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A simple one-dimensional Monte Carlo model has been developed to simulate the chemical vapour deposition (CVD) of a diamond (100) surface. The model considers adsorption, etching/desorption, lattice incorporation, and surface migration along and across the dimer rows. The top of a step-edge is considered to have an infinite Ehrlich-Schwoebel potent...
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Context 1
... block represents a generic C 1 adsorbing unit, which is most probably CH 3 but could be species such as C, CH, CH 2 or even CN. The adsorbed green block then has a number of possibilities, depending upon the local morphology where it landed, and each possible fate is tested sequentially at every time-step of the program. A block landing immediately adjacent to another block of any colour either to its left, right or both, is considered to undergo direct ER-type growth (see section 1.3 and figure 3). The block is coloured dark-blue and bonds to its neighbour, and remains there for the duration of the program. In this model, the diamond lattice itself (blue blocks) is considered unetchable, so once a moving block has added to the lattice, it cannot subsequently be removed (except in the special case of a β -scission reaction, see section 3.3). Alternatively, if the initial green block lands in a position with no blocks either to its left or right, the block can simply desorb (or be etched) back into the gas phase. Another random number, R 2 , is generated and compared with the probability of desorption/etching, P desorb (see section 2.2). If R 2 < P desorb the block desorbs and is removed. If the block remains on the surface, another possible fate for it is to stick permanently to form a static, unetchable defect (see section 1.3). A third random number R 3 is generated and compared with the probability for direct–defect formation, P dir − def . If R 3 < P dir − def the block is coloured black and attaches permanently to the lattice. If the block does not add to the lattice, desorb or permanently stick as a defect, then a final possibility is that it migrates. A fourth random number, R 4 , is generated and compared to the probability of migration, P mig (see later). If R 4 < P mig the block will jump left or right one space, with equal chance. If this block now finds itself next to another block of any colour, it will permanently bond to it and turn dark-blue. This is analogous to the LH model for growth (see section 1.3 and figure 3). But if the block still finds itself with no neighbours in its new position, it might form a static defect (with probability P jump − def ) in which case it is coloured brown, or remain temporarily adsorbed, ready to migrate again at the next time-step. P jump − def can be different from P dir − def since the mechanisms forming the static surface defect might be different in each case. There are two special cases that need to be considered. First, β -scission can be modelled by scanning the surface blocks after every time-step and identifying and deleting any 2- block pillars that may have arisen as a result of blocks landing or migrating (see figure 4). The probability that β -scission occurs, thereby deleting any individual 2-block pillar, is given by P beta . This can, in principle, be estimated from known reaction rates, but, in practice, is chosen to be either 0 ( β scission never happens) or 1 ( β -scission happens every time it is possible at each time-step). Second, there is the issue of blocks migrating off the top of step-edges (see section 1.2). Preliminary DFT calculations show that the probability of a migrating CH 2 group desorbing is not significantly different at the top of a (100) step-edge to that found anywhere else on the surface. This makes the ‘eagles’ scenario unlikely. Furthermore, the distance between the top and bottom of a step on the (100) diamond surface is too great to allow a migrating CH 2 group to bridge the gap (see figure 5). Hence, the ESP is effectively infinitely large, eliminating the ‘lemmings’ scenario as a plausible choice. Thus, we have adopted the ‘cowards’ scenario as the default process, and this choice leads directly to some of the surface morphologies that are predicted (see section 3.1). The program is cycled until it is stopped manually or until a set number of layers (typically 150 to provide statistical invariance) have grown, at which point the data are saved. Depending upon the choice of probabilities for the various events, the program can take from an hour to several hours to grow 150 layers (on a Pentium 4 PC). Thus, the evolution of the surface morphology can be directly viewed on the computer screen, giving insight into which parameters control different aspects of growth. In a Monte Carlo model of this type, the time-step is chosen to be equal to, or faster than, the fastest process occurring. This fastest process (which turns out to be surface migration) is normalized to give a probability of 1 (or less if required) to occur at each time-step, and the other processes are assigned probabilities based on their relative rates with respect to this fastest one. In order to simplify matters, we shall assume that the growth conditions are fixed for standard polycrystalline CVD grown at a substrate temperature of ∼ 900 ◦ C [17]. The first process to consider is the impact rate of CH 3 species on the surface. We shall assume that CH is the only ...
