CN115682964A - Wafer thickness large-range and high-precision rapid calculation method - Google Patents
Wafer thickness large-range and high-precision rapid calculation method Download PDFInfo
- Publication number
- CN115682964A CN115682964A CN202211361994.0A CN202211361994A CN115682964A CN 115682964 A CN115682964 A CN 115682964A CN 202211361994 A CN202211361994 A CN 202211361994A CN 115682964 A CN115682964 A CN 115682964A
- Authority
- CN
- China
- Prior art keywords
- thickness
- wafer
- range
- fourier transform
- measured
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Landscapes
- Length Measuring Devices By Optical Means (AREA)
Abstract
The invention relates to a wafer thickness wide-range high-precision rapid resolving method, which comprises the following steps: determining the refractive index of the wafer to be measured under the measurement wavelength; obtaining an optical model of a reflected light electric field vector of the wafer to be detected; obtaining an application interval of a Fourier transform method and a Hilbert transform method; obtaining an initial value of the optical thickness of the wafer to be detected; if the initial value of the optical thickness is larger than the set threshold value, the physical thickness of the wafer to be measured is obtained through a Hilbert transform method; otherwise, the physical thickness of the wafer to be measured is obtained through a Fourier transform method.
Description
Technical Field
The invention relates to the field of wafer optical thickness measurement, in particular to a wafer thickness large-range and high-precision rapid calculation method.
Background
As the most extensive substrate material of IC devices, in order to meet the advanced packaging technology requirements, the wafer needs to meet strict geometric accuracy when the back surface is thinned.
The current mainstream method for measuring the thickness of the wafer on line is an infrared interferometry, infrared light can penetrate through monocrystalline silicon and is reflected on the upper surface and the lower surface to form interference, and then frequency information of the monocrystalline silicon is obtained by a Fourier transform method so as to obtain the thickness of the silicon wafer. Wherein the two parameters of the measurement range and the resolution of the spectrometer influence the thickness range and the precision of the silicon wafer measurement. When a thicker silicon wafer is measured, the spectrometer has high resolution requirement, but the current high resolution spectrometer has poor measurement precision due to the wave band limitation. The most common method for realizing the high precision on the premise is realized by FFT zero padding, and the realization of the target calculation precision usually needs a large amount of zero padding, so that the calculation time is increased, and the measurement stability is poor.
Disclosure of Invention
Aiming at the prior art, the invention provides a wafer thickness large-range and high-precision rapid calculation method based on FFT and Hilbert by adopting a self-adaptive band-pass filtering, window function and fitting method based on spectral analysis and phase extraction. The technical scheme is as follows:
a wafer thickness wide-range high-precision quick resolving method comprises the following steps:
s1: determining the refractive index n of the wafer to be measured under the measurement wavelength;
s2: establishing an optical model of a reflected light electric field vector of the wafer to be detected;
s3: obtaining the applicable intervals of a Fourier transform method and a Hilbert transform method, wherein the method comprises the following steps:
selecting a thickness simulation range, generating a simulation reflection spectrum under the thickness by using an optical model of S2 for different thickness values in the range, calculating the thickness, respectively adopting a Fourier transform method and a Hilbert transform method to calculate the thickness when calculating the thickness, calculating the difference between the calculated thickness value and a theoretical value as an error, and using the standard difference of the calculated thickness by the two methods as a repeatability evaluation standard to obtain respective error curves of the two methods; according to respective error curves, searching an application interval of a Fourier transform method and a Hilbert transform method to obtain a thickness calculation threshold value d;
s4: collecting an original reflection spectrum of a wafer to be measured, carrying out median filtering on the original reflection spectrum, and filtering out a fundamental frequency to obtain a high-frequency signal;
s5: converting the high-frequency signal of the wafer sample to be measured into a wave number domain, performing fast Fourier transform, and obtaining an initial value D of the optical thickness of the oscillating waveform fast Fourier transform curve according to a horizontal coordinate corresponding to the maximum amplitude value of the oscillating waveform fast Fourier transform curve l ；
S6: if the initial value of optical thickness D l If the thickness is larger than D x n, the physical thickness D of the wafer to be measured is obtained through a Hilbert transform method; otherwise, the physical thickness D of the wafer to be measured is obtained through a Fourier transform method.
