Towards an integrated modeling of the plasma-solid interface
Michael Bonitz1(), Alexey Filinov1,2,3, Jan-Willem Abraham1, Karsten Balzer4, Hanno Kählert1, Eckhard Pehlke1, Franz X. Bronold5, Matthias Pamperin5, Markus Becker2, Dettlef Loffhagen2, Holger Fehske5
1. Institute for Theoretical Physics and Astrophysics, Kiel University, 24098 Kiel, Germany 2. Leibniz Institute for Plasma Research (INP), D-17489 Greifswald, Germany 3. Joint Institute for High Temperatures RAS, 125412 Moscow, Russia 4. Computing Center of Kiel University, D-24118 Kiel, Germany 5. Institute of Physics, Greifswald University, D-17489 Greifswald, Germany
Solids facing a plasma are a common situation in many astrophysical systems and laboratory setups. Moreover, many plasma technology applications rely on the control of the plasma-surface interaction, i.e., of the particle, momentum and energy fluxes across the plasma-solid interface. However, presently often a fundamental understanding of them is missing, so most technological applications are being developed via trial and error. The reason is that the physical processes at the interface of a low-temperature plasma and a solid are extremely complex, involving a large number of elementary processes in the plasma, in the solid as well as fluxes across the interface. An accurate theoretical treatment of these processes is very difficult due to the vastly different system properties on both sides of the interface: Quantum versus classical behavior of electrons in the solid and plasma, respectively; as well as the dramatically differing electron densities, length and time scales. Moreover, often the system is far from equilibrium. In the majority of plasma simulations surface processes are either neglected or treated via phenomenological parameters such as sticking coefficients, sputter rates or secondary electron emission coefficients. However, those parameters are known only in some cases and with very limited accuracy. Similarly, while surface physics simulations have often studied the impact of single ions or neutrals, so far, the influence of a plasma medium and correlations between successive impacts have not been taken into account. Such an approach, necessarily neglects the mutual influences between plasma and solid surface and cannot have predictive power.
In this paper we discuss in some detail the physical processes of the plasma-solid interface which brings us to the necessity of coupled plasma-solid simulations. We briefly summarize relevant theoretical methods from solid state and surface physics that are suitable to contribute to such an approach and identify four methods. The first are mesoscopic simulations such as kinetic Monte Carlo and molecular dynamics that are able to treat complex processes on large scales but neglect electronic effects. The second are quantum kinetic methods based on the quantum Boltzmann equation that give access to a more accurate treatment of surface processes using simplifying models for the solid. The third approach are ab initio simulations of surface process that are based on density functional theory (DFT) and time-dependent DFT. The fourths are nonequilibrium Green functions that able to treat correlation effects in the material and at the interface. The price for the increased quality is a dramatic increase of computational effort and a restriction to short time and length scales. We conclude that, presently, none of the four methods is capable of providing a complete picture of the processes at the interface. Instead, each of them provides complementary information, and we discuss possible combinations.
. [J]. Frontiers of Chemical Science and Engineering, 2019, 13(2): 201-237.
Michael Bonitz, Alexey Filinov, Jan-Willem Abraham, Karsten Balzer, Hanno Kählert, Eckhard Pehlke, Franz X. Bronold, Matthias Pamperin, Markus Becker, Dettlef Loffhagen, Holger Fehske. Towards an integrated modeling of the plasma-solid interface. Front. Chem. Sci. Eng., 2019, 13(2): 201-237.
K Ostrikov, E C Neyts, M Meyyappan. Plasma nanoscience: From nano-solids in plasmas to nano-plasmas in solids. Advances in Physics, 2013, 62(2): 113–224 https://doi.org/10.1080/00018732.2013.808047
D Prezzi, D Varsano, A Ruini, A Marini, E Molinari. Optical properties of graphene nanoribbons: The role of many-body effects. Physical Review. B, 2008, 77(4): 041404 https://doi.org/10.1103/PhysRevB.77.041404
6
I Adamovich, S D Baalrud, A Bogaerts, P J Bruggeman, M Cappelli, V Colombo, U Czarnetzki, U Ebert, J G Eden, P Favia, et al.. The 2017 plasma roadmap: Low temperature plasma science and technology. Journal of Physics. D, Applied Physics, 2017, 50(32): 323001 https://doi.org/10.1088/1361-6463/aa76f5
7
G J M Hagelaar, L C Pitchford. Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models. Plasma Sources Science & Technology, 2005, 14(4): 722–733 https://doi.org/10.1088/0963-0252/14/4/011
8
Z Donko, N Dyatko. First-principles particle simulation and Boltzmann equation analysis of negative differential conductivity and transient negative mobility effects in xenon. European Physical Journal D, 2016, 70(6): 135 https://doi.org/10.1140/epjd/e2016-60726-4
9
J Teunissen, U Ebert. 3D pic-mcc simulations of discharge inception around a sharp anode in nitrogen/oxygen mixtures. Plasma Sources Science & Technology, 2016, 25(4): 044005 https://doi.org/10.1088/0963-0252/25/4/044005
10
M M Becker, H Kählert, A Sun, M Bonitz, D Loffhagen. Advanced fluid modeling and PIC/MCC simulations of low-pressure ccrf discharges. Plasma Sources Science & Technology, 2017, 26(4): 044001 https://doi.org/10.1088/1361-6595/aa5cce
11
A Derzsi, I Korolov, E Schüngel, Z Donkó, J Schulze. Effects of fast atoms and energy-dependent secondary electron emission yields in PIC/MCC simulations of capacitively coupled plasmas. Plasma Sources Science & Technology, 2015, 24(3): 034002 https://doi.org/10.1088/0963-0252/24/3/034002
12
