Kinetic Monte Carlo Technique Research Articles

First-principles study of behaviors of point defects in Mo-14 Re alloy

Molybdenum alloys with rhenium additions of 14 % (Mo-14 Re) are regarded as structural materials for advanced nuclear reactors. The performance of Mo-14 Re alloy under irradiation is crucial for its application. Irradiation performance is related to the behaviors of point defects produced by irradiation. The behaviors of point defects in Mo-14 Re alloy were investigated using first-principles methods in this work. Compared with the results in pure Mo alloy, the formation energy and the migration energy of vacancy in Mo-14 Re were both reduced, and the migration energy of interstitial dumbbell increased while the formation energy decreased in Mo-14 Re. In Mo-14 Re, vacancy preferred to form and diffuse faster in Re-enriched environment. Knowing the number of Re atoms in the 1NN (first nearest neighbor) shell of the vacancy and saddle point, the vacancy formation energy and migration energy can be estimated. Since the interstitial atom has a certain orientation, the distribution of the atoms around it is anisotropic. To estimate the interstitial formation energy, it was necessary to count the number of Re atoms at the tensile and compressive sites at the 1NN shell around the interstitial. The interstitial motion was three-dimensional (3D) in Mo-14 Re. At 1200 K, the diffusion coefficient of Re atom was a little higher than that of Mo atom, which could lead to the segregation of Re atoms at defect sinks and the formation of Re-enriched phase. It is possible to investigate the longer-term evolution of microstructure using cluster dynamics (CD) or kinetic monte carlo (KMC) techniques based on these results.

Kinetic Monte Carlo simulation of polycrystalline silver metal electrodeposition: scaling of roughness and effects of deposition parameters.

In this work, a kinetic Monte Carlo (KMC) technique was used to simulate the growth morphology of electrodeposited polycrystalline Ag thin films under a galvanostatic condition (current density). The many-body Embedded Atom Method (EAM) potential has been used to describe the Ag-Ag atomic interaction. Herein, the surface morphology is affected by the kinetic diffusion of adatoms where four jump processes are considered, namely hopping, exchange, step-edge exchange and grain boundary. The results have shown that the surface roughness follows a power law behavior versus film thickness (∝Lα) and time (∝tβ), with the roughness and growth exponents α and β found to be α = 1.14 ± 0.01 and β = 0.57 ± 0.01. The surface morphology under different deposition parameters (current density and substrate temperature) has been discussed in detail. The surface roughness increases where the current density increases due to high deposition rates, which can accelerate the growth of island mode, especially on the (111) surface. In contrast, the surface roughness decreases the temperature of the substrate increases due to thermal agitation, allowing to transform nearly columnar grains to grains with a flat and smooth surface. Finally, the simulations provided information on the subsurface deposition rate of each grain that is not directly available for experimental investigations. It was observed that the (111) grain has a faster deposition rate compared to the (100) and (110) grains due to the low surface energy of the (111) grain.

Variability estimation in resistive switching devices, a numerical and kinetic Monte Carlo perspective

We have analyzed variability in resistive memories (Resistive Random Access Memories, RRAMs) making use of advanced numerical techniques to process experimental measurements and simulations based on the kinetic Monte Carlo technique. The devices employed in the study were fabricated using the TiN/Ti/HfO2/W stack. The switching parameters were obtained making use of new developed extraction methods. The appropriateness of the advanced parameter extraction methodologies has been checked by comparison to kinetic Monte Carlo simulations; in particular, the reset and set events have been studied and detected. The data obtained were employed to shed light on the resistive switching operation and the cycle-to-cycle variability. It has been shown that variability depends on the numerical technique employed to obtain the set and reset voltages, therefore, this issue must be taken into consideration in RS characterization and modeling studies. The proposed techniques are complementary and depending on the technology and the curves shape the features of a particular method could make it to be the most appropriate.

Solvable model of gas production decline from hydrofractured networks.

