Method for determining the thickness and refractive index of a layer

Abstract

Method for determining the thickness and refractive index of a layer (6) located on a substrate (26), wherein the layer (6) has a layer bottom side (30) facing the substrate (26) and a layer top side (28) facing away from the substrate (26), and wherein the following steps are carried out: a) Determining a lateral location of the layer (6), b) confocal microscopic imaging of the layer (6) at the lateral location and at several axial positions along an optical axis (8), c) determining a first axial position of a main or secondary maximum of an axial intensity distribution at the layer bottom (30) for the lateral location and determining a second axial position of the same main or secondary maximum of an intensity distribution at the layer top (28) for the lateral location, d) determining a first value of a shape feature of the intensity distribution at the layer bottom (30) for the lateral location and a second value of the same shape feature of the intensity distribution at the layer top (28) for the lateral location and e) determining the thickness and refractive index of the layer (6) at the lateral location from a difference between the first and second axial positions and a difference between the first and second values of the shape feature, wherein the shape feature comprises a distance between two maxima present in the intensity distribution, such that determining the difference between the first and second values of the shape feature comprises determining a change in a distance between maxima, and / or wherein the shape feature comprises an intensity ratio of maxima present in the intensity distribution, such that determining the difference between the first and second values of the shape feature comprises determining a change in the intensity ratio of maxima.

Description

[0001] The invention relates to a method for determining the thickness and refractive index of at least one layer lying on a substrate.

[0002] Measuring coating thickness is a common task. Optical coating thickness measurement usually requires knowledge of the coating's refractive index. In current technology, this must be determined using separate measurement methods. For example, the refractive index of the coating material can be determined from an optical measurement at a location with a known coating thickness and then extracted for the coating thickness measurement at another location.

[0003] If interference effects are used for optical layer thickness measurement, the state of the art generally requires spectrally resolved reflection measurements to be performed so that both the refractive index and layer thickness can be determined from the position of at least three local extrema. Spectrally resolved measurements are technically complex, particularly since the required spectral resolution is very high. Since the denominator of the calculation formula used contains a wavelength difference, there is also the requirement that the wavelengths used differ as much as possible. This increases the technical complexity. Another option for determining layer thickness and refractive index is ellipsometry. US 2004 / 0 085 544 A1 describes an ellipsometric method for characterizing layers and determining refractive index and layer thickness. EP 0 814 318 A2 describes a similar approach.However, this also requires a spectrally resolved measurement and numerous assumptions about the sample. JP 2002 - 323 659 A discloses a confocal optical method for determining the thickness and refractive index of a layer, as well as a scanning confocal microscope that uses this method.

[0004] The invention is based on the object of providing a method for determining the layer thickness and refractive index of a sample which does not require spectral analysis.

[0005] The invention is defined in claim 1. The dependent claims relate to preferred developments.

[0006] The method determines the thickness and refractive index of a layer on a substrate at least at one lateral location. The layer has two surfaces, namely a bottom surface facing the substrate and a top surface facing away from the substrate. This top surface can, but does not have to, be an exposed surface. The layer can therefore be part of a multilayer system and, in particular, also be an internal layer. The layer is imaged confocally microscopically along an optical axis in several axial positions. From these images of the two surfaces, an intensity distribution along the optical axis is recorded, e.g. the point spread function (hereinafter also "z-PSF"). For this purpose, the z-position of the object plane is varied around the surface, e.g. imaged in at least three axial positions of the object plane.The axial distance, i.e., the difference between the first axial position of a main or secondary maximum of the intensity distribution on the top side of the layer and the second axial position of the same main or secondary maximum on the bottom side of the layer, encodes the apparent thickness of the layer. In addition, a comparison of a shape feature is made between the intensity distributions, which has different values on the top and bottom sides of the layer. This then allows the thickness and refractive index of the layer to be determined.

[0007] One variation of the shape feature is a broadening of the same maximum. Another is the spacing of equal maxima.

[0008] In the first variant, the distance between maxima present in the intensity distributions is evaluated. This can be the distance between a main maximum and a secondary maximum, or the distance between secondary maxima. Here, too, a relative value is calculated by determining the change between the distance between the maxima occurring in the second point-spread blur function relative to the distance between the same maxima in the first point-spread blur function at the top of the layer. In the second variant, the width of a maximum (e.g., the main maximum) is evaluated. A relative broadening of the intensity distribution, e.g., of the point-spread blur function, is determined, namely relative to a width that the same maximum has at the other layer interface.

[0009] In options, the relative intensity of secondary maxima or the side on which maxima are located can be used. Each option corresponds to a specific scenario.

