Deal-Grove Model Research Articles

Pressure-Controlled Layer-by-Layer to Continuous Oxidation of ZrS2(001) Surface

Understanding oxidation mechanisms of layered semiconducting transition-metal dichalcogenides (TMDC) is important not only for controlling native oxide formation but also for synthesis of oxide and oxysulfide products. Here, reactive molecular dynamics simulations show that oxygen partial pressure controls not only the ZrS2 oxidation rate but also the oxide morphology and quality. We find a transition from layer-by-layer oxidation to amorphous-oxide-mediated continuous oxidation as the oxidation progresses, where different pressures selectively expose different oxidation stages within a given time window. While the kinetics of the fast continuous oxidation stage is well described by the conventional Deal-Grove model, the layer-by-layer oxidation stage is dictated by reactive bond-switching mechanisms. This work provides atomistic details and a potential foundation for rational pressure-controlled oxidation of TMDC materials.

Atomic and close-to-atomic scale polishing of Lu2O3 by plasma-assisted etching

This study presents a new method of in-process plasma-assisted etching (PaE) integrated with low-pressure polishing of lutetium oxide with high efficiency and without subsurface damage (SSD). The necessity of integrated low-pressure polishing is demonstrated through a quantum chemistry simulation. An improved Deal–Grove model for plasma treatment is established to predict the modification behavior. A modification rate of 136 nm/h can be obtained by simultaneously optimizing the plasma process. An atomically flat and SSD-free surface with a surface roughness in Sa of 0.14 nm is accomplished. The overall processing time is decreased to half the time of low-pressure slurry polishing. The new method is based on the OH* irradiation of lutetium oxide and the conversion of lutetium oxide into hydroxide, which rapidly reacts with 25% sulfuric acid droplets. The rapid planarization of the surface is then quickly realized by short low-pressure polishing. Finally, the in-process PaE quickly removes the SSD caused by low-pressure polishing. Aberration-corrected transmission electron microscopy of machined surfaces reveals the removal of the mechanically induced damage. The study shows that the new method has great potential as an environment-friendly processing technique in SSD-free finishing.

Ab initio -based approach for the oxidation mechanisms at SiO2 /4H-SiC interface: Interplay of dry and wet oxidants during interfacial reaction

Effects of the coexistence of dry and wet oxidants on the reaction process at ${\mathrm{SiO}}_{2}$/4H-SiC(0001) and ($000\overline{1}$) interfaces during SiC oxidation are systematically investigated by performing ab initio calculations. We find characteristic features of the interfacial reaction mechanisms, which are dependent on the plane orientation and wet oxidation condition. The incorporation of wet oxidants leads to lower barrier heights for the reaction of ${\mathrm{O}}_{2}$ molecules, resulting in the promotion of interfacial reaction at the ${\mathrm{SiO}}_{2}$/4H-SiC(0001) interface. In contrast, the coexisting ${\mathrm{O}}_{2}$ molecule assists the reactions by ${\mathrm{H}}_{2}\mathrm{O}$ molecule and OH groups at the ${\mathrm{SiO}}_{2}$/4H-SiC($000\overline{1}$) interface. Furthermore, we estimate the linear rate constants in the Deal-Grove model using the calculated barrier heights and reveal that the preferable wet ambient condition at the ${\mathrm{SiO}}_{2}$/4H-SiC(0001) interface is different from that at the ${\mathrm{SiO}}_{2}$/4H-SiC($000\overline{1}$) interface. The difference in the rate constants is caused by the difference in the rate-limiting reaction pathway between ${\mathrm{SiO}}_{2}$/4H-SiC(0001) and ($000\overline{1}$) interfaces. These calculated results offer better understanding of the atom-scale mechanisms for the significant enhancement of SiC oxidation by the interplay of dry and wet oxidants.

