Generalized linear-parabolic law: a mathematical model for thermal oxidation of silicon

Chiou, Y.L.; Sow, Chorng Haur; Ports, K. A.

doi:10.1109/55.31662

Cited by 10 publications

(4 citation statements)

References 15 publications

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“…Despite its success, the validity of the Deal-Grove model has been a subject of continual discussion. 16,17,18,19 In particular, there are modeling 17 and experimental studies 20 suggesting that a logarithmic rate law more generally provides a better description for thermal oxidation, which led to the reexamination of the Deal-Grove model presented in this paper. By relaxing the quasi-static diffusion assumption in the original Deal-Grove model, the new model naturally leads to the logarithmic (or power depending on the stoichiometry coefficient m) law at the early oxidation stage, followed by the parabolic law at long oxidation time.…”

Section: By Tammann Andmentioning

confidence: 93%

A generalized mathematical framework for thermal oxidation kinetics

Rosso

Bruemmer

2011

The Journal of Chemical Physics

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We present a generalized mathematical model for thermal oxidation and the growth kinetics of oxide films. The model expands long-standing classical models by taking into account the reaction occurring at the interface as well as transport processes in greater detail. The standard Deal-Grove model (the linear-parabolic rate law) relies on the assumption of quasi-static diffusion that results in a linear concentration profile of, for example, oxidant species in the oxide layer. By relaxing this assumption and resolving the entire problem, three regimes can be clearly identified corresponding to different stages of oxidation. Namely, the oxidation starts with the reaction-controlled regime (described by a linear rate law), is followed by a transitional regime (described by a logarithmic or power law depending on the stoichiometry coefficient m), and ends with the well-known diffusion-controlled regime (described by a parabolic rate law). The theory of Deal-Grove is shown to be the lower order approximation of the proposed model. Various oxidation rate laws are unified into a single model to describe the entire oxidation process.

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Section: By Tammann Andmentioning

confidence: 93%

A generalized mathematical framework for thermal oxidation kinetics

Rosso

Bruemmer

2011

The Journal of Chemical Physics

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“…Reaction-diffusion equations have been used to describe different systems, [30][31][32] including silicon oxide films thermally grown on Si. [11][12][13][14][15][16][17][18] Here they are also applied to the film growth kinetics and exactly solved through numerical iteration. The diffusing species is taken to be O 2 , to model what has been largely demonstrated by isotopic substitution experiments.…”

Section: The Modelmentioning

confidence: 99%

“…The solutions were obtained by either assuming a nearly steady state and/or a sharp interface, 11,12 similarly to the Deal and Grove solution, or else assuming variable diffusivities or reaction rates. [13][14][15][16][17][18] Although these models suggest possible physical or chemical phenomena, the simplifying assumptions do not allow an estimate of the relevance of the different processes. None of these models has been shown to be clearly correct and none of them has gained widespread acceptance.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of thermal growth of silicon oxide films on Si

et al. 2000

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Thermal growth of silicon oxide films on Si in dry O 2 is modeled as a dynamical system, assuming that it is basically a reaction-diffusion phenomenon. Relevant findings of the last decade are incorporated, as structure and composition of the oxide/Si interface and O 2 transport and reaction at initial stages of growth. The present model departs from the well-established Deal and Grove framework ͓B. E. Deal and A. S. Grove, J. Appl. Phys. 36, 3770 ͑1965͔͒ indicating that its basic assumptions, steady-state regime, and reaction between O 2 and Si at a sharp oxide/Si interface are only attained asymptotically. Scaling properties of these model equations are explored, and experimental growth kinetics, obtained for a wide range of growth parameters including the small thickness range, are shown to be well described by the model.

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“…Stress in silicon oxide [10] affects the parameters in linear-parabolic Deal-Grove model; modified parameters would be expressed as in Eq. 1-3 [10,11] which suggests that if stress is more the oxidation rate will reduce. This is also called as stress limited oxidation.…”

Section: Silicon Nanowires Process Designmentioning

confidence: 95%

Silicon nanowire arrays using g-line photolithography

Prajesh

Tholia

Agarwal

2012

16th International Workshop on Physics of Semiconductor Devices

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One and two micron wide silicon fin patterns realized using standard g-line UV lithography are oxidized to accomplish nanowires. Simulation results envisage the possibility of silicon nanowire fabrication using top down fabrication approach. Experimental results show the feasibility of the process. SEM imaging was used to characterize the nanowires. Silicon nanowires up to 150 nm are demonstrated by the mentioned top down approach. Silicon consumption from three sides of the fins reduces their cross-sectional geometries. Stress developed during the oxidation of silicon leads to pinch-off in the fins, with aspect ratios >3. This pinch-off divides the fin patterns into two parts vertically; upper part detaches from the lower one and converges into silicon Nanowire, buried in silicon oxide. Simulation and process results for different process temperatures, time and fin aspect ratios are presented in the paper.

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Generalized linear-parabolic law: a mathematical model for thermal oxidation of silicon

Cited by 10 publications

References 15 publications

A generalized mathematical framework for thermal oxidation kinetics

A generalized mathematical framework for thermal oxidation kinetics

Dynamics of thermal growth of silicon oxide films on Si

Silicon nanowire arrays using g-line photolithography

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