Development of a global model for BF 3 discharge Van Duy Cung, - PDF document

Transactions of the Korean Nuclear Society Virtual Spring Meeting July 9-10, 2020 Development of a global model for BF 3 discharge Van Duy Cung, Kyoung-Jae Chung*, Y. S. Hwang Department of Energy Systems Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, Korea *Corresponding author: jkjlsh1@snu.ac.kr 1. Introduction Table I : List of primary reactions Plasma processing has an important role in the electronics industry such as anisotropic etching in the Energy Reaction Process Ref. fabrication of micro-electric chips, implantation of many [eV] dopants in semiconductors [1]. In the ion implantation 1. e + BF 3 → BF 3+ + 2e Ionization 15.56 [1], [4] technique using boron trifluoride (BF 3 ) gas, the Dissociative 2. e + BF 3 → BF 2+ + F + 2e 15.76 [1], [3] characterization of ion species in the plasma source is of ionization great importance. In this work, we have developed a 3. e + BF 3 → BF 2 + F + 2e Dissociation 10.1 [1], [3] simplified global model for unmagnetized, low-pressure 4. e + BF 2 → BF 2+ + 2e Ionization 9.4 [1], [4] BF 3 plasma. In the particle balance equation, we consider 5. e + BF 2 → BF + F + e Dissociation 5.9 [1], [3] 5 neutral species (B, F, BF, BF 2 , BF 3 ) and 6 ion species (B + , B ++ , F + , BF + , BF 2+ , BF 3+ ). Not only the primary 6. e + BF → BF + + 2e Ionization 11.12 [1], [4] reactions such as the direct ionization, dissociation, and 7. e + BF → B + F + e Dissociation 8.1 [1], [3] dissociative ionization but also the surface reactions such 8. e + B → B + + 2e Ionization 8.30 [1], [4] as dissociative recombination of BF 3+ , BF 2+ , and BF + 9. e + B → B ++ + 3e Ionization 33.45 [1], [3] ions are included in the model. In this paper, the details of the global model and preliminary results are presented. 10. e + F → F + + 2e Ionization 17.4 [1], [6] 11. e + B + → B ++ + 2e Ionization 25.15 [1], [5] 2. Model In the present model, we consider the ion species ratio without the magnetic field effect and the power Table II : List of surface reactions balance equations, compared to the Patel’s model [1]. We only apply the particle balance equations for ion and Reaction Process Ref. neutral species, along with the conservation of charge 12. e + BF 3+ → BF 2 + F Dissociative recombination [1], [3] and atomic number. For the primary reactions, we 13. e + BF 2+ → BF + F consider the direct ionization, dissociation, and Dissociative recombination [1], [3] dissociative ionization. The surface reactions include the 14. e + BF + → B + F Dissociative recombination [1], [3] dissociative recombination of BF 3+ , BF 2+ , and BF + ions. Negative ions and metastables are not considered. Compared to the Patel’s model [1], the excitation For the Maxwellian distribution of electron energy, reactions (including vibrational excitation processes), 𝑔 𝑁 (𝐹) , the rate constants are given by [1] : momentum transfer reactions and charge transfer ∞ 1/2 𝑙 𝑗 = ( 2 reactions are not included in the present model. In this ) ∫ 𝜏 𝑗 (𝐹) √𝐹 𝑔 𝑁 (𝐹) 𝑒𝐹 , 𝑛 𝑓 present model, we do not consider two step ionization for any of the species, which is similar to Patel’s assumption 0 where 𝜏 𝑗 (𝐹) is the collision cross-section of 𝑗 th reaction, [1]. The present global model is developed based on the and 𝑛 𝑓 is the electron mass, E is the electron energy (eV). models provided by Patel [1], Choe [2] and Fukumasa et The differences between the present rate constants data al [7]. As an initial trial, a cylindrical chamber with a and Patel’s rate constants data [1] in two tables above are : radius of 1 cm and a length of 10 cm is considered. The in the ionization reactions of BF 3 , BF 2 , BF, B (the assumptions used in the present model is well described reactions of 1 st , 4 th , 6 th , 8 th processes, respectively), we elsewhere [1]. use the NIST cross section data [4] to calculate the rate From the species and the processes which are constants of these reactions, and for the ionization of F expressed above, all of the reactions (primary reactions (the 10 th process), the rate constant is obtained by using and surface reactions) of the global model are given in the Approximate Analytical Formulas of the Tables I and II. recommended cross section [6]. All of the rate constants of the remaining reactions are calculated by using the Patel’s data [1]. Figure 1 shows the rate coefficients of all reactions used in the present model depending on the electron temperature.

