CN114636372B - Spectrum dephasing method for wide-spectrum self-reference interference alignment system by using S transformation - Google Patents
Spectrum dephasing method for wide-spectrum self-reference interference alignment system by using S transformation Download PDFInfo
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Abstract
The invention discloses a spectrum dephasing method for applying S transformation to a wide-spectrum self-reference interference alignment system. The method comprises the steps of obtaining a spectrum signal containing alignment position information by using a wide-spectrum self-reference interference alignment system, and then carrying out S conversion on the spectrum signal to obtain a signal with the intensity changing along with two variables of wavelength and sampling frequency. And taking the point with the maximum mode of the signal under the same wavelength, namely the ridge point, combining all the ridge points into a ridge signal, dephasing the ridge signal, and unwrapping the phase. And performing linear function fitting on the unwrapped signal and the wave number, wherein the slope of the linear function contains the alignment position information. The method provided by the invention has the advantages that the working efficiency of the alignment system is ensured, and the precision and the stability of the acquired alignment position information are improved.
Description
Technical Field
The invention relates to the field of semiconductor manufacturing, in particular to a spectrum dephasing method for applying S transformation to a wide-spectrum self-reference interference alignment system.
Background
With the continuous improvement of the social informatization level, the integrated circuit has vigorous development and gradually becomes an indispensable part of modern daily life. Photolithography is an indispensable key technology for producing integrated circuits, and the further reduction in size and the achievement of higher integration of integrated circuits are required to rely on the continuous progress of photolithography. The photolithography technique is to coat a photoresist on a silicon wafer, then leave a circuit of the layer through multiple steps of exposure, development, baking, etching, and the like, and then form a final integrated circuit through the combination of multiple layers. The relative position of the pattern (current layer) left on the photoresist after exposure and development and the pattern (reference layer) on the substrate is called the overlay accuracy. Generally, the alignment precision is 1/3-1/5 of the resolution index of the photoetching machine, and if the alignment precision exceeds the required range, the function of the integrated circuit is greatly influenced. The factors for forming the overlay error are various, and the final overlay accuracy is greatly influenced by the alignment degree between the mask plate and the silicon wafer during projection exposure. Alignment techniques between the reticle and the silicon wafer to be exposed will greatly affect the quality of the final integrated circuit.
A broad spectrum self-reference interference alignment system is used for acquiring offset information of the alignment system and the position of an alignment mark, and the structure of the system is shown in figure 1. The shift information of the alignment system and the alignment mark position acquired by the wide-spectrum self-reference interference alignment system is contained in the spectrum signal, and the spectrum signal needs to be subjected to phase-dephasing processing. The existing phase extraction method has time phase shift method, fourier transform method, windowed Fourier transform method, wavelet transform method and the like. The accuracy of the solution of the phase using the time phase shift method is extremely high, but the time phase shift method requires a plurality of phase shift frames, which is disadvantageous to the efficiency of the alignment system. In contrast, the fourier transform method, the windowed fourier transform method, and the wavelet transform method only require a single spectrum signal to perform phase resolution to obtain alignment position information, which ensures the efficiency of the alignment system. The spectral signals obtained by the broad spectrum self-referencing interferometric alignment system are intensity signals that vary with wavelength and are collected at equal intervals with wavelength. The spectral signal collected by the wide-spectrum self-reference interference alignment system contains complex frequency information, and particularly when the alignment position deviation is increased, the frequency information of the spectral signal is more complex. Fourier transform is a global space-frequency processing method, and uses the same filtering window for signals, so that the accuracy is affected when processing multi-frequency information. The wavelet transform has a processing mode following signal frequency transform, but the signal after the wavelet transform is not directly related to a Fourier spectrum, so that the signal after the wavelet transform is easily influenced by high-frequency noise.
In 1996, stockwell proposed a new signal processing method, S transform, whose core is that the window function of the transform adjusts the width of the window function according to the sampling frequency. The S-transform is characterized by its frequency-dependent resolution while maintaining a direct relationship to the fourier spectrum, allowing for more detailed analysis of the signal, which has the advantage of making the S-transform widely used in PQD analysis, seismic wave analysis, and fourier profilometry.
Disclosure of Invention
In order to improve the accuracy and stability of the alignment position information of the wide-spectrum self-reference interference alignment system, the invention provides a spectrum dephasing method for applying S transformation to the wide-spectrum self-reference interference alignment system. The method ensures the efficiency of the alignment system and improves the accuracy and stability of acquiring the alignment position.