A V Phelps, Z L Petrović. Cold-cathode discharges and breakdown in argon: Surface and gas phase production of secondary electrons. Plasma Sources Science & Technology, 1999, 8(3): R21–R44 https://doi.org/10.1088/0963-0252/8/3/201
13
P Brault. Multiscale molecular dynamics simulation of plasma processing: Application to plasma sputtering. Frontiers in Physics, 2018, 6: 59 https://doi.org/10.3389/fphy.2018.00059
14
S Zhao, W Kang, J Xue, X Zhang, P Zhang. Comparison of electronic energy loss in graphene and BN sheet by means of time-dependent density functional theory. Journal of Physics Condensed Matter, 2015, 27(2): 025401 https://doi.org/10.1088/0953-8984/27/2/025401
15
K Balzer, N Schlünzen, M Bonitz. Stopping dynamics of ions passing through correlated honeycomb clusters. Physical Review. B, 2016, 94(24): 245118 https://doi.org/10.1103/PhysRevB.94.245118
16
D B Graves, P Brault. Molecular dynamics for low temperature plasma—surface interaction studies. Journal of Physics. D, Applied Physics, 2009, 42(19): 194011 https://doi.org/10.1088/0022-3727/42/19/194011
17
E C Neyts, P Brault. Molecular dynamics simulations for plasma-surface interactions. Plasma Processes and Polymers, 2017, 14(12): 1600145 https://doi.org/10.1002/ppap.201600145
18
J P Sheehan, N Hershkowitz, I D Kaganovich, H Wang, Y Raitses, E V Barnat, B R Weatherford, D Sydorenko. Kinetic theory of plasma sheaths surrounding electron-emitting surfaces. Physical Review Letters, 2013, 111(7): 075002 https://doi.org/10.1103/PhysRevLett.111.075002
A Sun, M M Becker, D Loffhagen. PIC/MCC simulation of capacitively coupled discharges in helium: Boundary effects. Plasma Sources Science & Technology, 2018, 27(5): 054002 https://doi.org/10.1088/1361-6595/aac30a
21
Y Li, D B Go. Using field emission to control the electron energy distribution in high-pressure microdischarges at microscale dimensions. Applied Physics Letters, 2013, 103(23): 234104 https://doi.org/10.1063/1.4841495
22
H Helmholtz. Ueber einige Gesetze der Vertheilung elektrischer Ströme in körperlichen Leitern mit Anwendung auf die thierischelektrischen Versuche. Annalen der Physik, 1853, 165(6): 211–233 (in German) https://doi.org/10.1002/andp.18531650603
23
R L Heinisch, F X Bronold, H Fehske. Electron surface layer at the interface of a plasma and a dielectric wall. Physical Review. B, 2012, 85(7): 075323 https://doi.org/10.1103/PhysRevB.85.075323
24
G Onida, L Reining, A Rubio. Electronic excitations: Density-functional versus many-body green’s-function approaches. Reviews of Modern Physics, 2002, 74(2): 601–659 https://doi.org/10.1103/RevModPhys.74.601
25
G Kotliar, S Y Savrasov, K Haule, V S Oudovenko, O Parcollet, C A Marianetti. Electronic structure calculations with dynamical mean-field theory. Reviews of Modern Physics, 2006, 78(3): 865–951 https://doi.org/10.1103/RevModPhys.78.865
26
W M C Foulkes, L Mitas, R J Needs, G Rajagopal. Quantum monte carlo simulations of solids. Reviews of Modern Physics, 2001, 73(1): 33–83 https://doi.org/10.1103/RevModPhys.73.33
J W Abraham. Formation of metal-polymer nanocomposites by plasma-based deposition methods: Kinetic monte carlo and molecular dynamics simulations. Dissertation for the Doctoral Degree. Kiel: Christian-Albrechts-Universität zu Kiel, 2018
29
M Daniil, T Carlos, G Vasco. Deterministic and monte carlo methods for simulation of plasma-surface interactions. Plasma Processes and Polymers, 2016, 14(1-2): 1600175
30
V Guerra, J Loureiro. Dynamical monte carlo simulation of surface atomic recombination. Plasma Sources Science & Technology, 2004, 13(1): 85–94 https://doi.org/10.1088/0963-0252/13/1/011
31
J W Abraham, N Kongsuwan, T Strunskus, F Faupel, M Bonitz. Simulation of nanocolumn formation in a plasma environment. Journal of Applied Physics, 2015, 117(1): 014305 https://doi.org/10.1063/1.4905255
32
K Fujioka. Kinetic Monte Carlo simulations of cluster growth in magnetron plasmas. Dissertation for the Doctoral Degree. Kiel: Christian-Albrechts-Universität zu Kiel, 2015
33
O Polonskyi, A M Ahadi, T Peter, K Fujioka, J W Abraham, E Vasiliauskaite, A Hinz, T Strunskus, S Wolf, M Bonitz,et al.Plasma based formation and deposition of metal and metal oxide nanoparticles using a gas aggregation source. European Physical Journal D, 2018, 72(5): 93 https://doi.org/10.1140/epjd/e2017-80419-8
34
L Rosenthal. Monte Carlo simulations of metal-polymer nanocomposite formation. Dissertation for the Doctoral Degree. Kiel: Christian-Albrechts-Universität zu Kiel, 2013
K Balzer, M Bonitz. Nonequilibrium Green’s Functions Approach to Inhomogeneous Systems. Berlin: Springer, 2013
37
N Schlünzen, M Bonitz. Nonequilibrium Green functions approach to strongly correlated fermions in lattice systems. Contributions to Plasma Physics, 2016, 56(1): 5–91 https://doi.org/10.1002/ctpp.201610003
38
A Marini, C Hogan, M Grüning, D Varsano. Yambo: An ab initio tool for excited state calculations. Computer Physics Communications, 2009, 180(8): 1392–1403 https://doi.org/10.1016/j.cpc.2009.02.003
J W Abraham, T Strunskus, F Faupel, M Bonitz. Molecular dynamics simulation of gold cluster growth during sputter deposition. Journal of Applied Physics, 2016, 119(18): 185301 https://doi.org/10.1063/1.4948375
44
A Nakano, R K Kalia, K Nomura, A Sharma, P Vashishta, F Shimojo, A C T van Duin, W A Goddard, R Biswas, D Srivastava, et al.. De novo ultrascale atomistic simulations on high-end parallel supercomputers. International Journal of High Performance Computing Applications, 2008, 22(1): 113–128 https://doi.org/10.1177/1094342007085015
45
S Piana, K Lindorff-Larsen, D E Shaw. Atomic-level description of ubiquitin folding. Proceedings of the National Academy of Sciences of the United States of America, 2013, 110(15): 5915–5920 https://doi.org/10.1073/pnas.1218321110
A Laio, M Parrinello. Escaping free-energy minima. Proceedings of the National Academy of Sciences of the United States of America, 2002, 99(20): 12562–12566 https://doi.org/10.1073/pnas.202427399
