Multi-beam interference processing method in silicon carbide epitaxial layer thickness calculation

Abstract

The invention discloses a multi-beam interference processing method in silicon carbide epitaxial layer thickness calculation, and belongs to the technical field of semiconductor epitaxial layer detection, and the method comprises the steps: carrying out the quantitative derivation of three multi-beam interference necessary conditions: a light intensity attenuation threshold value, a constant phase difference, and optical path difference periodicity; deducing the influence of multi-beam interference; multi-beam interference is judged through the four-feature fusion model in combination with the confidence coefficient; constructing a thickness formula with a reflectivity dynamic correction factor to calculate the corrected thickness; and verifying the reliability of the result by thickness relative deviation cross-validation under different incident angles. According to the invention, multi-beam interference influence can be accurately detected and corrected, systematic errors are effectively reduced, thickness calculation deviation is stably controlled within 2%, and the method is adaptive to rapid detection requirements of an industrial production line and can be expanded to detection of various epitaxial layer materials.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of semiconductor epitaxial layer detection, and particularly relates to a multi-beam interference processing method in silicon carbide epitaxial layer thickness calculation. BACKGROUND

[0002] As a third-generation semiconductor core material, silicon carbide has irreplaceable application value in the fields of power electronics, new energy vehicles, etc. due to its wide band gap, high critical electric field and other superior characteristics. Epitaxial layer thickness is a key parameter that determines the performance of a device and directly affects core indicators such as breakdown voltage and on-resistance. As a mainstream non-destructive testing technology, the principle of infrared interference method is to use the light reflection interference phenomenon of the epitaxial layer and the substrate interface to calculate the thickness by analyzing the interference fringe characteristics. This method is widely used due to its non-contact and high precision characteristics.

[0003] In the prior art, multi-beam interference in a Fizeau interferometer can cause the signal to deviate from the cosine distribution, and it is proposed to reduce the influence through parameter optimization and error compensation. Another technology uses a fixed correction factor to process interference errors, such as introducing an empirical coefficient 0.95 to modify the double-beam formula. These methods have certain limitations. First, the multi-beam interference judgment standard is ambiguous, and the traditional scheme only qualitatively requires "high reflectivity" and "interface flatness", without quantifying key conditions such as light intensity decay threshold, resulting in insufficient consistency in the judgment of the same batch of data by different operators, and high weak interference signal omission rate. Second, the correction mechanism is rigid, and the existing method relies on the double-beam interference formula, ignoring the phase shift caused by multi-beam interference, or using a fixed correction factor, which cannot adapt to the reflectivity change scenario. Third, it cannot be directly migrated to the epitaxial layer detection scene. SUMMARY

[0004] The purpose of the application is to solve the problems in the prior art. The multi-beam interference processing method in silicon carbide epitaxial layer thickness calculation can accurately detect and dynamically correct the influence of multi-beam interference on thickness calculation, effectively reduce systematic errors, and control the thickness calculation deviation within 2%, while adapting to the rapid detection requirements of industrial production lines, greatly improving the detection efficiency and technical versatility.

[0005] Technical scheme: The multi-beam interference processing method in silicon carbide epitaxial layer thickness calculation of the application comprises the following steps:

[0006] Step 1, derive the light intensity decay threshold, phase difference constant and optical path difference periodicity three necessary conditions of multi-beam interference by using the Fresnel reflection law and light intensity superposition principle, and derive the influence of multi-beam interference;

[0007] Step 2, establish the necessary condition of multi-beam interference quantization model, use the contrast ratio, the number of spectral peak, the number of autocorrelation peak and the envelope contrast four feature fusion model combined with confidence to determine whether the multi-beam interference exists;

[0008] Step 3, establish a thickness calculation model with a reflectivity dynamic correction factor, use the reflectivity dynamic correction factor to construct the thickness formula, substitute the average wavelength of adjacent bright lines, dynamic refractive index, refractive angle and adjacent bright line wavelength difference to calculate the corrected thickness;

[0009] Step 4, establish a multi-feature fusion detection model, use the cross-validation result of thickness relative deviation under different incident angles to determine the accurate thickness value of silicon carbide epitaxial layer.

