JP4613310B2 - Surface shape measuring device - Google Patents

Description

  The present invention relates to object surface shape measurement, and relates to obtaining a surface shape by scanning an object surface based on a difference in height between a plurality of measurement points.

There is a strong demand for precise measurement of the surface shape of large industrial products such as silicon wafers, optical flats, and grazing incidence mirrors for synchrotrons. The size of the silicon wafer is currently increased to 300 mm in diameter, and the length of the grazing incidence mirror has reached 1 m or more.
A commonly used optical device for measuring the shape of a surface is a Fizeau interferometer. The Fizeau interferometer determines the cross-sectional difference between a test surface (surface under test: SUT) and a reference optical flat (ROF) by analyzing an interference fringe pattern. However, some Fizzo interferometers have ROFs with a cross-sectional uncertainty (surface accuracy) of less than λ / 100 (eg, 6.33 nm accuracy when λ is 633 nm), but commercially available The uncertainty of a typical ROF provided in available equipment is on the order of λ / 20 (also 31.65 nm accuracy). The maximum size of ROF is currently 350 mm in diameter. Thus, the size and accuracy of the ROF limits the size of the SUT and the accuracy of the measurement.

The Fizeau interferometer requires a rigid and stable structure to prevent undesired effects due to mechanical vibration. For this reason, the optical path is aligned with a common axial direction, but the SUT and the ROF are installed independently. The Fizeau interferometer can measure all SUTs simultaneously, but the measurement sensitivity is fringe pattern analysis such as phase shift method (sometimes called fringe scan method). ) Method and Fourier transform method. The measurement sensitivity by the phase shift method is reported as λ / 100.
A long trace profiler (LTP) has been developed for large size measurements such as a grazing incidence mirror. This measuring instrument scans with a single beam that irradiates the SUT, and measures the tilted cross section based on the angular position conversion of the Fourier transform lens. It has recently been reported that a 500 mm long mirror has been measured with a standard deviation of 4.6 nm by controlling the temperature within ± 0.1 degrees Celsius.

One of the methods for solving the above-mentioned problems inherent to the Fizeau interferometer is a shared interferometry. This is because ROF is not necessary. The shared interferometer uses two probe beams shifted in the lateral direction, and measures the difference in surface shape from the interference signals of these beams. This type of interferometer can use heterodyne detection technology. This detection technique can obtain a sensitivity that is one digit higher than that of the phase stripe pattern analysis. However, in order to obtain all surface shapes, mechanical scanning with respect to the SUT is necessary, and the influence of the tilt of the scanning stage covers small variations in the surface shape. For this reason, the surface shape of the sub-nanometer has not yet been obtained by the conventional shared interference method.
As an example of the shared interferometry, a shared heterodyne interferometer is calibrated by placing one sensor at the center and rotating another sensor around it to increase the robustness to the environment. (Refer nonpatent literature 1). However, when rotating 360 degrees for calibration, it is not a condition to return to the same point (the loop at the time of calibration is not completely closed). The accuracy of is not obtained.
In addition, this is a shared interferometer that measures linearity and flatness with nanometer to sub-nanometer accuracy, and it separates the orthogonal dual-frequency laser light into two parallel light beams and configures a heterodyne shared interferometer for each light beam. In addition, there are those in which two interferometers are arranged so that one arm of each interferometer overlaps on the sample surface (see Non-Patent Document 3 and Patent Document 1). As a result, the two shearing interferometers illuminate three equally spaced points on a straight line on the sample plane, and measure the difference in height between the two points. The error due to the tilt of the sample surface can be corrected. This is characterized by three equally spaced points on a straight line.
There is also a three-point shearing heterodyne interferometer that measures flatness with sensitivity from nanometers to sub-nanometers by running an arc or spiral curve (see Patent Document 2). In this configuration, the orthogonal dual-frequency laser beam is divided into two optical paths, an optical rotation element and an element that splits the polarized light in two traveling directions are provided in each optical path, and two sets of polarizations of the two optical paths that have passed through the element. Are combined to form three luminous fluxes, and the direction of polarization of the three luminous fluxes is controlled by changing the direction of polarized light passing through the element, so that three points are placed on an arbitrary curve.
Combining two sets of shearing interferometers using orthogonal dual-frequency lasers as light sources so that one of the two beams coincides to form a shearing interferometer consisting of three points, measuring the difference between the three points, that is, the two optical paths, and measuring surface The error accompanying the movement of the unevenness and the side surface is measured simultaneously (see Patent Document 3). With this, it is possible to measure the degree of straightness and the unevenness of the surface along the curve with an accuracy of nanometer to subnanometer.
However, since these documents do not mention anything about the relative error between the two interferometers, the surface accuracy as described above remains.
Moreover, measuring the height difference of the measurement points to obtain the surface shape is well known not only by the optical interferometer described above, but also by a mechanical method using, for example, a capacitive displacement meter, Similar problems exist (see Non-Patent Document 2).
Gary E. Sommargren, "Optical heterodyne profilometry" Applied Optics Vol. 20, No. 4 pp.610-618 15 February 1981 Shiro Yamaguchi “Measurement of linear motion accuracy by the improved sequential three-point method” Journal of Precision Engineering, Vol. 59, No. 5, p. 71-76 (1993) T Yokoyama et. Al "Sub-nanometer double shearing heterodyne interferometry for profiling large scale planar surfaces", Measurement Science and Technology 15 (2004) 1-9 JP 2001-165640 A JP 2003-269910 A JP 2004-177392 A

