Asymptotic analysis of a non-linear model for substitutional diffusion in semiconductors

King, John R.; Meere, M. G.; Rogers, T. G.

doi:10.1007/bf00946243

Cited by 6 publications

(3 citation statements)

References 7 publications

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“…(a ) Formulation In this section we consider a different diffusion mechanism in which the im purity diffuses substitutionally by interchange w ith vacancies on neighbouring lattice sites. One-dimensional problems for this model have previously been studied by Zahari & Tuck (1982), Hearne (1988), King (1990) and King et al (1992). The equations in higher dimensions are derived in Meere (1992).…”

Section: T H E V a Ca N Cy M O D Elmentioning

confidence: 99%

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Asymptotic analysis of some two-dimensional diffusion problems

Meere

King

Rogers

1995

Proc. R. Soc. Lond. A

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In this paper we discuss two-dimensional surface source and implant problems for a substitutional-interstitial diffusion model. We present asymptotic solutions in the limit of the surface concentration of impurity (or peak concentration of the implant) being far greater than the equilibrium vacancy concentration. Using leading order composite solutions we plot contours of constant impurity concentration. Some of these contours differ markedly from those of the corresponding linear problem, having the ‘bird’s beak’ shape which is frequently observed in experiments. We also discuss a two-dimensional surface source problem for a vacancy model.

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Section: T H E V a Ca N Cy M O D Elmentioning

confidence: 99%

“…We now return to our discussion of the leading order equations in = 0(1), y < 0. These can be reduced to (compare the one-dimensional implant problem discussed in King et al 1992)…”

Section: Asymptotic Analysis Of Diffusion Problemsmentioning

confidence: 99%

Asymptotic analysis of some two-dimensional diffusion problems

Meere

King

Rogers

1995

Proc. R. Soc. Lond. A

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“…Within this context, nonlinear conceptualizations in research related to semiconductors have been evident in the literature for almost three decades [1,3,4], with respect to aspects such as structure [2], dynamics [2,11,12], optical behavior [11,13], energy applications [14], and physical properties [2,15]. Indicatively, the characteristic approaches in semiconductor research are built on nonlinear stochastic processes [11], quantum physics modeling of conductivity in semiconductors [3,5], nonlinear and chaotic time-series analysis [5][6][7]13], and the structural modeling of super-lattice topologies [12].…”

Section: Introductionmentioning

confidence: 99%

Examination of Chaotic Structures in Semiconductor or Alloy Voltage Time-Series: A Complex Network Approach for the Case of TlInTe2

Tsiotas

Magafas

Hanias

2020

Physics

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This paper proposes a method for examining chaotic structures in semiconductor or alloy voltage oscillation time-series, and focuses on the case of the TlInTe2 semiconductor. The available voltage time-series are characterized by instabilities in negative differential resistance in the current–voltage characteristic region, and are primarily chaotic in nature. The analysis uses a complex network analysis of the time-series and applies the visibility graph algorithm to transform the available time-series into a graph so that the topological properties of the graph can be studied instead of the source time-series. The results reveal a hybrid lattice-like configuration and a major hierarchical structure corresponding to scale-free characteristics in the topology of the visibility graph, which is in accordance with the default hybrid chaotic and semi-periodic structure of the time-series. A novel conceptualization of community detection based on modularity optimization is applied to the available time-series and reveals two major communities that are able to be related to the pair-wise attractor of the voltage oscillations’ phase portrait of the TlInTe2 time-series. Additionally, the network analysis reveals which network measures are more able to preserve the chaotic properties of the source time-series. This analysis reveals metric information that is able to supplement the qualitative phase-space information. Overall, this paper proposes a complex network analysis of the time-series as a method for dealing with the complexity of semiconductor and alloy physics.

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Matched Asymptotic Expansions

Holmes

2013

Texts in Applied Mathematics

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Asymptotic analysis of a non-linear model for substitutional diffusion in semiconductors

Cited by 6 publications

References 7 publications

Asymptotic analysis of some two-dimensional diffusion problems

Asymptotic analysis of some two-dimensional diffusion problems

Examination of Chaotic Structures in Semiconductor or Alloy Voltage Time-Series: A Complex Network Approach for the Case of TlInTe2

Matched Asymptotic Expansions

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