Oxidation kinetics of SiC in microwave oxygen plasma

A kinetic insight into microwave plasma oxidation on 4H-SiC is of great importance to improve the quality of SiO2 dielectric and SiO2/SiC interface in SiC MOSFETs. In this work, quantitative study on SiC plasma oxidation has been performed for a wide range of oxidation conditions by using Massoud’s empirical relation. In this relation, an additional exponential term related to the diffusion coefficient, the oxidation coefficient and the emission ratio of Si and C is introduced to describe the deviation of oxidation behavior relative to the Deal-Grove model. In plasma oxidation, the exponential term is dominant, especially in the growth-rate enhancement stage. Moreover, the contribution of the exponent increases with increasing temperature. Finally, a plausible kinetic model is proposed by considering exchange in the surface region, diffusion in oxide and reaction at the SiO2/SiC interface.

Thermal oxidation rates and resulting optical constants of Al0.83In0.17N films grown on GaN

The thermal oxidation rates of Al0.83In0.17N layers grown lattice-matched to GaN and the oxide's optical constants are studied. The ∼230 nm thick AlInN layers are placed into a horizontal furnace at elevated temperatures and exposed to either O2 (dry) or H2O vapor with an N2 carrier gas (wet). The samples are oxidized at different temperatures (830–870 °C) and at a constant time or at various times at a constant temperature of 830 °C. Spectroscopic ellipsometry is used to determine the oxide thicknesses, refractive index, and extinction coefficients. The oxidation rate for the wet conditions is faster than for the dry conditions, and both increase with temperature, as expected. However, the oxidation rate is also dynamic with time and can be fitted with the Deal–Grove model, suggesting reaction rate and diffusion-limited processes like other more mature semiconductors. Finally, the dry conditions produce oxides that expand more than the oxides produced under wet conditions. The ability to thermally oxidize Al0.83In0.17N layers lattice-matched to GaN is a promising process technique for producing new III-nitride-based electronic devices.

Experimental investigation and mathematical modelling of water vapour corrosion of Ti3SiC2 and Ti2AlC ceramics and their mechanical behaviour

Commercially available Ti3SiC2 and Ti2AlC ceramics were used in this study to investigate their wet corrosion and mechanical behaviour as they were under investigation for years for their applications in the field of nuclear as cladding materials and aerospace. The test coupons of dimension 3 × 4 × 40 mm3 and 3 × 4 × 20 mm3 were machined out from commercially available samples for the 3-pt bend test and wet corrosion test, respectively. The water vapour corrosion studies of these samples were carried out at 800 ℃, 1000 ℃, 1200 ℃ for 10, 20 and 100 h in gas flow condition containing 50 % steam + 50 % air. Phase analysis of the as-received Ti3SiC2 and Ti2AlC ceramics revealed the presence of other impurity phases such as TiC and TiSi2. The XRD patterns of the oxidised samples show the formation of rutile as the major phase in both materials. The oxidation layer formed on Ti3SiC2 sample was measured to be 280 μm after exposing the sample in steam for 100 h at 1200 °C. The water vapour corrosion studies reveal that Ti2AlC has high oxidation resistance compared with the Ti3SiC2 due to the formation of protective layers of TiO2 and Al2O3 which resulted in reduced weight gain and oxidation layer thickness. Three-point bend tests were conducted at room temperature for the samples after the water vapour corrosion test at 1000 °C/100 h. The TAC samples showed no degradation in the bending strength (244 MPa) whereas the TSC samples showed reduced strength of 320 MPa. The tensile strength of the samples was measured at room temperature and hydrothermal condition (250 °C and 250 bars pressure) and it was observed that Ti3SiC2 had high tensile strength (190 MPa) in hydrothermal conditions. The tensile strength results were validated using Finite element analysis (FEA) using ANSYS and the FEA results showed a negligible variance of 7 % compared with experimental method. Mathematical modelling based on one dimensional solution of diffusion equation combined with Deal-Grove model was employed to study and compare the oxidation thickness for the linear and parabolic models for the ceramics. The model was effective in validating the oxidation thickness of Ti3SiC2 showing that the experimental thickness was closer to that of mathematical model.