In order to achieve the above object, the present invention provides a method for spectrum dephasing using S transform in a broad spectrum self-reference interference alignment system, which comprises the following steps:
the method comprises the following steps: illuminating a wide-spectrum self-reference interference alignment system through a wide-spectrum light source, collecting a spectrum signal containing the position offset information of the alignment system and an alignment mark by using a spectrometer, wherein the collected spectrum signal is a signal with the intensity changing along with the collected wavelength and is stored in a computer;
step two: performing S-transform on the stored spectrum signal to obtain a signal whose intensity varies with two variables, i.e., wavelength and sampling frequency, and it is noted that the signal after S-transform is generally a complex signal having a real part and an imaginary part;
step three: for the signal after S conversion, under the same wavelength, taking the point with the maximum modulus of the signal, called the ridge point, wherein all ridge points form a new signal, called the ridge signal, and the ridge signal is a complex signal with the wavelength as a single variable;
step four: performing phase unwrapping on the ridge signal, and performing phase unwrapping on the unwrapped phase to obtain a phase signal;
step five: and representing the phase signal as a signal converted along with the wave number, fitting a linear function, wherein the slope of the obtained linear function contains the information of the position offset of the alignment system and the alignment mark, and the specific value of the position offset of the alignment system and the alignment mark, namely the alignment position information, can be obtained after processing.
Further, a signal containing alignment system and alignment mark position shift information is obtained by a broad spectrum self-reference interference alignment system and collected as a signal with intensity varying with wavelength by a spectrometer.
Further, the collected spectrum signal containing the alignment system and the alignment mark position shift information is subjected to S conversion to obtain a signal with the intensity varying with two variables of wavelength and sampling frequency.
Further, for the signal after the S conversion, under the same wavelength, a point with the maximum modulus of the signal is taken and called a ridge point, and all ridge points form a new signal called a ridge signal; performing phase unwrapping on the ridge signal to obtain a phase signal; and performing linear function fitting on the phase signal and the wave number, wherein the slope of the linear function contains information of the position offset of the alignment system and the alignment mark, and the specific value of the position offset of the alignment system and the alignment mark, namely the alignment position information, can be obtained after processing.
Further, for the same spectrum signal containing the alignment system and the alignment mark position shift information, compared with the traditional spectrum dephasing method using Fourier transform, windowed Fourier transform or wavelet transform, the spectrum dephasing method using S transform for the wide spectrum self-reference interference alignment system has higher measurement accuracy and stability.
The principle of the invention is as follows: and processing the spectrum signal acquired by the wide-spectrum self-reference interference alignment system by using S transformation, unwrapping the ridge signal by acquiring the ridge signal and performing linear function fitting on the unwrapped phase signal and the wave number, and acquiring alignment position information by using the slope of the fitted function.
Compared with the prior art, the invention has the advantages that: the alignment position information can be obtained by only needing a single spectrum signal, so that the working efficiency of the alignment system is ensured; the S transformation is used for performing phase resolution on the spectrum signal so as to obtain the alignment position information, and the precision and the stability of the obtained alignment position are improved; the signal after S conversion is a signal with the intensity changing along with two variables of wavelength sampling and frequency sampling, and is beneficial to performing detail processing such as local filtering, local analysis and the like on the spectrum signal.
Drawings
FIG. 1 is a flow chart of a spectral dephasing method for applying an S-transform to a wide-spectrum self-referencing interferometric alignment system according to the present invention.
FIG. 2 is a schematic diagram of a wide-spectrum self-referencing interferometric alignment system.
FIG. 3 is a diagram of a spectral signal as a function of a broad spectrum self-referencing interferometric alignment system.
FIG. 4 is a graphical representation of the phase of the ridge signal after dephasing as a function of wavelength.
FIG. 5 is a diagram showing phase as a function of wavenumber after phase unwrapping.
Detailed Description
To better illustrate the specific processes of the present invention, further details are provided below in conjunction with the appended drawings.
As shown in fig. 1, a method for resolving phase of a spectrum by using S transform in a broad spectrum self-reference interference alignment system includes the following steps:
the method comprises the following steps: illuminating a wide-spectrum self-reference interference alignment system through a wide-spectrum light source, collecting a spectrum signal containing the position offset information of the alignment system and an alignment mark by using a spectrometer, wherein the collected spectrum signal is a signal with the intensity changing along with the collected wavelength and is stored in a computer;
step two: performing S-transform on the stored spectrum signal to obtain a signal whose intensity varies with two variables, i.e., wavelength and sampling frequency, and it should be noted that the signal after S-transform is generally a complex signal having a real part and an imaginary part;
step three: for the signal after S conversion, under the same wavelength, taking the point with the maximum modulus of the signal, called the ridge point, wherein all ridge points form a new signal, called the ridge signal, and the ridge signal is a complex signal with the wavelength as a single variable;
step four: performing phase unwrapping on the ridge signal, and performing phase unwrapping on the unwrapped phase to obtain a phase signal;
step five: and representing the phase signal as a signal converted along with the wave number, fitting a linear function, wherein the slope of the obtained linear function contains the information of the position offset of the alignment system and the alignment mark, and the specific value of the position offset of the alignment system and the alignment mark, namely the alignment position information, can be obtained after processing.
