JP2529901B2 - Phase shift Fize-interferometer error correction method - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of correcting an error in a phase shift Fizeau interferometer, and more particularly to a method of correcting an error due to repeated reflection between a reference mirror and a sample surface to be tested.

[0002]

2. Description of the Related Art An interference microscope using a phase-shifting interferometric method has been attracting attention for non-contact measurement of a fine surface shape of an object to be measured. This phase shift Fizeau interferometer 1
As for 0, as shown in FIG. 5, the light emitted from the light source 12 is reflected downward in the figure by the beam splitter 14, a part of which is reflected by the reference mirror 16, and further the reference mirror 1
The light transmitted through 6 is reflected by the test sample 18. And
The reflected light from the reference mirror 16 and the reflected light from the test sample 18 are combined to generate interference light. Therefore, a phase shift is introduced into the interferometer to derive interference fringes, and the interference fringes at that time are detected by the camera 20 to obtain information on the surface shape of the sample.

In this phase shift interferometer, a four-point method phase derivation algorithm is often used to obtain information on the surface shape. The four-point method phase derivation algorithm is
In this method, one cycle of the interference fringes is divided into four, a phase shift of π / 2 is given to shift the interference fringes, and the phase is calculated from the data of the four interference fringes. That is, the test sample surface 18
If the reflectance of the reference mirror 16 is low and the influence of repeated reflection of the second or higher order can be ignored, the intensity distribution of the interference fringes on the image plane can be expressed by the following mathematical expression 1.

[0004]

## EQU1 ## I (x, y) = a (x, y) + b (x, y) cos {φ (x, y)} where φ (x, y) is 2π · ω (x, y) / Λ, and ω (x, y)
Is the height distribution of the surface to be inspected. Therefore, by obtaining this ω (x, y), the surface information of the test sample can be obtained. Further, a (x, y) and b (x, y) can be considered as constants at specific points on the surface to be inspected. Therefore, if the phase shift Δφ is introduced by some method, the above equation 1 can be replaced by the following equation 2.

[0005]

## EQU00002 ## I (x, y, .DELTA..phi.) = A (x, y) + b (x, y) cos {.phi. (X, y + .DELTA..phi.)} Then, .DELTA..phi. Is 0, .pi. / 2, .pi., 3.pi. By varying the intensity distributions I ₁ , I ₂ , I ₃ , and I ₄ by changing it to / 2, φ (x, y) can be obtained by the following equation 3.

[0006]

Φ (x, y) = tan ⁻¹ {(I ₄ −I ₂ ) / (I ₁ −I ₃ )} From this φ (x, y), information on the surface to be inspected is obtained.

[0007]

However, in the phase shift interferometer 10, an error caused by repeated reflection actually occurs between the reference mirror 16 and the sample 18 to be tested. That is, as shown in the enlarged view of FIG. 6, multiple reflections of the incident light L occur between the reference mirror 16 and the sample to be measured 18, and the reflected lights L ₁ , L ₂ , L ₃ ... It becomes.

As a method of reducing the influence of the repetitive reflection of the Fizeau interferometer, a method of inserting an attenuator between the reference mirror of the interferometer and the sample to be examined and absorbing the light passing therethrough can be considered. However, there are problems that the attenuator is expensive and easily broken, and that an installation space is required.

A method of coating the reference mirror with an absorption film to absorb the light reflected repeatedly can be considered. However, this method has a problem that the repeated reflection cannot be completely removed.

The present invention has been made in view of the above problems of the prior art, and an object thereof is to provide an error correction method for a phase shift Fizeau interferometer capable of reducing an error caused by repeated reflection.

[0011]

In order to achieve the above object, a phase shift Fizeau interferometer according to the present invention calculates a phase error by averaging the results of two measurements with the initial phase shifted by π / 4. To remove. That is, in the correction method of the phase shift interferometer of the present application, the initial phase is π / 4.
It is characterized in that the four times of the four interference fringe data which are shifted are collected, and the surface information of the test sample is obtained from the average of the test phases obtained from the respective four interference fringe data.

