Method for the optical characterization of materials without using a physical model

Translation of description of equivalent WO 2004061432 A2

CHARACTERIZATION METHOD OF OPTICAL MATERIALS WITHOUT USING PHYSICAL MODEL

DESCRIPTION

ECHNICAL FIELD

The present invention concerns a method for optical characterization of materials.

This method allows to characterize thin or thick layers of these materials, which are formed on the substrates. Physical values, that this method enables to determine, are:

- The thickness of a layer of a material,

- The refractive index of said material, and - the absorption coefficient of this material.

The optical characterization of the material is useful for one chemical analysis of these materials (including study of the absorption bands, densification properties and oxidation properties), in the fields of microelectronics, sensors, biology, of medicine), or for analysis of the thicknesses of deposition of these materials. For application examples, refer to document [1] which, like the other documents cited below, is mentioned at the end of this description.

The characterization of optical properties of a material is also useful when the material is structured by the following (to form are for example engravings or roughness) and the optical diffraction properties of the resulting structure must be calculated (see [2]).

Now indicate that the invention is particularly useful when the physical law followed by 1 complex refractive index of the material that is to be characterized is a priori unknown.

STATE OF THE PRIOR ART It is recalled that the optical measurements can be of various types:

It may be reflectometric measurements. In this case, the intensity reflection coefficient of a structure is measured on a spectrum (that is to say an interval) of wavelengths [λm, λ_M] •

The incidence of the illumination light angle may be non-zero. The reflection coefficient can be measured for various θ angles. We denote R (θ, λ, p) the reflectometric spectrum, where p is the polarization of the incident beam and λ the wavelength of the latter.

Generally, the angle θ is zero and p polarization indefinite. In the case where θ is not zero, you must know this polarization p. In general, it is of (S) where (P).

It can be also ellipsometric measurements. The measured values ​​are then the real and imaginary parts of the report of the coefficient polarization in reflection (P) polarization reflection coefficient (S).

generally noted p = | p | exp (jΔ) this complex relationship (with j²= -l). The quantities are generally treated Ipl, which is denoted tan (ψ) and cos (Δ), or combinations of both.

For example, variables derived from a phase-modulated ellipsometer are:

I_s= Sin (2ψ) sin (Δ) and I_c= Cos (2ψ). A conventional ellipsometer provides, meanwhile, the following variables: = (tan²ψ-l) / (tan²ψ + l) and β = cosΔ (l-α²)^1/2.

For the sake of generality, we denote S and S₂ treated quantities. If the spectra, ie, [1,2], are measured over a range of wavelengths [λ_π,, λ_M]. The angle of incidence can be arbitrary. Several spectra can be measured at different angles to get a richer spectrum. We denote s (θ, λ) = {Sι (θ, λ), S₂ (Θ, λ)} the ellipsometric spectrum.

Complementally goniometric measurements (reflection coefficient as a function of the angle of incidence) can be added to the measures for characterization, to determine the thickness of the various layers to one or more wavelengths. These measures are not sufficient in themselves because we want to determine the complex refractive index over a spectral range from A to Λ ,,,_M. To simplify the presentation, we will denote a set of Ψ réfleσtométrique spectra and / or ellipsometry (s) (and possibly DF for some wavelengths). Without losing any generality, we shall explain, in this specification, methods using the method of the prior art and of the present invention that in the case of a single thin layer of a material formed on a known substrate. The thickness of this layer is denoted by ε and

1 complex refractive index of the material at the wavelength λ is denoted by n * (λ).

It is recalled here that the real part (respectively imaginary) of the complex refractive index is denoted n (λ) (respectively (λ)) and called "refractive index" (respectively

"Extinction coefficient").

In addition there is Er (Ψ⁽¹⁾ , ψ⁽²⁾) An error function (eg standard deviation) between two spectra Ψ⁽¹⁾ and Ψ⁽²⁾ .

For example, one can take when one has ellipsometric spectra of several angles θi, is l..n {}, and a reflectometric spectrum:

E_r (Ψ ^<1) , Ψ ^{! 2}>) =

<img id="imgf000005_0001" he="19" wi="92" file="imgf000005_0001.tif" img-format="tif" img-content="drawing" orientation="portrait" inline="no" />

with Ψ⁽¹'(ΛMS_x⁽¹⁾ (Θi, λ), S₂⁽¹⁾ (Θi, λ), R^(1&gt; (Λ)} Ψ⁽²⁾ (ΛJ ≈CSx "(θ_yew λ&gt;, S₂^&lt;2&gt; (Θi, λ), R^f2) (Λ)} and ie {n} l ...

