DE102005023736B4 - Method for determining structure parameters - Google Patents

Abstract

Method for determining structure parameters, in particular the line width (L) or the line period (P) of an object, wherein a spectrum of an object is measured by a scatterometric method, in particular ellipsometry, and the measured spectrum is compared with a calculated model spectrum, wherein Structural parameters of the model spectrum are varied until the measured spectrum with the model spectrum matches so well that a predetermined match value is achieved, characterized in that the formula for calculating the model spectrum in sub-formulas is decomposed so that when calculating additional spectra with changed Model structure parameters only those sub-formulas must be recalculated, which have a changed model structure parameter.

Description

The invention relates to a method for determining structural parameters according to the preamble of claim 1.

For technical surfaces, especially in semiconductor manufacturing, it is often necessary to determine the structural parameters of the surfaces. For example, line widths and line profiles of structured layers applied during the manufacturing process must be controlled for their dimensions and regularity. Accurate compliance with line width specifications is critical to the product's functionality. Other structural parameters, such as the sidewall slope or the trench depth of lines, are also of great importance. Appropriate measuring methods are used to check these production parameters, in particular on lithographic masks, semiconductor wafers or other finely structured surfaces. In a special way, the scatterometry with which periodic structures can be measured with scattered light, which are smaller than the wavelength of the light used is suitable here. With relatively little technical effort can thus be considered structures in which other optical measurement methods fail due to the resolution limit. Such a non-destructive measuring method is, for example, ellipsometry. However, the measurements do not directly provide the desired material data, such as the above layer thickness, line width or period of the structure. Rather, it is necessary to calculate a theoretical spectrum with the help of a model with the theory of light scattering and to compare it with the measurement. Subsequently, the model structure parameters are changed until theory and measurement are in the best possible agreement. The model structure parameters to be varied are, for example, the line width of a periodic structure, its period, line or web height. If the shape of the webs are to be analyzed, they can be broken down into several layers, with the width of the layers obtained subsequently being separately fitted.

For example, the rigorous method of M. Moharam et al., Journal of the American Optical Society A. vol. 12 (1995), pp. 1077-1086. In this method, the Maxwell equations are solved exactly with the boundary conditions specified by the structure.

Those parameter values that lead to the best match between measurement and simulation are assumed to be a reasonable approximation of the real lattice parameters. In order to reduce the computational effort required for the described method, is in the DE19914696 A1 proposed to refrain from a precise quantitative evaluation and instead only to carry out a classification.

In order to achieve a further acceleration of the evaluation, the simulation can be carried out before the actual measurement is carried out and stored in a database. Then, with the help of a search algorithm, the simulation is selected with the underlying structure parameter that best matches the measurement results.

However, if a solution is to be used which works with the aid of the variation of the simulation parameters, these simulation parameters must be varied for a further rigorous simulation until the deviations of the simulation from the measurement lie below a predetermined value. This process is very time consuming and can usually be achieved in special cases, such as a vertical incidence of light, in the required speed results.

In order to further improve the speed of the evaluation, in the DE 10302868 A1 proposed to calculate as a basis for the simulation a function which maps at least one simulated beam parameter of the reflected or transmitted light beam onto at least one simulated beam parameter of the light beam directed onto the surface. The predefinable structural parameters are varied with the aid of an optimization method such that a difference function formed from the determined mapping rule and the calculated function assumes function values that are smaller than the functional values of a limit function. The simulation is performed using an approximation method and / or a learning system for calculating diffraction effects. The resulting structure parameters are then used for an optimization step using the rigorous calculation method. Thus, this method provides a library function that calculates a scatterometry spectrum after passing a model.

The standard procedure for a fit is the gradient method, because with its help the exact result can be found quickly. 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 method can lead to a secondary minimum without this error being clearly recognizable. An upstream process, the so-called Constant Mesh process, fulfills this task. Hereby everyone will be fit Scanned parameters at a specified interval with a certain increment.

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.

With the use of this method, however, it is still necessary to carry out the overall calculation again with changed model parameters, which requires a considerable time expenditure for the calculation.

In addition, from the prior art US Pat. No. 6,483,580 B1 which describes a method for measuring diffraction structure parameters on an underlying structure, as well as US 5,963,329 A , which describes a method for non-destructive determination of the line profile or topographic cross-section of repeating lines on a substrate.