[0012]

The present inventors analyzed the error of the phase shift Fizeau interferometer as follows. That is, the intensity distribution of the interference fringes when the repeated reflection is taken into consideration is as shown in the following Expression 4.

[0013]

## EQU00004 ## I = 1-b / {1-c.cos (.PHI. / 4)} Note that b and c depend only on the reflectance of the reference mirror and the sample to be inspected. As shown in.

[0014]

B = (1-r ₁ ² ) (1-r ₀ ² ) / (1 + r ₁ ² r ₂ ² ) r ₀ : Amplitude reflectance of light at the interface between glass and film r ₁ : Film and air Amplitude reflectance of light at the boundary surface of the surface r ₂ : Amplitude reflectance of light due to the surface of the test sample

[0015]

[6] _{c = 2r 1 r 2 / (} 1 + r 1 2 · r 2 2) In Equation 6, the phase shift Δφ = 0, π / 2, π, 3π
If / 2 is given, the intensity distributions of the corresponding interference fringes are

[0016]

Equation 7] _{I 1 = 1-b / (} 1-c · cosφ) I 2 = 1-b / {1-c · cos (φ + π / 2)} = 1
−b / (1 + c · sin φ) I ₃ = 1−b / {1-c · cos (φ + π)} = 1−b
/ (1 + c · cos φ) I ₄ = 1−b / {1-c · cos (φ + 3π / 2)} =
It becomes 1-b / (1-c · sin φ). Using the phase calculation algorithm of Equation 3 above,

[0017]

[Equation 8] I ₄ −I ₂ = 2bc · sin φ / (1−c ² sin ² φ) I ₃ −I ₁ = 2bc · cos φ / (1−c ² cos ² φ) From this equation 8, the phase φ ′ can be calculated as follows.

[0018]

Tan φ '= (I ₄ -I ₂ ) / (I ₃ -I ₁ ) = tan φ- (1-c ² cos ² φ) / (1-c ² sin ² φ) = tan φ + tan φ {(-c from ^{2 cos2φ) / (1-c} 2 sin 2 φ)} the number 9

[0019]

Tanφ′−tanφ = −c ² tanφ {cos2φ / (1-c ² sin ² φ)} Therefore, when the error is small and φ ′ and φ are close to each other,

[0020]

Equation 11] sin (φ'-φ) ≒ -c 2/2 · sin2φ · cos2φ / (1-c 2 sin 2 φ) = -c 2/4 · sin4φ / (1-c 2 sin 2 φ) becomes , further the reflectance of the reference mirror and the test sample surface is small, when _{r 1, r 2 << 1,} c << 1, the error epsilon is a ^{ε = φ'-φ ≒ -c 2} /4 · sin4φ Become. This is a sine function having a period four times as large as the phase to be detected, and is as shown in FIG. The intensity reflectance of the reference mirror in FIG. 7 is 25%, and the reflectance R ₂ of the test sample surface is 4%, 50% and 90%.

The present inventors have completed the present invention in view of the characteristics of such an error. That is, when calculated by the four-point method, the error changes in a cycle of four times the phase to be measured, and this error is calculated by taking the average value of two measurements with an initial phase shift of π / 4. I decided to remove it.

[0022]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows the basic configuration of a phase shift micro Fizeau interferometer according to an embodiment of the present invention.
In addition, the part corresponding to the related art shown in FIG.
0 is added and shown, and the description is omitted.

An interferometer 110 shown in FIG. 1 includes a light source 112 made of a red semiconductor laser and a beam splitter 114.
And a reference mirror 116. Then, the light source 112
The laser light emitted from the laser beam is collimated by the collimator lens 122 and is incident on the beam splitter 114 via the lenses 124, 126 and 128. The light reflected downward in the figure by the beam splitter 114 is collimated again by the objective lens 130, and further ¼
It becomes circularly polarized light at the wave plate 132. Then, the circularly polarized light illuminates the reference mirror 116, a part of the light is reflected on the surface of the reference mirror 116, and the light transmitted through the reference mirror 116 is reflected by the test sample 118. As a result,
The light reflected on the surface of the reference mirror 116 and the test sample 11
The light reflected at 8 is again superimposed by the reference mirror 116 to form coherent light. And again lens 1
30 and the beam splitter 114, and is guided upward in the figure. This light is imaged on the light receiving surface of the CCD camera 120 by the imaging lens 136.