Weighting factors can be made to the full so that the error function can take account of variations on the measuring accuracy of the spectra.

Optical characterization of layers of materials is generally based on two applications:

The first application is the dimensional control of the deposition of thin films as in microelectronics is used.

Generally one knows the deposited material, that is to say, we know well the complex refractive index of the material at the wavelengths of light used for characterization.

The laws followed by 1 complex refractive index are either tabulated or approached by known physical laws such as, for example, the model of Cauchy, model Sellmeier (see [3]), the laws of Forouhi ( see [4]), and harmonic oscillators statutes (see [5]). These laws are defined by a finite number of parameters.

For example, a Cauchy type law without absorption, two-parameter is defined as follows:

Re [ »* (A)] = n (λ) = a₀+ -5L- Lm [n * μ)] = k (λ) = 0

1 When one is sure of the value of the coefficients have to {0,1}) but we do not know thickness, a search algorithm is used to find the thickness that minimizes the error between the measurement and theoretical Ψ Ψ response given the modeled index. The search algorithm may be, for example, the Simplex method, research Tabou method Levendt-Marquart method or the simulated annealing (see Chapter 10 of the document [6]).

1 when the refractive index is approximate coefficients have integrated into the fitting procedure of Ψ and ψ. Have the coefficients of the research is a method for characterizing the refractive index.

However, when the law followed by the index of refraction is unknown (it happens that the material is unknown or that it is not well described by a known physical law), this method remains approximate and thickness may be false .

The second application is the characterization of materials.

The method used remains the same, except that the material is not well known. This is precisely the function of the refractive index of the closest complex reality that is referred. The type of law can be chosen by analogy with other materials. However, the law followed by 1 complex refractive index can be complicated, which is for example the case of a harmonic oscillator law:

<img id="imgf000007_0001" he="10" wi="67" file="imgf000007_0001.tif" img-format="tif" img-content="drawing" orientation="portrait" inline="no" /> In the above expression, j²= -l And the refractive index and the extinction coefficient are expressed not as a function of λ but E, with E = 1240 / λ (λ in nm). In this case, the coefficients of the oscillators are hard to find if you do not their size. Research is difficult to automate the search algorithms that may give the wrong answers and lost time can be considerable.

There is an alternative to research coefficients: point-to-point method (PAP). This method offers PAP not to choose physics law and seek 1 'complex refractive index of the material for each wavelength .lambda.i where I [1 ... n], with λi≈λ_m and λ_not= λ_M.

For each λ, a search algorithm tries to find the thickness, the index n (.lambda.i) and the extinction coefficient k (.lambda.i) which minimize the error between the measure ψ (.lambda.i) and the theoretical response <img id="imgf000008_0001" he="5" wi="42" file="imgf000008_0001.tif" img-format="tif" img-content="drawing" orientation="portrait" inline="no" />

Such a method has a problem because the various points (.lambda.i, ε, n (.lambda.i), k (.lambda.i)) are not necessarily physically compatible with each other: for example, the thickness found may vary depending on the length of wave and law followed by the complex refractive index, more simply called the index law, may have discontinuities. This method is generally applicable only when the thickness is very well known and that measures are of very good quality.

PRESENTATION OF THE INVENTION

The present invention aims to overcome the above drawbacks.

The object of the invention process allows to characterize a material without using a physical model, that is to say without using a physical law followed by the complex refractive index of the material studied. It is therefore particularly useful when such a law is not known.

This method is an alternative to the known characterization methods, mentioned above. It can be called "nodes method" because it uses "nodes" that is to say the coordinate points (n .lambda.i^* ), Where n is the value taken by the complex refractive index at the wavelength .lambda.i and i takes a limited number of values ​​(whole).

Specifically, the present invention relates to an optical characterization method of at least one layer of a material in a range of values ​​taken by a function α of an optical wavelength λ, where λ varies in a wavelength range, this layer being formed on a substrate, said process being characterized in that it comprises the following steps:

1) carrying a set of OTDR and / or ellipsometry on the interval In this set of measures leading to a measured spectrum, denoted Ψ, and we choose the methods of calculation associated with the type of measures and the type layer characterization, 2) selecting initial values ​​0 m.₁ O ..._not, The function α belonging to the interval A, m being an integer at least equal to 1, and determining a gap B as the set of α points of the range from the smallest to largest 0vi numbers of ... 0cm, when m is greater than 1, and as the interval A when m is 1,

