DE102005023737A1 - Calculation method e.g. for multiple spectrums of total reflection, involves measuring reflection spectrum of object and comparing it with computed model spectrum - Google Patents

Abstract

The method involves measuring a reflection spectrum of an object and comparing it with a computed model spectrum. The model parameters of the model spectrum are varied, until the measured reflection spectrum agrees with the model spectrum and that a given agreement value is reached. The formula is divided in such a way that the computation of the total reflection of the model spectrum into partial formulas that with computation of further spectra with changed parameters only those partial formulas must again be computed, which have a changed parameter.

Description

The The invention relates to a method for determining optical parameters, in particular layer thicknesses or dispersions of layers of a Object according to the preamble of claim 1.

at technical surfaces, especially in semiconductor manufacturing, it is often necessary the structural parameters of the surfaces to determine. For example, must while the production process applied line widths and line profiles of structured layers on their dimensions and their regularity controlled. The exact adherence to the specifications for the Linewidth is more crucial in terms of the product's functionality Importance. To check this Manufacturing parameters will reflect the sample at different wavelength measured. However, these measurements do not directly provide the desired Material data, such as the above-mentioned layer thickness. Much more it is necessary to adapt the calculated values to measured values and with the help of a model with the theory of light scattering calculate the theoretical spectrum and compare it with the measurement. Subsequently the model parameters are changed until theory and measurement in the best possible agreement lie.

The Reflection spectroscopy has long been known and widely used common method for studying layer systems in particular of wafers, and for determining layer thicknesses and other optical Parameters. This is a sample, preferably several layers having irradiated with light of a predetermined wavelength. Are the layers in the range of this wavelength transparent, so the light penetrates into the layer and becomes in the transition areas between two layers, including the transition between the uppermost Layer and the surrounding atmosphere heard, partly reflected. By overlay the incident and reflected light rays cause interference, what the intensity of the reflected light. The ratio of the intensities of incident and reflected light determines the so-called absolute Reflectance so that both intensities must therefore be measured. varies now the wavelength in a given range continuously, you get that Reflectance spectrum having maxima and minima as a function of wavelength. These are caused by the interference. The location of this Extrema hangs from the material properties of the examined sample. This determines hence the optical behavior. These optical parameters include e.g. the refractive index or the absorption coefficient. Furthermore influenced the layer thickness the position of the extrema in the reflection spectrum.

The basic formulas that are used to make the comparison of the model with the measurement to be able to calculate the desired quantities from the Fresnel's Derive diffraction theory.

These are for example in "Spectroscopic Ellipsometry and Reflectometry - A Users Guide "by H.G. Tompkins and W.A. McGahan.

When Reflection in this context is the ratio of the outgoing intensity to the incoming intensity, designated. She is going for both polarization planes "s" - corresponds vertically - and "p" - corresponds parallel - in each case calculated separately. The intensity in turn, is proportional to the square of the amplitude of the lightwave function.

The Equations (equation 1) describe the wave function in a simple way Surface, i.e. at a boundary layer of two media with different, possibly complex dispersions.

Has If you are another medium, it is called a single layer or even a film of thickness d. Also for this model can be the reflection R with a closed formula in each case for the polarization plane specify s and p (equation 2).

she consists of the Fresnel coefficients (equation 1) of the two boundary layers and from a complex e-function together, where for the lower Boundary layer the indices 1 and 2 must be replaced by 2 and 3.

hat die e-Funktion als Argument die komplexe optische Dicke d·Ñ und beschreibt mit ihrer Periodizität das schwingende Verhalten der Reflexion, welches durch Interferenzen innerhalb des Films entsteht. Mit Ñ2 = n2 – j·k2 (Gl. 4)sind die Werte für die Dispersion Ñ ebenso komplex, wie die der Kosinusfunktion cosϕ₂.With

has the e-function as an argument the complex optical thickness d · Ñ and describes with their periodicity the oscillatory behavior of the reflection, which is caused by interferences within the film. With Ñ 2 = n 2 - j · k 2 (Equation 4) the values for the dispersion Ñ are just as complex as those of the cosine function cosφ ₂ .