The object of the present invention is therefore to refine the known method for determining structural parameters in such a way that the time required for changing the model structural parameters is further reduced.

According to the present invention, this object is achieved by a method for determining structural parameters having the features according to claim 1.

In the method according to the invention for determining structural parameters of the object, a spectrum is first measured with the aid of a scatterometric method, for example ellipsometry, and the measured spectrum is compared with a calculated model spectrum. To determine the sought-after structure parameters, the model structure parameters of the model spectrum are varied until the measured spectrum matches the model spectrum so well that a predetermined match value is achieved. To increase the speed in the calculation of the spectra with the varied model structure parameters, the formula for calculating the model spectrum is subdivided into sub-formulas such that when calculating further spectra with changed model structure parameters only those sub-formulas need to be recalculated that have a changed model Have structural parameters.

In a preferred embodiment of the invention, the model spectrum for a new model structure parameter set is only calculated when all changing model structure parameters have been determined. If appropriate, the associated layers, in particular in the case of the calculation of the shape of webs, in which the model structure parameter has changed are also preferably stored for the modified model structure parameters. In this case, the storage of the layer is to be understood as meaning the position of the layer within the object.

The inventive method thus has several steps. In an initialization step, the formula for calculating the spectra 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. In a parameter step, all new values of the changed parameters are then stored together with the associated layers into which the parameter has changed. In a recalculation step of the spectrum, only those values of the N equations which actually also contain a changed model structure parameter are recalculated.

Preferably, the fit is performed by a gradient method whose starting values are determined by a constant mesh method.

For this purpose, in a further preferred embodiment of the invention, all model structure parameters to be varied are suitably sorted in order to further shorten the computing time. In particular, the sorting can be carried out according to which structural parameter, for example the line width, height or period, has changed.

The advantage of the method according to the invention is therefore that the time for the calculation can be significantly shortened by varying the parameters.

Further advantages and advantageous embodiments of the invention are the subject of the following figures and their descriptions.

• 1a, b typische mit dem erfindungsgemäßen Verfahren bestimmbare Struktur
• 2 schematisch die Hauptschritte des erfindungsgemäßen Verfahrens
• 3 den prinzipiellen Ablauf des Parameterschritts zum Festlegen der Variationsparameter
• 4 den prinzipiellen Ablauf des Neuberechnungsschritts des Spektrums nach Änderung der Modell-Strukturparameter der Linienhöhe
• 5 den prinzipiellen Ablauf des Neuberechnungsschritts des Spektrums am Beispiel der Änderung der Linienbreite
• 6 den prinzipiellen Ablauf der Neuberechnungsschritte für Änderung der Modell-Strukturparameter Linienbreite und Linienhöhe
• 7 den prinzipiellen Ablauf beim Einsatz des Verfahrens im Constant-Mesh.

They show in detail:

• 1a, b typical structure determinable by the method according to the invention
• 2 schematically the main steps of the method according to the invention
• 3 the basic procedure of the parameter step for setting the variation parameters
• 4 the basic procedure of the recalculation step of the spectrum after changing the model structure parameters of the line height
• 5 the basic procedure of the recalculation step of the spectrum with the example of the change of the line width
• 6 the basic sequence of the recalculation steps for changing the model structure parameters line width and line height
• 7 the basic procedure when using the method in Constant-Mesh.

In 1a a possible structure is shown whose structural parameters can be determined with the method according to the invention. In this case, a periodic structure is shown, the webs 13 having. The webs are linear and have a width L and a period P , The structure parameters can be determined with the aid of scatterometric methods. As in 1b shown schematically, the structure of a web 13 be approximated by having a plurality of layers 15 with different geometric masses such as width and height one above the other so arranged that the structure of the web 13 is essentially reproduced. The stacked layers 15 can be used in model calculations and provide model structure parameters that are used to calculate the structure of the web 13 can be varied.

