JP6047427B2 - Method for measuring film shape of thin film - Google Patents

Description

  The present invention relates to a film shape measuring method of a thin film for measuring the surface shape of a measurement object covered with a transparent film and the thickness of the transparent film, and in particular, non-contact and transparent using a plurality of monochromatic lights having three or more wavelengths. The present invention relates to a film shape measuring method of a thin film that measures the height of a film surface, the height of a surface to be measured, and the thickness of a transparent film.

  As a conventional device of this type, a surface shape measuring device using a method for measuring the uneven shape of a precision processed product such as a semiconductor wafer or a glass substrate for a liquid crystal display using interference of white light is widely known. As shown in FIG. 10, the conventional surface shape measuring apparatus guides white light from the white light source 90 to the half mirror 92 through the first lens 91, and focuses the white light reflected by the half mirror 92 by the second lens 93. An interferometer configured to irradiate the measurement target surface 96 with the white light via the beam splitter 95 is provided.

  In the beam splitter 95 of the interferometer, the white light applied to the measurement target surface 96 and the white light applied to the reference surface 94 are divided. The white light irradiated on the reference surface 94 is reflected by the reflecting portion 94a of the reference surface 94 and reaches the beam splitter 95 again. On the other hand, the white light that has passed through the beam splitter 95 is reflected on the measurement target surface 96 and reaches the beam splitter 95 again. The beam splitter 95 combines the white light reflected by the reflecting portion 94a of the reference surface 94 and the white light reflected by the measurement target surface 96 again in the same path. At this time, an interference phenomenon corresponding to the difference in distance between the distance L1 from the reference surface 94 to the beam splitter 95 and the distance L2 from the beam splitter 95 to the measurement target surface 96 occurs. The white light in which the interference phenomenon has occurred passes through the half mirror 92 and enters the CCD camera 98.

  The CCD camera 98 images the measurement target surface 96 together with the white light in which the interference phenomenon has occurred. Here, the wavelength of white light incident on the CCD camera 98 is intensified by changing the difference between the distance L1 and the distance L2 by changing the unit on the beam splitter 95 side up and down by a changing means (not shown). , Weaken each other. For example, when attention is paid to a specific part on the measurement target surface 96 in the region imaged by the CCD camera 98, the position of the beam splitter 95 is changed until the distance L2 <distance L1 to distance L2> distance L1. Thus, when the intensity of the interfered white light (hereinafter simply referred to as “interference light”) at a specific location is measured, a result as shown in FIG. 11 is theoretically obtained. By obtaining the position where the amplitude of the intensity value change of the interference light at this time is maximized, the height of the specific portion of the measurement target surface can be obtained. Similarly, the uneven shape of the measurement target surface is measured by obtaining the heights of a plurality of specific locations.

  Specifically, it is necessary to obtain the position where the amplitude of the change in the intensity value of the interference light is maximized from the data group of discrete intensity values of the interference light acquired by measuring the intensity value of the interference light at a predetermined interval. Therefore, as a method for obtaining the position where the amplitude is maximized, an average value of a discrete data group is calculated, the calculated average value is subtracted from each intensity value, and each calculated value is further squared. As a result, the data is converted into a data group in which the intensity value on the plus side is emphasized, and a curve (envelope) obtained by smoothing the data group is obtained. The surface height of the specific portion is obtained by obtaining the position where the maximum value of the smoothed curve is obtained.

Japanese Patent Laid-Open No. 11-023229 JP 2004-361218 A JP 2010-060420 A

  However, the conventional method has the following problems. That is, when the surface of the measurement object is covered with a transparent film, the interface with the measurement object that passes through the transparent film and is in contact with the back surface of the transparent film (hereinafter referred to as “measurement object surface” as appropriate). The reflected light reflected from the surface of the transparent film is superimposed on the reflected light reflected from (). In other words, when both superimposed reflected lights are converted into interference signals, each interference signal that must be obtained individually is superimposed. As a result, the reflected light on the surface of the transparent film becomes a disturbance, the height of the surface of the measurement object cannot be measured accurately, and consequently the surface shape of the measurement object cannot be measured accurately. is there.

  The appearance of the interference phenomenon at these two locations differs depending on the thickness of the transparent film. For example, as shown in the left side of FIG. 12, when the transparent film is thick, two interference phenomena appear individually, and the height of the transparent film surface, the height of the surface of the measurement object, and the film thickness can be obtained. . However, when the transparent film is thin as shown on the right side of FIG. 12, the interference phenomenon of reflected light from the surface of the transparent film and the surface of the measurement object is substantially superimposed, and each amplitude maximum value is Appears overlaid on the waveform. In such a case, the conventional method of obtaining the position information of the maximum amplitude value cannot separate the interference at two places. Therefore, there is a problem that the height information on the surface of the transparent film cannot be obtained, and the height information on the surface of the measurement object under the transparent film cannot be obtained.

  The present invention has been made in view of such circumstances, and the height of the transparent film surface at the specific location of the measurement object covered by the transparent film, the height of the measurement object surface, and the transparent film The main object is to provide a method for measuring the shape of a thin film capable of accurately obtaining the film thickness.