3) selecting m complex initial values ​​of a complex refractive index n^*Jk = n + m to the points ai, i from 1 to m, 4) where m is not 1, we choose an interpolation law that calculates the refractive index n (α) of the material on B range, from the points (I, i), with ni≈n (αi), i ranging from 1 to m, and when m is 1, n (α) is taken equal to the number nι (ι) throughout the interval B,

5) M variable parameters is chosen, M being less than or equal to 2m + l,

6) selecting an error function Er (Ψ, Ψ) that characterizes the difference between a measured spectrum and a theoretical spectrum Ψ Ψ,

7) using a function minimization Er (Ψ, Ψ) to M parameters, performs the following series of steps: a) using the interpolation law of (ai, ni) on the interval B, we deduce n (α), α belonging to B, b) by means of n (α) and the thickness ε of the layer, and of methods for calculating spectra, computing a theoretical spectrum ψ (n (α), ε), c) comparing ψ and ψ using Er (ψ, ψ), and if Er (Ψ, Ψ) is small enough, that is to say less than a predefined value a_, or is minimal, we go to step e), otherwise it goes to step d), d) we vary the M variable parameters so as to tend toward the minimum of Er (Ψ, Ψ) and one returns to step a), e) Er (Ψ, Ψ) is less than e, we obtain a set of M variable parameters, for which Er (Ψ, Ψ (n (α, F), ε)) is minimum and the refractive index is then set equal to that which was obtained last, and if Er ( Ψ, Ψ) is greater than or equal to e it proceeds to step 8), 8) increases the number m of initial values ​​of the function α and the process returns to step

2).

It is thus for example possible to eff ctuer optical characterization: - on a wavelength λ range, namely the range [λmin, λmax],

- Or on a range of lengths of waves inverse l / λ, in this case over an interval [{1 / λ) min, (1 / λ) max], where (l / λ) min is equal to 1 / (λmax) and (l / λ) max 1 / (λmin), or over a range of energies E (E = hv = hc / λ where h is Planck's constant, c is the speed of light in vacuum and the frequency corresponding to V λ), in this case over an interval [Emin, Emax] where Emin is hc / (λmax) and Emax for hc / (λmin), or more generally on an interval [αmin, αmax] values ​​taken by a function α of the variable λ.

It should also be noted that the invention is operable to characterize a spectrum or part spectrum. Each interpolation law can be chosen from linear interpolation laws, the cubic interpolation laws, polynomial interpolation of laws and interpolation laws for example of function "spline". According to a preferred implementation mode of the method of the invention, the spectrum is evenly sampled α (λ), that is to say that the initial values ​​of α function (see step 2) mentioned above) are uniformly distributed in the interval A, the distribution of nodes thus being homogenous.

As we have seen, α (λ) can be selected from λ 1 / λ and hc / λ or any other function of λ, where h is Planck's constant and c is the speed of light in vacuum. Preferably, in step 6) mentioned above, the error is measured on an interest range C which is included in the interval B or equal to the interval B. The variable parameters M may be the real parts of points have refractive indices, i ranging from 1 to m, or the imaginary parts of the refractive indices, these m or variable parameters may be constituted by the thickness of the material which it is desired refractive index.

The present invention also relates to another optical characterization method of at least one layer of a material in a range of wavelengths [λ min, λ max], this layer being formed on a substrate, this alternative process being characterized in that:

- Is carried out a series of OTDR and / or ellipsometry, this set of measures leading to a measured spectrum, denoted Ψ - we choose m initial wavelength λ .lambda.i ..._π, Belonging to that interval, m being an integer at least equal to 1, is associated to each wavelength, a refractive index,

- We choose a law of interpolation for at least the refractive index of the material for wavelengths lying between the initial wavelengths λι ... λ_m,

- M is chosen initial parameters, M being at least equal to m, namely a refractive index of original or for each initial wavelength .lambda.i, 1 ≤ i ≤ m, initial wavelengths being chosen so as to determine by interpolation at least one refractive index for any wavelength in the interval [λ min, λ max], the pairs (.lambda.i nor) being called nodes ,

- Is chosen calculation methods reflectometry and ellipsometry,

- Also selects an error function Er, representative of the difference between two spectra Ψi and Ψ₂The Ψi spectra Ψ₂ being calculated or measured on a number of points higher than the number of nodes m,

- Using m lengths initial wave of initial parameters M and interpolation law, it implements the following optimization process:

- A theoretical spectrum is determined, denoted Ψ, depending on the chosen calculation methods, and the index deduced by interpolation of its value in .lambda.i, i from 1 to m, on the spectrum [λmin, λmax] - we determines the error Er (ψ, ψ) between the measured spectrum and the theoretical spectrum,

- One minimizes this error by varying the position of the unknown indices of values ​​and / or the thickness of the layer and / or the values ​​of the refractive indices of the initial wavelengths, and a spectrum is obtained,

- Are added to the initial wavelengths wavelengths .lambda.i ... λ_mThe added wavelengths constituting new nodes, - The process is repeated by selecting a number m 'of initial wavelengths, m' being greater than m, and M 'initial settings, M' being greater than M, until the accuracy of each spectrum as shown at best be equal to a defined accuracy.