2 schematically shows the main steps of the method according to the invention. In order to be able to decompose the formula for calculating the model spectrum into sub-formulas such that when calculating further spectra with changed model-structure parameters only those sub-formulas having a changed model-structure parameter have to be recalculated, an initialization step is initially performed 10 carried out. This is the formula for calculating the model spectrum, such as in the DE 10302868 A1 in which 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 a subsequent parameter step 12 The model structure parameters to be changed are set and saved. In the parameter sorting step 14 , which is performed in a preferred embodiment, the changed model structure parameters are sorted 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 spectrum is recalculated for those equations of the N equations that contain modified model structure parameters so that the model spectrum of the structure can be recalculated.

Thus, the model spectrum of the structure is calculated with a set of model structure parameters, the so-called start parameters, at all nodes. The values for these equations are stored in a table. The equations themselves contain model structure parameters that can be varied to fit the curve of the spectrum calculated with the model to the measured curve. If the model spectrum of the structure is to be calculated for other model structure parameters, then only a small part of the above calculation has to be performed again. The setting of a model structure parameter and the new calculation of the model spectrum are separated from each other. The call for the calculation is only performed when all changing model structure parameters have been set. If several model structure parameters entail identical or partially identical calculations, these are not performed twice.

In 3 is the parameter step 12 , ie the sequence of the method for setting the model structure parameters using the example of the line width L and the line period P shown. First in the step 18 checks if a model structure parameter used during initialization has changed. If this is not the case, it is already returned at this point. Will in step 18 found that the model structure parameter has changed, so in step 20 stored this model structure parameter value. In step 22 it is checked whether the changed model structure parameter is a line width L is. If this is the case, then in step 24 set a so-called line width flag and in step 26 stored. Unless in step 22 it is determined that the line width L has not changed, so will the steps 24 and 26 skipped. In step 28 it is then checked if the changed model structure parameter is a line period P is. If this can be determined, then in the step 30 set a line period flag. Subsequently, in step 32 the new line period P saved. The in 2 The basically illustrated program sequence for the variation of the model structure parameters is now continued until it is clear that all model structure parameters that are to be changed are newly set, whereby also other model structure parameters than the line width L and the line period P can be included in additional loops. If this is the case, the recalculation of the structure spectrum can be continued with the changed model structure parameter values.

The basic procedure for calculating the structure spectrum changed model structure parameters using the example of the line width L is in 4 shown. The procedure for the calculation of the structure spectrum with changed line period P derives from the representation in 5 , Steps, both for changed line period P as well as the changed line width L are required are in 6 shown.

As in 4 First shown is whether the line width is shown L has changed. This can be done in the step 34 be done by checking whether a line width flag is set. If this is not the case, then immediately becomes the step 40 in 4 jumped. If the line width flag is set, then in step 36 in the initialization 10 anticipated calculations of the values for the line width parameters newly performed, ie recalculated these values. In step 38 these values are then saved.

As in 5 is then displayed for the calculation of the changed model structure parameters of the line period P passed. In step 40 First, it checks whether the line period P has changed. This can be detected by whether a line period flag is set. If this is not the case, the steps will take 42 and 44 skipped and it will be directly in 6 performed process steps performed. Has the line period P changed, so in the step 42 those specified in the initialization, for the line period P required recalculations of the equations. In step 44 the result is stored for the new model structure parameters.

In addition, it may be necessary for further computation steps specified in the initialization to be performed for those equations that either have the line period P , the line width L has changed or for which both have changed. In this case, the additional steps to be performed in 6 shown. In step 46 If necessary, these calculations are performed and the results in step 48 saved. In step 50 then all flags are 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 ( 2 ) can thus be used to further increase the speed.

A loop is required for each model structure parameter to be inserted. These loops are nested inside each other. The idea of increasing speed is to rarely change and calculate computationally expensive model structure parameters by varying them in outermost loops. Overall, this results in an additional time advantage, since only the changing part is recalculated.

In a preferred embodiment of the invention it is therefore proposed, before the calculation of the new model spectrum of the structure with the changed model structure parameter values, that an appropriate sorting of the model structure parameters, as in FIG 2 in step 14 shown to perform.