[0010] It is crucial that a calibration curve can be determined for the specific confocal system. Which shape features are most suitable can depend, for example, on the numerical aperture of the objective or the wavelength.

[0011] The invention exploits the fact that the apparent thickness is determined by the distance, e.g., between the main maxima of the axial intensity distribution on the two surfaces. This apparent layer thickness can be converted into the actual layer thickness if the refractive index is known. The relative change in a shape feature of the intensity distribution, e.g., the width of the main maximum of the intensity distribution, for the top and bottom of the layer allows the refractive index to be determined. At the top of the layer, the intensity distribution is narrower, e.g., diffraction-limited. Light reflected at the bottom of the layer, in contrast, displays an intensity distribution with significant distortions and thus altered shape features, e.g., due to spherical errors. A priori, one could not assume that these altered shape features would allow the refractive index to be determined.However, the inventors realized that while the width of the intensity distribution increases with layer thickness, it is not proportional to the layer thickness. The apparent layer thickness, on the other hand, is proportional to the layer thickness. This becomes particularly clear when considering the dependence on the other parameter, namely the refractive index: The apparent layer thickness is inversely proportional to the refractive index, thus decreasing with increasing refractive index. The aberrations, and thus, for example, the width of the intensity distribution, increase with increasing refractive index (although not necessarily proportionally).

[0012] For example, if you measure an apparent thickness of 100 µm for a layer (spacing of the main maxima), then this value can be caused by a 150 µm thick glass layer with n = 1.5, but also by a 200 µm layer with n = 2. Without considering the shape of the intensity distribution, it is impossible to distinguish between the two. If you look at the width, you can see that it increases both due to the increase in the actual thickness (from 150 µm to 200 µm) and due to the increase in the refractive index from 1.5 to 2.0. The intensity distribution must therefore be significantly wider (the extent to which depends on the optical parameters, such as the numerical aperture).

[0013] It follows that the two measured quantities, namely the difference in axial position (apparent layer thickness) and the changed shape feature, e.g., broadening of the maximum, are independent of each other and thus allow the determination of two independent physical parameters, namely the (actual) layer thickness and the refractive index.

[0014] A particular advantage of the method is that it can be performed with existing confocal microscopes without technical modifications to the optics or illumination. In particular, the simultaneous measurement of layer thickness and refractive index is possible with a single monochromatic light source.

[0015] The procedure can, of course, be repeated at different lateral locations to achieve a lateral characterization of the layer thickness and refractive index. This allows imaging to be obtained. It is also possible to analyze a single layer of a multilayer system. In this way, such a system can be analyzed layer by layer with regard to the thicknesses and refractive indices of the layers.

[0016] A particularly simple conversion of the broadening (or the change in the spacing of the maxima) into layer thickness and refractive index can be obtained for a given lens using a conversion curve. This conversion curve can either be determined experimentally beforehand or calculated from optical simulations.

[0017] Both the determination of the axial positions of the main or secondary maximum and the values of the shape feature of the intensity distribution on the bottom and top sides of the layer can each involve recording a so-called z-stack. This means that the confocal imaging is carried out at the lateral location with different axial focus positions. In its minimum version, the z-stack comprises three different axial positions. In addition, a model shape curve for the intensity distribution can optionally be used to reconstruct the intensity distribution from the values of the z-stack. This model shape curve can, for example, be based on the optical behavior of the imaging system, which is determined, for example, on a mirror surface in a reference measurement. This can, for example, already be carried out in the factory during the manufacture of the device with which the confocal imaging is carried out.

[0018] However, the axial positions of the main or secondary peaks can also be determined without z-stacks, namely by continuously shifting the axial position of the confocal image, i.e., the object plane from which the confocal image is taken. In this way, the intensity maximum can be easily located.

[0019] The value of the shape feature can also be determined without a z-stack, for example, by moving to two z-positions selected symmetrically to the determined axial position of the maximum, and obtaining the intensity values of the assigned positions from them. These values may already be sufficient in some embodiments to capture the value of the shape feature with sufficient accuracy or to serve as the value of the shape feature itself.

[0020] It is understood that the features mentioned above and those to be explained below can be used not only in the combinations indicated, but also in other combinations or on their own, without departing from the scope of the present invention.

[0021] The invention is explained in more detail below using exemplary embodiments with reference to the accompanying drawings, which also disclose features essential to the invention. These exemplary embodiments are for illustrative purposes only and are not to be interpreted as restrictive. For example, a description of an embodiment with a large number of elements or components should not be interpreted to mean that all of these elements or components are necessary for implementation. Rather, other embodiments may also contain alternative elements and components, fewer elements or components, or additional elements or components. Elements or components of different exemplary embodiments may be combined with one another unless otherwise stated. Modifications and variations described for one of the exemplary embodiments may also be applicable to other exemplary embodiments.To avoid repetition, identical or corresponding elements in different figures are designated by the same reference numerals and are not explained more than once. The figures show: Fig. 1 a schematic representation of a confocal microscope, Fig. 2 a flow chart for a method for measuring the thickness and refractive index of a layer with the microscope of Fig. 1 and Fig. 3A to 4B z-PSF, which in the procedure of Fig. 2 can be used.