In this case, according to a first particular mode of implementation, m is at least 2; according to a second particular implementation mode, m is 1 and is chosen initial refractive indices equal.

In this case also, according to a particular embodiment, the material is non-absorbent and the number M is equal to m, the extinction coefficient of the material being taken as equal to 0; according to another particular embodiment, M is at least 2 m, a further interpolation law is chosen for the extinction coefficient of the material for each initial .lambda.i wavelength, l ≤ i ≤ m, is selected further an initial extinction coefficient ki, initial wavelengths being further selected so as to determine by interpolation the extinction coefficient for any wavelength in the interval [λ min, λ max ] and in the optimization process, it minimizes the error by varying also the values ​​of the extinction coefficients at wavelengths initials and added wavelengths are also positioned so as to best represent the spectrum of the extinction coefficient of the material. In the case of this another specific embodiment, m may be equal to 1 and can be chosen initial refractive indices equal and equal initial extinction coefficients. Even in the case of this alternative process object of the invention, the material layer can be thin, that is to say having a thickness less than the coherence length of the light used for measurement, one can choose a additional initial parameter, namely an initial layer thickness, and in the optimization process error can be minimized by further varying the value of the layer thickness; alternatively, the material layer may be thicker, that is to say not to be thin, and M may be at most equal to 2 m; in another embodiment, the thickness of the material layer can be known with sufficient accuracy and M is at most equal to 2 m.

The distribution nodes may be homogeneous.

BRIEF DESCRIPTION OF DRAWINGS

The invention will be better understood from reading the description of embodiments given below, purely indicative and non-restrictive, with reference to the accompanying drawings, wherein:

- Figure 1 is a schematic view of devices for characterizing a layer according to the invention, - Figure 2 shows the variations of the refractive index as a function of wavelength, for a material according to a Cauchy

(Curve I) and to a material characterized according to the invention (curve II),

- 3A (3B respectively) shows the variations of the refractive index (extinction coefficient, respectively) as a function of wavelength, for a material according to a law with two harmonic oscillators (curve I) and a material characterized according to the invention, and

- 4 schematically illustrates the parameters used in a generalization of examples of the invention.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

The invention offers an alternative to conventional methods mentioned above. It allows to combine the consistency of a layer model (corresponding to a continuous index of law and constant physical thickness), the general index for the law to find (as in the PAP method). Moreover, the resolution is limited only by the resolution of the measured spectrum.

In the method of the invention, the index spectrum n * (λ) is characterized by:

- A reduced number of "nodes", which are the coordinate points (λ, n.ki) or (.lambda.i, n^*i) n = n (.lambda.i), k = k (.lambda.i) and n^*i = ni + jki, where j²= -l And - An interpolation law between nodes, which can be, for example, linear, cubic, type &lt;κ spline "or polynomial (to any degree).

This interpolation law calculates, from the nodes, the refractive indices and the extinction coefficients for wavelengths located between nodes.

For example, when the refractive index is characterized by a set of values ​​for lengths .lambda.i waves ... λ_m, Linear interpolation can be used between two lengths of waves and .lambda.i .lambda.i₊i for the index n to the wavelength λ (see [6] Chapter 3):

<img id="imgf000018_0001" he="10" wi="58" file="imgf000018_0001.tif" img-format="tif" img-content="drawing" orientation="portrait" inline="no" /> with .lambda.i &lt;λ &lt;.lambda.i_{+ i}

We can do the same for the extinction coefficient.

When the number of nodes allows, more complex interpolation formulas, involving neighboring nodes can be used (see [6] Chapter 3).

A layer model is characterized by ε thickness and knots of family.

The following gives an example of the method of the invention. In this example, the Ψ measures consist of a reflectometric measurement R (λ) and an ellipsometric measurement Sι,₂ (Θ, λ), where θ is the angle of incidence of the light beam which is sent on the working layer during the measurement of ellipsometry. This layer is a thin layer so that the thickness of this layer is as a variable of the problem. In addition, it is assumed that only one layer is unknown, this layer being formed on a known substrate.

First briefly explain this example, which uses an algorithm (the algorithm of "nodes method 'according to the invention).

