A new method for ellipsometric inversion with microcomputers: Characterization of optically absorbing films using multiple-angle-of-incidence

Easwarakhanthan, T.; Mas, Patrick; Renard, M.; Ravelet, S.

doi:10.1016/0039-6028(89)90653-5

Cited by 19 publications

(6 citation statements)

References 14 publications

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“…Finally, we take the MAI-based fixed-point inversion, called here inversion 'nkd M AI ', by which the absorbing film optical constants and thickness are sought [3,5,6]. In fact, the difficulty of finding these parameters from MAI data has always been expressed in terms of strong parameter correlation.…”

Section: Development Of Covariance Matrices For Fixed-point Inversionsmentioning

confidence: 99%

“…This problem is tackled here by postulating the sample as having two thicknesses d i (i = 1, 2) brought out from each set of experimental data { i , i , i ). In fact, the optical constants n and k can be first found independently of the thickness by transforming equation ( 14) into another form [3] and the two postulated thicknesses are then computed with their average value taken as the real film thickness. Obviously, these two thicknesses are completely correlated and coincide perfectly if the measured sets are ideally free of errors.…”

Section: Development Of Covariance Matrices For Fixed-point Inversionsmentioning

confidence: 99%

“…The optical constants and thicknesses of transparent and absorbing films grown on substrates have been commonly determined using fixed-point inversions [1][2][3][4][5][6][7][8] which directly invert the highly nonlinear ellipsometric equation relating them to the angles and measured at an angle of incidence . Sufficient data for such a determination can be obtained from the ellipsometric methods of multiple angle of incidence (MAI) and multiple sample analysis (MSA).…”

Section: Introductionmentioning

confidence: 99%

“…The absence of strong parameter correlation may be speculated upon here, but the few studies [14][15][16] which have been carried out on error propagation in fixedpoint inversions were limited to particular inversions without a general formalism. Emphasis had mostly been placed on the development of rapidly converging numerical algorithms, which are certainly required for these inversions [3][4][5][6][7][8] but which will not prevent the propagation of errors prevailing in a given physical system.…”

Section: Introductionmentioning

confidence: 99%

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Error propagation in fixed-point ellipsometric inversions

Easwarakhanthan¹,

Pigeat²

2003

Meas. Sci. Technol.

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Direct fixed-point inversions have been commonly used in ellipsometry for rapid determination of the optical constants and thickness of transparent and absorbing films formed on substrates. We formulate here the statistical covariance matrices of these optical parameters sought from a fixed-wave multiple sample, and multiple and single angle of incidence ellipsometric data using different known fixed-point inversions. Maple software used in the covariance matrix formulation offers the advantage of avoiding the manual calculation of the number of literal derivatives involved. The error propagation inherent in the inversions can thus be readily studied as a function of optical parameters before optical characterization with regard to the uncertainty produced in these parameters and to the correlation between them. We verify quantitatively, using illustrative examples, that strong parameter correlation is synonymous with large parameter uncertainties in these fixed-point inversions and show that the multiple sample-based inversions bring out relatively small uncertainties accompanied by low parameter correlation when the film thickness ranges are chosen appropriately.

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Section: Development Of Covariance Matrices For Fixed-point Inversionsmentioning

confidence: 99%

Section: Development Of Covariance Matrices For Fixed-point Inversionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Error propagation in fixed-point ellipsometric inversions

Easwarakhanthan¹,

Pigeat²

2003

Meas. Sci. Technol.

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“…A obtenção dos parâmetros do filme (índice de refração e espessura), a partir dos ângulos elipsomctricos, é um problema complexo, já que envolve a solução numérica de equações transcendentes de mais de uma variável. Na bibliogarfia [ 58 ] - [ 62 ], existem várias propostas para se resolver este problema, que de uma maneira ou outra, envolvem um algoritmo não triviaL O algoritmo adotado neste trabalho, minimiza a função de várias variáveis da equação ( 5-1 O ), obtendo desta maneira, os parâmetros da estrutura.…”

Section: Oistanctunclassified

Interações paramétricas em guias de ondas de semicondutores 43m crescidos epitaxialmente

MunozUribe¹

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Ao Prof. Navin B. Patel, pela amizade, apoio, interesse, dedicação, e sugestões ao longo do desenvolvimento deste trabalho. A minha esposa lvonne, pelo carinho, apoio, estimulo, e grande suporte computacional durante tudo o período de modelação, e redação deste trabalho. Aos meus Pais Raquel e Jcsús, e minhas irmãs Lupe e Vero, pelo apoio brindado durante estes anos. Ao Dr. Júlio Mendoza, do Departamento de Física do CINVESTAV-IPN, pela amizade, apoio, confiança, sugestões, e estimulo durante este período. Ao Dr. Gerardo Gonzalez de la Cruz "E/ Bato", do Departamento de Física do CINVESTAV-IPN, pela amizade e apoio. Ao Dr. Newton Frateschi, do Laboratório de Pesquisa em Dispositivos do IFGW-Unicamp, pelas sugestões e pela permanente disponibilidade para discutir resultados e dúvidas. A Maria Beny Zakia, pelo crescimento da maioria das amostras utilizadas, assim como pela corrcção do português.

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