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Citations
... The observed 2s defects provide a remarkable validation of accepted models for (100) diamond CVD growth [31]. These models have previously been established through ab initio simulations [32], mesoscale modelling of growth rates and surface morphology [33,34], and plasma experiments and simulation [35]. The STM analysis presented here provides further experimental validation of this model at the atomic scale. ...
Near-surface nitrogen-vacancy centres are critical to many diamond-based quantum technologies such as information processors and nanosensors. Surface defects play an important role in the design and performance of these devices. The targeted creation of defects is central to proposed bottom-up approaches to nanofabrication of quantum diamond processors, and uncontrolled surface defects may generate noise and charge trapping which degrade shallow NV device performance. Surface preparation protocols may be able to control the production of desired defects and eliminate unwanted defects, but only if their atomic structure can first be conclusively identified. This work uses a combination of scanning tunnelling microscopy (STM) imaging and first-principles simulations to identify several surface defects on H:C(100)-2x1 surfaces prepared using chemical vapour deposition (CVD). The atomic structure of these defects is elucidated, from which the microscopic origins of magnetic noise and charge trapping is determined based on modelling of their paramagnetic properties and acceptor states. Rudimentary control of these deleterious properties is demonstrated through STM tip-induced manipulation of the defect structure. Furthermore, the results validate accepted models for CVD diamond growth by identifying key adsorbates responsible for nucleation of new layers.
... There are (at least) two pathways by which an incident CH 3 radical can proceed via CCH 3 in Eq. (9) to a surface CH 2 group: (i) chemisorption on a pure radical site C* (with all adjacent surface atoms terminated as CH sites) followed by H abstraction by an impinging gas phase H atom; and (ii) chemisorption at a biradical site C** (i.e. a surface radical site with another nearby C* site) followed by H atom transfer from the CCH 3 group to this adjacent site [1,36,49,52,53]. The surface CH 2 group deriving from an incident CH 3 radical can suffer a range of fates, including migrating on the diamond surface, being etched back into the gas phase (by incident H atoms) or ultimate incorporation into a diamond film (e.g. at a step edge) [1,49,[52][53][54][55][56][57][58]. To develop the model further first requires some estimation of the fraction of adsorbed CH 3 groups that are further converted to surface CH 2 groups, migrate and ultimately incorporate into the growing diamond film. ...
... into the surface C-C dimer bond implicated in the accepted model for such C insertion [1]). These authors also reported energetically feasible reaction sequences leading to new layer growth propagating from the surface-embedded N atom and suggested that such surface C-N dimer bonds might serve as 'super-nucleating' species [55] capable of accelerating G in cases where new layer formation is the rate limiting step for growth. Such ideas chime with our recent suggestion that an incorporated N-atom (or small N-containing species) might serve as an anchor, immobilizing adjacent CH 2 groups on the diamond surface and thereby facilitating the formation of new, small islands that provide additional step-edges and encourage further incorporation [3]. ...
... This picture requires surface embedded N atoms, which act as 'anchor' sites and offer a mechanism for reduced CH 2 surface migration and more step-edges for irreversible incorporation of such migrating groups. Such a picture chimes with the concept of 'super-nucleation' sites [55] such as the recently recognized stable moiety formed by CH 2 insertion into a C-N dimer bond on the 2 × 1 reconstructed (100) diamond surface [36]. ...
... All those works used an accurate description of the crystal lattice. A lighter framework was introduced by May et al., [15] with a crystal lattice simplified to aligned square blocks in two dimensions, and a growth description limited to 3 possible processes: adsorption, desorption and migration. The rates were obtained with a chemical model previously developed by the same team [16] and the KMC simulation results were in good agreement with those obtained with this model. ...
... The processes of activation and deactivation of surface sites are not taken into account in the KMC code, contrary to some other works [12,14,15]. In our case, the ratio of active sites R H , which has been given in [16], is taken into account in the adsorption rate. ...
... The sticking coefficient S has been set to various values in previous works [15,17]. However, it has been shown that the sticking coefficient varies with the substrate temperature [23]. ...
A 3D Kinetic Monte-Carlo (KMC) model is implemented and used to simulate the growth of (1 0 0)-oriented diamond films. The model considers four processes: adsorption and desorption of CH3 radicals, etching of carbon atoms and migration of adsorbed radicals. The atomic structure of diamond is taken into account including the formation of dimer rows on the surface. The model correctly reproduces the step-flow growth mechanism of diamond (1 0 0) surfaces and the obtained growth rates are close to experimental data. The propagation of the steps shows a clear anisotropy. Steps are usually two atomic layers high but step bunching can be observed in presence of defects. The model thus can be used as a predictive tool to obtain growth rates and to understand the effect of atomic interactions on the film morphology.
