WO2004068070A1

WO2004068070A1 - Method for determining structural parameters of a surface

Info

Publication number: WO2004068070A1
Application number: PCT/DE2003/004287
Authority: WO
Inventors: Andrea Weidner; Andreas Erdmann; Claus Schneider
Original assignee: Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V.
Priority date: 2003-01-25
Filing date: 2003-12-23
Publication date: 2004-08-12
Also published as: DE10302868A1; DE10302868B4

Abstract

The invention relates to a method for determining structural parameters of a surface (4) consisting in optically measuring periodical structures (5) and in carrying out a simulation or in using an adapting system which make it possible to determine said structural parameters by calculation. Entry values treated by means of said simulation or an adaptive system are modified as far as calculated values are situated in a defined limit of tolerance with respect to the measured structural parameters. The inventive method is characterised in that the simulation is carried out with the aid of approximation and/or an adaptive system for calculating diffraction effects and the structural parameters calculated by means of approximation and/or the adaptive system are used for an optimisation stage requiring stringent calculations.

Description

Method for determining structural parameters of a

surface

Technical application area

The invention relates to a method for determining structural parameters of a surface, in which at least one coherent light beam of defined intensity and polarization is directed onto the surface, a beam reflected or transmitted by regular structures of the surface is detected and at least one imaging rule is determined, which is at least one Maps beam parameters of the reflected or transmitted light beam to at least one beam parameter of the light beam directed onto the surface. Furthermore, a simulation that is carried out on the basis of predefinable structural parameters is used to calculate a function that maps at least one simulated beam parameter of the reflected or transmitted light beam to at least one simulated beam parameter of the light beam directed onto the surface. The predefinable structure 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 function values of a limit function. State of the art

When determining the structural parameters of technical surfaces, especially in semiconductor manufacturing, line widths and profiles of structured layers often have to be checked during the manufacturing process. Precise compliance with the specifications for the line width is of crucial importance for the functionality of a product. In addition, there are other structural parameters such as B. trench depth or sidewall slope of great importance. Appropriate measuring methods are used to check these manufacturing parameters on lithography masks, semiconductor wafers or other finely structured surfaces.

Scatterometry, which includes reflectometry and ellipsometry in particular, is an efficient method for determining optical material properties and the thickness of thin layers. Scatterometry includes non-destructive measurement methods that change a light beam after it strikes a periodically structured one Measure and evaluate the surface. The advantages of these measuring methods are the high sensitivity, the non-destructive and even non-contact measurement as well as the simple practical handling. However, the measurements do not directly provide the desired material data, such as layer thickness, but rather require the calculated values to be adapted to the measured values. With this adjustment, the examined material properties are included in the calculation as model parameters. In scatterometry, as used for structure width measurement in the semiconductor industry, the intensity or polarization state of the beam reflected or transmitted at periodic structures is measured as a function of an angle or the wavelength. This functional dependence of the reflected beam is influenced by structural parameters such as line width or depth and is characteristic of the diffractive structure. However, it is not possible to determine the structural parameters directly from the measurement result, since this inverse diffraction problem cannot be solved mathematically. In contrast, a forward simulation of the measurement results of an assumed structural model is possible, for example using rigorous methods such as "Rigorous Coupled Wave Analysis", for example M. Moharam, et. Al., Journal of the American Optical Society A. vol. 12 (1995), pp. 1077-1086) The Maxwell equations are exactly solved with the boundary conditions given by the structure.

So far, these complex, rigorous methods have been used to simulate the diffraction effects, since the dimensions of the structures of less than 200 nm are in the range of the measuring wavelength. The measurement results are compared with the simulations in order to achieve an optimal match between simulation and measurement through an iterative variation of the simulation parameters and thus the structural parameters.

The problem here, however, is that fluctuations can occur with the previously known evaluation methods the line width for this optimization are not directly taken into account, but each optimization step requires a complete, time-consuming and computational simulation.

For example, DE 199 14 696 AI describes a device for quickly measuring angle-dependent diffraction effects on finely structured surfaces. The device consists of a coherent radiation source which emits in different directions, a spherical or aspherical mirror or mirror segments which are arranged such that they correspond to a spherical or aspherical mirror, and a detector unit for measuring the intensity of the radiation diffracted on a sample. The device described is essentially characterized in that the radiation deflected in different directions is reflected by the mirror arrangement in such a way that the coherent beam is deflected sequentially in succession at different angles of incidence onto the sample. For this purpose, the measuring beam is changed continuously or in small steps. The intensities of the direct reflex as well as the higher bending orders that may occur are measured. The evaluation of the intensity curves as a function of the varied angle of incidence allows conclusions to be drawn about the shape and material of the periodic structures examined.

