CN110823089B - Method and apparatus for measuring optical critical dimension of semiconductor device - Google Patents
Method and apparatus for measuring optical critical dimension of semiconductor device Download PDFInfo
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Abstract
Embodiments of the present disclosure relate to methods and apparatus for measuring optical critical dimensions of semiconductor devices. The method includes obtaining a measurement spectrum of the semiconductor device and a set of measurement wavelength points of the measurement spectrum. The method also includes selecting a first number of wavelength points from the set of measurement wavelength points. The method also includes obtaining a first fitted spectrum corresponding to the set of measured wavelength points by interpolation based on the first number of wavelength points. Further, the method includes determining an optical critical dimension of the semiconductor device based on the first number of wavelength points in response to a first error between the first fitted spectrum and the measured spectrum being less than a first threshold. By automatically selecting and calculating the set of wavelength sampling points of the theoretical spectrum in a self-adaptive method, the embodiment of the disclosure avoids the waste of calculation resources caused by over-sampling the wavelength, and does not cause the distortion of the spectrum.
Description
Technical Field
The present disclosure relates generally to the field of semiconductor manufacturing; and more particularly, to a method and apparatus for measuring an Optical Critical-Dimension (OCD) of a semiconductor device.
Background
As the semiconductor industry continues to advance toward deep submicron technology nodes, the size of semiconductor devices, such as integrated circuit devices, continues to shrink, and device structure designs become increasingly complex. In particular, the advent of three-dimensional devices has made process control increasingly important in semiconductor fabrication processes. Tight process control requires that defects on the wafer be inspected at various steps of the semiconductor manufacturing process to promote higher yields.
Optical Critical-Dimension (OCD) measurement technology, as a mainstream process control technology in current semiconductor manufacturing processes, provides higher measurement speed without damaging the sample. And when the corresponding theoretical spectrum is the same as the measurement spectrum, the periodic repeating structure corresponding to the theoretical spectrum is the appearance of the nanoscale measurement structure corresponding to the measurement spectrum.
Disclosure of Invention
The wavelength points of the calculated theoretical spectrum are generally consistent with the measured spectrum, which may result in too dense wavelength points for calculating the theoretical spectrum, resulting in serious waste of computing resources. In addition, the calculation requirement of wider band and higher calculation accuracy can only reduce the structure description parameters or shorten the wavelength calculation range properly under certain calculation resources. This may result in a reduction in OCD measurement capability and measurement accuracy.
To address at least in part the above and other potential problems, embodiments of the present disclosure provide methods and apparatus for measuring optical critical dimensions of a semiconductor device.
In a first aspect of the present disclosure, a method for measuring optical critical dimensions of a semiconductor device is provided. The method includes obtaining a measurement spectrum of the semiconductor device and a set of measurement wavelength points of the measurement spectrum. The method also includes selecting a first number of wavelength points from the set of measurement wavelength points. The method also includes obtaining a first fitted spectrum corresponding to the set of measured wavelength points by interpolation based on the first number of wavelength points. Further, the method includes determining an optical critical dimension of the semiconductor device based on the first number of wavelength points in response to a first error between the first fitted spectrum and the measured spectrum being less than a first threshold.
According to an embodiment of the first aspect, the method further comprises: in response to the first error being greater than a first threshold, selecting a second number of wavelength points from the set of measured wavelength points, wherein the second number is greater than the first number; obtaining a second fitted spectrum corresponding to the set of measured wavelength points by interpolation based on the second number of wavelength points; and determining an optical critical dimension of the semiconductor device based on the second number of wavelength points in response to a second error between the second fitted spectrum and the measured spectrum being less than a first threshold.
According to an embodiment of the first aspect, selecting the second number of wavelength points from the set of measurement wavelength points comprises: adding another wavelength point to the first number of wavelength points to obtain a second number of wavelength points, wherein the other wavelength point is the wavelength point at which the difference between the spectral values of the first fitted spectrum and the measured spectrum is maximal.
According to an embodiment of the first aspect, selecting the second number of wavelength points from the set of measurement wavelength points comprises: dividing a first number of wavelength points into a plurality of subsets; obtaining a third fitted spectrum by interpolation for a portion of the set of measurement wavelength points corresponding to the wavelength bands of the subset based on the subset of the plurality of subsets; and adding wavelength points to the subset in response to a third error between the third fitted spectrum and the portion of the measured spectrum corresponding to the wavelength band of the subset being greater than a second threshold, wherein the second number of wavelength points includes the first number of wavelength points and the added wavelength points.
According to an embodiment of the first aspect, determining the optical critical dimension of the semiconductor device based on the first number of wavelength points comprises: calculating a spectral value of the theoretical spectrum using rigorous coupled wave analysis for a first number of wavelength points; obtaining a spectrum value of a theoretical spectrum by interpolation using the calculated spectrum value for other wavelength points of the set of measurement wavelength points except for the first number of wavelength points, wherein an interpolation model used to obtain the theoretical spectrum is the same as an interpolation model used to obtain the first fitted spectrum; and comparing the theoretical spectrum with the measured spectrum to determine an optical critical dimension of the semiconductor device.
According to an embodiment of the first aspect, the first number of wavelength points comprises the end points of the measurement spectrum and the wavelengths corresponding to the extreme points.
According to an embodiment of the first aspect, the first threshold and/or the second threshold is based on a signal-to-noise ratio of the measured spectrum.
According to an embodiment of the first aspect, wherein the wavelength points of the subsets are consecutive and the other wavelength points of the different subsets, except the end points, do not overlap.
According to an embodiment of the first aspect, the method further comprises determining an optical critical dimension of the other semiconductor device based on the first number of wavelength points in response to the other semiconductor device having the same topography as the semiconductor device.
In a second aspect of the present disclosure, a method for measuring optical critical dimensions of a semiconductor device is provided. The method includes determining a topographical model and optical measurement conditions of the semiconductor device. The method also includes obtaining a measurement spectrum of the semiconductor device. The method further comprises determining a first number of wavelength points based on the measured spectrum, according to the method of the first aspect of the present disclosure. The method also includes determining a theoretical spectral computational model based on the topographical model, the optical measurement conditions, and the first number of wavelength points. In addition, the method further comprises the step of obtaining the optical critical dimension of the semiconductor device based on the theoretical spectrum calculation model and the measurement spectrum.
