CMS Comparisons of DFT-MD, TB- MD and classical MD calculations of radiation damage and plasmawallinteractions Kai Nordlund Department of Physics and Helsinki Institute of Physics University of Helsinki, Finland
Contents 0. Levels of molecular dynamics 1. Examples of comparisons of classical and quantum mechanical methods - Si: threshold displacement energy: DFT-MD vs. classical - Erosion and sticking of hydrocarbons in fusion reactors: TB-MD vs. classical Kai Nordlund, Department of Physics, University of Helsinki 2
0. Levels of molecular dynamics By increasing order of realism: Coarse-grained MD - Multimillions of objects - Now popular in biophysics Classical (analytical potential) MD - Hundreds of millions of atoms - Dominating by scopes of use Tight-binding MD - ~ A few hundred atoms - Has been used for some 20 years Density-functional theory MD - ~ One hundred atoms - Use widely increasing now Time-dependent density functional theory MD - ~ A few tens of atoms - Practical uses limited so far True Hartree-Fock ab initio - ~ A few tens of atoms - Practical uses limited so far Relevant for sputtering simulations But because of need for statistics, classical still dominates! - Although ideally everything better be done by DFT MD Kai Nordlund, Department of Physics, University of Helsinki 3
Threshold displacement energy in Si - Introduction The threshold displacement energy is the smallest amount of kinetic energy needed to permanently displace an atom from its lattice site to an interstitial position A vacancy is left behind so a Frenkel pair is produced Mathematically, where p is the probability for displacement, (α,φ) is the direction of recoils in spherical coordinates, T is the energy of the recoil, and T d (α,φ) is the threshold energy surface in 3D: Typically T d ~ 10-50 ev Kai Nordlund, Department of Physics, University of Helsinki 4
Threshold displacement energy in Si - Introduction Minimum vs. average threshold displacement energy: Direction-specific thresholds: T d,100, T d,110, Average threshold displacement energy: T d,ave ave Td(, ) <111>: B Open A Closed AVERAGE Minimum threshold displacement energy: T d,min min Td(, ) <110> <100> - Usually in one of principal directions Kai Nordlund, Department of Physics, University of Helsinki 5
Threshold displacement energy in Si Introduction: why? Why does T d matter? It is the single most important quantity in determining radiation damage in solids It determines directly the number of Frenkel pairs created N FP by high-energy electron irradiation It is also used to estimate the damage caused by neutron and ion irradiation via the Kinchin-Pease/NRT equation: N FP 0.8 Nuclear deposited energy 2T d, ave From here also the displacement-per-atom (dpa) value is obtained It is the threshold for vacancy production in TRIM/SRIM Kai Nordlund, Department of Physics, University of Helsinki 6
Threshold displacement energy in Si Introduction Why study T d in silicon? Silicon is the foundation for the semiconductor industry, where ion implantation is the most commonly used doping method Silicon appears in many other applications, where radiation is omnipresent (radiation detectors, sensors, etc.) In spite of this, T d is poorly known There is even confusion between the minimum and average of T d Kai Nordlund, Department of Physics, University of Helsinki 7
Threshold displacement energy in Si Introduction Why use molecular dynamics (MD) to study T d? The threshold displacement energy is difficult to determine experimentally: The experimental methods, which practically all rely on electron irradiation, cause problems in interpreting the results (spreading of the beam, isolated defects vs. clustered defects, annealing of damage etc.) MD (=simulation of atom motion) can determine it directly without these problems Why use Density Functional Theory (DFT) to study T d? The choice of classical MD potentials is a source of considerable deviation in the results values range around 10 23 ev DFT is a quantum mechanical, more basic level of theory Kai Nordlund, Department of Physics, University of Helsinki 8
Threshold displacement energy in Si Simulation methodology DFT MD is veeery slow Hence we took a 4-step approach: 1. Use classical MD in very large systems (thousands of atoms) for long times (~ 10 ps) to find a reliable value within the model used: Two widely different potentials: Stillinger-Weber and Tersoff 2. Scale down the system size and simulation time in the classical as much as possible while checking that the result does not change too much in either model 3. Find minimal basis set in DFT which keeps point defect energies ~ unchanged 4. Use DFT MD with the minimal system size and basis set to get a more reliable value of T d Kai Nordlund, Department of Physics, University of Helsinki 9
