6. Conclusion and Recommendations for Future Study 56
6.2 Recommendations for Future Work
Base on the viewpoint for improving the fluid modeling code, there are several possible directions of research are recommended for further studies and are summarized as follows:
1. To apply the fluid modeling code for simulating several challenging gas discharge prob-lems in the frequency range of RF and AC.
2. To further reduce the computational time in larges-scale low-pressure (or diffusion domi-nated) fluid modeling problem that may involve large number of ion and neutral species, we may adopt the following multiscale temporal marching scheme:
(a) Solve the electron continuity equation, electron energy density equation and Pois-son’s equation together with fully implicit scheme with an electron time step and repeat until an ion time step size (∼10-50 electron time steps) is reached.
(b) Solve the (linearized) continuity equations for all ion species implicitly one by one using the most updated (or mean) electric field for evaluating the transport coeffi-cients of ions.
(c) Repeat Step a and Step b until a neutral time step size (∼10,000-100,000 electron time steps) is reached.
(d) Solve the (linearized) continuity for all neutral species implicitly one by one using the most updated (or mean) electric field for evaluating the transport coefficients of ions.
(e) Repeat Steps a through d until the preset steady-state condition is reached.
In Step b, the steady-state continuity equation for each neutral species may be solved at each time step to further reduce the computational cost to reach steady-state flow condi-tion.
3. For treating gas discharges at higher pressure, in which the convection by the neutral flow is important, the Navier-Stokes equation needs to be solved at each neutral time step in the above after Step d.
4. For treating gas discharged with complex geometry, the fluid modeling equations need to be solved in the curvilinear coordinate frame.
5. To develop a Maxwell equation solver for solving discharge involving EM waves such as high-frequency and large-area PECVD and inductively coupled plasma (ICP) problems.
6. To incorporate an automatic DC-bias adjustment function into the fluid modeling code.
7. To couple an external circuit module with the fluid modeling code.
8. To extend the fluid modeling code into a three-dimensional version and couple with a time-dependent Maxwell equation solver (e.g., time-dependent finite-difference, TDFD) for several realistic PECVD cases, such as solar cell film deposition.
Figure 3.1: Comparison of simulated and experimental voltages and currents for atmospheric-pressure discharge with 1 mm gap spacing using sinusoidal 13.56 M Hz power source.
Figure 3.2: Current-voltage characteristic of numerical results and experimental data, using helium gas dielectric barrier discharge at 760 torr, applied wave frequency 60 KHz.
(a)
(b)
(c)
Figure 3.3: Comparison of simulated and measured discharged currents along with photo
im-Figure 3.4: Spatial-average temporal discharge properties of nitrogen DBD (60 kHz, d = 0.7 mm).
(a) (b)
(c) (d)
(e) (f)
Figure 3.5: Simulated cycle averaged plasma properties of helium GEC including (a) electron, (b) He+, (c) He+2, (d) He∗2, (e) He∗, and (f) Hemeta.
Applied Voltage (V) ElectronDensity(1015 cm-3 )
0 50 100 150 200 250
100 101 102 103
Simulation Present
Exp. M. E. Riley et. al. (1993) Theory M. E. Riley et. al. (1993) Symbol Method Source
Figure 3.6: A comparison of the simulated peak electron densities with the theoretical prediction and the experimental data [Riley et al., 1994] for various applied voltages
Number of Processors
Figure 3.7: The parallel performance including (a) speedup analysis and (b) runtime per time step as a function of the number of processors
(a)
(b)
Figure 4.1: Schematic diagram of (a) simple and (b) complicated helium plasma chemistry based on the magnitude of energy level.
Figure 4.2: Schematic diagram of (a) simple and (b) complicated helium plasma chemistry based on the magnitude of energy level.
Figure 4.3: Comparison of simulated and measured discharge currents in a quasi-pulse AC cycle (20 kHz).
(a)
(b)
Figure 4.4: (a) Comparison between experimental current and simulation using the simple plasma chemistry. (b) Power absorption by various mechanisms.
(a)
(b)
Figure 4.5: Snapshots of distribution of (a) plasma properties and (b) rate of generation of species in several reaction channels in region A (Long Townsend like) of a helium DBD driven by a quasi-pulse power source (20 kHz).