According to an embodiment of the second aspect, determining the theoretical spectral computational model comprises: the theoretical spectrum calculation model is further determined based on the same interpolation model as used to obtain the first fitted spectrum.
In a third aspect of the present disclosure, an apparatus for measuring an optical critical dimension of a semiconductor device is provided. The apparatus includes a first obtaining module for obtaining a measurement spectrum of the semiconductor device and a set of measurement wavelength points of the measurement spectrum. The apparatus also includes a first selection module for selecting a first number of wavelength points from the set of measurement wavelength points. The apparatus also includes a second obtaining module to obtain a first fitted spectrum corresponding to the set of measured wavelength points by interpolation based on the first number of wavelength points. In addition, the apparatus includes a first determination module to determine an optical critical dimension of the semiconductor device based on the first number of wavelength points in response to a first error between the first fitted spectrum and the measured spectrum being less than a first threshold.
According to an embodiment of the third aspect, the apparatus further comprises: a second selection module to select a second number of wavelength points from the set of measured wavelength points in response to the first error being greater than the first threshold, wherein the second number is greater than the first number; a third obtaining module, configured to obtain, based on the second number of wavelength points, a second fitted spectrum corresponding to the measurement wavelength point set through interpolation; and a second determination module to determine an optical critical dimension of the semiconductor device based on a second number of wavelength points in response to a second error between the second fitted spectrum and the measured spectrum being less than a first threshold.
According to an embodiment of the third aspect, the second selection module comprises a first adding sub-module for adding a further wavelength point to the first number of wavelength points to obtain a second number of wavelength points, wherein the further wavelength point is the wavelength point at which the difference between the spectral values of the first fitted spectrum and the measured spectrum is maximal.
According to an embodiment of the third aspect, the second selection module comprises: a partitioning submodule for partitioning the first number of wavelength points into a plurality of subsets; a first obtaining submodule configured to obtain, based on a subset of the plurality of subsets, a third fitted spectrum by interpolation for a portion of the set of measurement wavelength points corresponding to a wavelength band of the subset; and a second adding sub-module for adding wavelength points to the subset in response to a third error between the third fitted spectrum and the portion of the measured spectrum corresponding to the wavelength band of the subset being greater than a second threshold, wherein the second number of wavelength points comprises the first number of wavelength points and the added wavelength points.
According to one embodiment of the third aspect, the first determining module comprises: the calculation submodule is used for calculating a spectral value of the theoretical spectrum by using strict coupled wave analysis aiming at the first number of wavelength points; a second obtaining submodule for obtaining a spectrum value of a theoretical spectrum by interpolation using the calculated spectrum value for other wavelength points of the measurement wavelength point set except for the first number of wavelength points, wherein an interpolation model for obtaining the theoretical spectrum is the same as an interpolation model for obtaining the first fitted spectrum; and a comparison submodule for comparing the theoretical spectrum with the measured spectrum to determine an optical critical dimension of the semiconductor device.
According to an embodiment of the third aspect, wherein the first number of wavelength points comprises the end points of the measurement spectrum and the wavelengths corresponding to the extreme points.
According to an embodiment of the third aspect, wherein the wavelength points of the subsets are consecutive and the other wavelength points of the different subsets, except the end points, do not overlap.
In a fourth aspect of the present disclosure, an apparatus for measuring an optical critical dimension of a semiconductor device is provided. The apparatus includes a first determination module for determining a topographical model and optical measurement conditions of the semiconductor device. The apparatus also includes a first obtaining module for obtaining a measurement spectrum of the semiconductor device. The apparatus further comprises a second determination module for determining a first number of wavelength points based on the measured spectrum, according to the method of the first aspect of the present disclosure. The apparatus also includes a third determination module for determining a theoretical spectral calculation model based on the topographical model, the optical measurement conditions, and the first number of wavelength points. In addition, the equipment also comprises a second obtaining module for obtaining the optical critical dimension of the semiconductor device based on the theoretical spectrum calculation model and the measured spectrum.
According to an embodiment of the fourth aspect, the third determination module comprises a determination submodule for determining the theoretical spectral calculation model further based on the same interpolation model as used for obtaining the first fitted spectrum.
As will be understood from the following description, the embodiments of the present disclosure are advantageous in that: according to the optical key dimension measurement principle (namely consistency of the measured spectrum and the theoretical spectrum matched with the measured spectrum), the wavelength sampling point set of the theoretical spectrum is automatically selected and calculated in a self-adaptive method through analysis of the measured spectrum, so that spectrum distortion is avoided, and calculation resource waste caused by over-sampling of the wavelength is avoided.
This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the disclosure, nor is it intended to be used to limit the scope of the disclosure.
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The foregoing and other objects, features and advantages of the disclosure will be apparent from the following more particular descriptions of exemplary embodiments of the disclosure as illustrated in the accompanying drawings wherein like reference numbers generally represent like parts throughout the exemplary embodiments of the disclosure.
FIG. 1 shows a flow chart of a method for measuring optical critical dimensions of a semiconductor device according to an embodiment of the present disclosure;
FIG. 2 shows an example measured spectrum;
FIG. 3 shows an example of a first number of wavelength points selected based on the measurement spectrum shown in FIG. 2;
FIG. 4 shows a flow diagram of a method of segment fitting according to an embodiment of the present disclosure;
fig. 5 shows an example of a second number of wavelength points obtained on the basis of the first number of wavelength points shown in fig. 3;
FIG. 6 shows an example of a suitable number of wavelength points for calculating a theoretical spectrum;
FIG. 7 shows a flow chart of another method for measuring optical critical dimensions of a semiconductor device according to an embodiment of the present disclosure;
FIG. 8 illustrates an example of a topographical model of a semiconductor device;
FIG. 9 shows a block diagram of an apparatus for measuring optical critical dimensions of a semiconductor device according to an embodiment of the present disclosure; and
fig. 10 shows a block diagram of another apparatus for measuring optical critical dimensions of a semiconductor device according to an embodiment of the present disclosure.