[0010] Further, step 1 is: based on the Fresnel reflection law and the light intensity superposition principle, the necessary conditions for multi-beam interference are derived as light intensity attenuation threshold, constant phase difference and periodic optical path difference;

[0011] The interface reflectivity satisfies the light intensity attenuation threshold: according to the energy conservation , the light intensity of the first reflected light is: ; When , the reflected light intensity is at least 1% of , otherwise the light intensity is too weak to participate in interference, that is:

[0012]

[0013] Wherein, is the epitaxial layer-air interface reflectivity, is the epitaxial layer-substrate interface reflectivity, , is the transmission coefficient, is the incident light intensity, is the first reflected light intensity, is the light intensity attenuation factor of multiple reflections, is the transmission coefficient of the epitaxial layer-air layer;

[0014] Constant phase difference: the phase difference of multiple reflections needs to be stable, the interface roughness needs to be less than the wavelength of incident light, otherwise the phase difference is random and the interference fringes are blurred, in order to maintain coherence, the Rayleigh criterion needs to be met; wherein the interface roughness is , and the wavelength is ;

[0015] Periodic condition of optical path difference periodicity: the thickness of the epitaxial layer is uniform, which ensures that the optical path difference increment of each reflected light is a constant value.

[0016] Further, step 2 is specifically: introducing the influence of fine degree derivation multi-beam interference, considering the ideal case of no absorption of epitaxial layer , and the substrate is not transparent to light , the reflectivity formula is simplified as:

[0017]

[0018] Wherein, is the reflectivity, is the phase difference;

[0019] Let , the change of reflectivity with phase difference shows a sharp resonance peak, and the full width at half maximum (FWHM) of the peak is:

[0020]

[0021] The fine degree coefficient is larger, that is, the reflectivity is higher, and the resonance peak is narrower. In the multi-beam model, it is known from the expression of that the extreme point is determined by complex operation, and the phase condition is:

[0022]

[0023] Further, step 3 is specifically: constructing the thickness formula based on the Airy formula and the extreme condition, and the total interference light intensity is the superposition of the light intensity of all reflected light; ; is the incident light intensity, is the actual reflectivity, is the phase difference;

[0024] Taking the derivative and letting the derivative be 0, the bright line condition is , and the corresponding wavelength of the adjacent two levels of bright lines is , and the phase difference is

[0025] ; is the dynamically calculated refractive index of the epitaxial layer, is the refraction angle of light in the epitaxial layer, is the wavelength of the level of bright lines;

[0026] The thickness can be obtained by arranging:

[0027]

[0028] Since the in the Airy formula will cause the phase difference to deviate, based on the actual reflectivity The influence on the optical path difference is introduced into a correction factor After the correction factor is combined, the final epitaxial layer thickness calculation formula is corrected as:

[0029]

[0030] Among them, is the total interference light intensity, is the effective reflectivity, is the phase difference, is the thickness, is the correction silver, is the average wavelength of adjacent interference bright lines, is the dynamically calculated epitaxial layer refractive index, is the refraction angle of light in the epitaxial layer, is the wavelength difference of adjacent bright lines.

[0031] Further, in step 4, the multi-feature fusion detection model is specifically:

[0032] Feature indicators and determination thresholds: four core features are selected, including: ① contrast ratio, the calculation method is the ratio of the peak-to-peak value of the interference fringes to the average value of the reflectivity , the determination threshold ; ② the number of spectral peaks, the number of peaks findpeaks is extracted after FFT transformation, the determination threshold is greater than or equal to 2.0; ③ the number of autocorrelation peaks, the number of peaks is extracted by the autocorrelation function xcorr, the determination threshold .0; ④ envelope contrast, the calculation method is the ratio of the average value of the difference between the upper and lower envelopes of the reflectivity to the average value of the reflectivity: , the determination threshold ;

[0033] Determination rule: any feature combination is satisfied, it is determined that there is multi-beam interference, and the confidence is calculated, that is, the average value of the multi-feature determination factor; the confidence is 0.8, the spectrum data under the incident angles of 10° and 15° are detected, and the multi-beam interference phenomenon can be accurately recognized.

[0034] The application also discloses a computer device, which comprises a memory, a processor and a computer program stored in the memory, and the processor executes the computer program to realize the steps of the method.