(a)
(b)
Figure 4.6: Snapshots of distribution of (a) plasma properties and (b) rate of generation of species in several reaction channels in region B (Dark current like) of helium DBD driven by a quasi-pulse power source (20 kHz)
(a)
(b)
Figure 4.7: Snapshots of distribution of (a) plasma properties and (b) rate of generation of species in several reaction channels in region C (Primary short Townsend like) of a helium DBD driven by a quasi-pulse power source (20 kHz).
(a)
(b)
Figure 4.8: Snapshots of distribution of (a) plasma properties and (b) rate of generation of species in several reaction channels in region D (Secondary short Townsend like discharge) of a helium DBD driven by a quasi-pulse power source (20 kHz)
Figure 4.9: Time-average spatial power absorption by various mechanisms.
Figure 4.10: Spatial profiles of cycle-averaged discharge parameters
Figure 4.11: Spatial-average temporal power absorption by various mechanisms.
Figure 4.13: Phase diagram of electron number density distribution.
Figure 4.14: Phase diagram of He+2 number density distribution.
Figure 4.15: Phase diagram of electron temperature distribution.
Figure 5.1: Sketch of the PECVD chamber
Figure5.2:Thesketchofspecialtemporalmarchingscheme
(a)
(b)
(c)
(d)
Figure 5.3: Fluid modeling initial conditions which are obtained form Navier-Stock equations solver include: (a) Gas temperature (b) Background gas flow velocity (c) H2 density distribution and (d) SiH4 density distribution.
(a)
(b)
(c)
(d)
Figure 5.4: Plasma potential at difference phase of a RF cycle, where (a) φ = 0 (b) φ = 0.5π, φ = 1.5π and (d) φ = 2π.
Y (cm)
AveragedPotential(V)
0 0.5 1 1.5
-20 -10 0 10 20 30 40 50
Figure 5.5: Cycle averaged potential profile across the electrode gap at the center of the cham-ber.
(a)
(b)
(c)
(d)
Figure 5.6: Electron density at difference phase of a RF cycle, where (a) φ = 0 (b) φ = 0.5π, φ = 1.5π and (d) φ = 2π.
(a)
(b)
(c)
(d)
Figure 5.7: Electron temperature at difference phase of a RF cycle, where (a) φ = 0 (b) φ = 0.5π, φ = 1.5π and (d) φ = 2π.
(a)
(b)
(c)
(d)
Figure 5.8: Ion species distributions include positive ions (a) H2+ (b) SiH2+ (c) Si2H4+ and negative ion (d) SiH3−.
Y (cm) ChargeDensities(1015 m-3 )
0 0.5 1 1.5
0 0.5 1 1.5 2 2.5 3 3.5
Electron H2+ SiH2+ Si2H4+ SiH3
-Figure 5.9: Cycle averaged charged densities profile across the electrode gap at the center of the chamber.
(a)
(b)
(c)
Figure 5.10: Important radical species relate to s-Si deposition, include(a) H(b) SiH2 and (c) SiH3.
Y (cm) RadicalDensities(m-3 )
0 0.5 1 1.5
0 0.5 1 1.5 2 2.5 3
H ( x 10
19) SiH
2( x 10
16) SiH
3( x 10
18)
Figure 5.11: Cycle averaged radical densities profile across the electrode gap at the center of the chamber.
Figure 5.12: Comparison of deposition rate from numerical simulation and experiment data as well as SiH3flux to the subtract glass.
Table 3.1: Nitrogen plasma chemistry reaction channels.