The measurable reflection on the surface you calculate separately for vertically and horizontally polarized light from the amounts of Wave functions according to the equations (equation 5).

at an equal distribution of the polarizations in the irradiated light is the total unpolarized reflection by the arithmetic Mean according to equation (Equation 6).

gilt. Das Medium, welches das Schichtsystem umgibt, ist üblicherweise Luft. Mit einem reellen ϕ₀ ist auch sinϕ₀ reell, da für ϕ₀ nur n₀ und nicht k₀ berücksichtigt wird. ϕ₁ kann allerdings schon einen Komplexen Wert annehmen, wenn Ñ₀ oder Ñ₁ komplex sind. Mit bekanntem sinϕ₀ kann für alle Schichten sinϕ_i+1 berechnet werden. Der für die Berechnung der optischen Parameter benötigte cosϕ_i ergibt sich dann mit (sinϕ_i)² + (cosϕ_i)² = 1 zu:

Snell's law also applies to the complex sine function Ñ i + 1 · sinφ i + 1 = Ñ i · sinφ i , (Eq. 7) so that for the entrance angle of the ith layer

applies. The medium surrounding the layer system is usually air. With a real φ ₀ also sinφ _{0 is} real, since for φ ₀ only n ₀ and not k _{0 is} considered. However, φ ₁ may already take on a complex value if Ñ ₀ or Ñ _{1 are} complex. With known sinφ ₀ sinφ _{i + 1} can be calculated for all layers. The cosφ _i needed for the calculation of the optical parameters then results with (sinφ _i ) ² + (cosφ _i ) ² = 1 to:

The fitting of a theoretically calculated curve to a measured curve with the aid of a model of variable parameters is referred to below as Fit. For this purpose, the model parameters are varied so that the theory curve coincides as well as possible with the measurement curve. Therefore, many theory curves are often time consuming to achieve a good result. To reduce this amount of time, for example, in the DE 102 04 943 proposed to determine the optimization criterion by the sum of the amounts of the wavelength differences of all pairs of wavelengths. In this case, a pair of wavelengths is formed by those wavelengths which respectively correspond to a selected extremum in the measured reflection spectrum. The extremes are indexed in ascending or descending order. The comparison is then carried out with that extremum which has the same index in the modeled reflection spectrum.

The standard procedure for a fit is the gradient method, since with its help fast the exact Result can be found. The prerequisite for this is that the starting point is already close to the solution. If the model is only vaguely known, it is still necessary to find this starting point. Otherwise, the gradient process leads to a secondary minimum, without this error being clearly recognizable. An upstream process, the so-called Constant Mesh process, fulfills this task. Here each parameter to be fitted is scanned in a predetermined interval with a certain step size. If, for example, a layer thickness is to be determined by a fit and it is known that a layer with a thickness of about 1000 nm is present, an interval and a meaningful step size can then be determined with the aid of an automatism, the so-called Autoranger. The procedure for this is, for example, in the DE 10227376 A1 described. For a nominal value of the layer thickness of 1000 nm, an interval of 382.74 nm to 1617.25 nm results at a step size of 17.14 nm. The ConstantMesh then calculates the resulting 73 spectra and in each case the MSE. The layer thickness with the smallest MSE forms the starting value for the gradient method. If several parameters are to be fitted, the total number of spectra to be calculated results from the product of the number of spectra per parameter. With three layer thicknesses à 73 spectra, this is already 73 × 73 × 73 = 389,017 spectra. The calculation requires three nested loops. It can be seen that the computational effort increases sharply with the number of parameters to be varied. In production control, where analysis is used, time is the limiting factor. The more spectra that can be calculated within a given time, the more parameters can be varied. It is then possible to select larger intervals in which the solution is suspected, which leads to a greater probability of a hit.

at however, the known method requires time consuming ones Perform calculations by varying all parameters.

task Therefore, it is the time of calculation for the present invention on variation of the parameters further reduce.

To According to the present invention, this object is achieved by a method to calculate many spectra of total reflection with the features according to claim 1 solved.

at the method according to the invention for the determination of optical parameters is thus a reflection spectrum of the object measured and the measured reflection spectrum with a calculated model spectrum compared. To determine the searched Parameters become the model parameters of the model spectrum for so long varies until the measured reflectance spectrum matches the model spectrum so well matches, that a given match score is reached. To increase the calculation speed of the varied parameters becomes the Formula for calculating the total reflection of the model spectrum in Partial formulas decomposed so that when calculating additional spectra with amended Parameters only those sub-formulas must be recalculated, the a changed one Have parameters.