From information ε assumed on the thickness of the investigated layer and the refractive index n (λ) and the extinction coefficient k (λ) of the material of this layer, are built from nodes (in low number) and ε starting thickness.

Thus, there are m nodes and by interpolation, one can know n (λ) and k (λ) outside the range of wavelengths associated with nodes.

From the starting ε and thickness of these starting values ​​n (λ) and k (λ), we determine the theoretical spectrum Ψ using ellipsometry and réflectrométriques calculations.

Furthermore, by means of ellipsometry and reflectometry devices and a spectrometer is obtained Sι,₂ (Θ, λ) and R (λ) and we deduce the measures noted Ψ (for measuring conditions θ and λ).

then Ψ and Ψ are compared using an error function Er and it optimizes the value of the refractive index and the value of the extinction coefficient at the nodes, and the value of the thickness, seeking minimize Er (Ψ, Ψ). When these values ​​are optimized and if the accuracy of the spectrum n (λ), k spectrum (λ) and the thickness ε is not sufficient, adds new nodes is varied the thickness ε, and we again Ψ determining, comparing and Ψ Ψ and optimization which was mentioned above, etc.

Stopping the loop thus defined when the precision of each of the spectra n (λ) and k (λ) and the thickness ε is judged sufficient (satisfactory adjustment of Ψ and Ψ).

Spectra n (λ), k (λ) ε and thickness are thus characterized.

In an example given purely indicative and non-limiting, there is a thick ε equal to 212, 3 nm for the layer.

Figure 1 shows schematically the studied layer 2 formed on a substrate. Seen from ellipsometry device 5.6, the reflectometry device 8 and the spectrometer 10. It will be seen further electronic processing means 12, comprising a computer and to characterize n (λ), k (λ) and ε based on information provided by the spectrometer 10 and according to the process of one invention.

These means 12 are provided display means 14 which allow in particular to display the variation curve n in function of λ and the variation curve of k as a function of λ. Returning in more detail on the example.

Phase 1

The process of this example comprises a first initialization step.

The algorithm starts with a reduced number of nodes, specifically at least one node. so one can start with a single node, imposing a refractive index and an extinction coefficient remaining constant when the wavelength varies.

It takes positions nodes so that they can, from this node family, deduct the entire spectrum by interpolation. The layer model is therefore to 3 parameters or more, since the thickness is also a variable to determine. The index table on the spectrum is deduced by interpolation nodes.

This is the case when the layer thickness is 1 order of the wavelength variable (thin layers). But when the thickness of the layer is greater than the coherence length of the light source, the thickness hardly occurs more in the calculation of the response of the layer, and is therefore no longer a variable of the problem. For example, in the case of optical disks (CD-ROM) on which a very important layer is deposited (its thickness is of the order of

1 mm), the reflection coefficient of such a layer is not a function of the thickness of the layer but only the refractive index thereof, the coherence length of the incident light beam being less than the thickness of the layer. In this case, the coherence length of the incident beam is determined by the roughness of the layers.

Is chosen, for example, to place the first two end knots and λ min λ max of the spectrum. The values ​​of the complex index in these ends are chosen depending on the type of material studied. For example, on an ellipsometric spectrum between 300nm and 800nm ​​with a thin layer of photosensitive resin, it takes n (300nm) = n (800nm) = 1, 5 and k (300nm) = k (800nm) = 0.

When the spectrum is characterized by two nodes, the index between the extremes is determined by linear interpolation. In the case considered, therefore there are n (λ) = l, 5, and k (λ) = 0 for λ belonging to [300 nm, 800 nm].

From three knots, a cubic interpolation is rather chooses to obtain index law shapes softer than those obtained by linear interpolation.

The initial thickness is, in turn, selected as close as possible to the actual thickness.

Phase 2 is then performed at an optimal determination of zero values ​​of the refractive index and the extinction coefficient on the nodes and the value of the thickness.

To do this, the Ψ spectra (λ) are calculated using the layer model used, resulting from the selection of the nodes of the interpolation and the thickness of the layer law.

The physical model used to calculate Ψ is of course depending on the measurement method used, that is to say in particular the incidence angle of the light, the spectrum used and the model of thin layers or thick layers if necessary (eg diapers models stacked in the document [3]). The Ψ spectra being constituted by a set of different types of measure (e.g. ellipsometric measurements and reflectometric) used for the reflectometry measurements (respectively ellipsometry) a calculation method reflectometry (respectively ellipsometry).

