Detailed Description
To illustrate the solution of the present invention more clearly, the following description will first describe a principle of OCD measurement based on optically scattered light:
the implementation steps of the OCD measurement principle can comprise:
1) and the OCD measuring equipment establishes a theoretical spectrum database corresponding to the shape of the structure to be measured.
The specific implementation mode of the step comprises the following steps: firstly, OCD measuring equipment establishes a model of a structure to be measured according to the appearance and the process flow of the structure to be measured; secondly, the OCD measuring equipment sets a group of parameters describing the model for the structure model to be measured to perform theoretical simulation so as to obtain a theoretical spectrum of the set of given parameters corresponding to the structure to be measured; and then, the OCD measuring equipment establishes a theoretical spectrum database of the corresponding structure to be measured according to a series of theoretical spectra of the structure to be measured acquired by simulation.
The structure model to be tested can be determined through the structure parameter variable, and one structure to be tested is provided with a plurality of structure parameter variables. In general, a usable parameter vector x = (x)0,x1,...,xL-1)T,xjJ = 0.. gth, L-1, which represents all the structural parameters of the structure to be tested, and if the model of the structure to be tested shown in fig. 6 includes the structural parameters CD, SWA, t _ poly, t _ oxide, the available parameter vector x = (CD, SWA, t _ poly, t _ oxide)TTo describe the model of the structure under test. For a given specific structural parameter combination x, according to the light scattering principle of the periodic structure, the theoretical spectrum s (λ) of the structure to be measured corresponding to the structural model to be measured determined by the specific structural parameters can be calculated. Different theoretical spectra can be generated by giving combinations of different structural parameters, so that different theoretical spectra can be obtained according to different theoretical spectraAnd establishing a theoretical spectrum database of the structure to be tested.
As an example, theoretical spectral data of the structure to be measured may be acquired according to rigorous coupled Wave Analysis, RCWA (rigorous coupled-Wave Analysis).
It should be understood by those skilled in the art that the above-mentioned method of using RCWA method to obtain theoretical spectral data of the structure to be measured is merely an example, and any other method of calculating theoretical spectral data, such as the method that can be used with the present invention, should be included in the scope of the present invention and is included herein by reference.
2) And obtaining the measurement spectrum of the structure to be measured by the OCD measuring equipment.
Specifically, the OCD measurement device acquires a scattering signal containing structural information of the structure to be measured, and processes the received scattering signal into a measurement spectrum containing the structural information of the structure to be measured. The description form of the numerical value of the measurement spectrum includes but is not limited to: reflectivity Rs,RpDescriptions of changes in polarization states tan ψ and cos Δ, fourier coefficients of polarization state analysis α, β, Mueller Matrix (Mueller Matrix) for direct output description of scattering process, NCS spectrum type, and the like; where the NCS spectra type represents three polarization spectra referred to as N, C, S, respectively, N, C, S are elements of a stoke vector, respectively, and in the mueller matrix spectra type, the stoke vector is a way to represent outgoing light and incoming light.
3) And searching a characteristic spectrum which is best matched with the measured spectrum from the theoretical spectrum database so as to determine the structural parameters of the structure to be measured.
Specifically, the OCD measuring equipment matches the theoretical spectrum database of the structure to be measured established in the step 1) with the measured spectrum of the structure to be measured obtained in the step 2) according to a preset matching standard to obtain a characteristic spectrum which is in the theoretical spectrum database and is best matched with the measured spectrum, and obtains a parameter vector corresponding to the characteristic spectrumTo determine the structure parameters of the structure to be tested at the time of the best match, wherein xjJ = 0.. and L-1, representing all structural parameters of the structure to be measured. I.e. a parameter vectorCorresponding theoretical spectrum s (x)*λ) and the measured spectrum sM(λ) an optimal match can be achieved. Preferably, the predetermined matching criterion may be goodness of fit gof (goodness of fit) or root Mean Square error rmse (root Mean Square error), or the like.
Fig. 5 is a schematic flow chart of OCD measurement according to the foregoing principle of OCD measurement.
In the process of carrying out sensitivity analysis on the structural parameters of the structure to be detected, a sensitivity formula is defined as follows:
<math>
<mrow>
<mi>Sensitivity</mi>
<mo>=</mo>
<mfrac>
<mi>ΔSignal</mi>
<mi>ΔParameter</mi>
</mfrac>
</mrow>
</math>
wherein, Parameter is the value of the nominal value of a certain structural Parameter, and can also be symbolized as xj(ii) a Δ Parameter is a variation introduced in response to the structural Parameter, i.e., Δ xjThus, there are:
<math>
<mrow>
<msub>
<msub>
<mi>Sensitivity</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfrac>
<mi>ΔSignal</mi>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
</mfrac>
</mrow>
</math>
signal is a Signal value of a certain type of spectrum in a certain waveband range; Δ Signal is the structural parameter xjThe overall signal offset in this band range can be determined by the structural parameter xjIs a floating value Δ xjThe spectral signal shift amounts caused at the selected whole wavelength points are obtained by statistical processing.
Meanwhile, Δ S (x, Δ x) is definedj,λi) Representing a structural parameter xjAt a certain wavelength point λiA spectral signal offset at (i =1,... N). The following formula:
ΔS(x,Δxj,λi)=s(x,Δxj,λi)-s(x,0,λi)
wherein, s (x, Δ x)j,λi) Representing a structural parameter xjFloat Δ x based on its nominal valuejAt wavelength point λiProcessing the generated spectral data, and taking corresponding nominal values of other structural parameters; s (x,0, λ)i) Representing a structural parameter xjAt a wavelength point λ for its nominal valueiThe spectral data generated here, i.e. the overall structural parameters, are taken to their nominal values.
In general, Δ Signal processes the spectral variation value of the selected measurement band by means of root mean square error calculation, N represents the number of wavelength points included in the selected band, and λi(i = 1.... N), binding pair Δ S (x, Δ x)j,λi) The definition of (A) is as follows,
<math>
<mrow>
<mi>ΔSignal</mi>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mi>N</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mi>ΔS</mi>
<msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math>
correspondingly, at each wavelength point, a certain structural parameter x to be measuredjSensitivity of (2)The following can be defined:
<math>
<mrow>
<msub>
<msub>
<mi>SSt</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
<mi>ΔS</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
normalized sensitivity of a single structural parameter to be measured at each wavelength pointThe following can be defined:
<math>
<mrow>
<mover>
<msub>
<msub>
<mi>SSt</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<msub>
<mi>SSt</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<msub>
<mi>Sensitivity</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
</mfrac>
</mrow>
</math>
the present invention is described in further detail below with reference to the attached drawing figures.
Fig. 1 is a schematic flow chart of a method for screening wavelength bands in OCD measurement according to a preferred embodiment of the present invention, wherein the screening wavelength bands are sub-wavelength bands with different sensitivity characteristics; the method for screening the wave band mainly relates to the step of carrying out sensitivity analysis on the structural parameters of the structure to be tested as shown in figure 5.
The method of the embodiment is mainly implemented by computer equipment. Preferably, said computer device according to the invention comprises an OCD measuring device.
It should be noted that the OCD measuring device is only an example, and other existing or future computer devices may be applicable to the present invention, and are included in the scope of the present invention and are incorporated by reference herein.
The method according to the present embodiment includes step S1 and step S2.
In step S1, for each of a plurality of structural parameters of the structural model to be tested, the computer device determines the sensitivity of each wavelength point of the structural parameter at the corresponding spectrum according to the spectral signal offset of the wavelength point caused by the change of the structural parameter; the spectral signal offset of each wavelength point on the corresponding spectrum caused by the change of the structural parameter may be obtained by calculating the difference between the theoretical spectral data of the nominal value and the adjacent value of the structural parameter in some way in advance, and then provided to the computer device, or may be calculated by the computer device, and the specific method for calculating the spectral signal offset of each wavelength point on the corresponding spectrum caused by the change of the structural parameter by the computer device will be described in detail in the following embodiments. Then, through step S1, the sensitivity of each of the plurality of structural parameters at each wavelength point may be determined. The variation of the above-mentioned structural parameters is often slight.
The structure model to be tested is a simulation model of the structure to be tested, and the simulation model is a model capable of representing materials and structure information of the structure to be tested; the structural parameters may be various parameters for representing structural characteristics of the structural model to be tested, such as critical dimension cd (critical dimension), film thickness (thickness), sidewall angle swa (side Wall angle), height HT, trapezoidal footing and top circle, etc. of the structural model to be tested.
For example, fig. 6 is a schematic diagram of a to-be-tested structure model obtained after simulation of a polysilicon to-be-tested structure, where the to-be-tested structure model can represent material and structure information of the polysilicon to-be-tested structure. As can be seen from fig. 6, the materials of the structure to be measured are, from bottom to top: silicon, silicon dioxide, polysilicon; the structural parameters of the structure to be tested comprise: critical dimension CD, sidewall angle SWA, polysilicon gate height HT, etc.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any various parameters for representing the structural features of the structural model to be tested should be included in the definition scope of the structural parameters of the present invention.
Preferably, for each of a plurality of structural parameters of the structural model under test, the computer device may determine the sensitivity of the structural parameter at each wavelength point based on the sensitivity formula at the selected wavelength band based on the spectral signal offset for each wavelength point on the corresponding spectrum resulting from the change in the structural parameter.