No. Reaction Channel Threshold Energy (eV) Rate Coefficient
1 e + N2→ e + N2 0.00 cross section
Table4.1:Summaryofsimpleandcomplicatedheliumplasmachemistry. NoReactionTypeReactionChannelsComplicatedSimpleThresholdEnergy(eV) 00Momentumtransfere−+He→e−+HeBOLSIG+BOLSIG+0 01e-impactexcitation(2S)e−+He→e−+He∗ meta(3S1)BOLSIG+2.308×10−16T0.31 eexp(−2.297×105 Te)19.82 02e-impactexcitation(2S)e−+He→e−+He∗ meta(1S1)BOLSIG+20.61 03e-impactexcitation(23P)e−+He→e−+He∗∗(23P)BOLSIG+0 04e-impactexcitation(21P)e−+He→e−+He∗∗(21P)BOLSIG+0 05e-impactexcitation(3SPD)e−+He→e−+He∗∗(3SPD)BOLSIG+0 06e-impactexcitation(4SPD)e−+He→e−+He∗∗(4SPD)BOLSIG+0 07e-impactexcitation(5SPD)e−+He→e−+He∗∗(5SPD)BOLSIG+0 08e-impactionizatione−+He→2e−+He+BOLSIG+2.584×10−18T0.68 eexp(−2.854×105 Te)24.58 09e-impactionizatione−+He∗ meta→2e−+He+BOLSIG+4.611×10−16T0.6 eexp(−5.546×104 Te)4.78 10e-impactde-excitatione−+He∗ meta→e−+He2.9×10−151.099×10−17T0.31 e-19.8 11e-impactdissociatione−+He∗ 2→e−+2He3.8×10−151.268×10−18T0.71 eexp(−3.945×104 Te)-17.9 12e-ionrecombination2e−+He+→e−+He∗ meta6×10−32-4.78 13e-iondissociativerecombination2e−+He+ 2→e−+He∗ meta+He2.8×10−325.386×10−13T−0.5 e0 14e-iondissociativerecombinatione−+He+ 2+He→He∗ meta+2He3.5×10−390 15e-ionrecombination2e−+He+ 2→e−+He∗ 21.2×10−330 16e-ionrecombinatione−+He+ 2+He→He∗ 2+He1.5×10−390 17Hombeck-MolnarassociativeionizationHe∗∗+He→e−+He+ 21.5×10−170 18Metastable-metastableassociativeionizationHe∗ meta+He∗ meta→e−+He+ 22.03×10−15-18.2 19Metastable-metastableionizationHe∗ meta+He∗ meta→e−+He++He8.7×10−162.7×10−16-15.8 20ionconversionHe++2He→He+ 2+He6.5×10−442.584×10−18T0.68 eexp(1×1045 Te)0 21Metastable-inducedassociationHe∗ meta+2He→He∗ 2+He1.9×10−461.3×10−450 22Metastable-induceddissociativeionizationHe∗ meta+He∗ 2→e−+He++2He5×10−16-13.5 23Metastable-inducedionizationHe∗ meta+He∗ 2→e−+He+ 2+He2×10−15-15.9 24Dimer-induceddissociativeionizationHe∗ 2+He∗ 2→e−+He++3He3×10−16-11.3 25Dimer-inducedionizationHe∗ 2+He∗ 2→e−+He+ 2+2He1.2×10−15-13.7 26He-atominduceddissociationHe∗ 2+He→3He4.9×10−220
Table 5.1: Silane/Hydrogen plasma chemistry reaction channels.
No. Reaction Rate Coefficient Threshold Energy(eV)
01 SiH4+ e−→ SiH+2 + 2H + 2e− cross section 11.9
Reference
Balay, Satish, Gropp, William D., McInnes, Lois C., and Smith, Barry F. “PETSc home page.”, 2001. http://www.mcs.anl.gov/petsc.
Bartnikas, R., Radu, I., and Wertheimer, M.R. “Dielectric Electrode Surface Effects on Atmo-spheric Pressure Glow Discharges in Helium.” Plasma Science, IEEE Transactions on 35, 5:
(2007) 1437–1447. 10.1109/TPS.2007.902797.
Bhandarkar, U V, Swihart, M T, Girshick, S L, and Kortshagen, U R. “Modelling of silicon hydride clustering in a low-pressure silane plasma.” Journal of Physics D: Applied Physics 33, 21: (2000) 2731. http://stacks.iop.org/0022-3727/33/i=21/a=311.
Birdsall, CK, and Langdon. Plasma Physics via Computer Simulation (Series on Plasma Physics). Taylor & Francis, 1991. http://www.amazon.ca/exec/obidos/
redirect?tag=citeulike09-20&path=ASIN/0750301171.
Bleecker, K. De, Bogaerts, A., Goedheer, W., and Gijbels, R. “Investigation of growth mecha-nisms of clusters in a silane discharge with the use of a fluid model.” Plasma Science, IEEE Transactions on 32, 2: (2004a) 691–698. 10.1109/TPS.2004.826095.
Bleecker, Kathleen De, Bogaerts, Annemie, Gijbels, Renaat, and Goedheer, Wim. “Numerical investigation of particle formation mechanisms in silane discharges.” Physical Review E 69, 5: (2004b) 056,409. http://link.aps.org/doi/10.1103/PhysRevE.69.
056409.