... Recent Monte-Carlo modeling has emphasized the importance of critical nuclei for propagating layer growth. These are immobile surface features, such as a lone C-C dimer, which act as nucleation points [35,36]. Furthermore, the inclusion of super-nucleating species in Monte-Carlo models has been found to catalyze diamond growth. ...
... These are adsorbates or surface defects (hypothesised to be N-based) which quickly form critical nuclei following formation. When growth is limited by nucleation of new layers (i.e., growth is dominated by step-flow), supernucleating species have demonstrated ten-fold enhanced growth rates [35]. The search for a N-based super-nucleating species is therefore well founded and forms the primary aim of this work. ...
... Under such circumstances, we propose that surface-embedded N acts as a super-nucleation species for new-layer C growth and subsequently the formation of critical nuclei on the surface. This provides an atomic mechanism for enhanced growth rates observed in some Monte-Carlo studies [35]. Note, however, that the catalytic mechanism identified here cannot be universal for all N-enhanced diamond growth, particularly that observed for diamond surfaces other than (100). ...
Nitrogen is frequently included in chemical vapour deposition feed gases to accelerate diamond growth. While there is no consensus for an atomistic mechanism of this effect, existing studies have largely focused on the role of sub-surface nitrogen and nitrogen-based adsorbates. In this work, we demonstrate the catalytic effect of surface-embedded nitrogen in nucleating new layers of (100) diamond. To do so we develop a model of nitrogen overgrowth using density functional theory. Nucleation of new layers occurs through C insertion into a C--C surface dimer. However, we find that C insertion into a C--N dimer has substantially reduced energy requirements. In particular, the rate of the key dimer ring-opening and closing mechanism is increased 400-fold in the presence of nitrogen. Full incorporation of the substitutional nitrogen defect is then facilitated through charge transfer of an electron from the nitrogen lone pair to charge acceptors on the surface. This work provides a compelling mechanism for the role of surface-embedded nitrogen in enhancing (100) diamond growth through the nucleation of new layers. Furthermore, it demonstrates a pathway for substitutional nitrogen formation during chemical vapour deposition which can be extended to study the creation of technologically relevant nitrogen-based defects.
... Initial experimental and theoretical work indicated that C 2 dimers play a critical role in the UNCD film nucleation and growth [1,13] because C 2 dimers have low activation energy (~ 6 kcal/ mol) for insertion into the substrate surface, thus establishing the nucleation characteristics of UNCD films. Modeling [14], subsequent to the first one [13] suggested that while the C 2 population in the plasma is high, the population near the surface may be low, and other hydrocarbon radicals (e.g., CH 3 , C 2 H 2 ) are also substantial or the main contributors to the UNCD film growth [14]. However, this model [14] did not fully explain the low temperature growth (≤ 400˚C) of UNCD films. ...
... Initial experimental and theoretical work indicated that C 2 dimers play a critical role in the UNCD film nucleation and growth [1,13] because C 2 dimers have low activation energy (~ 6 kcal/ mol) for insertion into the substrate surface, thus establishing the nucleation characteristics of UNCD films. Modeling [14], subsequent to the first one [13] suggested that while the C 2 population in the plasma is high, the population near the surface may be low, and other hydrocarbon radicals (e.g., CH 3 , C 2 H 2 ) are also substantial or the main contributors to the UNCD film growth [14]. However, this model [14] did not fully explain the low temperature growth (≤ 400˚C) of UNCD films. ...
... Modeling [14], subsequent to the first one [13] suggested that while the C 2 population in the plasma is high, the population near the surface may be low, and other hydrocarbon radicals (e.g., CH 3 , C 2 H 2 ) are also substantial or the main contributors to the UNCD film growth [14]. However, this model [14] did not fully explain the low temperature growth (≤ 400˚C) of UNCD films. Clearly, further experimental and theoretical work is need. ...
... Numerical simulation of the CVD generally follows two approaches: the first is based on Molecular Dynamics and Monte Carlo Simulation [4,5,6,7,8,9,10], and is aimed to a microscopic description of chemical process responsible of the surface coating and the film growth. The second possible approach is based on Computational Fluid Dynamics (CFD) and describes the process in terms of macroscopic quantities like the fluid density, specific momentum and spe-cific energy, as well as species concentrations in the fluid. ...