The observation result by the camera 120 is displayed on the monitor 14.
0 and the frame memory 142
The data is stored in the memory, is subjected to desired data processing by the microcomputer 144, and is output to the XY plotter 146.

In this embodiment, the injection current control command from the microcomputer 144 is given to the injection current control means 150 via the interface 148 so that the injection power to the semiconductor laser 112 can be changed.
The temperature control means 152 controls the temperature of the semiconductor laser 112 to be constant.

That is, as the injection current i of the semiconductor laser increases, the wavelength λ increases in proportion to the increase of the injection current i.
Has a linear region of increasing. In this embodiment,
Surface information is obtained by utilizing this characteristic property of the semiconductor laser.

Equation 1 can be rewritten as follows using the wavelength λ as a parameter.

## EQU12 ## I (x, y, λ) = a (x, y) + b (x, y) cos [{2π · 2ω (x, y) + L} / λ ₀ −Δφ] Then, the Δφ is changed. Then, I _{1 to} I ₄ are obtained. Note that L is the optical path length difference between the reference mirror 116 and the surface of the sample 118 to be tested. Here, when the injection current of the semiconductor laser 112 is changed, not only the oscillation wavelength but also the laser intensity is changed. Therefore, the laser intensity is monitored and the intensity of the interference fringes is normalized, or the optical path difference of the interferometer is increased. The change in injection current required to obtain the required phase difference is minimized and the change in laser output is minimized. As a result, even when the laser wavelength is deviated as in the present invention, the bias a and the amplitude b of the intensity distribution of the interference fringes of the equation 12 can be regarded as constant.

On the other hand, when the injection current i is changed and the oscillation wavelength is changed from λ ₁ to λ ₂ , the phases can be displayed as follows. λ ₁ : φ ₁ = 2π · (L / 2 × 2) / λ ₁ = 2πL / λ ₁ λ ₂ : φ ₂ = 2π · (L / 2 × 2) / λ ₂ = 2πL / λ ₂ Therefore, the phase difference the _{Δφ = φ 2 -φ 1 = 2πLΔλ} / λ 1 2. Therefore, it can be expressed as Δφ = 2πLΔλ / λ ² . That is, Δφ = 2πLΔλ / λ ² = 0 Δφ = 2πL Δλ / λ ² = π / 2 Δφ = 2πL Δλ / λ ² = π Δφ = 2πL Δλ / λ ² = 3π / 2 The injection current i is changed. I ₁ ,
All that is required is to obtain I ₂ , I ₃ , and I ₄ .

By the way, since the change amount Δλ of the wavelength is proportional to the change Δi of the injection current, Δλ = α · Δi, that is, 2πLΔλ / λ ² = 2πLαΔi / λ ² = 2π, for example, Δi = λ ² / Lα. In the case of a general red laser, 670 at 20 ° C
Since α = 0.017 nm / mA with respect to the reference wavelength of nm, if L = 24 mm, the change in current required for a change of 2π is Δi (mA) = (670 × 10 ⁻³ ) ² / (24 × 0.017) = 1.100 mA.

Therefore, the injection currents of π / 2, π and 3π / 2 are 0.275 mA, 0.550 mA and 0.82, respectively.
It only has to change by 5mA. Since the linear region of the semiconductor laser is about 10 mA, it is easy to change the current to this extent. As described above, in the present embodiment, since the desired phase difference is obtained by controlling the injection current to the semiconductor laser 112, extremely accurate phase control is possible.

The characteristic feature of the present invention is that when calculated by the four-point method phase derivation algorithm, the error changes in a cycle of four times the phase to be detected, and the error is two times with an initial phase shift of π / 4. This error is eliminated by taking the average value of the measurement of. That is, FIG. 2 shows a flowchart of the error correction method according to the embodiment of the present invention. As is clear from the figure, upon the start of measurement, the initial phase is set to 0, a 90 ° phase shift is applied, the interference fringe data is taken in, and this scanning is repeated four times to obtain I _{1 to} I ₄ .

Next, the initial phase is set to 45 °, a phase shift of 90 ° is given to take in interference fringes, and this scanning is repeated four times to obtain I _{5 to} I ₈ . Then, based on the above I _{1 to} I ₄ ,

[0033]

Φ ₁ = tan ⁻¹ {(I ₃ −I ₁ ) / (I ₄ −I ₂ )} is calculated. Next, based on I _{5 to} I ₈ above,

[0034]

## EQU14 ## Φ ₂ = tan ⁻¹ {(I ₇ −I ₅ ) / (I ₈ −I ₆ )} − π / 4 is calculated. Then, the average of the obtained Φ ₁ and Φ ₂ is obtained. Φ = (Φ ₁ + Φ ₂ ) / 2

As a result, as shown in FIG. 3, when Φ ₁ has the error characteristic as shown by the solid line in the figure, Φ ₂ has the error characteristic as shown by the dotted line in the figure, and the average value of both is shown. Just cancels the error of Φ ₁ and Φ ₂ .
In this embodiment, the shift state has to be returned after measuring I ₄ , but it has an advantage that it can be easily applied to the phase shift interferometer currently implemented.

FIG. 4 shows a flow chart of the error correction method according to the second embodiment of the present invention. In the present embodiment, the measurement is performed by giving a phase shift of 45 ° at the same time as the measurement is started, and I ₁ , I ₅ , I ₂ , I ₆ , I ₃ , I ₇ , I and I are measured.
Data is obtained in the order of ₄ and I ₈ . And the above number 1
3, Φ ₁ and Φ ₂ are obtained by using Equation 14, and the average of both is obtained. In this embodiment, since the phase data is continuously obtained from the beginning, there is an advantage that it is not necessary to return the shift state.

As described above, according to the phase shift interferometer according to each of the above-described embodiments, the four-point method is performed twice by shifting the phase by π / 4, and the two are averaged.
It is possible to obtain accurate surface information of the test sample without adding a special configuration to the conventional device.

Further, according to the micro Fizeau interferometer of the present embodiment, since there is no mechanically movable part such as a piezo element, the system is stabilized, and even if the measurement is shifted by π / 4 phase, it is extremely high. It can be dealt with accurately. still,
In the present embodiment, the method of controlling the injection current to the semiconductor laser is used to give the phase shift, but by the method of moving the reference mirror using a piezo element or the like as in a general phase shift interferometer. Good.

[0039]

As described above, according to the phase shift micro Fizeau interferometer according to the present invention, the four-point method can
Since it is performed twice with four phases shifted and the average of both is taken, surface information with less error can be obtained with a simple configuration.

[Brief description of drawings]

FIG. 1 is a structural explanatory view of a phase shift Fizeau interferometer according to an embodiment of the present invention.

FIG. 2 is a flowchart showing the schematic steps of the correction method according to the first embodiment of the present invention.

FIG. 3 is an explanatory diagram of an operation of the correction method according to the first embodiment.

FIG. 4 is a flowchart showing a schematic process of a correction method according to a second embodiment of the present invention.

FIG. 5 is an explanatory diagram of a general phase shift interferometer.

FIG. 6,

FIG. 7 is an explanatory diagram of a problem of the conventional phase shift interferometer.

[Explanation of symbols]

 12,112 Semiconductor laser 16,116 Reference mirror 18,118 Test sample

 ─────────────────────────────────────────────────── ─── Continuation of front page (56) References JP-A-2-198307 (JP, A) JP-A-3-156304 (JP, A)

Claims (1)

(57) [Claims] 1. A reference mirror that reflects a part of the light emitted from a light source, a test sample that reflects another part of the light emitted from the light source, a reflected light from the reference mirror, and the sample. Surface information of the sample to be inspected by deriving a to-be-inspected phase from four interference fringe data whose phases are shifted by π / 2 of the interference fringes. In the phase shift Fizeau interferometer to obtain
Phase shift characterized in that the surface information of the sample to be tested is obtained from the average of the test phases obtained from each of the four interference fringe data, by collecting the data of four degrees of interference fringes with the initial phase shifted by π / 4. Fizeau interferometer error correction method.