For example, for the structure model under test shown in fig. 6, the structure parameters of the structure model under test include: critical dimension CD, sidewall angle SWA, gate height HT. The computer equipment can respectively calculate the structural parameters CD, SWA and HT at the wavelength point lambda according to the following formulaiSensitivity of (c):
<math>
<mfenced open='' close=''>
<mtable>
<mtr>
<mtd>
<msub>
<msub>
<mi>SSt</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
</mfrac>
<mi>ΔS</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>x</mi>
<mo>=</mo>
<mo>[</mo>
<mi>CD</mi>
<mo>,</mo>
<mi>SWA</mi>
<mo>,</mo>
<mi>HT</mi>
<mo>]</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
</math>
where x is a parameter vector representing each structural parameter related to the structural model to be tested (in this example, the profile of the structure to be tested is described by the structural parameters CD, SWA, and HT, x = [ CD, SWA, HT = CD, SWA, HT)]Denotes the composition of CD, SWA and HTStructural parameter vector of (1).Representing a structural parameter xjAt wavelength point λiSensitivity of (c), xjRepresenting a certain structural parameter, Δ x, in x that is being investigatedjRepresenting a structural parameter xjA floating value, Δ S (x, Δ x), around its nominal valuej,λi) Representing a structural parameter xjAt a certain wavelength point λi(i = 1.... N.) the spectral signal offset, N, represents the number of wavelength points contained by the selected band. The name symbol of the specific structure parameter to be tested related in the example is substituted for deltaxjHaving the formula:
<math>
<mrow>
<msub>
<mi>SSt</mi>
<mi>CD</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>ΔCD</mi>
</mfrac>
<mi>ΔS</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>ΔCD</mi>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>SSt</mi>
<mi>SWA</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>ΔSWA</mi>
</mfrac>
<mi>ΔS</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>,</mo>
<mi>ΔSWA</mi>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>SSt</mi>
<mi>HT</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>ΔHT</mi>
</mfrac>
<mi>ΔS</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>ΔHT</mi>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
wherein, SStCD(λi),SStSWA(λ i) and SStHT(λ i) denotes the structural parameters CD, SWA and HT, respectively, at the wavelength point λiThe sensitivity of (c). Fig. 7 is a schematic diagram of the distribution of the sensitivities of the three structural parameters of the structural model to be tested along with the wavelength shown in fig. 6, and three curves in the diagram are respectively the distribution curves of the sensitivities of the structural parameters CD, SWA, and HT of the structural model to be tested along with the wavelength shown in fig. 6, wherein the horizontal axis represents the wavelength, and the vertical axis represents the sensitivity.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner for determining, for each structural parameter in a plurality of structural parameters of a structural model to be measured, the sensitivity of the structural parameter at each wavelength point according to the spectral signal offset of each wavelength point on the corresponding spectrum caused by the change of the structural parameter should be included in the scope of the present invention.
In step S2, the computer device screens one or more spectral bands according to the sensitivity of the plurality of structure parameters of the structure model to be measured at each wavelength point thereof, respectively.
In particular, the computer device may screen one or more spectral bands in a number of ways depending on the sensitivity of the plurality of structural parameters at each of their respective wavelength points.
For example, a sensitivity threshold is manually set for each of a plurality of structural parameters, and the computer device directly screens out one or more spectral bands according to the sensitivity of the plurality of structural parameters at each wavelength point thereof and in combination with the sensitivity thresholds; at each wavelength point in the screened one or more spectral bands, the sensitivity of each structural parameter is higher than the sensitivity threshold corresponding to the structural parameter.
As another example, a uniform sensitivity threshold is manually set. Before screening the spectral bands, the computer device normalizes the sensitivity of each structural parameter in the plurality of structural parameters at each wavelength point and screens one or more spectral bands according to the normalized sensitivity and the unified sensitivity threshold; wherein at each wavelength point in the one or more screened spectral bands, the sensitivity of each structural parameter is above the uniform sensitivity threshold.
As a preferable mode of step S2, step S2 includes step S21 and step S22.
In step S21, the computer device unifies the sensitivities of all the structural parameters at each wavelength point according to the sensitivities of the structural parameters at each wavelength point, and obtains a unified total sensitivity at each wavelength point.
The method comprises the steps of performing unified processing on the sensitivity of all structural parameters at a wavelength point, wherein the unified processing represents that a plurality of sensitivities corresponding to all the structural parameters at the wavelength point are processed into one sensitivity which corresponds to the wavelength point and can reflect the comprehensive sensitivity of all the structural parameters; for example, by unifying the three sensitivities corresponding to all the structural parameters HT, CD, and SWA, respectively, at the wavelength point 390 shown in fig. 8, one sensitivity reflecting the integrated sensitivity of the structural parameters HT, CD, and SWA at the wavelength point 390 shown in fig. 9 can be obtained.
Specifically, the implementation manner of the computer device performing the unification processing on the sensitivities of all the structural parameters at each wavelength point according to the sensitivities of the plurality of structural parameters at each wavelength point respectively includes, but is not limited to:
1) and drawing a sensitivity curve of each structural parameter in the plurality of structural parameters according to the sensitivity of the plurality of structural parameters at each wavelength point, performing unification processing on the sensitivity of all the structural parameters at each wavelength point through curve combination by the computer equipment, wherein one sensitivity curve obtained after combination can be used for representing the unified total sensitivity, and the sensitivity of one corresponding wavelength point on the sensitivity curve is the unified total sensitivity of the wavelength point. Preferably, before the normalization operation, the sensitivities of the plurality of structural parameters at each wavelength point thereof may be normalized.
Wherein, curve merging treatment can be carried out in various modes. For example, the sensitivities of all the structural parameters at each wavelength point are averaged based on the following formula, and the series of averages corresponding to the respective wavelength points are taken as the normalized total sensitivity at each wavelength point, thereby obtaining a merged sensitivity curve:
<math>
<mrow>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<msub>
<mi>SSt</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mi>L</mi>
</mfrac>
</mrow>
</math>
wherein, SStTotal(λi) Is a wavelength point lambdaiThe normalized total sensitivity of (d);is a structural parameter xjAt wavelength point λiThe sensitivity of (c); and L is the total number of all structural parameters of the structure to be detected.
2) In the present implementation, step S21 includes step S21-1 and step S21-2.
In step S21-1, the computer device normalizes the sensitivity of each of the plurality of structural parameters at each of the wavelength points thereof to obtain normalized sensitivities of the plurality of structural parameters at each of the wavelength points thereof, respectively.
For example, for each of a plurality of structural parameters, the computer device may normalize the sensitivity of the structural parameter at each wavelength point based on the following formula to obtain a normalized sensitivity of the structural parameter at each wavelength point:
<math>
<mrow>
<mover>
<msub>
<msub>
<mi>SSt</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<msub>
<mi>SSt</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<msub>
<mi>Sensitivity</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
</mfrac>
</mrow>
</math>
wherein,is a structural parameter xjAt wavelength point λiNormalized sensitivity of (d);is a structural parameter xjAt wavelength point λi(iii) the non-normalized sensitivity of (iv);the structural parameter x being such that it takes into account the contribution of the whole set of wavelength points contained in the selected full bandjWherein the full band is a predetermined spectral band range for performing the measurement.
AsTaking the structural model to be measured shown in fig. 6 as an example, the fourier coefficients α and β of polarization state analysis are used to represent the spectrum type, and the computer device can calculate the sensitivity of each structural parameter of the structural model to be measured when the contribution of all wavelength points in the full band is considered according to the following formula:
<math>
<mrow>
<msub>
<msub>
<mi>Sensitivity</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>2</mn>
<mi>N</mi>
</mrow>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mrow>
<mo>(</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math>
wherein,representing the structure parameter x taking into account the contributions of all wavelength pointsjThe sensitivity of (c); n is the number of all wavelength points; combining the above equations, one can obtain:
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mi>CD</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>N</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>CD</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mi>SWA</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>N</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>SWA</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mi>HT</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>N</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>HT</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
</mrow>
</math>
wherein, SensitivityCD,SensitivitySWAAnd SensitivityHTThe sensitivities of the structural parameters CD, SWA, and HT of the structural model to be measured shown in fig. 6 are shown in consideration of the contributions of all wavelength points of the full band. The computer device may then normalize the sensitivity of the structural parameters CD, SWA, HT at each wavelength point according to the following formula:
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>CD</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>SSt</mi>
<mi>CD</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>Sensitivity</mi>
<mi>CD</mi>
</msub>
</mfrac>
</mrow>
</math>
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>SWA</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>SSt</mi>
<mi>SWA</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>Sensitivity</mi>
<mi>SWA</mi>
</msub>
</mfrac>
</mrow>
</math>
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>HT</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>SSt</mi>
<mi>HT</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>Sensitivity</mi>
<mi>HT</mi>
</msub>
</mfrac>
</mrow>
</math>
wherein,respectively shows the structural parameters CD, SWA and HT at the wavelength point lambdaiNormalized sensitivity of (d). Fig. 8 is a schematic diagram showing the normalized distribution of the sensitivity of the three structural parameters of the structural model to be measured along with the wavelength shown in fig. 6.