We address questions that arose from studying gas and oil production from hydrofractured wells. Does past production predict the future? This depends on deducing from production as much as possible about the plausible geometries of the fracture network. We address the problem through a solvable model and use kinetic Monte Carlo and Green's function techniques to solve it. We have three main findings. First, at sufficiently long times, the production from all compact fracture networks is described by a universal function with two scaling parameters, one of which is the diffusivity of unbroken rock α and the second of which is a parameter V_{ext} with units of volume. Second, for fracture networks where the power-law distribution of fracture spacings falls below a critical value (and this appears to be the case in practice), early-time production always scales as one over the square root of time. Third, the diffusivity α that sets the scale for late-time production is inherently difficult to estimate from production data, but the methods here provide the best hope of obtaining it and thus can determine the physics that will govern the decline of unconventional gas and oil wells.

Coexistence of first-order and second-order desorption processes during temperature-programmed desorption of Bi on Ni(100) analyzed by kinetic Monte Carlo techniques

The application of temperature-programmed desorption (TPD) techniques in heterogeneous catalysis to probe, among other things, the nature of the reactions on the surface solid catalyst, and ultimately, the kinetics of desorbed species, is hampered by the inability to make direct observations of adsorbates when they are most catalytically active. Thus, it is almost impossible to make a direct association between a given elementary surface process and a key feature on the TPD spectra, such as the nature and number of peaks. What kinetic Monte Carlo simulations have shown, on the other hand, is that the complex surface evolution during TPD is controlled effectively by just a few parameters that relate to the surface kinetics and energetics. In this study, we will use kinetic Monte Carlo approach to show that double-peaked TPD spectra obtained from adsorption of Bi adsorbates on Ni(100) at an initial temperature of 800 K and subsequent TPD runs for high preadsorbed coverages can indeed be explained satisfactorily by assuming predominant first-order desorption kinetics coupled with adsorbate-adsorbate lateral interactions, in agreement with prior studies. While not totally discounting the presence of Bi dimers, and thus second-order desorption, our study is sensitive enough to reveal the extent of their presence. In other words, we propose that dimers can coexist with Bi adatoms in small amounts while retaining the key features of the TPD spectra, provided the kinetic parameters associated with dimer formation (and dissolution) are well within a certain range. On the other hand, any model in which dimers are present to a degree in which they are not totally dominated by adatoms cannot produce TPD spectra that are consistent with the experiment.

The dominant mechanisms for the formation of solute-rich clusters in low-Cu steels under irradiation

The formation of nano-sized, coherent, solute-rich clusters (NSRC) is known to be an important factor causing the degradation of the macroscopic properties of steels under irradiation. The mechanisms driving their formation are still debated. This work focuses on low-Cu reactor pressure vessel (RPV) steels, where solute species are generally not expected to precipitate. We rationalize the processes that take place at the nanometer scale under irradiation, relying on the latest theoretical and experimental evidence on atomic-level diffusion and transport processes. These are compiled in a new model, based on the object kinetic Monte Carlo (OKMC) technique. We evaluate the relevance of the underlying physical assumptions by applying the model to a large variety of irradiation experiments. Our model predictions are compared with new experimental data obtained with atom probe tomography and small angle neutron scattering, complemented with information from the literature. The results of this study reveal that the role of immobilized self-interstitial atoms (SIA) loops dominates the nucleation process of NSRC.

