KR20140133992A - Measuring Method For Three-dimensional Thickness Profile - Google Patents

Abstract

The present invention provides a signal processing method for the thickness and shape of a thin film. The signal processing method comprises: a step of extracting a measurement phase signal by processing an interference signal containing information of the thickness and surface shape of a thin film in the provided refractive index of the thin film and the provided incident angle; a step of calculating the thickness of the thin film corresponding to the information on the thickness of the thin film using the theoretical phase of the thin film according to the thickness of the thin film and a wave number and the measurement phase signal; and a step of extracting the height of the top surface corresponding to the information on the surface shape using the difference between the measurement phase signal and the theoretical phase of the thin film.

Description

{Measuring Method For Three-dimensional Thickness Profile}

The present invention relates to a thin film thickness measuring method, and more particularly, to a thin film thickness measuring method using a white light interference method.

(Patent Document 1) KR10-0290086 B

(Patent Document 1) KR10-0290086 B

(Patent Document 1) KR10-0290086 B

BACKGROUND ART White-light scanning interferometry is used to measure a three-dimensional profile of a pattern having a size of micrometers or less, such as a semiconductor pattern.

The white light scanning interferometry overcomes the phase ambiguity (2π ambiguity) of the conventional phase-shifting interferometry to produce a measurement surface with a rough surface or high step height, resolution).

The basic measurement principle of the white light scanning interferometry utilizes the short coherence length characteristic of white light. The white light scanning interferometry uses the principle that an interference signal occurs only when the reference light and the measurement light separated by the beam splitter undergo substantially the same optical path difference.

Therefore, by observing the interference signal at each measurement point in the measurement area while moving the measurement object by a minute distance of several nanometers in the direction of the optical axis, a short interference signal occurs at a point where each point has the same optical path difference as the reference mirror .

When the generation position of such an interference signal is calculated at all measurement points within the measurement region, the three-dimensional shape of the measurement plane can be measured.

A problem to be solved by the present invention is to provide a method of accurately measuring a thin film thickness with a small calculation amount.

According to an embodiment of the present invention, there is provided a signal processing method comprising: extracting a measured phase signal by processing an interference signal including thin film thickness information and surface shape information at a given refractive index and a given incident angle; Calculating a thin film thickness corresponding to thin film thickness information using the theoretical thin film phase according to thin film thickness and wave number and the measured phase signal; And extracting a top surface height corresponding to the surface shape information using the difference between the measured phase signal and the theoretical thin film phase.

In one embodiment of the present invention, the step of processing the interference signal to generate a measured phase signal includes filtering the interference signal to remove a low frequency component by Fourier transforming the interference signal; Extracting a signal including a phase function using a high-frequency filter in a signal from which a low-frequency component has been removed; Performing inverse-Fourier transformation on the signal including the phase function; And extracting an imaginary part of the inverse Fourier transformed signal to generate a measured phase signal according to the wave number.

In one embodiment of the present invention, the step of calculating the thin film thickness corresponding to the thin film thickness information using the theoretical thin film phase according to the thin film thickness and the number of waves and the measured phase signal includes the step of: Separating into non-linear measured phase signal components; Generating a theoretical nonlinear thin film phase component according to a thin film thickness and a wave number; And determining the thin film thickness to minimize the difference between the nonlinear measured phase signal component and the theoretical nonlinear thin film phase component according to the wavenumbers.

In one embodiment of the present invention, the step of extracting the upper surface height corresponding to the surface shape information using the difference between the measured phase signal and the theoretical thin film phase may be performed by using the determined thin film thickness, ; And extracting a top surface height corresponding to the surface shape information using the difference between the measured phase signal and the theoretical thin film phase.

In an embodiment of the present invention, the interference signal according to frequency or wavenumber including thin film thickness information and surface shape information can be obtained using white light, a broadband light source, or a wavelength tunable light source.

In one embodiment of the present invention, there is provided a method of producing a white light source, comprising: providing a white light source to a reference surface and providing the white light source to a sample comprising a thin film on a surface; And obtaining the interference signal according to frequency or wave number using the optical sensor array using the sample and the light reflected from the reference surface.

In one embodiment of the present invention, there is provided a method of fabricating a semiconductor device, comprising: providing a tunable light source to a reference surface and providing the tunable light source to a sample comprising a thin film on a surface; And obtaining the interference signal according to frequency or wave number using the optical sensor array using the sample and the light reflected from the reference surface.

In one embodiment of the present invention, the method may further include spatially scanning the sample to obtain the interference signal according to the position of the sample.

In one embodiment of the present invention, the method may further comprise preparing the interference signal according to a frequency or a wavenumber.

In one embodiment of the present invention, the method further comprises preparing an interference signal according to a scan distance of a reference mirror of the interferometer, wherein the interference signal may be a wavelength-integrated signal.

In one embodiment of the present invention, the step of processing the interference signal to generate a measured phase signal comprises: Fourier transforming the interference signal and extracting a specific carrier spatial frequency component using a filter; And generating the measured phase signal from the phase of the filtered signal.