In 7 this method is basically based on the changed model structure parameters line width L and line period P shown. First, in step 52 all the varying model structure parameters are sorted according to whether they are the line width L or the line period P to change. In step 54 Then, the line width parameters to be varied are sorted according to how computationally the change in this model structure parameter is. In step 56 then becomes an order for forming calculation loops of the line period P established. Subsequently, in step 58 checks whether all line period parameters have already been sorted and thus used to form a calculation loop. If this is not the case, then the next line period parameter is returned to the step 56 continued. If it has been determined that all line period parameters have already been used to form calculation loops, then in step 60 with continued, the line period to be varied P sort by how expensive the change of this model structure parameter is. In step 62 then becomes an order for forming calculation loops of the line period P established.

In step 64 It is checked whether all line period parameters have already been sorted and thus used to form a calculation loop. If this is not the case, then the next line period parameter is returned to the step 62 continued. If a loop is also formed for the last line period parameter, a loop exists for each line period to be varied and the method is in step after the calculation loop is formed 66 completed.

With this method, inner and outer calculation loops can be formed. As a result, these interleaved loops can be arranged so that computationally expensive model structure parameters are rarely changed and to be computed by being varied in outermost loops. As a result, the calculation effort can be significantly reduced and the calculation can be performed much faster.

The procedure was based on the two model structure parameters line width L and line period P described. However, it goes without saying that other model structure parameters can also be included accordingly or instead of the two concrete model structure parameters P and L can be used.

LIST OF REFERENCE NUMBERS

10

initialization

12

parameters step

13

web

14

Parameter sort step

15

layers

16

Recalculation step of total reflection

18

Changed model structure parameters?

20

Save parameter value

22

Model structure parameter is line width L ?

24

Set line width flag

26

Save new line width L

28

line period P changed?

30

Set line period flag

32

Save new line period P

34

Line width flag set?

36

Recalculation Equation with new line width

38

to save

40

Line Period flag set?

42

Recalculation Equation with new line period

44

to save

46

Recalculation of equations with new model structure parameters

48

to save

50

Reset all flags

52

Sort model structure parameters by line width and line period

54

Sort line width parameters according to calculation effort

56

Determination sequence line width parameters

58

All changed line width parameters considered?

60

Sort line period parameters according to calculation effort

62

Determining sequence of line period parameters

64

All changed line period parameters taken into account?

66

The End

L

linewidth

P

line period

N

Number of equations

ST

Number of interpolation points

Claims (9)

Method for determining structure parameters, in particular the line width (L) or the line period (P) of an object, wherein a spectrum of an object is measured by a scatterometric method, in particular ellipsometry, and the measured spectrum is compared with a calculated model spectrum, wherein Structural parameters of the model spectrum are varied until the measured spectrum with the model spectrum matches so well that a predetermined match value is achieved, characterized in that the formula for calculating the model spectrum in sub-formulas is decomposed so that when calculating additional spectra with changed Model structure parameters only those sub-formulas must be recalculated, which have a changed model structure parameter. Method according to Claim 1 in which a new spectrum for a new model structure parameter set is only calculated when all changing model structure parameters have been defined in a parameter step (12). Method according to Claim 2 , wherein for the changed model structure parameters also the associated layers (15) of the object are stored, in which the respective model structure parameter has changed. Method according to one of Claims 1 to 3 , wherein the changed model structure parameter is the line width (L) of a structure, the line period (P) of a structure, or the geometric shape of a layer (15) for calculating a ridge (13). Method according to one of Claims 1 to 4 in which, in an initialization step (10), the formula for calculating the spectrum 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, - all in one parameter step (12) new values of the changed parameters if necessary stored together with the associated layers into which the model structure parameter has changed, and - in a recalculation step (16) of the spectrum, those values of the N equations containing a changed model structure parameter are recalculated. Method according to one of Claims 1 to 5 wherein a fit is performed by means of a gradient method. Method according to Claim 6 in which the gradient method employs a constant-mesh method in which each model structure parameter to be fitted is scanned in a predetermined interval with a certain step size. Method according to Claim 6 or 7 in which all the parameters to be varied are sorted according to whether they change the line width (L) or a line period (P) to produce a first line width parameter set (L ₁ , ..., L _n ) having model structure parameters change the line width (L) and a second line period parameter set (P ₁ , ..., P _n ) that has model structure parameters that change the line period (P). Method according to Claim 8 , wherein prior to the implementation of the respective fit for the line width parameter set (L ₁ , ..., L _n ) and the line period parameter set (P ₁ , ..., P _n ), the determination of loops for a subsequent program flow.

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