Such a diffraction analysis can be divided into two steps. First, the intensity of the scattered or diffracted light is measured. Then the measured intensity Distribution compared with simulated diffraction effects, the grating parameters being varied within a predetermined range. Those parameter values that lead to the best agreement between measurement and simulation are considered reasonable approximations of the real ones

Grid parameters accepted. In order to reduce the computational effort required for the described method, it is proposed in this publication to dispense with an exact quantitative evaluation and instead to merely carry out a classification. Due to the large number of influencing variables, however, a clear classification of the grating parameters is only possible if a sufficient number of intensity measurement values are available for the examined measuring point.

There are currently two approaches to speed up the evaluation of the measurement. In one solution, the simulations are carried out before the actual measurements and stored in a database.

The simulation with the underlying structural parameters that best matches the measurement results is then selected by a search algorithm. In contrast, the second solution for evaluating diffraction effects is to vary the simulation parameters. For a rigorous simulation, the simulation parameters are varied until the simulation deviates from the measurement below a certain value. However, the rigorous simulation methods used can usually only be used for special cases, such as for vertical incidence, in order to achieve the required speed. Such a method for determining structural parameters of the surfaces, in particular of semiconductor components, is evident from US Pat. No. 5,963,329. In this case too, a function is determined that maps the intensity of the output beam to the wavelength of the reflected beam. In addition, a simulation is carried out for which the simulation parameters are varied. Here, the Maxwell equations are compared with those by

Structure specified boundary conditions exactly solved. A disadvantage of this method is that a considerable computing time is required for exact results, or the simulation has to be simplified in order to shorten the required computing time, thus limiting a possible measurement setup.

Starting from the known prior art, the invention is therefore based on the object of a method for determining structural parameters

Specify the surface that enables the detection of regular surface structures with any measurement setup and also enables a quick evaluation of the diffraction effects. In particular, the speed of the evaluation should also enable integrated measurement during the process.

Presentation of the invention

The solution to the problem on which the invention is based is specified in claim 1. advantageous

Developments of the inventive concept are the subject of the dependent claims and from the following Descriptive text with reference to the embodiments can be found.

According to the invention, there is a method for determining structural parameters of a surface, in which at least one coherent light beam of defined intensity and / or polarization is directed onto the surface, a beam reflected or transmitted by regular structures of the surface is detected and at least one imaging rule is determined, which has at least one beam parameter of the reflected or transmitted light beam onto at least one beam parameter of the light beam directed onto the surface. Furthermore, a simulation that is carried out on the basis of predefinable structural parameters is used to calculate a function that maps at least one simulated beam parameter of the reflected or transmitted light beam to at least one simulated beam parameter of the light beam directed onto the surface. The predefinable structure 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 function values of a limit function. The method is characterized in that the simulation is carried out using an approximation method and / or an adaptive system for calculating diffraction effects, and in that the

Approximation method and / or the learning system calculated structural parameters for an optimization step that uses rigorous calculation methods.

The method according to the invention for determining structural parameters of a surface thus ensures on the one hand that the results are not discretized, that a preliminary simulation is not necessary and that there is no restriction to previously simulated structure types. On the other hand, the method according to the invention is characterized in that the computing power for calculating the diffraction effects is minimized and the diffraction effects are thus evaluated quickly and reliably.

Should the approximation be the diffractive

If the structure is not described precisely enough, this can be recognized by optical effects that are outside the scope of the approximation method. These effects cannot therefore be simulated with sufficient agreement. In such a case, the structural parameters calculated with the approximation method are preferably used for an optimization step that uses rigorous calculation methods, such as a rigorous coupled wave analysis.

In this case, too, the computing time required for the simulation of the diffraction effects is minimized and the accuracy of the measuring method is increased.

In a particularly preferred embodiment of the method according to the invention, a regression method is used as the optimization method. Using the optimization process, the parameters of the simulated structure are varied until the calculated function within predefinable limit values, which determine the permitted deviation of the simulation from the measurement, has approached a limit function. It is irrelevant whether the measurement detects the reflection, transmission or both effects together.