In a preferred embodiment The invention becomes the reflection for a new parameter set calculated only when all changing parameters are set were. It is preferred to the changed parameters and the associated Stored layers in which the parameter has changed. The position of the layer is below the storage of the layer within the object.

The Inventive method thus has several steps. In an initialization step the Fresnel formula is decomposed into a number N of equations, where the values of the N equations for all wavelengths a desired one Number ST of interpolation points be calculated. In a parameter step then all new Values of the changed Parameters together with the associated Stored layers in which the parameter has changed. In a recalculation step of total reflection then only even those values of the N equations are recalculated, too indeed a changed parameter contain.

Prefers the fit is performed with a gradient method whose Starting values can be determined with a Constant Mesh method.

In a further preferred embodiment of the invention, all parameters that are to be varied are sorted appropriately in order to further shorten the computing time. In particular, the sorting can be done according to whether they change the dispersion or a layer thickness. The dispersion parameters and the layer thickness parameter They can then be further sorted according to how far they are from the layer into which the light is incident. This allows internal and external calculation loops to be defined. As a result, these interleaved loops can be arranged so that computationally expensive parameters are rarely alterable and to be calculated by being varied in outermost loops.

Of the Advantage of the method according to the invention is thus that the time for the calculation by variation the parameter significantly shortened can be.

Further Advantages and advantageous embodiments The invention are the subject of the following figures and their Descriptions.

It show in detail:

1 schematically the main steps of the method according to the invention

2 the basic procedure of the initialization step

3 the basic procedure of the parameter step for setting the variation parameters

4 the basic sequence of the recalculation step of the total reflection after changing the parameters of the dispersion

5 the principle of the recalculation step of the total reflection after changing the parameters of the thickness

6 the basic sequence of recalculation steps for changing the parameters of thickness and dispersion

7 the basic procedure when using the process in Constant Mesh.

1 schematically shows the main steps of the method according to the invention. In order to be able to decompose the formula for calculating the total reflection of the model spectrum into sub-formulas such that when calculating further spectra with changed parameters only those sub-formulas having a changed parameter have to be recalculated, the initialization step first becomes 10 carried out. Here, the Fresnel formula is decomposed into a number N of equations, where the values of the N equations for all wavelengths of a desired number ST of interpolation points are calculated and stored in a table. In the following parameter step 12 define and save the parameters to be changed. In the parameter sorting step 14 , which is carried out in a preferred embodiment, the changed parameters are sorted depending on the position of the layer in which they are changed and depending on the calculation effort resulting from them so that the most favorable order for the subsequent calculation can be formed , In the recalculation step 16 Finally, the Totalreflexion recalculates the values for the equations of the N equations that contain changed parameters so that the model total reflection can be recalculated.

• 1. Für alle Schichten die komplexe Dispersion im Schritt 18.
• 2. Für alle Schichten der komplexe Kosinus (cosϕ_i)_Komplex mit (Gl. 8) und (Gl. 9) als Funktion der beteiligten komplexen Dispersionen und des reellen Einfallswinkels des Lichtes an der obersten Grenzschicht im Schritt 20. Der Index i bezeichnet dabei die jeweilige Schichtnummer. Beim Ziehen der komplexen Wurzel gibt es genau zwei Lösungen, von denen genau eine im 1. oder 4. Quadranten der Gaußebene liegt. Diese ist zu nehmen. Falls k_i = 0 kann der komplexe Quotient vereinfacht werden. In diesem Fall muss auch überprüft werden, ob 1–sinϕ_i ≥ 0. Ist dies der Fall, so zieht man nur die reelle Wurzel.
• 3. Für alle Schichten außer der Umgebung Ñ_i·cosϕ_i–1, sowie für alle Schichten Ñ_i·cosϕ_i und weiterhin für alle Schichten außer dem Substrat Ñ_i·cosϕ_i+1 im Schritt 22.
• 4. Für alle Grenzschichten die Fresnelkoeffizienten beider Polarisationsrichtung nach (Gl.1) im Schritt 24. Dabei ist der Nenner der Division für den Real- und den Imaginärteil gleich und wird gemeinsam berechnet, jedoch einmal für die p- und einmal für die s-Polarisation.
• 5. Den Quotienten
  