Multi-Scale Modeling of Void Evolution at Li/SEI Interface during Delithiation

Lithium metal electrodes promise high energy density batteries due to its high specific capacity (3,860 mAhg–1) and lowest reduction potential, but Li dendrite growth still occurs in both liquid electrolyte and solid electrolytes. In liquid electrolytes, the Li metal surface is always covered by inorganic and organic layers which is called solid electrolyte interphase (SEI) due to the reduction of electrolytes. In solid electrolytes, the Li metal surface is either covered by solid electrolytes itself or by an interlayer formed by the decomposed solid electrolytes. Therefore, the atomistic level of Li stripping and plating processes occur at the Li/SEI interfaces. Maintaining a smooth Li surface during cycling will prevent non-uniform current distribution and suppress Li dendrite growth. The Li surface becomes non-smooth, as collections of Li vacancies (voids) are generated when the stripping process removes Li atoms from the Li/SEI interface faster than vacancies being filled. The accumulation of voids can lead to the interface delamination or pitting as well as to nonuniform current distributions at the interface of Li metal, promoting Li dendrite growth in the following plating process. Ideally, if Li atom diffusion toward the Li/SEI interface is comparable with the rate of Li removal, the surface voids will be digested (filled) by the Li from the bulk, thus a smooth Li surface will be achieved during Li stripping. Therefore, we developed a multi-scale modeling method combining density functional theory (DFT) and Kinetic Monte Carlo (KMC) techniques to study the evolution/formation of voids at different Li/SEI interfaces. The KMC method simulates the void's evolution by capturing the competition between voids generation due to Li removal with the processes to fill the voids, including Li atom diffusion in all directions and the mechanical deformation. DFT is used to determine the stable Li/SEI interfaces, adhesion, Li vacancy formation and diffusion near the Li/SEI interface, and more importantly, providing the Li diffusion barriers toward and away from the Li/SEI interface as the key inputs for the KMC simulation. Based on Li vacancy formation energy landscapes, when voids are generated at the interfaces, Li/LiF interface tends to trap Li vacancies at the interface, while Li/Li2O interface tends to repel the Li vacancies. KMC simulations show consistent results that the voids created at the Li/LiF interface do not migrate to the bulk portion of the Li metal, while the voids at the Li/Li2O interface are filled by diffusion of Li atoms from the bulk, in other words, the voids are digested by the bulk Li. Thus, by varying coating materials, the Li/coating interaction will lead to different morphology of voids evolution at the Li metal surface. This multi-scale modeling approach is anticipated to be applied to a wide range of SEI and SEE materials to maintain a smooth Li surface during the striping process, in order to prevent Li dendrite growth.

Kinetic Monte Carlo simulations of the dynamics of a coupled system of free and localized carriers in AlGaN

A model for the dynamics of a coupled system of free and localized carriers in semiconductors with strong carrier localization is suggested. Kinetic Monte Carlo technique is exploited for simulations. The model is verified by fitting the simulated and experimental temperature dependences of photoluminescence (PL) band intensity, peak position, and band width, and the carrier density dependence of PL efficiency in AlGaN quantum wells. The influence of carrier localization conditions on the dominating carrier migration and recombination processes is revealed. The efficiency droop effect is shown to be caused by peculiarities of carrier localization without significant influence of Auger recombination.

Epidemic outbreaks on two-dimensional quasiperiodic lattices

We present a novel kinetic Monte Carlo technique to study the susceptible-infected-removed model in order to simulate epidemic outbreaks on two quasiperiodic lattices, namely, Penrose and Ammann-Beenker. Our analysis around criticality is performed by investigating the order parameter, which is defined as the probability of growing a spanning cluster formed by removed sites, evolving from an initial system configuration with a single random chosen infective site. This system is studied by means of the cluster size distribution, obtained by the Newman-Ziff algorithm. Additionally, we obtained the mean cluster size, and a cumulant ratio to estimate the epidemic threshold. In spite of the quasiperiodic order moves the transition point, compared to periodic lattices, this is not able to alter the universality class of the model, leading to the same critical exponents. In addition, our technique can be generalized to study epidemic outbreaks in networks and diffusing populations.

The Dominating Mechanisms for the Formation of Solute-Rich Clusters in Steels under Irradiation

The formation of nano-sized, coherent, solute-rich clusters (NSRC) is known to be an important factor degrading the macroscopic properties of steels under irradiation. The mechanisms driving their formation are still debated. This work focuses on low-Cu reactor pressure vessel (RPV) steels, where solute species are generally not expected to precipitate. We rationalize the processes taking place at the nanometre scale under irradiation, relying on the latest theoretical and experimental evidence on atomic-level diffusion and transport processes. These are compiled in a new model, based on the object kinetic Monte Carlo (OKMC) technique. We evaluate the relevance of the underlying physical assumptions by applying the model to a large variety of irradiation experiments. Our model predictions are compared with new experimental data obtained with atom probe tomography and small angle neutron scattering, complemented with information from the literature. The results of this study reveal that the role of immobilized self-interstitial atoms (SIA) loops dominates the nucleation process of NSRC.

Modeling the Distribution of Functional Groups in Semibatch Radical Copolymerization: An Accelerated Stochastic Approach

While Kinetic Monte Carlo (KMC) techniques provide a powerful means to model polymer microstructure, the associated computational cost has been a barrier to their widespread adoption. The case of radical semibatch polymerization under starved-feed policy is a particularly challenging application: at the initial stage, a large simulation volume is required to accurately represent the low concentration of radicals generated at the start of the reaction, while the reactant feed dictates the further increase of the simulation volume with time. A combination of approaches is implemented in a stepwise fashion to greatly accelerate the KMC representation of this system. First, a correction factor is developed to maintain a constant simulation volume in order to improve the efficiency of the solution, followed by scaling of the reaction rates to preserve accuracy at low control volumes and further reduce computational effort. A novel strategy for storing the explicit chain sequences and parallel analysis of the s...

Dynamic coupling of a finite element solver to large-scale atomistic simulations

We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that follows the geometry defined by atomistic data. On this mesh, different multiphysics problems can be solved to obtain distributions of physical quantities of interest, which can be fed back to the atomistic system. The simulation flow is optimized to maximize computational efficiency while maintaining good accuracy. This is achieved by providing the modules for a) optimization of the density of the generated mesh according to requirements of a specific geometry and b) efficient extension of the finite element domain without a need to extend the atomistic one. Our method is organized as an open-source C++ code. In the current implementation, an efficient Laplace equation solver for calculating the electric field distribution near a rough atomistic surface demonstrates the capability of the suggested approach.

Molecular modeling of the microstructure evolution during carbon fiber processing.

The rational design of carbon fibers with desired properties requires quantitative relationships between the processing conditions, microstructure, and resulting properties. We developed a molecular model that combines kinetic Monte Carlo and molecular dynamics techniques to predict the microstructure evolution during the processes of carbonization and graphitization of polyacrylonitrile (PAN)-based carbon fibers. The model accurately predicts the cross-sectional microstructure of the fibers with the molecular structure of the stabilized PAN fibers and physics-based chemical reaction rates as the only inputs. The resulting structures exhibit key features observed in electron microcopy studies such as curved graphitic sheets and hairpin structures. In addition, computed X-ray diffraction patterns are in good agreement with experiments. We predict the transverse moduli of the resulting fibers between 1 GPa and 5 GPa, in good agreement with experimental results for high modulus fibers and slightly lower than those of high-strength fibers. The transverse modulus is governed by sliding between graphitic sheets, and the relatively low value for the predicted microstructures can be attributed to their perfect longitudinal texture. Finally, the simulations provide insight into the relationships between chemical kinetics and the final microstructure; we observe that high reaction rates result in porous structures with lower moduli.

Monte Carlo analysis of field-dependent electron avalanche coefficients in nitrogen at atmospheric pressure

Calculations of electron impact ionization of nitrogen gas at atmospheric pressure are presented based on the kinetic Monte Carlo technique. The emphasis is on energy partitioning between primary and secondary electrons, and three different energy sharing schemes have been evaluated. The ionization behavior is based on Wannier's classical treatment. Our Monte Carlo results for the field-dependent drift velocities match the available experimental data. More interestingly, the field-dependent first Townsend coefficient predicted by the Monte Carlo calculations is shown to be in close agreement with reported data for E/N values ranging as high as 4000 Td, only when a random assignment of excess energies between the primary and secondary particles is used.