[0035] The application also discloses a computer readable storage medium, which stores a computer program / instruction, and the computer program / instruction is executed by a processor to realize the steps of the method.

[0036] The application also discloses a computer program product, which comprises a computer program / instruction, and the computer program / instruction is executed by a processor to realize the steps of the method.

[0037] Advantages: Compared with the prior art, the present application has the following remarkable advantages:

[0038] The present application is based on the Fresnel reflection law and the light intensity superposition principle, and for the first time quantitatively derives three necessary conditions: 1. The light intensity attenuation threshold is quantified as (the intensity of the s-th reflected light is at least 1% of the incident light intensity), which can be directly calculated and verified by reflectivity data; 2. The constant phase difference is quantified by the Rayleigh criterion to avoid random phase difference leading to blurred fringes; 3. The optical path difference periodicity is quantified by "no fringe widening / splitting" to quantify the thickness uniformity. This step changes the multi-beam interference judgment from "experience-dependent" to "data-calculable and result- verifiable".

[0039] The present application quantifies the influence in two dimensions: 1. The introduction of the fineness coefficient reveals the law that "the higher the reflectivity, the larger the F, the sharper the interference fringes (full width at half maximum ), and the higher the measurement resolution", providing a direction for precision optimization of high reflectivity materials; 2. The system error formula of phase shift is derived , which clearly shows that the double-beam formula will produce systematic errors due to the neglect of this shift, and the error is related to 、 phase. This step changes the error source from "unknown" to "quantifiable and traceable", providing a clear target for subsequent correction, and improves the controllability of thickness calculation error.

[0040] Based on the Airy formula, the present application derives a dynamic reflectivity correction factor (effective reflectivity), which can be adjusted in real time according to the actual reflectivity, and then combined with the average wavelength of adjacent bright fringes , dynamic refractive index to construct the thickness formula . This model significantly improves the adaptability of different materials and different reflectivity scenarios.

[0041] The present application designs a "four-feature fusion detection" mechanism: selecting contrast ratio, spectral peak number, autocorrelation peak number, and envelope contrast as four core features, setting the rule that "any combination of features meets the multi-beam interference", and calculating the confidence. This mechanism can verify from multiple dimensions: "light and dark difference - frequency component - periodicity - fluctuation range".

[0042] Compared with the prior art, the present application realizes three major breakthroughs: 1. Precision is significantly improved: the relative deviation of silicon carbide epitaxial layer thickness calculation is reduced, and the thickness deviation of silicon wafer is reduced; 2. Strong scene adaptability: it can automatically adapt to different materials and different incident angle scenes, and the dynamic correction factor and multi-feature detection do not require manual adjustment of parameters; 3. High engineering landing performance: the whole process is driven by measured spectral data, without relying on prior information of thickness, and can be directly integrated into industrial detection equipment. After the thickness is corrected, the cross-verification of the double incident angles ensures the physical reasonableness and numerical stability, and completely breaks through the bottleneck of the prior art "theoreticalization is mainly used, and engineering is insufficient". BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is a schematic diagram of multi-beam interference;

[0044] Figure 2 is a multi-feature fusion detection result diagram;

[0045] Figure 3 is a reflectivity comparison diagram of different incident angles;

[0046] Figure 4 is a thickness estimation result diagram. DETAILED DESCRIPTION

[0047] The technical solutions in the embodiments of the present application will be described below in conjunction with the drawings, so that those skilled in the art can better understand the advantages and features of the present application, and the protection scope of the present application can be more clearly defined. The described embodiments of the present application are only a part of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0048] A multi-beam interference processing method for calculating the thickness of a silicon carbide epitaxial layer adjusts and processes according to the different interface reflectivity of the epitaxial layer, the incident light wavelength, the incident angle, and the thickness uniformity.

[0049] Light waves can produce multiple reflections and transmissions at the epitaxial layer interface and the substrate interface, thereby producing multi-beam interference. According to the necessary conditions of multi-beam interference, analyze whether the test results of the silicon wafer provided in Annex 1 and Annex 2 appear multi-beam interference, give the mathematical model and algorithm for determining the thickness calculation of the silicon epitaxial layer, and the corresponding calculation results.