  Further, there are already known examples for obtaining a surface shape using a light source composed of white light or monochromatic light. However, in the methods of Patent Documents 2 and 3, the model is complicated and it is necessary to obtain apparatus parameters in advance. There is. However, in the method according to the present invention, even when the surface of the measurement object is covered with a transparent thin film of submicron order, the height of the surface of the transparent film, the height of the surface of the measurement object, and the film of the transparent film are relatively easy. An object of the present invention is to provide a method for measuring the shape of a thin film capable of measuring the thickness.

In order to achieve such an object, the present invention has the following configuration.
That is, the invention according to claim 1 varies the distance between the measurement object surface and the reference surface while irradiating illumination light on the measurement object surface and the reference surface of the measurement object covered with the transparent film. By causing the interference light to change due to reflected light that is reflected from the surface of the measurement object and the reference surface and returns on the same optical path, a transparent film at a specific location of the measurement object is determined based on the intensity value of the interference light at this time. In the method for measuring the shape of a thin film for obtaining at least one of the height of the surface, the height of the surface of the measurement object, and the thickness of the transparent film,
Illumination light includes a plurality of single wavelengths of three or more wavelengths , changes the optical path difference between the surface of the measurement object having a transparent film and the reference surface, captures interference images by reflected light from both surfaces, and obtains interference A model function is applied to the luminance signal to obtain the height of the transparent film surface, the height of the surface of the measurement object, and the film thickness of the transparent film ,
The model function is a sum of an interference signal due to reflection on the reference surface and reflection on the transparent film surface, and an interference signal model due to reflection on the reference surface and reflection on the surface of the measurement object,

Here, g (i, j) is a model function value of wavelength number j with data number i, a (j) is a direct current component (= average value) of wavelength number j, b ₁ (J) is the amplitude of the transparent film surface luminance AC component of wavelength number j, b ₂ (J) is the amplitude of the surface luminance alternating current component of the wavelength number j, λ (j) is the wavelength of the wavelength number j, z (i) is the height of the data number i, z ₁ Is the surface height of the transparent film, z ₂ Is the height of the surface of the measurement object,
It is characterized by expressing as.

According to this method, by adjusting the interference light observation luminance value for each single wavelength to the interference fringe physical model, the height of the measurement object surface of the measurement object, the height of the transparent film surface, and the transparent film surface The film thickness can be easily obtained. In particular, even when the thickness of the transparent film is less than 1 micron, which is difficult to measure using white light, the height of the surface of the object to be measured and the height of the surface of the transparent film can be separated and obtained with high accuracy. become.

According to a second aspect of the present invention, in the film shape measuring method of the thin film according to the first aspect, the amplitude ratio of the amplitude of the transparent film surface luminance AC component and the amplitude of the measurement target surface luminance AC component is measured. It is characterized by assuming a constant common to each wavelength used.

According to a third aspect of the invention, the film shape measuring method of a thin film of any crab of claims 1 or claim 2, as a method at the time of the adaptation, the actual measurement value and the model function value in the evaluation function (sampling point Is the square error)

Here, g (i, j) and gi, j are the model function value and observation luminance value of data number i and wavelength number j, M is the number of wavelengths used, N is the number of observation data,
The least square method that minimizes F is used.

The invention according to claim 4
By irradiating illumination light to the measurement object surface and the reference surface of the measurement object covered with the transparent film, the distance between the measurement object surface and the reference surface is changed to change the measurement object surface and the reference surface. The interference light is reflected by the reflected light and returned from the same optical path to cause a change in the interference fringe. Based on the intensity value of the interference light at this time, the height of the transparent film surface at the specific location of the measurement object, the height of the measurement object surface In the method for measuring the film shape of a thin film for obtaining at least one of the thickness of the transparent film,
Illumination light includes a plurality of single wavelengths of three or more wavelengths, changes the optical path difference between the surface of the measurement object having a transparent film and the reference surface, captures interference images by reflected light from both surfaces, and obtains interference A model function is applied to the luminance signal to obtain the height of the transparent film surface, the height of the surface of the measurement object, and the film thickness of the transparent film,
When the height of the surface of the measurement object is uniform in at least one direction and the surface height of the transparent film is uniform in at least the one direction, the distance between the surface of the measurement object and the reference surface is determined in the one direction. The reference plane is tilted so as to vary spatially, and an interference fringe is generated in the one direction by reflected light that is reflected from the surface of the measurement object and the reference plane and returns on the same optical path. A change in the orthogonal direction is captured as an interference image, and a model function is applied to the obtained interference luminance signal to obtain the height of the transparent film surface, the height of the surface of the measurement object, and the film thickness of the transparent film, A method for measuring a film shape of a thin film, characterized by obtaining a distribution in a direction orthogonal to the one direction ,
The model function is a sum of an interference signal due to reflection on the reference surface and reflection on the transparent film surface, and an interference signal model due to reflection on the reference surface and reflection on the surface of the measurement object ,

Here, g (i, j) is a model function value of wavelength number j with data number i, a (j) is a direct current component (= average value) of wavelength number j, b ₁ (J) is the amplitude of the transparent film surface luminance AC component of wavelength number j, b ₂ (J) is the amplitude of the surface luminance alternating current component of the wavelength number j, f (j) is the spatial frequency of the stripe of wavelength number j, x (i) is the position of data number i, x ₁ Is the transparent film surface peak position, x ₂ Is the peak surface position of the measurement object,
It is characterized by expressing as.