Deal–Grove model revisited for a new insight into the oxidation of molten aluminum alloy: The A356 alloy, as a model system

AbstractOxidation of A356 aluminum alloy at molten state is investigated from thermogravimetric analyses. Linear kinetics followed by unexpected logarithmic kinetics is observed during the oxidation process. Scanning electron microscopy imaging coupled with wavelength‐dispersive X‐ray spectroscopy analyses reveal a heterogeneous oxide layer composed of spinel (MgAl2O4) embedded in a nonoxidized alloy matrix. Nonlinear diffusion of magnesium through the heterogeneous oxide layer is the key mechanism proposed to explain the logarithmic kinetics. The growth of spinel phase causes a growing complexification of the aluminum network through which magnesium is diffusing. To model the magnesium transport through the oxide layer, an effective diffusion coefficient, build from the pioneering approach developed by Davies et al. (Davies, D., Evans, U. & Agar, J. (1954) Proc. Roy. Soc. London. A., 225, 443), is introduced in the Deal–Grove model.

Thermodynamic insights into Henry's constant in hyperthermal oxidation of silicon for fabricating optical waveguides.

Hyperthermal oxidation of silicon is envisaged to be an alternative to silicon-on-insulator (SOI) waveguide fabrication for photonic integrated circuit (PIC) devices, and thus the local oxidation of silicon (LOCOS) technique has attracted attention. In this article, starting with the thermodynamic insights into the Deal-Grove model for defining the thermal oxidation, we model the Henry's law constant in the silicon oxidation process with the ensemble contributions of thermodynamic and chemical energies, and extract an empirical model with the published statistical data. Then, the simulations show the dramatic temperature/time dependences of Henry's constant, and the different effects of the thermodynamic and chemical energies. Systematic simulations of the temperature/time dependences of both the growth rate and thickness of oxide are carried out where the temperature dependence of the oxidant diffusivity is also considered. Consequently, the simulation results from the two models astonishingly agree with each other. Typically, at 1100 °C, with a 3 h oxidation time, 2.10 and 1.34 μm SiO2 layers can be grown with the thermodynamic model under two diffusivity models, while with the empirical one, the two extreme cases can grow 2.10 and 1.28 μm SiO2 layers, respectively.

A novel Deal–Grove‐inspired model for fluorine‐based plasma jet etching of borosilicate crown optical glass

AbstractThe Deal–Grove model is a state‐of‐the‐art approach proposed for describing the thermal oxidation of silicon and the oxide thickness over time. In this study, the Deal–Grove concept provided the inspiration for a mathematical model for simulating plasma jet‐based dry etching process of borosilicate crown glass (N‐BK7®). The whole process is contained in two so‐called Deal–Grove parameters, which are extracted from experimental data including local etching depth and surface temperature distribution. The proposed model is extended for the evolution of dynamic etch profiles, and the obtained results are validated experimentally. By establishing such a model, it is possible to predict the effect of the residual layer and surface temperature on the evolution of local etching depths over dwell time.

Surface oxidation of transition metal sulfide and phosphide nanomaterials

Many transition metal sulfides and phosphides are susceptible to surface oxidation under ambient conditions. The formed surface oxidation layer, which is likely to further restructure under reaction conditions, alters the chemical properties of the pristine material but has not been well studied. In this work, we for the first time use X-ray photoelectron spectroscopy to quantify the natural surface oxidation of transition metal phosphide and sulfide nanoparticles and employ a simplified Deal-Grove model to analyze the kinetics. We show that CoS2 oxidizes faster than CoS whereas CoP2 is more difficult to oxidize compared to CoP, and there exists an inverse correlation between the surface oxidation rate and the Co-S/P distance in the pristine structure. More inclusive investigation unveils different types of surface oxidation behavior: CoS, NiS and FeS are limited by their reactivity with oxygen; CoS2 is the most reactive and its oxidation is governed by oxygen diffusion; CoP2 is influenced by both reactivity and diffusion; CoP, Ni2P, Cu3P and MoP exhibit high initial oxidation degrees and the kinetics are not well-defined; MoS2 is largely stable against oxidation.