Further, the method of S1 is as follows: and collecting an original reflection spectrum of the standard sample, calculating the optical thickness of the standard sample through FFT (fast Fourier transform), and dividing the optical thickness by the physical thickness of the standard sample to obtain the refractive index n.
Further, the method of S2 is as follows: and establishing an upper surface reflected light electric field vector model by taking the upper surface of the wafer to be detected as a 0 optical path reference surface based on Snell law to obtain an optical model of the reflected light electric field vector of the wafer to be detected.
Further, the simulation range of the thickness selected in S3 is 100um-770um; in this range, a thickness value is taken every 10 um.
Further, the thickness calculation threshold d =300.
Further, in S6, the method for obtaining the physical thickness D of the wafer to be measured by the hilbert transform method is as follows:
s61: extracting a high-frequency signal of an original reflection spectrum, and solving a phase through Hilbert transform;
s62: solving the physical thickness of the wafer to be detected according to the phase and the refractive index:
where phase _ slope is the slope of the phase curve.
Further, in S6, the method for obtaining the physical thickness D of the wafer to be measured by the fourier transform method is as follows:
s61: by initial value of optical thickness D l Constructing a digital band-pass filter by taking the corresponding spectrum signal frequency as a central frequency; the digital band-pass filter selects a Butterworth filter, and self-adaptive band-pass filtering is carried out on the high-frequency signal of the original reflection spectrum to obtain an oscillation waveform after secondary filtering;
s62: adding a Hamming window to the filtered signal to perform zero filling and performing second fast Fourier transform; gaussian spectrum interpolation is carried out to obtain the accurate Peak position Peak index ：
Wherein k is m The index of the abscissa of the FFT peak value of the second fast Fourier transform is used, and S is the mapping from the index of the abscissa to the FFT amplitude;
s63: calculating the physical thickness of the wafer to be measured:
wherein Peak index Indexing the exact peak position, λ, for Gaussian spectral interpolation min Lower limit of wavelength, λ, of the spectral data max The upper wavelength limit of the spectral data.
Compared with the prior art, the invention has the beneficial effects that:
(1) The measurement range is large, and the thickness of the submillimeter-level wafer can be stably measured;
(2) The measurement system is simple, the measurement is quick, and the integration into the wafer thinning process is easy to realize online measurement;
(3) The measurement precision is high.
Drawings
FIG. 1 is a process flow diagram of a wafer thickness wide-range, high-precision and rapid calculation method of the present invention;
FIG. 2 is a schematic diagram of a measurement system according to an embodiment of the present invention
The reference numerals have the following meanings:
1-light source 2-spectrometer 3-optical fiber coupler 4-lens group 5-wafer to be measured
FIG. 3 raw spectral signal
High frequency signal in the spectrum of FIG. 4
FIG. 5 fft spectrum of spectral high frequency signal
FIG. 6 error curve
FIG. 7 phase curve
FIG. 8 Filter response curves
FIG. 9 spectral signal through bandpass filter
FIG. 10 FFT atlas of filtered Signal
Detailed Description
The invention provides a wafer thickness large-range high-precision rapid resolving method through self-adaptive filtering, window functions, gaussian spectrum interpolation and the like on the basis of spectrum analysis and phase extraction. The following detailed description of embodiments of the invention will be made with reference to the accompanying drawings.
For light to interfere on the top and bottom surfaces of the wafer, the interference model can be expressed as:
where A (r) is the electric vector of the reflected light, A (i) is the incident electric vector,
where λ is the wavelength, n is the refractive index of the single crystal silicon, R is the reflectivity of the upper surface of the single crystal silicon, and h is the thickness of the single crystal silicon.
The oscillating waveform seen in the spectrometer is due to the presence of a sine-like term e in the model iσ The invention aims to accurately, stably and quickly extract the sine-like frequency information in the signal.
As shown in fig. 2, light emitted from the light source 1 is converged on the surface of the sample 5 through the optical fiber 3 and the lens 4, light reflected from the upper and lower surfaces of the sample interferes, and the spectrometer 2 acquires an interference signal. And processing the signals collected by the spectrometer.