It should be noted that, the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of normalizing the sensitivity of each of the plurality of structural parameters at each wavelength point thereof to obtain the normalized sensitivity of the plurality of structural parameters at each wavelength point thereof respectively is included in the scope of the present invention.
In step S21-2, the computer device unifies the normalized sensitivities of all the structural parameters at each wavelength point, and obtains a unified total sensitivity at each wavelength point.
Specifically, the implementation manner of the computer device performing the normalization processing on the normalized sensitivity of all the structural parameters at each wavelength point to obtain the normalized total sensitivity at each wavelength point includes, but is not limited to:
1) and the computer equipment directly carries out systematization processing on the normalized sensitivity of all the structural parameters at each wavelength point according to the normalized sensitivity of all the structural parameters at each wavelength point, so as to obtain the systematized total sensitivity at each wavelength point.
For example, the computer device averages the normalized sensitivities of all the structural parameters at each wavelength point according to the normalized sensitivities of all the structural parameters at each wavelength point based on the following formula, and takes the series of average values corresponding to each wavelength point as the normalized total sensitivity at each wavelength point:
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<mover>
<msub>
<mi>SSt</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mi>L</mi>
</mfrac>
</mrow>
</math>
wherein,is a wavelength point lambdaiThe normalized total sensitivity of (d);is a structural parameter xjAt wavelength point λiNormalized sensitivity of (d); and L is the number of all structural parameters of the structure to be tested.
2) Preferably, the computer device performs a normalization process on the normalized sensitivities of all the structural parameters at each wavelength point by combining the respective normalization weights of the plurality of structural parameters, so as to obtain the normalized total sensitivity at each wavelength point.
The unified weight can be used for representing the contribution degree of the structural parameter to the total sensitivity, and the higher the unified weight of the structural parameter is, the greater the contribution of the sensitivity of the structural parameter is; preferably, the statistical weighting of the structural parameters may be determined based on at least one of:
i) and the importance degree of the structural parameters corresponding to the unified weight in process control.
For example, for the model of the structure to be tested of the polysilicon device shown in fig. 6, in the integrated circuit planar manufacturing process, the structural parameter CD (critical dimension) therein has the highest importance in the process control, so the unified weight of the structural parameter CD can be set to be the highest.
ii) the user attention of the structural parameter corresponding to the unified weight.
For example, for the structural model to be measured shown in fig. 6, the user attention degrees sequentially from high to low are: the structure parameter CD, the structure parameter SWA, and the structure parameter HT, so the normalization weight of the structure parameter CD can be set to be the highest, and the normalization weight of the structure parameter HT can be set to be the lowest.
As an example, the computer device may perform a normalization process on the normalized sensitivities of all the structural parameters at each wavelength point based on the following formula and in combination with the respective normalization weights of the plurality of structural parameters, to obtain the normalized total sensitivity at each wavelength point:
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
<mover>
<msub>
<msub>
<mi>SSt</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
</mrow>
</math>
wherein, wjIs a structural parameter xjThe normalized weights of (1).
For example, taking the structural model to be tested shown in fig. 6 as an example, the unified weights of the structural parameters CD, SWA and HT are set as w1,w2,w3Then, the total sensitivity of all structural parameters at each wavelength point can be obtained based on the following formula:
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>w</mi>
<mn>1</mn>
</msub>
<mover>
<msub>
<mi>SSt</mi>
<mi>CD</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>2</mn>
</msub>
<mover>
<msub>
<mi>SSt</mi>
<mi>SWA</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>3</mn>
</msub>
<mover>
<msub>
<mi>SSt</mi>
<mi>HT</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>w</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>3</mn>
</msub>
</mrow>
</mfrac>
</mrow>
</math>
wherein,andrespectively, at a wavelength point λiNormalized sensitivities of the structural parameters CD, SWA, HT;expressing the structural parameters CD, SWA, HT at the wavelength point lambdaiThe normalized overall sensitivity of (c). FIG. 9 shows the drawing taken in w1=w2=w3Fig. 6 is a schematic diagram of the distribution of the normalized total sensitivity of the structural model to be measured with the wavelength when = 1; wherein the horizontal axis represents wavelength and the vertical axis represents the normalized total sensitivity; wherein the solid line is a distribution curve of the total sensitivity of all structural parameters along with the wavelength, and the dotted line is a sensitivity screening threshold. FIG. 10 shows the drawing taken in w1=20,w2=2,w3Fig. 6 is a schematic diagram of the distribution of the normalized total sensitivity of the structural model to be measured with the wavelength when = 2; the horizontal axis represents wavelength, and the vertical axis represents the normalized total sensitivity. Comparing fig. 9 and 10 with fig. 7, respectively, it can be seen that since the structural parameter CD is given a higher normalization weight, the shapes of the total sensitivity vs. wavelength distribution curve after normalization in fig. 10 and the sensitivity vs. wavelength distribution curve of the structural parameter CD in fig. 7 are closer.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of performing the normalization process on the normalized sensitivities of all the structural parameters at each wavelength point to obtain the normalized total sensitivity at each wavelength point is included in the scope of the present invention.
It should be noted that, the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of obtaining the normalized total sensitivity at each wavelength point by performing the normalization process on the sensitivities of all the structural parameters at each wavelength point according to the sensitivities of the plurality of structural parameters at each wavelength point respectively should be included in the scope of the present invention.
In step S22, the computer device screens one or more spectral bands based on the normalized total sensitivity at each wavelength point.
In particular, implementations of the computer device to screen the one or more spectral bands according to the normalized overall sensitivity at each wavelength point include, but are not limited to:
1) and (3) manually setting a sensitivity screening rule, and directly screening one or more spectral bands which accord with the sensitivity screening rule by the computer equipment according to the unified total sensitivity of each wavelength point and the sensitivity screening rule.
For example, the sensitivity screening rule sets the sensitivity range satisfying the screening condition to (0.8, 1.0), and the computer device screens one or more bands satisfying the sensitivity range (0.8, 1.0) according to the normalized total sensitivity at each wavelength point.
2) Preferably, before step S22, the computer device determines a sensitivity screening threshold from the normalized total sensitivity at each wavelength point obtained in step S21; in step S22, the computer device screens the one or more spectral bands according to the normalized total sensitivity at each wavelength point in combination with the sensitivity screening threshold.
For example, the computer device may determine the sensitivity screening threshold in conjunction with the normalized overall sensitivity at each wavelength point based on the following equation:
<math>
<mrow>
<mi>T</mi>
<mo>=</mo>
<munder>
<mi>min</mi>
<mi>i</mi>
</munder>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>η</mi>
<mrow>
<mo>(</mo>
<munder>
<mi>max</mi>
<mi>i</mi>
</munder>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<munder>
<mrow>
<mi>min</mi>
</mrow>
<mi>i</mi>
</munder>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</math>
wherein T is a sensitivity screening threshold value,for the minimum in the normalized total sensitivity at each wavelength point,and eta is a sensitivity adjustment coefficient which is the maximum value of the unified total sensitivity at each wavelength point and can be manually adjusted according to requirements. Taking the structural model to be tested shown in fig. 6 as an example, when η is 1/2, the computer device screens the normalized total sensitivity at each wavelength point according to the structural model to be tested shown in fig. 9 based on the sensitivityThe calculation formula of the selection threshold can obtain a sensitivity screening threshold of T =0.976, as shown by the dotted line in fig. 9; in step S22, the computer device can screen three spectral bands larger than the sensitivity screening threshold according to the normalized total sensitivity at each wavelength point and in combination with the sensitivity screening threshold, which are: (300,305), (435,455), (630,800).
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation of screening one or more spectral bands according to the normalized total sensitivity at each wavelength point should be included in the scope of the present invention.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation of screening one or more spectral bands according to the sensitivity of the plurality of structural parameters at each wavelength point thereof should be included in the scope of the present invention.
As a preferable solution of this embodiment, the method of this embodiment further includes, before step S1, performing the following steps: for each structural parameter in a plurality of structural parameters of the structural model to be measured, under a given measurement mode, floating the structural parameter to obtain the spectral signal offset of the structural parameter at each wavelength point on the spectrum of the structural parameter. Preferably, the given measurement mode is an optimal measurement mode capable of satisfying measurement requirements.
Preferably, for each structural parameter in the structural parameters of the structural model to be measured, in a given measurement mode, the computer device sets the structural parameters except the structural parameter at the nominal value thereof, obtains one piece of spectral data generated on the structural model to be measured when the value of the structural parameter is the nominal value thereof, and two pieces of spectral data generated on the structural model to be measured when the value of the structural parameter is two values obtained after the nominal value thereof is floated up and down by a preset maximum error value, and obtains the spectral signal offset of the structural parameter at each wavelength point on the spectrum thereof according to the three pieces of spectral data.
Wherein, the preset maximum error value is used for representing the allowable error range of the structural parameter. For example, the preset maximum error value of the structural parameter is 0.1, which means that the error range of the structural parameter is (-0.1, + 0.1).
The spectral data may be processed by using a plurality of calculation methods, such as a mean square error calculation method, a root mean square error calculation method, and a mean absolute percentage error calculation method, to obtain the spectral signal offset of the structural parameter at each wavelength point on the spectrum.
For example, for the structural model to be measured shown in fig. 6, the fourier coefficients α and β for polarization state analysis are used to represent the spectrum type, and the computer device can obtain the spectral signal offset of the structural parameter at each wavelength point according to the following formula.