[0022] Fig. 1 schematically shows a confocal microscope 2 with which a layer 6 arranged on a sample stage 4 is analyzed, i.e. measured, with regard to layer thickness and refractive index. The confocal microscope 2 images the layer 6 in reflected light microscopy along an optical axis 8. For this purpose, it has an objective 10 and a downstream tube lens 12, which produce a confocal image by means of a pinhole 14 and record the confocally detected radiation with a detector 16. A scanner 18 shifts the lateral location from which the radiation is confocally detected transversely to the optical axis 8 across the layer 6. By adjusting the objective 10 or the sample stage 4, the z-coordinate, i.e. the object plane to which a plane in which the pinhole 14 is located is conjugate, can also be adjusted along the optical axis 8.Layer 6 is illuminated via a beam splitter 20, which is arranged downstream of scanner 18 in the imaging direction and couples in the illumination radiation from a light source 22. The entire microscope 2 is controlled by a control unit 24, which is connected to the corresponding units via control lines shown in dashed lines. In the illustration of the . Fig. 1 shows a variant in which the depth adjustment, ie the adjustment along the optical axis 8, is achieved by adjusting the lens 10. This is purely exemplary.

[0023] The layer 6 is located above or (as shown) directly on a substrate 26 and has a layer bottom side 30 associated with the substrate 26 and a layer top side 28 facing the objective 10 and thus away from the substrate 26.

[0024] The confocal microscope 2 is designed as a reflected-light microscope, which, in the illustrated design, is a scanning microscope. However, these features are optional. The microscope 2 can also be designed without the scanner 18, particularly if the refractive index and layer thickness are to be determined only at one location on the layer 6.

[0025] To determine the layer thickness d of layer 6 and the refractive index n of layer 6, the Fig. 2 is carried out. In a step S1, the slice 6 is confocally imaged from a location, e.g., with a fixed setting of the optional scanner 18, wherein the depth setting along the optical axis 8 is set to the slice top 28. Subsequently, in a step S2, the axial intensity distribution in the form of the z-PSF at the slice top 28 is determined. For this purpose, the intensity is determined in a z-stack around the slice top 28 for several z-positions, e.g., three, five, or more positions. The z-position of the slice top 28 can be determined beforehand based on the refractive index jump present there, which causes a reflection, and can thus be roughly approached.

[0026] The resulting curve for the z-PSF is shown in Fig. 3A. The z-PSF is shown as a curve consisting of a main maximum and subordinate secondary maxima and is characterized by the aforementioned z-variation along the optical axis 8.

[0027] Subsequently, in step S3, layer 6 is imaged on the layer bottom 30. The z-PSF is also determined for this purpose. This is done in step S4. The resulting z-PSF is shown in Fig. 3B shown.

[0028] The distance between equal maxima in the z-PSF for the two surfaces, namely the layer top surface 28 and the layer bottom surface 30, yields an apparent layer thickness d'. This is determined in step S5. For this purpose, the main maximum is expediently used.

[0029] Now we evaluate the extent to which the z-PSFs differ at the bottom of the layer 30 and the top of the layer 28. There are two alternatives for this.

[0030] In a first variant, in a step S6a, the distance between identical maxima in the z-PSF is evaluated for a relative change. The distance between two selected maxima of the z-PSF at the layer bottom 30 is compared to the distance between identical maxima of the z-PSF at the layer top 28. The term "identical maxima" is understood here to mean that the functionally identical distance is measured, for example, the distance between the main maximum and the first secondary maximum, or between the main maximum and the second secondary maximum, or between the first secondary maximum and the second secondary maximum, etc.

[0031] In a second variant, the broadening of the same maximum, for example, the broadening of the main maximum, is determined in step S6b. Here, too, a relative value is obtained, i.e., the width of a selected maximum at the layer bottom 30 is set in relation to the width of the same maximum of the z-PSF at the layer top 28.

[0032] One of the two variants is executed, i.e., either step S6a or step S6b. Both variants allow the refractive index n and the (actual) layer thickness d of layer 6 to be determined in a step S7 from the determined relative value and the apparent layer thickness d'. Instead of the one-step step S7, a stepwise approach is also possible, in which the refractive indices are first determined from the relative values and the apparent layer thickness d', followed by the layer thickness d.