Boltzmann, Ludwig. Sitzungsberichte der Akademie der Wissenschaften , Wien , II 66: (1872) 275.
Bukowski, J. D., Graves, D. B., and Vitello, P. “Two-dimensional fluid model of an induc-tively coupled plasma with comparison to experimental spatial profiles.” Journal of Ap-plied Physics 80, 5: (1996) 2614. http://link.aip.org/link/JAPIAU/v80/
i5/p2614/s1&Agg=doi.
Cai, Xiao-chuan, Casarin, Mario A., Elliott, Frank W., and Widlund, Olof B. “Overlap-ping Schwarz algorithms for solving Helmholtz’s equation.” In Contemporary Mathematics.
American Mathematical Society, 1998a, 391–399.
. “Overlapping Schwarz algorithms for solving Helmholtz’s equation.” In Contemporary Mathematics. American Mathematical Society, 1998b, 391–399.
Cai, Xiao-chuan, Gropp, William D., and Keyes, David E. “A comparison of some domain de-composition and ILU preconditioned iterative methods for nonsymmetric elliptic problems.”
In in Fifth International Symposium on Domain Decomposition Methods for Partial Differ-ential Equations. 1994, 477–504.
Chirokov, A, Khot, S N, Gangoli, S P, Fridman, A, Henderson, P, Gutsol, A F, and Dolgopol-sky, A. “Numerical and experimental investigation of the stability of radio-frequency (RF) discharges at atmospheric pressure.” Plasma Sources Science and Technology 18, 2: (2009) 025,025. http://iopscience.iop.org/0963-0252/18/2/025025.
Choi, Y.H., Kim, J.H., and Hwang, Y.S. “One-dimensional discharge simula-tion of nitrogen DBD atmospheric pressure plasma.” Thin Solid Films 506-507: (2006) 389–395. http://www.sciencedirect.com/science/article/
B6TW0-4H2PJDV-8/2/a9b909fa527abb5b848a2c447d2594fb.
van Dijk, Jan, Peerenboom, Kim, Jimenez, Manuel, Mihailova, Diana, and van der Mullen, Joost. “The plasma modelling toolkit Plasimo.” Journal of Physics D: Applied Physics 42, 19: (2009) 194,012. http://iopscience.iop.org/0022-3727/42/19/
194012.
FumiyoshiTochikubo, TakumaChiba, and TsuneoWatanabe. “Structure of Low-Frequency He-lium Glow Discharge at Atmospheric Pressure between Parallel Plate Dielectric Electrodes.”
Japanese Journal of Applied Physics 38: (1999) 5244–5250. http://jjap.ipap.jp/
link?JJAP/38/5244/.
Gallagher, Alan. “Model of particle growth in silane discharges.” Physical Review E 62, 2:
(2000) 2690. http://link.aps.org/doi/10.1103/PhysRevE.62.2690.
Gogolides, Evangelos, and Sawin, Herbert H. “Continuum modeling of radio-frequency glow discharges. I. Theory and results for electropositive and electronegative gases.” Journal of Applied Physics 72, 9: (1992) 3971–3987. http://link.aip.org/link/?JAP/72/
3971/1.
Golubovskii, Yu B, Maiorov, V A, Behnke, J, and Behnke, J F. “Modelling of the homogeneous barrier discharge in helium at atmospheric pressure.” Journal of Physics D: Applied Physics 36, 1: (2003) 39–49. http://iopscience.iop.org/0022-3727/36/1/306.
Grubert, G. K., Becker, M. M., and Loffhagen, D. “Why the local-mean-energy approximation should be used in hydrodynamic plasma descriptions instead of the local-field approxima-tion.” Physical Review E 80, 3: (2009) 036,405. http://link.aps.org/doi/10.
1103/PhysRevE.80.036405.
Hagelaar, Gerjan. “BOLSIG+ : user-friendly solver for electron
Boltz-mann equation.”, 2009. http://www.laplace.univ-tlse.fr/
groupes-de-recherche/groupe-de-recherche-energetique/
projets-en-cours/bolsig-resolution-de-l-equation-de/article/
bolsig-resolution-de-l-equation-de?lang=fr.
Hu, Meng-Hua. personal communication, 2010.
Hwang, Feng-Nan, and Cai, Xiao-Chuan. “A parallel nonlinear additive Schwarz precondi-tioned inexact Newton algorithm for incompressible Navier-Stokes equations.” J. Comput.