Detailed Description
Preferred embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
The term "include" and variations thereof as used herein is meant to be inclusive in an open-ended manner, i.e., "including but not limited to". Unless specifically stated otherwise, the term "or" means "and/or". The term "based on" means "based at least in part on". The terms "one example embodiment" and "one embodiment" mean "at least one example embodiment". The term "another embodiment" means "at least one additional embodiment". The terms "first," "second," and the like may refer to different or the same object. Other explicit and implicit definitions are also possible below.
For convenience of description, an embodiment of the present invention will be described below mainly with a Rigorous Coupled Wave Analysis (RCWA) algorithm as an exemplary algorithm for calculating a theoretical spectrum. It should be understood, however, that the algorithms described herein for calculating theoretical spectra may also include other suitable algorithms, whether presently known or developed in the future.
Optical Critical-Dimension (OCD) measurement technology, as a mainstream process control technology in current semiconductor manufacturing processes, provides higher measurement speed without damaging the sample. Optical critical dimension measurement techniques typically use scatterometry and reflectometry and related electromagnetic field algorithms to derive critical dimensions, film thickness, material parameters, and other parameters of nanoscale measurement structures. Typically, the measurement structure comprises a measurement sample consisting of a thin film or a periodically repeating structure.
The relevant electromagnetic field algorithm generally employs a Rigorous Coupled Wave Analysis (RCWA) algorithm to calculate the theoretical spectrum. The strict coupled wave analysis method is a vector diffraction modeling theory based on a differential form of Maxwell equation, and is characterized in that the dielectric constant and the electromagnetic field of a periodic repeating structure are subjected to Fourier series expansion, a coupled wave equation is established, numerical solution is carried out, and finally required diffraction electromagnetic field information is obtained. The method is particularly suitable for optical characteristic modeling and optical scattering measurement of the repetitive structure. And when the corresponding theoretical spectrum is the same as the measurement spectrum, the periodic repeating structure corresponding to the theoretical spectrum is the appearance of the nanoscale measurement structure corresponding to the measurement spectrum. Further, the measured optical critical dimension of the semiconductor device can be obtained.
The wavelength point corresponding to the measured spectrum is related to the spectrometer used by the measuring machine. The wavelength points of the calculated theoretical spectrum in the electromagnetic field algorithm are generally consistent with the measured spectrum, which may result in too dense wavelength points for calculating the theoretical spectrum and waste of calculation resources. According to the continuity characteristic of the spectrum, the theoretical spectrum is generally calculated by adopting wavelength points at certain intervals in the prior art, and the wavelength points which are lacked relative to the measured spectrum are obtained by adopting a linear interpolation method. However, in order to ensure that the spectrum is not distorted, the wavelength points are collected too densely, which results in waste of computing resources and storage resources.
With the development of processes, the structures of semiconductor devices such as integrated circuit devices become more and more complex, the materials become more and more diversified, and the requirements for measurement are increased accordingly. OCD measurements require smaller and smaller parameter resolution, more and more complex geometries and material compositions, multi-parameter correlations, and measurement capability for opaque materials, among others. This not only requires that the OCD modeling parameters be sampled sufficiently, but also requires that the sample be tested across the ultraviolet to infrared wavelength bands to reduce the correlation between parameters and improve the ability to measure opaque materials. The calculation requirement of wider wave band and higher calculation precision can only reduce the sampling of model parameter properly under certain calculation resource. This may result in a reduction in OCD measurement capability and measurement accuracy.
According to the OCD measuring principle, the theoretical spectrum corresponding to the morphology of the finally measured semiconductor device is basically consistent with the corresponding measured spectrum. According to the method, the set of wavelength sampling points of the measured spectrum is automatically found in a self-adaptive method according to the curve characteristics of the measured spectrum through the analysis of the measured spectrum, and the set is used as the set of wavelength points for calculating the theoretical spectrum, so that the theoretical spectrum is not distorted, and the waste of calculation resources caused by over-sampling of the wavelength is avoided.
Fig. 1 shows a flow chart of a method 100 for measuring optical critical dimensions of a semiconductor device according to an embodiment of the present disclosure. For example, method 100 may be performed by any Optical Critical Dimension (OCD) measurement device, whether now known or developed in the future. It should be understood that method 100 may also include additional blocks not shown and/or may omit blocks shown, as the scope of the present disclosure is not limited in this respect.
According to the method 100, in block 110, a measurement spectrum of a semiconductor device and a set of measurement wavelength points of the measurement spectrum are obtained. For example, the OCD measuring device can measure the spectrum reflected from the semiconductor device under test (also referred to as the sample under test)(referred to as a measurement spectrum). The measured measurement spectrum can be expressed as S ═ S (λ), where λ is the set of measurement wavelength points of the measurement spectrum, i.e., λ ═ { λ ═ λ1,λ2,…,λNAnd N represents the total N wavelength points of the measured spectrum.
Fig. 2 shows an example measured spectrum 200. An exemplary measurement spectrum 200 shown in fig. 2 is S (λ) ═ α (λ), β (λ) ]. In fig. 2, fourier coefficients α, β are taken as examples of the reflection spectrum, but the present disclosure is not limited to this spectrum type, and other measurement spectrum types may be included. The set of measurement wavelength points of the example measurement spectrum 200 includes a number of wavelength points between 300nm and 800 nm. Assuming the measurements are made in 1nm steps, the set of measurement wavelength points for the example measurement spectrum 200 has 501 wavelength points. Usually, the theoretical spectrum is calculated for these 501 wavelength points. As will be appreciated from the following description, this is not necessary and is thus a waste of computing resources.
According to the method 100, in block 120, an OCD measurement device selects a first number of wavelength points (also referred to as original wavelength sampling points) from a set of measurement wavelength points. The first number of wavelength points may include the end points (including the start and end values) of the measured spectrum and the wavelengths corresponding to the extreme points. Thus, the sampled spectrum corresponding to the first number of wavelength points may be expressed as Sp＝[S(λ1),S(λN),S(λa),S(λb)]Where S (λ 1) is the starting value of the measurement spectrum, e.g. 300nm in fig. 2; s (lambda)N) Is the end value of the measured spectrum, e.g. 800nm in fig. 2; s (lambda)a) Is the maximum of the measured spectrum, i.e. S (lambda)a)＝max[S(λi) I ═ 1,2, …, N; and S (lambda)b) Is the minimum of the measured spectrum, i.e.
max and min represent the maximum and minimum values of the acquisition sequence, respectively. Wavelength [ lambda ]1,λN,λa,λb]Arranged from small to large, and taken as lambda'1＝λ1、λ′2＝min(λa,λb)、λ′3＝max(λa,λb)、λ4′＝λNThen the first number of wavelength points may be expressed as λ '═ λ'1,λ′2,λ′3,λ′4]。
Fig. 3 shows an example 300 of a first number of wavelength points selected based on the measurement spectrum shown in fig. 2. As shown by the large open circles in fig. 3, an example 300 of the first number of wavelength points includes 6 wavelength points, respectively 2 wavelength points corresponding to the two end points of the measured spectrum (i.e., 300nm and 800nm), the maximum and minimum of the alpha spectrum, and 2 wavelength points corresponding to the maximum and minimum of the beta spectrum. The 6 wavelength points are ordered sequentially from small to large as a set λ' of a first number of wavelength points. The discrete spectrum corresponding to the set λ' can be expressed as Sp＝[S(λ′1),S(λ′2),…,S(λ′6)]。
According to the method 100, in block 130, a fitted spectrum (referred to as a first fitted spectrum) corresponding to the set of measured wavelength points is obtained by interpolation based on the first number of wavelength points. For example, the OCD measuring device may interpolate all wavelength points corresponding to the measured spectrum by using discrete spectrum values (from the measured spectrum) corresponding to the sampled first number of wavelength points, so as to obtain a corresponding fitted spectrum. The interpolation model may include, but is not limited to, linear interpolation, rational interpolation, and the like. Taking rational interpolation as an example, the first fitting spectrum form may be:
wherein the coefficient [ a0,a1,…,ap]And [ b)1,b2,…,bq]It can be calculated from the values of the measurement spectrum corresponding to a first number of wavelength point sets λ', p and q being two exponentials, and p + q-1 can be set to M, where M represents the number of currently sampled wavelength points, i.e. the first number. In the example shown in fig. 3, M is 6.
In fig. 3, the first fitted spectrum S' (λ) obtained by linear interpolation is also shown by a black solid line.
In block 140 of the method 100, an error between the measured spectrum S (λ) and the first fitted spectrum S' (λ) is calculated and a determination is made as to whether the error exceeds a threshold. Specifically, an optical critical dimension of the semiconductor device is determined based on the first number of wavelength points in response to an error between the first fitted spectrum and the measured spectrum (referred to as a first error) being less than a threshold (referred to as a first threshold). The calculation of the error includes but is not limited to calculating the mean square error between the two spectra,
if the first error χ is less than a first threshold, e.g., 0.001, then the first number of wavelength points that have been found are output as the set of optimal wavelength sampling points. In this way, based on the measured spectrum, an appropriate number of wavelength points for calculating the theoretical spectrum are automatically found. The first threshold may be obtained from, but is not limited to, a signal-to-noise ratio measured with the spectrum, e.g. comparable to the signal-to-noise ratio of the measured spectrum.
According to the OCD measurement principle, the theoretical spectrum and the measured spectrum that are finally needed are the same, and then the set of suitable wavelength sampling points of the theoretical spectrum and the set of suitable wavelength sampling points of the measured spectrum are the same. Therefore, only the theoretical spectrum needs to be calculated for the set of suitable wavelength sampling points, and the interpolation calculation for other wavelength points can adopt the same model as that for fitting the measured spectrum.
According to one example, determining the optical critical dimension of the semiconductor device based on the first number of wavelength points comprises: calculating a spectral value of the theoretical spectrum using rigorous coupled wave analysis for a first number of wavelength points; obtaining a spectrum value of a theoretical spectrum by interpolation using the calculated spectrum value for other wavelength points of the set of measurement wavelength points except for the first number of wavelength points, wherein an interpolation model used to obtain the theoretical spectrum is the same as an interpolation model used to obtain the first fitted spectrum; and comparing the theoretical spectrum with the measured spectrum to determine an optical critical dimension of the semiconductor device.
In block 150 of the method 100, if the first error χ exceeds a first threshold, e.g., 0.001, it indicates that the number of wavelength points needs to be increased because the number of current wavelength sampling points is too small. In particular, in response to the first error being greater than a first threshold, a second number of wavelength points is selected from the set of measured wavelength points, wherein the second number is greater than the first number; obtaining a fitted spectrum (referred to as a second fitted spectrum) corresponding to the set of measured wavelength points by interpolation based on the second number of wavelength points; and determining an optical critical dimension of the semiconductor device based on the second number of wavelength points in response to an error between the second fitted spectrum and the measured spectrum (referred to as a second error) being less than a first threshold.
As one example of increasing the number of wavelength points, another wavelength point may be added to the first number of wavelength points to obtain a second number of wavelength points. The further wavelength point may be the wavelength point at which the difference between the spectral values of the first fitted spectrum and the measured spectrum is maximal. Error calculation between two spectral points includes, but is not limited to, calculating the difference in spectral values between the two points. The error in the point correspondence of the ith wavelength points of the two spectra can be expressed as δi＝|S(λi)-S′(λi) L. Traversing all wavelength points of the measured spectrum, and taking the wavelength point with the maximum corresponding error as a new wavelength sampling point. That is, δ can be selectedc＝max[δ1,δ2,…,δN]Corresponding lambdacAdded as new wavelength sampling points to the first number of wavelength points
As another example of increasing the number of wavelength points, a piecewise fitting method may be employed to speed up finding the appropriate number of wavelength points for calculating the theoretical spectrum.
Fig. 4 shows a flow diagram of a method 400 of segment fitting according to an embodiment of the present disclosure. In block 410, a first number of wavelength points may be divided into a plurality of subsets. The set λ' of the first number of wavelength points may be sequentially divided into several subsets. The subset of requirements is chosen by taking successive points in the set lambda' and dividing between two different subsetsTwo wavelength points (end points) at the head and the tail are obtained, and other wavelength points are not overlapped. For example, a subset may contain only two wavelength points. Assume that the set of the first number of wavelength points is λ '═ { λ'1,λ′2,…,λ′MAnd M represents that the current sampling point set has M wavelength points. The number of subsets is at most M-1, i.e. { λ'1,λ′2,…,λ′M}＝{[λ′1,λ′2],[λ′2,λ′3],…,[λ′M-1,λ′M]}. Its corresponding measured spectrum will also be divided into M-1 segments, λ ═ λ1,λ2,…,λM-1]And the wavelength range of the i-th section can be expressed as lambdai＝[λi1,λi2,…,λim]Wherein λ isi1＝λ′i、λim＝λ′i+1And im represents m wavelength points of the measured spectrum of the ith waveband.
In block 420, a fitted spectrum (referred to as a third fitted spectrum) is obtained by interpolation for a portion of the set of measurement wavelength points corresponding to the wavelength bands of the subsets, based on the subsets of the plurality of subsets. The OCD measuring equipment can model the discrete spectrum corresponding to the sub-concentrated wavelength points in sequence to obtain a fitted spectrum curve of the OCD measuring equipment. The ith subset of wavelength sampling points may be expressed as λ'i＝{λ′i1,λ′i2,…,λ′im} corresponding to a discrete spectrum of
Modeling obtains a fitting spectrum (namely a third fitting spectrum) of S'i＝S′i(λi)＝fi(λi,λ′i) Wherein λ isiDenotes a wavelength region of λ'i1And λ'imSet of wavelength points corresponding to the measured spectrum, fiAn interpolated fitting model corresponding to the ith subset is represented. Alternatively, the processing of multiple subsets may be performed in parallel to speed up the computation.
An error between the third fitted spectrum corresponding to the subset and the corresponding measured spectrum portion is calculated (referred to as a third error) and a determination is made as to whether the third error exceeds a threshold value of, for example, 0.001 (referred to as a second threshold value). If the third error does not exceed the second threshold, it indicates that the wavelength sampling points corresponding to the subset are sufficient, and it is not necessary to add wavelength sampling points. If the third error exceeds the second threshold, it indicates that the wavelength sampling points corresponding to the subset are not enough, and the wavelength sampling points need to be increased. Similar to the first threshold described above, the second threshold may also be based on the signal-to-noise ratio of the measured spectrum.
In block 430, wavelength points are added to the subset in response to a third error between the third fitted spectrum and the portion of the measured spectrum corresponding to the wavelength band of the subset being greater than a second threshold, wherein the second number of wavelength points includes the first number of wavelength points and the added wavelength points. For example, the wavelength point in the subset where the difference between the fitted spectral value and the measured spectral value (the difference δ between the spectral values) is the largest can be found as the newly added wavelength sampling point in the subset.
The acts of obtaining a fitted spectrum, determining the error magnitude, and adding wavelength points to the subsets as described above may be performed for each subset. For example, the set at the first number of wavelength points as described above is λ '═ { λ'1,λ′2,…,λ′MWhere the number of subsets is M-1, the errors of the fitted spectrum and the measured spectrum for each wavelength range can be calculated sequentially from i-1 to i-M-1, i.e. the error of the fitted spectrum and the measured spectrum for each wavelength range is calculated sequentially
And determines whether the error exceeds a second threshold. The second number of wavelength points may be the sum of the first number of wavelength points and the wavelength points added to all subsets. The reduction of the error between the fitted spectrum and the measured spectrum is accelerated by a piecewise interpolation between the fitted spectrum and the measured spectrum.
Fig. 5 shows an example 500 of a second number of wavelength points obtained on the basis of the first number of wavelength points shown in fig. 3. As shown in fig. 5, the dots with open-ended cross-hatching represent newly added wavelength sampling points.
If a second error between the second fitted spectrum and the measured spectrum corresponding to the second number of wavelength points still exceeds the first threshold, continuing to add wavelength points to the second number of wavelength points until the error between the fitted spectrum and the measured spectrum is less than the first threshold. The set of wavelength sampling points when the error between the fitted spectrum and the measured spectrum is less than the first threshold is a suitable number of wavelength points for calculating the theoretical spectrum.
Fig. 6 shows an example 600 of a suitable number of wavelength points for calculating a theoretical spectrum. The empty dots in fig. 6 are the set of suitable wavelength sampling points corresponding to the measured spectrum shown in fig. 2, and there are 33 dots in total, and the error between the fitted spectrum and the measured spectrum is less than the threshold value of 0.001.
Overall, the measured measurement spectrum can be expressed as S ═ S (λ), where λ is the set of measurement wavelength points of the measurement spectrum, i.e., λ ═ { λ ═ λ1,λ2,…,λNAnd N represents the total N wavelength points of the measured spectrum. The measurement spectrum is sampled in an adaptive manner, and the corresponding sampled wavelength point set is represented as λ '═ { λ'1,λ′2,…,λ′MM denotes a total of M wavelength samples, and
and interpolating all wavelength points corresponding to the measurement spectrum according to the sampled wavelength points to obtain a corresponding fitted spectrum S '═ S' (λ) ═ f (λ, λ '), wherein f (λ, λ') is an interpolation model. The error between the fitted spectrum and the measured spectrum can be determined. The error between the two spectra will start to be smaller and smaller as the number of sampling points λ' increases, i.e. as M increases. When the number of sampling points is large enough, the error between the two spectra tends to be stable, and λ' at this time can be called as a set of suitable wavelength sampling points.
By the above actions of the method 100, a suitable number of wavelength points for calculating the theoretical spectrum may be determined quickly and automatically based on the measured spectrum. The first threshold and the second threshold may be equal or unequal. The threshold may be obtained, but is not limited to, a signal-to-noise ratio measured with a spectrum, e.g. a first threshold may be comparable to the signal-to-noise ratio of the entire measured spectrum and a second threshold may be comparable to the signal-to-noise ratio of the measured spectrum within the wavelength range of the corresponding subset of wavelength points.
In this way, a minimum number of sets of suitable wavelength sampling points are employed to calculate the theoretical spectrum. Namely, the non-distortion of the spectrum is realized, and the sampling of wavelength points is not too dense. The method ensures that the computing resources are not wasted, can enable more computing resources to describe the appearance of the semiconductor device to be measured, can accelerate the subsequent processing speed of the theoretical spectrum, and can also obtain the spectrum in a wider wavelength range under the same computing resources. Thereby increasing the ability of semiconductor optical measurements, such as measurements on high-k materials.
Further, in block 160 of the method 100, an optical critical dimension of another semiconductor device is determined based on the first number of wavelength points in response to the other semiconductor device having the same topography as the semiconductor device. Depending on the process requirements, the semiconductor devices produced under the same process are identical in morphology, i.e. their measured spectra are similar. Therefore, it can be considered that appropriate wavelength sampling points of the measured spectrum of the semiconductor devices produced in the same process are uniform. In other words, the first number of wavelength points may all be used to determine the optical critical dimension.
Fig. 7 shows a flow chart of another method 700 for measuring optical critical dimensions of a semiconductor device in accordance with an embodiment of the present disclosure. For example, method 700 may be performed by any Optical Critical Dimension (OCD) measurement device, whether now known or developed in the future. It should be understood that method 700 may also include additional blocks not shown and/or may omit blocks shown, as the scope of the present disclosure is not limited in this respect.
In block 710, an OCD measurement device may determine a topographical model and optical measurement conditions of the semiconductor device. Information (e.g., manufacturing process conditions) of the semiconductor device under test can be collected to theoretically establish a topographical model of the material distribution of the sample under test.
Fig. 8 illustrates an example 800 of a topographical model of a semiconductor device. FIG. 8 shows three critical dimensions that need to be measured: middle line width (MCD), Height (HT), and sidewall angle (SWA).
Optical measurement conditions may also be collected. Wherein the optical measurement conditions include the incident light basic information and the type of optical measurement. The basic information of the incident light includes, but is not limited to, the incident direction, polarization, and numerical aperture information of the incident light, etc. Types of optical measurements include, but are not limited to, scatterometry, ellipsometry, reflectometry, and the like. Different types of measurement spectra are generated corresponding to different measurement types.
In block 720, a measurement spectrum of the semiconductor device is obtained. The OCD measuring device may perform actual optical measurements on the semiconductor device to acquire a measurement spectrum.
In block 730, a first number of wavelength points is determined based on the measured spectrum, e.g., the method 100 according to the present disclosure. The first number of wavelength points is the appropriate number of wavelength points determined by the method 100 for calculating the theoretical spectrum. The OCD measurement device may analyze the measured spectrum to obtain a set of suitable wavelength sampling points and an interpolated model thereof describing the measured spectrum.
In block 740, a theoretical spectral computational model is established based on the established topographical model of the sample to be measured, the optical measurement conditions, and the first number of wavelength points. Theoretical spectral computational models can be built using electromagnetic field theory, such as rigorous coupled wave analysis. The theoretical spectral calculation model may be further determined based on the same interpolation model as the interpolation model corresponding to the first number of wavelength points.
Further, in block 750, the OCD measurement device may obtain an optical critical dimension of the semiconductor device based on the theoretical spectral computational model and the measured spectrum. And obtaining the optical key dimension measurement result corresponding to the corresponding measurement spectrum by using the theoretical spectrum calculation model. Optical critical dimensions generally include critical dimensions of the semiconductor device to be tested, film thickness, material parameters, and other parameters.
Methods for obtaining the measurement results corresponding to the corresponding measured spectra using theoretical spectral computation models generally include regression analysis and/or library matching. And (3) performing regression analysis, namely finding the relation between the matching degree between the theoretical spectrum and the measured spectrum corresponding to the morphology model, obtaining the morphology model corresponding to the spectrum which is optimally matched with the measured spectrum by using a regression analysis method, and finally obtaining the value of the characteristic parameter of the sample to be measured. And establishing a library for matching, namely establishing a theoretical spectrum database, finding a spectrum which is optimally matched with the measured spectrum and a morphology model corresponding to the spectrum in the theoretical spectrum database, and finally obtaining the value of the characteristic parameter of the sample to be measured.
Fig. 9 shows a block diagram of an apparatus 900 for measuring optical critical dimensions of a semiconductor device according to an embodiment of the present disclosure.
As shown in fig. 9, the apparatus 900 may include a first obtaining module 910 for obtaining a measurement spectrum of a semiconductor device and a set of measurement wavelength points of the measurement spectrum. The apparatus 900 may further comprise a first selection module 920 for selecting a first number of wavelength points from the set of measurement wavelength points. The apparatus 900 may further comprise a second obtaining module 930 for obtaining a first fitted spectrum corresponding to the set of measured wavelength points by interpolation based on the first number of wavelength points. Further, the apparatus 900 may also include a first determining module 940 for determining an optical critical dimension of the semiconductor device based on the first number of wavelength points in response to a first error between the first fitted spectrum and the measured spectrum being less than a first threshold.
In some embodiments, device 900 may further include: a second selection module to select a second number of wavelength points from the set of measured wavelength points in response to the first error being greater than the first threshold, wherein the second number is greater than the first number; a third obtaining module, configured to obtain, based on the second number of wavelength points, a second fitted spectrum corresponding to the measurement wavelength point set through interpolation; and a second determination module to determine an optical critical dimension of the semiconductor device based on a second number of wavelength points in response to a second error between the second fitted spectrum and the measured spectrum being less than a first threshold.
In some embodiments, the second selection module may include: a first adding sub-module for adding a further wavelength point to the first number of wavelength points to obtain a second number of wavelength points, wherein the further wavelength point is the wavelength point at which the difference between the spectral values of the first fitted spectrum and the measured spectrum is maximal.
In some embodiments, the second selection module may include: a partitioning submodule for partitioning the first number of wavelength points into a plurality of subsets; a first obtaining submodule configured to obtain, based on a subset of the plurality of subsets, a third fitted spectrum by interpolation for a portion of the set of measurement wavelength points corresponding to a wavelength band of the subset; and a second adding sub-module for adding wavelength points to the subset in response to a third error between the third fitted spectrum and the portion of the measured spectrum corresponding to the wavelength band of the subset being greater than a second threshold, wherein the second number of wavelength points comprises the first number of wavelength points and the added wavelength points.
In some embodiments, the first determining module 940 may include: the calculation submodule is used for calculating a spectral value of the theoretical spectrum by using strict coupled wave analysis aiming at the first number of wavelength points; a second obtaining submodule for obtaining a spectrum value of a theoretical spectrum by interpolation using the calculated spectrum value for other wavelength points of the measurement wavelength point set except for the first number of wavelength points, wherein an interpolation model for obtaining the theoretical spectrum is the same as an interpolation model for obtaining the first fitted spectrum; and a comparison submodule for comparing the theoretical spectrum with the measured spectrum to determine an optical critical dimension of the semiconductor device.
