Kinetic Lattice Monte Carlo Model Research Articles

Size distribution of clusters and nucleation preference of trimers during SiC (0001) surface epitaxial growth under low coverage

In order to better understand the microscopic nucleation behavior during the epitaxial growth of a SiC crystal, a lattice kinetic Monte Carlo model is developed, in which Si and C particles are set as the basic elements. The events list is built up to implement group search and binary search, which can improve the efficiency of the algorithm. In addition, the Hoshen–Kopelman algorithm is also used to calculate the statistics of the properties of clusters. Then, the cluster size distribution function and the nucleation preference of trimers are analyzed. The results show that the cluster size distribution function obeys the Gauss distribution, and the proportion of crystal nuclei close to the average size gradually increases. Moreover, the growth temperature mainly affects the trapping rate of adatoms by dimers, and the C/Si ratio affects the formation of different types of dimers and the concentration of adatoms.

Effects of surface diffusion in electrocatalytic CO2 reduction on Cu revealed by kinetic Monte Carlo simulations.

Kinetic Monte Carlo (KMC) methods are frequently used for mechanistic studies of thermally driven heterogeneous catalysis systems but are underused for electrocatalysis. Here, we develop a lattice KMC approach for electrocatalytic CO2 reduction. The work is motivated by a prior experimental report that performed electroreduction of a mixed feed of 12CO2 and 13CO on Cu; differences in the 13C content of C2 products ethylene and ethanol (Δ13C) were interpreted as evidence of site selectivity. The lattice KMC model considers the effect of surface diffusion on this system. In the limit of infinitely fast diffusion (mean-field approximation), the key intermediates 12CO* and 13CO* would be well mixed on the surface and no evidence of site selectivity could have been observed. Using a simple two-site model and adapting a previously reported microkinetic model, we assess the effects of diffusion on the relative isotope fractions in the products using the estimated surface diffusion rate of CO* from literature reports. We find that the size of the active sites and the total surface adsorbate coverage can have a large influence on the values of Δ13C that can be observed. Δ13C is less sensitive to the CO* diffusion rate as long as it is within the estimated range. We further offer possible methods to estimate surface distribution of intermediates and to predict intrinsic selectivity of active sites based on experimental observations. This work illustrates the importance of considering surface diffusion in the study of electrochemical CO2 reduction to multi-carbon products. Our approach is entirely based on a freely available open-source code, so will be readily adaptable to other electrocatalytic systems.

Effect of Temperature on the Morphology of Planar GaAs Nanowires (Simulation)

The self-catalyzed growth of planar GaAs nanowires is analyzed using the lattice kinetic Monte Carlo model. Vapor–liquid–solid nanowire growth on (111)A and (111)B substrates is investigated. The effect of temperature and the location of gallium droplets on the morphology and growth direction of planar GaAs nanowires is examined. The temperature range of the stable growth of planar GaAs nanowires on the GaAs(111)A surface is revealed. Special asymmetric arrangement of the droplets is shown to ensure unidirectional nanowire growth.

Влияние температуры на морфологию планарных нанопроволок GaAs (моделирование)

Using a kinetic lattice Monte Carlo model, the self-catalyzed growth of planar GaAs nanowires was analyzed. The nanowire growth via the vapor-liquid-crystal mechanism was considered. The effect of temperature and the catalyst droplet location on the morphology and growth direction of planar GaAs nanowires was studied. For GaAs(111)A and GaAs(111)B substrates, a temperature range corresponding to stable growth of planar GaAs nanowires was revealed. The special asymmetric arrangement of droplets allows the one-directional nanowire growth.

Initial Stages of Planar GaAs Nanowire Growth—Monte Carlo Simulation

The initial stages of planar self-catalyzed GaAs nanowire growth via the vapor-liquid-solid mechanism are considered by a kinetic lattice Monte Carlo model. The shapes of the nanocrystals being formed under a catalyzed droplet are presented for three GaAs substrate orientations (111)A, (111)B, (001). The most stable planar GaAs nanowire growth was observed on GaAs(111)A substrates.

Monte Carlo Simulation of Ga Droplet Movement during the GaAs Langmuir Evaporation

A kinetic lattice Monte Carlo model is used to study the Ga droplets self-propelled motion along GaAs(111)A and (111)B surfaces during the initial stage of high-temperature annealing. An estimation of the droplet velocity, running along (111)A and (111)B surfaces, in a wide temperature range, is carried out. The mechanism of small Ga drops movement during high-temperature annealing is suggested. Different directions of droplets motion and the morphology of drop-crystal interface on (111)A and (111)B substrates are determined by a difference in the etching rate of (111)A and (111)B facets by liquid gallium. It is shown that metal droplets can cause step bunching.