A further embodiment provides that an intensity and / or a polarization state of the reflected or transmitted light beam as

Beam parameters of the reflected or transmitted light beam is used. An angle of incidence and / or a wavelength of this beam are preferably used as the beam parameters of the light beam directed onto the surface. In this way, the intensity or polarization state of the beam reflected or transmitted at the periodic structures is measured as a function of an angle of incidence or over the wavelength of the incident light beam. This functional dependence of the reflected

Beam is influenced by structural parameters, volume width or depth and is characteristic of the diffractive structure.

A special embodiment provides shape birefringence as an approximation method for calculating diffraction effects. With the help of this method, the diffraction effects that occur on periodic structures can be approximately calculated. The procedure can be used for trench-line structures

Periods that are significantly smaller than the wavelength of the incident beam can be used. In this way, the structure is effective by two Refractive indices are described, which are calculated by a series development according to the ratio period to wavelength.

Of course, other approximation methods which have a suitable convergence behavior can also be used for the method according to the invention. In a further embodiment of the method according to the invention, approximation methods are used that take into account the ratio of structure thickness to wavelength.

It is also advantageous to use scalar calculation methods, such as, for example, a complex-amplitude transmittance method. The latter method is particularly suitable for structures that have periods that are significantly larger than the wavelength of the incident beam.

An alternative embodiment of the method according to the invention provides that the structure parameters are determined not with the aid of a simulation method but with the aid of a system capable of learning using a suitable algorithm. In this method, a function is calculated with the aid of the learnable system, which maps at least one beam parameter of the reflected and / or the transmitted light beam to at least one beam parameter of the light beam directed onto the surface. A difference function is determined from the calculated function and the mapping rule determined in advance. The individual process steps are repeated catches up until the function values of the difference function assume values that are smaller than function values of a previously defined limit function. The above-described method is characterized in that the structural parameters calculated with the adaptable system are ultimately used for an optimization step that uses rigorous calculation methods.

An adaptive system for determining structure parameters of a surface is preferably used if the structure parameters are to be determined from the intensity profile of the measured values. The main difference when using an adaptive system instead of an approximation method is that a backward correlation of the calculated values can be carried out in this way.

A device with which the invention

A method for determining structure parameters of a surface can be implemented, has a radiation source that emits coherent light, a detection unit that detects at least one light beam reflected and / or transmitted by regular structures of the surface and determines at least one beam parameter of the reflected light beam, and a simulation unit to calculate diffraction effects. With such a device, in a particularly suitable manner,

Determine structural parameters of a surface. In particular, this device ensures that the results are neither discretized nor a preliminary simulation is necessary and there is also no restriction to previously simulated structure types. In addition, the computing power required to calculate the diffraction effects is minimized in such a way that the diffraction effects can be evaluated quickly and reliably.

The method according to the invention for determining structural parameters on a surface and the device for implementing it will be explained in more detail below.

Ways of Carrying Out the Invention

The invention is described below without restricting the general inventive concept

Exemplary embodiments described. Here show:

Figure 1: Carrying out a reflectometry measurement; FIG. 2: process scheme for determining structural parameters with the aid of an optimization process; and

Figure 3: Process scheme for determining structure parameters with the help of two optimization methods, the different

Use calculation algorithms.

FIG. 1 schematically shows a spectral reflectometry measurement with light radiation 2 directed onto a sample 1 and the light radiation 3 reflected from the surface 4 of the sample 1. With the help of the measurement, the spectral and spatial Distribution of the light radiation 3 reflected by the periodic structures 5 arranged on the surface 4 is measured and characterized.

The measurement on the sample 1, which has periodic line-trench structures 5 on the surface 4, takes place either with a reflectometer or a combined ellipso-reflectometer and provides the measurement result as the reflectivity or transmission as a function of the wavelength. This feature that the

Mapping reflectivity or transmission to the wavelength is referred to as a so-called signature (Imess (λ)) and represents a measured mapping rule.

With the help of the determined measured values, a

Defined start model that describes the layer sequence 6 exactly and the layer thicknesses 7 and the structure shape roughly. The signature of this model is calculated using the extended form birefringence according to Rytov and supplies the calculated signature

(Isi _m (λ)). The measured signature is then compared with the calculated signature taking into account the mean square error (MSE: Mean Square Error). The mean square error is calculated as follows:

The structural parameters, such as layer thicknesses, line widths or periods are varied as long as until the value for MSE is below a defined value.