  im Schritt 26, wobei 4π / λ als einmal zu berechnende Konstante festgelegt wird.
• 6. Für alle Schichten außer der Umgebung und dem Substrat
  
  im Schritt 28.
• 7. Für alle Schichten außer der Umgebung und dem Substrat
  
  komplexe Exponent aus (Gl. 2) im Schritt 30.
• 8. Mit der bekannten Wellenfunktion am Substrat berechnet man im Schritt 32 die Wellenfunktion an der nächst höher liegenden Grenzschicht. Setzt man diese wieder in (Gl. 2) ein, so erhält man wieder die Wellenfunktion der nächst höher liegenden Grenzschicht. Dies führt man bis zur obersten Grenzschicht durch. Gleichung (Gl. 2) kann mit den aus 7. erhaltenen Exponenten berechnet werden. Dies wird für alle Schichten außer der Umgebung und dem Substrat, beginnend mit der Schicht oberhalb vom Substrat durchgeführt. Dabei wird für die i-te Schicht R^p durch Rp i–1,i R^s durch Rs i–1,i, rp 12 durch rp i–1,i und rs 12 durch rs i–1,i, rp 23 durch Rp i,i+1, und rs 23 durch Rs i,i+1 ersetzt. Beim ersten Schleifendurchlauf für die Schicht oberhalb vom Substrat wird außerdem rp 23 durch rp i,i+1, und rs 23 durch rs i,i+1 ersetzt, also der Grenzschicht am Substrat. Der Nenner der Division ist für den Real- und den Imaginärteil gleich und wird gemeinsam berechnet, jeweils einmal für die p- und einmal für die s-Polarisation.
• 9. Aus der Wellenfunktion der obersten Grenzschicht wird dann im Schritt 34 mit (Gl. 5) und (Gl. 6) die messbare Gesamtreflexion berechnet.

To calculate the total reflection of a model, it is assumed that an object has a plurality of layers. Hereinafter, for the sake of simplicity, the material surrounding the layers, the so-called environment, and the substrate, that is to say the material to which the layers are applied, are referred to as layers, although the thickness is unknown and also irrelevant. In both cases, only the dispersion is interesting. To obtain the total reflection of the model, the initialization step (equation 10) is first performed. For this purpose, as in 2 First, the values of the following equations are calculated for all wavelengths of the desired interpolation points and stored in a table:

• 1. For all layers the complex dispersion in the step 18 ,
• 2. For all layers the complex cosine (cosφ _i ) _complex with (equation 8) and (equation 9) as a function of the involved complex dispersions and the real angle of incidence of the light at the upper boundary layer in the step 20 , The index i designates the respective layer number. When dragging the complex root, there are exactly two solutions, of which exactly one lies in the 1st or 4th quadrant of the Gaussian plane. These is to take. If k _i = 0, the complex quotient can be simplified. In this case it must also be checked whether 1-sinφ _i ≥ 0. If this is the case, then only the real root is drawn.
• 3. For all layers except the environment Ñ _i · cosφ _i-1 , as well as for all layers Ñ _i · cosφ _i and furthermore for all layers except the substrate Ñ _i · cosφ _{i + 1} in the step 22 ,
• 4. For all boundary layers, the Fresnel coefficients of both polarization directions according to (Gl.1) in step 24 , Here, the denominator of the division for the real and the imaginary part is the same and is calculated together, but once for the p- and once for the s-polarization.
• 5. The quotient
  
  in step 26 where 4π / λ is set as a constant to be calculated once.
• 6. For all layers except the environment and the substrate
  
  in step 28 ,
• 7. For all layers except the environment and the substrate
  
  Complex exponent from (equation 2) in step 30 ,
• 8. With the known wave function at the substrate one computes in the step 32 the wave function at the next higher boundary layer. If these are put back into (equation 2), the wave function of the next higher boundary layer is again obtained. This is done up to the top boundary layer. Equation (equation 2) can be calculated with the exponents obtained from 7.. This is done for all layers except the environment and the substrate, starting with the layer above the substrate. In this case, for the i-th layer R ^p through Rp i-1, i R ^s through Rs i-1, i, rp 12 through rp i-1, i and rs 12 through rs i-1, i, rp 23 by Rp i, i + 1, and rs 23 are replaced by Rs i, i + 1. During the first loop pass for the layer above the substrate, rp 23 is also replaced by rp i, i + 1, and rs 23 by rs i, i + 1, ie the boundary layer on the substrate. The denominator of the division is the same for the real and the imaginary part and is calculated together, once for the p-polarization and once for the s-polarization.
• 9. From the wave function of the upper boundary layer is then in step 34 calculates the measurable total reflection with (equation 5) and (equation 6).