Analysis of the statistical and convergence properties of ionic transport coefficients with application to the solid electrolyte Li2OHCl

The challenge of computing ionic transport coefficients from first principles is to achieve the necessary convergence with respect to system size, simulation time, and configurational sampling. Unfortunately current computer resources are not yet available for such convergence studies at the fully first principles level. In this work, a lattice kinetic Monte Carlo model is used to study the convergence properties of transport coefficients, using the Li sub-lattice of the Li ion electrolyte Li2OHCl as an example system. The specific transport coefficients representing tracer diffusion, effective diffusion, and mobility are carefully studied for their convergence properties. Additionally, ion pair correlations of the effective diffusion are recast as a sum over events which allows for a detailed study of the nature of the correlation in terms of time and spatial separation. This experience suggests a general method of performing simulations by using first a kinetic Monte Carlo model followed by a first principles molecular dynamics study. For the Li2OHCl system, the kinetic Monte Carlo results provide both a reference for the Haven ratio due to purely geometric effects and a measure of the computational effort needed to obtain meaningful molecular dynamics results. The combination of the two methods provides further evidence of anti-correlated Li-ion motion in this system as predicted in a previous study.

Concentric GaAs nanorings formation by droplet epitaxy — Monte Carlo simulation

A kinetic lattice Monte Carlo model is used to study the GaAs nanorings growth by droplet epitaxy. The dependences of GaAs nanoring morphology on temperature, arsenic flux and the surface density of gallium droplets are analyzed. The condition of single, double and triple rings formation is discussed. It is demonstrated that the nanoring shape depends on the relationship between the value of gallium diffusion length along the surface and the distance between Ga droplets. The necessary condition for double ring formation – the distance between the drops should exceed the gallium diffusion double length. The variants of the single ring growth are considered.

Simulated growth of GaAs nanowires: Catalytic and self-catalyzed growth

The kinetic lattice Monte Carlo model of GaAs nanowire growth by the vapor-liquid-crystal mechanism is suggested. The catalytic and self-catalyzed growth of nanowires on the GaAs (111)B surface is simulated. The dependence of the morphology of the growing nanowires on the growth parameters is demonstrated. Upon self-catalyzed growth with gallium drops serving as the growth catalyst, the growth rate of the nanowires linearly depends on the arsenic flow in a wide range of arsenic flow rates. The decreasing dependence of the self-catalyzed growth rate of the nanowires on the initial gallium drop diameter is less steep, and the optimal growth temperature is higher than that for catalytic growth. It is shown that self-catalyzed growth is more sensitive to the ratio between the gallium and arsenic flow rates than catalytic growth.

Study of millisecond laser annealing on recrystallization, activation, and mobility of laser annealed SOI doped via arsenic ion implantation

Millisecond anneal techniques have been demonstrated to achieve fully recrystallized, highly activated, shallow, and abrupt junctions in silicon with both p- and n-type dopants due to the technique's fast time scale and high temperature. To understand and model the effects of millisecond laser annealing, knowledge of the true thermal profile experienced by the active semiconductor region must be known. This work simulates the impacts of a scanning laser in a series of shallow implants, and compares those results to experimental results. Arsenic ion (As+) implant energies of 10, 19, and 25 keV at doses of 1.5 × 1015 and 3 × 1015 cm−2 into a silicon-on-insulator substrate are studied to achieve different doping levels and amorphization depths. The recrystallization, activation, and mobility of the laser annealed, ion implanted experimental cells are then analyzed. For each experiment, Sentaurus technology computer aided design is used to create a calibrated 2D laser model to approximate the thermal budget of the lasing recipes (850–1250 °C) then using that output as an input into lattice kinetic Monte Carlo (LKMC) to simulate the solid phase epitaxial regrowth (SPER) during anneal of the various implant conditions. Sheet resistance and Hall effect measurements were used to correlate dopant activation and mobility with the regrowth process during laser anneal, showing the onset of high conductivity associated with completion of SPER in the films. The LKMC model shows an excellent agreement with cross section transmission electron microscopy, correlating the increase of conductivity with completion of crystal regrowth, increased activation, and crystal quality at various temperatures. Shallow, lower dose implants are capable of single crystal regrowth, producing high levels of activation >1 × 1020 cm−2 and nominal mobilities for highly arsenic-doped silicon. However, higher energy implants that fully amorphize the film regrow polycrystalline silicon with low mobilities even at very high temperatures (1250 °C), unsuitable for source–drain formation in logic devices.