Phys. 204, 2: (2005) 666–691.
Jung, Mi-Hee, and Choi, Ho-Suk. “Surface treatment and characterization of ITO thin films using atmospheric pressure plasma for organic light emitting diodes.” Journal of Colloid and Interface Science 310, 2: (2007) 550–558.
http://www.sciencedirect.com/science/article/B6WHR-4N1T1S4-B/
2/8d37a2614096bbbaac14d98b8022b287.
Kanazawa, S, Kogoma, M, Moriwaki, T, and Okazaki, S. “Stable glow plasma at atmospheric pressure.” Journal of Physics D: Applied Physics 21, 5: (1988) 838. http://stacks.
iop.org/0022-3727/21/i=5/a=028.
Kim, HS, Kang, WS, Kim, GH, and Hong, SH. “Plasma Flow Characteristics in a Spray-Type Dielectric Barrier Discharge Reactor.” IEEE TRANSACTIONS ON PLASMA SCIENCE 37, 6: (2009) 773–784. http://apps.isiknowledge.com/full_record.
do?product=WOS&colname=WOS&search_mode=CitingArticles&qid=
49&SID=S1FfG8I@ee3dipihlE9&page=1&doc=5.
Kolobov, VI, and Arslanbekov, RR. “Simulation of electron kinetics in gas discharges.”
IEEE TRANSACTIONS ON PLASMA SCIENCE 34, 3: (2006) 895–909. http://
apps.isiknowledge.com/full_record.do?product=WOS&search_mode=
GeneralSearch&qid=3&SID=S1FfG8I@ee3dipihlE9&page=8&doc=71.
Kushner, Mark J. “Hybrid modelling of low temperature plasmas for fundamental investigations and equipment design.” Journal of Physics D: Applied Physics 42, 19: (2009) 194,013.
http://iopscience.iop.org/0022-3727/42/19/194013.
Lieberman, Michael A., and Lichtenberg, Allan J. Principles of Plasma Discharges and Mate-rials Processing. Wiley-Interscience, 1994, 1 edition.
Lin, Ming-Chang. personal communication, 2010.
Lymberopoulos, D.P., and Economou, D.J. “Two-dimensional simulation of polysilicon etching with chlorine in a high density plasma reactor.” Plasma Science, IEEE Transactions on 23, 4: (1995) 573–580. 10.1109/27.467977.
Mangolini, L, Anderson, C, Heberlein, J, and Kortshagen, U. “Effects of current limita-tion through the dielectric in atmospheric pressure glows in helium.” Journal of Physics D: Applied Physics 37, 7: (2004) 1021–1030. http://iopscience.iop.org/
0022-3727/37/7/012.
Martens, T., Bogaerts, A., Brok, W. J. M., and van der Mullen, J. J. A. M. “Modeling study on the influence of the pressure on a dielectric barrier discharge microplasma.” Journal of Analytical Atomic Spectrometry 22, 9: (2007a) 1033–1042. http://dx.doi.org/10.
1039/b704903j.
Martens, Tom, Bogaerts, Annemie, Brok, Wouter, and van Dijk, Jan. “Computer simulations of a dielectric barrier discharge used for analytical spectrometry.” Analytical and Bioan-alytical Chemistry 388, 8: (2007b) 1583–1594. http://dx.doi.org/10.1007/
s00216-007-1269-0.
Massines, Francoise, Rabehi, Ahmed, Decomps, Philippe, Gadri, Rami Ben, Segur, Pierre, and Mayoux, Christian. “Experimental and theoretical study of a glow discharge at atmospheric pressure controlled by dielectric barrier.” Journal of Applied Physics 83, 6: (1998) 2950.
http://link.aip.org/link/JAPIAU/v83/i6/p2950/s1&Agg=doi.
Messmer, Peter, and Bruhwiler, David L. “A parallel electrostatic solver for the VORPAL code.” Computer Physics Communications 164, 1-3: (2004) 118–121.
http://www.sciencedirect.com/science/article/B6TJ5-4CX71G2-3/
2/53b90ac363afd6f2d7ba3c3d7c58cd9d.
Meyyappan, M. Computational Modeling in Semiconductor Processing. Artech House Pub-lishers, 1994.
Nienhuis, G. J. Plasma models for silicon deposition. Ph.D. thesis, Utrecht University, Nieuwegein, The Netherlands, 1998.