Specific embodiments are described below:
firstly, determining the refractive index of a sample to be measured at a measurement wavelength: and collecting an original spectrum of the standard sample by using a measuring system, calculating the optical thickness of the standard sample by FFT (fast Fourier transform), and dividing the optical thickness by the physical thickness of the standard sample to obtain the refractive index n. The calculation formula is as follows:
equation 1:
where N is the abscissa index of the peak of the FFT result (index starting from 0); lambda min Lower wavelength limit, λ, for spectral data max The upper wavelength limit of the spectral data; d is the physical thickness of the standard.
Establishing an optical model according to the sample, and establishing a reflected light electric field vector model of the upper surface based on Snell law by taking the upper surface of the wafer to be detected as a 0 optical path reference surface to obtain the optical model of the reflected light electric field vector of the wafer to be detected; the incident light is vertically incident to the wafer to be measured, and an original light intensity signal with the light intensity distributed along with the wavelength is obtained, as shown in fig. 3.
And carrying out median filtering on the original reflection spectrum, and filtering out the fundamental frequency. A high frequency signal is obtained as in fig. 4.
Converting the high-frequency signal from wavelength to wave number domain, performing fast Fourier transform, according to the abscissa corresponding to the maximum amplitude of the fast Fourier transform curve of the oscillation waveform, the FFT atlas is shown in figure 5, and the initial value D of the optical thickness is obtained by the thickness calculation formula 2 l 。
Equation 2:
where N is the abscissa index of the peak of the FFT result (index starting from 0); lambda [ alpha ] min Lower limit of wavelength, λ, of the spectral data max The upper wavelength limit of the spectral data.
In order to obtain the applicable intervals of the fourier transform method and the hilbert transform method more accurately, it is first necessary to obtain an error curve of the corresponding method. In the range of 100um-770um, a thickness value is taken at an interval of 10um, a simulated reflection spectrum under the thickness is generated by using the former model, the thickness calculation is carried out, the process is repeated for 100 times for each thickness, the difference between the calculated thickness mean value and the theoretical value is calculated to be used as an error, the standard difference of the calculated thickness is used as a repeatability evaluation standard, and an error curve shown in figure 6 can be obtained by the method.
The error curve shows that when the simulated reflection spectrum is used, the Fourier transform method can achieve the measurement accuracy of 0.5% in the complete thickness interval; the Hilbert transform method has a large error due to multi-beam interference and frequency extraction problems at low thicknesses, but performs excellently at d > 300 μm.
According to the test performance of Hilbert and FFT methods in different thicknesses, a thickness calculation threshold value of 300um is set, when the initial value of the optical thickness is larger than 300um, a Hilbert transform method is selected, and when the thickness is lower than 300um, a Fourier transform method is selected.
If the initial value of the optical thickness is larger than the preset thickness calculation threshold value multiplied by the refractive index, extracting an original spectrum high-frequency signal, and solving the phase through Hilbert transform (figure 7); solving the physical thickness of the sample (formula 3) according to the phase and the refractive index;
equation 3:
where phase _ slope is the slope of the phase curve and n is the refractive index
If the initial value of the optical thickness is smaller than the set thickness calculation threshold value multiplied by the refractive index, taking the initial value as the central frequency, and constructing a digital band-pass filter; selecting a Butterworth filter as the digital band-pass filter, and setting the maximum attenuation Ap =3 of a pass band; minimum attenuation As =20 that should be achieved for the stop band; the filter response curve is shown in fig. 8, and adaptive band-pass filtering is performed on the original spectrum to obtain an oscillation waveform after the second filtering, which is shown in fig. 9;
then adding Hamming window to perform zero filling to perform the second fast Fourier transform, the FFT map is shown in figure 10, and the index k is indexed according to the abscissa of the FFT peak value m Gaussian spectrum interpolation is carried out by using formula 4 to improve FFT frequency measurement resolution ratio to obtain accurate Peak position Peak index The refractive index is used in combination with equation 5 and equation 1 to calculate the precise thickness D. S is the mapping of the abscissa index to the FFT magnitude.
