Deal-Grove Model Research Articles

Doping Dependence of Thermal Oxidation on n-Type 4H-SiC

The doping dependence of dry thermal oxidation rates in n-type 4H-SiC was investigated. The oxidation was performed in the temperature range 1000C to 1200C for samples with nitrogen doping in the range of 6.5e15/cm3 to 9.3e18/cm3, showing a clear doping dependence. Samples with higher doping concentrations displayed higher oxidation rates. The results were interpreted using a modified Deal-Grove model. Linear and parabolic rate constants and activation energies were extracted. Increasing nitrogen led to an increase in linear rate constant pre-exponential factor from 10-6m/s to 10-2m/s and the parabolic rate constant pre-exponential factor from 10e9m2/s to 10e6m2/s. The increase in linear rate constant was attributed to defects from doping-induced lattice mismatch, which tend to be more reactive than bulk crystal regions. The increase in the diffusion-limited parabolic rate constant was attributed to degradation in oxide quality originating from the doping-induced lattice mismatch. This degradation was confirmed by the observation of a decrease in optical density of the grown oxide films from 1.4 to 1.24. The linear activation energy varied from 1.6eV to 2.8eV, while the parabolic activation energy varied from 2.7eV to 3.3eV, increasing with doping concentration. These increased activation energies were attributed to higher nitrogen content, leading to an increase in effective bond energy stemming from the difference in C-Si (2.82eV) and Si-N (4.26eV) binding energies. This work provides crucial information in the engineering of SiO2 dielectrics for SiC MOS structures, which typically involve regions of very different doping concentrations, and suggests that thermal oxidation at high doping concentrations in SiC may be defect mediated.

Degradation of Atomic Surface Flatness of SiO2 Thermally Grown on a Si Terrace

In this study, the atomic-scale roughness and uniformity of thermally grown on an atomically flat Si surface were investigated. The surface roughness increased with increasing oxide thickness in the initial rapid oxidation region of the Deal–Grove model. This roughness growth was a result of reoxidation of SiO species near the surface, which were emitted from the interface during oxidation. However, the surface roughness growth is saturated in the linear-rate oxidation region. This is because the emitted SiO species within the were reoxidized without thickness increment, and the generated oxidation stress was absorbed within the film. Although the amount of the emitted SiO decreases by the surpassing relaxation effect, the surface roughness is kept without shrinking. An incubation period before the onset of roughening was found, during which the surface roughness remained unchanged.

Experimental evidence of oxidant-diffusion-limited oxidation of SiGe alloys

Rate-limiting step, as well as self-limited oxidation of SiGe alloys is so far under controversy. Contrasting to the monoparabolic growth mode for oxidation of Si, a parabolic growth mode and self-limited oxidation of SiGe alloys at different temperature are clearly observed depending on the oxidation time. With modified Deal–Grove model, we extract the parabolic rate constants related to the oxygen diffusion at different temperature and the activation energy of oxygen diffusivity finding that oxygen diffusion is still the rate-limiting step. We attribute this oxidation behavior to the strain effects associated with the volume change in converting Si/SiGe to SiO2/mixed oxide at different oxidation stages.

2-D Roughening of SiO2 Thermally Grown on Atomically Flat Si Surface

In this study, the atomic-scale roughness and uniformity of SiO2 thermally grown on atomically flat Si surface are investigated. The SiO2 surface roughness increases with increasing oxide thickness in the initial rapid oxidation region in the Deal-Grove model. This roughness growth can be related to re-oxidation of SiO emitted from the Si/SiO2 interface near the SiO2 surface. On the other hand, the roughness growth is saturated in the linear rate oxidation region. It is explained that the emitted SiOs within the SiO2 are re-oxidized and the generated oxidation stress is absorbed within the film.

Size-dependent oxidation behavior for the anomalous initial thermal oxidation process of Si

To have a clear insight into the physical origin of the anomalous initial oxidation behavior for silicon oxidation, we proposed a kinetics model by introducing the nanosize effect into the oxidation process. The rate equation of oxide growth was calculated based on our model, and these results are in excellent agreement with experiments. Notably, the present model not only bridges the breakdown of Deal–Grove model [B. E. Deal and A. S. Grove, J. Appl. Phys. 36, 3770 (1965)] in the anomalous initial region but also accurately describes the oxidation process in the whole oxidation regions over a wide temperature range.