According to an embodiment of the present invention, there is provided a computer-readable recording medium for processing an interference signal including thin film thickness information and surface shape information at a given incident angle and a refractive index of a given thin film to generate a measured phase signal. Calculating a thin film thickness corresponding to thin film thickness information using the theoretical thin film phase according to thin film thickness and wave number and the measured phase signal; And extracting a top surface height corresponding to the surface shape information using the difference between the measured phase signal and the theoretical thin film phase.

An apparatus for measuring thickness and shape according to an embodiment of the present invention includes a light source; An interferometer that receives the output light of the light source and combines the reference beam by the reference mirror and the object beam by the sample; A spectroscope unit for receiving an output signal of the interferometer and performing spectroscopy according to a frequency; A light sensing unit for acquiring an output signal of the light splitting unit according to a frequency; And a processing unit for processing the interference signal of the light sensing unit. The processing unit processes the interference signal including the thin film thickness information and the surface shape information at a given incident angle and a refractive index of a given thin film to extract a measured phase signal and uses the theoretical thin film phase according to the thin film thickness and the wave number and the measured phase signal The thin film thickness corresponding to the thin film thickness information is calculated and the top surface height corresponding to the surface shape information is extracted by using the difference between the measured phase signal and the theoretical thin film phase.

An apparatus for measuring thickness and shape according to an embodiment of the present invention includes: a tunable light source; An interferometer that receives the output light of the wavelength variable light source and combines the reference beam by the reference mirror and the object beam by the sample; A light sensing unit for acquiring an output signal of the interferometer according to a frequency; And a processing unit for processing the interference signal of the light sensing unit. The processing unit processes the interference signal including the thin film thickness information and the surface shape information at a given incident angle and a refractive index of a given thin film to extract a measured phase signal and uses the theoretical thin film phase according to the thin film thickness and the wave number and the measured phase signal The thickness of the thin film corresponding to the thin film thickness information is calculated and the height of the top surface corresponding to the surface shape information is extracted by using the difference between the measured phase signal and the theoretical thin film phase.

An apparatus for measuring thickness and shape according to an embodiment of the present invention includes a light source; An interferometer that receives the output light of the light source and combines the reference beam by the reference mirror and the object beam by the sample; A light sensing unit for acquiring an output signal of the interferometer according to a scan distance of the reference mirror; And a processing unit for processing the interference signal of the light sensing unit. The processing unit processes the interference signal including the thin film thickness information and the surface shape information at a given incident angle and a refractive index of a given thin film to extract a measured phase signal and uses the theoretical thin film phase according to the thin film thickness and the wave number and the measured phase signal The thickness of the thin film corresponding to the thin film thickness information is calculated and the height of the top surface corresponding to the surface shape information is extracted by using the difference between the measured phase signal and the theoretical thin film phase.

The signal processing method according to an embodiment of the present invention includes thin film thickness information and surface shape information at a given refractive index of a thin film and a given incident angle and efficiently processes an interference signal according to a frequency or a wavenumber, Thickness and height of the top surface can be measured.

The signal processing method according to an embodiment of the present invention includes thin film thickness information and surface shape information at a given incident angle and a refractive index of a given thin film and efficiently processes the interference signal according to the scan distance of the reference mirror, The height can be measured.

FIG. 1 is a schematic diagram based on a Mirau-type low coherence interferometry for measuring a three-dimensional film thickness shape.
Fig. 2 is a view for explaining the interlaced interferometer of Fig. 1. Fig.
FIG. 3 is a view for explaining the light separating unit and the light sensing unit of FIG. 1;
4 and 5 are flowcharts of a signal processing method according to an embodiment of the present invention.
6A shows a phase function and a linear phase function component and a nonlinear phase function component corresponding to the phase function.
6B shows the thin film phase and the linear thin film function component corresponding to the thin film phase and the nonlinear thin film phase component.
FIG. 7A shows a low coherence interfering signal according to wavenumbers, and FIG. 7B shows a phase function distribution and corresponding linear and non-forming components. 7C shows the measured nonlinear phase function component (black solid line) and the analytical nonlinear thin film phase model (red x-mark). 7D shows the spectral phase function associated with the film thickness and surface height and the relative phase relative to the surface height.
FIG. 8A shows the approximate film thickness d 'calculated by calculating the best fitted slope to the simulated thin film phase.
Figure 8b shows the percent error of the approximate film thickness d 'of Figure 8a.
FIG. 8C shows the peak-to-valley of the non-linear thin film phase according to the thin film thickness.
8D shows the thickness of the thin film according to the present invention.
FIG. 8E shows the percentage error in FIG. 8D.
9A shows a spectroscopic image acquired through a 2D photosensor array through a line-scan imaging element. The horizontal axis provides spatial information for the 2D photo sensor array, and the vertical axis provides spectral information for each pixel in the imaged line.
FIG. 9B shows the top surface shape and the bottom surface shape of one line obtained by analyzing the 2D spectroscopic image of FIG. 9A obtained using the present invention.
FIG. 9C shows a volumetric thickness profile of a sample obtained by scanning with a microstage in a lateral direction or a y-axis direction.
10 is a view for explaining a thickness and shape measuring apparatus according to another embodiment of the present invention.
11 is a view for explaining a thickness and shape measuring apparatus according to another embodiment of the present invention.
12 is a view for explaining a thin film thickness and shape measuring apparatus according to another embodiment of the present invention.
13 is a flow chart for explaining a method of measuring the thickness and shape of a thin film using the thin film thickness and shape measuring apparatus of FIG.

White-light inferemetry has attracted attention in the field of semiconductor devices as a 3D shape means. However, the application of white light interference was limited to measurements of opaque surfaces only.

Studies using white-light extended sources have simultaneously measured the bottom and top surfaces of thin film structures. Specifically, when the thickness of the thin film is thinner than the coherence length of the light source, the two waves reflected from the top and bottom surfaces of the film overlap and the interference signal is more complex than that produced on the opaque surface do. Therefore, it is essential to clearly separate the thickness of the thin film from the surface height from the complex interferograms.

According to an embodiment of the present invention, a thin film thickness and a top surface height profile can be measured by a simple signal processing process. A Mirau-type low coherence interferometer may provide an interfering signal necessary for the signal processing.

In the signal processing method according to an embodiment of the present invention, measurement errors according to film thickness are shown through simulation and applied to a patterned silicon oxide film structure.

With the rapid advances in manufacturing technology, the shape and structure of discrete components becomes increasingly complex. In particular, the complex surface of a thin film deposited on a patterned surface is required to satisfy device performance and package requirements.

Moreover, efficient manufacturing processes for these components are important for mass production and cost savings. The manufacturing process involves an appropriate evaluation process. Non-destructive optical methods such as reflectometry, ellipsometry, and interferometry have been developed for the evaluation of the fabrication process.

Reflectometry is a simple and inexpensive technique for measuring the intensity of reflected light over a broadband wavelength under normal incidence conditions. The elliptically polarized reflection method is a precise method of analyzing and performing the change of the polarization state of the light reflected from the sample. These methods are basically pint-by-point measurements, require a multi-axial stage to measure a large area, and have a three-dimensional film thickness or surface profile, .

The interference method uses a low coherent light source to acquire interference fringe patterns using a spectral scanning device or a mechanical scanner. The phase information obtained according to the wavelength of the broadband light source provides three-dimensional geometric information about the object to be measured.

Scanning white light interferometry can measure volumetric film thickness and top surface profiles in the presence of a transparent film. When the film thickness is thinned, the overlapped interference signals caused by the film interfaces become more complicated. Therefore, it is difficult to simultaneously separate the thin film thickness information and the top surface shape information in a complicated signal. Therefore, it is important to separate thin film thickness information from top surface shape information in overlapped interference signals). A typical method for film thickness shape measurement is to optimally fit measured phase and analytical phase model into two parameters, thickness and height. However, this optimization method is a time-consuming process requiring a large amount of computation by a multidimensional nonlinear approach.

In recent years, the inventors of the present invention independently collected only self-interference generated in a multi-reflected beam from a thin film to measure the thickness of the thin film, and considering the thin film thickness already measured We proposed a method to extract the surface shape. However, this method uses both spectral phase information and reflectance information. Therefore, this method takes much time in terms of signal processing and requires a multi-step process.

According to one embodiment of the present invention, we propose an apparatus and method that can simultaneously measure film thickness and top surface shape with a simple measuring procedure. The device may be a low coherence microscope structure based on a Mirau configuration. Unlike conventional methods, this measurement method uses only spectral phase information to separate film thickness and surface height information from overlapping interferece signals.

Low coherence interferometry or white light interferometry may use a broadband light source and provide a narrowly localized interferogram. A narrowly localized interferogram may be a mixture of many monochromatic interference fringe patterns. The broadband light source may include a xenon lamp or a tungsten lamp that covers all visible light areas. Thus, low coherence interference fringes include phase and amplitude information of all frequencies of the light source. Thus, we can use the encrypted information in the interferogram to identify the film properties.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the following drawings, like reference numerals refer to like elements, and the size of each element in the drawings may be exaggerated for clarity and convenience of explanation.

FIG. 1 is a schematic diagram based on a Mirau-type low coherence interferometry for measuring a three-dimensional film thickness shape.

Fig. 2 is a view for explaining the interlaced interferometer of Fig. 1. Fig.

FIG. 3 is a view for explaining the light separating unit and the light sensing unit of FIG. 1;

1 and 2, the thickness and shape measuring apparatus 100 includes a light source 110, an interferometer 130, and an interference signal of an object beam reflected from the sample 10 and a reference beam reflected from the reference surface And a light sensing unit 160 for acquiring light.

The light source 110 may be a white light source, a femtosecond laser, a broadband light source, or a wavelength variable light source. The light source 110 may be a tungsten halogen lamp that emits a spectrum in the range of 450 nm to 700 nm.

The sample 10 may include a patterned substrate 12 and a transparent thin film 14 deposited on the substrate 12.

The lens unit 120 may include a first lens 122, a second lens 124, and a third lens 126. The light source 110 may be disposed at the left focal point of the first lens 122. Accordingly, the first lens 122 can output parallel light. The second lens 124 may focus the light passing through the first lens 122 to the focal point of the second lens 124. The third lens 126 and the second lens 124 may have the same focal point. Accordingly, the third lens 126 can provide parallel light having an enlarged diameter of the beam.

The output light of the lens unit 120 may be provided to the interferometer 130. The interferometer 130 may be a Marauch interferometer including a beam splitter 132 and a mirau objective lens 134. The beam splitter 132 may provide the beam of the light source 110 to the mirou objective lens 134. The micro eye objective lens 134 may provide a reference beam reflected from a reference mirror and an object beam reflected from the sample.

The mirau objective lens 134 may include a microscope lens 134a, a reference mirror 134b, and a semi-transmission mirror 134c. The sample 10 is placed at the focal point of the microscope lens 134a and a part of the beam transmitted through the microscope lens 134a is reflected by the transflective mirror 134c and transmitted through the microscope lens 134a The remaining part of one beam can pass through the transflective mirror 134c.

The beam reflected from the transflective mirror 134c may be reflected at the reference mirror 134b and may be reflected back at the transflective mirror to provide a reference beam to the microscope lens 134a.

The beam transmitted through the semi-transmission mirror can be reflected by the sample 10, transmitted through the semi-transmission mirror 134c, and transmitted through the microscope lens 134a to provide an object beam. The reference beam and the object beam may provide interference signals.

The interferometer 130 may be a Marau interferometer. The interferometer 130 may include a Mirau interference objective with a numerical aperture NA = 0.4 and a 20x magnification. The interferometer 130 may generate a reference beam reflected from a reference surface and an object beam reflected from a measurement surface of the sample.

The cross-correlated interference signal between the reference beam and the object beam includes surface topography defined by two parameters, h and d. Where h is the standard height off the reference plane and d is the film thickness.

The reference beam and the object beam are again provided to the beam splitter 132. [ The reference beam and the object beam are transmitted through the beam splitter 132 and provided to the spatial filter unit 140. The spatial filter 140 may define a line-shaped region of the sample 10 to be measured. The spatial filter unit 140 may include a first lens 142, a slit 144 extending in the x-axis direction, and a second lens 144. The light passing through the first lens 142 passes through the slit 144 and defines a region to be observed. The second lens 146 provides the interference signal to the spectroscopic unit 150 through the slit.

The spectroscopic unit 150 can measure an interference signal according to a wavelength. The spectroscopic unit 150 may include a diffraction grating or a prism. The spectroscopic unit 150 may include a diffraction grating 152 and a lens 154. The spectroscopic unit 150 may spatially decompose input light according to wavelengths. The first beam B1 and the second beam B2 at different positions can be spatially separated. The first beam can be spatially separated according to frequency. For example, the first beam may be spatially resolved at a first frequency f1, a second frequency f2, and a third frequency f3.

The light sensing unit 160 may be a two-dimensional optical sensor array. When the slit 144 extends in the x-axis direction, the light sensing unit 160 detects the optical signal I (X '(x), Y' (x ') along the Y' f))) can be measured. The arrangement plane of the light sensing unit 160 may be an X'Y 'plane. The optical signal I (X '(x), Y' (f)) may provide an interference signal according to the wave number or the frequency at a specific position.

 The obtained interferogram can be analyzed by a line-scan spectroscopic image element. The line-scan spectroscopic image element may comprise a dispersive device and a two-dimensional photodetector array.

The horizontal axis of the two-dimensional photosensor array or light sensing unit 160 may provide spatial information on the imaged line and the vertical axis of the two-dimensional photosensor array may provide spectroscopic information at a fixed location. Thus, for 3D inspection, the sample 10 can be moved in a line by line or in a y-axis direction through a moving stage.

The processing unit 170 processes the optical signal I (X '(x), Y' (f)) obtained by the optical sensing unit 160 or an interference signal.

Hereinafter, the process of the processing unit will be described.

4 and 5 are flowcharts of a signal processing method according to an embodiment of the present invention.

4 and 5, the signal processing method includes preparing the interference signal according to a frequency or a wavenumber (S110), calculating a thin film thickness at a given incident angle and a refractive index of a given thin film, Calculating a thin film thickness corresponding to the thin film thickness information by using the theoretical thin film phase according to the thin film thickness and the number of waves and the measured phase signal (step S120) S130) and extracting a top surface height corresponding to the surface shape information using the difference between the measured phase signal and the theoretical thin film phase (S140).

The step of generating the measured phase signal by processing the interference signal includes a step of filtering the interference signal by Fourier transform to remove the low frequency component in operation S122, A step S124 of performing inverse Fourier transform on the signal including the phase function, and a step S126 of extracting an imaginary part of the inverse Fourier transformed signal, And generating (S128) a measured phase signal corresponding to the measured phase signal.

(S130) of calculating a thin film thickness corresponding to the thin film thickness information using the theoretical thin film phase according to the thin film thickness and the number of waves and the thin film thickness information using the measured phase signal is performed by using the measured phase signal as a linear measured phase signal component and a non- (S134) of generating a theoretical nonlinear thin film phase component according to the thin film thickness and the number of waves, and a step (S134) of separating the nonlinear thin film phase component And determining a thickness (S136).

The step of extracting the upper surface height corresponding to the surface shape information using the difference between the measured phase signal and the theoretical thin film phase (S140) includes calculating a theoretical thin film phase according to the wave number using the determined thin film thickness And extracting a top surface height corresponding to the surface shape information using the difference between the measured phase signal and the theoretical thin film phase (S144).

The spectrally resolved interference signal I (h, d; k) may be given in the spectral domain or the k-domain as S110.

Where I ₀ (k) is the spectral intensity of the two beams reflected from the reference surface and the top surface of the specimen. I ₁ (k) represents a visibility function related to cross interference between the reference beam reflected from the reference surface and the sample beam reflected from the thin film of the sample. k is the wave number of the electromagnetic wave (k = 2π / λ; λ is the wavelength of the electromagnetic wave). ? (H, d; k) is a phase function (? (H, d; k)). h is the height between the upper surface of the sample and the reference surface, and d is the thickness of the thin film. The interference signal may be obtained from the optical signal of the light sensing unit 160.

The phase function Φ (h, d; k) can be expressed as:

Where d (k) is the thin film phase of the multiple reflected beam in the film. The thin film phase depends only on the film thickness and wave number.

The thin film phase can be expressed as follows.

Where r ₀₁ is the Fresnel reflection coefficient at the top interface of the film and r ₁₂ is the Fresnel reflection coefficient at the bottom interface of the film. N is the refractive index of the thin film, and [theta] is the incident angle of the incident beam incident on the thin film.

The thin film phase can be expressed as follows.

Ψ _linear (d '; k) denotes a linear thin-film phase component, and Ψ _nonlinear (d; k) denotes a nonlinear thin-film phase component. d 'is an approximate value of the thin film thickness d obtained using linear fitting in the thin film phase.

Therefore, the phase function can be given as follows.

Here, the linear phase function _{(Φ linear (h, d '} ; k)) is a 2 (h + d') is given by k, non-linear phase function _{(Φ nonlinear (d; k)} ) is a linear thin-phase component (Ψ _nonlinear (d; k)).

The slope of the linear fitting data of the phase function is 2 (h + d '). A non-linear phase function _{(Φ nonlinear (d; k)} ) is the phase function (Φ (h, d; k )) from the linear fit of data or a linear phase function; obtained by subtracting the _{(Φ linear (h, d '} k)) .

6A shows a phase function and a linear phase function component and a nonlinear phase function component corresponding to the phase function.

6B shows the thin film phase and the linear thin film function component corresponding to the thin film phase and the nonlinear thin film phase component.

6A and 6B, simulation results of a phase function and a thin film phase are displayed when a 2-micrometer silicon oxide film is deposited on a silicon substrate and a height between a top surface of the silicon oxide film and a reference surface is 5 μm . The nonlinear component of the phase function corresponds exactly to the nonlinear component of the thin film phase. This means that the nonlinear thin film phase component can be obtained by removing the linear phase component in the phase function.

FIG. 7A shows a low coherence interfering signal according to wavenumbers, and FIG. 7B shows a phase function distribution and corresponding linear and non-forming components. 7C shows the measured nonlinear phase function component (black solid line) and the analytical nonlinear thin film phase model (red x-mark). 7D shows the spectral phase function associated with the film thickness and surface height and the relative phase relative to the surface height.

Referring to Figs. 7A to 7D, how the thin film thickness d and the top surface height h are determined will be described.

Referring to FIG. 7A, the interference signal I (h, d; k) may be extracted from the optical signal of the light sensing unit 160. The interference signal includes the thin film thickness information d and the surface shape information h at a given incident angle and a refractive index of a given thin film, and is given as a function of a wavenumber (k) (S110).

I ₀ (k) includes a low-frequency component as the frequency distribution function of the light source. Therefore, in order to eliminate I ₀ (k) included in Equation 1, a high-pass filter may be used. For this purpose, the interference signal I (h, d; k) may be Fourier transformed. Subsequently, the low-frequency component can be removed by performing the operation of the high-frequency filter (S122). If the signal from which the low-frequency component has been removed is inverse Fourier transformed, the filtered interference signal I '(h, d; k) is expressed as follows.

In Equation (6), in order to separate the phase function? (H, d; k), Equation (6) can be Fourier transformed and expressed as follows.

을 나타내고, B는

를 나타낸다. Here, FT represents Fourier transform, and A represents

And B represents

.

Therefore, in Equation (7), the A component in the Fourier domain can be extracted using a high-frequency filter (S124). Then, the A component may be a component including a phase function. The component including the phase function may be subjected to inverse Fourier transform (S126).

Thus, a phase function can be given as follows.

Here, IFT represents Inverse Fourier Transformation.

When a natural logarithm is performed in Equation (8), Equation (8) is given as follows.

If only the imaginary term that is the second term of the right side in Equation 9 is extracted, the phase function? (H, d; k) can be obtained (S128).

Referring to Equation (5), the phase function? (H, d; k) may be divided into a linear component and a non-linear component (S132).

Referring to Equation (3), a theoretical nonlinear thin film phase component according to the thickness and wave number of the thin film can be prepared. In this case, the refractive index and incident angle of the thin film are already given. Further, the refractive index of the substrate is already determined. Thus, the reflection coefficient at the interface can be calculated. Accordingly, the nonlinear component of the thin film phase can be calculated according to the thickness of the thin film (S134).

The thickness d of the thin film can be determined through the following nonlinear fitting (S136).

는 메릿 함수(merit function)이다.

는 수학식 3 및 수학식 4를 이용하여 이론적으로 계산한 비선형 박막 위상이다(S134).

은 측정된 간섭 신호(I(h,d;k)를 처리하여 얻은 위상 함수(Φ(h,d;k))의 비선형 성분이다. 비선형 최적화 기술(nonlinear optimization techinque)를 사용하여 박막 두께(d)는 구해질 수 있다(S136).here,

Is a merit function.

Is the nonlinear thin film phase calculated theoretically using Equations (3) and (4) (S134).

Is a nonlinear component of the phase function Φ (h, d; k) obtained by processing the measured interference signal I (h, d; k). Using a nonlinear optimization techinque, Can be obtained (S136).

 When the thin film thickness d is obtained, the thin film phase? (D; k) can be obtained for all the wavenumber using the equation (2) (S142). However, for calculation of the thin film phase (d (k)), the refractive index and incident angle of the thin film are already known.

Next, referring to equations (4) and (5), the height h of the top surface is determined by the difference between the measured phase function? (H, d; k) and the previously determined thin film phase? Can be obtained as follows (S144).

는 측정 위상 함수(Φ(h,d;k))와 박막 위상(Ψ(d;k))의 차이를 나타내는 상대 위상이다.here,

Is a relative phase indicating the difference between the measured phase function? (H, d; k) and the thin film phase? (D; k).

A series of simulations were performed to evaluate the measurement performance of the proposed method with film thickness. The silicon oxide film layer is deposited on the silicon substrate, and the thickness of the silicon oxide film layer is 10 nm to 5 占 퐉. The spectrum of the light source is 450 nm to 700 nm.

FIG. 8A shows the approximate film thickness d 'calculated by calculating the best fitted slope to the simulated thin film phase.

Figure 8b shows the percent error of the approximate film thickness d 'of Figure 8a.

FIG. 8C shows the peak-to-valley of the non-linear thin film phase according to the thin film thickness.

8D shows the thickness of the thin film according to the present invention.

FIG. 8E shows the percentage error in FIG. 8D.

Referring to Figures 8A-8E, in the approximate film thickness d ', the percent error oscillates until it reaches near 0.6 μm and stabilizes when it exceeds 0.6 μm. This is similar to the peak-to-valley tendency of the magnitude of the nonlinear component of the thin film phase. Although there is a large percentage error in the approximate film thickness d ', in the case of measuring the thin film thickness of the sample according to the present invention, the approximate film thickness d' can provide a good estimate of the thin film thickness .

9A shows a spectroscopic image acquired through a 2D photosensor array through a line-scan imaging element. The horizontal axis provides spatial information for the 2D photo sensor array, and the vertical axis provides spectral information for each pixel in the imaged line.

FIG. 9B shows the top surface shape and the bottom surface shape of one line obtained by analyzing the 2D spectroscopic image of FIG. 9A obtained using the present invention.

FIG. 9C shows a volumetric thickness profile of a sample obtained by scanning with a microstage in a lateral direction or a y-axis direction.

9A to 9C, measurement results of a silicon oxide film having a thickness of 2 mu m are shown on a silicon substrate having a linear pattern with a height of 1 mu m. The vertical walls of the pattern could not be accurately measured. This is interpreted as a result of the diffraction occurring at the edge of the pattern. The diffraction can show a jump or spike at the edge of the step. As a daughter, we removed these artifacts by replacing them with appropriate neighbors.

The measurement accuracy of the proposed method is demonstrated by comparison with the thin film thickness measured by reflectometry substrate technology. Correct comparisons at the same location are virtually impossible. Thus, three measurements were performed at different locations. Measurements at each location were averaged at 15 points on the sample. The measurement error between these two methods is within the range of 15 nm maximum difference.

No Film Thickness measurement by our proposed technique Film Thickness by reflectometry Deviation between two thickness values One 1905.1 nm 1890.9 nm 14.2 nm 2 1892.6 nm 1885.1 nm 7.5 nm 3 1892.7 nm 1884.5 nm 8.2 nm

10 is a view for explaining a thickness and shape measuring apparatus according to another embodiment of the present invention.

10, the thickness and shape measuring apparatus 100a includes a light source 110, an interferometer 130a, and an optical detector 130a for acquiring an interference signal of an object beam reflected from the sample 10 and a reference beam reflected from the reference surface, (160).

The light source 110 may be a white light source. The interferometer 130a may include a beam splitter 132a and a reference mirror 134a. The distance between the beam splitter 132a and the reference mirror 134a is L. [ Therefore, the distance between the reference position at the upper surface of the sample is h. The interferometer 130a can be modified in various ways as long as it can form an interference signal.

The spectroscopic unit 150 can spatially decompose the interference signal according to the wavelength. The light sensing unit 160 measures the spatially resolved interference signal, and the processing unit 170 may measure thickness and shape through the algorithm described above.

11 is a view for explaining a thickness and shape measuring apparatus according to another embodiment of the present invention.

11, the thickness and shape measuring apparatus 200 includes a light source 210, an interferometer 130a, and an optical detector 130 for obtaining an interference signal of an object beam reflected from the sample 10 and a reference beam reflected from the reference surface, (260). The light source 210 may be a wavelength variable light source. Thus, the spectroscopic portion can be removed. Accordingly, in order to obtain the interference signal according to Equation (1), the optical sensing unit 260 may measure the optical signal according to the wavelength of the light source. The light sensing unit 260 may be a 2D light sensor array.

12 is a view for explaining a thin film thickness and shape measuring apparatus according to another embodiment of the present invention.

13 is a flow chart for explaining a method of measuring the thickness and shape of a thin film using the thin film thickness and shape measuring apparatus of FIG.

12 and 13, the thin film thickness and shape measuring apparatus 300 includes a light source 310, an interferometer 330, and an interference signal of an object beam reflected from the sample 10 and a reference beam reflected from the reference surface And a light sensing unit 360 for acquiring the light. The processing unit 170 processes the interference signal acquired by the light sensing unit 360.

The light source 310 may be a white light source. The interferometer 330 may include a beam splitter 332 and a reference mirror 334. The sample is fixed, and the reference mirror 334 can scan in the optical axis direction (X axis direction) with time. To adjust the scan distance of the reference mirror 334, an actuator such as a PZT may be used.

According to a modified embodiment of the present invention, the reference mirror 334 is fixed, and instead, the sample 10 can scan in the optical axis direction (Y axis direction) with time.

The light sensing unit 360 may measure an interference signal according to the scan distance z of the reference mirror 334. [ The light sensing unit 360 may be a 2D light sensor array. Accordingly, an interference signal G (h, d; z) of a similar form to the white light interference pattern can be obtained (S210).

When the optical path is changed by moving the sample or reference plane in the optical axis direction, the wavelength integration interference signal G (h, d; z) can be expressed as follows.

The scan distance along the optical axis direction of the sample or reference plane is z. G ₀ Is a background light of a white light interference pattern. and? is a visibility function. k is the electromagnetic wave number (wave number; k = 2π / λ; λ is a wavelength of the electromagnetic wave), k _c is the center frequency and, Δk is the bandwidth of the light source (310), Φ (h, d; k) is the wavelength And F (k) is a function of the frequency distribution of the light source 310. In this case, h is the height between the upper surface of the sample and the reference surface, and d is the thickness of the thin film. The phase function includes information about h and d. (D; k) is the thin film phase of the multiple reflected beam in the film. The thin film phase depends only on the film thickness and wave number.

The wavelength integration interference signal G (h, d; z) obtained according to the scan distance z may be Fourier transformed based on the scan distance z. In this case, the Fourier transformed expression is expressed as follows.

Here, A represents the spatial frequency of the white light interference signal. The first term represents the DC component of the white light interfering signal and the second term represents the carrier spatial frequency (Λ / 2) of the phase function (Φ (h, d; k) (A frequency region of a white light source).

If a part of the second term of Equation 13 is extracted using a filter, it can be expressed as follows (S222).

If only the phase function for the frequency domain is extracted in Equation (14), it is given as follows (S224).

Therefore, the phase function can be obtained in the same manner as in Equation (2). Therefore, the algorithm described below in Equation (2) can be applied (S230, S240). Therefore, the thickness of the thin film and the shape of the sample can be obtained.

Equation (1) represents the spectroscopic interference signal obtained according to the wave number, and Equation (12) represents the wavelength integrated interference signal obtained according to the scan distance. However, the same algorithm for obtaining the thickness of the thin film and the shape of the sample after the phase function is obtained is applied.

A signal processing method according to an embodiment of the present invention includes a step 210 of preparing an interference signal according to a scan distance of a reference mirror of an interferometer, an interference including a thin film thickness information and a surface shape information at a given incident angle, (S130) of calculating a thin film thickness corresponding to thin film thickness information by using the theoretical thin film phase according to thin film thickness and wave number and the measured phase signal, And extracting a top surface height corresponding to the surface shape information using a difference between the measured phase signal and the theoretical thin film phase (S140). The interference signal may be a wavelength-integrated signal.

The step (S220) of processing the interference signal to generate a measurement phase signal includes a step (S222) of extracting a specific carrier spatial frequency component using the Fourier transform of the interference signal and using a filter, And generating a measurement phase signal (S224).

(S130) of calculating a thin film thickness corresponding to the thin film thickness information using the theoretical thin film phase according to the thin film thickness and the number of waves and the thin film thickness information using the measured phase signal is performed by using the measured phase signal as a linear measured phase signal component and a non- (S134) of generating a theoretical nonlinear thin film phase component according to the thin film thickness and the number of waves, and a step (S134) of separating the nonlinear thin film phase component And determining a thickness (S136).

(S240) of extracting a top surface height corresponding to the surface shape information using the difference between the measured phase signal and the theoretical thin film phase, calculating a theoretical thin film phase according to the number of waves using the determined thin film thickness (S142 And extracting a top surface height corresponding to the surface shape information using the difference between the measured phase signal and the theoretical thin film phase (S144).