Nienhuis, G. J., Goedheer, W. J., Hamers, E. A. G., van Sark, W. G. J. H. M., and Bezemer, J. “A self-consistent fluid model for radio-frequency discharges in SiH[sub 4]–H[sub 2] compared to experiments.” Journal of Applied Physics 82, 5: (1997) 2060. http://link.aip.
org/link/JAPIAU/v82/i5/p2060/s1&Agg=doi.
Nieter, Chet, and Cary, John R. “VORPAL: a versatile plasma simulation code.” Journal of Computational Physics 196, 2: (2004) 448–473. http:
//www.sciencedirect.com/science/article/B6WHY-4B954G3-1/2/
675d7d4de2f99f1448034cb90ce46f8e.
Park, Jaeyoung, Henins, I., Herrmann, H. W., Selwyn, G. S., and Hicks, R. F. “Discharge phenomena of an atmospheric pressure radio-frequency capacitive plasma source.” Journal of Applied Physics 89, 1: (2001) 20. http://link.aip.org/link/JAPIAU/v89/
i1/p20/s1&Agg=doi.
Phelps, Arthur V., and Brown, Sanborn C. “Positive Ions in the Afterglow of a Low Pressure Helium Discharge.” Physical Review 86, 1: (1952) 102. http://link.aps.org/doi/
10.1103/PhysRev.86.102.
Pitaevskii, L. P., and Lifshitz, E.M. Physical Kinetics: Volume 10. Butterworth-Heinemann, 1981.
Riley, M. E., Greenberg, K. E., Hebner, G. A., and Drallos, P. “Theoretical and experimental study of low-temperature, capacitively coupled, radio-frequency helium plasmas.” Journal of Applied Physics 75, 6: (1994) 2789. http://link.aip.org/link/JAPIAU/v75/
i6/p2789/s1&Agg=doi.
Saad, Youcef, and Schultz, Martin H. “GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems.” SIAM J. Sci. Stat. Comput. 7, 3: (1986) 856–869.
Salabas, A, Gousset, G, and Alves, L L. “Two-dimensional fluid modelling of charged particle transport in radio-frequency capacitively coupled discharges.” Plasma Sources Science and Technology 11, 4: (2002) 448–465. http://iopscience.iop.org/0963-0252/
11/4/312.
Schade, K., Stahr, F., Kuske, J., R¨ohlecke, S., Steinke, O., Stephan, U., and Dekkers, H.F.W.
“High temperature line electrode assembly for continuous substrate flow VHF PECVD.” Thin Solid Films 502, 1-2: (2006) 59–62. http://www.sciencedirect.com/science/
article/B6TW0-4HVDYJ1-2/2/7cf791c89774f442faf701bd5d8b1929.
Scharfetter, D.L., and Gummel, H.K. “Large-signal analysis of a silicon Read diode oscillator.”
Electron Devices, IEEE Transactions on 16, 1: (1969) 64–77.
Shang, Wanli, Wang, Dezhen, and Zhang, Yuantao. “Radio frequency atmospheric pressure glow discharge inααα and γγγ modes between two coaxial electrodes.” Physics of Plasmas 15, 9: (2008) 093,503. http://link.aip.org/link/PHPAEN/v15/i9/p093503/
s1&Agg=doi.
Vahedi, V, DiPeso, G, Birdsall, C K, Lieberman, M A, and Rognlien, T D. “Capacitive RF discharges modelled by particle-in-cell Monte Carlo simulation. I. Analysis of numerical
techniques.” Plasma Sources Science and Technology 2, 4: (1993) 261. http://stacks.
iop.org/0963-0252/2/i=4/a=006.
Ventzek, Peter L. G., Sommerer, Timothy J., Hoekstra, Robert J., and Kushner, Mark J.
“Twodimensional hybrid model of inductively coupled plasma sources for etching.” Applied Physics Letters 10.1063/1.109963.
van der Vorst, H. A. “Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems.” SIAM Journal on Scientific and Statistical Computing 13, 2: (1992) 631–644. http://link.aip.org/link/?SCE/13/631/
1.
Walsh, J. L., Shi, J. J., and Kong, M. G. “Contrasting characteristics of pulsed and sinu-soidal cold atmospheric plasma jets.” Applied Physics Letters 88: (2006) 1501. http:
//adsabs.harvard.edu/abs/2006ApPhL..88q1501W.
