Linear-parabolic Model Research Articles

Effects of External Stresses on the Low Temperature Thermal Oxidation of Silicon

Thermal oxidation of silicon was conducted under the application of external compressive or tensile stress at relatively low oxidation temperature. The effect of external stress appeared in different ways depending on the oxidation temperature. While the stress effect of oxidation at 800°C was well interpreted with the linear-parabolic oxidation model (L-P model), that at a temperature lower than 700°C contradicted the L-P model and strongly suggested the existence of an oxidation reaction of interstitial silicon atoms in the oxide.

Kinetics of Rapid Thermal Oxidation of Silicon

We have proposed, for the first time, a practical model for ultrathin (<10 nm) SiO2 film growth in rapid thermal oxidation (RTO) kinetics. The results showed that the overall RTO growth can be well described by the linear-parabolic model proposed by Deal and Grove [J. Appl. Phys. 36 (1965) 3770]. Moreover, the model proposed indicates that in order to fit the experimental data, the oxide growth in a ramp-up process must be included in the linear-parabolic scheme. As a result, we have succeeded in explaining the RTO growth kinetics in the RTO temperature range from 950 to 1200°C and in a wide thickness range from 15 to 250 Å without making any special assumptions. The resultant activation energies for the linear rate constant (B/A) and for the parabolic rate constant (B) are 2.0 eV and 1.74 eV, respectively.

Thin thermal oxides of silicon and the orientation effect: An empirical approach

Within a linear-parabolic model of oxide growth on silicon in dry oxygen a set of linear and of parabolic rate constants has been constructed. Data from multiple sources have been collected and correlated with some general concepts. One activation energy for the linear rate constants was found to apply to all silicon orientations. The activation energies for the parabolic rate constants for the several silicon orientations are different. In the fitting of data it is found that the oxygen pressure dependence of oxidation is sublinear and the coefficient for 〈100〉 silicon is not the same as for 〈111〉 silicon. Numerical values for these temperature- independent coefficients are chosen. An initial rapid oxidation appears essentially as a small, limited, growth step. Comparisons of calculated oxidation curves are made with reported orientation effect data.

The Kinetics of Low Pressure Rapid Thermal Oxidation of Silicon

ABSTRACTA study of the oxidation kinetics of lightly doped (100) silicon in dry oxygen has been carried out at different pressures (0.03 atm. to 1.0 atm.) and temperatures (900ºC to 1200ºC) for short times (&lt; 500 seconds). The data can be fit equally well to the parabolic model as it can to the linearparabolic or parallel oxidation models. The activation energy derived from analysis of the parabolic rate constant is 0.94 eVand is the same at 1.0 and 0.1 atmosphere dry O2. It was also found that the parabolic rate constant displayed a linear dependence on the O2 pressure.

ChemInform Abstract: Thermal Oxidation of Silicon: New Experimental Results and Models

Abstract Most studies of Si oxidation commence with a discussion of the linear-parabolic oxidation model developed by a number of workers in the 1960's. The limits of the model are pure diffusion of oxidant for thick SiO2 films and a surface reaction limitation for thin films. The steady state picture of this series reaction scheme is discussed and used to explain new experimental results. New data relevant to Si oxidation is presented on the following subjects: five orientations of Si; photonic excitement; intrinsic film stress; silicide oxidation. The role of electrons on the oxidation kinetics is elucidated. A thermionic emission model for the initial stages of oxidation is proposed.

The morphology and characteristics of TaSi2/Si films oxidized at high pressure

The oxidation of Ta silicide on Si substrates has been investigated for pressures from 1 to 10.7 atm. The oxidation of these films fits the Deal–Grove linear–parabolic model, with a direct proportionality of the rate constants to the oxidation pressure. In contrast to results reported for single‐crystal Si, the activation energies of the rate constants are found to depend upon pressure. Morphologically, transmission electron microscope micrographs show these oxidized silicide films to be rough, and possess SiO2 between grain boundaries. In addition, the dielectric strength of these oxides is found to be between 4 and 8 MV/cm.

Thermal oxidation of silicon: New experimental results and models

Most studies of Si oxidation commence with a discussion of the linear-parabolic oxidation model developed by a number of workers in the 1960's. The limits of the model are pure diffusion of oxidant for thick SiO 2 films and a surface reaction limitation for thin films. The steady state picture of this series reaction scheme is discussed and used to explain new experimental results. New data relevant to Si oxidation is presented on the following subjects: five orientations of Si; photonic excitement; intrinsic film stress; silicide oxidation. The role of electrons on the oxidation kinetics is elucidated. A thermionic emission model for the initial stages of oxidation is proposed.

Silicon Dry Oxidation Kinetics: Effects of the Choice of Integration Constant on Fits to the Linear Parabolic Model

not Available.

