COLLEGE OF ENGINEERING Division of Electronics and Electrical Engineering DOCTOR OF PHILOSOPHY DISSERTATION PRESENTATION The Electron Collision Cross Sections and the Electron Transport Coefficients in BF3 and C2F6 molecules By: Pham Xuan Hien Advisor: Professor Byung-Hoon Jeon th Korea, December 17 2015 Contents Introduction Electron swarm method Electron collision cross sections for BF3 molecule 3.1 Derived electron collision cross section set for BF3 molecule 3.2 Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures Electron collision cross sections for C2F6 molecule Conclusion Introduction Plasma processing Depositing a film Coating the surface with a photoresist Optically projecting a pattern onto the photoresist Developing the resist, removing the exposed resist regions and leaving behind a patterned resist mask Etching the metal that is not protected by the mask Removing the mask Fig Subtractive processing scheme used in fabrication microelectronic integrated circuit Introduction Electron collision cross sections (1/2) Electron collisions directly connect to entire processing plasma chemistry • Electron Collision • • Other Input Data Cross Sections The accurate and detailed of electron collision • • • cross sections are necessary • • Transport and Reaction Coefficients • • Modeling and Simulation of Plasma Processing Fig Sample basic procedure of semiconductor fabrication • Semiconductor • Fabrication Introduction Electron collision cross sections (2/2) Electron swarm Electron beam method method Electron Electron Collision transport Cross Sections coefficient Momentum transfer Vibrational cross section Excitation cross section Dissociation cross section cross section Fig Electron collision cross sections Attachment cross section Ionization cross section Introduction General properties and application of BF3 molecule - Boron trifluoride (BF3): hard acid, non-flammable, toxic, corrosive to the skin, halogen-containing gas - Application: + Plasma-assisted fabrication of microcircuits + Alternative agent for plasma doping and metal surface treatment + Suggested to replace di-borane (used as a p-type dopant of amorphous Si films in solar cells) + BF3 – SiH4 and BF3 – Ar mixtures are used in microwave plasma, glow-discharge process Introduction General properties and application of C2F6 molecule Perfluoroethane (C2F6) is a man-made gas widely used in: - Etching plasma processing - PECVD chamber cleaning - Gaseous dielectrics (discharge switches, gas insulator in high voltage equipment ) Introduction Objectives Because of their industrial importance, the reliable sets for BF3 and C2F6 molecules and electron transport coefficients in binary mixtures of the BF3 and C2F6 with buffer gases are necessary for understanding discharges plasma (2) (1) Determine the sets of electron collision cross sections for BF3 and C2F6 molecules for a quantitative numerical modeling of a plasma discharge for processing procedures with materials containing these molecules by using an electron swarm method * The accurate electron collision cross sections and electron transport coefficients, not only in pure gaseous molecules but also in the binary gas mixtures, are necessary to understand quantitatively plasma phenomena and ionized gases Analyse electron transport coefficients in BF3 -Ar and BF3 –SiH4 mixtures by u sing a two-term approximation of the Boltzmann equation analysis for quantitativ ely modeling Electron swarm method - The electron transport coefficients in given gases are functions only of the ratio E/N, the gas temperature T, and when a magneti c field is present, of B/N They are related to the electron collision cross sections by complex integral expressions involving the el ectron energy distribution function (EEDF) The EEDF can be obtained theoretically by solving the Boltzmann equation - A two-term approximation of the Boltzmann equation for the energy given by Tagashira et al.