In order to calculate smaller details of the structure, measurement results that are outside the scope of the approximation method are also taken into account. In the present case, these are the intensity values for wavelengths that are less than or equal to the period of the structure. Therefore, the model calculated using the shape birefringence is called

Start model used for further optimization steps. Rigorous simulation models, such as a rigorous coupled wave analysis, are used for these further optimization steps. The measurement signature is then compared to this rigorously calculated signature. To increase the speed, it is possible to consider only the wavelengths for which the approximation method is no longer valid.

In Figure 2 is a process flow in the

Determination of structure parameters of a surface is shown, in which diffraction effects are only approximately calculated with the help of an optimization algorithm and the structure parameters are thus determined. In this way, the parameters of the simulated structure are varied by means of an optimization process until a difference function formed from the determined mapping rule and the calculated function assumes, as a comparison standard, function values that are smaller than the function values of a limit function that represents a desired accuracy criterion. FIG. 3 shows a further method according to the present invention for determining structural parameters of a surface. First, surface parameters are also determined using an optimization process that uses an approximation process for the simulation of diffraction effects. However, the surface parameters are then determined in more detail by using an optimization method that uses rigorous methods for the simulation of diffraction methods and that uses the approximately calculated model as the start model, until the structure parameters are varied until a given criterion for comparing the results of measurement and simulation is fulfilled, that is to say one formed from the determined mapping rule and the calculated function

Difference function as a benchmark assumes function values that are smaller than the function values of a limit function that represents a desired accuracy criterion.

Reference numerals;

Sample incident light radiation reflected light radiation Sample surface Periodic structure Layer sequence Layer thickness

Claims

claims

1. A method for determining structural parameters of a surface, in which at least one light beam (2) of defined intensity and polarization is directed onto the surface (4), a light beam (3.) Reflected and / or transmitted by regular structures (5) of the surface (4) ) detected and at least one

A mapping rule is determined which maps at least one beam parameter of the reflected and / or transmitted light beam (3) to at least one beam parameter of the light beam (2) directed onto the surface (4), in which simulation is carried out on the basis of predefinable structural parameters , a function is calculated which maps at least one simulated beam parameter of the reflected and / or transmitted light beam (3) to at least one simulated beam parameter of the light beam (2) directed onto the surface (4), and in which the predefinable structural parameters for the simulation are included With the aid of an optimization method, it can be varied such that a difference function formed from the determined mapping rule and the calculated function assumes function values that are smaller than function values of a limit function, characterized in that the simulation is carried out using a

Approximation method and / or a learning system for calculating diffraction effects is carried out and that with the approximation method and / or the system parameters that are capable of learning are used for an optimization step that uses rigorous calculation methods.

2. The method according to claim 1, characterized in that a regression method is used as the optimization method.

3. The method according to claim 1 or 2, characterized in that an intensity and / or a polarization state of the reflected or transmitted light beam (3) is used as a beam parameter of the reflected or transmitted light beam (3).

4. The method according to any one of claims 1 to 3, characterized in that an angle and / or an angle as the beam parameter of the light beam (2) directed onto the surface

Wavelength is used.

5. The method according to any one of claims 1 to 4, characterized in that an effective medium model, in particular shape double refraction, is used as an approximation method for calculating diffraction effects.

6. The method according to any one of claims 1 to 5, characterized in that an approximation method is used which takes into account the ratio of structure thickness to wavelength.

7. The method according to any one of claims 1 to 6, characterized in that a scalar calculation method, in particular the complex amplitude transmittance method, is used as the approximation method.

8. Method for determining structure parameters of a surface, in which at least one light beam (2) of defined intensity and polarization is directed onto the surface (4), a light beam (3.) Reflected and / or transmitted by regular structures (5) of the surface (4) ) is detected and at least one mapping rule is determined, which maps at least one beam parameter of the reflected and / or transmitted light beam (3) to at least one beam parameter of the light beam (2) directed onto the surface (4), in which a function can be learned with a system capable of learning, which maps at least one beam parameter of the reflected and / or transmitted light beam (3) to at least one beam parameter of the light beam (2) directed onto the surface (4), determined and on the basis of the calculated function

Selects structure parameters in such a way that a difference function formed from the determined mapping rule and the calculated function assumes function values that are smaller than function values of a limit function, characterized in that those calculated with the system capable of learning

Structure parameters for an optimization step that uses rigorous calculation methods.

9. Device for performing the method according to one of claims 1 to 8 with a radiation source that emits light, with a detection unit that detects at least one of regular structures (5) of a surface (4) reflected and / or transmitted light beam (3) and determines at least one beam parameter of the reflected light beam (3) and with a simulation unit for calculating diffraction effects according to the method.