<math>
<mrow>
<mi>ΔS</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<msup>
<mi>ΔS</mi>
<mo>+</mo>
</msup>
<msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math>
Wherein,
<math>
<mfenced open='' close=''>
<mtable>
<mtr>
<mtd>
<msup>
<mi>ΔS</mi>
<mo>+</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>|</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>+</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>|</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>=</mo>
<msup>
<mrow>
<mo>[</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>+</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>+</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>]</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mtd>
</mtr>
<mtr>
<mtd>
<msup>
<mi>ΔS</mi>
<mo>-</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>|</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>-</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>|</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>=</mo>
<msup>
<mrow>
<mo>[</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>-</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>-</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>]</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mtd>
</mtr>
</mtable>
</mfenced>
</math>
wherein x represents all structural parameters related to the structural model to be tested; Δ xjRepresenting a structural parameter xjCan be considered to correspond to the structural parameter xjControllable measurement accuracy of (2); Δ S (x, Δ x)j,λi) Representing a structural parameter xjAt wavelength point λiThe spectral signal offset of (d); delta S+(x,Δxj,λi) Representing a structural parameter xjAt wavelength point λiIs floated by + Δ x based on its nominal valuejSpectral signal offset between the temporal spectral data and the spectral data that it produces when taking its value as a nominal value; delta S-(x,Δxj,λi) Representing a structural parameter xjWave inLong point lambdaiBased on its nominal value floating by- Δ xjSpectral signal offset between the temporal spectral data and the spectral data that it produces when taking its value as a nominal value; s (x, + Δ x)j,λi) Representing a structural parameter xjFloat + Deltax based on its nominal valuejAt wavelength point λi(ii) spectral data generated therefrom; s (x,0, λ)i) Representing a structural parameter xjAt a wavelength point λ for its nominal valuei(ii) spectral data generated therefrom; s (x, - Δ x)j,λi) Representing a structural parameter xjFloat- Δ x based on its nominal valuejAt wavelength point λiThe spectral data generated.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of floating the structural parameter to obtain the spectral signal offset of the structural parameter at each wavelength point on the spectrum of the structural parameter in a given measurement mode for each structural parameter in the plurality of structural parameters of the structural model to be measured should be included in the scope of the present invention.
As a preferable solution of this embodiment, the method of this embodiment further includes, before step S1, the following steps: and establishing the structure model to be tested by the computer equipment according to the material of the structure to be tested and the structure parameters.
For example, for the structure to be tested shown in fig. 6, the materials thereof include: silicon, silicon dioxide, polysilicon. The structural parameters comprise: critical dimension CD, sidewall angle SWA, gate height HT. The computer device may build the model of the structure to be tested shown in fig. 6 according to the nominal values of the above-mentioned material and structure parameters.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and are not limiting to the present invention, and those skilled in the art should understand that any implementation manner of establishing the model of the structure to be tested according to the material and the structure parameters of the structure to be tested should be included in the scope of the present invention.
The sensitivity of different devices to be measured and process structure parameters are distributed differently in the wavelength dimension, and the prior art can not combine the structure parameters of a specific structure to be measured to set the fitting weights of a spectrum wavelength range and different wavelength bands in a targeted manner, so that the signal-to-noise ratio and the accuracy of OCD measurement are not further improved and promoted. According to the method of the embodiment, in a given measurement mode, one or more spectral bands conforming to the screening rule can be screened by analyzing the sensitivity of each structural parameter of the structural model to be measured and combining the normalized weight of each structural parameter. According to the method, the importance of the structural parameters in process control and the attention of a user can be flexibly combined, and meanwhile, the fitting weight coefficients of the sub-bands with different sensitivity characteristics in fitting evaluation are organically set based on the sensitivity analysis results of the structural parameters, so that the signal-to-noise ratio and the accuracy of OCD fitting are improved, and the stability of measurement is improved.
Fig. 2 is a schematic flow chart of a method for screening bands in OCD measurement according to another preferred embodiment of the present invention. The method of the present embodiment is mainly implemented by computer equipment, and any description of the computer equipment described in the embodiment shown in fig. 1 is included in the present embodiment by way of reference. The method of the present embodiment includes step S1, step S2, step S3, step S4, and step S5. Step S1 and step S2 are already described in detail with reference to fig. 1, and are not described herein again.
In the present embodiment, the following steps S3, S4, and S5 are performed on one spectral band of the one or more spectral bands screened in step S2. Preferably, steps S3, S4, and S5 may be performed for each of the one or more spectral bands.
In step S3, the computer device obtains the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band according to the non-normalized sensitivity of the plurality of structural parameters of the structural model to be measured at each wavelength point of the currently processed spectral band.
Wherein the non-normalized sensitivity of the structural parameter within the spectral band takes into account the contributions of all wavelength points within the spectral band, i.e. for a structural parameter, one spectral band corresponds to one non-normalized sensitivity.
For example, the computer device may obtain the non-normalized sensitivity of each of the plurality of structural parameters within the spectral band based on the non-normalized sensitivity of the plurality of structural parameters at each wavelength point of the spectral band, respectively, based on the following formula:
<math>
<mrow>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>n</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>∈</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>a</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
wherein,representing a structural parameter xjIn the spectral band λSub-BandNon-normalized sensitivity over a range;representing a structural parameter xjAt wavelength point λiAt, non-normalized sensitivity, n being the spectral band λSub-BandNumber of inner wavelength points, λi(i=1,...,n),n≤N。
For example, based on the model of the structure to be measured, λ, as shown in FIG. 6Sub-BandSelecting a spectral band for the computer device in step S2; in step S3, the computer device can determine the structural parameters CD, SWA, HT of the structural model under test in the spectral band λ according to the following formulaSub-BandNon-normalized sensitivity over range:
<math>
<mrow>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>CD</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>n</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>CD</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>∈</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>a</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
<math>
<mrow>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>SWA</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>n</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>SWA</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>∈</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>a</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
<math>
<mrow>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>HT</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>n</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>HT</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>∈</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>a</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
wherein, sensitvity'CD、Sensitivity'SWAAnd sensitvity'HTRespectively representing the structural parameters CD, SWA and HT at the spectral band lambdaSub-BandNon-normalized sensitivity over a range; SStCD(λi),SStSWA(λi) And SStHT(λi) Respectively shows the structural parameters CD, SWA and HT at the wavelength point lambdai(iii) the non-normalized sensitivity of (iv);
in step S4, the computer device unifies the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band, and determines the unified sensitivity of the spectral band.
Specifically, the computer device performs a normalization process on the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band, and the implementation manner of determining the normalized sensitivity of the spectral band includes but is not limited to:
1) the computer device directly processes the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band based on the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band, and determines the normalized sensitivity of the spectral band.
For example, the computer device averages the non-normalized sensitivity of each of the plurality of structural parameters within the spectral band based on the following formula and takes the series of averages corresponding to each wavelength point as the normalized sensitivity of the spectral band:
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
</mrow>
<mi>L</mi>
</mfrac>
</mrow>
</math>
wherein, SensitivitySub-BandRepresents the band λSub-BandNormalized sensitivity of (a); l represents the number of structural parameters included in the structural model to be measured, xj,j=0,...,L-1。
2) And the computer equipment combines the respective statistical weights of the plurality of structural parameters to perform statistical processing on the non-normalized sensitivity of each structural parameter in the plurality of structural parameters in the spectral band, and determines the statistical sensitivity of the spectral band.
As an example, the computer device may determine the normalized sensitivity of the spectral band by performing a normalization process on the non-normalized sensitivity of each of the plurality of structural parameters within the spectral band based on the following formula in combination with the respective normalization weights of the plurality of structural parameters:
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mrow>
<mi>Vub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
</msub>
</mrow>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
</mrow>
</math>
for example, based on the model of the structure to be measured shown in fig. 6, in step S3, the computer device obtains the structural parameters CD, SWA, HT in the spectral band λSub-BandThe unnormalized sensitivities in the range are respectively sensitvity'CD、Sensitivity'SWA、Sensitivity'HT(ii) a In step S4, the computer device determines the spectral band λSub-BandThe normalized sensitivity of (a) is:
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>w</mi>
<mn>1</mn>
</msub>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>CD</mi>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>2</mn>
</msub>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>SWA</mi>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>3</mn>
</msub>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>HT</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>w</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>3</mn>
</msub>
</mrow>
</mfrac>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>∈</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>a</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math> wherein, w1,w2,w3Respectively, the unified weights of the structural parameters CD, SWA and HT.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of performing the normalization processing on the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band to determine the normalized sensitivity of the spectral band is included in the scope of the present invention.
In step S5, the computer device determines a ratio of the normalized sensitivity of the spectral band to the normalized sensitivity of the full band based on the normalized sensitivity of the spectral band and the normalized sensitivity of the full band, and determines a coefficient of the spectral band in spectral fitting based on the ratio.
The implementation manner of the computer device determining the normalized sensitivity of the full band is the same as or similar to the implementation manner of the step S4 determining the normalized sensitivity of the screened spectral band, and is not described herein again.
The computer device can determine the coefficient of the spectral band in the spectral fitting according to the ratio of the normalized sensitivity of the spectral band to the normalized sensitivity of the full band in various ways.