Equation 4:
wherein k is m Is the FFT peak abscissa index (index starting from 0), S is the mapping of the abscissa index to the FFT magnitude.
Equation 5:
wherein Peak index Indexing the exact peak position by Gaussian spectral interpolation, λ min Lower limit of wavelength, λ, of the spectral data max N is the refractive index for the upper wavelength limit of the spectral data.
TABLE 1 measurement data
The calculation method is applied to obtain the measurement effect with high stability and high precision in the measurement of the wafers with different thicknesses.
Claims (7)
1. A wafer thickness wide-range and high-precision rapid calculation method comprises the following steps:
s1: determining the refractive index n of the wafer to be measured under the measurement wavelength;
s2: establishing an optical model of a reflected light electric field vector of the wafer to be detected;
s3: obtaining the applicable intervals of a Fourier transform method and a Hilbert transform method, wherein the method comprises the following steps:
selecting a thickness simulation range, generating a simulation reflection spectrum under the thickness by using an optical model of S2 for different thickness values in the range, calculating the thickness, respectively adopting a Fourier transform method and a Hilbert transform method to calculate the thickness when calculating the thickness, calculating the difference between the calculated thickness value and a theoretical value as an error, and using the standard difference of the calculated thicknesses of the two methods as a repeatability evaluation standard to obtain respective error curves of the two methods; according to respective error curves, searching an application interval of a Fourier transform method and a Hilbert transform method to obtain a thickness calculation threshold d;
s4: collecting an original reflection spectrum of a wafer to be measured, carrying out median filtering on the original reflection spectrum, and filtering out a fundamental frequency to obtain a high-frequency signal;
s5: converting the high-frequency signal of the wafer sample to be measured into a wave number domain, performing fast Fourier transform, and obtaining an initial value D of the optical thickness of the oscillating waveform fast Fourier transform curve according to a horizontal coordinate corresponding to the maximum amplitude value of the oscillating waveform fast Fourier transform curve l ；
S6: if the initial value of optical thickness D l If the thickness is larger than D x n, the physical thickness D of the wafer to be measured is obtained through a Hilbert transform method; otherwise, solving the physical thickness D of the wafer to be measured by a Fourier transform method.
2. The wafer thickness wide-range and high-precision rapid calculation method according to claim 1, wherein the method of S1 is as follows: and collecting an original reflection spectrum of the standard sample, calculating the optical thickness of the standard sample through FFT, and dividing the optical thickness by the physical thickness of the standard sample to obtain the refractive index n.
3. The wafer thickness wide-range and high-precision rapid calculation method according to claim 1, wherein the method of S2 is as follows: and establishing an upper surface reflected light electric field vector model by taking the upper surface of the wafer to be detected as a 0 optical path reference surface based on Snell's law to obtain an optical model of the reflected light electric field vector of the wafer to be detected.
4. The wafer thickness wide-range and high-precision rapid calculation method according to claim 1, wherein the thickness simulation range selected in S3 is 100um-770um; in this range, a thickness value is taken at intervals of 10 um.
5. The wafer thickness wide-range and high-precision fast solution method as recited in claim 1, wherein a thickness calculation threshold d =300.
6. The wafer thickness wide-range and high-precision rapid calculation method as claimed in claim 1, wherein the method for calculating the physical thickness D of the wafer to be measured in S6 by using the hilbert transform method is as follows:
s61: extracting a high-frequency signal of an original reflection spectrum, and solving a phase through Hilbert transform;
s62: solving the physical thickness of the wafer to be detected according to the phase and the refractive index:
where phase _ slope is the slope of the phase curve.