Fig. 2 shows a schematic structural diagram of a wide-spectrum self-reference interference alignment system, in which a wide-spectrum light source is on an illumination alignment mark, and reflected light is collected by a lens system to form a plurality of diffraction spots of positive and negative diffraction orders. The multi-level diffraction light spots are split by the self-reference interference optical module, and then the light spots of positive and negative levels corresponding to the two split signals are superposed with each other after the light spots are rotated by 180 degrees relatively. And collecting the spectral signals of the diffraction spots of each order by using a spectrometer. The spectral signal g (λ) formed by the broad spectrum self-referencing interferometric alignment system as a function of wavelength λ can be expressed as:
wherein, I 0 (λ) is the background light intensity as a function of wavelength, V (λ) is the spectral signal contrast as a function of wavelength,
representing the optical path difference introduced by the alignment position shift, L is the position shift of the alignment system and the alignment mark. FIG. 3 shows a functional diagram of the spectral signal of a broad spectrum self-referencing interferometric alignment system.
Further, the spectral signal is subjected to S conversion to obtain a signal with the intensity varying with two variables of wavelength and sampling frequency. The general form of the S-transform can be expressed as:
wherein g (. Lamda.) is the spectral signal in formula (1),
is a Gaussian window function adjusted with a frequency variable f, x is the wavelength shiftAnd the dynamic factor represents a translation parameter of the center of the Gaussian window. In the formation of the spectral signal, I 0 (λ) and V (λ) are almost constant and can be regarded as constants I 0 And V. For a particular wavelength shift factor x 0 ，
It can be approximated by a first order taylor series:
wherein the content of the first and second substances,
is a wavelength shift factor x 0 The introduced optical path difference.
Substituting equation (4) into equation (3) yields an S-transformed signal:
S(x 0 ,f)＝S 1 (x 0 ,f)+S 2 (x 0 ,f)+S 3 (x 0 ,f), (5)
wherein:
S 1 (x 0 ,f)＝I 0 exp(-2π 2 )exp(-i2πx 0 f), (6)
for a specific wavelength shift factor x 0 When | S (x) 0 If f) is the maximum value, corresponding to a ridge point f r . Because of x 0 > 0, when | S (x) 0 And f) i takes the maximum value:
for each wavelength a shift factor x 0 Retaining only the ridge point f r Corresponding to the value of S transform, the resulting ridge signal may be represented by S r (x 0 ) And (4) showing. The formula (9) is substituted into the formula (6) because exp (-2 π) 2 ) Is approximately equal to 0, so S 1 (x 0 F) ≈ 0. Bringing formula (9) into formula (7),
bringing formula (9) into formula (8) because
So S 3 (x 0 F) ≈ 0. Thus S r (x 0 ) Can be expressed as:
S r the phase of (c) can be obtained by:
the function diagram after the ridge signal dephases is shown in fig. 4.
The alignment position information L can be differentiated by equation (2):
where k =1/λ represents the wave number.
A diagram of phase as a function of wavenumber after phase unwrapping is shown in fig. 5. By changing the phase>
Expressed as a function of wavenumber, k, the function is fitted to a first order function,the slope of the first order function is->
Thereby, the alignment position information L can be obtained. />
Claims (5)
1. A method for spectral dephasing using an S transform for a broad spectrum self-referenced interferometric alignment system, comprising: the method comprises the following steps:
the method comprises the following steps: illuminating a wide-spectrum self-reference interference alignment system through a wide-spectrum light source, collecting a spectrum signal containing the position offset information of the alignment system and an alignment mark by using a spectrometer, wherein the collected spectrum signal is a signal with the intensity changing along with the collected wavelength and is stored in a computer;
step two: performing S-transform on the stored spectrum signal to obtain a signal whose intensity varies with two variables, i.e., wavelength and sampling frequency, and it is noted that the signal after S-transform is generally a complex signal having a real part and an imaginary part;
step three: for the signal after S conversion, under the same wavelength, taking the point with the maximum modulus of the signal, called the ridge point, wherein all ridge points form a new signal, called the ridge signal, and the ridge signal is a complex signal with the wavelength as a single variable;
step four: performing phase unwrapping on the ridge signal, and performing phase unwrapping on the unwrapped phase to obtain a phase signal;
step five: expressing the phase signal as a signal converted along with the wave number, and fitting a linear function, wherein the slope of the obtained linear function contains the information of the position offset of the alignment system and the alignment mark, and the specific value of the position offset of the alignment system and the alignment mark, namely the alignment position information, can be obtained after processing;