[1] (used for BF3) - A multi-term approximation of the Boltzmann equation for the energy was developed at James-Cook university [2] (used for C 2F6) [1] H Tagashira, Y Sakai and S Sakamoto: J Phys D 10, 1051 (1977) [2] R E Robson and K F Ness, Phys Rev A 33, 2068 (1986) Electron swarm method Procedures of determination of the electron collision cross section set Step 1: Modification of the low energy inelastic cross sections in order until calculated and measured electron transport coefficients (W, ND L, NDT, DL/μ and DT/μ) in the mixtures of object gas are in good agreement Step 2: Modification of the momentum transfer cross section until the calculated and measured electron transport coefficients (ND L, NDT, DL/μ and DT/μ) in the pure object gas are good in agreement when the inelastic cross sections determined in step are not altered Step 3: Modification of high energy inelastic cross sections such as electronic excitation, dissociation, attachment and ionization cross sections until calculated and measured electron transport coefficients (mainly α/N, η/N, and (α-η)/N) not only in pure but also in mixtures of object gas are in good agreement when the electron collision cross sections determined in step and are not altered -Where W is electron drift velocity, NDL is density-normalized longitudinal coefficient, NDT is density-normalized transverse diffusion coefficients, D L/μ is ratio of the longitudinal diffusion coefficient (DL) to the electron mobility (μ), DT/μ is ratio of the transverse diffusion coefficient (DT) to the μ, α/N is Townsend first ionization coefficient, η/N is electron attachment coefficient, and (α - η)/N is density-normalized effective ionization coefficient Electron collision cross sections for BF3 3.2 Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (6/9) Fig 17 Electron attachment coefficient η/N as functions of E/N for the BF3 -Ar mixtures with 1, 5, 10, 30, 50, 70, and 90% BF3 molecule Fig 18 Electron attachment coefficient η/N as functions of E/N for the BF3 –SiH4 mixtures with 10, 30, 50, 70, and 90% SiH4 Electron collision cross sections for BF3 3.2 Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (7/9) Fig 19 Variation in α/N in BF3 –SiH4 mixtures at E/N = 200 Td with the mixture ratio of BF3 Electron collision cross sections for BF3 3.2 Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (8/9) The electron energy distribution in the 90% BF3-SiH4 mixture relatively significantly differs from that in the pure BF3 while there are no significant differences between the pure SiH4 molecule and the 10% BF3-SiH4 mixture Fig 20 Electron energy distribution functions for pure BF3 , pure SiH4, a 10% BF3 -90% SiH4 mixture, and a 90% BF3-10% SiH4 mixture at E/N = 200 Td Electron collision cross sections for BF3 3.2 Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (9/9) The momentum transfer cross section for the BF3 molecule is much larger than that for pure SiH4 The mean electron energy in the pure BF3 therefore, is dramatically lower than that in the pure SiH4 Fig 21 Mean electron energy as a function of E/N for pure BF3, pure SiH4, and BF3 –SiH4 mixtures Electron collision cross sections for C2F6 molecule -Pirgov and Stefanov [6] and Hayashi and Niwa [7] presented two sets of electron-collision cross section for the C2F6 molecule: + Using two-term Boltzmann analysis + Based on measured W and DT/µ in the pure C2F6 molecule + Based on measured W in the C2F6 -Ar mixtures -Set of Pirgov and Stefanov includes the momentum transfer cross section and overall inelastic cross section -Set of Hayashi and Niwa includes the momentum transfer cross section, three vibrational-excitation cross sections, the dissociative attachment cross section, two electro nic excitation cross sections, the dissociation cross section and the ionization cross section -Okuma and Nakamura [8] have also obtained the set: + By modifying the inelastic cross sections of Hayashi and Niwa using multi-term Boltzmann analysis + Based on new their measurements of W and NDL in 0.524% and 5.47% C2F6 -Ar mixtures [6] P Pirgov and B Stefanov, J. Phys. B At. Mol Opt Phys 23, 2879 (1990) [7] M Hayashi and A Niwa, in Gaseous Dielectrics V: Proceedings of the Fifth International Symposium on Gaseous Dielectrics, Knoxville, Tennessee, (USA, May 3—7, 1987, Elsevier, 2013) Electron collision cross sections for C2F6 molecule C2F6 has fairly large inelastic cross sections, which are greater than momentum-transfer cross section at low energies, multi-term Boltzmann analysis is often recommended to apply for modifying The set of Okumo and Nakamura [8] is more reliable than the set of Hayashi and Niwa [7] >> Initial set: chosen from Okumo and Nakamura Fig 22 Set of electron-collision cross sections for the C F molecule The solid and broken curves show the initial and present cross sections, respectively [8] Okumo and Y Nakamura, Nist Special Publication, 265 (1998) Electron collision cross sections for C2F6 molecule With initial set: the differences between the calculated and measured NDL in the E/N range of 3-10 Td in 0.524% C2F6-Ar mixture, were significant With present set: in good agreement Fig 23 W and NDL in 0.524% C2F6-Ar Mixture Electron collision cross sections for C2F6 molecule Differences between calculated and measured NDL in the E/N range of 8-25 Td in 5.47% C2F6-Ar mixture With present set: in good agreement Fig 24 W and NDL in 5.47% C2F6-Ar Mixture Electron collision cross sections for C2F6 molecule The measured W indicated a small region of NDC in the range of 20-70 Td Fig 25 W in pure C2F6 molecule Electron collision cross sections for C2F6 molecule -The differences between calculated and measured NDL in the E/N range of 4-100 Td -With present set: in good agreement Fig 26 NDL in pure C2F6 molecule Conclusion For the BF3 molecule: -The currently best available electron collision cross section set for the BF3 molecule was determined from the measured electron transport coefficien ts in pure BF3 molecule using two-term Boltzmann equation analysis -The remarkable synergism in the Townsend first ionization coefficient was point out and discussed in BF3-SiH4 mixtures For the C2F6 molecule: - The currently best available electron collision cross section set for the C 2F6 molecule was determined from the measured electron transport coefficie nts not only in pure C2F6 molecule but also in 0.524% and 5.47% C2F6-Ar mixtures using multi-term Boltzmann equation analysis Conclusion  Two best available of electron collision cross sections for the BF3 and C2F6 molecules is the important database for modeling and simulation of pl asma discharges for processing procedures with materials containing BF and C2F6 molecules in various industrial applications such as plasma proces sing, gas discharge switches, gas insulator in high voltage equipments etc Achievements Pham Xuan Hien, Do Anh Tuan and Byung-Hoon Jeon, Electron collision cross sections for the TMS molecule and electron transport coefficients in TMS-Ar and TMS-O2 mixtures, Journal of the Korean Physical Society, 61, 62 (2012) Pham Xuan Hien, Byung-Hoon Jeon and Do Anh Tuan, Electron collision cross sections for the BF3 molecule and electron transport coefficients in BF3 -Ar and BF3 –SiH4 mixtures, Journal of the Physical Society of Japan 82, 034301 (2013) Pham Xuan Hien and Byung-Hoon Jeon, Determination of the electron collision cross sections for the C2H4 molecule by using the electron swarm method, Journ al of the Korean Physical Society, 64, 1314 (2014) Pham Xuan Hien and Byung-Hoon Jeon, Electron transport coefficients and electron collision cross section set for the C2F6 molecule, Journal of the Korean Phy sical Society (Submitted) Future works Measure electron transport coefficient in rare Re-determine inelastic cross sections at low gas-BF3 mixtures energy Present electron collision cross section set for BF3 molecule Calculate electron transport Use Monte Carlo simulation Re-determine ionization and coefficients in mixture gas of attachment cross sections C2F6 molecule Present electron collision New electron collision cross cross section set for C2F6 section set for C2F6 molecule molecule Acknowledgments  Dissertation Committee Professors  All of Professors with Division of Electronics and Electrical Engineering, College of Engineering, Dongguk University  Professor Byung-Hoon Jeon  This work was supported by College of Engineering, Dongguk University, South Korea Thank you for your attention! ... pure SiH4, a 10% BF3 -90% SiH4 mixture, and a 90% BF3-10% SiH4 mixture at E/N = 200 Td 3 Electron collision cross sections for BF3 3.2 Electron transport coefficients in BF3-Ar and BF3 -SiH4. .. pure SiH4 The mean electron energy in the pure BF3 therefore, is dramatically lower than that in the pure SiH4 Fig 21 Mean electron energy as a function of E/N for pure BF3, pure SiH4, and BF3 SiH4. .. in the 90% BF3 -SiH4 mixture relatively significantly differs from that in the pure BF3 while there are no significant differences between the pure SiH4 molecule and the 10% BF3 -SiH4 mixture Fig