... This section describes the solution of the multi-parametric heat transfer model in terms of the AC frequency, the flow rate and the electrical input power. Eq. (4) is extended to the parametric domain: where 3,4,5), I rad = (7,11,12,13,14,15) and I h = (1, 3, 5). The Stefan-Boltzmann constant is denoted by ς = 5.67 · 10 −8 W/m 2 K 4 , while T 0 = 298 K is the ambient temperature. ...
Purpose
The purpose of this paper is to present a reduced order computational strategy for a multi-physics simulation involving a fluid flow, electromagnetism and heat transfer in a hot-wall chemical vapour deposition reactor. The main goal is to produce a multi-parametric solution for fast exploration of the design space to perform numerical prototyping and process optimisation.
Design/methodology/approach
Different reduced order techniques are applied. In particular, proper generalized decomposition is used to solve the parameterised heat transfer equation in a five-dimensional space.
Findings
The solution of the state problem is provided in a compact separated-variable format allowing a fast evaluation of the process-specific quantities of interest that are involved in the optimisation algorithm. This is completely decoupled from the solution of the underlying state problem. Therefore, once the whole parameterised solution is known, the evaluation of the objective function is done on-the-fly.
Originality/value
Reduced order modelling is applied to solve a multi-parametric multi-physics problem and generate a fast estimator needed for preliminary process optimisation. Different order reduction techniques are combined to treat the flow, heat transfer and electromagnetism problems in the framework of separated-variable representations.
... External conditions such as the temperature distribution within the chamber and walls [2] have a significant impact on the results. While film growth reactions between radicals and the growing film in CVD deposition can be studied e.g., by using the kinetic Monte Carlo simulation method [3] and also the involved multi-species gas phase reaction kinetics can be investigated in detail [4,5], this work focuses on the gas phase transport simulation within realistic three-dimensional HWCVD reactor geometries. ...
Hot wire chemical vapor deposition (HWCVD) is a powerful technology for deposition of high quality films on large area, where drawbacks of plasma based technology such as defect generation by ion bombardment and high equipment costs are omitted. While processes for diamond coatings using H2 and CH4 as precursor have been investigated in detail since 1990 and have been transferred to industry, research also focuses on silicon based coatings with H2, SiH4 and NH3 as process gases. HWCVD of silicon based coatings is a promising alternative for state-of-the-art radiofrequency-plasma enhanced chemical vapor deposition reactors. The film formation in HWCVD results from an interaction of several concurrent chemical reactions such as gas phase chemistry, film deposition, abstraction of surplus hydrogen bonds and etching by atomic hydrogen. Since there is no easy relation between process parameters and resulting deposition profiles, substantial experimental effort is required to optimize the process for a given film specification and the desired film uniformity. In order to obtain a deeper understanding of the underlying mechanisms and to enable an efficient way of process optimization, simulation methods come into play. While diamond deposition occurs at pressures in the range of several kPa HWCVD deposition of Si based coatings operates at pressures in the 0.1–30 Pa range. In this pressure regime, particle based simulation methods focused on solving the Boltzmann equation are computationally feasible. In comparison to computational fluid dynamics this yields improved accuracy even near small gaps or orifices, where characteristic geometric dimensions approach the order of the mean free path of gas molecules. At Fraunhofer IST, a parallel implementation of the Direct Simulation Monte Carlo (DSMC) method extended by a reactive wall chemistry model is developed. To demonstrate the feasibility of three-dimensional simulation of HWCVD processes on realistic reactor geometries, we present DSMC simulations of static silicon deposition profiles on steel substrates in an in-line HWCVD coater in comparison with accordant experiments.
... This growth model was then used as the basis for kinetic Monte Carlo (KMC) simulations of diamond growth. [16][17][18][19][20][21][22][23] Such simulations are based on a model diamond (usually (100)) surface and a set of all relevant processes, such as adsorption, etching/desorption, migration, and so on, and at each step of the simulation, a process is chosen with a probability proportional to its rate. Over the past 15 years, these KMC simulations have gradually become more sophisticated as the gas-phase and gassurface chemical processes have become better understood. ...