For example, the computer device may determine the coefficients for the spectral band in the spectral fit based on a predetermined formula based on the ratio of the normalized sensitivity of the spectral band to the normalized sensitivity of the full band, e.g., the computer device may determine the coefficients for the spectral fit based on the following formula based on the spectral band λSub-BandNormalized sensitivity and full band lambdaFull-BandTo determine the coefficients of the spectral band in spectral fitting:
<math>
<mrow>
<msub>
<mi>υ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>Sensitivity</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Bmad</mi>
</mrow>
</msub>
<msub>
<mi>Sensitivity</mi>
<mi>FullBand</mi>
</msub>
</mfrac>
<mo>·</mo>
<msub>
<mi>υ</mi>
<mi>Total</mi>
</msub>
<mo>·</mo>
<mi>ξ</mi>
</mrow>
</math>
wherein, SensitivitySub-BandAs the spectral band λSub-Band∈(λa,λb) The sensitivity of (c); sensingFull BandIs full wave band lambdaFull Band∈(λStart,λEnd) The sensitivity of (c); upsilon isSub-BandRepresenting the spectral band lambda in the spectral fittingSub-Band∈(λa,λb) The coefficient of (a); upsilon isTotalFitting coefficients for the full band, which may be generally taken to be 1; xi represents the fitting weight adjusting coefficient of the sub-wave band and can be manually adjusted according to requirements.
It should be noted that the above examples are only for better illustrating the technical solution of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of determining the ratio of the normalized sensitivity of the spectral band to the normalized sensitivity of the full band according to the normalized sensitivity of the spectral band and the normalized sensitivity of the full band, and determining the coefficient of the spectral band in the spectral fitting according to the ratio should be included in the scope of the present invention.
According to the method of the embodiment, the ratio of the unified sensitivity of the screened one or more spectral bands to the unified sensitivity of the full band can be determined by combining the unified weight of each structural parameter, so that the coefficient of the one or more spectral bands during spectral fitting can be determined, the coefficients of different wavelength regions during fitting can be set in a targeted manner, and the accuracy and stability of the OCD measurement result can be greatly improved.
Fig. 3 is a schematic structural diagram of a band screening apparatus for screening bands in OCD measurement according to a preferred embodiment of the present invention, wherein the screening bands are sub-bands having different sensitivity characteristics.
The band filtering apparatus according to the present embodiment includes a first determination apparatus 1 and a filtering apparatus 2.
For each structural parameter in a plurality of structural parameters of the structural model to be measured, the first determining device 1 determines the sensitivity of the structural parameter at each wavelength point according to the spectral signal offset of each wavelength point on the corresponding spectrum caused by the change of the structural parameter; the spectral signal offset of each wavelength point on the corresponding spectrum caused by the change of the structural parameter may be obtained by calculating the difference between the theoretical spectral data of the nominal value and the adjacent value of the structural parameter in a certain manner in advance, and then directly provided to the first determining device 1, or may be calculated by the band filtering device, and the specific manner of calculating the spectral signal offset of each wavelength point on the corresponding spectrum caused by the change of the structural parameter by the band filtering device will be described in detail in the following embodiments. The sensitivity of each of the plurality of structural parameters at each wavelength point can be determined by the operation performed by the first determination device 1. The variation of the above-mentioned structural parameters is often slight.
The structure model to be tested is a simulation model of the structure to be tested, and the simulation model is a model capable of representing materials and structure information of the structure to be tested; the structural parameters may be various parameters used for representing structural characteristics of the structure model to be tested, such as a critical dimension CD, a film thickness, a sidewall angle SWA and a height HT of the structure model to be tested, a trapezoidal footing and a trapezoidal top circle, and the like.
For example, fig. 6 is a schematic diagram of a to-be-tested structure model obtained after simulation of a polysilicon to-be-tested structure, where the to-be-tested structure model can represent material and structure information of the polysilicon to-be-tested structure. As can be seen from fig. 6, the materials of the structure to be measured are, from bottom to top: silicon, silicon dioxide, polysilicon (poly); the structural parameters of the structure to be tested comprise: critical dimension CD, sidewall angle SWA, polysilicon gate height HT, etc.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any various parameters for representing the structural features of the structural model to be tested should be included in the definition scope of the structural parameters of the present invention.
Preferably, for each of a plurality of structural parameters of the structural model to be measured, the first determining means 1 may determine the sensitivity of the structural parameter at each wavelength point based on the sensitivity formula at the selected wavelength band according to the spectral signal offset of each wavelength point on the corresponding spectrum caused by the change of the structural parameter.
For example, for the structure model under test shown in fig. 6, the structure parameters of the structure model under test include: critical dimension CD, sidewall angle SWA, gate height HT. The first determination device 1 may be according toRespectively calculating the structural parameters CD, SWA and HT at the wavelength point lambda by a formulaiSensitivity of (c):
<math>
<mfenced open='' close=''>
<mtable>
<mtr>
<mtd>
<msub>
<msub>
<mi>SSt</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
<mi>ΔS</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mo>,</mo>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>x</mi>
<mo>=</mo>
<mo>[</mo>
<mi>CD</mi>
<mo>,</mo>
<mi>SWA</mi>
<mo>,</mo>
<mi>HT</mi>
<mo>]</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
</math>
where x is a parameter vector representing each structural parameter related to the structural model to be tested (in this example, the profile of the structure to be tested is described by the structural parameters CD, SWA, and HT, x = [ CD, SWA, HT = CD, SWA, HT)]Representing a structural parameter vector consisting of CD, SWA and HT).Representing a structural parameter xjAt wavelength point λiMedicine for curing fracture and injurySensitivity, xjRepresenting a certain structural parameter, Δ x, in x that is being investigatedjRepresenting a structural parameter xjA floating value, Δ S (x, Δ x), around its nominal valuej,λi) Representing a structural parameter xjAt a certain wavelength point λi(i = 1.... N.) the spectral signal offset, N, represents the number of wavelength points contained by the selected band. The name symbol of the specific structure parameter to be tested related in the example is substituted for deltaxjHaving the formula:
<math>
<mrow>
<msub>
<mi>SSt</mi>
<mi>CD</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>ΔCD</mi>
</mfrac>
<mi>ΔS</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>ΔCD</mi>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>SSt</mi>
<mi>SWA</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>ΔSWA</mi>
</mfrac>
<mi>ΔS</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>ΔSWA</mi>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>SSt</mi>
<mi>HT</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>ΔHT</mi>
</mfrac>
<mi>ΔS</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>ΔHT</mi>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
wherein, SStCD(λi),SStSWA(λi) And SStHT(λi) Respectively representing the structural parameters CD, SWA and HT at the wavelength point lambdaiThe sensitivity of (c). Fig. 7 is a schematic diagram of the distribution of the sensitivities of the three structural parameters of the structural model to be tested along with the wavelength shown in fig. 6, and three curves in the diagram are respectively the distribution curves of the sensitivities of the structural parameters CD, SWA, and HT of the structural model to be tested along with the wavelength shown in fig. 6, wherein the horizontal axis represents the wavelength, and the vertical axis represents the sensitivity.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner for determining, for each structural parameter in a plurality of structural parameters of a structural model to be measured, the sensitivity of the structural parameter at each wavelength point according to the spectral signal offset of each wavelength point on the corresponding spectrum caused by the change of the structural parameter should be included in the scope of the present invention.
The screening device 2 screens one or more spectral bands according to the sensitivity of a plurality of structural parameters of the structural model to be tested at each wavelength point of the structural model.
In particular, the screening device 2 may screen one or more spectral bands in a variety of ways depending on the sensitivity of the plurality of structural parameters at each of their respective wavelength points.
For example, a sensitivity threshold is manually set for each of a plurality of structural parameters, and the screening device 2 directly screens out one or more spectral bands according to the sensitivity of the plurality of structural parameters at each wavelength point thereof respectively and in combination with the sensitivity thresholds; at each wavelength point in the screened one or more spectral bands, the sensitivity of each structural parameter is higher than the sensitivity threshold corresponding to the structural parameter.
As another example, a uniform sensitivity threshold is manually set. Before screening the spectral bands, the screening device 2 normalizes the sensitivity of each structural parameter of the plurality of structural parameters at each wavelength point, and screens one or more spectral bands according to the normalized sensitivity and the unified sensitivity threshold; wherein at each wavelength point in the one or more screened spectral bands, the sensitivity of each structural parameter is above the uniform sensitivity threshold.
As a preferred embodiment of the screening apparatus 2, the screening apparatus 2 comprises a first obtaining apparatus (not shown) and a first sub-screening apparatus (not shown).
And the first acquisition device is used for carrying out unification processing on the sensitivity of all the structural parameters at each wavelength point according to the sensitivity of the structural parameters at each wavelength point, so as to obtain the unified total sensitivity at each wavelength point.
The method comprises the steps of performing unified processing on the sensitivity of all structural parameters at a wavelength point, wherein the unified processing represents that a plurality of sensitivities corresponding to all the structural parameters at the wavelength point are processed into one sensitivity which corresponds to the wavelength point and can reflect the comprehensive sensitivity of all the structural parameters; for example, by unifying the three sensitivities corresponding to all the structural parameters HT, CD, and SWA, respectively, at the wavelength point 390 shown in fig. 8, one sensitivity reflecting the integrated sensitivity of the structural parameters HT, CD, and SWA at the wavelength point 390 shown in fig. 9 can be obtained.
Specifically, the implementation manner of the first obtaining device performing the unification processing on the sensitivities of all the structural parameters at each wavelength point according to the sensitivities of the plurality of structural parameters at each wavelength point respectively includes, but is not limited to:
1) the first acquisition device draws a sensitivity curve of each structural parameter in the plurality of structural parameters according to the sensitivity of the plurality of structural parameters at each wavelength point, unifies the sensitivity of all the structural parameters at each wavelength point through curve merging, and a sensitivity curve obtained after merging can be used for representing the unified total sensitivity, wherein the sensitivity of one corresponding wavelength point on the sensitivity curve is the unified total sensitivity of the wavelength point. Preferably, before the normalization operation, the sensitivities of the plurality of structural parameters at each wavelength point thereof may be normalized.
The first acquisition device can perform curve merging processing in various ways. For example, the sensitivities of all the structural parameters at each wavelength point are averaged based on the following formula, and the series of averages corresponding to the respective wavelength points are taken as the unified total sensitivity at each wavelength point, thereby obtaining a merged sensitivity curve:
<math>
<mrow>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<msub>
<mi>SSt</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mi>L</mi>
</mfrac>
</mrow>
</math>
wherein, SStTotal(λi) Is a wavelength point lambdaiThe normalized total sensitivity of (d);is a structural parameter xjAt wavelength point λiThe sensitivity of (c); l is the total number x of all structural parameters of the structure to be testedj,j=0,...,L-1。
2) In this implementation, the first obtaining device includes a first sub-obtaining device (not shown) and a second sub-obtaining device (not shown).
The first sub-acquisition device normalizes the sensitivity of each structural parameter in the plurality of structural parameters at each wavelength point to obtain the normalized sensitivity of the plurality of structural parameters at each wavelength point.
For example, for each of the plurality of structural parameters, the first sub-acquisition means may normalize the sensitivity of the structural parameter at each wavelength point based on the following formula to obtain a normalized sensitivity of the structural parameter at each wavelength point:
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<msub>
<mi>SSt</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<msub>
<mi>Sensitivity</mi>
<mi>s</mi>
</msub>
<mi>j</mi>
</msub>
</mfrac>
</mrow>
</math>
wherein,is a structural parameter xjAt wavelength point λiNormalized sensitivity of (d);is a structural parameter xjAt wavelength point λi(iii) the non-normalized sensitivity of (iv);the structural parameter x being such that it takes into account the contribution of the whole set of wavelength points contained in the selected full bandjWherein the full band is a predetermined spectral band range for performing the measurement.
AsTaking the structural model to be measured shown in fig. 6 as an example, the fourier coefficients α and β of polarization state analysis are used to represent the spectrum type, and the first sub-obtaining device can calculate the sensitivity of each structural parameter of the structural model to be measured when the contribution of all wavelength points of the full band is considered according to the following formula:
<math>
<mrow>
<msub>
<msub>
<mi>Sensitivity</mi>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>2</mn>
<mi>N</mi>
</mrow>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mrow>
<mo>(</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math>
wherein,representing the structural parameter x when the contribution of all wavelength points is consideredjThe sensitivity of (c); n is the number of all wavelength points; combining the above equations, one can obtain:
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mi>CD</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>N</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>CD</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
<mo></mo>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mi>SWA</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>N</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>SWA</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
<mo></mo>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mi>HT</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>N</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>HT</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
<mo></mo>
</mrow>
</math>
wherein, SensitivityCD,SensitivitySWAAnd SensitivityHTThe sensitivities of the structural parameters CD, SWA, and HT of the structural model to be measured shown in fig. 6 are shown in consideration of the contributions of all wavelength points of the full band. Then, the first sub-acquiring device may normalize the sensitivity of the structural parameters CD, SWA, HT at each wavelength point according to the following formula:
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>CD</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>SSt</mi>
<mi>CD</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>Sensitivity</mi>
<mi>CD</mi>
</msub>
</mfrac>
</mrow>
</math>
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>SWA</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>SSt</mi>
<mi>SWA</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>Sensitivity</mi>
<mi>SWA</mi>
</msub>
</mfrac>
</mrow>
</math>
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>HT</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>SSt</mi>
<mi>HT</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>Sensitivity</mi>
<mi>HT</mi>
</msub>
</mfrac>
</mrow>
</math>
wherein,andrespectively shows the structural parameters CD, SWA and HT at the wavelength point lambdaiNormalized sensitivity of (d). Fig. 8 is a schematic diagram showing the normalized distribution of the sensitivity of the three structural parameters of the structural model to be measured along with the wavelength shown in fig. 6.
It should be noted that, the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of normalizing the sensitivity of each of the plurality of structural parameters at each wavelength point thereof to obtain the normalized sensitivity of the plurality of structural parameters at each wavelength point thereof respectively is included in the scope of the present invention.
And the second sub-acquisition device performs normalization processing on the normalized sensitivity of all the structural parameters at each wavelength point to obtain the normalized total sensitivity at each wavelength point.
Specifically, the second sub-acquiring device unifies the normalized sensitivities of all the structural parameters at each wavelength point, and the implementation manner of obtaining the unified total sensitivity at each wavelength point includes but is not limited to:
1) the second sub-acquisition device directly performs unification processing on the normalized sensitivity of all the structural parameters at each wavelength point according to the normalized sensitivity of all the structural parameters at each wavelength point, and obtains the unified total sensitivity at each wavelength point.
For example, the second sub-acquiring device calculates an average value of the normalized sensitivities of all the structural parameters at each wavelength point based on the following formula according to the normalized sensitivities of all the structural parameters at each wavelength point, and takes the series of average values corresponding to each wavelength point as the normalized total sensitivity at each wavelength point:
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<mover>
<msub>
<mi>SSt</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mi>L</mi>
</mfrac>
</mrow>
</math>
wherein,is a wavelength point lambdaiThe normalized total sensitivity of (d);is a structural parameter xjAt wavelength point λiNormalized sensitivity of (d); and L is the number of all structural parameters of the structure to be tested.
2) Preferably, the second sub-acquisition means comprises third sub-acquisition means (not shown). And the third sub-acquisition device combines the respective statistical weights of the plurality of structural parameters to perform statistical processing on the normalized sensitivity of all the structural parameters at each wavelength point, so as to obtain the normalized total sensitivity at each wavelength point.
The unified weight can be used for representing the contribution degree of the structural parameter to the total sensitivity, and the higher the unified weight of the structural parameter is, the greater the contribution of the sensitivity of the structural parameter is; preferably, the statistical weighting of the structural parameters may be determined based on at least one of:
i) and the importance degree of the structural parameters corresponding to the unified weight in process control.
For example, for the model of the structure to be tested of the polysilicon device shown in fig. 6, in the integrated circuit planar manufacturing process, the structural parameter CD (critical dimension) therein has the highest importance in the process control, so the unified weight of the structural parameter CD can be set to be the highest.
ii) the user attention of the structural parameter corresponding to the unified weight.
For example, for the structural model to be measured shown in fig. 6, the user attention degrees sequentially from high to low are: the structure parameter CD, the structure parameter SWA, and the structure parameter HT, so the normalization weight of the structure parameter CD can be set to be the highest, and the normalization weight of the structure parameter HT can be set to be the lowest.
As an example, the third sub-obtaining device may perform normalization processing on the normalized sensitivities of all the structural parameters at each wavelength point based on the following formula and in combination with the respective normalization weights of the plurality of structural parameters, to obtain the normalized total sensitivity at each wavelength point:
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
<mover>
<msub>
<mi>SSt</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
</mrow>
</math>
wherein, wjIs a structural parameter xjThe normalized weights of (1).
For example, taking the structural model to be tested shown in fig. 6 as an example, the unified weights of the structural parameters CD, SWA and HT are set as w1,w2,w3Then, the third sub-acquisition means may obtain the total sensitivity of all the structural parameters at each wavelength point based on the following formula:
<math>
<mrow>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>w</mi>
<mn>1</mn>
</msub>
<mover>
<msub>
<mi>SSt</mi>
<mi>CD</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>2</mn>
</msub>
<mover>
<msub>
<mi>SSt</mi>
<mi>SWA</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>3</mn>
</msub>
<mover>
<msub>
<mi>SSt</mi>
<mi>HT</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>w</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>3</mn>
</msub>
</mrow>
</mfrac>
</mrow>
</math>
wherein,andrespectively, at a wavelength point λiNormalized sensitivities of the structural parameters CD, SWA, HT;expressing the structural parameters CD, SWA, HT at the wavelength point lambdaiThe normalized overall sensitivity of (c). FIG. 9 shows the drawing taken in w1=w2=w3Fig. 6 is a schematic diagram of the distribution of the normalized total sensitivity of the structural model to be measured with the wavelength when = 1; wherein the horizontal axis represents wavelength and the vertical axis represents the normalized total sensitivity; wherein the solid line is a distribution curve of the total sensitivity of all structural parameters along with the wavelength, and the dotted line is a sensitivity screening threshold. FIG. 10 shows the drawing taken in w1=20,w2=2,w3Fig. 6 is a schematic diagram of the distribution of the normalized total sensitivity of the structural model to be measured with the wavelength when = 2; the horizontal axis represents wavelength, and the vertical axis represents the normalized total sensitivity. Comparing fig. 9 and 10 with fig. 7, respectively, it can be seen that since the structural parameter CD is given a higher normalization weight, the shapes of the total sensitivity vs. wavelength distribution curve after normalization in fig. 10 and the sensitivity vs. wavelength distribution curve of the structural parameter CD in fig. 7 are closer.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of performing the normalization process on the normalized sensitivities of all the structural parameters at each wavelength point to obtain the normalized total sensitivity at each wavelength point is included in the scope of the present invention.