According to this method, when the measurement object has a uniform surface height in at least one direction and the surface height of the transparent film is at least uniform in the one direction, the above-described 1 It is possible to separate the height of the surface of the measurement object and the height of the transparent film surface in a direction orthogonal to the direction, and obtain the distribution with high accuracy.

According to a fifth aspect of the present invention, in the method for measuring a film shape of a thin film according to the fourth aspect, the amplitude ratio between the amplitude of the transparent film surface luminance AC component and the amplitude of the measurement target surface luminance AC component is measured. It is characterized by assuming a constant common to each wavelength used.

According to a sixth aspect of the present invention, in the method for measuring the shape of a thin film according to any one of the fourth or fifth aspect , an evaluation function (an actual measurement value and a model function value at a sample point) is used as the method for the adaptation. Is the square error)

Here, g (i, j) and gi, j are the model function value and observation luminance value of data number i and wavelength number j, M is the number of wavelengths used, N is the number of observation data,
The least square method that minimizes F is used.

  In the present invention, using a method of adapting the model function to the interference luminance data, the shape of the transparent thin film on the surface of the measurement object using a plurality of single-wavelength light sources, the height of the transparent film surface, which is an unknown parameter, The height of the measurement object surface and the film thickness of the transparent film can be determined.

  In particular, it is possible to determine the height and film thickness of the transparent film surface and the surface of the object to be measured with high accuracy in the case of a thin film with a film thickness of 1 micrometer or less, which was difficult with conventional measurement. I have to.

  In addition, when performing thin film measurement, the present invention can be implemented with an interference microscope, a three-wavelength illumination device, a color camera, a vertical scanning mechanism (not shown), and a personal computer.

It is a figure which shows schematic structure of the surface shape measuring apparatus of Example 1 which concerns on this application. It is a figure which shows the theoretical interferogram (interference figure) in Example 1. FIG. It is a figure which shows the transparent film surface luminance signal in Example 1. FIG. It is a figure which shows the measurement object surface luminance signal in Example 1. FIG. It is a figure which shows schematic structure of the surface shape measuring apparatus of Example 2. FIG. It is a figure which shows the shape of the measuring object of Example 2. FIG. FIG. 6 is a diagram illustrating an image captured in Example 2. It is a figure which shows the transparent film surface luminance signal of the nominal film thickness 200nm part in Example 2. FIG. It is a figure which shows the transparent film surface luminance signal of the nominal film thickness 300nm part in Example 2. FIG. It is a figure which shows schematic structure of the surface shape measuring apparatus which concerns on a prior art example. It is a figure explaining the process which calculates | requires the peak position of a specific function. It is a figure which shows the measurement principle corresponding to a transparent film of the conventional method.

  Hereinafter, the process performed by the whole surface shape measuring apparatus which is the characteristic part of this invention is demonstrated concretely. First, Embodiment 1 of the present invention will be specifically described with reference to the drawings. FIG. 1 is a diagram showing a schematic configuration of a surface shape measuring apparatus according to Embodiment 1 of the present invention.

  This surface shape measuring apparatus includes a transparent film 31 that covers the surface of the measurement object 30 such as a semiconductor wafer, a glass substrate, or a metal substrate, and a fine object formed on the measurement object 30 that is bonded to the back surface side of the transparent film 31. An optical system unit 1 that irradiates light on a simple pattern and a control system unit 2 that controls the optical system unit 1 are configured.

  The optical system unit 1 includes a white light source 10 that generates white light that irradiates the measurement object surface 30A that is the surface of the measurement object 30, the transparent film surface 31A that is the surface of the transparent film 31, and the reference surface 15, and a white light source. The collimating lens 11 that converts white light into parallel light from 10, the band-pass filter 12 that passes only monochromatic light in a specific frequency band, and the monochromatic light that has passed through the band-pass filter 12 are reflected in the direction of the measurement object 30. On the other hand, the half mirror 13 that passes white light from the direction of the measurement object 30, the objective lens 14 that condenses the monochromatic light reflected by the half mirror 13, and the monochromatic light that has passed through the objective lens 14, It is divided into reference light reflected to the reference surface 15 and measurement light passed to the measurement object surface 30A and the transparent film surface 31A, and reflected by the reference surface 15 The reference light and the measurement light reflected by the measurement object surface 30A and the transparent film surface 31A are recombined to form a beam splitter 16 that generates interference fringes and a monochromatic light in which the reference light and measurement light are combined. The imaging lens 17 for imaging and the imaging device 18 for imaging the measurement object surface 30A together with the interference fringes are provided. The imaging device 18 may have any configuration as long as it can individually convert two-dimensional luminance images of a plurality of monochromatic lights having different wavelengths into image data. For example, a CCD solid-state imaging device, a MOS image sensor, a CMOS image sensor, or the like is used. .

  The white light source 10 is a white light lamp, for example, and generates white light in a relatively wide frequency band. The white light generated from the white light source 10 is collimated by the collimating lens 11 and enters the bandpass filter 12.

  The bandpass filter 12 is a filter for allowing only monochromatic light in a specific frequency band to pass, and is attached to the optical path from the white light source 10 to the imaging device 18. Preferably, it is attached to the optical path between the position where the white light from the white light source 10 is divided into the reference light to the reference surface 15 and the measurement light on the measurement object surface 30A. In this embodiment, for example, it is attached to the optical path between the collimating lens 11 and the half mirror 13. As the bandpass filter 12, for example, a band-pass optical interference filter having center wavelengths of 480 nm, 560 nm, and 600 nm is used. Each monochromatic light that has passed through the bandpass filter 12 has its frequency band narrowed, and only each monochromatic light in a specific frequency band passes through the bandpass filter 12.

  The half mirror 13 reflects each monochromatic light in a specific frequency band that has passed through the bandpass filter 12 toward the direction of the measurement object 30, while allowing each monochromatic light returned from the direction of the measurement object 30 to pass therethrough. Is. Each monochromatic light of a specific frequency band reflected by the half mirror 13 enters the objective lens 14.

  The objective lens 14 is a lens that collects each incident monochromatic light toward the focal point. Each monochromatic light condensed by the objective lens 14 passes through the reference surface 15 and reaches the beam splitter 16.

  The beam splitter 16 reflects each monochromatic light collected by the objective lens 14 by, for example, the reference light reflected on the upper surface of the beam splitter 16 and the measurement object surface 30A and the transparent film surface 31A. And the measurement light that is reflected by the reference surface 15 and the measurement light are combined again to generate interference fringes. Each monochromatic light reaching the beam splitter 16 is divided into reference light reflected by the upper surface of the beam splitter 16 and measurement light passing through the beam splitter 16, and the reference light reaches the reference surface 15, and the measurement light Reaches the measurement target surface which is the transparent film surface 31A of the measurement object 30 covered with the transparent film 31 and the measurement object surface 30A joined to the back surface of the transparent film 31.

  The reference surface 15 is provided with a reflecting portion 15a for reflecting the reference light in the direction of the beam splitter 16, and the reference light reflected by the reflecting portion 15 reaches the beam splitter 16, and further, this reference The light is reflected by the beam splitter 16.

  The measurement light that has passed through the beam splitter 16 is condensed toward the focal points P0 and P1, and is reflected on the measurement object surface 30A and the transparent film surface 31A. The reflected two measurement lights reach the beam splitter 16 and pass through the beam splitter 16.

  The beam splitter 16 combines the reference light and the measurement light again. At this time, an optical path difference is generated due to a difference in distance between the distance L1 between the reference surface 15 and the beam splitter 16 and the distance L2 between the beam splitter 16 and the transparent film surface 31A. According to this optical path difference, the reference light and the measurement light interfere with each other, thereby generating interference fringes. The monochromatic light in a state where the interference fringes are generated passes through the half mirror 13, is imaged by the imaging lens 17, and enters the imaging device 18.

  The imaging device 18 captures images near the focal point P0 of the measurement object surface 30A and the focal point P1 of the transparent film surface 31A projected by the measurement light for each monochromatic light in a state where interference fringes are generated. The captured image data is collected by the control system unit 2. Further, as will be apparent later, for example, the optical system unit 1 is driven up and down by the drive unit 24 of the control system unit 2 corresponding to the changing means of the present invention. In particular, when the optical system unit 1 is driven in the vertical direction, the difference between the distance L1 and the distance L2 changes. As a result, the interference fringes gradually change according to the difference between the distance L1 and the distance L2. The CCD camera 18 captures images of the measurement object surface 30A and the transparent film surface 31A along with changes in interference fringes at predetermined sampling intervals described later, and the image data is collected by the control system unit 2. The CCD camera 18 corresponds to the image pickup means in the present invention.

  The control system unit 2 performs overall control of the entire surface shape measuring apparatus and CPU 20 for performing predetermined calculation processing, and various data such as image data sequentially collected by the CPU 20 and calculation results by the CPU 20. Memory 21 to be stored, input unit 22 such as a mouse or keyboard for inputting sampling intervals and other setting information, a monitor 23 for displaying an image of the surface 30A to be measured, and an optical system unit according to instructions from the CPU 20 1 is driven vertically and horizontally. For example, it is comprised by the computer system provided with the drive part 24 comprised with drive mechanisms, such as a triaxial drive type servomotor. The CPU 20 corresponds to sampling means and arithmetic means in the present invention, the memory 21 corresponds to storage means in the present invention, and the drive unit 24 corresponds to fluctuation means in the present invention.

  The CPU 20 is a so-called central processing unit that controls the imaging device 18, the memory 21, and the driving unit 24, and measures the measurement target based on the image data of the measurement target surface 30 </ b> A including the interference fringes captured by the imaging device 18. Calculation processing is performed to obtain the height of the transparent film surface 31A at a specific location of the object 30, the height of the measurement object surface 30A, and the film thickness D of the transparent film 31. Further, a monitor 23 and an input unit 22 such as a keyboard and a mouse are connected to the CPU 20, and the operator can observe various operation information displayed on the monitor 23 from the input unit 22. Input. On the monitor 23, after the measurement is completed, the height of the measurement object surface 30A, the height of the transparent film surface 31A, the film thickness D of the transparent film 31, the uneven shape of the measurement target surface, and the like are displayed as numerical values and images. Is done.

  The drive unit 24 has a fixed distance L1 between the reference surface 15 in the optical system unit 1 and the beam splitter 16, and a variable distance L2 between the beam splitter 16 and the measurement target surface 30A. In order to change the difference, the optical system unit 1 is moved in the orthogonal three-axis directions, and the optical system unit 1 is driven in the X, Y, and Z-axis directions according to instructions from the CPU 20, for example, a three-axis drive type servo. It is comprised with the drive mechanism provided with a motor. The drive unit 24 corresponds to a changing unit in the present invention, and the relative distance in the present invention is the distance L1 between the reference surface 15 and the beam splitter 16, and the beam splitter 16 and the transparent film surface 31A. The difference with the distance L2 is shown. In this embodiment, the optical system unit 1 is operated. For example, a table (not shown) on which the measurement object 30 is placed may be varied in the three orthogonal axes.

Next, a model function used in the first embodiment will be described.
First, a model function equation g ₀ (i, j) when i is an actually measured data number and j is a wavelength number is represented by the following equation as a basic equation of an interference luminance signal in the case of two light beams.

Here, a ₀ (j) is the luminance direct current component (= average value) of wavelength number j, b ₀ (j) is the amplitude of the luminance alternating component of wavelength number j, λ (j) is the wavelength of wavelength number j, z ₀ is the height of the reflecting surface.
Based on this, the interference luminance g ₁ (i, j) due to reflection on the surface of the transparent film, the interference luminance g ₂ (i, j) due to reflection on the surface of the measurement object, and the sum of these values are expressed as g (i, j j) is expressed as follows.

Here, a (j) is the luminance direct current component (= average value) of wavelength number j, b ₁ (j) is the amplitude of the transparent film surface luminance alternating current component of wavelength number j, and b ₂ (j) is the wavelength number j. The amplitude of the surface luminance AC component of the measurement object, α is the amplitude ratio [= b ₁ (j) / b ₂ (j)] (note: assumed to be a constant independent of wavelength), and λ (j) is the wavelength of wavelength number j , Z ₁ is the height of the transparent film surface (0th order peak position of the transparent film surface luminance signal), and z ₂ is the height of the measurement object surface (0th order peak position of the measurement object surface luminance signal).
On the other hand, if the measured interference luminance value is g _ij , a reasonable model function can be obtained if a parameter that minimizes the square error between the measured value and the model function value in the following evaluation function equation can be obtained.

Here, M is the number of wavelengths used for measurement, and N is the number of observation data.

By the way, the cos wave model is represented by Bcos (x + φ) excluding the DC component. Therefore, for one wavelength, two parameters B and φ are obtained from the observed waveform. However, if this is decomposed into two waveforms, the parameters become four variables B ₁ , B ₂ , φ ₁ , φ ₂ , It cannot be solved as it is. However, when the following two preconditions are provided: Premise 1: Zero phase of each wavelength is the same (phases φ ₁ and φ ₂ are common to each wavelength)
Assumption 2: Amplitude ratio of each wavelength is constant (α is independent of wavelength as described in equation (4) above)
If the number of wavelengths is m, the number of unknown parameters related to the phase that should originally be 2 m is 2 under assumption 1, and the number of unknown parameters related to the amplitude that should be 2 m under assumption 2 is m + 1.

  Based on this assumption, the number of observation parameters is 2 m and the number of unknown parameters is m + 3 with respect to the number of wavelengths m. If m is 3 or more, 2m ≧ m + 3, and the value of the unknown parameter can be obtained.

Therefore, in the following, a case where monochromatic light of three wavelengths is used will be described as an example.
First, as for the evaluation function, when M is set to 3 and Expression (4) is substituted into Expression (5), the following expression is obtained.

... (6)

  Next, an initial value for optimum value search is determined using the following method.

a (j): DC component; = observed luminance average value b ₂ (j): amplitude; = 1 / (1 + α) times of observed luminance range (max-min) α: amplitude ratio; estimated from the refractive index of the film and the substrate Z ₁ : height of transparent film surface, Z ₂ : height of surface of measurement object
The initial value calculation of Z ₁ and Z ₂ is as follows, assuming that the zeroth-order fringe height obtained from the observed luminance value is z ₀ .
When α> 1: Z ₁ = Z ₀ (assuming that the transparent film surface is at the zero-order fringe position); Z ₂ = Z ₀ -nt
When α <1: Z ₂ = Z ₀ (assuming that the surface of the measurement object is a zero-order fringe position); Z ₁ = Z ₀ + nt
Here, n represents the refractive index of the transparent film.

Finally, based on the above, the height and film thickness of the transparent film surface and the surface to be measured are calculated.
That is, when the transparent film surface peak position Z ₁ and the measurement object surface peak position Z ₂ are converted into heights,
(1) Height of transparent film surface S = Z ₁
(2) Film thickness t = (Z ₁ −Z ₂ ) / n
(3) Height of measurement object surface b = St
Are obtained.

Hereinafter, an experimental example obtained using a calculation method based on the vertical scanning method is shown as Example 1.
Example 1
1-1. experimental method:
(1) Target signal: A theoretical interferogram (interference diagram) was created under the following conditions.

-Wavelengths used: 470 nm, 560 nm, 600 nm
・ Transparent film surface interference signal:
a ₁ (1) = a ₁ (2) = a ₁ (3) = 1;
b ₁ (1) = b ₁ (2) = b ₁ (3) = 1
・ Measurement surface interference signal:
a ₂ (1) = a ₂ (2) = a ₂ (3) = 0.5;
b ₂ (1) = b ₂ (2) = b ₃ (3) = 0.5
・ Z1 = 0nm, z2 = -200nm
-Observation data interval: 5nm
・ Observation data range: ± 500nm
(2) Estimation method:
-Software used: SOLVER, an optimization tool for MSExcel
Initial values: z1 = 50 nm, z2 = −250 nm, α = 2.5
・ Other initial values: As described above,
a (j): DC component; = observed luminance average value
b ₂ (j): Amplitude of surface AC brightness component of measurement object;
= 1 / (1 + α) times the observed luminance range (max-min)
α: Amplitude ratio; estimated from refractive index of film and substrate
z ₁ : height of transparent film surface, z ₂ : height of measurement object surface
further,
The initial values of z ₁ and z ₂ are calculated as follows, assuming that the zeroth-order fringe height obtained from the observed luminance value is z ₀ .

When α> 1: z ₁ = z ₀ (assuming that the transparent film surface is at the zero-order fringe position); z ₂ = z ₀ -nt
When α <1: z ₂ = z ₀ (assuming that the surface of the measurement object is a zero-order fringe position); z ₁ = z ₀ + nt

1-2. Experimental result:
The experimental results are shown in Table 1. As a result, nine unknown variables including the film thickness of 200 nm were correctly estimated. Further, the adapted transparent film surface luminance signal is shown in FIG. 3, and the measurement object surface luminance signal is shown in FIG.

Subsequently, when the height of the surface of the measurement object is uniform in at least one direction and the surface height of the transparent film is uniform in at least the one direction, the surface of the transparent film in the direction orthogonal to the one direction is measured. A calculation method for collectively obtaining the height, the height of the surface of the measurement object, and the film thickness of the transparent film will be described as a second embodiment.

[Embodiment 2 (calculation method by batch imaging method)]
Embodiment 2 of the present invention will be described below with reference to the drawings.

  FIG. 5 is a diagram showing a schematic configuration of the surface shape measuring apparatus according to the second embodiment of the present invention, which is substantially the same as the surface shape measuring apparatus according to the first embodiment shown in FIG. The reference plane 15A is inclined so that the difference between the distance L2 and the distance L2 fluctuates in the x direction, and the distance L2 at the time of measurement is not variable but fixed, and the imaging is performed collectively.

  Further, in the second embodiment, the shape of the measurement object 30 and the transparent film 31 to be measured is uniform in the height of the measurement object surface 30A in at least one direction as shown in FIG. The height of the transparent film surface 31A needs to be uniform in at least the one direction, and the one direction is arranged to be the x direction in FIG.

  Since the measurement object arranged as described above has a constant height of the measurement object surface 30A and a height of the transparent film surface 31A in the x direction, the distance L1 varies in the x direction. The difference between the distance L1 and the distance L2 fluctuates, that is, interference fringes can be generated in the same manner as when the distance L2 is changed in the measurement of the specific point in the first embodiment.

  The interference fringes can be acquired as an image by the imaging device 18, and interference fringes corresponding to the height of the measurement object surface 30A and the height of the transparent film surface 31A in the y direction perpendicular to the x direction appear in the x direction.

  Hereinafter, with the configuration of the surface shape measuring apparatus shown in FIG. 5, the luminance data and the model function are fitted to each line by the least square method using the batch imaging method, and the height and film thickness of the front and back surfaces are calculated. Explain the procedure.

First, the model function used here will be described.
A model function equation g ₀ (i, j) where i is an actually measured data number and j is a wavelength number is expressed by the following equation as a basic equation of an interference luminance signal in the case of two light beams.

Here, a ₀ (j) is the luminance direct current component (= average value) of wavelength number j, b ₀ (j) is the amplitude of the luminance alternating component of wavelength number j, λ (j) is the wavelength of wavelength number j, x ₀ is the position of the reflecting surface.
Based on this, the interference luminance g1 (i, j) due to reflection on the surface of the transparent film, the interference luminance g2 (i, j) due to reflection on the surface of the measurement object, and the sum of these values are expressed as g (i, j). Is expressed as follows.

Here, a (j) is the luminance direct current component (= average value) of wavelength number j, b ₁ (j) is the amplitude of the transparent film surface luminance alternating current component of wavelength number j, and b ₂ (j) is the wavelength number j. The amplitude of the surface luminance AC component of the measurement object, α is the amplitude ratio [= b ₁ (j) / b ₂ (j)] (Note: It is assumed that it is a wavelength independent constant) f (j) is the spatial frequency of wavelength number j , x ₁ is the transparent film surface peak position (0-order peak position of the transparent film surface luminance signal), x ₂ is the measurement object surface peak position (0-order peak position of the measurement object surface brightness signal)
On the other hand, assuming that the measured interference luminance value is gi, j, as in the description of the first embodiment, it is reasonable if a parameter that minimizes the square error between the measured value and the model function value in the following evaluation function equation can be obtained. A model function can be obtained. ,

Here, M is the number of wavelengths used for measurement, and N is the number of observation data.

  Therefore, substituting equation (10) into equation (5) and using 3 wavelengths, so that M is 3,

It becomes.

Next, when a single wavelength of three types of wavelengths is used for the method according to the method, there are three types of parameters including the variable j, so the unknown parameters are a (j), b2 (j), f ( 3) Ten of x ₁ , x ₂ and α,
Conversion parameter: f (2) = f (3) × λ ₃ / λ ₂ ,
f (1) = f (3) × λ ₃ / λ ₁
It becomes.
The initial value is set by the following method.

DC component a (j) = luminance average value
Amplitude b ₂ (j) = 1 / {2 (1 + α)} times the luminance range
・ Amplitude ratio α = Estimated value from refractive index of transparent film and refractive index of measurement object
・ Frequency f (3) = Visual estimated value from the number of stripes
Other frequency f (2) = f (3) × λ ₃ / λ ₂ ,
f (1) = f (3) × λ ₃ / λ ₁
Pixel-height conversion coefficient: Δ = (λ / 2) × f (unit: nm / pixel)
The transparent film surface peak position x ₁ and the measurement object surface peak position x ₂ are estimated as follows based on α and the surface tilt direction.

When α> 1: x ₁ = 0, x ₂ = −nt / Δ
When α <1: x ₂ = 0, x ₁ = nt / Δ
Further, as the data range at the time of fitting (conformity), data in the set measurement region is used. In this case, the zero-order fringe position was set as the coordinate origin (x = 0).

Next, the height of the surface of the transparent film, the height of the surface of the measurement object, and the film thickness of the transparent film are calculated.
In this case, the obtained transparent film surface peak position (x ₁ ) and measurement target object surface peak position (x ₂ ) are corrected by adding the 0th-order fringe position and converted into a height.

  That is, the following calculation is performed.

(1) Height of transparent film surface s = (x ₁ + 0th order fringe position) × Δ
(2) Film thickness of transparent film t = abs (x ₁ −x ₂ ) × Δ / n
(3) Height of measurement object surface b = s−t
Further, in the above “calculation method by the collective imaging method”, a modification example may be further performed as described below.
One is “normalization of luminance data”, and this purpose is performed to alleviate the imbalance in luminance signal intensity of three wavelengths. Specifically, before fitting, the luminance value is normalized, and the luminance value is approximately within the range of [0 to 2]. The normalization method is
Normalized luminance value = [(luminance value−average value) / {(maximum value−minimum value) / 2} +1]
And

Furthermore, in the “calculation method using the batch imaging method”, an optimum value can be searched using the “wide area search mode” method as a solution when a correct result cannot be obtained from the set initial value. This is a method of searching for an optimum value while changing the initial value of the film thickness. For example, the evaluation function value having the minimum value is selected.
(Example 2)
An experimental example obtained using the above-mentioned [Calculation method by collective imaging method] is shown as Example 2.
2-1. Implementation method:
(1) Target signal of measurement object: A film thickness difference sample was used.

          -Film thickness (nominal value): 200 nm portion and 300 nm portion are formed stepwise.

-Film type: silicon oxide film on wafer (refractive index 1.46)
(2) Imaging method
・ Optical system: Interference microscope
・ Imaging device camera: 3-plate color camera
Light source: Three-wavelength mixed illumination with wavelengths: 470 nm, 560 nm, and 600 nm.

(3) Estimation method
-Fit algorithm: Non-linear optimization method.

Unknown parameters: a (j), b (j), x ₁ , x ₂ , f (3), α
2-2. Implementation results.

  FIG. 7 shows an acquired image obtained by the batch imaging method of a film thickness difference sample. Although a monochrome display is shown in FIG. 7, a color image is actually acquired, and intensities for each of the three wavelengths can be obtained. FIG. 8 shows the change in the transparent film surface luminance signal at each wavelength (B is 470 nm, G is 560 nm, R is 600 nm, and so on) in the X direction when the nominal film thickness is 200 nm, and FIG. 9 shows the nominal film thickness. Represents each wavelength image in the X direction at a portion of 300 nm. Based on the data shown in the graphs of FIGS. 8 and 9, the estimation of the unknown parameter was obtained using SOLVER, an optimization tool of Microsoft Excel, and at that time, the initial value was set by the method described above. . Specifically, the initial values of a (j) and b2 (j) are shown in FIG. 8 and FIG. 9 and Table 2 and the assumption that α = 0.5 are shown in Table 3 for the part with a nominal film thickness of 200 nm as shown in Table 3. Table 5 and the assumption that α = 0.5 are obtained as shown in Table 5 for the part where the nominal film thickness is 300 nm.

  The estimated values of the unknown parameters finally obtained are as shown in Table 6 for the part with the nominal film thickness of 200 nm and as shown in Table 7 for the part with the nominal film thickness of 300 nm.

The film thickness obtained using the estimated value of the parameter is such that the pixel-height conversion count Δ is obtained as Δ = λ (3) / 2 × f (3) = 6.12 (nm), and the film thickness t = ( x1−x2) absolute value × Δ / n, and the refractive index of the silicon oxide film is 1.46. Therefore, the nominal value is 205 nm at the nominal film thickness of 200 nm, and the nominal value is 293 nm at the nominal film thickness of 300 nm. A value close to was obtained.

  According to the present invention, the present invention relates to a surface shape and a film thickness measuring method for measuring an uneven shape and a thickness of a measurement target surface covered with a transparent film, and in particular, non-contact using a plurality of monochromatic lights (three or more wavelengths). Thus, the height of the surface of the transparent film on the measurement object, the height of the surface of the measurement object, and the film thickness of the transparent film can be measured. In particular, even when there are many unknown parameters that have not been specified, it is possible to efficiently perform measurement at the nm level by appropriately setting initial values.