  An object of the present invention is to provide a measurement by scanning in which a high resolution is achieved without being influenced by a relative error when a surface shape is obtained by measuring a height difference between measurement points.

In order to achieve the above object, the present invention provides a surface shape measuring apparatus for obtaining a surface shape of a sample by obtaining a difference in height between the sample and the sensor by a plurality of sensors, the surface shape measuring apparatus comprising: Laser light source having a frequency difference between polarizations by resonator mirror anisotropy, a splitter for extracting a reference beam from a beam of the light source, a photodiode for extracting a reference beat signal between polarizations from the reference beam, and the splitter From the parallel plate, the two parallel beams as two equally spaced beams, one of which is output so as to overlap, and 3 from the optical element. A photodiode that strikes one surface of the sample, reflects the reflected beam back into two beams through the optical element, and extracts a beat signal from the beam; and the reference A sample signal, two phase meters that receive two beat signals and take out a phase difference signal, and the sample is placed and moved relative to the three beams. A stage that performs scanning, and the scanning of the sample and the three beams is performed by measuring the phase difference signal N times at equal intervals and calculating the height difference ΔZ _A (i), _{ΔZ B (i) (i =} 0, ..., N) that returns to the starting point of scanning while storing a scanned closed to the end point of the starting point, the starting point and the end point at the same height Z ₀ Using a certain feature, the relative error between the two phase meters is obtained from the following equation (8) , and the relative error is calibrated to obtain the surface shape of the sample.

The surface shape measuring apparatus of the present invention can obtain a surface shape by performing a closed scan and calculating and removing it when the relative error scan is completed.
In addition, the double shared heterodyne interferometer can obtain a cross-section with sub-nanometer resolution without being affected by the relative error between the two interferometers by performing a closed scan. The double shared heterodyne interferometer of the present invention is composed of a pair of common optical path sharing interferometers. For this reason, the effects of mechanical vibration and temperature change are almost cancelled. Based on this optical configuration and heterodyne detection, the dual shared heterodyne interferometer according to the present invention realizes sub-nanometer order sensitivity and measurement that is safe against disturbance of the measurement environment.