Transactions of the Korean Nuclear Society Virtual Spring Meeting July 9-10, 2020 In the equations which are expressed above, we consider the ratio of 𝜐 1 , 𝜐 2 , 𝜐 3 , 𝜐 4 , 𝜐 5 , 𝜐 6 to be the ratio of the square root of the respective ion masses, and also RATE CONSTANTS OF BF 3 PLASMA DISCHARGE (PRESENT) consider the ratio of 𝑈 1 , 𝑈 2 , 𝑈 3 , 𝑈 4 to be the ratio of the -10 Log 10 k 01 square root of the respective atomic or molecular masses Log 10 k 02 Log 10 k 03 [2,7]. 𝜐 1 and 𝑈 1 are calculated as two unknown variables. Log 10 k 04 -15 Log 10 k 05 3. Preliminary results 3 /s) Log 10 k 06 Log 10 k (m Log 10 k 07 -20 Log 10 k 08 As preliminary results, we calculate the dependence Log 10 k 09 Log 10 k 10 of ion species fractions on plasma density, gas pressure -25 Log 10 k 11 without considering the relation between pressure and Log 10 k 12 electron temperature. Figure 2 illustrates the ion species Log 10 k 13 Log 10 k 14 fractions when changing the plasma density from 10 15 m - -30 1 10 100 3 to 10 19 m -3 at fixed operating pressure p = 20 mTorr, the Electron temperature (eV) recombination coefficient and the electron temperature are set as γ = 0.1 and T e = 3 eV, respectively [2]. We can Fig. 1. Rate coefficients of reactions used in the present model. see that the ion species fraction is greatly influenced by the plasma density. When the plasma density increases, According to the assumptions in the present model, the ion species fractions of B + , F + , BF + , and BF 2+ increase, we formulate the particle balance equations for all while the ion species fraction of BF 3+ decreases neutral and ion species as following [1,2,7] : significantly, indicating the BF 3+ is negligible at very 𝑂 3 𝑜 𝑓 𝑙 07 + 𝑙 14 𝑜 4 𝑜 𝑓 − 𝑂 1 𝑜 𝑓 𝑙 08 − 𝑂 1 𝑜 𝑓 𝑙 09 − high plasma density regime. The ion species fraction of 𝛿 𝑂 1 𝑈 ⁄ = 0 (1) BF 2+ is always higher than that of B + , B ++ , F + , and BF + . 