Wang, Qi, Sun, Jizhong, and Wang, Dezhen. “Numerical analysis of two homogeneous dis-charge modes at atmospheric pressure with a self-consistent model.” Physics of Plasmas 16, 4: (2009) 043,503. http://link.aip.org/link/PHPAEN/v16/i4/p043503/
s1&Agg=doi.
Wang, Qiang, Economou, Demetre J., and Donnelly, Vincent M. “Simulation of a direct current microplasma discharge in helium at atmospheric pressure.” Journal of Applied Physics 100, 2: (2006) 023,301. http://link.aip.org/link/JAPIAU/v100/i2/p023301/
s1&Agg=doi.
White, R D, Robson, R E, Schmidt, B, and Morrison, Michael A. “Is the classical two-term approximation of electron kinetic theory satisfactory for swarms and plasmas?” Journal of Physics D: Applied Physics 36, 24: (2003) 3125–3131. http://iopscience.iop.
org/0022-3727/36/24/006.
Yuan, Xiaohui, and Raja, Laxminarayan L. “Role of trace impurities in large-volume noble gas atmospheric-pressure glow discharges.” Applied Physics Letters 81, 5: (2002) 814.
http://link.aip.org/link/APPLAB/v81/i5/p814/s1&Agg=doi.
Yuan, Xiaohui, and Raja, L.L. “Computational study of capacitively coupled high-pressure glow discharges in helium.” Plasma Science, IEEE Transactions on 31, 4: (2003) 495–503.
10.1109/TPS.2003.815479.
List of Publications
Journals:(*corresponding author)
1. S. S. Liaw*, C. C. Yang, R. T. Liu, and J. T. Hong, “Turing model for the patterns of lady beetles”, Phys. Rev. E, 64, 041909, 2001.
2. K.-H. Hsu, P.-Y. Chen, C.-T. Hung, L.-H. Chen and J.-S. Wu*, “Development of a par-allel Poisson’s equation solver with adaptive mesh refinement and its application in field emission prediction,” Computer Physics Communications, Vol. 174, pp. 948-960, 2006.
3. P.-Y. Chen, K.-H. Hsu, Y.-L. Hsu, K.-W. Cheng, C.-T. Hung, J.-S. Wu* and J.-P. Yu,
“Modeling of the integrated magnetic focusing and gated field-emission device with sin-gle carbon nanotube,” Journal of Vacuum Science and Technology-B, Vol. 25, Issue 1, pp. 74-81, 2007. This article was selected for the Virtual Journal of Nanoscale Science
& Technology- January 15, 2007, Volume 15, Issue 2. http://www.vjnano.org
4. J.-S. Wu*, K.-H. Hsu, F.-L. Li, C.-T. Hung and S.-Y. Jou, “Development of a parallelized 3D electrostatic PIC-FEM code and its applications,” Computer Physics Communica-tions, Vol. 177, pp. 98-101, 2007. (SCI)
5. C.-T. Hung, M.-H. Hu, J.-S. Wu* and F.-N. Hwang, “A New Paradigm for Solving Plasma Fluid Modeling Equations,” Computer Physics Communications, Vol. 177, pp. 138-139, 2007. (SCI)
6. A. Aliat, C.-T. Hung, C.-J. Tsai and J.-S. Wu*, “Effect of Free Electrons on Nanoparti-cle Charging in a Wire-Tube Negative Corona Discharge”, Applied Physics Letter, 93, 154103, 2008. This article was selected for the Virtual Journal of Nanoscale Science
& Technology- October 27, 2008, Volume 18, Issue 17. http://www.vjnano.org
7. A. Aliat, C.-T. Hung, C.-J. Tsai and J.-S. Wu*, “Modelling Nanoparticle Charging in the Positive and Negative Direct Current Air Corona Chargers,” Journal of Physics D:
Applied Physics, Vol. 42 (2009), 125206 (10 pp).
8. C.-T. Hung, Y.-M. Chiu, F.-N. Hwang, J.-S. Wu*, “Development of a Parallel Implicit Solver of Fluid Modeling Equations for Gas Discharges,” Computer Physics Commu-nications(accepted on June 2, 2010).
9. Y.-M. Chiu, C.-T. Hung, F.-N. Hwang, M.-H. Chiang, J.-S. Wu*, S.-H. Chen, “Effect of Plasma Chemistry on the Simulation of Helium Atmospheric-Pressure Plasmas,” Com-puter Physics Communications(accepted in June 2010).