Lattice kinetic Monte Carlo simulation of epitaxial growth of silicon thin films in H2/SiH4 chemical vapor deposition systems

The use of lattice kinetic Monte Carlo techniques for reproducing epitaxial growth of silicon using H2/SiH4 chemistry is described in this work. The implementation of the surface mechanisms is limited to silane and hydrogen adsorption, surface dissociation of higher order hydrides and recombinative hydrogen desorption. Good agreement between simulation and experimental results available in the literature was obtained for H2 desorption peak positions, equilibrium hydrogen coverages and Si growth rates. The formation of (111) and (113) planes is also reproduced, however no evidence of (131) was found even at 850° C, and (119) planes were not formed at the same position than actual grown structures.

Multi-scale modelling to relate beryllium surface temperature, deuterium concentration and erosion in fusion reactor environment

Beryllium (Be) has been chosen as the plasma-facing material for the main wall of ITER, the next generation fusion reactor. Identifying the key parameters that determine Be erosion under reactor relevant conditions is vital to predict the ITER plasma-facing component lifetime and viability. To date, a certain prediction of Be erosion, focusing on the effect of two such parameters, surface temperature and D surface content, has not been achieved. In this work, we develop the first multi-scale KMC-MD modeling approach for Be to provide a more accurate database for its erosion, as well as investigating parameters that affect erosion. First, we calculate the complex relationship between surface temperature and D concentration precisely by simulating the time evolution of the system using an object kinetic Monte Carlo (OKMC) technique. These simulations provide a D surface concentration profile for any surface temperature and incoming D energy. We then describe how this profile can be implemented as a starting configuration in molecular dynamics (MD) simulations. We finally use MD simulations to investigate the effect of temperature (300–800 K) and impact energy (10–200 eV) on the erosion of Be due to D plasma irradiations. The results reveal a strong dependency of the D surface content on temperature. Increasing the surface temperature leads to a lower D concentration at the surface, because of the tendency of D atoms to avoid being accommodated in a vacancy, and de-trapping from impurity sites diffuse fast toward bulk. At the next step, total and molecular Be erosion yields due to D irradiations are analyzed using MD simulations. The results show a strong dependency of erosion yields on surface temperature and incoming ion energy. The total Be erosion yield increases with temperature for impact energies up to 100 eV. However, increasing temperature and impact energy results in a lower fraction of Be atoms being sputtered as BeD molecules due to the lower D surface concentrations at higher temperatures. These findings correlate well with different experiments performed at JET and PISCES-B devices.

Continuum and Kinetic Simulations of Heat Transfer Trough Rarefied Gas in Annular and Planar Geometries in the Slip Regime

Steady-state heat transfer through a rarefied gas confined between parallel plates or coaxial cylinders, whose surfaces are maintained at different temperatures, is investigated using the nonlinear Shakhov (S) model kinetic equation and Direct Simulation Monte Carlo (DSMC) technique in the slip regime. The profiles of heat flux and temperature are reported for different values of gas rarefaction parameter δ, ratios of hotter to cooler surface temperatures T, and inner to outer radii ratio R. The results of S-model kinetic equation and DSMC technique are compared to the numerical and analytical solutions of the Fourier equation subjected to the Lin and Willis temperature-jump boundary condition. The analytical expressions are derived for temperature and heat flux for both geometries with hotter and colder surfaces having different values of the thermal accommodation coefficient. The results of the comparison between the kinetic and continuum approaches showed that the Lin and Willis temperature-jump model accurately predicts heat flux and temperature profiles for small temperature ratio T=1.1 and large radius ratios R≥0.5; however, for large temperature ratio, a pronounced disagreement is observed.

Time dependent modeling of single particle displacement damage in silicon devices

An approach combining molecular dynamics simulations with Kinetic Monte Carlo simulations is proposed to model the temporal evolution of single particle displacement damage in silicon. The three dimensional distributions of primary defects induced by Si recoils within 10ps are obtained by molecular dynamics simulations and subsequently the long-term evolution (over 105s) of multiple types of defects is simulated with Kinetic Monte Carlo technique fed by molecular simulation results. Based on classical Shockley–Read–Hall theory, the annealing factors of radiation-induced dark current related to the evolution of defects are predicted for photodiodes of 0.18μm CMOS image sensors under neutron irradiation. The calculation results are consistent with the experimental data.

