Nano-film thickness measurement method based on terahertz sub-wavelength interference enhancement

Abstract

The invention discloses a nano-film thickness measurement method based on terahertz sub-wavelength interference enhancement. The method comprises the following steps: S1, acquiring a terahertz time domain signal of a to-be-measured sample formed by a film / substrate in a reflection or transmission mode; s2, performing frequency domain transformation on the time domain signal to obtain an amplitude spectrum of the time domain signal; s3, extracting a characteristic frequency interval of a periodic oscillation signal generated by multi-beam interference in the thin film; and S4, based on the characteristic frequency interval and the refractive index n of the thin film material, calculating to obtain the physical thickness d of the thin film. According to the nano-film thickness measurement method based on terahertz sub-wavelength interference enhancement, the multi-beam interference effect generated by terahertz waves reflected or transmitted by the upper interface and the lower interface of an ultrathin film is utilized, tiny thickness information is converted into periodic interference fringes easy to observe in the frequency domain, and accurate inversion of the sub-wavelength thickness is achieved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of precision nondestructive testing, and particularly relates to a nanometer film thickness measurement method based on terahertz subwavelength interference enhancement. BACKGROUND

[0002] In the field of micro-nano manufacturing, accurate control of film thickness is the key to ensuring device performance. Traditional film thickness measurement techniques, such as spectroscopic ellipsometry and atomic force microscope step meter, can achieve nanometer-level precision, but the former has high requirements for the optical model of the material, and the latter is a contact measurement that may damage the sample. Terahertz time-domain spectroscopy, as a non-contact, non-ionizing nondestructive testing method, has shown advantages in material characterization.

[0003] However, the thickness resolution of conventional terahertz reflection or transmission measurement is limited by the time-domain width of the terahertz pulse or the detection bandwidth of the system. When the film thickness decreases to the order of hundreds of nanometers or even tens of nanometers (i.e., "subwavelength" scale, much smaller than the typical wavelength of terahertz waves (hundreds of microns)), the time-domain delay or attenuation of terahertz pulses caused by the film itself becomes extremely weak, making it difficult to effectively extract from noise, resulting in measurement failure. SUMMARY

[0004] The main purpose of the present application is to provide a nanometer film thickness measurement method based on terahertz subwavelength interference enhancement, which utilizes the multi-beam interference effect of terahertz waves reflected or transmitted by the upper and lower interfaces of an ultra-thin film to convert the tiny thickness information into periodic interference fringes (i.e., Fabry-Perot oscillation) in the frequency domain, which are easy to observe. By analyzing the characteristic frequency interval of the interference fringes, the subwavelength thickness can be accurately inverted.

[0005] To achieve the above purpose, the present application provides a nanometer film thickness measurement method based on terahertz subwavelength interference enhancement, comprising the following steps: Step S1: using a terahertz time-domain spectroscopy system to obtain the terahertz time-domain signal of a sample to be measured composed of a film and a substrate in reflection or transmission mode; Step S2: performing frequency domain transformation on the time domain signal to obtain its amplitude spectrum; Step S3: identifying and extracting the characteristic frequency interval of the periodic oscillation signal generated by multi-beam interference in the film from the amplitude spectrum ; Step S4: based on the characteristic frequency interval and the refractive index n of the film material, and according to the formula , the physical thickness d of the film is calculated, where c is the speed of light in vacuum.

[0006] As a further preferred technical solution to the above technical solution, the extraction of feature frequency intervals in step S3... This is achieved by performing Fourier analysis, autocorrelation analysis, or peak localization fitting algorithms on the oscillating part of the amplitude spectrum.

[0007] As a further preferred technical solution to the above technical solution, in step S4, a transmission line theoretical model or interference model containing the film thickness d and refractive index n is established to numerically fit the measured amplitude spectrum, and at the same time, the film thickness d and refractive index n are inverted.

[0008] As a further preferred technical solution to the above technical solution, in step S4, for materials with unknown refractive index, the thickness d and refractive index n can be inverted simultaneously by combining a model fitting algorithm.

[0009] As a further preferred technical solution to the above technical solution, the thickness of the thin film is on the order of nanometers to submicrometers, which is much smaller than the typical wavelength of the terahertz wave used.

[0010] The beneficial effects of this invention are as follows: By utilizing the inherent multi-beam interference effect of thin films, nanoscale thickness information, which is difficult to detect directly, is transformed into a periodic oscillation signal in the frequency domain that is significant and easy to measure accurately, thereby breaking through the resolution limit of traditional terahertz time-domain methods at the subwavelength scale. This method does not require complex devices such as near-field probes and can be implemented on conventional far-field terahertz time-domain spectroscopy systems. It has advantages such as being non-contact, non-destructive, fast, and highly applicable to transparent / semi-transparent thin films, providing a powerful new tool for realizing online and rapid thickness monitoring of nanofilms on industrial production lines. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating the present invention. Detailed Implementation

[0012] The following description is intended to disclose the present invention and enable those skilled in the art to implement it. The preferred embodiments described below are merely examples, and other obvious variations will occur to those skilled in the art. The basic principles of the invention defined in the following description can be applied to other embodiments, modifications, improvements, equivalents, and other technical solutions that do not depart from the spirit and scope of the invention.

[0013] In the preferred embodiments of the present invention, those skilled in the art should note that the terahertz time-domain spectroscopy system and the like involved in the present invention can be considered as prior art.

[0014] Preferred embodiment (Example 1).