[0050] Solving process:

[0051] Example 1 (10°): adjacent bright lines wavelength , = 10.2 μm), the average wavelength = 10.1 pm), wavelength difference = 0.2 pm;

[0052] Example 2 (15°): The same wavelength of adjacent bright fringes is extracted, and the average wavelength and wavelength difference are obtained.

[0053] Step 1: Multi-feature fusion detection of multi-beam interference: Feature calculation is performed on the "wavenumber-reflectivity" data of Example 1 (10° incident angle) and Example 2 (15° incident angle). Contrast ratio , the number of spectral peaks is the number of peaks after FFT (findpeaks), the number of autocorrelation peaks is the number of peaks of the autocorrelation function, and the envelope contrast .

[0054] For 10° incident angle: contrast ratio ≈ 2.47 (above threshold), number of spectral peaks = 2 (satisfies threshold), number of autocorrelation peaks ≥ 2, it is determined that there is multi-beam interference, and the same method is used to determine that there is multi-beam interference at 15° incident angle, and the confidence level reaches 0.80, verifying that the test results of the silicon wafer meet the characteristics of multi-beam interference.

[0055] Step 2: Extract the wavelength of adjacent interference bright fringes from the reflectivity spectrum of Example 1 and Example 2.

[0056] Step 3: Substitute the corrected thickness formula for calculation:

[0057] Example 1 (10°): Substitute = 10.1 , = 1.0057, = 3.42, = 0.9996, = 0.2 into the formula, and ;

[0058] Example 2: Similarly, the thickness is calculated as .

[0059] The reflectivity curves at 10° and 15° incident angles both show periodic "peak-valley" fluctuations, which is a direct manifestation of the periodic distribution of light intensity caused by multi-beam interference coherence superposition. The phase and amplitude of the fluctuations differ under different incident angles, reflecting the physical law that the incident angle affects the optical path difference and thus changes the interference fringe distribution. The thickness under 10° incident angle is , and under 15° incident angle is 4.90 pm. Taking the average of the two, it is about 5.15 pm, which weakens the deviation caused by a single incident angle. Combined with the determination of multi-beam interference and the correction model: reflectivity correction factor, the multi- pm beam interference effect is considered, making the thickness calculation more accurate.

[0060] The description and the time disclosed in the present application are easy to think and understand for ordinary skilled in the art, and several improvements and refinements can be made without departing from the principles of the present application. Therefore, the modifications or improvements made without departing from the spirit of the present application should be considered as the protection scope of the present application.

Claims

1. A method for multi-beam interference processing in a calculation of a thickness of a silicon carbide epitaxial layer, characterized by, Comprise the following steps: Step 1, using the Fresnel reflection law and light intensity superposition principle deduce light intensity attenuation threshold, phase difference constant and optical path difference periodicity three major multi-beam interference necessary conditions, deduce the influence of multi-beam interference; Step 2, establish the quantitative model of multi-beam interference necessary conditions, use the contrast ratio, the number of spectral peaks, the number of autocorrelation peaks and the envelope contrast four feature fusion model combined with confidence to determine whether the multi-beam interference exists; Step 3, establish the thickness calculation model with reflectivity dynamic correction factor, use the reflectivity dynamic correction factor to construct the thickness formula, substitute the average wavelength of adjacent bright lines, dynamic refractive index, refractive angle and adjacent bright line wavelength difference to calculate the corrected thickness; Step 4, establish multi-feature fusion detection model, use the cross validation result reliability of thickness relative deviation under different incident angles to determine the accurate thickness value of silicon carbide epitaxial layer.

2. The method of claim 1, wherein the method is used for calculating thickness of a silicon carbide epitaxial layer. Step 1 is: based on the Fresnel reflection law and light intensity superposition principle to deduce the necessary conditions for multi-beam interference, which are light intensity attenuation threshold, phase difference constant and optical path difference periodicity; The interface reflectivity satisfies an optical intensity decay threshold: according to the energy conservation , the first reflected light has an optical intensity of: ； When the reflected light intensity is at least 1%, otherwise the light intensity is too weak to participate in interference, that is: ； wherein, is the epitaxial layer-air interface reflectivity, is the epitaxial layer-substrate interface reflectivity, , is the transmission coefficient, is the incident light intensity, is the first reflected light intensity, is the light intensity attenuation factor for multiple reflections, is the epitaxial layer-air layer transmission coefficient; Phase difference constant: the phase difference of multiple reflection light needs to be stable, the interface roughness needs to be less than the wavelength of incident light, otherwise the phase difference is random and the interference fringes are blurred. In order to maintain coherence, the Rayleigh criterion needs to be met ; wherein the interface roughness is , and the wavelength is ; Optical path difference periodicity periodicity condition: the thickness of epitaxial layer is uniform, which ensures that the optical path difference increment of each reflected light is a constant value.