While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

10: Sample 110: Light source
120: lens unit 130: interferometer
140: spatial filter unit 150:
160: light sensing unit 170:

Claims (15)

Extracting a measured phase signal by processing an interference signal including thin film thickness information and surface shape information at a given incident angle and a refractive index of a given thin film;
Calculating a thin film thickness corresponding to thin film thickness information using the theoretical thin film phase according to thin film thickness and wave number and the measured phase signal; And
And extracting a top surface height corresponding to the surface shape information using a difference between the measured phase signal and the theoretical thin film phase. The method according to claim 1,
Wherein processing the interference signal to generate a measured phase signal comprises:
Filtering the interference signal by Fourier transform to remove a low-frequency component;
Extracting a signal including a phase function using a high-frequency filter in a signal from which a low-frequency component has been removed;
Performing inverse-Fourier transformation on the signal including the phase function; And
And extracting an imaginary part of the inverse Fourier transformed signal to generate a measured phase signal according to a wavenumber. The method according to claim 1,
Calculating the thin film thickness corresponding to the thin film thickness information according to the thin film thickness and the number of waves and the thin film thickness corresponding to the thin film thickness information using the measured phase signal includes:
Separating the measured phase signal into a linear measured phase signal component and a non-linear measured phase signal component;
Generating a theoretical nonlinear thin film phase component according to a thin film thickness and a wave number;
And determining the thin film thickness to minimize a difference between the nonlinear measured phase signal component and the theoretical nonlinear thin film phase component according to a wavenumber. The method according to claim 1,
Wherein the step of extracting the top surface height corresponding to the surface shape information using the difference between the measured phase signal and the theoretical thin film phase comprises:
Calculating a theoretical thin film phase according to a wavenumber using the determined thin film thickness; And
And extracting a top surface height corresponding to the surface shape information using a difference between the measured phase signal and the theoretical thin film phase. The method according to claim 1,
Wherein the interference signal according to a frequency or a wavenumber includes thin film thickness information and surface shape information and is obtained using a white light, a broadband light source, or a variable wavelength light source. The method according to claim 1,
Providing a white light source to a reference surface and providing the white light source to a sample comprising a thin film on a surface; And
Further comprising the step of acquiring the interference signal according to frequency or wave number by using the optical sensor array for the light reflected from the sample and the reference plane. The method according to claim 1,
Providing a tunable light source to a reference surface and providing the tunable light source to a sample comprising a thin film on a surface;
Further comprising the step of acquiring the interference signal according to frequency or wave number by using the optical sensor array for the light reflected from the sample and the reference plane. The method according to claim 1,
Further comprising the step of spatially scanning the sample to obtain the interference signal according to the position of the sample. The method according to claim 1,
Further comprising the step of preparing the interference signal according to a frequency or a wavenumber. The method according to claim 1,
Further comprising the step of preparing an interference signal according to the scan distance of the reference mirror of the interferometer,
Wherein the interference signal is a wavelength-integrated signal. 11. The method according to claim 1 or 10,
Wherein processing the interference signal to generate a measured phase signal comprises:
Performing Fourier transform on the interference signal and extracting a specific carrier spatial frequency component using a filter; And
And generating the measured phase signal from the phase of the filtered signal. Processing an interference signal including thin film thickness information and surface shape information at a given incident angle with a refractive index of a given thin film to generate a measured phase signal;
Calculating a thin film thickness corresponding to thin film thickness information using the theoretical thin film phase according to thin film thickness and wave number and the measured phase signal; And
And extracting a top surface height corresponding to the surface shape information using a difference between the measured phase signal and the theoretical thin film phase. Light source;
An interferometer that receives the output light of the light source and combines the reference beam by the reference mirror and the object beam by the sample;
A spectroscope unit for receiving an output signal of the interferometer and performing spectroscopy according to a frequency;
A light sensing unit for acquiring an output signal of the light splitting unit according to a frequency;
And a processing unit for processing an interference signal of the light sensing unit,
Wherein the processing unit comprises:
Processing the interference signal including thin film thickness information and surface shape information at a given incident angle and a refractive index of a given thin film to extract a measured phase signal,
The thin film thickness corresponding to the thin film thickness information is calculated by using the theoretical thin film phase according to the thin film thickness and the wave number and the measured phase signal,
Wherein the upper surface height corresponding to the surface shape information is extracted using the difference between the measured phase signal and the theoretical thin film phase. A wavelength tunable light source;
An interferometer that receives the output light of the wavelength variable light source and combines the reference beam by the reference mirror and the object beam by the sample;
A light sensing unit for acquiring an output signal of the interferometer according to a frequency;
And a processing unit for processing an interference signal of the light sensing unit,
Wherein the processing unit comprises:
Processing the interference signal including thin film thickness information and surface shape information at a given incident angle and a refractive index of a given thin film to extract a measured phase signal,
The thin film thickness corresponding to the thin film thickness information is calculated by using the theoretical thin film phase according to the thin film thickness and the wave number and the measured phase signal,
Wherein the upper surface height corresponding to the surface shape information is extracted using the difference between the measured phase signal and the theoretical thin film phase. Light source;
An interferometer that receives the output light of the light source and combines the reference beam by the reference mirror and the object beam by the sample;
A light sensing unit for acquiring an output signal of the interferometer according to a scan distance of the reference mirror;
And a processing unit for processing an interference signal of the light sensing unit,
Wherein the processing unit comprises:
Processing the interference signal including thin film thickness information and surface shape information at a given incident angle and a refractive index of a given thin film to extract a measured phase signal,
The thin film thickness corresponding to the thin film thickness information is calculated by using the theoretical thin film phase according to the thin film thickness and the wave number and the measured phase signal,
Wherein the upper surface height corresponding to the surface shape information is extracted using the difference between the measured phase signal and the theoretical thin film phase.

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