In the embodiment of the present invention, an interferometric measurement method named double sharing heterodyne interferometry is used. This measurement method is composed of two heterodyne shared interferometers. Here, a test surface (surface under test: SUT) is irradiated at three points that are equidistant on the scan by a pair of shared interferometers, and the difference in height between two adjacent points is measured. The contribution of the scan stage tilt to the measured height difference can be offset because the relative error between the two interferometers is determined by the closed scan returning to the starting point. In this way, a cross-section of the SUT can be obtained by obtaining a secondary difference. In each shared interferometer, the two probe beams travel in an almost common optical path using an anisotropic uniaxial crystal (AUC) as a beam splitter. Due to the configuration of the common optical path, the effects of refractive index fluctuations due to mechanical vibrations and air turbulence are substantially offset. In addition, changes due to the temperature of the two shared interferometers are also offset by a suitable subtraction process.
Hereinafter, a double shared heterodyne interferometer configured by a pair of shared interferometers used in the embodiment will be described in detail.

An overview of the optical system is shown in FIG. The light source of the system is a frequency-stabilized transversal Zeeman He-Ne laser (λ = 633 nm) 110. The output power is 2 mW, and the beam diameter (peak intensity e ⁻² ) is 0.8 mm. The output light is linearly polarized light, and the polarization directions are orthogonal due to the Zeeman effect. The frequency difference between the two orthogonal lights due to the resonator mirror anisotropy is about 190 kHz.

After passing through a half wave plate (HWP) 112, half of the laser light is reflected by a beam splitter (BS) 114, and an orthogonal polarization field is combined with a polarizer (PL) 116, and a PID photodiode (PD) Detected at 118. The reference beat signal (frequency 190 kHz) is generated by the PD 118 according to the square law of the detector. The laser light transmitted through the BS 114 is divided into two parallel beams by a parallel plate 120. The spatial separation of the two beams is equal to the instrument sampling interval ΔX. These parallel beams are transmitted via other BSs. Each beam is an anisotropic uniaxial crystal (AUC) 136, and is further converted into normal light (ordinary ray) and non-normal light (extraordinary ray) (indicated by o and e in FIG. 1, respectively). Divided. The size of the AUC 136 is designed so that the separation distance between normal light and non-normal light is the same as ΔX. Since the optical axes of AUC and N are set in a plane including two incident parallel beams, the two pairs of normal light and non-normal light are in the same plane. Regular light from one input beam and non-regular light from another input beam are superimposed at the output end of the AUC 136. For this reason, the output of the AUC 136 is composed of three parallel beams. These three beams irradiate three points, X _n−1 , X _n , and X _{n + 1,} which are located at equal intervals on the scan on the SUT 138.

Since the HWP 112 rotates, one direction of the two orthogonal polarizations is in the plane containing N and the input beam. This realizes that one polarized light becomes regular light and the other polarized light becomes non-regular light. Thus, each pair of normal and non-normal light forms a shared interferometer heterodyne probe with a frequency difference of 190 kHz. The output beam of AUC 136 is reflected at SUT 138 and a pair of normal and non-normal light is again superimposed at the front end of AUC 136. Each superimposed beam includes two frequency components and carries interference information of two adjacent spots on the SUT 138. Thus, the optical configuration forms two heterodyne shared interferometers that measure the height difference between _Xn-1 and _Xn and between _Xn and _{Xn + 1} .

  After reflection by the BS 122, the two frequency components of each beam are combined by PLs 124 and 126, and a beat signal having a frequency of 190 kHz is generated and detected by avalanche photo diodes (APD) 128 and 130. The relative phase difference between the reference beat signal and these beat signals is measured by two phase meters (PMA and PMB) 132 and 134 and stored in a computer (not shown) for each ΔX operation of the scanning stage.

Ｘ_ｎ−１とＸ_ｎとの間及びＸ_ｎとＸ_ｎ＋１との間の、計測された高さの差は、それぞれΔＺ_Ａ（ｎ）とΔＺ_Ｂ（ｎ）と表される。走査ステージの傾きがΔＸに対してΔＴ_ｎのとき、計測された高さの差は、高さの差ΔＺ_ｎ−１及びΔＺ_ｎに加えて、ΔＴ_ｎを含む。そのため、ΔＺ_Ａ（ｎ）とΔＺ_Ｂ（ｎ）は、下に示すように表される。

ここで、式（２．２）に現れるΔＺ_ｅｒは、２つの独立した干渉計の間の相対的誤差を表している。この誤差は、初期段階の較正処理で導入される。
式（２．１）と（２．２）から、下に示すような再帰的な式が得られる。

そして、ΔＺ_ｎは下のように表される。

<Section acquisition>
As shown in FIG. 1, the samples at the heights at the positions X _n−1 , X _n and X _{n + 1} are Z _n−1 , Z _n and Z _{n + 1} , respectively. The height differences ΔZ _n−1 and ΔZ _n are defined as shown below.