Oxidation of SiC investigated by ellipsometry and Rutherford backscattering spectrometry

Oxidation of SiC was performed in Ar–O2 mixture of atmospheric pressure at 1100 °C and compared with that of Si. The partial pressure of O2 varied from 100 to 1000 mbar, while the oxidation time ranged from 0.5 to 45 h. The thickness of the oxide films was determined by spectroscopic ellipsometry and Rutherford backscattering spectrometry. The time and the pressure dependence of the oxidation kinetics of SiC are well described by the modified Deal–Grove model. In the diffusion-limited region, even for the faster case, the oxidation kinetics of the C-terminated face of SiC is not clearly limited by oxygen indiffusion, as for pure silicon. To interpret the ellipsometry spectra, two models of possible structure were used. In the case of the one-layer model, for layer thicknesses above 30 nm, the refractive index of the oxide layers is identical to that of thermally oxidized Si, and it increases rapidly with decreasing thickness below about 15 nm. This increase is significantly larger for C-terminated than for Si-terminated faces, and this difference can be explained by a transition layer introduced into the two-layer model. This model contains a pure SiO2 layer and a transition layer modeled by a mixture of 50 % SiO2 and 50 % SiC. The transition layer is thicker on the C-terminated surface than on the Si-terminated one. The thickness ratio of the transition layers is slightly larger than the surface roughness ratio on the two different sides determined by atomic force microscopy. The density of the oxide films, which can be determined from the backscattering and spectroscopic ellipsometry spectra, decreases with decreasing thickness below about 30 nm. For thicker films, the density of the oxide is equal to the bulk density of SiO2.

Thermochemical and Mechanical Stabilities of the Oxide Scale of ZrB2+SiC and Oxygen Transport Mechanisms

Refractory diboride with silicon carbide additive has a unique oxide scale microstructure with two condensed oxide phases (solid+liquid), and demonstrates oxidation resistance superior to either monolithic diboride or silicon carbide. We rationalize that this is because the silica‐rich liquid phase can retreat outward to remove the high SiO gas volatility region, while still holding onto the zirconia skeleton mechanically by capillary forces, to form a “solid pillars, liquid roof ” scale architecture and maintain barrier function. Basic assessment of the oxygen carriers in the borosilicate liquid in oxygen‐rich condition is performed using first‐principles calculations. It is estimated from entropy and mobility arguments that above a critical temperature TC∼1500°C, the dominant oxygen carriers should be network defects, such as peroxyl linkage or oxygen‐deficient centers, instead of molecular O2* as in the Deal–Grove model. These network defects will lead to sublinear dependence of the oxidation rate with external oxygen partial pressure. The present work suggests that there could be significant room in improving the high‐temperature oxidation resistance by refining the oxide scale microstructure as well as controlling the glass chemistry.

In situ observation of wet oxidation kinetics on Si(100) via ambient pressure x-ray photoemission spectroscopy

The initial stages of wet thermal oxidation of Si(100)−(2×1) have been investigated by in situ ambient pressure x-ray photoemission spectroscopy, including chemical-state resolution via Si 2p core-level spectra. Real-time growth rates of silicon dioxide have been monitored at 100 mTorr of water vapor. This pressure is considerably higher than in any prior study using x-ray photoemission spectroscopy. Substrate temperatures have been varied between 250 and 500 °C. Above a temperature of ∼400 °C, two distinct regimes, a rapid and a quasisaturated one, are identified, and growth rates show a strong temperature dependence which cannot be explained by the conventional Deal-Grove model.

Pressure dependence of SiO2 growth kinetics and electrical properties on SiC

Dry oxidations between 0.25 and 4 atm at 1150 °C are used to characterize the pressure dependence of the growth kinetics of SiO2 along three orientations of the 4H-SiC polytype. The growth curves are studied using the Deal-Grove model. The extracted linear and parabolic constants are found to scale linearly with the pressure up to 2 atm. However, the data indicate that the (0001) Si-face exhibits a retarded growth rate above 2 atm. It is also found that, like Si, there is a critical oxide thickness below which the linear-parabolic model cannot be applied. This value is found to be between 36 and 40 nm for SiO2 on 4H-SiC, and is apparently independent of the crystal orientation and oxidation pressure. The extracted critical thickness and its properties are similar to what is observed on Si, suggesting that the fast growth regime is dictated by the nature of the oxide. Finally, it is shown that the density of interface states (Dit) on the (0001) Si-face is not reduced by faster oxide growth rates within the monitored energy window.

Real-time observation of the dry oxidation of the Si(100) surface with ambient pressure x-ray photoelectron spectroscopy

We have applied ambient-pressure x-ray photoelectron spectroscopy with Si 2p chemical shifts to study the real-time dry oxidation of Si(100), using pressures in the range of 0.01–1Torr and temperatures of 300–530°C, and examining the oxide thickness range from 0to∼25Å. The oxidation rate is initially very high (with rates of up to ∼225Å∕h) and then, after a certain initial thickness of the oxide in the range of 6–22Å is formed, decreases to a slow state (with rates of ∼1.5–4.0Å∕h). Neither the rapid nor the slow regime is explained by the standard Deal-Grove model for Si oxidation.