[0033] When executing step S7, a conversion curve can be used, which is provided before the step is executed. The conversion curve specifies, for example, the relationship between n and the relative change in distance or widening, or the relationship between n and d and the relative distance or widening and the apparent layer thickness d'. The conversion curve can be calculated from optical simulations for the specific lens 10 or can be determined experimentally for the specific lens 10.

[0034] When executing step S7, knowledge of the lens properties is relevant, since the broadening or the change in distance between the maxima depends on the lens. This is determined from the difference between the Fig. 3A / 3B on the one hand and 4A / 4B on the other hand. Fig. 4A and Fig. 4B show the z-PSF on the layer top 28 and bottom 30, as well as the Fig. 3A and Fig. 3B. Fig. 3A / B and Fig. 4A / B differ, however, in terms of the thickness of the layer and the lens properties. The curves of the Fig. 3A and Fig. 3B were obtained on a 1 mm thick, mirrored glass layer with a 10x / 0.25 objective lens, the curves of the Fig. 4A and Fig. 4B on a 0.17 mm thick coverslip layer on a reflective surface as substrate 26. A 50x / 0.7 objective was used. It can be seen that the broadening effect is particularly pronounced for objectives with a high numerical aperture.

[0035] Since the broadening of the z-PSF, or the change in the distance between the maxima of the z-PSF, depends on the properties of the lens, the procedure naturally stipulates that the same lens should always be used. Furthermore, its optical imaging properties should always be kept at the same settings when measuring surfaces 28 and 30, for example, with regard to a correction ring, etc.

[0036] Using the method described above, it is also possible to obtain an image with regard to the layer thickness profile and refractive index profile of layer 6, namely if the method is carried out for different lateral locations, for example, the corresponding adjustment of the scanner 18. In this case, it is of course possible to first scan with a z-adjustment to the layer top 28 and then with a z-adjustment to the layer interface 30. This procedure should generally be faster, since conventional scanners 18 operate faster than a z-adjustment on the objective 10 or the sample stage 4.

[0037] Likewise, a layer system consisting of several layers can also be analyzed layer by layer.

Claims

[1] Method for determining the thickness and refractive index of a layer (6) located on a substrate (26), wherein the layer (6) has a layer bottom side (30) facing the substrate (26) and a layer top side (28) facing away from the substrate (26), and wherein the following steps are carried out: a) Determining a lateral location of the layer (6), b) confocal microscopic imaging of the layer (6) at the lateral location and at several axial positions along an optical axis (8), c) determining a first axial position of a main or secondary maximum of an axial intensity distribution at the layer bottom (30) for the lateral location and determining a second axial position of the same main or secondary maximum of an intensity distribution at the layer top (28) for the lateral location, d) determining a first value of a shape feature of the intensity distribution at the layer bottom (30) for the lateral location and a second value of the same shape feature of the intensity distribution at the layer top (28) for the lateral location and e) determining the thickness and refractive index of the layer (6) at the lateral location from a difference between the first and second axial positions and a difference between the first and second values of the shape feature, wherein the shape feature comprises a distance between two maxima present in the intensity distribution, such that determining the difference between the first and second values of the shape feature comprises determining a change in a distance between maxima, and / or wherein the shape feature comprises an intensity ratio of maxima present in the intensity distribution, such that determining the difference between the first and second values of the shape feature comprises determining a change in the intensity ratio of maxima. [2] Method according to claim 1, wherein in step c) and / or step d) a z-stack with at least three axial positions is recorded at the lateral location on the layer top and bottom sides (30, 28). [3] Method according to claim 1 or 2, wherein in step d) a width of the main or secondary maximum is determined as a shape feature. [4] Method according to one of claims 1 to 3, wherein, for carrying out steps c) and d), a first point image blurring function resolved along the optical axis (8) at the layer bottom (30) and a second point image blurring function resolved along the optical axis (8) at the layer top (28) are determined at the lateral location, and the point image blurring functions are used as intensity distributions. [5] Method according to one of claims 1 to 4, wherein the method is repeated for different lateral locations of the layer (6) in order to determine a lateral distribution of refractive index and layer thickness by scanning. [6] Method according to one of claims 1 to 4, wherein an objective (10) is used for confocal microscopic imaging and a conversion curve is provided for this objective (10), which indicates the refractive index of the layer (6) as a function of the difference between the first and second axial position and the difference between the first and second value of the shape feature. [7] Method according to one of claims 1 to 6, wherein the layer (6) is part of a multi-layer system. [8] Method according to claim 7, wherein the layer (6) is an inner layer in the multi-layer system.

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