The measured height differences between X _n−1 and X _n and between X _n and X _{n + 1} are denoted as ΔZ _A (n) and ΔZ _B (n), respectively. When the inclination of the scanning stage is [Delta] T _n with respect to [Delta] X, the difference between the measured height, in addition to the difference in height [Delta] Z _n-1 and [Delta] Z _n, including [Delta] T _n. Therefore, ΔZ _A (n) and ΔZ _B (n) are expressed as shown below.

Here, ΔZ _er appearing in Equation (2.2) represents a relative error between two independent interferometers. This error is introduced in the initial calibration process.
From equations (2.1) and (2.2), a recursive equation as shown below is obtained.

ΔZ _n is expressed as follows.

そして、Ｚ_ｎは式（４）と式（５）から求められる。Ｚ_ｎに対する最終表現は以下のようになる。

ステージの傾きΔＴ_ｎは、式（２．１）及び式（４）から求められる。

式（４）から式（７）において、Ｚ_０は点Ｘ_０における初期高さであり、ΔＺ_０は、Ｘ_０とＸ_１との初期高さの差である。断面の取得に関して、Ｚ_０およびΔＺ_０は、一般性を失わずにどんな値を選んでもよいことに留意されたい。これは、これらが高さと傾きの原点に過ぎないからである。また、相対誤差ΔＺ_ｅｒは、多項式における２次の偏り（式（６）参照）を断面Ｚ_ｎに与えることに注目されたい。また、相対誤差ΔＺ_ｅｒはステージ傾きΔＴ_ｎに対して、多項式における１次の偏り（式（７）参照）を与えている。 The sample height Z _n is given by equation (1.1) and is as follows:

And _Zn is calculated _| required from Formula (4) and Formula (5). The final expression for Z _n is as follows.

The stage inclination ΔT _n is obtained from the equations (2.1) and (4).

In the equations (4) to (7), Z ₀ is the initial height at the point X ₀ , and ΔZ ₀ is the difference between the initial heights of X ₀ and X ₁ . It should be noted that Z ₀ and ΔZ ₀ can be chosen any value without loss of generality for cross-section acquisition. This is because these are only the origin of height and tilt. Note also that the relative error ΔZ _er gives the section Z _{n a} quadratic bias in the polynomial (see equation (6)). Further, the relative error ΔZ _er gives a first-order bias in a polynomial (see Expression (7)) with respect to the stage inclination ΔT _n .

この式（８）を、そのときまでの計測された位相計から計測値であるΔＺ_Ａ（ｉ），ΔＺ_Ｂ（ｉ）（ｉ＝０，…，Ｎ）を用いて計算を行うことで、ΔＺ_ｅｒを計算できる。この計算で得られたΔＺ_ｅｒを用いて、式（６）から誤差を補正した高さＺ_ｎを得ることができる。また、式（７）から傾きΔＴ_ｎも求まることになる。
この操作により、原理的には光子雑音限界で決まる位相（表面変位）測定精度が達成できる。例えば、現在市販されている高性能なロックインアンプ（ＮＦ社製６５１０）を使用した場合の位相測定精度は０．１°であることから、光源波長λを６３３ｎｍとしたとき、約０．１ｎｍ（６３３ｎｍ／２×０．１°／３６０°＝０．０８７９≒０．１ｎｍ）の変位分解能が得られることを表している。
In order to determine the true value of ΔZ _er , it is necessary to compare the output signals of two independent interferometers using a perfectly flat plane. However, providing such a reference plane is not practical. For this reason, the present invention is characterized in that, in order to calculate the value of ΔZ _er , a closed scan that returns to the starting point is performed as a scan (closed loop method). For example, the stage is rotated and scanning is performed circumferentially. In this way, since the same point is returned in the equation (6), the heights of the starting point and the ending point are the same, and Z ₀ = Z _N ,

