Method and apparatus for x-ray fluorescence analysis

Method and equipment for X-ray fluorescence analysis

METHOD AND APPARATUS FOR X-RAY FLUORESCENCE ANALYSIS

<b>Cross reference of related applications</b>

This application claims the rights of U.S. Provisional Patent Application 61/992,234 filed on May 13, 2014, and the disclosure of this case is incorporated herein by reference.

The present invention generally relates to X-ray analysis, and specifically relates to methods and systems for analyzing thin layers on a substrate.

As one of the methods used to test semiconductor wafers, X-ray fluorescence (XRF) measurement and specifically, X-ray microfluorescence (that is, X-ray fluorescence using sub-millimeter focused excitation beams) is increasing Be concerned. XRF itself is a well-known technique used to determine the size (such as thickness) and element composition of a sample. The XRF analyzer generally includes: an X-ray source for irradiating the sample; and an X-ray detector for detecting the X-ray fluorescence emitted by the sample in response to the irradiation. Each element in the sample emits X-ray fluorescence in the energy band that is the characteristic of the element. The detected X-ray fluorescence is analyzed to find the energy or equivalently the wavelength and respective intensity of the detected photons, and the qualitative and/or quantitative thickness and composition of the sample are determined based on this analysis.

The use of X-ray microfluorescence to test semiconductor wafers is described in various publications. Examples of the prior art are provided below.

US Patent 6,108,398 describes an XRF analyzer and method for analyzing samples, and the disclosure of the case is incorporated herein by reference. The analyzer includes an X-ray beam generator, which generates an X-ray beam incident on a light spot on the sample and generates a plurality of fluorescent X-ray photons. An array of semiconductor detectors is arranged around the light spot to capture fluorescent X-ray photons. The analyzer generates electrical pulses suitable for analyzing samples.

US Patent 6,351,516 describes a non-destructive method for testing the deposition and/or removal of a material in a recess on the surface of a sample, and the disclosure of the case is incorporated herein by reference. An excitation beam is guided to an area of the sample near the concave portion, and an intensity of X-ray fluorescence emitted from the area is measured. The amount of material deposited in the recess is determined in response to the measured strength.

Lankosz et al. described X-ray microfluorescence in a paper entitled "Research in Quantitative X-ray Fluorescence Microanalysis of Patterned Thin Films" (Advances in X-ray Analysis 43 (1999), pages 497 to 503) Another application of light, this paper is incorporated into this article by reference. The author describes a method of using a collimated microbeam for X-ray fluorescence microanalysis. This method is used to test the thickness and uniformity of thin films prepared by ion sputtering technology.

An embodiment of the present invention described herein provides a method for X-ray fluorescence (XRF) analysis, which comprises: directing an X-ray beam onto a sample; and wherein the sample is formed on a substrate In a reference measurement of one or more first layers, and in a target measurement after one or more second layers except the first layers are formed on the substrate, the measurement is performed from the The sample excites an XRF signal to generate a reference XRF spectrum and a target XRF spectrum respectively. The reference XRF spectrum is used to reduce one of the first layers' contributions to the target XRF spectrum. The target XRF spectrum in which the contribution of the first layers has been reduced is used to estimate at least one of the parameters of the second layers.

In some embodiments, the parameter includes the thickness of at least one of the second layers Spend. In other embodiments, the parameter includes an elemental composition of at least one of the second layers. In other embodiments, the first layers and the second layers are formed on the respective first and second opposite surfaces of the substrate such that the second surface faces the X-ray beam.

In one embodiment, the contribution of the first layers to the target XRF spectrum is caused by the excitation of the X-ray beam in the first layers after penetrating the substrate. In another embodiment, the first layers or the second layers include under bump metallization (UBM) layers or bumps. In another embodiment, reducing the contribution of the first layers includes: estimating the difference between a first spectral line in the reference XRF spectrum and a second spectral line in the target XRF spectrum that overlaps the first spectral line. One contribution to one intensity.

In some embodiments, estimating the contribution of the first spectral line includes estimating that the first spectral line is attenuated by one of the second layers. In other embodiments, estimating the attenuation includes iteratively evaluating the attenuation as a function of the respective estimated parameters of the second layers. In other embodiments, evaluating the attenuation iteratively includes evaluating the function in an initial iteration using the nominal parameters of the second layers.

In addition, according to an embodiment of the present invention, there is provided an apparatus for X-ray fluorescence (XRF) analysis, which includes an X-ray source, a detector, and a processor. The X-ray source is configured to guide an X-ray beam onto the sample. The detector is configured to measure an XRF signal excited from the sample. The processor is configured to respectively measure from one of the detectors in which the sample includes one or more first layers formed on a substrate, and to measure in one or more of the first layers except the first layers. After a second layer is formed on the substrate, it is measured from a target of the detector to generate a reference XRF spectrum and a target XRF spectrum, so as to use the reference XRF spectrum to reduce the first layer to the target XRF spectrum A contribution, and the target XRF spectrum in which the contribution of the first layers has been reduced is used to estimate at least one of the parameters of the second layers.

The following detailed description of the embodiments of the present invention obtained from the combined drawings will fully understand the present invention.

<p>20X-ray microfluorescence system</p><p>22Semiconductor wafer/sample</p><p>24X-ray tube/source</p><p>26High Voltage Power Supply Unit (PSU)</p><p>28X-ray optics</p><p>30Small area</p><p>32Detector</p><p>34Processor</p><p>36Interface</p><p>38Signal Processing Unit</p><p>40XY stage</p><p>42Semiconductor Wafer</p><p>44Under bump metallization (UBM)</p><p>46Solder bump</p><p>48Under bump metallization (UBM)</p>

Fig. 1 is a schematic diagram of a system for X-ray fluorescence (XRF) measurement according to an embodiment of the present invention; Figs. 2A and 2B are based on Fig. 1 according to an embodiment of the present invention A schematic cross-sectional view of a sample of the system analysis; and FIG. 3 schematically illustrates the use of XRF analysis according to an embodiment of the present invention for estimating the thickness and/or composition of the UBM layer A flow chart of one method.

X-ray fluorescence (XRF) technology is used for thickness and element composition measurement during the manufacturing process of semiconductor devices. In some semiconductor devices, one or more metal layers having a thickness of about 10 μm or less are formed on both sides of a substrate having a typical thickness of about 100 μm. The layers on both sides of the substrate may include similar materials, such as copper, nickel, gold, palladium, silver, or tin.

The thickness and/or composition of the measurement layer is based on analyzing the spectral lines in the spectrum of the XRF signal excited from the layers. In some practical cases, the detection of the XRF spectrum excited by the layer on one surface of the substrate may also include a contribution from the XRF spectrum excited by the layer on the opposite surface. This interference is especially noticeable when the substrate is thin (thin enough to allow the X-ray beam to penetrate) and when the layers on both sides have a common elemental composition (causing the XRF spectral lines to overlap).

Therefore, when measuring the thickness and/or layer composition of the layer formed on the upper surface, the XRF signal excited from the layer formed on the lower surface can interfere with the XRF signal excited from the layer formed on the upper surface, thus limiting Measure the estimated accuracy of the thickness or composition of the layer formed on the upper surface. When measuring the thickness and composition of the layer on the lower surface, similar interference can occur.

The embodiments of the present invention described herein provide an improved method for estimating the parameters of a thin film laminated on the other surface of the same substrate by evaluating and reducing the interference contribution of the XRF signal excited from one surface of a thin substrate And system. The embodiments described in this article are mainly about the estimation of layer thickness, but the disclosed technique can be used to estimate other suitable parameters. Such as layer element composition.

In some embodiments, the thickness and/or composition of the layer on one side are measured in two measurement steps. In a first measurement step, the spectrum of the XRF signal excited from a substrate including the layer on the lower surface is measured before the layer on the upper surface is formed, and it is saved as an evaluated background spectrum. In a second measurement step, a second XRF spectrum is performed after the substrate has included one or more of the layers on the upper surface. The XRF spectrum obtained in the first measurement is used to reduce the contribution of the layer on the lower surface to the XRF spectrum excited in the second measurement to improve the estimation accuracy of the thickness and/or composition of the layer on the upper surface.

The layers on the substrate can have different geometric configurations. In some cases, the geometric properties (for example, thickness or width) of the layer on the upper surface can attenuate the intensity of the background component of the spectrum in the second measurement step relative to the evaluated background spectrum, and thus can reduce the estimated thickness And the accuracy of the composition. In other embodiments, the nominal thickness and/or composition of the layer on the upper surface can be used to evaluate the intensity of the background component in the excitation spectrum due to the attenuation of the geometric configuration of the layer on the upper surface.

In still other embodiments, an iterative process may be applied to improve the accuracy of the estimated thickness and/or composition of the layer on the upper surface. The estimated thickness or composition of the layer on the upper surface can be used to re-evaluate the background spectrum. The re-evaluated background spectrum can be used to re-evaluate the thickness and/or composition of the layer more accurately. This iterative procedure can be repeated until a desired accuracy is reached. In one embodiment, a convergence threshold ε can be used to control the iterative loop. Therefore, when the absolute value of the difference between the estimated thickness and/or composition obtained in the last two iterations is less than ε, the iteration loop ends. Other suitable criteria for ending the iteration loop can also be used.

The disclosed technology is useful for providing accurate feedback of layer deposition systems during semiconductor (and other electronic component) manufacturing processes. Improved control of critical parameters (such as thickness and element composition) reduces process variation and therefore improves the electrical performance of manufactured electronic devices.

For the specificity and convenience of the description, the embodiments described below will be used to provide electricity The under-bump metallization (UBM) layer formed on a wafer and the solder bumps formed on the UBM are referred to as part of a wafer-level packaging (WLP) technology. However, the disclosed technology can be similarly implemented using other types of processes, electronic substrates and devices, materials, and geometric configurations.

System specification

FIG. 1 is a schematic diagram of an X-ray microfluorescence system 20 according to an embodiment of the present invention. The configuration of the system 20 is described in detail in the aforementioned US Patent 6,108,398. The system 20 is configured to inspect a semiconductor wafer 22 (or any other suitable sample) to, for example, use the method described below to identify faults in the wafer manufacturing process.

As known in the art, the system 20 generally includes an excitation source, such as an X-ray tube 24, driven by a high voltage power supply unit (PSU) 26. The X-ray tube sends X-rays with a suitable energy range and power flux to the X-ray optics 28. The optical device may include, for example, a polycapillary array. The optical device 28 focuses the X-ray beam onto a small area 30 (usually a spot with a diameter of about 10 μm to 20 μm) on the surface of the sample 22. The irradiated area emits fluorescent X-rays, and the fluorescent X-rays are captured by an array of detectors or detectors 32 arranged around the area 30 and inclined toward it. In response to the captured photons, the detector 32 generates an electrical signal that is sent to a signal processing unit 38. The unit 38 includes: a processor 34 configured to process electrical signals; and an interface 36 for communicating with the processor 34 electrical signals from the detector 32.

The example in Figure 1 refers to a specific configuration of an X-ray system. However, this configuration was chosen only for the sake of conceptual concreteness. In an alternative embodiment, after appropriate modifications (mutatis mutandis), the disclosed technique can be used in various other types of fluorescent systems or used to analyze modules known in the art, including any suitable excitation source , Power supply, focusing optics, and detection system can be used to implement the methods described in this article.

As known in the art, the processor 34 generally includes an energy dispersive pulse processing system that determines an intensity spectrum of X-ray photons captured by the detector. Alternatively, you can use a Wavelength dispersion detection and processing system. Each chemical element excited by the X-ray from the tube 24 in the irradiated area emits X-rays in the characteristic spectral line. The intensity of the characteristic spectral line of a given element is proportional to the mass of the element in the region 30. Therefore, the processor 34 uses the determined intensity spectrum to determine how much a specific material exists in the area of the region 30. The processor 34 usually includes a general-purpose computer, which performs these functions under the control of suitable software. The software can be downloaded to the processor in electronic form via a network, for example, or it can be provided on tangible media such as optical, magnetic or electronic memory media.

As shown in FIG. 1, the system 20 is used to inspect the area 30 on the wafer 22. In one embodiment, the sample is mounted on a movable platform (such as an XY stage 40) so that the sample can be moved relative to the X-ray beam. Alternatively, the sample is mounted on a suitable fixture and the tube 24, optics 28, and detector 32 are moved so that the X-ray beam scans the wafer.

The system 20 may further be configured to capture and process X-rays scattered from the wafer 22 by other mechanisms, such as reflection, diffraction, and/or small-angle scattering. Multifunctional systems of this kind are described in, for example, US Patent Nos. 6,381,303 and 6,895,075. The disclosures of these patents are incorporated herein by reference.

Estimate the thickness and composition of the film

2A is a schematic cross-sectional view of a sample 22 analyzed by the system 20 according to an embodiment of the present invention. Sample 22 represents a wafer in a typical stack of two or more semiconductor wafers packaged on top of each other using, for example, wafer level packaging (WLP) technology. For example, in face-to-face (FTF) WLP, two wafers are stacked such that a first wafer faces up and a second wafer faces down and is positioned on top of the first wafer. Each wafer typically includes an array of bumps formed on the wafer using a controlled collapse chip connection (C4) manufacturing technology. Bumps can be formed on both the upper and lower surfaces of some wafers to connect between semiconductor wafers in the WLP package.