Threshold displacement energy in Si Simulation methodology Choose a random direction (α,φ), set E = E0 (8 ev) Simulate a recoil in the direction (α,φ) with energy E E = E + ΔE NO Frenkel pair formed? YES Threshold energy in the direction (α,φ) found Kai Nordlund, Department of Physics, University of Helsinki 10
Threshold displacement energy in Si Simulation methodology: scaling results Results of the classical scaling tests: N atoms has to be > 100 We chose 144 atom periodic non-cubic cell Simulation time was similarly optimized Time has to be >= 3 ps We chose 3 ps Kai Nordlund, Department of Physics, University of Helsinki 11
Threshold displacement energy in Si II. Simulation methodology: DFT Parameter Scanning The general parameters of the dynamical simulation were now optimized The next step was to optimize the DFT parameters The goal was to find one suitable LDA set and one suitable GGA set Criteria for a suitable set: Reasonable calculation time (a few days per recoil simulation) Good energetics for the basic point defects The DFT code we used was SIESTA Final sets: LDA: SZ, 4 k points, 100 Ry cutoff, Ceperley-Alder GGA: SZ, 4 k points, 250 Ry cutoff, Perdew-Burke-Ernzerhof Kai Nordlund, Department of Physics, University of Helsinki 12
Threshold displacement energy in Si Results Formation of close FP in closed 111 direction: Kai Nordlund, Department of Physics, University of Helsinki 13
Threshold displacement energy in Si Results Recombination effects are major: 110 direction, 20 ev Kai Nordlund, Department of Physics, University of Helsinki 14
Threshold displacement energy in Si The DFT simulations Our goal was to find the average threshold displacement energy of silicon within a statistical error limit of 2 ev The average threshold energy in the LDA scheme 40 random directions for A 111 direction, 20 ev 40 random directions for B The GGA scheme was used to confirm the average obtained by LDA 10 random directions for A 10 random directions for B 112 direction, 20 ev Kai Nordlund, Department of Physics, University of Helsinki 15
Threshold displacement energy in Si The DFT simulations: Results Two surprising effects were observed: A large fraction of defects formed were IV pairs (= Bond Defects, BD) These usually formed at lower E s than Frenkel pairs Big difference to classical MD Majority of real Frenkel pairs contained a tetrahedral rather than a dumbbell interstitial Explanation: Frenkel pair with tetrahedral interstitial lower in E Kai Nordlund, Department of Physics, University of Helsinki 17
Threshold displacement energy in Si The DFT simulations: Results Results for minimum threshold: DFT: T d, min = 12.5 ± 1.5 SYST ev, open 111 direction Experiment: T d, min = 12.9 ± 0.6 ev, 111 direction [Loferski and Rappaport, Phys. Rev. 111 (1958) 432] Excellent agreement! This gave us great confidence that we can reliably predict the average threshold displacement energy Results for average threshold: Counting IV pair or Frenkel pairs: - LDA DFT: T d, ave = 24 ± 1 STAT ± 2 SYST ev - GGA DFT: T d, ave = 23 ± 2 STAT ± 2 SYST ev Counting only Frenkel pairs: - LDA DFT: T d, ave = 36 ± 2 STAT ± 2 SYST ev - GGA DFT: T d, ave = 35 ± 4 STAT ± 2 SYST ev Kai Nordlund, Department of Physics, University of Helsinki 18
Threshold displacement energy in Si How good are the classical models? We also compared the classical potentials systematically with the quantum mechanical ones => Stillinger-Weber (SW) does best of the classical potentials [E. Holmström et al, Phys. Rev. B 78, 045202 (2008)] Kai Nordlund, Department of Physics, University of Helsinki 19
Threshold displacement energy in Si 3D displacement energy surface The classical models have sufficient statistics that we can plot the full 3D displacement energy surface T d (α,φ) Minimum in all around open 111 direction Maximum in all around <144> directions (~ 45 o off closed 111) A bit below straight impact to 2nd-nearest neighbor from A Kai Nordlund, Department of Physics, University of Helsinki 20
Threshold displacement energy in Si Conclusions There are considerable differences between DFTMD and classical MD results of the threshold displacement energy in Si Even qualitative: the large production of Bond Defects is not reproduced by any of the classical potentials [E. Holmström et al, Phys. Rev. B 78, 045202 (2008)] Even so, classical MD can help DFT-MD: Use first classical MD to determine acceptable system size and simulation conditions for DFT! Kai Nordlund, Department of Physics, University of Helsinki 21
And now Let's switch gears Kai Nordlund, Department of Physics, University of Helsinki 22
Erosion of carbon in fusion reactors Erosion of hydrocarbons: classical vs. TB In 1999-2001 we showed that the athermal part of the carbon erosion can be explained by the swift chemical sputtering mechanism Athermal, rapid, endothermal [Salonen et al, Europhys. Lett. 52 (2000) 504; Phys. Rev. B 63 (2001) 195415] Kai Nordlund, Department of Physics, University of Helsinki 23