A three-dimensional kinetic Monte Carlo model has been developed to simulate the chemical vapor deposition of a diamond (100) surface under conditions used to grow single-crystal diamond (SCD), microcrystalline diamond (MCD), nanocrystalline diamond (NCD), and ultrananocrystalline diamond (UNCD) films. The model includes adsorption of CHx (x = 0, 3) species, insertion of CHy (y = 0-2) into surface dimer bonds, etching/desorption of both transient adsorbed species and lattice sidewalls, lattice incorporation, and surface migration but not defect formation or renucleation processes. A value of ∼200 kJ mol(-1) for the activation Gibbs energy, ΔG(‡) etch, for etching an adsorbed CHx species reproduces the experimental growth rate accurately. SCD and MCD growths are dominated by migration and step-edge growth, whereas in NCD and UNCD growths, migration is less and species nucleate where they land. Etching of species from the lattice sidewalls has been modelled as a function of geometry and the number of bonded neighbors of each species. Choice of appropriate parameters for the relative decrease in etch rate as a function of number of neighbors allows flat-bottomed etch pits and/or sharp-pointed etch pits to be simulated, which resemble those seen when etching diamond in H2 or O2 atmospheres. Simulation of surface defects using unetchable, immobile species reproduces other observed growth phenomena, such as needles and hillocks. The critical nucleus for new layer growth is 2 adjacent surface carbons, irrespective of the growth regime. We conclude that twinning and formation of multiple grains rather than pristine single-crystals may be a result of misoriented growth islands merging, with each island forming a grain, rather than renucleation caused by an adsorbing defect species.
... Recent modeling indicates that while the C 2 population in the plasma is high, the population near the surface may be low, and other hydrocarbon radicals (e.g., CH 3 , C 2 H 2 ) are also substantial or the main contributors to the UNCD fi lm growth. 6 This model, however, could not fully explain the low temperature growth ( ≤ 400°C) of UNCD fi lms. Clearly, more experimental and modeling studies are needed. ...
A novel multifunctional and biocompatible ultrananocrystalline diamond (UNCD) film technology developed recently represents a new material with a unique combination of functionalities, including biocompatibility, to enable a new generation of implantable medical devices and scaffolds for tissue engineering. Following a description of the synthesis and properties of UNCD films and a comparison with other diamond film technologies, this article focuses on descriptions of key UNCD-based medical devices to treat specific medical conditions requiring effective therapies: (1) A UNCD-coated microchip (artificial retina) implantable inside the eye on the retina to restore partial vision to people blinded by retinitis pigmentosa and macular degeneration produced by genetically induced degeneration of the retina photoreceptors. (2) A UNCD-coated intraocular device for treatment of glaucoma in the eye. (3) UNCD-coated metal dental implants with potential order of magnitude longer life and superior performance than current implants.
... 6 Methyl radical chemistry is important in the combustion of hydrocarbons 7,8 and chemical vapour deposition of diamond films. 9,10 In addition, methyl radicals may be an integral part of a catalytic cycle for partial oxidation of methane to formaldehyde or methanol for chemical feedstocks. 11 From a theoretical perspective, accurate close-coupling DCSs for methyl scattering are computationally tractable for collisions involving the H 2 or D 2 molecule because their large rotational constants [B(H 2 ) = 60.853 ...
Comparisons are presented of experimental and theoretical studies of the rotationally inelastic scattering of CD3 radicals with H2 and D2 collision partners at respective collision energies of 680 ± 75 and 640 ± 60 cm(-1). Close-coupling quantum-mechanical calculations performed using a newly constructed ab initio potential energy surface (PES) provide initial-to-final CD3 rotational level (n, k → n', k') integral and differential cross sections (ICSs and DCSs). The DCSs are compared with crossed molecular beam and velocity map imaging measurements of angular scattering distributions, which serve as a critical test of the accuracy of the new PES. In general, there is very good agreement between the experimental measurements and the calculations. The DCSs for CD3 scattering from both H2 and D2 peak in the forward hemisphere for n' = 2-4 and shift more to sideways and backward scattering for n' = 5. For n' = 6-8, the DCSs are dominated by backward scattering. DCSs for a particular CD3 n → n' transition have a similar angular dependence with either D2 or H2 as collision partner. Any differences between DCSs or ICSs can be attributed to mass effects because the PES is unchanged for CD3-H2 and CD3-D2 collisions. Further comparisons are drawn between the CD3-D2 scattering and results for CD3-He presented in our recent paper [O. Tkáč, A. G. Sage, S. J. Greaves, A. J. Orr-Ewing, P. J. Dagdigian, Q. Ma, and M. H. Alexander, Chem. Sci. 4, 4199 (2013)]. These systems have the same reduced mass, but are governed by different PESs.