2A, the sample 22 includes a semiconductor wafer 42 (also referred to herein as a substrate), which is generally made of silicon and has a thickness of about 100 μm or less. Gold under a bump A generalization (UBM) 44 is formed on the lower surface of the wafer 42. UBM 44 includes one or more layers, usually a stack of thin metal layers. The layers are usually made of copper, nickel, palladium or gold, but other metals can also be used. A solder bump 46 is formed on the UBM 44, and the UBM 44 provides electrical and physical (eg, adhesive) connections between the wafer 42 and the bump 46. In the example of Sample 22, the solder bump 46 has a dome shape. However, other types of bump materials and shapes can be used to apply the disclosed technology, such as copper pillar bumps widely used in advanced WLP structures.

As described above, bumps are usually formed on both sides of the wafer 22. FIG. 2A shows a manufacturing step that occurs before the UBM and bumps are formed on the upper surface of the wafer 42. In some embodiments, the tube 24 directs the X-ray beam through the optics 28 onto the area 30, and thus the sample 22 excites the XRF signal. The detector 32 captures the excitation signal. One or more detectors 32 are usually arranged around the sample 22 at equal elevation angles (about 45° in this example). The processor 34 calculates the spectral lines corresponding to the elements existing in the area 30 and derives the mass of each element in the area 30 from the intensity of the spectral lines. As will be shown and described in FIG. 2B below, the XRF spectrum obtained from the measurement of FIG. 2A is stored in the processor 34 as a later to be used to accurately estimate the mass and therefore the thickness of each of the layers of a UBM 48 One of the reference measurements.

2B is a schematic cross-sectional view of a sample 22 analyzed by the system 20 according to an embodiment of the present invention. The sample 22 includes the UBM 48 formed on the upper surface of the wafer 22 in one of the steps described in FIG. 2A and one of the next process steps. UBM 48 includes one or more layers, usually a stack of thin metal layers, which can be similar to the film of UBM 44. In other embodiments, the structure of UBM 48 is different from the structure of UBM 44, but the layer of UBM 48 may include elements similar to those of UBM 44 (for example, copper, nickel, and palladium).

The sample 22 is analyzed in the system 20 by applying an XRF analysis program similar to that described in FIGS. 1 and 2A. During the analysis of the sample 22 in FIG. 2B, the X-ray beam is irradiated on the sample 22, and XRF signals are excited from the metal layers of the two UBMs 44 and 48. Since the output of the detector 32 includes the spectral lines derived from the metal layers of the two UBM 44 and 48 made of similar metals, the processor 34 cannot distinguish between the signal excited by the UBM 44 and the signal excited by the UBM 48 Signal. In addition, the UBM 48 attenuates some of the incident X-ray radiation toward the source 24 of the UBM 44, and also attenuates some of the XRF signals excited from the UBM 44 toward the detector.

Therefore, some of the spectral lines excited from UBM 44 are attenuated by UBM 48 and are different from the reference spectral lines acquired and saved in the reference XRF analysis of sample 22 (FIG. 2A) before UBM 48 is formed. Therefore, the processor 34 may not be able to isolate the net signal excited from the UBM 48, and therefore cannot accurately determine the thickness and/or composition of the layer of the UBM 48.

The method described herein provides a technique for accurately determining the thickness of the UBM 48 layer and has been proven for the micro-bump measurement WLP in the F2F WLP structure. The disclosed technology can additionally be applied to the precise determination of the element composition of the UBM 48 layer. In this case, the thin substrate is a thinned device wafer having a thickness of about 100 μm or less. However, it can be understood that the method described herein can be applied to other situations, specifically, measuring small features containing a specific element on both sides of a thin substrate.

In order to calculate the XRF spectral line intensity of the UBM 48, the processor 34 can use the fundamental parameter (FP) technology, however, the interference of the structure on the incident X-ray beam and the fluorescent X-ray beam should be considered. The rigorous mathematical processing of this FP calculation is known in the art, and further details of these mathematical processing are described in the following documents, for example: B. Beckhoff et al. "Handbook of Practical X-Ray Fluorescence Analysis" (Springer-Verlag, Berlin, Heidelberg, 2006), which is incorporated herein by reference; DKGde Boer "Calculation of X-Ray Fluorescence Intensities from Bulk and Multilayer Samples" (X-RAY SPECTROMETRY, 19, 145-154, 1990); And M. Mantler "X-ray fluorescence analysis of multiple-layer films" (Analytica chimica acta, 188, 25-35, 1986), and other documents are also incorporated herein by reference.

Equation 1 below provides an explicit expression for estimating the XRF intensity Ii of a given analyzed spectral line (denoted as analyte line) i in a multilayer structure (such as UBM 48): Equation 1:<i>I</i>_<i>i</i>=<i>f</i>_<i>i</i>．<i>P</i>(<i>I</i>₀<i>,t</i>₁<i>,t</i>₂<i>,</i>...<i>,t</i>_<i>n</i>)

In Equation 1, t_iIs the thickness of one layer i, one of the number of n series layers, and P is considering the incident beam (intensity I₀) And a function of the possibility of exciting the interaction between the XRF beam and the multilayer structure, and f_iIt is an empirical factor that takes into account all other factors not included in the P function (such as system geometry and a response function of the detector 32).

Calculate the thickness t of layer 1...n of UBM 48 in order to measure the strength_i, Cannot form a direct inverse function of function P. Since P is a non-linear function, it is found that the inverse calculation can be done directly using an iterative calculation. For example, in "How Accurate is the Fundamental Parameter approach? XRF Analysis of Bulk and Multilayer Samples" (X-RAY Spectrometry, Volume 22, Page 33 to Page 38, 1993), which is incorporated herein by reference.

The disclosed technology provides a method and system for extracting layer thickness and/or composition from a model that only considers the XRF signal from the features on the front surface of the substrate and processes the XRF intensity contributed by the back side of the substrate as One of the background signals should be measured separately.

The method described in this article relies on two measurements: the first measurement, as depicted in Figure 2A, is performed before UBM 48 is formed, and is expressed as a background or reference measurement (the terms "background" and "reference" are in The present disclosure can be used interchangeably); the second measurement, as described in FIG. 2B, is performed after the UBM 48 is formed, and is called a target measurement. Some disclosed embodiments use a modified version of the FP algorithm to discover the contribution of the background signal to the intensity of the XRF spectral line excited from the UBM 48.

To estimate that a given spectral line i (denoted as I_i^Measured) The intensity of the background contribution (denoted as I_i^Background), the attenuation of the background by UBM 48 can be calculated. It should be noted that there are some situations where the excited background XRF may not be attenuated by the UBM 48. For example, as shown in FIG. 2A and FIG. 2B, when the detector 32 is positioned at an angle of 45° with the incident beam, and when the UBM 48 is plated with a diameter in the range of 50 μm to 70 μm Typical lateral dimension of UBM (for example, width) when on wafer 42 of thickness It is about 30 μm, which is larger than the typical diameter of an x-ray beam. It should be noted that for thicker wafers 22 and/or wider UBM layers and it should be taken into account that the excitation beam decays to a lower intensity.

Approximate background attenuation

As a first-order approximation, it can be assumed that the background system has E=κ. E_edgeOne beam of energy is excited, where E_edgeIt is the lower threshold of XRF excitation energy. Generally, the factor κ is a number in the range 1 to 2. Therefore, the measured intensity I of the background to a spectral line i should be_iThe contribution of is added to the intensity calculated from FP (as given by Equation 1):<chemistry general="n"><img he="228" wi="1677" file="TWI650552B_D0001.tif" img-content="drawing" img-format="tif" orientation="portrait" inline="no" /></chemistry>in<chemistry general="n"><img he="334" wi="1677" file="TWI650552B_D0002.tif" img-content="drawing" img-format="tif" orientation="portrait" inline="no" /></chemistry>And where the expression<i>μ</i>_<i>j</i>(<i>E</i>) Represents a mass attenuation coefficient of layer j at energy E.

The factor κ should be empirically tuned to suppress the nonlinear attenuation of the incident beam. This can be done, for example, by fitting the calculated intensity to the measured intensity of a reference structure (for example, an industry standard sample). It should be noted that in Equations 2 and 3, it is assumed that the XRF beam includes a quasi-monochromatic beam. To accurately model the condition of a multicolor beam, the tube spectrum should be measured or modeled and then the integral of the total intensity obtained from the tube spectrum should be obtained. The term quasi-monochromatic refers to the mathematical approximation E=κ. E_edge. The disclosed technique can be applied to a monochromatic beam as well as a polychromatic beam.

Calculate the thickness t of the UBM 48 layer by solving equations 2 and 3 iteratively_i i=1...n. In the present invention, the nominal layer thickness is assumed at the beginning of the iterative calculation to overcome the possible numerical difficulties associated with an instantaneous attenuation of the background approximately. Therefore, in a first iteration, the assumed nominal thickness of the layer of UBM 48 is used instead of the instantaneous thickness (as calculated in Equation 3) to evaluate the background attenuation by UBM 48. Then, replace this evaluated background attenuation back into Equation 2, and calculate the layer thickness of the UBM 48 layer by solving Equation 2.

In a second iteration, the calculated thickness of each layer of UBM 48 (as obtained from Equation 2) is applied to Equation 3 to re-evaluate the background attenuation. The estimated number of attenuated background intensity obtained from Equation 3 is placed in Equation 2 (instead of the value based on the nominal thickness in the first iteration) to calculate the thickness of the UBM 48 layer with a higher accuracy. This iterative procedure is repeated until the difference between the calculated thicknesses from two consecutive steps decreases below a threshold ε. At this point, the thickness measurement is completed and the output thickness is transmitted to a statistical program control (SPC) or to any suitable program control system.

FIG. 3 schematically illustrates a flow chart of a method of analyzing XRF to estimate the thickness and/or composition of one or more layers of UBM 48 according to an embodiment of the present invention. The term "UBM measurement" refers to the measurement of one or more layers of interest in UBM 48, and the term "thickness" can be replaced by the term "element composition" because the disclosed technology can be applied to the analysis of the measurement The thickness and/or element composition of the layer. In addition, when a quasi-monochromatic beam approximation is used or an accurate solution of the appropriate multicolor beam spectrum is used, the disclosed method can be applied.

In a background measurement step 100, the method starts with the system 20 measuring the intensity of one or more XRF spectral lines excited from the sample 22 before the UBM 48 is formed. In this manufacturing stage, the UBM 48 has not yet been formed on the wafer 42 so that the measured intensity of the XRF spectral line represents the background or reference intensity.

In a target measurement step 102, after the UBM 48 is formed on the wafer 42, the system 20 again measures the intensity of the XRF spectral line excited from the sample 22. In a background evaluation step 104, the processor 34 evaluates the background intensity of various XRF spectral lines attenuated by the UBM 48. The processor 34 uses Equation 3 to evaluate the background intensity based on the assumed nominal thickness of the UBM 48 layer and the measured background intensity. In a thickness calculation step 106, the processor 34 calculates the thickness of the UBM 48 layer by feeding back the measured intensity and the evaluated background obtained in the UBM measurement step 102 to Equation 2.

In a background re-evaluation step 108, the processor 34 replaces the calculated UBM thickness to re-evaluate the intensity of the attenuated background. Compared to the background evaluation step 104, the re-evaluated number provides a higher degree of accuracy of the background intensity because the calculated thickness value is used instead of the assumed nominal value.

In a thickness recalculation step 110, the processor 34 recalculates the thickness of the UBM 48 by using the re-evaluated background in Equation 2. Compared with the thickness calculated in the thickness calculation step 106, the thickness recalculated at this stage is usually more accurate, because the background intensity with higher accuracy is used in this calculation.

The procedure described in the above four steps iteratively improves the accuracy of the calculated thickness of the UBM 48 layer and is expected to converge. In some embodiments, to determine whether the iterative procedure has converged and therefore whether the calculated thickness obtained is sufficiently accurate, a convergence threshold ε may be used.

In a comparison step 112, the processor 34 compares the absolute value of the difference between the recalculated thickness (calculated in the recalculation step 110) and the previously calculated thickness with ε. If the difference is greater than ε, the procedure has not yet converged, and the method loops back to the background re-evaluation step 108. If the absolute difference is less than ε, the procedure converges, the obtained thickness is final and the method ends in an end step 114.

It will be understood that the above-mentioned embodiments are listed as examples, and the scope of the following patent applications is not limited to the content that has been specifically shown and described above. In fact, the category includes the combinations and sub-combinations of the various features described above, as well as the changes and modifications of the present invention that those familiar with the art will think of after reading the foregoing description and are not disclosed in the prior art. Documents incorporated in this patent application by reference shall be regarded as an integrated part of this application, but to a certain extent, these documents are incorporated into the document to be explicitly or implicitly carried out in this specification. Any term is defined as one way of conflicting definitions, except for the definitions in this specification should only be considered.