Multiscale modeling of defect formation during solid-phase epitaxy regrowth of silicon

This work presents a multiscale approach to understanding the defect formation during the evolution of solid-phase epitaxy regrowth in Si. A molecular dynamics (MD) simulation technique has been used to elucidate the defect formation mechanisms, as well as to determine their nature. A hybrid lattice kinetic Monte Carlo (LKMC)–finite element method (FEM) model fed by the outcome of MD was subsequently implemented. It scales up the simulation times and sizes, while reproducing the important features of the defected regrowth predicted previously. FEM calculations provide the strain pattern due to the density variation between the amorphous and crystalline phases, which is then taken into account by the LKMC model by including the effect of the strain in the rates of recrystallization. Overall, this multiscale modeling provides a physical explanation of the generation of defects and its relation with the presence of strain. The model also captures the character of formed defects. It distinguishes two types: twins formed at {111} planes and dislocations produced by the collapse of the two recrystallization fronts. Simulation results are validated by comparing them with significant experiments reported in the literature.

Substrate orientation dependence on the solid phase epitaxial growth rate of Ge

The solid phase epitaxial growth process has been studied at 330 °C by transmission electron microscopy for Ge wafers polished at 10°–15° increments from the [001] to [011] orientations. The velocity showed a strong dependence on substrate orientation with the [001] direction displaying a velocity 16 times greater than the [111] direction. A lattice kinetic Monte Carlo model was used to simulate solid phase epitaxial growth (SPEG) rates at different orientations, and simulations compared well with experimental results. Cross sectional transmission electron microscopy and plan view transmission electron microscopy revealed stacking fault and twin defect formation in the [111] orientation where all other orientations showed only hairpin dislocations. The twin defects formed from Ge SPEG were comparatively less dense than what has previously been reported for Si, which gave rise to higher normalized velocities and a constant [111] SPEG velocity for Ge.

Understanding Si(111) solid phase epitaxial regrowth using Monte Carlo modeling: Bi-modal growth, defect formation, and interface topology

This work studies the intriguing experimental observations that Si(111) solid phase epitaxial regrowth velocity is not constant as recrystallization progresses, but has a sudden change after recrystallization of ≈100 nm and progresses faster afterward.[L. Csepregi, J. W. Mayer, and T. W. Sigmon, Appl. Phys. Lett. 29(2), 92 (1976)] These two modes have important implications in the quality of the recrystallized silicon. The first recrystallization produces a flat advancing front leaving a heavy dense network of small and parallel to the surface twins behind, while the second mode creates a more rough advancing front that leaves bigger, although less dense inclined twins. By using a comprehensive and efficient lattice kinetic Monte Carlo model that explicitly accounts for the formation of different crystalline twin orientations, we simulate and expose the physical explanation of such observations. We explain the origin for the formation and subsequent evolution of different type of twins (parallel to the interface and inclined) and its implication in the overall evolution of Si(111) recrystallization.

A blend of first-principles and kinetic lattice Monte Carlo computation to optimize samarium-doped ceria

Solid oxide fuel cells (SOFCs) have been acknowledged as a possible future source for clean and efficient electric power generation. One of the most important goals in the SOFCs research is to decrease the operating temperature, which in turn will improve the stability and decrease the cost of various components enabling its widespread utilization. For realizing the aforementioned goal, it is imperative to identify suitable electrolyte materials that show enhanced conductivity in the intermediate temperature range (773–1,073 K). Sm-doped ceria (SDC) is considered a promising candidate for use as an electrolyte material for SOFC operation in intermediate temperature range due to the high oxygen ion conductivity. In this article, we present a theoretical investigation using first-principles and kinetic lattice Monte Carlo (KLMC) computations to highlight the trends in oxygen ion conductivity as a function of dopant content and temperature in SDC. Using first-principles calculations, oxygen vacancy formation and migration were examined at first, second, and third nearest neighbor positions to a Sm ion. The activation energies for oxygen vacancy migration along various pathways in SDC computed using first-principles were used as input to the KLMC model to study vacancy mediated diffusion. SDC with 20 % mole fraction of dopant content yields the maximum conductivity, which is in very good agreement with experimentally identified compositions. Rationale for increase in conductivity as a function of increase in dopant content and subsequent decrease in conductivity at higher dopant fractions in SDC is presented. This combined methodology of first-principles and KLMC computations is a useful tool for the design and identification of various ceria-based electrolyte materials used in SOFCs.