Using atomistic simulations to model cadmium telluride thin film growth

Cadmium telluride (CdTe) is an excellent material for low-cost, high efficiency thin film solar cells. It is important to conduct research on how defects are formed during the growth process, since defects lower the efficiency of solar cells. In this work we use computer simulation to predict the growth of a sputter deposited CdTe thin film. On-the-fly kinetic Monte Carlo technique is used to simulate the CdTe thin film growth on the (1 1 1) surfaces. The results show that on the (1 1 1) surfaces the growth mechanisms on surfaces which are terminated by Cd or Te are quite different, regardless of the deposition energy ( eV). On the Te-terminated (1 1 1) surface the deposited clusters first form a single mixed species layer, then the Te atoms in the mixed layer moved up to form a new layer. Whilst on the Cd-terminated (1 1 1) surface the new Cd and Te layers are formed at the same time. Such differences are probably caused by stronger bonding between ad-atoms and surface atoms on the Te layer than on the Cd layer.

Multi-scale simulations of single particle displacement damage in silicon

Silicon devices are extensively used in space and other radiation-rich environments. They must withstand radiation damage processes that occur over wide range of time and length. Ion implantation technique, one of the most important process in the fabrication of integrated circuits, can also create the displacement damage in silicon lattice. Exposure of silicon wafer or silicon device to radiation causes the creations of variety of defects and has adverse effects on the electrical properties of devices. Although phenomenological studies on the radiation effects in silicon have been carried out in the past decades, the features of multi-scale of displacement damage make it difficult to characterize the defect production and evolution experimentally or theoretically. Recently, the silicon device with ultra-low leakage current was shown to be very sensitive to the permanent displacement damage induced by single particles, called single particle displacement damage (SPDD) event. To the best of our knowledge, the investigation of single particle displacement damage (SPDD) event in silicon device by the coupling molecular dynamics (MD) and kinetic Monte Carlo (KMC) techniques has not yet been reported so far. In this paper, MD simulations are combined with KMC simulations to investigate the formation and evolution of SPDD event in silicon. In MD simulations, Tersoff potential is used to describe the Si-Si atomic interactions. The potential smoothly joins to Ziegler-Biersack-Littmark potential that describes the energetic short range interactions well. All atoms in the MD cell are allowed to evolve 0.205 ns to track the damage production and short-term evolution. A multi-phase simulations are performed to improve the simulation efficiency. Then the nearest neighbor criterion is employed to identify the configurations and spatial distributions of interstitials and vacancies, which are used as input in KMC simulations to study the thermal diffusion and interactions of those defects in the time interval from 0.205 ns to 1000 s. The results show that no defects are missing when transferring from MD to KMC simulation and the whole damage obtained in MD simulations is reproduced in KMC simulations. Since the production and evolution of defects are simulated, the SPDD current could be calculated based on Shockley-Read-Hall theory. We derive the formula to calculate the SPDD current and its annealing factor related to interstitials and vacancies in the depletion region. The calculated annealing factors of defects are compared with the annealing factors of SPDD currents and also with the experimental results. The results show that an annealing factor of defects has the same value as the annealing factor of an SPDD current when only one type of defect is considered in the calculations, while there are some differences between these two annealing factors when two and more types of defects are considered. The annealing factors of defects can be used to represent the annealing behaviors of SPDD currents since the divergences between these two annealing factors are not significant. Finally, SPDD current annealing factor based MD simulation results obtained with Tersoff potential are compared with the results in our previous study in which the Stillinger-Weber potential is used, and also compared with experimental results. The comparisons show that the simulation results with considering both Stillinger- Weber potential and Tersoff potential are in good agreement with experimental results. Compared with the calculated results with considering the Tersoff potential, the results with considering the Stillinger-Weber potential are closer to experimental results.