It should be noted that, the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of obtaining the normalized total sensitivity at each wavelength point by performing the normalization process on the sensitivities of all the structural parameters at each wavelength point according to the sensitivities of the plurality of structural parameters at each wavelength point respectively should be included in the scope of the present invention.
The first sub-screening device screens one or more spectral bands according to the normalized total sensitivity at each wavelength point.
Specifically, the first sub-screening device screens one or more spectral bands according to the normalized total sensitivity at each wavelength point by means of, but not limited to:
1) and manually setting a sensitivity screening rule, and directly screening one or more spectral bands conforming to the sensitivity screening rule by the first sub-screening device according to the unified total sensitivity of each wavelength point and the sensitivity screening rule.
For example, the sensitivity screening rule sets the sensitivity range satisfying the screening condition to (0.8, 1.0), and the first sub-screening means screens one or more bands satisfying the sensitivity range (0.8, 1.0) according to the normalized total sensitivity at each wavelength point.
2) Preferably, the screening device 2 comprises second determining means (not shown), and the first sub-screening device comprises second sub-screening devices (not shown). Before the second sub-screening device executes the operation, the second determining device determines a sensitivity screening threshold according to the normalized total sensitivity at each wavelength point obtained by the first obtaining device; and the second sub-screening device screens the one or more spectral bands according to the normalized total sensitivity of each wavelength point and the sensitivity screening threshold value.
For example, the second determining means may determine the sensitivity screening threshold in combination with the normalized total sensitivity at each wavelength point based on the following formula:
<math>
<mrow>
<mi>T</mi>
<mo>=</mo>
<munder>
<mi>min</mi>
<mi>i</mi>
</munder>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>η</mi>
<mrow>
<mo>(</mo>
<munder>
<mi>max</mi>
<mi>i</mi>
</munder>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<munder>
<mrow>
<mi>min</mi>
</mrow>
<mi>i</mi>
</munder>
<mover>
<msub>
<mi>SSt</mi>
<mi>Total</mi>
</msub>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</math>
wherein T is a sensitivity screening threshold value,for the minimum in the normalized total sensitivity at each wavelength point,normalized total reflection for each wavelength pointThe maximum value in the sensitivity, eta, is a sensitivity adjustment coefficient and can be manually adjusted according to requirements. Taking the structure model to be tested shown in fig. 6 as an example, when η is taken as 1/2, the second determining device obtains the sensitivity screening threshold T =0.976 based on the calculation formula of the sensitivity screening threshold according to the normalized total sensitivity at each wavelength point of the structure model to be tested shown in fig. 9, as shown by the dotted line in fig. 9; the second sub-screening device can screen three spectral bands larger than the sensitivity screening threshold value according to the unified total sensitivity of each wavelength point and by combining the sensitivity screening threshold value, and the three spectral bands are respectively as follows: (300,305), (435,455), (630,800).
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation of screening one or more spectral bands according to the normalized total sensitivity at each wavelength point should be included in the scope of the present invention.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation of screening one or more spectral bands according to the sensitivity of the plurality of structural parameters at each wavelength point thereof should be included in the scope of the present invention.
As a preferable aspect of the present embodiment, the band filtering apparatus of the present embodiment further includes third acquiring means (not shown) that performs an operation before the first determining means 1. For each structural parameter in the plurality of structural parameters of the structural model to be measured, under a given measurement mode, the third obtaining device floats the structural parameter to obtain the spectral signal offset of the structural parameter at each wavelength point on the spectrum of the structural parameter. Preferably, the given measurement mode is an optimal measurement mode capable of satisfying measurement requirements.
Preferably, for each structural parameter in the structural parameters of the structural model to be measured, in a given measurement mode, the third obtaining device sets the structural parameters except the structural parameter at the nominal value thereof, obtains one piece of spectral data generated on the structural model to be measured when the value of the structural parameter is the nominal value thereof, and two pieces of spectral data generated on the structural model to be measured when the value of the structural parameter is two values obtained after the nominal value thereof is floated up and down by a preset maximum error value, and obtains the spectral signal offset of the structural parameter at each wavelength point on the spectrum thereof according to the three pieces of spectral data.
The preset maximum error value is used for representing an allowable error range of the structural parameter. For example, the preset maximum error value of the structural parameter is 0.1, which means that the error range of the structural parameter is (-0.1, + 0.1).
The spectral data may be processed by using a plurality of calculation methods, such as a mean square error calculation method, a root mean square error calculation method, and a mean absolute percentage error calculation method, to obtain the spectral signal offset of the structural parameter at each wavelength point on the spectrum.
For example, for the structural model to be measured shown in fig. 6, the fourier coefficients α and β for polarization state analysis are used to represent the spectrum type, and the third obtaining device can obtain the spectral signal offset of the structural parameter at each wavelength point according to the following formula.
<math>
<mrow>
<mi>ΔS</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<msup>
<mi>ΔS</mi>
<mo>+</mo>
</msup>
<msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math>
Wherein,
<math>
<mfenced open='' close=''>
<mtable>
<mtr>
<mtd>
<msup>
<mi>ΔS</mi>
<mo>+</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>|</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>+</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>|</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>=</mo>
<msup>
<mrow>
<mo>[</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>+</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>+</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>]</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mtd>
</mtr>
<mtr>
<mtd>
<msup>
<mi>ΔS</mi>
<mo>-</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>|</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>-</mo>
<msub>
<mi>Δx</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>|</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>=</mo>
<msup>
<mrow>
<mo>[</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>-</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>α</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mo>-</mo>
<mi>Δ</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>β</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>]</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mtd>
</mtr>
</mtable>
</mfenced>
</math>
wherein x represents all structural parameters related to the structural model to be tested; Δ xjRepresenting a structural parameter xjCan be considered to correspond to the controllable measurement accuracy of the structural parameter xj; Δ S (x, Δ x)j,λi) Denotes the structural parameter xj at the wavelength point λiThe spectral signal offset of (d); delta S+(x,Δxj,λi) Representing a structural parameter xjAt wavelength point λiIs floated by + Δ x based on its nominal valuejSpectral signal offset between the temporal spectral data and the spectral data that it produces when taking its value as a nominal value; delta S-(x,Δxj,λi) Denotes the structural parameter xj at the wavelength point λiBased on its nominal value floating by- Δ xjSpectral signal offset between the temporal spectral data and the spectral data that it produces when taking its value as a nominal value; s (x, + Δ x)j,λi) Representing that the structural parameter xj floats + Δ x based on its nominal valuejAt wavelength point λi(ii) spectral data generated therefrom; s (x,0, λ)i) At wavelength point λ representing the structural parameter xj as its nominal valuei(ii) spectral data generated therefrom; s (x, - Δ x)j,λi) Representing a structural parameter xjFloat- Δ x based on its nominal valuejAt wavelength point λiThe spectral data generated.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of floating the structural parameter to obtain the spectral signal offset of the structural parameter at each wavelength point on the spectrum of the structural parameter in a given measurement mode for each structural parameter in the plurality of structural parameters of the structural model to be measured should be included in the scope of the present invention.
As a preferable aspect of the present embodiment, the band filtering apparatus of the present embodiment further includes a model building apparatus (not shown) that performs an operation before the first determination apparatus 1. And the model establishing device establishes the model of the structure to be tested according to the material of the structure to be tested and the structure parameters.
For example, for the structure to be tested shown in fig. 6, the materials thereof include: silicon, silicon dioxide, polysilicon. The structural parameters comprise: critical dimension CD, sidewall angle SWA, gate height HT. The model building apparatus can build the model of the structure to be tested shown in fig. 6 according to the nominal values of the above-mentioned material and structure parameters.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and are not limiting to the present invention, and those skilled in the art should understand that any implementation manner of establishing the model of the structure to be tested according to the material and the structure parameters of the structure to be tested should be included in the scope of the present invention.
The sensitivity of different devices to be measured and process structure parameters are distributed differently in the wavelength dimension, and the prior art can not combine the structure parameters of a specific structure to be measured to set the fitting weights of a spectrum wavelength range and different wavelength bands in a targeted manner, so that the signal-to-noise ratio and the accuracy of OCD measurement are not further improved and promoted. According to the band screening apparatus of the present embodiment, in a given measurement mode, one or more spectral bands that meet the screening rules can be screened by analyzing the sensitivity of each structural parameter of the structural model to be measured and combining the normalized weight of each structural parameter. According to the method, the importance of the structural parameters in process control and the attention of a user can be flexibly combined, and meanwhile, the fitting weight coefficients of the sub-bands with different sensitivity characteristics in fitting evaluation are organically set based on the sensitivity analysis results of the structural parameters, so that the signal-to-noise ratio and the accuracy of OCD fitting are improved, and the stability of measurement is improved.