Erosion of carbon in fusion reactors Comparison of classical vs TB MD Results of comparison: Exactly same simulation cell, about 200 atoms Relaxed in each model before bombardments Kai Nordlund, Department of Physics, University of Helsinki 24
Sticking of radicals on dangling bonds Introduction: Radicals in the reactor The MD simulations show both CH x and C 2 H y erosion As well as larger hydrocarbons Fraction depends on surface structure and ion energy Experiments show that CH 3 and C 2 H 2 are the most abundantly sputtered species from plasma-facing carbon materials in fusion devices [E Vietzke and A. A. Haasz, in Physical Processes of the Inaction of Fusion Plasmas with Solids, Chap. 4 (1996)] Kai Nordlund, Department of Physics, University of Helsinki 25
Sticking of radicals on dangling bonds Methods We have carried out simulations of radical sticking We have limited ourselves to model surfaces with a welldefined dangling bond nature (or lack of it) Classical: Brenner (1 st generation) potential with bond conjugation terms - But cutoff extended to 2.46 Å (this reproduces better the diamond-to-graphite phase transition [Nordlund et al, PRL 77, 699 (1996)] ) Tight-binding: Density-functional based tight-binding model of Frauenheim et al. Implemented into our own code as force model Kai Nordlund, Department of Physics, University of Helsinki 26
Sticking of radicals on dangling bonds Sticking of CH 3 : dependence on db neighbourhood 7 DB: sticking cross section = average area per surface site, 5.9 Å 2 Kai Nordlund, Department of Physics, University of Helsinki 27
Sticking of radicals on dangling bonds Sticking of CH 3 : angular dependence We find a major dependence of the sticking probability vs. distance from unsaturated carbon site at different angles of incidence of CH 3 angles of incidence [Träskelin et al, J. Appl. Phys. 93, 1826 (2003)] Kai Nordlund, Department of Physics, University of Helsinki 28
Sticking of radicals on dangling bonds Sticking of CH 3 : animation of TB case Kai Nordlund, Department of Physics, University of Helsinki 29
Sticking of radicals on dangling bonds Sticking of CH 3 : model dependence There is a model dependence between the TB and classical results TB likely to be more reliable [Träskelin et al, J. Nucl. Mater. 334, 65 (2004).)] Kai Nordlund, Department of Physics, University of Helsinki 30
Sticking of radicals on dangling bonds Sticking of CH 3 : comparison to experiments and analytical model The TB results are in excellent agreement with experiments Angular dependence can be explained by a simple analytical model [Träskelin et al, J. Nucl. Mater. 334, 65 (2004).)] Kai Nordlund, Department of Physics, University of Helsinki 31
Sticking of radicals on dangling bonds Sticking of C 2 H x We have also studied the sticking of C 2 H x molecules on similar model surfaces Incoming molecule equilibrated at 300 or 2100 K Surface at 0 K initially Kai Nordlund, Department of Physics, University of Helsinki 32
Sticking of radicals on dangling bonds Animation... C 2 H 2 on 7db surface Kai Nordlund, Department of Physics, University of Helsinki 33
Sticking of radicals on dangling bonds Results at 300 K, 1db surface Sticking probability decreases with increasing amount of H atoms Not surprising at all => more H makes them less chemically reactive [Träskelin, J. Nucl. Mater. 375, 270 (2008)]. Kai Nordlund, Department of Physics, University of Helsinki 34
Sticking of radicals on dangling bonds Results at 2100 K, 1db surface [Träskelin, J. Nucl. Mater. 375, 270 (2008)]. Kai Nordlund, Department of Physics, University of Helsinki 35
Sticking cross section (Å) Sticking of radicals on dangling bonds Comparison of results with amount of H What is very interesting is that the sticking cross section is non-monotonous with x in C 2 H x Reason: basic chemistry: odd x are radicals, even x not! x = Number of H atoms [Träskelin, J. Nucl. Mater. 375, 270 (2008)]. Kai Nordlund, Department of Physics, University of Helsinki 36
Sticking of radicals on dangling bonds New results: DFT MD of hexane on Si C 6 H 14 deposition on Si (100) surface No sticking because of no dangling bonds in molecule Kai Nordlund, Department of Physics, University of Helsinki 37
Sticking of radicals on dangling bonds Conclusions Our results show that hydrocarbon sticking on dangling bonds in carbon-based materials is: Not so sensitive to the incoming molecule temperature Somewhat sensitive to the simulation model used Very sensitive to the dangling bond neighbourhood Very sensitive to the incoming angle Very sensitive to the number of hydrogens in the molecule Kai Nordlund, Department of Physics, University of Helsinki 38
Conclusions - Overall conclusions Classical interatomic potentials can easily have systematic errors DFT-MD starts to be of practical value now w.r.t. sticking and reflection calculations But will remain out of reach for larger systems for years DFT checks and calibrations of classical MD a good way to assess their reliability Kai Nordlund, Department of Physics, University of Helsinki 39