[0015] like Figure 1As shown, this invention discloses a method for measuring the thickness of nanofilms based on terahertz subwavelength interference enhancement, comprising the following steps: Step S1: Use a terahertz time-domain spectroscopy system to acquire the terahertz time-domain signal of the sample under test, which is composed of a thin film / substrate, in reflection or transmission mode. Step S2: Perform frequency domain transformation on the time domain signal to obtain its amplitude spectrum (this can be done using the Fourier transform method). Step S3: Identify and extract the characteristic frequency intervals of the periodic oscillation signal generated by multi-beam interference within the thin film from the amplitude spectrum. ; Step S4: Based on the characteristic frequency interval and the refractive index n of the thin film material (known or determined by other methods), and according to the formula The physical thickness d of the thin film was calculated, where c is the speed of light in a vacuum. Because the interference effect significantly amplifies the influence of the thin film on the overall spectrum, it becomes possible to measure the thickness of films even thinner than a few hundred nanometers.

[0016] Specifically, the extraction of feature frequency intervals in step S3 This is achieved by performing Fourier analysis, autocorrelation analysis, or peak localization fitting algorithms on the oscillating part of the amplitude spectrum.

[0017] Furthermore, in step S4, a transmission line theory model or interference model containing the film thickness d and refractive index n is established to numerically fit the measured amplitude spectrum, and at the same time, the film thickness d and refractive index n are inverted.

[0018] Furthermore, in step S4, for materials with unknown refractive index, a model fitting algorithm, such as the Levenberg-Marquardt algorithm, can be used to simultaneously invert the thickness d and the refractive index n.

[0019] Preferably, the thickness of the film is on the order of nanometers to submicrometers, which is much smaller than the typical wavelength of the terahertz wave used.

[0020] Example 2: Measurement of thermal oxidation on silicon substrate Thin film thickness: Preparation: A wafer with a nominal thickness of 150nm grown on a silicon substrate. Thin film sample.

[0021] Measurement: A reflective terahertz time-domain spectroscopy system was used. A femtosecond laser pulse excited a photoconductive antenna to generate a terahertz wave, which was collimated and focused by a parabolic mirror and incident on the sample surface at an angle close to the normal. The detection system recorded the reflected terahertz time-domain waveform.

[0022] Signal processing: The reflected time-domain waveform was subjected to a Fourier transform to obtain the amplitude spectrum. A significant periodic oscillation was observed in the range of 0.2-2 THz.

[0023] Period Extraction: Fast Fourier Transform (FFT) analysis is performed on the oscillating portion of the spectrum, yielding a main peak in the spatial frequency domain (1 / frequency). The reciprocal of the corresponding spatial frequency is the interference period Δf. Δf is calculated to be approximately 0.33 THz. Thickness Calculation: The average refractive index of SiO2 in the terahertz band is known to be approximately 2.1. Substituting into the formula: Considering the errors caused by refractive index dispersion and model simplification, this result is on the same order of magnitude as the nominal value of 150 nm, demonstrating the effectiveness of the method. More accurate measurements require global fitting by establishing a complete transmission line model.

[0024] Example 3: Rapid scanning of polymer coating thickness uniformity: A transmission-based measurement system was employed. A flexible substrate coated with a polymer layer at the 100-nanometer scale was fixed on a two-dimensional translation stage. The system rapidly acquired the transmission time-domain signal at each measurement point and performed FFT and interference period extraction in real time. Δf was mapped to a thickness value using a pre-calibrated polymer refractive index. This resulted in a thickness distribution cloud map of the entire sample area, clearly identifying regions of coating inhomogeneity (thickness variation > 10 nm).

[0025] It is worth mentioning that the terahertz time-domain spectroscopy system and other technical features involved in this patent application should be regarded as prior art. The specific structure, working principle, and possible control methods and spatial arrangement of these technical features can be adopted using conventional choices in the field, and should not be regarded as the inventive point of this patent. This patent will not be further elaborated in detail.

[0026] For those skilled in the art, modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. A method for measuring the thickness of nanofilms based on terahertz subwavelength interferometry enhancement, characterized in that, Includes the following steps: Step S1: Use a terahertz time-domain spectroscopy system to acquire the terahertz time-domain signal of the sample under test, which is composed of a thin film / substrate, in reflection or transmission mode. Step S2: Perform frequency domain transformation on the time domain signal to obtain its amplitude spectrum; Step S3: Identify and extract the characteristic frequency intervals of the periodic oscillation signal generated by multi-beam interference within the thin film from the amplitude spectrum. ; Step S4: Based on the characteristic frequency interval and the refractive index n of the thin film material, and according to the formula The physical thickness d of the film is calculated, where c is the speed of light in a vacuum.

2. The method for measuring the thickness of nanofilms based on terahertz subwavelength interference enhancement according to claim 1, characterized in that, The extraction of feature frequency intervals in step S3 This is achieved by performing Fourier analysis, autocorrelation analysis, or peak localization fitting algorithms on the oscillating part of the amplitude spectrum.

3. The method for measuring the thickness of nanofilms based on terahertz subwavelength interference enhancement according to claim 1, characterized in that, In step S4, a transmission line theoretical model or interference model containing the film thickness d and refractive index n is established to numerically fit the measured amplitude spectrum, and at the same time, the film thickness d and refractive index n are inverted.

4. The method for measuring the thickness of nanofilms based on terahertz subwavelength interference enhancement according to claim 3, characterized in that, In step S4, for materials with unknown refractive index, a model fitting algorithm can be used to simultaneously invert the thickness d and the refractive index n.

5. The method for measuring the thickness of nanofilms based on terahertz subwavelength interference enhancement according to claim 1, characterized in that, The thickness of the thin film is on the order of nanometers to submicrometers, much smaller than the typical wavelength of the terahertz waves used.

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