A Kinetic Equation for Thermal Oxidation of Silicon Replacing the Deal–Grove Equation

A formulated kinetic theory for thermal oxidation of silicon is presented in detail. The theory does not involve the rate-limiting step of the interfacial oxidation reaction, instead it is supposed that the diffusivity is suppressed in a strained oxide region near the interface. The expression of the parabolic constant is the same as that of the Deal–Grove model, while the linear constant makes a clear distinction with the model. The estimated thickness using the expression is close to , which compares well with the thickness of the structural transition layer. The origin of the deviation from the linear-parabolic relationship observed at initial oxidation stages can be explained by the enhanced diffusion hypothesis, which is the opposite conclusion to the Deal–Grove theory.

A New Kinetic Equation for Thermal Oxidation of Silicon Replacing the Deal-Grove Equation

A newly formulated kinetic theory for thermal oxidation of silicon is reviewed. The new theory does not involve the rate- limiting step of the interfacial oxidation reaction, instead it is supposed that the diffusivity is suppressed in a strained oxide region near the SiO2/Si interface. The expression of the parabolic constant is the same as that of the Deal-Grove model, while the linear constant makes a clear distinction with the model. The estimated thickness using the new expression is close to 1 nm, which compares well with the thickness of the structural transition layer. The origin of the deviation from the linear-parabolic relationship observed at initial oxidation stages can be explained by the enhanced diffusion hypothesis, which is opposite conclusion to the Deal- Grove theory.

Reply to “Comment on ‘Dynamics of thermal growth of silicon oxide films on Si’ ”

In a Comment on ``Dynamics of thermal growth of silicon oxide films on Si'' [Phys. Rev. B 61, 12992 (2000)], Roura and Farjas argue that the values of the kinetics parameters obtained from the model proposed in that paper are not reliable and that the solutions given for different partial pressures are erroneous. Moreover, that the solution from such model is unable to predict the oxidation rate experimentally observed in the thin oxide regime neither the width of the interface. Resorting to experimental results, and old and new results obtained from our model, we show in this Reply that none of the criticisms are solid and that the results of the original paper represent indeed an improvement over the Deal-Grove model. Finally, motivated by one of the issues raised by Roura and Farjas, we present here new fittings of experimental data using our model together with experimental estimates for the interface width between the oxide layer and the silicon substrate. This turned a two parameter fitting problem into a much simpler one parameter procedure.

Oxidation treatments for SiC particles and its compatibility with glass

Different thermal treatments were performed to produce a protective coating on the surface of SiC particles in order to allow their incorporation in a glass matrix. These oxidation treatments were carried out in air at different temperatures ranging from 800 °C to 1500 °C and different times at 1200 °C (10 min–48 h). The oxidation kinetics followed the Deal–Grove model and the thickness of the protective coating increased with temperature and SiC particle size. Protected SiC particles with different particle sizes were incorporated in a borosilicate glass. With small particles sizes foam glasses were obtained, whereas particles with higher grain size, i.e., higher coating thickness, were stable in the glass matrix and a smooth glass was obtained.

New Linear-Parabolic Rate Equation for Thermal Oxidation of Silicon

We propose a new oxidation rate equation for silicon supposing only a diffusion of oxidizing species but not including any rate-limiting step by interfacial reaction. It is supposed that diffusivity is suppressed in a strained oxide region near SiO(2)/Si the interface. The expression of a parabolic constant in the new equation is the same as that of the Deal-Grove model, while a linear constant makes a clear distinction with that of the model. The estimated thickness using the new expression is close to 1 nm, which compares well with the thickness of the structural transition layers.

The stoichiometry of thermal oxidation

At a stoichiometrical relation of silicon and oxygen during the growth of a rapid thermal silicon-oxide layer (RTO) the electrical parameters of the corresponding metal-insulator-semiconductor capacitor show significant behavior. Combining the Henry-Dalton law and the Boyle-Mariotte law with the Deal-Grove model allows an estimation of the fundamental (T, t, C) process, parameters, temperature, time and concentration of the reactive gas for a stoichiometrical processing of ultra thin SiO/sub 2/ films. Electrical measurements show the (T, t, C)-dependency of I-V, time dependent dielectric breakdown (TDDB) and C-V measurements especially of direct tunneling currents j/sub DT/, relative difference of tunneling currents /spl Delta//sub RDT/, charge-to-breakdown Q/sub BD/ and interface state density D/sub it/.