the wide-spectrum light source is arranged on the irradiation alignment mark, reflected light is collected by the lens system to form a plurality of diffraction spots of positive and negative diffraction orders, the multi-level diffraction spots are split by the self-reference interference optical module, then the positive and negative diffraction orders corresponding to the split two signals are mutually superposed after the relative 180-degree rotation, the spectrum signal of the diffraction spots of each order is collected by the spectrometer, and the spectrum signal g (lambda) formed by the wide-spectrum self-reference interference alignment system can be expressed as follows the change of the wavelength lambda:
wherein, I 0 (λ) is the background light intensity as a function of wavelength, V (λ) is the spectral signal contrast as a function of wavelength,
represents the optical path difference introduced by the alignment position deviation, L is the position deviation of the alignment system and the alignment mark;
the spectral signal is S-transformed to obtain a signal with intensity varying with two variables, i.e. wavelength and sampling frequency, and the general form of S-transformation can be expressed as:
wherein g (. Lamda.) is the spectral signal in formula (1),
is a Gaussian window function adjusted along with a frequency variable f, x is a wavelength shifting factor and represents a translation parameter of the center of the Gaussian window, and I is the frequency of the spectral signal in the forming process 0 (λ) and V (λ) are almost constant and can be regarded as constants I 0 And V, for a specific wavelength shift factor x 0 ，
It can be approximated by a first order taylor series:
wherein the content of the first and second substances,
is a wavelength shift factor x 0 The introduced optical path difference;
substituting equation (4) into equation (3) yields an S-transformed signal:
S(x 0 ,f)＝S 1 (x 0 ,f)+S 2 (x 0 ,f)+S 3 (x 0 ,f), (5)
wherein:
S 1 (x 0 ,f)＝I 0 exp(-2π 2 )exp(-i2πx 0 f), (6)
for a particular wavelength shift factor x 0 When | S (x) 0 When f) is the maximum value, corresponding to a ridge point f r Because of x 0 >0, when | S (x) 0 And f) | takes the maximum value:
for each wavelength shift factor x 0 Retaining only the ridge point f r Corresponding to the value of S transform, the resulting ridge signal may be represented by S r (x 0 ) As a result, the formula (9) is substituted into the formula (6) because exp (-2. Pi.) 2 ) Is approximately equal to 0, so S 1 (x 0 F) ≈ 0, brings formula (9) into formula (7),
general formula (9)) Into formula (8) because
So S 3 (x 0 F) is approximately equal to 0, thus S r (x 0 ) Can be expressed as:
S r the phase of (c) can be obtained by:
the alignment position information L can be differentiated by equation (2):
wherein k =1/λ represents a wave number by phase
Expressed as a function of the wave number k, the function is fitted to a linear function, the slope of which is->
Thereby, the alignment position information L can be obtained.
2. The method of spectral dephasing using an S-transform for a broad spectrum self-referencing interferometric alignment system according to claim 1, wherein: firstly, a signal containing the position deviation information of the alignment system and the alignment mark is obtained through a broad spectrum self-reference interference alignment system, and the signal with the intensity changing along with the wavelength is collected by a spectrometer.
3. The method of spectral dephasing for a broad spectrum self-referencing interferometric alignment system using an S-transform as claimed in claim 1, wherein: and performing S conversion on the collected spectral signals containing the position deviation information of the alignment system and the alignment mark to obtain a signal with the intensity varying with two variables of wavelength and sampling frequency.
4. The method of spectral dephasing using an S-transform for a broad spectrum self-referencing interferometric alignment system according to claim 1, wherein: for the signal after S conversion, taking the point with the maximum modulus of the signal under the same wavelength, and calling the point as a ridge point, wherein all ridge points form a new signal, and the new signal is called a ridge signal; performing phase unwrapping on the ridge signal, and performing phase unwrapping on the unwrapped phase to obtain a phase signal; the phase signal is expressed as a signal converted along with the wave number, linear function fitting is carried out, the slope of the obtained linear function contains the information of the position deviation of the alignment system and the alignment mark, and the specific value of the position deviation of the alignment system and the alignment mark, namely the alignment position information, can be obtained after processing.
5. The method of spectral dephasing using an S-transform for a broad spectrum self-referencing interferometric alignment system according to claim 1, wherein: compared with the traditional spectrum dephasing method by utilizing Fourier transform, windowed Fourier transform or wavelet transform, the spectrum dephasing method using S transform for the wide spectrum self-reference interference alignment system has higher measurement accuracy and stability for the same spectrum signal containing the alignment system and the alignment mark position offset information.
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