1 𝑂 5 𝑜 𝑓 𝑙 02 + 𝑂 5 𝑜 𝑓 𝑙 03 + 𝑂 4 𝑜 𝑓 𝑙 05 + 𝑂 3 𝑜 𝑓 𝑙 07 + 𝑙 14 𝑜 4 𝑜 𝑓 + 𝑙 13 𝑜 5 𝑜 𝑓 + 𝑙 12 𝑜 6 𝑜 𝑓 − 𝑂 2 𝑜 𝑓 𝑙 10 − 𝛿 𝑂 2 𝑈 ⁄ = 0 (2) 2 Fixed parameters : p = 20 mTorr,  = 0.1, T e = 3 eV (Present) 𝑂 4 𝑜 𝑓 𝑙 05 + 𝑙 13 𝑜 5 𝑜 𝑓 − 𝑂 3 𝑜 𝑓 𝑙 06 − 𝑂 3 𝑜 𝑓 𝑙 07 − 100 ⁄ 𝛿 𝑂 3 𝑈 = 0 (3) 3 𝑂 5 𝑜 𝑓 𝑙 03 + 𝑙 12 𝑜 6 𝑜 𝑓 − 𝑂 4 𝑜 𝑓 𝑙 04 − 𝑂 4 𝑜 𝑓 𝑙 05 − 80 Ion species fraction (%) 𝛿 𝑂 4 𝑈 ⁄ = 0 (4) + B 4 ++ B 𝑂 1 𝑜 𝑓 𝑙 08 − 𝑜 1 𝑜 𝑓 𝑙 11 − 𝑜 1 𝜐 1 ⁄ = 0 (5) 60 + F ⁄ + 𝑂 1 𝑜 𝑓 𝑙 09 + 𝑜 1 𝑜 𝑓 𝑙 11 − 𝑜 2 𝜐 2 = 0 (6) BF + BF 2 𝑂 2 𝑜 𝑓 𝑙 10 − 𝑜 3 𝜐 3 ⁄ = 0 (7) 40 + BF 3 𝑂 3 𝑜 𝑓 𝑙 06 − 𝑜 4 𝜐 4 ⁄ − 𝑙 14 𝑜 4 𝑜 𝑓 = 0 (8) 20 ⁄ 𝑂 5 𝑜 𝑓 𝑙 02 + 𝑂 4 𝑜 𝑓 𝑙 04 − 𝑜 5 𝜐 5 − 𝑙 13 𝑜 5 𝑜 𝑓 = 0 (9) 𝑂 5 𝑜 𝑓 𝑙 01 − 𝑜 6 𝜐 6 ⁄ − 𝑙 12 𝑜 6 𝑜 𝑓 = 0 . (10) 0 1E15 1E16 1E17 1E18 1E19 -3 ) Plasma density (m The charge and particle number conservations are [1,2,7] : Fig. 2. The dependence of ion species fractions on plasma 1 𝑜 1 + 2 𝑜 2 + 𝑜 3 + 𝑜 4 + 𝑜 5 + 𝑜 6 = 𝑜 𝑓 (11) density. 𝑂 1 + 𝑜 1 + 𝑜 2 + 𝑂 3 + 𝑜 4 + 𝑂 4 + 𝑜 5 + 𝑂 5 + 𝑜 6 = 𝑂 0 = 𝑞 𝑙𝑈 ⁄ (12) 0 𝑂 2 + 𝑜 3 + 𝑂 3 + 𝑜 4 + 2𝑂 4 + 2𝑜 5 + 3𝑂 5 + 3𝑜 6 = 17 m -3 ,  = 0.1, T e = 3 eV (Present) Fixed parameters : n e = 10 ⁄ 3𝑂 0 = 3 𝑞 𝑙𝑈 (13) 100 0 where 𝑂 1 , 𝑂 2 , 𝑂 3 , 𝑂 4 , 𝑂 5 are the densities of B, F, BF, 80 + B Ion species fraction (%) BF 2 , BF 3 , respectively; 𝑜 1 , 𝑜 2 , 𝑜 3 , 𝑜 4 , 𝑜 5 , 𝑜 6 are the ++ B + F densities of B + , B ++ , F + , BF + , BF 2+ , BF 3+ , respectively; 𝑈 60 1 , + BF 𝑈 2 , 𝑈 3 , 𝑈 4 are the transit times of B, F, BF, BF 2 across the + BF 2 40 + chamber, respectively; 𝜐 1 , 𝜐 2 , 𝜐 3 , 𝜐 4 , 𝜐 5 , 𝜐 6 are the BF 3 containment times of B + , B ++ , F + , BF + , BF 2+ , BF 3+ , 20 respectively; and the containment times of B, F, BF, BF 2 4 /𝛿 ; γ is the sticking factor would be 𝑈 1 /𝛿 , 𝑈 2 /𝛿 , 𝑈 3 /𝛿 , 𝑈 0 of B, F, BF, BF 2 at the wall; p is the BF 3 gas pressure; 𝑈 0 0 10 20 30 40 50 Pressure (mTorr) is the ion and neutral temperature (= 600 K); 𝑜 𝑓 is the electron density; 𝑂 0 is the density of BF 3 molecules before discharge.