Ellipsometric characterization of inhomogeneous non‐stoichiometric silicon nitride films

Nečas, David; Franta, Daniel; Ohlı́dal, Ivan; Poruba, A.; Wostry, P.

doi:10.1002/sia.5250

Cited by 11 publications

(6 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, new efficient methods for the optical characterization of the inhomogeneous thin films had to be developed. These methods are presented, for example, in papers [29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Optics of Inhomogeneous Thin Films with Defects: Application to Optical Characterization

2020

Self Cite

View full text Add to dashboard Cite

This review paper is devoted to optics of inhomogeneous thin films exhibiting defects consisting in transition layers, overlayers, thickness nonuniformity, boundary roughness and uniaxial anisotropy. The theoretical approaches enabling the inclusion of these defects into formulae expressing the optical quantities of these inhomogeneous thin films are summarized. These approaches are based on the recursive and matrix formalisms for the transition layers and overlayers, averaging of the elements of the Mueller matrix using local thickness distribution or polynomial formulation for the thickness nonuniformity, scalar diffraction theory and Rayleigh-Rice theory or their combination for boundary roughness and Yeh matrix formalism for uniaxial anisotropy. The theoretical results are illustrated using selected examples of the optical characterization of the inhomogeneous polymer-like thin films exhibiting the combination of the transition layers and thickness nonuniformity and inhomogeneous thin films of nonstoichiometric silicon nitride with the combination of boundary roughness and uniaxial anisotropy. This characterization is realized by variable angle spectroscopic ellipsometry and spectroscopic reflectometry. It is shown that using these optical techniques, the complete optical characterization of the mentioned thin films can be performed. Thus, it is presented that the values of all the parameters characterizing these films can be determined.

show abstract

Section: Introductionmentioning

confidence: 99%

Optics of Inhomogeneous Thin Films with Defects: Application to Optical Characterization

2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…Each of the dielectric functions

{\overset{ϵ}{true}}_{U}

and

{\overset{ϵ}{true}}_{L}

was calculated using the 3‐parametric dispersion model with imaginary part of the dielectric function given as

ϵ_{normali, q} false(E false) = \frac{N_{q} {false(E - E_{normalg, q} false)}^{2} {false(E_{normalh, q} - E false)}^{2}}{C_{q} E^{2}}

for E g, q < E < E h, q and equal to zero below E g, q and above E h, q . The index q = U,L is used to distinguish between the dielectric functions at the upper and lower boundaries.…”

Section: Methodsmentioning

confidence: 99%

“…In the literature, many procedures for calculating of the optical quantities of inhomogeneous layers have been published, eg, previous studies . The theoretical procedures can be divided into those providing the exact solution and those providing approximate solution.…”

Section: Introductionmentioning

confidence: 99%

Use of the Richardson extrapolation in optics of inhomogeneous layers: Application to optical characterization

Vohánka

Ohlı́dal

Ženíšek

et al. 2018

Surface & Interface Analysis

Self Cite

View full text Add to dashboard Cite

A new approach to calculation of optical quantities of inhomogeneous layers is presented. In this approach, the Richardson extrapolation is used to improve the accuracy of the method, in which the inhomogeneous layer is approximated by a stack of thin homogeneous layers. The results presented in this paper are based on the assumption that the media are isotropic and the inhomogeneity is along the axis normal to the boundary. The results obtained by the new method are compared with those obtained without the Richardson extrapolation. The Richardson extrapolation brings significant improvement in accuracy, especially if the number of approximating layers is large. Moreover, the method using the Richardson extrapolation proceeds in steps with an error estimate available in each step; thus, the calculation can be stopped when the desired accuracy is reached. The use of the method is illustrated by means of the optical characterization of strongly inhomogeneous film of non-stoichiometric silicon nitride. KEYWORDS ellipsometry, inhomogeneous layers, optical characterization, silicon nitride 1 INTRODUCTION Within the optical characterization and optical synthesis of thin films, inhomogeneous layers play an important role. While there are many works devoted to methods usable in optical characterization and optical synthesis of homogeneous thin films (see, eg, previous studies 1-18 ), less attention has been devoted to the methods enabling us to characterize or perform optical synthesis of inhomogeneous thin films exhibiting refractive index profiles. Therefore, it is necessary to develop new procedures usable in the optics of inhomogeneous layers.In the literature, many procedures for calculating of the optical quantities of inhomogeneous layers have been published, eg, previous studies. 11,[19][20][21][22][23][24][25][26][27][28][29][30] The theoretical procedures can be divided into those providing the exact solution and those providing approximate solution.The exact solution is known only for few special refractive index profiles (eg, linear profile and exponential profile 24 ); thus, the approximate methods are usually used in practice. As more and more sophisticated methods of the optical characterization and optical synthesis are developed, the approximate methods with increased precision and reduced calculation time are required.The general approximate method enabling us to calculate the optical quantities of inhomogeneous layers with arbitrary refractive index profile is based on dividing these layers into a stack of thin homogeneous layers. 19,20,22,24 We will refer to this method as to homogeneous layers approximation (HLA). Unfortunately, to calculate the optical quantities with high accuracy, a very large number of approximating layers is required in this method. In this paper, we will show that the Richardson extrapolation (RE) can be used to increase the accuracy of this method. The RE 31,32 is a mathematical method that can be used to increase the rate of convergence of a series, provided certain criteria ...

show abstract

“…In other words, functions of single variable describe courses of the refractive index and extinction coefficient from the lower to upper boundaries of these inhomogeneous thin films (single variable corresponds to axis perpendicular to parallel boundaries of these films). As for optics of inhomogeneous thin films one can recommend, for example, these papers [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Within the last three decades an interest concerning optics of inhomogeneous thin films was intensified.…”

Section: Introductionmentioning

confidence: 99%

“…This is especially true if inhomogeneous thin films exhibit unusual and complicated refractive index profiles. Representatives of the complex inhomogeneous thin films are silicon nitride films that are rich in silicon (see eg [23,24]). In general it is possible to state that chemical and plasma chemical technologies frequently produce the thin films exhibiting more or less degree of optical inhomogeneity.…”

Section: Introductionmentioning

confidence: 99%

Approximate methods for the optical characterization of inhomogeneous thin films: Applications to silicon nitride films

Ohlı́dal

Vohánka

Franta

et al. 2019

Journal of Electrical Engineering

Self Cite

View full text Add to dashboard Cite

In this paper the overview of the most important approximate methods for the optical characterization of inhomogeneous thin films is presented. The following approximate methods are introduced: Wentzel–Kramers–Brillouin–Jeffreys approximation, method based on substituting inhomogeneous thin films by multilayer systems, method based on modifying recursive approach and method utilizing multiple-beam interference model. Principles and mathematical formulations of these methods are described. A comparison of these methods is carried out from the practical point of view, ie advantages and disadvantages of individual methods are discussed. Examples of the optical characterization of three inhomogeneous thin films consisting of non-stoichiometric silicon nitride are introduced in order to illustrate efficiency and practical meaning of the presented approximate methods.

show abstract

Ellipsometric characterization of inhomogeneous non‐stoichiometric silicon nitride films

Cited by 11 publications

References 39 publications

Optics of Inhomogeneous Thin Films with Defects: Application to Optical Characterization

Optics of Inhomogeneous Thin Films with Defects: Application to Optical Characterization

Use of the Richardson extrapolation in optics of inhomogeneous layers: Application to optical characterization

Approximate methods for the optical characterization of inhomogeneous thin films: Applications to silicon nitride films

Contact Info

Product

Resources

About