DESCRIPTION OF SYMBOLS 1 Optical system unit 2 Control system unit 10 White light source 11 Collimating lens 12 Band pass filter 13 Half mirror 14 Objective lens 15, 15A Reference surface 16 Beam splitter 17 Imaging lens 18 Imaging device 20 CPU
21 Memory 22 Input Unit 23 Monitor 24 Drive Unit 30 Measurement Object 30A Measurement Object Surface 31 Transparent Film 31A Transparent Film Surface

Claims (6)

By irradiating illumination light to the measurement object surface and the reference surface of the measurement object covered with the transparent film, the distance between the measurement object surface and the reference surface is changed to change the measurement object surface and the reference surface. The interference light is reflected by the reflected light and returned from the same optical path to cause a change in the interference fringe. Based on the intensity value of the interference light at this time, the height of the transparent film surface at the specific location of the measurement object, the height of the measurement object surface In the method for measuring the film shape of a thin film for obtaining at least one of the thickness of the transparent film,
Illumination light includes a plurality of single wavelengths of three or more wavelengths , changes the optical path difference between the surface of the measurement object having a transparent film and the reference surface, captures interference images by reflected light from both surfaces, and obtains interference A model function is applied to the luminance signal to obtain the height of the transparent film surface, the height of the surface of the measurement object, and the film thickness of the transparent film ,
The model function is a sum of an interference signal due to reflection on the reference surface and reflection on the transparent film surface, and an interference signal model due to reflection on the reference surface and reflection on the surface of the measurement object,

Here, g (i, j) is a model function value of data number i and wavelength number j, a (j) is a direct current component (= average value ) of wavelength number j , and b ₁ (j) is transparent of wavelength number j. The amplitude of the film surface luminance AC component, b ₂ (j) is the amplitude of the surface luminance AC component of the measurement object having wavelength number j, λ (j) is the wavelength of wavelength number j, and z (i) is the height of data number i. , Z ₁ is the surface height of the transparent film, z ₂ is the height of the surface of the measurement object,
The film shape measuring method of the thin film characterized by expressing as follows. 2. The thin film shape measuring method according to claim 1 , wherein the amplitude ratio between the amplitude of the transparent film surface luminance AC component and the amplitude of the measurement object surface luminance AC component is a constant common to each wavelength used for measurement. A method for measuring a film shape of a thin film, characterized by assuming. In the film shape measuring method of the thin film according to claim 1 or 2 , as an approach when the fit is performed, an evaluation function (a square error between an actual measurement value and a model function value at a sample point) is F,


Here, g (i, j) and gi, j are the model function value and observation luminance value of data number i and wavelength number j, M is the number of wavelengths used, N is the number of observation data,
A method for measuring a film shape of a thin film, wherein a least square method for minimizing F is used. By irradiating illumination light to the measurement object surface and the reference surface of the measurement object covered with the transparent film, the distance between the measurement object surface and the reference surface is changed to change the measurement object surface and the reference surface. The interference light is reflected by the reflected light and returned from the same optical path to cause a change in the interference fringe. Based on the intensity value of the interference light at this time, the height of the transparent film surface at the specific location of the measurement object, In the method for measuring the film shape of a thin film for obtaining at least one of the thickness of the transparent film,
Illumination light includes a plurality of single wavelengths of three or more wavelengths, changes the optical path difference between the surface of the measurement object having a transparent film and the reference surface, captures interference images by reflected light from both surfaces, and obtains interference A model function is applied to the luminance signal to obtain the height of the transparent film surface, the height of the surface of the measurement object, and the film thickness of the transparent film,
When the height of the surface of the measurement object is uniform in at least one direction and the surface height of the transparent film is uniform in at least the one direction, the distance between the surface of the measurement object and the reference surface is determined in the one direction. The reference plane is tilted so as to vary spatially, and an interference fringe is generated in the one direction by reflected light that is reflected from the surface of the measurement object and the reference plane and returns on the same optical path. A change in the orthogonal direction is captured as an interference image, and a model function is applied to the obtained interference luminance signal to obtain the height of the transparent film surface, the height of the surface of the measurement object, and the film thickness of the transparent film, A method for measuring a film shape of a thin film, characterized by obtaining a distribution in a direction orthogonal to the one direction ,
The model function is a sum of an interference signal due to reflection on the reference surface and reflection on the transparent film surface, and an interference signal model due to reflection on the reference surface and reflection on the surface of the measurement object,

Here, g (i, j) is a model function value of data number i and wavelength number j, a (j) is a direct current component (= average value ) of wavelength number j , and b ₁ (j) is transparent of wavelength number j. The amplitude of the film surface brightness alternating current component, b ₂ (j) is the amplitude of the surface brightness alternating current component of the wavelength number j, f (j) is the spatial frequency of the stripe of wavelength number j, and x (i) is the data number i. A film shape measuring method for a thin film , wherein x ₁ is a transparent film surface peak position, and x ₂ is a measurement object surface peak position. 5. The thin film film shape measuring method according to claim 4 , wherein the amplitude ratio of the amplitude of the transparent film surface luminance AC component and the amplitude of the measurement object surface luminance AC component is a constant common to each wavelength used for measurement. A method for measuring a film shape of a thin film, characterized by assuming. In the film shape measuring method for a thin film according to any one of claims 4 and 5 , an evaluation function (a square error between an actual measurement value and a model function value at a sample point) is set as F as a method for the adaptation.


Here, g (i, j) and gi, j are the model function value and observation luminance value of data number i and wavelength number j, M is the number of wavelengths used, N is the number of observation data,
A method for measuring a film shape of a thin film, wherein a least square method for minimizing F is used.