48
M R Sørensen, A F Voter. Temperature-accelerated dynamics for simulation of infrequent events. Journal of Chemical Physics, 2000, 112(21): 9599–9606 https://doi.org/10.1063/1.481576
49
K M Bal, E C Neyts. Merging metadynamics into hyperdynamics: Accelerated molecular simulations reaching time scales from microseconds to seconds. Journal of Chemical Theory and Computation, 2015, 11(10): 4545–4554 https://doi.org/10.1021/acs.jctc.5b00597
50
M Bonitz, A Filinov, J W Abraham, D Loffhagen. Extending first principle plasma-surface simulations to experimentally relevant scales. Plasma Sources Science & Technology, 2018, 27(6): 064005 https://doi.org/10.1088/1361-6595/aaca75
51
J W Abraham, M Bonitz. Molecular dynamics simulation of Ag–Cu cluster growth on a thin polymer film. Contributions to Plasma Physics, 2018, 58(2-3): 164–173 https://doi.org/10.1002/ctpp.201700151
52
A Franke, E Pehlke. Diffusion of 1,4-butanedithiol on Au(100)(1x1): A DFT-based master-equation approach. Physical Review. B, 2010, 82(20): 205423 https://doi.org/10.1103/PhysRevB.82.205423
53
A Filinov, M Bonitz, D Loffhagen. Microscopic modeling of gas-surface scattering. I. A combined molecular dynamics-rate equation approach. Plasma Sources Science & Technology, 2018, 27(6): 064003 https://doi.org/10.1088/1361-6595/aac61e
54
M Schwartzkopf, G Santoro, C J Brett, A Rothkirch, O Polonskyi, A Hinz, E Metwalli, Y Yao, T Strunskus, F Faupel, et al. Real-time monitoring of morphology and optical properties during sputter deposition for tailoring metal-polymer interfaces. ACS Applied Materials & Interfaces, 2015, 7(24): 13547–13556 https://doi.org/10.1021/acsami.5b02901
55
J W Abraham, A Hinz, T Strunskus, F Faupel, M Bonitz. Formation of polymer-based nanoparticles and nanocomposites by plasma-assisted deposition methods. European Physical Journal D, 2018, 72(5): 92 https://doi.org/10.1140/epjd/e2017-80426-9
56
M Bonitz. Quantum Kinetic Theory. 2nd ed. Berlin: Springer, 2016
57
A Filinov, M Bonitz, D Loffhagen. Microscopic modeling of gas-surface scattering: II. Application to argon atom adsorption on a platinum (111) surface. Plasma Sources Science & Technology, 2018, 27(6): 064002 https://doi.org/10.1088/1361-6595/aac620
58
M A Lieberman, A J Lichtenberg. Principles of Plasma Discharges and Materials Processing. New York: Wiley-Interscience, 2005
59
J W Rabalais. Low Energy Ion-surface Interaction. New York: Wiley and Sons, 1994
H P Winter, J Burgdörfer. Slow Heavy-particle Induced Electron Emission from Solid Surfaces. Berlin: Springer, 2007
62
M Daksha, B Berger, E Schuengel, I Korolov, A Derzsi, M Koepke, Z Donko, J Schulze. A computationally assisted spectroscopic technique to measure secondary electron emission coefficients in radio frequency plasmas. Journal of Physics. D, Applied Physics, 2016, 49(23): 234001 https://doi.org/10.1088/0022-3727/49/23/234001
63
A Marcak, C Corbella, T de los Arcos, A von Keudell. Note: Ion-induced secondary electron emission from oxidized metal surfaces measured in a particle beam reactor. Review of Scientific Instruments, 2015, 86(10): 106102 https://doi.org/10.1063/1.4932309
64
W More, J Merino, R Monreal, P Pou, F Flores. Role of energy-level shifts on auger neutralization processes: A calculation beyond the image potential. Physical Review. B, 1998, 58(11): 7385–7390 https://doi.org/10.1103/PhysRevB.58.7385
65
D M Newns, K Makoshi, R Brako, J N M van Wunnik. Charge transfer in inelastic ion and atom-surface collisions. Physica Scripta, 1983, T6: 5–14 https://doi.org/10.1088/0031-8949/1983/T6/001
M Pamperin, F X Bronold, H Fehske. Ion-induced secondary electron emission from metal surfaces. Plasma Sources Science & Technology, 2018, 27(8): 084003 https://doi.org/10.1088/1361-6595/aad4db
69
N P Wang, E A García, R Monreal, F Flores, E C Goldberg, H H Brongersma, P Bauer. Low-energy ion neutralization at surfaces: Resonant and auger processes. Physical Review A., 2001, 64(1): 012901 https://doi.org/10.1103/PhysRevA.64.012901
70
D Valdés, E C Goldberg, J M Blanco, R C Monreal. Linear combination of atomic orbitals calculation of the auger neutralization rate of He+ on Al(111), (100), and (110) surfaces. Physical Review. B, 2005, 71(24): 245417 https://doi.org/10.1103/PhysRevB.71.245417
71
J Marbach, F X Bronold, H Fehske. Resonant charge transfer at dielectric surfaces. European Physical Journal D, 2012, 66(4): 106 https://doi.org/10.1140/epjd/e2012-30014-8
72
J Marbach, F X Bronold, H Fehske. Pseudoparticle approach for charge-transferring molecule-surface collisions. Physical Review. B, 2012, 86(11): 115417 https://doi.org/10.1103/PhysRevB.86.115417
73
A Iglesias-García, E A García, E C Goldberg. Role of He excited configurations in the neutralization of He+ ions colliding with a HOPG surface. Physical Review. B, 2013, 87(7): 075434 https://doi.org/10.1103/PhysRevB.87.075434
74
A Iglesias-García, E A García, E C Goldberg. Importance of considering helium excited states in He+ scattering by aluminum surfaces. Physical Review. B, 2014, 90(19): 195416 https://doi.org/10.1103/PhysRevB.90.195416
75
M Pamperin, F X Bronold, H Fehske. Many-body theory of the neutralization of strontium ions on gold surfaces. Physical Review. B, 2015, 91(3): 035440 https://doi.org/10.1103/PhysRevB.91.035440
F M Propst. Energy distribution of electrons ejected from tungsten by He+. Physical Review, 1963, 129(1): 7–11 https://doi.org/10.1103/PhysRev.129.7
80
D R Penn, P Apell. Theory of spin-polarized metastable-atomdeexcitation spectroscopy: Ni–He. Physical Review. B, 1990, 41(6): 3303–3315 https://doi.org/10.1103/PhysRevB.41.3303
81
D C Langreth, P Nordlander. Derivation of a master equation for charge-transfer processes in atom-surface collisions. Physical Review. B, 1991, 43(4): 2541–2557 https://doi.org/10.1103/PhysRevB.43.2541
82
H Shao, D C Langreth, P Nordlander. Many-body theory for charge transfer in atom-surface collisions. Physical Review. B, 1994, 49(19): 13929–13947 https://doi.org/10.1103/PhysRevB.49.13929