10. K.-W. Cheng, C.-T. Hung, M.-H. Chiang, F.-N. Hwang, J.-S. Wu∗, “One-dimensional Simulation of Nitrogen Dielectric Barrier Discharge Driven by a Quasi-Pulsed Power Source and Its Comparison with Experiments,” Computer Physics Communications (accepted in June 2010).
11. Matthew R. Smith*, Chieh-Tsan Hung, Kun-Mo Lin, J.-S. Wu and Jen-Perng Yu, “De-velopment of a semi-implicit fluid modeling code using finite-volume method based on Cartesian grids,” Computer Physics Communications (accepted in June 2010).
12. M.R. Smith, K.-M. Lin, C.-T. Hung, Y.-S. Chen and J.-S. Wu*, “Development of an Improved Spatial Reconstruction Technique for the HLL Method and Its Applications,”
Journal of Computational Physics(under 2nd review; resubmitted on July 5, submitted on February 27, 2010).
13. C.-T. Hung, Y.-M. Chiu, M.-H. Chiang, J.-S. Wu∗, F.-N. Hwang, Y.-C. Wang and Shiaw-Huei Chen, “Investigation of Helium Dielectric Barrier Discharge Driven by a Realistic Distorted-Sinusoidal Voltage Power Source,” Plasma Chemistry and Plasma Process-ing(submitted on April 27, 2010).
14. S.-Y. Jou, C.-T. Hung, Y.-M. Chiu, J.-S. Wu∗, B.-Y. Wei, “Enhancement of VUV Emis-sion from a Coaxial Xenon Excimer Ultraviolet Lamp Driven by Distorted Bipolar Square Voltages,” Plasma Sources Science and Technology (submitted on May 13, 2010).
Invited Conference Papers:
1. C.-T. Hung, M.-H. Hu and J.-S. Wu*, “Fluid Modeling of a Plasma Backlight Source for
LCD Panel,” 4th International Conference on Quantum Enginerring, Tainan, TAI-WAN, July 8, 2006. (invited paper & poster)
2. J.-S. Wu*, K.-H. Hsu, F.-L. Li, C.-T. Hung and S.-Y. Jou, “Development of a Parallelized 3D PIC-FEM Code and Its Applications,” Conference on Computational Physics, Geongju, KOREA, August 28-September 1, 2006. (invited speech) (http://ccp2006.postech.edu/), 3. C.-T. Hung, M. H. Hu, Y. M. Chiu, K. M. Lin, Y. C. Wang, J. S. Wu*, and F. N. Hwang,
“Non-Thermal Plasma Simulation Using Parallel 2D Fluid Modeling Code,” Workshop on High Performance Simulation of Physical Systems, HPSPS’09, March 2-5 (2009), Kaohsiung, Taiwan. (invited speech)
International Conference Papers (include those which are invited papers in previous section):(*corresponding author)
1. J.-S. Wu*, K.-H. Hsu and C.-T. Hung, “On the Performance Improvement of a Pallelized 3-D PIC-FEM Code,” ICOPS-2006, Traverse City, Michigan, USA, June 4-8, 2006.
2. C.-T. Hung, M.-H. Hu and J.-S. Wu*, “Fluid modeling of a plasma backlight source for LCD panel,” 4thInternational Conference on Quantum Engineering Science, pp.
53-56, Tainan, TAIWAN, July 8, 2006. (invited paper & poster)
3. J.-S. Wu*, K.-H. Hsu, F.-L. Li and C.-T. Hung, “Development of a Parallelized 3D PIC-FEM Code and Its Applications,” Conference on Computational Physics, Geongju, KOREA, August 28-September 1, 2006 (invited speech).
4. C.-T. Hung, M.-H. Hu, J.-S. Wu* and F.-N. Hwang, “A New Paradigm for Solving Plasma Fluid Modeling Equations,” Conference on Computational Physics, Geongju, KOREA, August 28-September 1, 2006.
5. K.-H. Hsu, C.-T. Hung, F.-L. Li and J.-S. Wu*, “Development of a Parallelized 3D PIC-FEM Code and Its Applications,” 25th International Symposium on Rarefied Gas Dy-namics, St. Petersburg, RUSSIA, July 21-28, 2006.