In some embodiments, the first number of wavelength points includes wavelengths corresponding to the end points and the extreme points of the measurement spectrum.
In some embodiments, the first threshold and/or the second threshold is based on a signal-to-noise ratio of the measured spectrum.
In some embodiments, the wavelength points of the subsets are contiguous, and the other wavelength points of the different subsets, except for the end points, do not overlap.
In some embodiments, device 900 may further include: a third determining module for determining an optical critical dimension of another semiconductor device based on the first number of wavelength points in response to the another semiconductor device having the same topography as the semiconductor device.
Fig. 10 shows a block diagram of another apparatus 1000 for measuring optical critical dimensions of a semiconductor device according to an embodiment of the present disclosure. As shown in fig. 10, the apparatus 1000 may include a first determining module 1010 for determining a topography model and optical measurement conditions of the semiconductor device. The apparatus 1000 may further comprise a first obtaining module 1020 for obtaining a measurement spectrum of the semiconductor device. The apparatus 1000 may further comprise a second determining module 1030 for determining the first number of wavelength points according to the method 100 shown in fig. 1 based on the measured spectrum. The apparatus 1000 may further comprise a third determination module 1040 for determining a theoretical spectral calculation model based on the topographical model, the optical measurement conditions, and the first number of wavelength points. In addition, the apparatus 1000 may further include a second obtaining module 1050 for obtaining an optical critical dimension of the semiconductor device based on the theoretical spectral calculation model and the measured spectrum.
In some embodiments, the third determination module 1040 of the apparatus 1000 may comprise a determination sub-module for determining the theoretical spectral calculation model further based on the same interpolation model as used for obtaining the first fitted spectrum.
For clarity, certain optional modules of the device 900 and the device 1000 are not shown in fig. 9 and 10. However, it should be understood that the various features described above with reference to FIGS. 1-8 apply equally to apparatus 900 and apparatus 1000. Further, each module of the apparatus 900 and the apparatus 1000 may be a hardware module or a software module. For example, in certain embodiments, device 900 and device 1000 may be implemented in part or in whole using software and/or firmware, e.g., as a computer program product embodied on a computer-readable medium. Alternatively or additionally, the device 900 and the device 1000 may be partly or entirely implemented on hardware basis, e.g. as Integrated Circuits (ICs), Application Specific Integrated Circuits (ASICs), system-on-a-chip (SOCs), Field Programmable Gate Arrays (FPGAs), etc. The scope of the present disclosure is not limited in this respect.
In the conventional scheme, 81 wavelength points are taken at equal intervals from a measurement wavelength point set for library matching, but in the present disclosure, as shown in fig. 6, 33 acquired wavelength sampling point sets are used for library matching. Due to the optimized sampling of the wavelength points in the present disclosure, the calculation time is less than half of the conventional time. Taking the measurement result of the intermediate line width (MCD) as an example, the following table 1 shows the measurement result of the conventional scheme and the measurement result of the scheme of the present disclosure, respectively, which are substantially the same. The present disclosure thus saves at least half of the computational resources and computational time without having an impact on the measurement results.
TABLE 1
| MCD(nm) | |
Sample 2 | Sample 3 | Sample No. 4 | Sample No. 5 | Sample No. 6 | Sample 7 | |
| The disclosure provides | 46.25 | 47.26 | 46.30 | 48.09 | 46.52 | 48.04 | 48.49 | 48.21 |
| Conventional solutions | 46.30 | 47.30 | 46.33 | 48.11 | 46.54 | 48.06 | 48.53 | 48.24 |
| δ％ | 0.12％ | 0.08％ | 0.07％ | 0.03％ | 0.05％ | 0.06％ | 0.09％ | 0.08％ |
Compared with the traditional method, the method has the advantages that the wavelength sampling point set of the theoretical spectrum is automatically selected in a self-adaptive method through analysis of the measured spectrum, spectrum distortion is avoided, and waste of computing resources caused by over-sampling of the wavelength is avoided. Meanwhile, more computing resources can be used for describing the structure, so that more structure information can be obtained by OCD measurement. The method and the device can improve the utilization rate of computing resources and effectively save time and labor cost while ensuring the computing precision. This is particularly advantageous for a large number of tests in current semiconductor manufacturing, which helps to increase production efficiency.
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
Having described embodiments of the present disclosure, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terms used herein were chosen in order to best explain the principles of the embodiments, the practical application, or technical improvements to the techniques in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.
Claims (16)
1. A method for measuring optical critical dimensions of a semiconductor device, comprising:
obtaining a measurement spectrum of the semiconductor device and a set of measurement wavelength points of the measurement spectrum;
selecting a first number of wavelength points from the measurement wavelength point set, the first number of wavelength points including wavelengths corresponding to an end point and an extreme point of the measurement spectrum;
obtaining a first fitted spectrum corresponding to the set of measured wavelength points by interpolation based on the first number of wavelength points; and
determining a theoretical spectrum based on the first number of wavelength points in response to a first error between the first fitted spectrum and the measured spectrum being less than a first threshold,
comparing the theoretical spectrum to the measured spectrum to determine an optical critical dimension of the semiconductor device.
2. The method of claim 1, further comprising:
in response to the first error being greater than the first threshold, adding another wavelength point to the first number of wavelength points to obtain a second number of wavelength points, wherein the other wavelength point is the wavelength point at which the difference between the spectral values of the first fitted spectrum and the measured spectrum is greatest, wherein the second number is greater than the first number;
obtaining a second fitted spectrum corresponding to the set of measured wavelength points by interpolation based on the second number of wavelength points; and
determining an optical critical dimension of the semiconductor device based on the second number of wavelength points in response to a second error between the second fitted spectrum and the measured spectrum being less than the first threshold.
3. The method of claim 1, further comprising:
in response to the first error being greater than the first threshold, selecting a second number of wavelength points from the set of measured wavelength points, comprising:
dividing the first number of wavelength points into a plurality of subsets;
obtaining a third fitted spectrum by interpolation for a portion of the set of measurement wavelength points corresponding to a band of the subset based on a subset of the plurality of subsets; and
adding wavelength points to the subset in response to a third error between the third fitted spectrum and a portion of the measured spectrum corresponding to a band of the subset being greater than a second threshold, wherein the second number of wavelength points includes the first number of wavelength points and the added wavelength points;
obtaining a second fitted spectrum corresponding to the set of measured wavelength points by interpolation based on the second number of wavelength points; and
determining an optical critical dimension of the semiconductor device based on the second number of wavelength points in response to a second error between the second fitted spectrum and the measured spectrum being less than the first threshold.
4. The method of claim 1, wherein determining the theoretical spectrum based on the first number of wavelength points comprises:
calculating a spectral value of a theoretical spectrum using rigorous coupled wave analysis for the first number of wavelength points; and
obtaining spectral values of the theoretical spectrum by interpolation using the calculated spectral values for other wavelength points of the set of measurement wavelength points than the first number of wavelength points, wherein the interpolation model used to obtain the theoretical spectrum is the same as the interpolation model used to obtain the first fitted spectrum.
5. The method of claim 3, wherein the first threshold and/or the second threshold is based on a signal-to-noise ratio of the measured spectrum.
6. The method of claim 3, wherein the wavelength points of the subsets are contiguous and the other wavelength points of different subsets, except for the end points, do not overlap.
7. The method of claim 1, further comprising:
determining an optical critical dimension of another semiconductor device based on the first number of wavelength points in response to the other semiconductor device having the same topography as the semiconductor device.
8. A method for measuring optical critical dimensions of a semiconductor device, comprising:
determining a morphology model and optical measurement conditions of the semiconductor device;
obtaining a measurement spectrum of the semiconductor device;
determining the first number of wavelength points according to the method of any one of claims 1-7 based on the measured spectrum;
determining a theoretical spectral calculation model based on the topography model, the optical measurement conditions, and the first number of wavelength points; and
and obtaining the optical key size of the semiconductor device based on the theoretical spectrum calculation model and the measured spectrum.
9. The method of claim 8, wherein determining a theoretical spectral computational model comprises:
the theoretical spectrum calculation model is further determined based on the same interpolation model as used to obtain the first fitted spectrum.
10. An apparatus for measuring optical critical dimensions of a semiconductor device, comprising:
a first obtaining module for obtaining a measurement spectrum of the semiconductor device and a set of measurement wavelength points of the measurement spectrum;
a first selection module, configured to select a first number of wavelength points from the measurement wavelength point set, where the first number of wavelength points includes an end point of the measurement spectrum and a wavelength corresponding to an extreme point;
a second obtaining module, configured to obtain, based on the first number of wavelength points, a first fitted spectrum corresponding to the measurement wavelength point set through interpolation; and
a first determination module to determine a theoretical spectrum based on the first number of wavelength points and to determine an optical critical dimension of the semiconductor device based on the theoretical spectrum and the measured spectrum in response to a first error between the first fitted spectrum and the measured spectrum being less than a first threshold.
11. The apparatus of claim 10, further comprising:
a second selection module for selecting a second number of wavelength points from the set of measurement wavelength points in response to the first error being greater than the first threshold, wherein the second selection module comprises a first addition submodule that adds another wavelength point to the first number of wavelength points to obtain the second number of wavelength points, wherein the other wavelength point is a wavelength point at which a difference between spectral values of the first fitted spectrum and the measurement spectrum is greatest, wherein the second number is greater than the first number;
a third obtaining module, configured to obtain, based on the second number of wavelength points, a second fitted spectrum corresponding to the measurement wavelength point set through interpolation; and
a second determination module to determine an optical critical dimension of the semiconductor device based on the second number of wavelength points in response to a second error between the second fitted spectrum and the measured spectrum being less than the first threshold.
12. The apparatus of claim 10, further comprising:
a second selection module to select a second number of wavelength points from the set of measured wavelength points in response to the first error being greater than the first threshold, wherein the second selection module comprises:
a partitioning submodule for partitioning the first number of wavelength points into a plurality of subsets;
a first obtaining submodule configured to obtain, based on a subset of the plurality of subsets, a third fitted spectrum by interpolation for a portion of the set of measurement wavelength points corresponding to a wavelength band of the subset; and
a second adding sub-module for adding wavelength points to the subset in response to a third error between the third fitted spectrum and a portion of the measured spectrum corresponding to a wavelength band of the subset being greater than a second threshold, wherein the second number of wavelength points includes the first number of wavelength points and the added wavelength points;
a third obtaining module, configured to obtain, based on the second number of wavelength points, a second fitted spectrum corresponding to the measurement wavelength point set through interpolation; and
a second determination module to determine an optical critical dimension of the semiconductor device based on the second number of wavelength points in response to a second error between the second fitted spectrum and the measured spectrum being less than the first threshold.
13. The apparatus of claim 10, wherein the first determination module comprises:
a calculation submodule for calculating a spectral value of a theoretical spectrum using rigorous coupled wave analysis for the first number of wavelength points;
a second obtaining sub-module for obtaining spectral values of the theoretical spectrum by interpolation using the calculated spectral values for other wavelength points of the set of measured wavelength points than the first number of wavelength points, wherein an interpolation model used for obtaining the theoretical spectrum is the same as an interpolation model used for obtaining the first fitted spectrum; and
a comparison submodule for comparing the theoretical spectrum with the measured spectrum to determine an optical critical dimension of the semiconductor device.
14. The apparatus of claim 12, wherein the wavelength points of the subsets are contiguous and the wavelength points of different subsets other than the end points do not overlap.
15. An apparatus for measuring optical critical dimensions of a semiconductor device, comprising:
a first determination module for determining a topography model and optical measurement conditions of the semiconductor device;
a first obtaining module for obtaining a measurement spectrum of the semiconductor device;
a second determination module for determining the first number of wavelength points based on the measured spectrum according to the method of any one of claims 1-7;
a third determination module for determining a theoretical spectral calculation model based on the topography model, the optical measurement conditions, and the first number of wavelength points; and
and the second obtaining module is used for obtaining the optical key size of the semiconductor device based on the theoretical spectrum calculation model and the measured spectrum.
16. The apparatus of claim 15, the third determination module comprising:
a determination submodule for determining the theoretical spectrum calculation model further based on an interpolation model identical to the interpolation model used for obtaining the first fitted spectrum.
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