Si nanocrystals by ultra-low energy ion implantation for non-volatile memory applications

In nanocrystal (nc) metal-oxide-semiconductor (MOS) memory structures, a fine control of nc location and population is required for pinpointing the optimal device architectures. In this work, we show how to manipulate and control the depth-position, size and surface density of two dimensional (2D) arrays of Si ncs embedded in thin (<10 nm) SiO 2 layers, fabricated by ultra-low energy (typically 1 keV) ion implantation and subsequent annealing. The influence of implantation and annealing conditions on the nc characteristics (e.g. size, density) and the charge storage properties of associated MOS structures is reported with particular emphasis upon the effect of annealing in N 2-diluted–O 2 gas mixture. The latter annealing conditions restore the integrity of the oxide and allow for the fabrication of non-volatile memory devices operating at low-gate voltages. Annealing in diluted oxygen has also an effect on the population of silicon ncs. Their evolution has been studied as a function of the annealing duration under N 2 + O 2 at 900 °C. An extended spherical Deal–Grove model for the self-limiting oxidation of embedded Si ncs has been carried out. It shows that stress effects, due to the deformation of the oxide, slows down the chemical oxidation rate and leads to a self-limiting oxide growth. The model predictions are in agreement with the experimental results.

Kinetics of laser-induced oxidation of silicon near room temperature

The growth of ultra-thin (<6 nm) silicon-dioxide films on Si(100):H, Si(111):H, and a-Si:H surfaces in a dry oxygen atmosphere (0.1–10 Pa) at low temperatures (35–200 °C) was investigated. Oxidation was induced by pulsed F2-laserradiation at 157 nm. The thickness and composition of the growing films were monitored in real time by spectroscopic ellipsometry in the photon energy range of 1.15–4.75 eV. The kinetics of low-temperature oxidation was similar for the Si surfaces investigated and differs from that of high-temperature thermal oxidation (900–1200 °C) that can be described by the Deal–Grove model. To explain the faster growth at the initial stage, it is proposed that oxidation occurs by diffusion of oxygen atoms O and/or ions O-rather than oxygen molecules. The recombination of diffusive species to oxygen molecules limits their penetration into the bulk. A diffusion model is developed for low-temperature oxidation which takes into account the recombination process of the diffusive species. Good agreement between theory and experiment is found. The activation energy of diffusion of the active species was found to be 0.15 eV, in agreement with previous results and recent calculations for O- ions.

A Novel Wafer Reclaim Method for Amorphous SiC and Carbon Doped Oxide Films

Amorphous SiC (a-SiC) films are the most promising dielectric diffusion barriers to replace silicon nitride in Cu-interconnect technology. However, reclaim of wafers with a-SiC films is a challenge issue for mass production. In this paper, a novel wafer reclaim method is proposed. It is observed that a-SiC can be oxidized to SiO/sub 2/ in both dry O/sub 2/ and steam ambients at temperatures as low as 550/spl deg/C. The oxidation mechanism can be described by the Deal-Grove model that is traditionally used to describe oxidation of Si. Experiments prove that the oxidation process is clean and uniform. It is also observed that carbon doped oxide (CDO) films can be oxidized easily, too. Therefore, oxidation followed by HF etching could be a universal process to reclaim wafers deposited with a-SiC or CDO films. Since the oxidation rate of Si substrates at medium temperatures is much lower than that of a-SiC and CDO films, the oxidation process is virtually self-limiting. Compared with a traditional reclaim method based on wafer polishing, this universal oxidation-etching method exhibits great benefits in terms of low cost, high throughput, and the ability to perform nearly unlimited numbers of reclaim cycles.

Si nanocrystals by ultra-low-energy ion beam-synthesis for non-volatile memory applications

In this work, we show how to manipulate two-dimensional arrays of Si NCs in thin (⩽10 nm) SiO 2 layers by ultra-low-energy (⩽1 keV) ion implantation and subsequent thermal annealing. The influence of implantation parameters (dose, energy), annealing conditions (temperature, duration, ambient) and oxide thickness on the NCs characteristics (position, size, density) is reported. Particular emphasis is placed upon post-implantation thermal treatments performed in nitrogen-diluted-oxygen ambient that significantly improve the integrity of the oxide and allow for the fabrication of non-volatile memory devices operating at low-gate voltages. Thermal oxidation in N 2-diluted-O 2 of high-temperature pre-formed silicon NCs has been also examined and modeled using an extended three-dimensional Deal–Grove model. This model reveals that stress effects, due to the deformation of the oxide, slow down the chemical oxidation rate and lead to a self-limiting oxidation of NCs. The model predictions are in agreement with the experimental results.