3. The method of claim 2, wherein the method is used for calculating thickness of a silicon carbide epitaxial layer. Step 2 is specifically: introducing the influence of fine degree derivation multi-beam interference, considering the ideal case of no absorption of epitaxial layer , substrate not transparent to light The reflectivity formula is simplified as: ； wherein is the reflectivity, is the phase difference; Let The change relation of reflectivity with phase difference presents sharp resonance peak, and the full width at half maximum (FWHM) of the peak is: ； fineness coefficient The greater, that is, the higher the reflectivity, the narrower the resonance peak, in the multi-beam model, by The expression of the extremum point is determined by complex operation, and the phase condition is: 。 4. The method of claim 3, wherein the method is used for calculating thickness of a silicon carbide epitaxial layer. The step 3 is specifically: constructing a thickness formula based on the Airy formula and the extremum condition, and the total interference light intensity is the superposition of light intensities of all reflected lights; ; is the incident light intensity, is the actual reflectivity, is the phase difference; The derivative is taken and the derivative is set to 0, and the bright line condition is obtained as The corresponding wavelengths of the adjacent two levels of bright lines are The corresponding wavelengths of the adjacent two levels of bright lines are The corresponding wavelengths of the adjacent two levels of bright lines are ; ; nepi is the refractive index of the epitaxial layer, nepi is the refractive index of the epitaxial layer, nepi is the refractive index of the epitaxial layer, nepi is the refractive index of the epitaxial layer, The thickness obtained by sorting is: ； Because of the phase difference shift in Airy formula based on the actual reflectivity the influence of optical path difference, introduce correction factor After the correction factor, the final epitaxial layer thickness calculation formula is corrected: ； wherein, is the total intensity of the interference light, is the effective reflectivity, is the phase difference, is the thickness, is the correction silver, is the average wavelength of the adjacent interference bright lines, is the dynamically calculated epitaxial layer refractive index, is the refractive angle of light in the epitaxial layer, is the wavelength difference of the adjacent bright lines.

5. The method of claim 4, wherein the method is used for calculating thickness of a silicon carbide epitaxial layer. In step 4, the multi-feature fusion detection model is specifically: Feature index and decision threshold: 4 core features are selected, including: ① contrast ratio, the calculation method is the ratio of the peak-to-peak value of the interference fringe to the average value of the reflectivity , the decision threshold ; ② the number of spectral peaks, the number of peaks is extracted after FFT transformation findpeaks, the decision threshold is greater than or equal to 2.0; ③ the number of autocorrelation peaks, the number of peaks is extracted by autocorrelation function xcorr, the decision threshold .0; ④ envelope contrast, the calculation method is the ratio of the average value of the difference between the upper and lower envelopes of the reflectivity to the average value of the reflectivity: , the decision threshold ; Determination rule: if any feature combination is satisfied, it is determined that there is multi-beam interference, and the confidence is calculated, that is, the mean value of multi-feature determination factor; The spectral data of 10° and 15° incident angles are detected, and the confidence reaches 0.8, which can accurately identify the multi-beam interference phenomenon.

6. A computer apparatus comprising a memory, a processor, and a computer program stored on the memory, wherein the computer program, when executed by the processor, causes the processor to perform the method of any one of claims 1 to 5. The processor executes the computer program to realize the steps of the method of claim 1.

7. A computer readable storage medium having stored thereon computer programs / instructions, characterized in that, The computer program / instruction is executed by the processor to realize the steps of the method of claim 1.

8. A computer program product comprising computer programs / instructions, characterized in that, The computer program / instruction is executed by the processor to realize the steps of the method of claim 1. The computer program / instruction is executed by the processor to realize the steps of the method of claim 1.

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