83
H Shao, D C Langreth, P Nordlander. Theoretical description of charge transfer in atom-surface collisions. In Rabalais J W, ed. Low Energy Ion-surface Interaction. New York: Wiley and Sons, 1994, 117
84
D Marx, J Hutter. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods. Cambridge: Cambridge University Press, 2009
85
J Hafner. Ab-initio simulations of materials using VASP: Density-functional theory and beyond. Journal of Computational Chemistry, 2008, 29(13): 2044–2078 https://doi.org/10.1002/jcc.21057
T D Kühne. Second generation car–parrinello molecular dynamics. Wiley Interdisciplinary Reviews. Computational Molecular Science, 2014, 4(4): 391–406 https://doi.org/10.1002/wcms.1176
88
M Baer. Beyond Born-Oppenheimer: Electronic Nonadiabatic Coupling Terms and Conical Intersections. New-York: Wiley-Interscience, 2006
89
S Nosé. A unified formulation of the constant temperature molecular dynamics methods. Journal of Chemical Physics, 1984, 81(1): 511–519 https://doi.org/10.1063/1.447334
90
G Henkelman, H Jónsson. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. Journal of Chemical Physics, 2000, 113(22): 9978–9985 https://doi.org/10.1063/1.1323224
91
G Henkelman, B P Uberuaga, H Jónsson. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. Journal of Chemical Physics, 2000, 113(22): 9901–9904 https://doi.org/10.1063/1.1329672
92
G H Vineyard. Frequency factors and isotope effects in solid state rate processes. Journal of Physics and Chemistry of Solids, 1957, 3(1): 121–127 https://doi.org/10.1016/0022-3697(57)90059-8
93
A Laio, F L Gervasio. Metadynamics: A method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science. Reports on Progress in Physics, 2008, 71(12): 126601 https://doi.org/10.1088/0034-4885/71/12/126601
94
R M Martin. Electronic Structure: Basic Theory and Practical Methods. Cambridge: Cambridge University Press, 2004
95
K Burke. Perspective on density functional theory. Journal of Chemical Physics, 2012, 136(15): 150901 https://doi.org/10.1063/1.4704546
96
A D Becke. Perspective: Fifty years of density-functional theory in chemical physics. The Journal of Chemical Physics, 2014, 140(18): 18A301
97
H S Yu, S L Li, D G Truhlar. Perspective: Kohn-Sham density-functional theory descending a staircase. Journal of Chemical Physics, 2016, 145(13): 130901 https://doi.org/10.1063/1.4963168
W Kohn, L J Sham. Self-consistent equations including exchange and correlation effects. Physical Review, 1965, 140(4A): A1133–A1138 https://doi.org/10.1103/PhysRev.140.A1133
100
J Klimes, A Michaelides. Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory. Journal of Chemical Physics, 2012, 137(12): 120901 https://doi.org/10.1063/1.4754130
101
J P Perdew, J A Chevary, S H Vosko, K A Jackson, M R Pederson, D J Singh, C Fiolhais. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Physical Review. B, 1992, 46(11): 6671–6687 https://doi.org/10.1103/PhysRevB.46.6671
102
J P Perdew, K Burke, M Ernzerhof. Generalized gradient approximation made simple. Physical Review Letters, 1996, 77(18): 3865–3868 https://doi.org/10.1103/PhysRevLett.77.3865
103
J Tao, J P Perdew, V N Staroverov, G E Scuseria. Climbing the density functional ladder: Nonempirical meta–generalized gradient approximation designed for molecules and solids. Physical Review Letters, 2003, 91(14): 146401 https://doi.org/10.1103/PhysRevLett.91.146401
104
G Kresse, J Furthmüller. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science, 1996, 6(1): 15–50 https://doi.org/10.1016/0927-0256(96)00008-0
G Kresse, J Hafner. Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium. Physical Review. B, 1994, 49(20): 14251–14269 https://doi.org/10.1103/PhysRevB.49.14251
107
G Kresse, J Furthmüller. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review. B, 1996, 54(16): 11169–11186 https://doi.org/10.1103/PhysRevB.54.11169
108
P Giannozzi, S Baroni, N Bonini, M Calandra, R Car, C Cavazzoni, D Ceresoli, G L Chiarotti, M Cococcioni, I Dabo, et al.. Quantum espresso: A modular and open-source software project for quantum simulations of materials. Journal of Physics Condensed Matter, 2009, 21(39): 395502 https://doi.org/10.1088/0953-8984/21/39/395502
109
P Giannozzi, O Andreussi, T Brumme, O Bunau, M B Nardelli, M Calandra, R Car, C Cavazzoni, D Ceresoli, M Cococcioni, et al.. Advanced capabilities for materials modelling with quantum espresso. Journal of Physics Condensed Matter, 2017, 29(46): 465901 https://doi.org/10.1088/1361-648X/aa8f79
110
A E Mattsson, P A Schultz, M P Desjarlais, T R Mattsson, K Leung. Designing meaningful density functional theory calculations in material science—a primer. Modelling and Simulation in Materials Science and Engineering, 2005, 13(1): R1–R31 https://doi.org/10.1088/0965-0393/13/1/R01
N Trouiller, J L Martins. Efficient pseudopotentials for plane-wave calculations. Physical Review. B, 1991, 43(3): 1993–2006 https://doi.org/10.1103/PhysRevB.43.1993
113
M Fuchs, M Scheffler. Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory. Computer Physics Communications, 1999, 119(1): 67–98 https://doi.org/10.1016/S0010-4655(98)00201-X
114
D Vanderbilt. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Physical Review. B, 1990, 41(11): 7892–7895 https://doi.org/10.1103/PhysRevB.41.7892
G Kresse, D Joubert. From ultrasoft pseudopotentials to the projector augmented-wave method. Physical Review. B, 1999, 59(3): 1758–1775 https://doi.org/10.1103/PhysRevB.59.1758
R Brako, D M Newns. Theory of electronic processes in atom scattering from surfaces. Reports on Progress in Physics, 1989, 52(6): 655–697 https://doi.org/10.1088/0034-4885/52/6/001
119
G A Kimmel, B H Cooper. Dynamics of resonant charge transfer in low-energy alkali-metal-ion scattering. Physical Review. B, 1993, 48(16): 12164–12177 https://doi.org/10.1103/PhysRevB.48.12164
C P Race, D R Mason, M W Finnis, W M C Foulkes, A P Horsfield, A P Sutton. The treatment of electronic excitations in atomistic models of radiation damage in metals. Reports on Progress in Physics, 2010, 73(11): 116501 https://doi.org/10.1088/0034-4885/73/11/116501
122
A Wucher, A Duvenbeck. Kinetic excitation of metallic solids: Progress towards a microscopic model. Nuclear Instruments & Methods in Physics Research. Section B, Beam Interactions with Materials and Atoms, 2011, 269(14): 1655–1660 https://doi.org/10.1016/j.nimb.2010.11.012
123
M Lindenblatt, E Pehlke, A Duvenbeck, B Rethfeld, A Wucher. Kinetic excitation of solids: The concept of electronic friction. Nuclear Instruments & Methods in Physics Research. Section B, Beam Interactions with Materials and Atoms, 2006, 246(2): 333–339 https://doi.org/10.1016/j.nimb.2006.01.006
D Diesing, E Hasselbrink. Chemical energy dissipation at surfaces under uhv and high pressure conditions studied using metal-insulator-metal and similar devices. Chemical Society Reviews, 2016, 45(13): 3747–3755 https://doi.org/10.1039/C5CS00932D
126
O Bünermann, H Jiang, Y Dorenkamp, A Kandratsenka, S M Janke, D J Auerbach, A M Wodtke. Electron-hole pair excitation determines the mechanism of hydrogen atom adsorption. Science, 2015, 350(6266): 1346–1349 https://doi.org/10.1126/science.aad4972
127
A M Wodtke. Electronically non-adiabatic influences in surface chemistry and dynamics. Chemical Society Reviews, 2016, 45(13): 3641–3657 https://doi.org/10.1039/C6CS00078A
128
S P Rittmeyer, J Meyer, J I Juaristi, K Reuter. Electronic friction-based vibrational lifetimes of molecular adsorbates: Beyond the independent-atom approximation. Physical Review Letters, 2015, 115(4): 046102 https://doi.org/10.1103/PhysRevLett.115.046102
129
S P Rittmeyer, V J Bukas, K Reuter. Energy dissipation at metal surfaces. Advances in Physics: X, 2018, 3(1): 1381574
130
M Alducin, R D Muiño, J I Juaristi. Non-adiabatic effects in elementary reaction processes at metal surfaces. Progress in Surface Science, 2017, 92(4): 317–340 https://doi.org/10.1016/j.progsurf.2017.09.002
131
S M Janke, D J Auerbach, A M Wodtke, A Kandratsenka. An accurate full-dimensional potential energy surface for H-Au(111): Importance of nonadiabatic electronic excitation in energy transfer and adsorption. Journal of Chemical Physics, 2015, 143(12): 124708 https://doi.org/10.1063/1.4931669
132
G J Kroes, M Pavanello, M Blanco-Rey, M Alducin, D J Auerbach. Ab initio molecular dynamics calculations on scattering of hyperthermal H atoms from Cu(111) and Au(111). Journal of Chemical Physics, 2014, 141(5): 054705 https://doi.org/10.1063/1.4891483
133
S Monturet, P Saalfrank. Role of electronic friction during the scattering of vibrationally excited nitric oxide molecules from Au(111). Physical Review. B, 2010, 82(7): 075404 https://doi.org/10.1103/PhysRevB.82.075404
134
M S Mizielinski, D M Bird, M Persson, S Holloway. Electronic nonadiabatic effects in the adsorption of hydrogen atoms on metals. Journal of Chemical Physics, 2005, 122(8): 084710 https://doi.org/10.1063/1.1854623
135
M S Mizielinski, D M Bird, M Persson, S Holloway. Spectrum of electronic excitations due to the adsorption of atoms on metal surfaces. Journal of Chemical Physics, 2007, 126(3): 034705 https://doi.org/10.1063/1.2431362
136
M S Mizielinski, D M Bird, M Persson, S Holloway. Newnsanderson model of chemicurrents in H/Cu and H/Ag. Surface Science, 2008, 602(14): 2617–2622 https://doi.org/10.1016/j.susc.2008.06.015
137
M S Mizielinski, D M Bird. Accuracy of perturbation theory for nonadiabatic effects in adsorbate-surface dynamics. Journal of Chemical Physics, 2010, 132(18): 184704 https://doi.org/10.1063/1.3424765
138
D M Bird, M S Mizielinski, M Lindenblatt, E Pehlke. Electronic excitation in atomic adsorption on metals: A comparison of ab initio and model calculations. Surface Science, 2008, 602(6): 1212–1216 https://doi.org/10.1016/j.susc.2008.01.026
139
M Lindenblatt, J van Heys, E Pehlke. Molecular dynamics of nonadiabatic processes at surfaces: Chemisorption of H/Al(111). Surface Science, 2006, 600(18): 3624–3628 https://doi.org/10.1016/j.susc.2006.01.066
140
M Lindenblatt, E Pehlke. Time-dependent density-functional molecular-dynamics study of the isotope effect in chemicurrents. Surface Science, 2006, 600(23): 5068–5073 https://doi.org/10.1016/j.susc.2006.08.034
141
M Lindenblatt, E Pehlke. Ab initio simulation of the spin transition during chemisorption: H/Al(111). Physical Review Letters, 2006, 97(21): 216101 https://doi.org/10.1103/PhysRevLett.97.216101
142
M Grotemeyer, E Pehlke. Electronic energy dissipation during scattering of vibrationally excited molecules at metal surfaces: Ab initio simulations for HCl/Al(111). Physical Review Letters, 2014, 112(4): 043201 https://doi.org/10.1103/PhysRevLett.112.043201
143
M Timmer, P Kratzer. Electron-hole spectra created by adsorption on metals from density functional theory. Physical Review. B, 2009, 79(16): 165407 https://doi.org/10.1103/PhysRevB.79.165407
144
S Zhao, W Kang, J Xue, X Zhang, P H Zhang. + (D+,T+) beryllium collisions studied using time-dependent density functional theory. Physics Letters, 2015, 379(4): 319–326 (Part A) https://doi.org/10.1016/j.physleta.2014.11.008
145
C L Moss, C M Isborn, X Li. Ehrenfest dynamics with a time-dependent density-functional-theory calculation of lifetimes and resonant widths of charge-transfer states of Li+ near an aluminum cluster surface. Physical Review A., 2009, 80(2): 024503 https://doi.org/10.1103/PhysRevA.80.024503
146
A Castro, M Isla, J I Martínez, J A Alonso. Scattering of a proton with the Li4 cluster: Non-adiabatic molecular dynamics description based on time-dependent density-functional theory. Chemical Physics, 2012, 399: 130–134 https://doi.org/10.1016/j.chemphys.2011.07.005
147
A V Krasheninnikov, Y Miyamoto, D Tománek. Role of electronic excitation in ion collisions with carbon nanostructures. Physical Review Letters, 2007, 99(1): 016104 https://doi.org/10.1103/PhysRevLett.99.016104
148
S Bubin, B Wang, S Pantelides, K Varga. Simulation of high-energy ion collisions with graphene fragments. Physical Review. B, 2012, 85(23): 235435 https://doi.org/10.1103/PhysRevB.85.235435
149
A Ojanperä, A V Krasheninnikov, M Puska. Electronic stopping power from first-principles calculations with account for core electron excitations and projectile ionization. Physical Review. B, 2014, 89(3): 035120 https://doi.org/10.1103/PhysRevB.89.035120
150
Z Wang, S S Li, L W Wang. Efficient real-time time-dependent density functional theory method and its application to collision of an ion with a 2D material. Physical Review Letters, 2015, 114(6): 063004 https://doi.org/10.1103/PhysRevLett.114.063004
151
D C Yost, Y Yao, Y Kanai. Examining real-time time-dependent density functional theory nonequilibrium simulations for the calculation of electronic stopping power. Physical Review. B, 2017, 96(11): 115134 https://doi.org/10.1103/PhysRevB.96.115134
152
A Schleife, Y Kanai, A A Correa. Accurate atomistic first-principles calculations of electronic stopping. Physical Review. B, 2015, 91(1): 014306 https://doi.org/10.1103/PhysRevB.91.014306
153
A A Correa, J Kohanoff, E Artacho, D Sánchez-Portal, A Caro. Nonadiabatic forces in ion-solid interactions: The initial stages of radiation damage. Physical Review Letters, 2012, 108(21): 213201 https://doi.org/10.1103/PhysRevLett.108.213201
154
M A Zeb, J Kohanoff, D Sánchez-Portal, A Arnau, J I Juaristi, E Artacho. Electronic stopping power in gold: The role of d electrons and the H/He anomaly. Physical Review Letters, 2012, 108(22): 225504 https://doi.org/10.1103/PhysRevLett.108.225504
155
R Ullah, F Corsetti, D Sánchez-Portal, E Artacho. Electronic stopping power in narrow band gap semiconductor from first principles. Physical Review. B, 2015, 91(12): 125203 https://doi.org/10.1103/PhysRevB.91.125203
156
Time-dependent Density Functional Theory. M arques M A L, Ullrich C A, Nogueira F, Rubio A, Burke K, Gross E K U, eds. Berlin: Springer, 2006
157
Fundamentals of Time-Dependent Density Functional Theory. Marques M A L, Maitra N T, Nogueira F M S, Gross E K U, Rubio A, eds. Berlin: Springer, 2012
158
C A Ullrich. Time-Dependent Density-Functional Theory. Oxford: Oxford University Press, 2012
159
C A Ullrich, Z H Yang. A brief compendium of time-dependent density functional theory. Brazilian Journal of Physics, 2014, 44(1): 154–158 https://doi.org/10.1007/s13538-013-0141-2
160
N T Maitra. Perspective: Fundamental aspects of time-dependent density functional theory. Journal of Chemical Physics, 2016, 144(22): 220901 https://doi.org/10.1063/1.4953039
E K U Gross, W Kohn. Local density-functional theory of frequency-dependent linear response. Physical Review Letters, 1985, 55(26): 2850–2852 https://doi.org/10.1103/PhysRevLett.55.2850
163
M R Provorse, C M Isborn. Electron dynamics with real-time time-dependent density functional theory. International Journal of Quantum Chemistry, 2016, 116(10): 739–749 https://doi.org/10.1002/qua.25096
164
R Nagano, K Yabana, T Tazawa, Y Abe. Time-dependent mean-field description for multiple charge transfer processes in Ar8+–Ar collisions. Physical Review A., 2000, 62(6): 062721 https://doi.org/10.1103/PhysRevA.62.062721
165
V U Nazarov, J M Pitarke, Y Takada, G Vignale, Y C Chang. Including nonlocality in the exchange-correlation kernel from time-dependent current density functional theory: Application to the stopping power of electron liquids. Physical Review. B, 2007, 76(20): 205103 https://doi.org/10.1103/PhysRevB.76.205103
166
J C Tully. Molecular dynamics with electronic transitions. Journal of Chemical Physics, 1990, 93(2): 1061–1071 https://doi.org/10.1063/1.459170
167
N Shenvi, S Roy, J C Tully. Nonadiabatic dynamics at metal surfaces: Independent-electron surface hopping. Journal of Chemical Physics, 2009, 130(17): 174107 https://doi.org/10.1063/1.3125436
168
M A L Marques, A Castro, G F Bertsch, A Rubio. Octopus: A first-principles tool for excited electron-ion dynamics. Computer Physics Communications, 2003, 151(1): 60–78 https://doi.org/10.1016/S0010-4655(02)00686-0
169
N O Foglia, U N Morzan, D A Estrin, D A Scherlies, M C G Lebrero. Role of core electrons in quantum dynamics using TDDFT. Journal of Chemical Theory and Computation, 2017, 13(1): 77–85 https://doi.org/10.1021/acs.jctc.6b00771
170
G Avendaño Franco. Charge transfer processes in atomic collisions from first principles. Dissertation for the Doctoral Degree. Louvain-la-Neuve: Université Catholique de Louvain, 2013
171
K A H German, C B Weare, J A Yarmoff. Inner-shell promotions in low-energy Li+–Al collisions at clean and alkali-covered Al(100) surfaces. Physical Review. B, 1994, 50(19): 14452–14466 https://doi.org/10.1103/PhysRevB.50.14452
172
A Castro, H Appel, M Oliveira, C A Rozzi, X Andrade, F Lorenzen, M A L Marques, E K U Gross, A Rubio. Octopus: A tool for the application of time-dependent density functional theory. Physica Status Solidi. B, Basic Research, 2006, 243(11): 2465–2488 https://doi.org/10.1002/pssb.200642067
173
X Andrade, D Strubbe, U De Giovannini, A H Larsen, M J T Oliveira, J Alberdi-Rodriguez, A Varas, I Theophilou, N Helbig, M J Verstraete, et al.. Real-space grids and the octopus code as tools for the development of new simulation approaches for electronic systems. Physical Chemistry Chemical Physics, 2015, 17(47): 31371–31396 https://doi.org/10.1039/C5CP00351B
174
A A Shukri, F Bruneval, L Reining. Ab initio electronic stopping power of protons in bulk materials. Physical Review. B, 2016, 93(3): 035128 https://doi.org/10.1103/PhysRevB.93.035128
175
S N Markin, D Primetzhofer, M Spitz, P Bauer. Electronic stopping of low-energy H and He in Cu and Au investigated by timeof-flight low-energy ion scattering. Physical Review. B, 2009, 80(20): 205105 https://doi.org/10.1103/PhysRevB.80.205105
176
D R Mason, J le Page, C P Race, W M C Foulkes, M W Finnis, A P Sutton. Electronic damping of atomic dynamics in irradiation damage of metals. Journal of Physics Condensed Matter, 2007, 19(43): 436209 https://doi.org/10.1088/0953-8984/19/43/436209
177
M K Grotemeyer. Ab initio Berechnungen zur Anregung von Elektronen-Loch-Paaren durch Molekülschwingungen am Beispiel von HCl auf Al(111). Dissertation for the Doctoral Degree. Kiel: Christian-Albrechts-Universität zu Kiel, 2016 (in German)
178
R D’Agosta, M Di Ventra. Foundations of stochastic time-dependent current-density functional theory for open quantum systems: Potential pitfalls and rigorous results. Physical Review. B, 2013, 87(15): 155129 https://doi.org/10.1103/PhysRevB.87.155129
179
C A Ullrich. Time-dependent density-functional theory beyond the adiabatic approximation: Insights from a two-electron model system. Journal of Chemical Physics, 2006, 125(23): 234108 https://doi.org/10.1063/1.2406069
N Lorente, R Monreal, M Alducin. Local theory of auger neutralization for slow and compact ions interacting with metal surfaces. Physical Review A., 1994, 49(6): 4716–4725 https://doi.org/10.1103/PhysRevA.49.4716
182
R C Monreal. Auger neutralization and ionization processes for charge exchange between slow noble gas atoms and solid surfaces. Progress in Surface Science, 2014, 89(1): 80–125 https://doi.org/10.1016/j.progsurf.2014.01.001
183
K Balzer, M Rasmussen, N Schlünzen, J P Joost, M Bonitz. Doublon formation by ions impacting a strongly correlated finite lattice system. Physical Review Letters, 2018, 121(26): 267602 https://doi.org/10.1103/PhysRevLett.121.267602
184
L Keldysh. Diagram technique for nonequilibrium processes. . Soviet Physics, JETP, 1965, 20(4): 1018–1026
185
L Kadanoff, G Baym. Quantum Statistical Mechanics. New York: Benjamin, 1962
186
M Bonitz, D Kremp. Kinetic energy relaxation and correlation time of nonequilibrium many-particle systems. Physics Letters, 1996, 212(1-2): 83–90 (Part A) https://doi.org/10.1016/0375-9601(96)00056-4
187
M Bonitz, D Kremp, D C Scott, R Binder, W D Kraeft, H S Köhler. Numerical analysis of non-Markovian effects in charge-carrier scattering: One-time versus two-time kinetic equations. Journal of Physics Condensed Matter, 1996, 8(33): 6057–6071 https://doi.org/10.1088/0953-8984/8/33/012
D Kremp, M Bonitz, W Kraeft, M Schlanges. Non-Markovian Boltzmann equation. Annals of Physics, 1997, 258(2): 320–359 https://doi.org/10.1006/aphy.1997.5703
190
P Danielewicz. Quantum theory of nonequilibrium processes ii. Application to nuclear collisions. Annals of Physics, 1984, 152(2): 305–326 https://doi.org/10.1016/0003-4916(84)90093-9
L Bányai, D B T Thoai, E Reitsamer, H Haug, D Steinbach, M U Wehner, M Wegener, T Marschner, W Stolz. Exciton–lophonon quantum kinetics: Evidence of memory effects in bulk gaas. Physical Review Letters, 1995, 75(11): 2188–2191 https://doi.org/10.1103/PhysRevLett.75.2188
R Binder, H S Köhler, M Bonitz, N Kwong. Green’s function description of momentum-orientation relaxation of photoexcited electron plasmas in semiconductors. Physical Review. B, 1997, 55(8): 5110–5116 https://doi.org/10.1103/PhysRevB.55.5110
195
M Bonitz, K Balzer, R van Leeuwen. Invariance of the Kohn center-of-mass mode in a conserving theory. Physical Review. B, 2007, 76(4): 045341 https://doi.org/10.1103/PhysRevB.76.045341
196
K Balzer, M Bonitz, R van Leeuwen, A Stan, N E Dahlen. Nonequilibrium Green’s function approach to strongly correlated few-electron quantum dots. Physical Review. B, 2009, 79(24): 245306 https://doi.org/10.1103/PhysRevB.79.245306
197
D Kremp, T Bornath, M Bonitz, M Schlanges. Quantum kinetic theory of plasmas in strong laser fields. Physical Review. E, 1999, 60(4): 4725–4732 https://doi.org/10.1103/PhysRevE.60.4725
198
M Bonitz, T Bornath, D Kremp, M Schlanges, W D Kraeft. Quantum kinetic theory for laser plasmas. Dynamical screening in strong fields. Contributions to Plasma Physics, 1999, 39(4): 329–347 https://doi.org/10.1002/ctpp.2150390407
199
G Stefanucci, R van Leeuwen. Nonequilibrium Many-body Theory of Quantum Systems. Cambridge: Cambridge University Press, 2013
200
K Balzer, S Bauch, M Bonitz. Efficient grid-based method in nonequilibrium Green’s function calculations: Application to model atoms and molecules. Physical Review A., 2010, 81(2): 022510 doi:10.1103/PhysRevA.81.022510
201
K Balzer, S Bauch, M Bonitz. Time-dependent second-order Born calculations for model atoms and molecules in strong laser fields. Physical Review A., 2010, 82(3): 033427 https://doi.org/10.1103/PhysRevA.82.033427
202
C Verdozzi, A Wacker, C O Almbladh, M Bonitz. Progress in nonequilibrium Green’s functions (PNGF VI). Journal of Physics: Conference Series, 2016, 696(1): 011001
203
N Schlünzen, S Hermanns, M Bonitz, C Verdozzi. Dynamics of strongly correlated fermions: Ab initio results for two and three dimensions. Physical Review. B, 2016, 93(3): 035107 https://doi.org/10.1103/PhysRevB.93.035107
204
M Bonitz, M Scharnke, N Schlünzen. Time-reversal invariance of quantum kinetic equations II: Density operator formalism. Contributions to Plasma Physics, 2018, 58(10): 58 https://doi.org/10.1002/ctpp.201700052
205
TRIM and SRIM code packages. Available at the website of srim.org (accessed March 11, 2019)
206
S Heese. Dielectric function of graphene with yambo. Dissertation for the Bachelor Degree. Kiel: Christian-Albrechts-Universität zu Kiel, 2017
207
M Bonitz, K Balzer, N Schlünzen, M Rodriguez Rasmussen, J P Joost. Ion Impact Induced Ultrafast Electron Dynamics in Correlated Materials and Finite Graphene Clusters. Physica Status Solidi, 2019, 1800490: (b)
208
M Pamperin, F X Bronold, H Fehske. Many-body theory of the neutralization of strontium ions on gold surfaces. Physical Review. B, 2015, 91(3): 035440 https://doi.org/10.1103/PhysRevB.91.035440
209
W Brenig. Theory of inelastic atom-surface scattering: Average energy loss and energy distribution. Zeitschrift für Physik B, Condensed Matter, 1979, 36(1): 81–87
210
M Bonitz, L Rosenthal, K Fujioka, V Zaporojtchenko, F Faupel, H Kersten. Towards a particle based simulation of complex plasma driven nanocomposite formation. Contributions to Plasma Physics, 2012, 52(10): 890–898 https://doi.org/10.1002/ctpp.201200038
211
W Brenig, E Pehlke. Reaction dynamics of H2 on Si. Ab initio supported model calculations. Progress in Surface Science, 2008, 83(5): 263–336 https://doi.org/10.1016/j.progsurf.2008.06.001
212
F X Bronold, H Fehske. Kinetic modeling of the electronic response of a plasma-facing solid. Journal of Physics. D, Applied Physics, 2017, 50(29): 294003 https://doi.org/10.1088/1361-6463/aa7901
213
I Langmuir, H Mott-Smith. Studies of electric discharges in gases at low pressure. General Electric Review, 1924, 27: 449
R P Brinkmann. From electron depletion to quasi-neutrality: The sheath-bulk transition in rf modulated discharges. Journal of Physics. D, Applied Physics, 2009, 42(19): 194009 https://doi.org/10.1088/0022-3727/42/19/194009
L A Schwager, C K Birdsall. Collector and source sheaths of a finite ion temperature plasma. Physics of Fluids. B, Plasma Physics, 1990, 2(5): 1057–1068 https://doi.org/10.1063/1.859279
219
M D Campanell, M V Umansky. Strongly emitting surfaces unable to float below plasma potential. Physical Review Letters, 2016, 116(8): 085003 https://doi.org/10.1103/PhysRevLett.116.085003
220
S Langendorf, M Walker. Effect of secondary electron emission on the plasma sheath. Physics of Plasmas, 2015, 22(3): 033515 https://doi.org/10.1063/1.4914854
221
J P Sheehan, N Hershkowitz, I D Kaganovich, H Wang, Y Raitses, E V Barnat, B R Weatherford, D Sydorenko. Kinetic theory of plasma sheaths surrounding electron-emitting surfaces. Physical Review Letters, 2013, 111(7): 075002 https://doi.org/10.1103/PhysRevLett.111.075002
222
D Sydorenko, I D Kaganovich, Y Raitses, A Smolyakov. Breakdown of a space charge limited regime of a sheath in a weakly collisional plasma bounded by walls with secondary electron emission. Physical Review Letters, 2009, 103(14): 145004 https://doi.org/10.1103/PhysRevLett.103.145004
223
F Taccogna, S Longo, M Capitelli. Plasma-surface interaction model with secondary electron emission effects. Physics of Plasmas, 2004, 11(3): 1220–1228 https://doi.org/10.1063/1.1647567
224
P N Hu, S Ziering. Collisionless theory of a plasma sheath near an electrode. Physics of Fluids, 1966, 9(11): 2168–2179 https://doi.org/10.1063/1.1761586
225
R N Franklin. Plasma Phenomena in Gas Discharges. Oxford: Clarendon Press, 1976
226
M M Becker, G K Grubert, D Loffhagen. Boundary conditions for the electron kinetic equation using expansion techniques. European Physical Journal Applied Physics, 2010, 51(1): 11001 https://doi.org/10.1051/epjap/2010073
227
M J Kushner. Modeling of microdischarge devices: Pyramidal structures. Journal of Applied Physics, 2004, 95(3): 846–859 https://doi.org/10.1063/1.1636251
228
Y B Golubovskii, V A Maiorov, J Behnke, J F Behnke. Influence of interaction between charged particles and dielectric surface over a homogeneous barrier discharge in nitrogen. Journal of Physics. D, Applied Physics, 2002, 35(8): 751–761 https://doi.org/10.1088/0022-3727/35/8/306
229
R Dussart, L J Overzet, P Lefaucheux, T Dufour, M Kulsreshath, M A Mandra, T Tillocher, O Aubry, S Dozias, P Ranson, et al.. Integrated micro-plasmas in silicon operating in helium. European Physical Journal D, 2010, 60(3): 601–608 https://doi.org/10.1140/epjd/e2010-00272-7
230
M K Kulsreshath, L Schwaederle, L J Overzet, P Lefaucheux, J Ladroue, T Tillocher, O Aubry, M Woytasik, G Schelcher, R Dussart. Study of dc micro-discharge arrays made in silicon using cmos compatible technology. Journal of Physics. D, Applied Physics, 2012, 45(28): 285202 https://doi.org/10.1088/0022-3727/45/28/285202
231
J G Eden, S J Park, J H Cho, M H Kim, T J Houlahan, B Li, E S Kim, T L Kim, S K Lee, K S Kim, et al.. Plasma science and technology in the limit of the small: Microcavity plasmas and emerging applications. IEEE Transactions on Plasma Science, 2013, 41(4): 661–675 https://doi.org/10.1109/TPS.2013.2253132
232
P A Tchertchian, C J Wagner, T J Houlahan Jr, B Li, D J Sievers, J G Eden. Control of the interface between electron-hole and electron-ion plasmas: Hybrid semiconductor-gas phase devices as a gateway for plasma science. Contributions to Plasma Physics, 2011, 51(10): 889–905 https://doi.org/10.1002/ctpp.201100037
233
N P Ostrom, J G Eden. Microcavity plasma photodetectors: Photosensitivity, dynamic range, and the plasma-semiconductor interface. Applied Physics Letters, 2005, 87(14): 141101 https://doi.org/10.1063/1.2072767
234
Z Sternovsky. The effect of ion-neutral collisions on the weakly collisional plasma-sheath and the reduction of the ion flux to the wall. Plasma Sources Science & Technology, 2005, 14(1): 32–35 https://doi.org/10.1088/0963-0252/14/1/004
235
K U Riemann. Kinetic analysis of the collisional plasma-sheath transition. Journal of Physics. D, Applied Physics, 2003, 36(22): 2811–2820 https://doi.org/10.1088/0022-3727/36/22/007
236
T E Sheridan, J Goree. Collisional plasma sheath model. Physics of Fluids. B, Plasma Physics, 1991, 3(10): 2796–2804 https://doi.org/10.1063/1.859987
237
T V Tsankov, U Czarnetzki. Information hidden in the velocity distribution of ions and the exact kinetic bohm criterion. Plasma Sources Science & Technology, 2017, 26(5): 055003 https://doi.org/10.1088/1361-6595/aa5f45
238
D Lacroix, S Hermanns, C M Hinz, M Bonitz. Ultrafast dynamics of finite Hubbard clusters: A stochastic mean-field approach. Physical Review. B, 2014, 90(12): 125112 https://doi.org/10.1103/PhysRevB.90.125112
239
M Hopjan, D Karlsson, S Ydman, C Verdozzi, C O Almbladh. Merging features from green’s functions and time dependent density functional theory: A route to the description of correlated materials out of equilibrium? Physical Review Letters, 2016, 116(23): 236402 https://doi.org/10.1103/PhysRevLett.116.236402