Two-dimensional modeling of ion implantation with spatial moments

Hobler, G.; Langer, E.; Selberherr, S.

doi:10.1016/0038-1101(87)90175-4

Cited by 35 publications

(12 citation statements)

References 16 publications

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“…Oven (1985, 1986) incorporated this correlation by introducing a new parameter called the depth-dependent lateral standard deviation σ x (z), and Oven and Ashworth (1987) demonstrated the inadequacy of the depth-independent model. Hobler et al (1987) then presented a generalization of equation (1) of the form…”

Section: D Density Functionsmentioning

confidence: 99%

“…2D models based on equation ( 2) have been reviewed by Ashworth et al (1991a) who formally identified F L (x, z), in the notation of statistics, as the conditional density function, f c (x|z). The suitability of symmetrical Pearson and modified Gaussian forms (Hobler et al 1987) for f c (x|z) was examined by Ashworth et al (1991a) and an extended set of results is presented here. Also, the suitability of symmetrical Johnson curves is investigated.…”

Section: D Density Functionsmentioning

confidence: 99%

“…It is a well established fact (Hofker et al 1975, Mylroie 1975, Ryssel and Biersack 1986) that for fabrication of micrometre and sub-micrometre circuitries the description of implantation profiles based on two moments (using the Gaussian density function) is inadequate. For a realistic description of one-dimensional profiles, determined both experimentally (Hofker et al 1975, Wilson 1980, Fink et al 1990 and by MC simulation (Petersen et al 1983, Hobler et al 1987, four moments must be taken into account. It should be noted that there are objections to employing density functions determined by more than four moments.…”

Section: Introductionmentioning

confidence: 99%

“…In such cases, the use of semi-infinite moments to construct profiles using density functions, defined on the positive and negative half-planes, is strictly invalid (Ashworth et al 1990b). For B and P ions implanted into a-Si, SiO 2 and Si 3 N 4 , semi-infinite moments obtained from MC simulations into a real target (Hobler et al 1987) should not be used as data for profile reconstruction (Bowyer et al 1992a).…”

Section: Introductionmentioning

confidence: 99%

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Generating ion implantation profiles in one and two dimensions. 1: density functions

Bowyer

Ashworth

Oven

1996

J. Phys. D: Appl. Phys.

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In this, the first of two papers, the problem of constructing ion implantation profiles in one and two dimensions from depth-independent spatial moments is discussed. Comparisons are made between Pearson and Johnson curves, constructed from moments produced by a transport equation solver, and profiles obtained directly from Monte Carlo simulations. A set of such comparisons, using consistent input quantities, is performed over a range of ion-target mass ratios and energies. For projected range distributions of the ions B, P and As into a-Si, a single Johnson type (S B) describes the implants over the energy range 1 keV to 1 MeV. The description using Pearson curves requires two types (I and VI). Also, taking the Monte Carlo data as a reference, the Johnson curves are equivalent, if not superior, to the Pearson curves in terms of fit accuracy. For lateral distributions of the same ion types over the same energy range it is shown that if the depth-dependent lateral kurtosis is less than 3.0, then the Pearson type II (bounded), Johnson type S B (bounded) and the modified Gaussian (unbounded) curves prove acceptable representations. If the depth-dependent lateral kurtosis is greater than 3.0 then the Pearson type VII (unbounded) and Johnson type S U (unbounded) curves are good representations.

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Section: D Density Functionsmentioning

confidence: 99%

Section: D Density Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generating ion implantation profiles in one and two dimensions. 1: density functions

Bowyer

Ashworth

Oven

1996

J. Phys. D: Appl. Phys.

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“…by R p (the mean projected range), σ z (the vertical standard deviation), γ z (the vertical skewness) and β z (the vertical kurtosis), and f c (x|z) can be represented by symmetrical Pearson or Johnson curves, or the modified Gaussian, as determined by the depth-dependent lateral moments, i.e. by σ x (z) (the depth-dependent lateral standard deviation) and β x (z) (the depth-dependent lateral kurtosis) (see Hobler et al 1987, Ashworth et al 1990, 1991a, Bowyer et al 1996a). The functions σ x (z) and β x (z) cannot be obtained directly from TE solvers as they produce only depth-independent moments.…”

Section: Introductionmentioning

confidence: 99%

Generating ion implantation profiles in one and two dimensions. 2: depth-dependent moments and line-source responses

Bowyer¹,

Ashworth²,

Oven³

1996

J. Phys. D: Appl. Phys.

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In this, the second of two papers, various techniques and models are proposed for the extraction of depth-dependent lateral moments from the depth-independent mixed moments produced by transport equation solvers. These depth-dependent moments are then compared with those obtained directly from Monte Carlo simulations. A set of such comparisons, using consistent input quantities, is performed over a range of ion - target mass ratios and energies. The depth-dependent moments are then combined with Pearson and/or Johnson curves to form two-dimensional ion implantation profiles. Comparisons are made between these line-source responses (LSRs) and LSRs obtained directly from Monte Carlo simulations into a-Si for the various models over a range of energies and ion types. Selection of appropriate models leads to LSRs for the ions B, P and As implanted into a-Si which are in good agreement with Monte Carlo simulations over three orders of magnitude of profile concentration. The techniques described will enable two-dimensional profile information to be stored and regenerated, quickly and efficiently, within process simulators so that rapid optimization of processing parameters may be achieved.

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Monte Carlo Analysis

Lugli

1999

Wiley Encyclopedia of Electrical and Electronics Engineering

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Two-dimensional modeling of ion implantation with spatial moments

Cited by 35 publications

References 16 publications

Generating ion implantation profiles in one and two dimensions. 1: density functions

Generating ion implantation profiles in one and two dimensions. 1: density functions

Generating ion implantation profiles in one and two dimensions. 2: depth-dependent moments and line-source responses

Monte Carlo Analysis

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