By calculating this equation (8) using ΔZ _A (i), ΔZ _B (i) (i = 0,..., N) that are measured values from the phase meter measured up to that time, ΔZ _er can be calculated. Using a [Delta] Z _er obtained by this calculation, it is possible to obtain the height Z _n obtained by correcting the error from the equation (6). Further, the slope ΔT _n is also obtained from the equation (7).
By this operation, phase (surface displacement) measurement accuracy determined in principle by the photon noise limit can be achieved. For example, when using a commercially available high-performance lock-in amplifier (NF10 6510), the phase measurement accuracy is 0.1 °. Therefore, when the light source wavelength λ is 633 nm, the phase measurement accuracy is about 0.1 nm. This indicates that a displacement resolution of (633 nm / 2 × 0.1 ° / 360 ° = 0.0879≈0.1 nm) can be obtained.

FIG. 2 is a diagram showing a result of simulating the assumed shape by circular measurement (circular scanning by the closed loop method). 2 is the sample shape (parabolic shape) assumed by “original”, “Zerr estimation” is the same method as in Non-Patent Document 3, and the sample is assumed to be flat on the average, and the least square method is used. It is a shape reproduction result when the relative phase Zer of the interferometer is estimated. It can be seen that this is far from the assumed sample shape. Also, “circumference measurement” is a plot in which Zer is calibrated on the spot by the closed loop method and the sample shape is reproduced with a slight shift. It can be seen that the assumed sample shape is reproduced. In addition, although the simulation which added the tilt fluctuation | variation to the stage which mounted the said assumption sample was also performed, the tilt fluctuation | variation was isolate | separated and the sample shape was not influenced.
<About closed scanning (closed loop method)>
Although the above-described scanning has been described by way of example as being performed circumferentially, the scanning is not limited to this, and any scanning may be used as long as the starting point and the end point of scanning coincide with each other. For example, the measurement may be performed by placing a sample on a two-axis turntable.
<Application to other measurement methods>
In the above-described embodiment, a double shared heterodyne interferometer is used. However, the measurement of the surface shape by the above-mentioned closed scanning (closed loop method) is applied to the case where the measurement point is scanned with respect to the sample and the surface shape is measured by the difference signal of the height of the measurement point at regular intervals. Is possible. For example, the present invention can also be applied to a measurement method known as a sequential three-point method (for example, see the above-mentioned Non-Patent Document 2 as a method using a capacitance displacement meter).

It is a figure which shows the structure of the double sharing interferometer of embodiment. It is a figure which shows the result of having simulated the assumed shape by the circumference measurement.

Claims (1)

Due to the resonator mirror anisotropy, a laser light source having a frequency difference between polarized light, and
A splitter for extracting a reference beam from the beam of the light source;
A photodiode for extracting a reference beat signal between polarizations from the reference beam;
A parallel plate that converts the beam from the splitter into two parallel beams;
An optical element that outputs the two parallel beams as two equally spaced beams, one of which overlaps,
A photodiode that impinges three beams from the optical element on the sample surface, makes the reflected beam again two beams through the optical element, and extracts a beat signal from the beam;
Two phase meters for inputting the reference beat signal and two beat signals to extract a phase difference signal;
A stage for placing the sample, moving relative to the three beams, and scanning the surface of the sample with the beams;
In the scanning of the sample and the three beams, the phase difference signal is measured N times at equal intervals, and the height difference ΔZ _A (i), ΔZ _B (i) (i = 0, ..., that return to the starting point of scanning while storing N), a scanning closed to the end point of the starting point,
Using the start point and the end point being the same height Z ₀ ,

From obtaining a relative error [Delta] Z _er between the two phases meter, characterized in that to obtain the surface shape of the sample to calibrate the relative error [Delta] Z _er, based on double shared heterodyne interferometer surface Shape measuring device.

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