In Situ Measurement of Phase Boundary Kinetics during Initial Lithiation of Crystalline Silicon through Picosecond Ultrasonics

Studying the kinetics of phase transformation and phase boundary propagation during initial lithiation of silicon electrodes in lithium ion batteries is relevant to understanding their performance. Such studies are usually challenging due to the difficulties in measuring the phase boundary velocity in the interior of the sample. Here we introduce a non-invasive, in situ method to measure the progression of the phase boundary in a planar specimen geometry while maintaining well-controlled lithium flux and potential. We developed an apparatus integrating an electrochemical cell with picosecond ultrasonics to probe the propagating phase boundary in real time. Phase propagation during initial lithiation of crystalline silicon, which is an example of a high capacity anode, is investigated. The primary objective of this manuscript is to report on the experimental technique development and some preliminary results. For lithiation normal to the (100) plane, we observe the phase boundary velocity to be approximately 12 pm/s and x to be 3.73 in LixSi under galvanostatic lithiation with a current density of 40 μA/cm2. The growth rate of the lithiated phase and the reaction rate coefficient are examined using a Deal-Grove type model.

Nanometer-scale oxidation of Silicon surface by ICP plasma

An experimental study of growth kinetic of silicon oxide during the initial stage of plasma enhanced oxidation is performed. Measurements were done in situ by means of spectroscopic ellipsometry with time resolution of 1 s. It was shown that oxidation of silicon in plasma does not comply with Deal-Grove model of oxidation. Measurements of concentration of oxygen in plasma and ion flux were performed to define mechanisms of oxidation. Obtained results could be applied for the development of multistage plasma processes involved in formation of nanostructures in advanced processes like atomic layer etching (ALE) and area selective atomic layer deposition.

Oxidation of ß-SiC at high temperature in Ar/O2, Ar/CO2, Ar/H2O gas mixtures: Kinetic study of the silica growth in the passive regime

The kinetics of silica growth during passive oxidation of SiC was studied using an original interferometric method carried out in a reactor specifically designed for that purpose. The influence of various oxidant species, O2, H2O, CO2 as well as their mixtures was investigated in a high temperature domain ranging from 1550 °C to 1850 °C at atmospheric pressure. This method is an efficient way to measure the various oxidation regimes usually described by the Deal-Grove model. Both the linear and parabolic rate constants are found to be independent of gas phase composition above 1700 °C, and to increase with oxygen partial pressure below 1700 °C for PO2 > 20 kPa. In the parabolic growth regime, we observed a transition from a low temperature interstitial-dominant to a high temperature network-dominant oxygen transport in the silica scale. The present results suggest the existence of a similar transition in the linear growth regime.

Investigation of anodic oxidation mechanism of 4H-SiC (0001) for electrochemical mechanical polishing

In an attempt to realize the high-quality and highly efficient polishing of SiC, the anodic oxidation mechanism of SiC was studied to enable the application of electrochemical mechanical polishing (ECMP). Through linear scanning voltammetry (LSV) and anodic oxidation experiments, the etch pits on the processed surface were found to be generated by oxidation on the sites where breakdown occurs in the anodic oxidation process. The origin of the etch pits was investigated through observing the same area on a SiC substrate during the oxidation process using atomic force microscopy (AFM), and they were confirmed to be atomic-scale pits mechanically introduced in the chemical mechanical polishing (CMP) process. The Deal-Grove model was used to model the growth process of the etch pits. It was found that their growth is controlled by a charge transfer process in the initial growth stage, which changes to a diffusion process in the late growth stage. The results of this research provide a reference for obtaining atomically smooth SiC surfaces by applying ECMP.

Evaluation of effective length of the enhanced oxidation of active oxygen produced using SrTixMg1−xO3−δ catalyst for low-temperature oxidation

Thermal oxidation using the SrTixMg1−xO3−δ catalyst to produce oxygen atoms in a furnace is investigated to determine the effective length of the enhanced oxidation of atomic oxygen. An experimental study was carried out by placing the catalyst material at the side of a Si wafer in a furnace and measuring the thickness of silicon dioxide. The activation energy of linear rate constant in the Deal–Grove model was found to decrease with decreasing distance from the catalyst. The thickness distribution was found to be fitted by the Gaussian distribution, which gave us the effective length of atomic oxygen up to 24 mm.