Predicting the optimal dopant concentration in gadolinium doped ceria: a kinetic lattice Monte Carlo approach

Gadolinium doped ceria (GDC) is a promising alternative electrolyte material for solid oxide fuel cells that offers the possibility of operation in the intermediate temperature range (773–1073 K). To determine the optimal dopant concentration in GDC, we have employed a systematic approach of applying a 3D kinetic lattice Monte Carlo (KLMC) model of vacancy diffusion in conjunction with previously calculated activation energies for vacancy migration in GDC as inputs. KLMC simulations were performed including the vacancy repelling effects in GDC. Increasing the dopant concentration increases the vacancy concentration, which increases the ionic conductivity. However, at higher concentrations, vacancy–vacancy repulsion impedes vacancy diffusion, and together with vacancy trapping by dopants decreases the ionic conductivity. The maximum ionic conductivity is predicted to occur at ≈20% to 25% mole fraction of Gd dopant. Placing Gd dopants in pairs, instead of randomly, was found to decrease the conductivity by ≈50%. Overall, the trends in ionic conductivity results obtained using the KLMC model developed in this work are in reasonable agreement with the available experimental data. This KLMC model can be applied to a variety of ceria-based electrolyte materials for predicting the optimum dopant concentration.

Importance of twin defect formation created by solid-phase epitaxial growth: An atomistic study

A lattice kinetic Monte Carlo model is used to show the importance of twin defect formation created during solid-phase epitaxial growth (SPEG) to properly account for SPEG rates at different silicon substrate orientations. In particular, SPEG defect creation is fundamental to understanding the growth velocities in substrate angles close to Si(3 1 1) and Si(1 1 1). The model is compared with experimental observations and shows the feedback of twin defects on SPEG rates, shape evolution and interface roughness for different Si substrates.

{111} local configurations: The main source of silicon defects during solid phase epitaxial regrowth modeled by lattice kinetic Monte Carlo

A lattice kinetic Monte Carlo model for defect generation during solid phase epitaxial regrowth (SPER) is presented. It assumes two simple causes for defective Si formation: amorphous atoms in local {111} configurations having a probability to become defective and random nucleation and growth creating alternative crystalline seeds. Simulations are compared with experimental results for (001) and (011) Si substrates with different topologies and aligned to ⟨100⟩ and ⟨110⟩ crystalline axes, showing the model accuracy and validating its assumptions. {111} local recrystallization is the main cause for defective Si generation during SPER, by providing the seeds for defects propagated by SPER.

Kinetic lattice Monte Carlo model for oxygen vacancy diffusion in praseodymium doped ceria: Applications to materials design

Kinetic lattice Monte Carlo (KLMC) model is developed for investigating oxygen vacancy diffusion in praseodymium-doped ceria. The current approach uses a database of activation energies for oxygen vacancy migration, calculated using first-principles, for various migration pathways in praseodymium-doped ceria. Since the first-principles calculations revealed significant vacancy–vacancy repulsion, we investigate the importance of that effect by conducting simulations with and without a repulsive interaction. Initially, as dopant concentrations increase, vacancy concentration and thus conductivity increases. However, at higher concentrations, vacancies interfere and repel one another, and dopants trap vacancies, creating a “traffic jam” that decreases conductivity, which is consistent with the experimental findings. The modeled effective activation energy for vacancy migration slightly increased with increasing dopant concentration in qualitative agreement with the experiment. The current methodology comprising a blend of first-principle calculations and KLMC model provides a very powerful fundamental tool for predicting the optimal dopant concentration in ceria related materials.

A density functional study of defect migration in gadolinium doped ceria

Oxygen ion conductivity of doped ceria is observed to be two-three orders of magnitude higher than yttria stabilized zirconia, the most widely used solid electrolyte material at temperatures below 600 degrees C. Gadolinium doped ceria (GDC) is known to be one of the most promising solid electrolyte materials for operation of solid oxide fuel cells below 600 degrees C. To understand the atomic defect migration in GDC, we have used total energy calculations within the framework of density functional theory to follow oxygen vacancy migration in GDC. We report activation energies for various oxygen vacancy migration pathways in GDC. Oxygen vacancy formation and migration were evaluated for first, second, and third nearest neighbor positions to a Gd(3+) ion. Due to the comparable ionic radii of Gd(3+) and host Ce(4+) ions, the first nearest neighbor site with respect to the dopant cation is found to be the most favorable oxygen vacancy formation site. The migration pathway where the vacancy migrates from a second to first nearest neighbor is found to be most favorable. The calculated activation energies for oxygen vacancy migration in GDC are compared against the reported measured and calculated values from the literature. This work will provide a foundation for the development of a kinetic lattice Monte Carlo model for vacancy diffusion in GDC, which will improve the understanding of oxygen ion conductivity in doped ceria.

Facet formation during solid phase epitaxy regrowth: A lattice kinetic Monte Carlo model

An atomistic model to account for the formation of facets during solid phase epitaxy regrowth (SPER) is shown. This model relies on a lattice kinetic Monte Carlo approach. The lattice atoms produce different crystalline planes growing with different planar velocities. In particular, the model explains the arrow tip formation during SPER of thin silicon fins typical for fin field effect transistors and the formation of trenches in rectangular-shaped amorphized regions in (001) and (011) silicon, caused by the distortion of the lattice by shear strain and propagated by (111) facets.