The reflectometric and ellipsometric measurements are combined by 1 via an error function Er (Ψ, Ψ) which is for example of the kind that is defined by equation (1). With a search function, we minimize the gap between Ψ (λ) and Ψ (λ), by varying the value of one refractive index and the value of the extinction coefficient at the position of each node as well that the layer thickness (if the thickness is an important factor in the calculation of

Ψ). When the gap is minimum that is to say when Er (Ψ, Ψ) is a minimum, this means that the reflectometric and ellipsometric measurements coincide at best (for a given number of nodes). At this stage, is obtained for a known number of nodes and a known spectral position for each of these nodes, the model layer (refractive index, extinction coefficient and thickness) which best fits the actual layer.

The validity of the model is found even more assured that the number of steps is large. To have a large number of measurements, one can for example use multiple angles of incidence of the light θi, 1 ≤ i ≤ i for ellipsometric spectra, make a reflectometric measurement and DF make additional measures.

Phase 3

Next, one increases the number of nodes. Adding a finite number of nodes. In a first embodiment, the added nodes are positioned to best represent the spectrums n (λ) and k (λ). For example, placing these additional nodes at the locations where the difference between Ψ and Ψ is a maximum or places in which the nodes are further apart. And one returns to phase 2 as the accuracy of each of the spectra n (λ) and k (λ) and the thickness ε is not sufficient, that is to say, is not equal to a defined accuracy.

In a second embodiment, one interpolates new nodes between two nodes of the set of previously selected nodes, the new node being distributed evenly over the spectrum.

However, it should note the following. When increasing the number of nodes, it is not necessary to keep the position of the old nodes. For example, say we uniformly samples a 400nm to 800nm ​​of spectrum with 3 knots. These nodes are therefore situated respectively 400 nm, 600 nm and 800 nm. When moving at 6 knots, the three additional nodes can be placed so that the spectrum is evenly sampled if we keep the position of the old nodes. 6 the position of nodes can be defined, if it is desired uniform sampling by the values ​​400, 480, 560, 640, 720, 800 nm. Former central node 600nm therefore disappears. To calculate the value of the index at these positions from the old nodes is performed by interpolation.

In the following, we give two common examples of application of the invention. These examples involve two types of materials that follow different laws. From ellipsometric and reflectometric measurements, we propose to find the physical laws followed by these materials.

We proceed as follows:

A fictitious material is created, following a material known theoretical law (a Cauchy or harmonic oscillators Act), with parameters we set arbitrarily. Variations of 1 complex refractive index depending on the wavelength are perfectly known. We impose in addition to the material thickness 200,00nm on a silicon substrate, it is also very well known.

Fictitious measurements (ellipsometric measurements, reflectometric measurements) is calculated, then noisy so as to introduce a default fitting.

It is as if we had real measurements carried out on the material. But contrary to reality, we know perfectly the complex refractive index because we have set, as we set the thickness of the layer of material.

Here we test the method "blind", that is to say, we start from a false thickness (220nm) and complex refractive indices false, since they are supposed to be unknown.

We apply the method of the invention then compares the complex refractive index found the index of refraction theoretical complex. We find much the same laws, precisely, and the same layer thickness.

As a first example, consider a material 1 'complex refractive index follows a Cauchy as: n (λ) = 1.5 + 0 - ^ - ^ rk + W- (λ) = 0

This law index is typical photoresists (in the spectral range from 300nm to 800nm). To find 1 using the method of joints (that is to say, the object of the invention) the index above mentioned law, we perform two steps, namely a measure ellipsometric a angle of 70 ° and a reflectometric measurement.

The processing conditions are:

- The Treaty spectrum is between 300 nm and 800 nm,

- Initially, the nodes are the positions (300 nm, 1.6) and (800 nm, 1.6), that is to say that the index is considered as varying linearly between 300 nm and 800 nm, and its value is constant (equal to 1.6), - the number of nodes is increased iteratively according 2- sequence "4-&gt; 6

- During the process of increase of the nodes, the wavelength position of each node is calculated so that the sampling by 1 / λ is uniform (λ: wavelength), the point density is therefore of increased towards the low wavelengths,

- The interpolation law is a cubic law, when the number of nodes is greater than 2, otherwise it is linear, and

- The minimization algorithm used is a Simplex algorithm.

Figure 2 compares 1 refractive index corresponding to the fictional material that perfectly follows a Cauchy distribution (curve I) to the refractive index we find the nodes method (Curve II), using 6 nodes (represented by^' circles in Figure 2). We used a compound Ψ a measure ellipsometric {S_α (Λ), S₂ (Λ)} to 70 ° and a reflectometric measurement R (λ). We end up with a thickness of

199,8384nm.

As a second example, consider a material whose complex refractive index follows a two harmonic oscillators, such as:

<img id="imgf000028_0001" he="11" wi="76" file="imgf000028_0001.tif" img-format="tif" img-content="drawing" orientation="portrait" inline="no" /> with j² ≈ -1 0 E = 12 / λ (λ in nm) <img id="imgf000028_0002" he="5" wi="57" file="imgf000028_0002.tif" img-format="tif" img-content="drawing" orientation="portrait" inline="no" />

E_!= 1240/400 E₂= 1240/300 G_{1 =}0.3 billion₂= 0.3

In this second example, the method of joints is applied to a set of ellipsometric measurements performed between 250nm and 800nm, 75 °, 70 °, 60 ° and 45 °, with a more reflectometric measurement. The actual thickness of the material being 200nm, there is a thickness of 200.25 nm with the method of joints. The adjustment to the index law considered in this second example is very good, as shown in Figures 3A and 3B. These figures 3A and 3B respectively illustrate the reconstruction of curves n (λ) and k (λ) of the material using the method of joints. The reconstruction is performed at 1 with four ellipsometric spectra and a reflectometric spectrum. The actual absorption peaks are very well represented by the curve obtained by cubic interpolation between nodes (represented by circles in Figures 3A and 3B).

3A, the curve I (or II) corresponds to a refractive index n which completely follows the law chosen

(Respectively a refractive index n found by the method of joints).

3B, the curve I (respectively II) is an extinction coefficient k following perfectly the law chosen

(Respectively an extinction coefficient k found by the method of joints).

Just described examples of the invention. It will be noted in more general way that in the latter, it is considered a set values ​​of X, with X = {nι, n₂, ..., Or .. jι_m, Kι, k₂, ..., Ki, ..., k_m, Ε}, where neither is the value of one refractive index (real) to the node corresponding to .lambda.i, ie the {...} m, m is the number of nodes ki is the value of the absorption coefficient at the node corresponding to .lambda.i, is {l ... m}, ε is the thickness of the layer studied.

In this case, the error Er minimization operation (ψ, Ψ) is equivalent to finding all or "vector" X such that Er is minimum.

When it imposes no particular constraint, the minimization is a minimization 2xm + l parameters. Of course we can add constraints to reduce the number of variables. In particular, if it is known that the material is non-absorbent, is imposed ki = 0 for all i from {l ... m} and X is: <img id="imgf000030_0001" he="5" wi="39" file="imgf000030_0001.tif" img-format="tif" img-content="drawing" orientation="portrait" inline="no" />

If, for a supplementary measurement (e.g. measurement of goniometry or a non-direct optical measurement), there is known the thickness of the treated layer with sufficient accuracy, the thickness ε is not a variable and were X = {nι, n₂ , ..., Or ... n_ra, Ki, k₂, ..., K, ..., k_m}. Of course, the above two options can be combined.

It is explained in the following an implementation mode of the invention in a more general form that the examples given above. Let α (λ) a function of the wavelength λ of the light used for measurements. One can for example choose: α (λ) = λ (see Figures 3A and 3B where the spectrum is evenly sampled λ) α (λ) = l / λ (see Figure 2 where the spectrum is evenly sampled in l / λ) α (λ) = hσ / λ where h is Planck's constant and c is the speed of light in vacuum, α (λ) then being homogeneous energy. Let A be the range of the measurement spectrum, B spectral range described by the "nodes" C and the interval of interest.

The interval C is included in the interval B or equal to the interval B. Similarly, the range B is included in the interval or equal to the interval A.

It states that each of the intervals A, B and C is the type [θ_mO_M] WHERE ot_πIs smaller than α_M and there are two lengths of waves and λk such as .lambda.i <img id="imgf000031_0001" he="5" wi="45" file="imgf000031_0001.tif" img-format="tif" img-content="drawing" orientation="portrait" inline="no" /> . In a purely indicative and non-limiting, Figure 4 shows an example of the intervals A, B and C and variations curves

Ψ and Ψ as a function of α (λ) being in fact a function Ψ n^*(Α (λ)).

Circles represent N nodes. not^* is the complex index, which is expressed here as a function of α (λ) and whose real and imaginary parts are respectively denoted n (α (λ)) and k (α (λ)).

Also seen, purely indicative and non-limiting example of the variation curve n (respectively k) depending on α (λ) via the contact points (or, I) (or (ki, have ), or <img id="imgf000031_0002" he="5" wi="39" file="imgf000031_0002.tif" img-format="tif" img-content="drawing" orientation="portrait" inline="no" /> ki≈k (ai), l≤i≤m (m positive integer).

In Figure 4, note the correspondence between the nodes N, items (ni, ai) and points (ki, ai). In the implementation mode considered, an algorithm is used comprising the steps of:

1. we make the Ψ measures the interval A and the methods of calculation is chosen associated with measurements (ellipsometric or reflectometric calculations); 2. m is chosen numbers ai (component m initial values ​​of the function α), i belonging to {l, ..., m}, with m≥l, and c {i} A (I corresponding to "nodes" ); where m&gt; l, B is defined as the set of points like α min (ai) ≤a≤ max (I); when m = l, we have B = A;

3. we choose m initial values ​​of complex index n^* to m points ai, i belonging to {l, ..., m};

4. If m ≠ s choosing an interpolation law that calculates the refractive index n (α) over the interval B from points (ai, ni), i belonging to {l ... , m}; if m = l, then n (α) = n_x(Αι) over the entire interval B;

5. M variable parameters are chosen with M≤2m + 1; these parameters can be: the real parts of the refractive indices i points i belonging to {l, ..., m}, or

- The imaginary parts of the refractive indices at these same points, or - the thickness of the material which it is desired refractive index;

6. choosing an error function Er (Ψ, ψ) that characterizes the difference between a measured spectrum and the theoretical spectrum; in general, the error is measured on the interval C;

7. by means of a function minimization Er (Ψ, Ψ) to M parameters, is carried out the following series of steps: a) using the interpolation function of (ai, n) B, we deduce n (a) with α belonging to B; b) using n (α) of ε and thickness calculation methods spectrum, calculate the theoretical spectrum Ψ (n (α), ε); c) comparing Ψ and Ψ using

Er = Er (Ψ, Ψ); if Er is small enough (that is, if Er is less than a predetermined value e), or if Er is minimal, we go to step e), otherwise it goes to step d); d) the parameters M is varied so as to tend toward the minimum of Er and the process returns to step a); e) where Er is thus less than e is obtained a set of M parameters such as Er (Ψ, Ψ (n (α, F), ε)) is minimum and the calculation of the refractive index is completed: this index is taken equal to that which was obtained last; and if Er is greater than or equal to e, it proceeds to step 8);

8. m is increased and it returns to step 2).

It should be noted that the present invention can be used not only wavelength sampling (λ) but the sampling frequency (c / λ or simply 1 / λ), energy (hc / λ) and, more generally, parameter depending on the wavelength.

It should also be noted that an essential step of the algorithm (step 8) mentioned above) is not limited to adding a node to the existing nodes: it includes the more general case where the number of nodes increases. That means, in a particular embodiment of the invention, after minimization with 3 nodes, if one wants to go to 6 knots in total, the 3 knots old position is "erased" so for example , to have a constant density of nodes on the spectrum. In practice, this is the best option. Information on the former position of the old nodes is not lost because the value of the indices former nodes is used to calculate the values ​​of 6 new nodes (actually 3 new nodes over three former nodes).

Thus, according to a particular implementation mode of the object of the invention, one can increase the number of initial values ​​of the α function by adding one or more values ​​to the existing initial values; but according to a preferred implementation, we can increase the number of initial values ​​of α function by replacing the existing initial values ​​with new initial values ​​whose number exceeds the number of existing baseline.

The present invention is not limited to the characterization of thin films. It also applies to the characterization of thick layers.

In addition, the present invention is not limited to the characterization of a single layer formed on a substrate. It also applies to characterization of two, or more than two layers formed on a substrate. Documents cited in this specification are the following:

[1] RMA Azzam and NM Bashara, Ellipsometry and Polarized Light, North-Holland Physics Publishing, 1997, Chapter 6.

[2] BK Minhas, SA Coulombe, S. Sohail H. Naqvi and JR McNeil Ellipsometric scatterometry for the metrology of sub-microns-Ol-linewidth structures, Applied Optics, 37 (22): 5112-5115, 1998. [ 3] M. Born and E. olf, Principle of

Optics, Cambridge University Press edition.

[4] AR Forouhi and I. Bloomer, Optical dispersion relationship for amorphous semiconductors and amorphous dielectrics, Physical Review B, 34 (10): 7018-7026, November 1986.

[5] FL Terry, Jr., A modified harmony oscillator approximation scheme for the dielectric constant of Al_xGaι-_xAs, Journal of Applied Physics, 70 (1), 1991, 409-417 pages. [6]. H. Press, SA Teukolsky,. T.

Vetterling and BP Flannery, Numerical Recipes in C, Cambridge University Press, 1992, Chapters 3 and 10.