Thermal xidation of silicon in dry oxygen: - the role of crystallographic orientation -

AbstractBased upon the linear-parabolic growth model of silicon oxidation, accurate kinetic rate constants are determined for various crystallographic orientation wafers in the 900 −1100°C range. The parabolic rate constant is independent of substrate orientation above 1000 °C, while, at 900°C, it depends on the orientation of the underlying substrate. The behavior of the parabolic rate constant at low temperature can be explained by accounting for Si-O bond-breaking due to stress during the oxide growth. The linear rate constant is observed to depend on the crystallographic orientation of the silicon surface in all temperature range. The orientation dependence of the linear rate constant is explained by both strain relaxation of the oxide film and areal atomic density of silicon at the silicon/oxide interface.

New results on low-temperature thermal oxidation of silicon

Abstract The commonly accepted linear-parabolic oxidation model for the thermal oxidation of Si includes two rate processes in the steady state: a reaction between Si and oxidant at the Si-SiO2, interface and transport of oxidant through the SiO2, film. Based on available data, it is argued that the former process seems dominant for thin-film growth in dry O2. A number of measured SiO2, film and Si-SiO2, interface properties are reported, as well as the variation of the these properties with oxidation temperature and Si substrate orientation. These properties include refractive index, density, intrinsic stress, interface fixed oxide charge and interface trapped charge. It is also observed that all of these properties display similar oxidation-temperature and inert-anneal behaviour together with a complex orientation dependence. Through the use of a modified form for the interface reaction, a better understanding is obtained of both the origin of these measured properties, and of new oxidation data taken o...

ChemInform Abstract: Models for the Oxidation of Silicon

Since the 1960’s many adaptations to the linear parabolic model for silicon oxidation have been proposed. For the purposes of process engineering, curve fitting procedures which are sometimes devoid of physical content but numerically precise are employed. However, a truly unified physical model which is in quantitative accord with all known facts is still lacking. In this review we will discuss the ‘‘facts’’ and newer models.

Models for the oxidation of silicon

Since the 1960’s many adaptations to the linear parabolic model for silicon oxidation have been proposed. For the purposes of process engineering, curve fitting procedures which are sometimes devoid of physical content but numerically precise are employed. However, a truly unified physical model which is in quantitative accord with all known facts is still lacking. In this review we will discuss the ‘‘facts’’ and newer models.

Point-defect generation during oxidation of silicon in dry oxygen. II. Comparison to experiment

In the companion paper [J. Appl. Phys. 59, 2541 (1986)], we developed a model based on a continuity equation approach for the supersaturation of interstitials during oxidation in dry O2. The analysis resulted in an expression having the experimentally observed sublinear dependence of oxidation rate without requiring any assumptions of nonlinearity. Through observations of the dependence of the linear rate constant at the linear-parabolic model of oxidation on ambient oxygen pressure, predictions were made of how the interstitial supersaturation will vary with oxidation rate at a given temperature. In this paper, those predictions are compared to data for the enhanced diffusion of phosphorus in 〈100〉 silicon during oxidation at 900 and 1000 °C in both 100% O2 and O2-Ar mixtures as well as existing data for oxidation enchanced diffusion and stacking fault growth.

Point-defect generation during oxidation of silicon in dry oxygen. I. Theory

In this paper, we consider how oxidation in dry O2 influences the point-defect densities in silicon. By using relationships based on the continuity equations in the oxide and applying a proposed set of boundary conditions to the oxidizing Si-SiO2 system, we derive an analytic expression for the supersaturation of interstitials during oxidation. The analysis results in an expression having the experimentally observed sublinear dependence on oxidation rate without requiring any assumptions of nonlinearity. In addition, through observations of the dependence of the linear rate constant in the linear-parabolic model of oxidation on ambient oxygen pressure, it is possible to predict how the interstitial supersaturation will vary with oxidation rate at a given temperature. A companion paper [J. Appl. Phys. 59, 2551 (1986)] compares the predictions of the model with experimental results.

Oxidation behaviour of double layers of TiSi 2 on polycrystalline silicon

The oxidation of TiSi 2 on Si(100) and on polycrystalline silicon films in H 2O-O 2 and dry O 2 was studied in the temperature range 700–1050°C. The same mechanism was found for both types of structures. As in the case of the oxidation of silicon the reaction may be described by a linear-parabolic two-step model. In the initial phase of the process the rate is limited by the reaction at the TiSi 2-oxide interface, and later by the diffusion of the oxidant to the interface. Only during the first stage may small amounts of TiO 2 be formed. Contamination of the starting surface by TiO 2 is most probably responsible for the conflicting results reported in the literature.

Silicon oxidation studies: A revised model for thermal oxidation

A number of recent experimental silicon oxidation studies has suggested that the present form of the linear-parabolic oxidation model is inadequate in explaining the results. However, the best available oxidation data are linear-parabolic in shape. The present study relieves this dilemma by revising the linear-parabolic model. The revisions are essentially twofold: a new transport flux, viz., transport in micropores is invoked and the viscoelastic properties of SiO2 are utilized. A revised linear-parabolic model is obtained which better explains high and low temperature oxidation behavior, the formation higher density SiO2, and the initial oxidation regime.