In order to is the total reflection for a model with a set of parameters, the so-called start parameters, at all interpolation points calculated. The values for these equations are stored in a table. The equations even contain parameters that match the model calculated curve of total reflection to the measured curve varies can be. Let now the total reflection for other parameters are calculated, so only a small one has to be added Part of the above calculation will be redone. Putting a Parameters and the calculation of the reflection for each other separated. The call to calculate the reflection will only then carried out, if all are changing Parameters were set. If several parameters are equal or partial same calculations, they will not be duplicated carried out.

In 3 is the parameter step 12 , So the flow of the method for setting a parameter using the example of the layer thickness or the dispersion shown. First, in step 36 checks if a parameter used during initialization has changed. If this is not the case, it is already returned at this point. Will in step 36 found that the parameter has changed, so in step 38 this parameter value is saved. In step 40 it is checked whether the changed parameter value is a layer thickness d. If this is the case, then in step 42 set a so-called layer thickness flag and in step 44 the layer with which the parameter is saved has changed value. Unless in step 40 If it is determined that the layer thickness d has not changed, the steps become 42 and 44 skipped. In step 46 is then checked whether the changed parameter value is a dispersion Ds. If this can be determined, then in the step 48 set a dispersion flag. Subsequently, in step 50 stored the layer with the parameter value in which the dispersion has changed. The in 3 The basic program sequence for varying the parameters is now continued until it is clear that all the parameters that are to be changed are reset. If this is the case, the recalculation of the total reflection with the changed parameter values can be continued.

The basic procedure for the calculation of the total reflection with changed parameter values for a dispersion parameter is in 4 shown. The procedure for the calculation of the total reflection with changed thickness parameters results from the representation in 5 , Steps required for both changed thickness parameters as well as changed dispersion parameters are in 6 shown.

As in 4 shown is first checked whether the dispersion has changed in one of the layers. This can be done in the step 52 be done by checking whether a dispersion flag is set. If this is not the case, then immediately becomes the step 64 in 5 jumped. If the dispersion flag is set, it is subsequently checked whether the dispersion of the environment has changed, which is generally air. If this is the case, then in step 56 set a dispersion flag for all layers of the object. This is necessary because according to (equation 9), the angle of incidence in all other layers has changed in this case, so that the calculation has to be performed anew. If the dispersion in the environment has not changed, then step 56 skipped. In step 58 is then point for all layers in which a dispersion flag is set 1 and 2 initialization, ie recalculating these values. In step 60 is then subsequently stored, which of these layers is closest to the substrate. In step 62 then becomes point for all boundary layers 3 recalculated the initialization for which the dispersion of one of the adjacent layers has changed. Furthermore, the calculation of the point takes place for all boundary layers 4 the initialization for which the dispersion of one of the adjacent layers has changed.

As in 5 is then transferred to calculate the changed parameter values of the thickness. In step 64 First, it is checked whether the thickness has changed in one of the layers. This can be detected by whether a thickness flag is set. If not, the steps become 66 and 68 skipped and jumped the in 6 performed calculation steps performed. If a thickness parameter d has changed, then in step 66 for all the layers for which the thickness has changed, period 6 initialization. In step 68 is stored, which of these layers is closest to the substrate.

For all layers in which the thickness d or the dispersion Ds has changed, the additional steps to be performed in 6 shown. In step 70 is here first point 7 initialization for the new parameter values. Starting with the layer which is closest to the substrate of the layers in which the thickness d or the dispersion Ds has changed, in step 72 Point 8th The initialization was redone for all layers above it to the environment. In step 74 becomes point 9 initialization, ie the new total reflection is calculated. Ultimately, in step 76 all flags reset.

The standard procedure for the fit is the gradient method. In order to be able to determine the start parameters as well as possible, the Constant Mesh method can be preceded. A method for sorting the changed parameter values 14 ( 1 ) can be used to further increase the speed.