7. The method for rapidly calculating the wafer thickness with large range and high precision as claimed in claim 1, wherein the method for calculating the physical thickness D of the wafer to be measured by the Fourier transform method in S6 is as follows:
s61: by initial value of optical thickness D l Constructing a digital band-pass filter by taking the corresponding spectrum signal frequency as a central frequency; digital band-pass filterThe filter selects a Butterworth filter, and self-adaptive band-pass filtering is carried out on the high-frequency signal of the original reflection spectrum to obtain an oscillation waveform after secondary filtering;
s62: adding a Hamming window to the filtered signal to perform zero filling and performing second fast Fourier transform; gaussian spectrum interpolation is carried out to obtain the accurate Peak position Peak index ：
Wherein k is m The index of the abscissa of the FFT peak value of the second fast Fourier transform is used, and S is the mapping from the index of the abscissa to the FFT amplitude;
s63: calculating the physical thickness of the wafer to be measured:
wherein Peak index Indexing the exact peak position, λ, for Gaussian spectral interpolation min Lower limit of wavelength, λ, of the spectral data max The upper wavelength limit of the spectral data.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211361994.0A CN115682964A (en) | 2022-11-02 | 2022-11-02 | Wafer thickness large-range and high-precision rapid calculation method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211361994.0A CN115682964A (en) | 2022-11-02 | 2022-11-02 | Wafer thickness large-range and high-precision rapid calculation method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115682964A true CN115682964A (en) | 2023-02-03 |
Family
ID=85047854
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211361994.0A Pending CN115682964A (en) | 2022-11-02 | 2022-11-02 | Wafer thickness large-range and high-precision rapid calculation method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115682964A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116878407A (en) * | 2023-09-08 | 2023-10-13 | 法博思(宁波)半导体设备有限公司 | Epitaxial wafer thickness measuring method and device based on infrared interference |
-
2022
- 2022-11-02 CN CN202211361994.0A patent/CN115682964A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116878407A (en) * | 2023-09-08 | 2023-10-13 | 法博思(宁波)半导体设备有限公司 | Epitaxial wafer thickness measuring method and device based on infrared interference |
| CN116878407B (en) * | 2023-09-08 | 2023-12-01 | 法博思(宁波)半导体设备有限公司 | Epitaxial wafer thickness measuring method and device based on infrared interference |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN104316158A (en) | Heterodyne interferometer vibration measurer based on laser doppler effect | |
| CN103308151B (en) | Heterodyne laser vibration measuring device and method | |
| CN101393015A (en) | On-line measurement method and device for micro/nano deep trench structure | |
| WO2018227975A1 (en) | Film thickness measuring system and method | |
| CN115682964A (en) | Wafer thickness large-range and high-precision rapid calculation method | |
| CN204115856U (en) | A kind of heterodyne interference type vialog based on laser doppler | |
| CN112051583B (en) | Beat frequency signal nonlinear correction method in FMCW distance measurement system | |
| CN204556093U (en) | A kind of low noise micro-cantilever thermal vibration signal measurement apparatus | |
| CN107632964A (en) | A kind of plane GEOMAGNETIC FIELD downward continuation recurrence cosine transform method | |
| CN109238153A (en) | Double frequency comb thickness measuring light channel structures, system, method, apparatus and storage medium | |
| CN113418469B (en) | Spectrum confocal scanning common-path digital holographic measurement system and measurement method | |
| CN110632596A (en) | Terahertz SAR multi-frequency vibration error compensation method | |
| CN105785386A (en) | High-precision frequency-modulation continuous wave laser ranging system based on F-P etalon | |
| CN109540007A (en) | The measurement method and measuring device of super thick film | |
| CN114543690A (en) | Optical characteristic modeling method, photoacoustic measurement method and device | |
| CN109631758A (en) | The detection device and detection method at sample center | |
| CN106123805B (en) | Plated film device three-dimensional topography measurement method based on white light scanning interference | |
| CN115289985A (en) | Light spot adjusting method and film thickness measuring method | |
| CN208780142U (en) | A kind of double frequency comb thickness measuring light channel structures and system | |
| CN118031823A (en) | Reflection spectrum processing method, device and equipment for wafer and storage medium | |
| CN111624614B (en) | Method and system for ranging through laser coherent detection | |
| CN114184583B (en) | Optical measurement and evaluation method for depth consistency of high aspect ratio microstructure | |
| CN116222400A (en) | Metal film thickness measuring device and method | |
| CN108398098A (en) | A kind of optical surface spacing non-contact measurement apparatus and method | |
| CN109655012A (en) | A kind of method of optical interface surface type measurement |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |