential cross sections (SDCS) as a function of secondary electron energy and double differential cross sections (DDCS) as a function of secondary electron energy and incident angle of electron, by using modified Jain and Khare semi-empirical approach [^{+}, ^{+}, PF^{2+}, F^{+}, and P^{2+} resulting through the direct and dissociative ionization of PF_{3} by electron collision show good agreement with the available theoretical data [_{3} molecule were not available till now. We have also evaluated the ionization rate coefficients for integral ionization cross sections by using Maxwell-Boltzmann energy distribution [

The partial integral cross sections by using modified Jain-Khare semi-empirical approach [^{th} type of ion is given by

Here all symbols have their usual meanings as defined in Refs [

Single differential cross sections (SDCS) formulism can be obtained by differentiation of (Equation (1)) w.r. to secondary electron energy i.e.

For the evaluation of double differential cross sections (DDCS) we have used formula derived by Kumar et al. [

and the total cross section is obtained by

For PF_{3} molecule the oscillator strengths and ionization potentials of various cations (^{+}, ^{+}, ^{+}, and P^{2+}) are taken from the experimental results of J. W. Au et al. [^{+}, ^{+}, ^{+}, and P^{2+} are available up to 130 eV. For higher energies, the same data have been extrapolated by the Thomas-Reiche-Kuhn (TRK) sum rule, within 10% error bars [_{i} = 0.03789) and mixing parameters (ɛ_{0} = 45 eV) have been calculated as for other molecules [

Ionization rate coefficients are important quantities in plasma processes which are determined by using M-B distribution of temperature/energy [

where k, T and m are the Boltzmann constant, absolute temperature and mass of the electron, respectively.

The phosphorus trifluoride molecule, which has trigonal pyramidal geometry and belongs to the C_{3v} symmetry group, has a ground state (_{1}A^{1}) electronic configuration in the independent particle model [

Differential and partial integral ionization cross sections for PF_{3} were not available till now, therefore a wide scope is available for the researcher. Partial and total single differential cross sections (SDCS) as a function of secondary electron energy at fixed incident energies of 100 and 200 eV are evaluated and are shown in _{max}/2) and angle (10˚ to 180˚) are represented in _{max}/2, where the energies of primary and the secondary electrons are almost equal, except some irregular behavior at lower energy side. The present calculations account the contribution of exchange effects and resonances through the second part of the formulation (Equations (1)-(3)). In the present formulation (Equations (1)-(3)) the first part known as Born- Bethe cross section for slow secondary electron, corresponds to the growing contribution of the dipole-allowed interaction and resembles the photoionization cross-section and second part, the Mott cross section accounts for the electron exchange effect, is the non-dipole part which defines the knock-on collision. The figures clearly show the weight contribution of the molecular and atomic cations. The cross sections for molecular ions are much larger than the atomic ions.

The partial ionization cross sections corresponding to the formation of various cations^{+}, ^{+}, PF^{2+}, F^{+}, and P^{2+} in electron impact ionization of PF_{3} in the impinging electron energy range varying from ionization threshold to 1000 eV are evaluated and shown in

evaluated by Minaxi Vinodkumar et al. [

where m is defined in term of charge z on the residual ion i.e.

These consistency checks provide the consistency and reliability of the present results.

We have also evaluated a set of ionization rate coefficients as a function of electron energy for the individual cations produced in electron collision with the PF_{3} molecule. The calculations are made using the calculated ionization cross sections and Maxwell-Boltzmann energy distribution (Equation (5)) and the results are presented in

The present calculation for energy dependent differential and integral ionization cross sections is an attempt

towards the wider applicability of a modified Jain-Khare semi-empirical formalism. First time, we have evaluated the differential and partial ionization cross sections leading to the various cations in electron-PF_{3} collision processes and the results are predictive to the experimentalist for measurement. However, the total ionization cross-sections revealed a reasonable good agreement with the available theoretical data. The ionization rate

W (eV) | PF+ | P^{+} | PF^{2}^{+} | F^{+} | P^{2}^{+} | Total | ||||
---|---|---|---|---|---|---|---|---|---|---|

15 | 0.009568 | 0.009568 | ||||||||

19 | 0.114882 | 0.0845 | 0.199382 | |||||||

25 | 0.333381 | 0.347592 | 0.000589 | 0.681562 | ||||||

31 | 0.470326 | 0.943523 | 0.014863 | 0.000234 | 1.428946 | |||||

37 | 0.551466 | 1.434225 | 0.04706 | 0.006544 | 0.000786 | 2.040081 | ||||

39 | 0.570854 | 1.56836 | 0.057217 | 0.019072 | 0.001025 | 0.000009 | 2.216537 | |||

43 | 0.601196 | 1.805313 | 0.07516 | 0.046509 | 0.002047 | 0.000015 | 0.000054 | 0.000047 | 2.530341 | |

53 | 0.646061 | 2.24549 | 0.112408 | 0.11312 | 0.020779 | 0.00073 | 0.000982 | 0.000748 | 0.000023 | 3.140341 |

61 | 0.663659 | 2.492106 | 0.134705 | 0.158906 | 0.037968 | 0.001509 | 0.002747 | 0.002467 | 0.000176 | 3.494243 |

71 | 0.673414 | 2.728337 | 0.157995 | 0.206475 | 0.059736 | 0.002502 | 0.005114 | 0.005223 | 0.001604 | 3.8404 |

81 | 0.674802 | 2.909387 | 0.176678 | 0.245934 | 0.082341 | 0.003325 | 0.007521 | 0.008058 | 0.003593 | 4.111639 |

91 | 0.671105 | 3.041464 | 0.191385 | 0.278917 | 0.105168 | 0.004086 | 0.009654 | 0.010975 | 0.005922 | 4.318676 |

101 | 0.664009 | 3.136233 | 0.203297 | 0.305955 | 0.127601 | 0.004772 | 0.011804 | 0.01383 | 0.00831 | 4.475811 |

121 | 0.643301 | 3.239978 | 0.21975 | 0.345475 | 0.16934 | 0.005937 | 0.015557 | 0.019027 | 0.013545 | 4.67191 |

141 | 0.61863 | 3.264648 | 0.228161 | 0.369222 | 0.203152 | 0.006676 | 0.018332 | 0.02309 | 0.018369 | 4.75028 |

149 | 0.608393 | 3.258124 | 0.229835 | 0.375181 | 0.214271 | 0.00691 | 0.019178 | 0.024385 | 0.019993 | 4.75627 |

201 | 0.5434 | 3.103192 | 0.227909 | 0.384706 | 0.258083 | 0.007655 | 0.021868 | 0.029318 | 0.025113 | 4.601244 |

301 | 0.444126 | 2.681593 | 0.203441 | 0.350853 | 0.269084 | 0.007445 | 0.021293 | 0.030289 | 0.024917 | 4.033041 |

401 | 0.375108 | 2.323381 | 0.178658 | 0.309975 | 0.252237 | 0.00677 | 0.019245 | 0.028225 | 0.022419 | 3.516018 |

501 | 0.325441 | 2.04502 | 0.158355 | 0.2752 | 0.231471 | 0.00611 | 0.017279 | 0.025804 | 0.02002 | 3.1047 |

601 | 0.288109 | 1.827099 | 0.14206 | 0.246893 | 0.212069 | 0.00554 | 0.015605 | 0.023581 | 0.017999 | 2.778955 |

701 | 0.259009 | 1.65291 | 0.128851 | 0.223799 | 0.195027 | 0.00506 | 0.014208 | 0.021647 | 0.016327 | 2.516838 |

801 | 0.235658 | 1.510731 | 0.117971 | 0.204721 | 0.180284 | 0.004655 | 0.013038 | 0.019983 | 0.014937 | 2.301978 |

901 | 0.216479 | 1.392507 | 0.108869 | 0.188739 | 0.167533 | 0.00431 | 0.012048 | 0.018551 | 0.01377 | 2.122806 |

1000 | 0.200718 | 1.294465 | 0.101288 | 0.175421 | 0.15666 | 0.004019 | 0.011218 | 0.017333 | 0.012795 | 1.973917 |

coefficients as a function of electron energy are also evaluated. These results are useful in plasma simulation and modeling.

Author is thankful to reviewers for good suggestions in improvement of paper quality.

RajeevKumar, (2015) Electron Ionization Cross Sections of PF_{3} Molecule. Journal of Applied Mathematics and Physics,03,1671-1678. doi: 10.4236/jamp.2015.312192