Fig. 4 is a schematic structural diagram of a band screening apparatus for screening a band in OCD measurement according to another preferred embodiment of the present invention. The band filtering apparatus of the present embodiment includes a first determining apparatus 1, a filtering apparatus 2, a second acquiring apparatus 3, a third determining apparatus 4, and a fourth determining apparatus 5. The first determining device 1 and the screening device 2 are described in detail with reference to fig. 3, and are not described herein again.
In the present embodiment, the second obtaining means 3, the third determining means 4 and the fourth determining means 5 are used for performing an operation on one spectral band of the one or more spectral bands screened by the screening means 2. Preferably, the second acquiring means 3, the third determining means 4 and the fourth determining means 5 are triggerable to perform an operation for each of the one or more spectral bands.
The second obtaining device 3 obtains the non-normalized sensitivity of each structural parameter in the plurality of structural parameters in the spectral band according to the non-normalized sensitivity of the plurality of structural parameters of the structural model to be measured at each wavelength point of the currently processed spectral band.
Wherein the non-normalized sensitivity of the structural parameter within the spectral band takes into account the contributions of all wavelength points within the spectral band, i.e. for a structural parameter, one spectral band corresponds to one non-normalized sensitivity.
For example, the second obtaining device 3 may obtain the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band according to the non-normalized sensitivity of the plurality of structural parameters at each wavelength point of the spectral band based on the following formula:
<math>
<mrow>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>n</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>∈</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>a</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
wherein,representing a structural parameter xjIn the spectral band λSub-BandNon-normalized sensitivity over a range;representing a structural parameter xjAt wavelength point λiAt, non-normalized sensitivity, n being the spectral band λSub-BandNumber of inner wavelength points, λi(i=1,...,n),n≤N。
For example, based on the model of the structure to be measured, λ, as shown in FIG. 6Sub-BandA spectral band selected by the screening device 2; the second acquiring means 3 can determine the structural parameters CD, SWA, HT of the structural model to be measured in the spectral band λ according to the following formulaSub-BandNon-normalized sensitivity over range:
<math>
<mrow>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>CD</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>n</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>CD</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>∈</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>a</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
<math>
<mrow>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>SWA</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>n</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>SWA</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>∈</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>a</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
<math>
<mrow>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>HT</mi>
</msub>
<mo>=</mo>
<msqrt>
<mfrac>
<mn>1</mn>
<mi>n</mi>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>SSt</mi>
<mi>HT</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msqrt>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>∈</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>a</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
wherein, sensitvity'CD、Sensitivity'SWAAnd sensitvity'HTRespectively representing the structural parameters CD, SWA and HT at the spectral band lambdaSub-BandNon-normalized sensitivity over a range; SStCD(λi),SStSWA(λ i) and SStHT(λ i) represents the structural parameters CD, SWA, HT at the wavelength point λi(iii) the non-normalized sensitivity of (iv);
the third determining means 4 performs a normalization process on the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band, and determines the normalized sensitivity of the spectral band.
Specifically, the third determining device 4 performs a normalization process on the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band, and the implementation manner of determining the normalized sensitivity of the spectral band includes but is not limited to:
1) the third determining means 4 directly determines the normalized sensitivity of each of the plurality of structural parameters in the spectral band by normalizing the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band based on the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band.
For example, the third determination device 4 averages the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band based on the following formula, and takes the series of average values corresponding to the respective wavelength points as the normalized sensitivity of the spectral band:
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>x</mi>
</msub>
<mi>j</mi>
</msub>
</mrow>
<mi>L</mi>
</mfrac>
</mrow>
</math>
wherein, SensitivitySub-BandRepresents the band λSub-BandNormalized sensitivity of (a); l represents the number of structural parameters included in the structural model to be measured.
2) The third determining device 4 combines the normalization weights of the plurality of structural parameters to perform normalization processing on the non-normalized sensitivity of each structural parameter in the plurality of structural parameters in the spectral band, and determines the normalized sensitivity of the spectral band.
As an example, the third determining device 4 may determine the normalized sensitivity of the spectral band by performing a normalization process on the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band based on the following formula in combination with the normalization weight of each of the plurality of structural parameters:
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mrow>
<mi>Vub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
</msub>
</mrow>
<mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
</mrow>
</math>
for example, based on the structural model to be measured shown in fig. 6, the second obtaining device 3 obtains the structural parameters CD, SWA, HT in the spectral band λSub-BandThe unnormalized sensitivities in the range are respectively sensitvity'CD、Sensitivity'SWA、Sensitivity'HT(ii) a Third determination means 4 determine the spectral band λSub-BandThe normalized sensitivity of (a) is:
<math>
<mrow>
<msub>
<mi>Sensitivity</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>w</mi>
<mn>1</mn>
</msub>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>CD</mi>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>2</mn>
</msub>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>SWA</mi>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>3</mn>
</msub>
<msub>
<mrow>
<mi>Sensitivity</mi>
<mo>′</mo>
</mrow>
<mi>HT</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>w</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>w</mi>
<mn>3</mn>
</msub>
</mrow>
</mfrac>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>∈</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>λ</mi>
<mi>a</mi>
</msub>
<mo>,</mo>
<msub>
<mi>λ</mi>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math> wherein, w1,w2,w3Respectively, the unified weights of the structural parameters CD, SWA and HT.
It should be noted that the above examples are only for better illustrating the technical solutions of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of performing the normalization processing on the non-normalized sensitivity of each of the plurality of structural parameters in the spectral band to determine the normalized sensitivity of the spectral band is included in the scope of the present invention.
The fourth determining means 5 determines a ratio of the normalized sensitivity of the spectral band to the normalized sensitivity of the full band based on the normalized sensitivity of the spectral band and the normalized sensitivity of the full band, and determines a coefficient of the spectral band in the spectral fitting based on the ratio.
The implementation manner of the fourth determining device 5 determining the normalized sensitivity of the full band is the same as or similar to the implementation manner of the third determining device 4 determining the normalized sensitivity of the screened spectral band, and is not described herein again.
The fourth determining device 5 may determine the coefficient of the spectral band in the spectral fitting according to the ratio of the normalized sensitivity of the spectral band to the normalized sensitivity of the full band in various ways.
For example, the fourth determination means 5 may determine the coefficient of the spectral Band at the time of spectral fitting based on a predetermined formula based on the ratio of the normalized sensitivity of the spectral Band to the normalized sensitivity of the full Band, e.g., the fourth determination means 5 may determine the coefficient of the spectral Band at the time of spectral fitting based on the following formula based on the normalized sensitivity of the spectral Band λ Sub-Band and the full Band λFull BandTo determine the coefficients of the spectral band in spectral fitting:
<math>
<mrow>
<msub>
<mi>υ</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Band</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>Sensitivity</mi>
<mrow>
<mi>Sub</mi>
<mo>-</mo>
<mi>Bmad</mi>
</mrow>
</msub>
<msub>
<mi>Sensitivity</mi>
<mi>FullBand</mi>
</msub>
</mfrac>
<mo>·</mo>
<msub>
<mi>υ</mi>
<mi>Total</mi>
</msub>
<mo>·</mo>
<mi>ξ</mi>
</mrow>
</math>
wherein, SensitivitySub-BandAs the spectral band λSub-Band∈(λa,λb) The sensitivity of (c); sensingFull BandIs full wave band lambdaFull Band∈(λStart,λEnd) The sensitivity of (c); upsilon isSub-BandRepresenting the spectral band lambda in the spectral fittingSub-Band∈(λa,λb) The coefficient of (a); upsilon isTotalFitting coefficients for the full band, which may be generally taken to be 1; xi represents the fitting weight adjusting coefficient of the sub-wave band and can be manually adjusted according to requirements.
It should be noted that the above examples are only for better illustrating the technical solution of the present invention, and not for limiting the present invention, and those skilled in the art should understand that any implementation manner of determining the ratio of the normalized sensitivity of the spectral band to the normalized sensitivity of the full band according to the normalized sensitivity of the spectral band and the normalized sensitivity of the full band, and determining the coefficient of the spectral band in the spectral fitting according to the ratio should be included in the scope of the present invention.
According to the band screening device of the embodiment, the ratio of the unified sensitivity of the screened one or more spectral bands to the unified sensitivity of the full band can be determined by combining the unified weight of each structural parameter, so that the coefficient of the one or more spectral bands during spectrum fitting can be determined, the coefficients of different wavelength regions during fitting can be set in a targeted manner, and the accuracy and stability of OCD measurement results can be greatly improved.
It is noted that the present invention may be implemented in software and/or in a combination of software and hardware, for example, the apparatus of the present invention may be implemented in an Application Specific Integrated Circuit (ASIC) or any other similar hardware device. In one embodiment, the software program of the present invention may be executed by a processor to implement the steps or functions described above. Also, the software programs (including associated data structures) of the present invention can be stored in a computer readable recording medium, such as RAM memory, magnetic or optical drive or diskette and the like. Further, some of the steps or functions of the present invention may be implemented in hardware, for example, as circuitry that cooperates with the processor to perform various steps or functions.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned. Furthermore, it is obvious that the word "comprising" does not exclude other elements or steps, and the singular does not exclude the plural. A plurality of units or means recited in the system claims may also be implemented by one unit or means in software or hardware. The terms first, second, etc. are used to denote names, but not any particular order.