• – Die Änderung eines Dispersionsparameters ist deutlich aufwendiger als die einer Schichtdicke. Die Größe des Mehraufwandes hängt vom verwendeten Materialmodell ab, welches die optischen Eigenschaften des Materials beschreibt.
• – Die Änderung eines Parameters einer Schicht, wie etwa der Dispersion Ds oder der Dicke d wird um so aufwendiger, je weiter sie von der Schicht entfernt ist, in die das Licht einfällt. Der Grund dafür liegt in der iterativen Berechnung nach Hauge.

For every parameter to be inserted a loop is necessary. These loops are nested inside each other. The idea of increasing speed is to rarely change and calculate computationally expensive parameters by varying them in outermost loops. Overall, this results in an additional time advantage, since only the changing part is recalculated. Differences in computational effort exist as follows:

• - The change of a dispersion parameter is much more complicated than that of a layer thickness. The size of the extra effort depends on the material model used, which describes the optical properties of the material.
• - The change of a parameter of a layer, such as the dispersion Ds or the thickness d becomes more complex, the farther it is from the layer in which the light is incident. The reason for this lies in the iterative calculation according to Hauge.

In a preferred embodiment of the invention it is therefore proposed, before the calculation of the new total reflection curve with the changed parameter values, that a suitable sorting of the parameter values, as in FIG 1 in step 14 shown to perform.

In 7 this procedure is shown in detail. First, in step 78 sort all the parameters to be varied according to whether they change the dispersion or a layer thickness. In step 80 the dispersion parameters to be varied are sorted by how far the layer in which they lie is removed from the layer into which the light is incident. In step 82 then the dispersion parameter corresponding to the farthest layer is selected. This will then be in step 84 initially formed an outer calculation loop. Subsequently, in step 86 checks whether all dispersion parameters have already been used to form a loop. If this is not the case, then with the next dispersion parameter again in the step 82 continued. If it has been determined that all dispersion parameters have already been used to form loops, then in step 88 continued to sort the varying layer thicknesses by how far the layer is from the layer into which the light is incident. In step 90 Then, that layer thickness is selected which corresponds to the farthest layer. With this the next loop is formed in step 92 , In step 94 It is checked whether all varying layer thicknesses have already been used to form loops. If this is not the case, then step 90 continued. If a loop has already been formed for the last layer thickness, a loop exists for each layer thickness to be varied.

With The loops thus formed are now each in the order Looping this order recalculates the parameters. Thereby The calculation effort can be significantly reduced and the calculation performed much faster become.

The Increase the speed of the new process in comparison to the previously known method is based on the following table specified. Here are the values for the time, those in the analyzes to determine the result, for three typical, applications used in practice have been compared. The measurements were made on the same calculator under the same conditions and are relative to each other.

from that It can be seen that the speed advantage of the method according to the invention especially in the cases becomes apparent in which several parameters are varied and calculated Need to become. It can be more than a hundred times depending on the application. This now also allows applications with many fit parameters, the previously took too long.

10

initialization

12

parameters step

14

Parameter sort step

16

recalculation step the total reflection

18

calculation the complex dispersion

20

calculation of the complex cosine

22

Calculation of Ñ _i · cosφ _i-1

24

calculation Fresnel coefficients of both polarization directions

26

calculation of the quotient 4π / λ

28

Calculation of d _i 4π / λ

30

calculation of the complex exponent (Eq.

32

calculation the wave function

34

calculation the measurable total reflection

36

parameter changed?

38

to save parameter value

40

parameter a layer?

42

Put Thick flag

44

to save layer

46

dispersion changed

48

Put Dispersion Flag

50

to save layer

52

dispersion changed?

54

dispersion changed the environment?

56

Set Dispersion flag for all layers

58

calculation of Inj. 1 and 2

60

to save closest layer

62

calculation Inition 3 and 4 for boundary layers

64

thickness changed?

66

calculation Inischritt 6 for all changed layers

68

to save closest layer

70

calculation Ini step 7

72

calculation Ini step 8

74

calculation Ini step 9

76

Reset to default all flags

78

sort by according to the type of parameter

80

sort by the dispersion parameter according to the position of the layer

82

Select the dispersion parameter

84

Form the outer calculation loop

86

All amended Calculated dispersion parameter?