Investigating the oxidation mechanism of tantalum nanoparticles at high heating rates

Reduced diffusion length scales and increased specific surface areas of nanosized metal fuels have recently demonstrated increased reaction rates for these systems, increasing their relevance in a wide variety of applications. The most commonly employed metal fuel, aluminum, tends to oxidize rapidly near its melting point (660 °C) in addition to undergoing a phase change of the nascent oxide shell. To further expand on the understanding of nanosized metal fuel oxidation, tantalum nanoparticles were studied due to their high melting point (3017 °C) in comparison to aluminum. Both traditional slow heating rate and in-situ high heating rate techniques were used to probe the oxidation of tantalum nanoparticles in oxygen containing environments in addition to nanothermite mixtures. When oxidized by gas phase oxygen, the oxide shell of the tantalum nanoparticles rapidly crystallized creating cracks that may attribute to enhanced oxygen diffusion into the particle. In the case of tantalum based nanothermites, oxide shell crystallization was shown to induce reactive sintering with the metal oxide resulting in a narrow range of ignition temperatures independent of the metal oxide used. The oxidation mechanism was modeled using the Deal-Grove model to extract rate parameters, and theoretical burn times for tantalum based nanocomposites were calculated.

Thermal oxidation kinetics of germanium

Thermal oxidation kinetics of Ge was investigated by the 18O tracing study and re-oxidation experiments of the SiO2/GeO2 stacked oxide-layer. The results suggest that Ge oxidation kinetics is completely different from that expected from the Deal-Grove model and that Ge is oxidized by GeO2 on Ge instead of O2 at the interface. This oxidation process forms large amounts of oxygen vacancies in GeO2, which facilitate the diffusion of oxygen atoms in GeO2. This means that oxygen atoms diffuse through GeO2 with an exchange type of process. Based on experimental results, a possible kinetics for Ge oxidation is discussed.

Phase Field Modeling of Metal Oxidation Kinetics

The oxidation kinetics of metals/alloys at elevated temperatures is essential to the corrosion-life prediction of the structural materials in advanced energy systems. The growth of oxide film on a metal surface typically involves coupling of chemical reaction and diffusion of charged point defects. A phase-field model is developed to address the essential physics during metal oxidation over a continuous range of time and film thickness. The model is able to reproduce the classic Deal-Grove model with respect to the linear-parabolic transition. In particular, the model reproduces Wagner’s theory in the thick film limit and predicts a deviation from the Wagner-parabolic growth when the oxide film thickness is on the order of Debye length. The essential characteristics of electric field developed in an oxide film during high temperature metal oxidation and some other progresses in terms of realistic oxidation modeling will also be discussed.

Parametric Study of the Synthesis of Carbon Nanotubes by Spray Pyrolysis of a Biorenewable Feedstock: α-Pinene

We present a parametric study on the growth of carbon nanotubes (CNTs) by spray pyrolysis of a biorenewable feedstock obtained from living pine trees, namely α-pinene. The analyzed variables were the type of catalyst, catalyst concentration, flow of reactants, and reaction time; all at a fixed temperature of 800 °C. The evaluation and optimization of these parameters was performed based on the yield and crystallinity of produced CNTs which were monitored by Raman spectroscopy, thermogravimetric analysis, X-ray diffraction, and high resolution transmission electron microcopy. Ferrocene as catalyst produced highly crystalline multiwalled CNTs while Co- and Fe-phtalocyanine produced nitrogen-doped CNTs. A ferrocene concentration of 37 mg/mL and 5000 sccm flow were the optimal conditions to obtain the highest yield of crystalline CNTs. The variation of time produced crystalline CNTs with different lengths without modifying their crystallinity. The growth kinetics of MWCNTs follows a Deal–Grove model which ind...

Thermodynamic understanding and analytical modeling of interfacial SiO2 scavenging in HfO2 gate stacks on Si, SiGe, and SiC

This work thermodynamically and experimentally generalizes the interfacial SiO2 scavenging in HfO2 gate stacks from on Si to on other channel materials including SiGe and SiC and proposes a generalized formulation for this process. By paying attention to the Si chemical potential in the SiO2 interfacial layer (SiO2-IL) significantly affected by the substrate, it clarifies that Si in the substrate is indispensable to trigger the scavenging process. Thanks to this understanding, we demonstrate that the scavenging is extendable to next generation of channel materials containing Si such as SiGe and SiC with well-controlled high-k gate stacks. In addition, via formulating the diffusion-reaction-diffusion kinetics, an analytical relation like the Deal-Grove model is obtained for SiO2-IL scavenging in high-k gate stacks.