88

sort by all thickness parameters according to the position of the layer

90

Select the Dick parameter

92

Form the inner calculation loop

94

All amended Thickness parameter calculated?

d

layer thickness

ds

dispersion

N

number equations

ST

number the support points

Claims (14)

Method for determining optical parameters, in particular the layer thickness (d) or the dispersion (Ds) of layers of an object, wherein a reflection spectrum of the object is measured and the measured reflection spectrum is compared with a calculated model spectrum, wherein the model parameter of the model spectrum varies so long until the measured reflection spectrum agrees so well with the model spectrum that a predetermined match value is achieved, characterized in that the formula for calculating the total reflection of the model spectrum is subdivided into sub-formulas such that when calculating further spectra with changed parameters only those sub-formulas are new must be calculated, which have a changed parameter. A method according to claim 1, characterized in that the reflection is calculated for a new parameter set only when all the changing parameters in a parameter step ( 12 ). Method according to claim 2, characterized that to the changed ones Parameters also the associated Layers of the object are stored, in which the respective Changed parameters Has. Method according to one of claims 1 to 3, characterized that changed Parameter the layer thickness (d) of a layer or the dispersion (Ds) is a layer. Method according to one of claims 1 to 4, characterized in that - in an initialization step ( 10 ) the Fresnel formula is decomposed into a number N of equations, the values of the N equations being calculated for all wavelengths of a desired number ST of interpolation points, - parameter step ( 12 ) all new values of changed parameters are stored together with the corresponding layers into which the parameter has changed and - in a recalculation step ( 16 ) of the total reflection those values of the N equations are recalculated, which contain a changed parameter. Method according to claim 5, characterized in that in the initialization step - for all layers the complex dispersion, - for all layers of the complex cosine (cosφ _i ) _complex with (equation 8) and (equation 9) as a function of the involved complex dispersions and the real angle of incidence of the light at the uppermost boundary layer, - for all layers except the neighborhood Ñ _i · cosφ _i-1 , for all layers Ñ _i · cosφ _i , as well as for all layers except the substrate Ñ _i · cosφ _{i + 1} , - For all boundary layers the Fresnel coefficients of both polarizations, - the quotient

with 4π as the constant to be calculated, - For all layers except the environment and the substrate

- For all layers except the environment and the substrate

For all layers starting with the known wavefunction on the substrate, the wavefunction at the next higher boundary layer up to the uppermost boundary layer, from the wavefunction of the uppermost boundary layer, in particular using (Equation 5) and (Equation 6), the measurable total reflection calculated become. Method according to one of Claims 1 to 6, characterized that the fit is performed by means of a gradient method. Method according to claim 7, characterized in that the gradient method employs a constant mesh method in which at a given interval with a certain Increment of each parameter to be inserted is scanned. A method according to claim 7 or 8 are sorted to varying parameters according to whether they change the dispersion or a layer thickness, so that a first parameter set Ds ₁ ... Ds _n is formed having parameters that change the dispersion and a second parameter set d ₁ ... d _n , which has parameters that change the thickness. A method according to claim 9, characterized in that the first parameter set Ds ₁ ... Ds _{n is} sorted by how far the layer in which they lie is removed from the layer into which the light is incident. A method according to claim 10, characterized in that the fit is first calculated for the dispersion parameter Ds _i resulting from the farthest layers and subsequently proceeding to the dispersion parameter closest to the layer of the dispersion parameter Ds _i , until the fit is carried out for each dispersion parameter Ds ₁ ... Ds _n to be varied. Method according to claim 10 or 11, characterized in that the layer thicknesses d ₁ ... d _n to be varied are sorted by how far the layer is from the layer into which the light is incident. Method according to claim 12, characterized in that according to the fit of the dispersion parameters Ds ₁ ... Ds _n the fit for that thickness parameter d _i is calculated first, which results from the farthest layers and is then continued with the thickness parameter which the Layer of the thickness parameter d _{i is} closest and is continued until the fit is performed for each thickness parameter d ₁ ... d _n to be varied. Method according to one of claims 11 to 13, characterized in that prior to the implementation of the respective fit for the dispersion parameters Ds ₁ ... Ds _n and the thickness parameters d ₁ ... d _n , the definition of loops for a subsequent program sequence takes place.