Abstract:
To provide a technique that can measure a surface profile of any test object in a nondestructive manner and noncontact manner, highly accurately, and in a wide tilt angle dynamic range. In white light interference method using a dual beam interferometer, the technique is configured to be capable of changing a surface orientation of a standard plane with respect to an incident optical axis on the standard plane, acquires, while relatively changing the surface orientation of the standard plane with respect to a local surface orientation in any position on a test surface, a plurality of interferograms generated by interference of reflected light from the test surface and reflected light from the standard plane, and calculates the local surface orientation on the test surface from the interferograms to thereby measure a surface profile of the test surface.

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to a surface profile measurement method and a surface profile measurement device for measuring a surface profile of a three-dimensional object. For example, in particular, the present invention relates to a surface profile measurement method and a surface profile measurement device suitable for measuring an optical element, a reflective surface or a refractive surface of which consists of a curved surface, in a nondestructive manner and noncontact manner, highly accurately, and in a wide tilt angle dynamic range using light. 
       BACKGROUND ART 
       [0002]    As a technique for measuring a surface profile of a three-dimensional object in a nondestructive and noncontact manner and highly accurately using light, for example, as described in NPL 1 and U.S. Pat. No. 5,398,113 specification (publication) (PTL 1), there has been a technique for combining a light source, which emits white light, and a dual beam interferometer and detecting, with a two-dimensional image sensor, an interference figure (an interferogram) obtained by causing reflected light from a micro region on a sample surface and reflected light from a standard plane incorporated in the dual beam interferometer to interfere with each other through an objective lens to thereby measure a height distribution of the sample surface. In this technique, in each of pixels of the two-dimensional image sensor, the reflected light from the sample surface made incident to an effective light sensing area of the pixel and the reflected light from the standard plane cause interference. At least during surface profile measurement of the sample, a surface orientation of the standard plane is fixed and used without being configured to be changed with respect to an incident optical axis of the reflected light. Information concerning a tilt angle distribution of the sample surface is not directly measured. JP-A-2006-242853 (PTL 2) discloses a technique including a mechanism for, instead of setting a standard plane having high surface accuracy as a standard plane, setting, in a dual beam interferometer used in monochromatic interferometry, a reference object having a surface profile substantially equal to a surface profile of a sample and adjusting a surface orientation of the standard plane. 
         [0003]    On the other hand, as another conventional technique, for example, as described in pp. 306 to 307 of NPL 2, there is also a technique for measuring a tilt angle distribution on a sample surface using an autocollimator. In this technique, it is also possible to obtain a height distribution on the sample surface by integrating the tilt angle distribution. 
       CITATION LIST 
     Patent Literature 
       [0000]    
       
         PTL 1: U.S. Pat. No. 5,398,113 
         PTL 2: JP-A-2006-242853 
       
     
       Non Patent Literature 
       [0000]    
       
         NPL 1: “Advanced Metrology of Surface Texture by Scanning White Light Interferometry”, Atsushi SATO, The journal of the Surface Finishing Society of Japan, Vol. 57. No. 8, pp. 554 to 558, issued in 2006 
         NPL 2: “A survey on surface metrology for flatness standard”, Yohan KONDO, AIST bulletin of Metrology, Vol. 8, No. 3, pp. 299 to 310, issued in September 2011 
       
     
       SUMMARY OF INVENTION 
     Technical Problem  
       [0008]    In the surface profile measurement technique of the white light interference system described in U.S. Pat. No. 5,398,113 specification (publication) (PTL 1), wave fronts of the two reflected lights are parallel. That is, when an angle formed with respect to a surface orientation in a measured region corresponding to the pixel on the sample surface and an incident optical axis on the measured region and an angle formed by a surface orientation of the standard plane and an incident optical axis on the standard plane are the same, since an optical path difference between the two reflected lights is equal irrespective of a place in the pixel, a uniform interference effect is obtained. However, when the two wave fronts are not parallel and tilt at a certain angle each other, since the optical path difference changes between the two reflected lights according to a place in the pixel, the interference effect is not uniform. When a difference between optical path differences in the pixel is equal to or larger than an illumination wavelength, since the interference effect is cancelled by averaging, a surface profile cannot be measured. Further, to enable detection at a sufficient S/N without attenuating the interference effect, the difference between the optical path differences in the pixel needs to be kept within approximately a half of the illumination wavelength. In the technique, at least during surface profile measurement of the sample, the surface orientation of the standard plane is fixed and used without being configured to change with respect to the incident optical axis of the reflected light. Therefore, when the surface orientation in the measured region on the sample surface changes, a situation in which the interference effect is attenuated occurs in this way. 
         [0009]    The width of each of the pixels is represented as d, a point image width of the objective lens is represented as d′, the illumination wavelength is represented as λ, and a difference between the angle formed with respect to the surface orientation in the measured region corresponding to the pixel on the sample surface and the incident optical axis on the measured region and the angle formed by the surface orientation of the standard plane and the incident optical axis on the standard plane is represented as θ. The point image width d′ indicates width from a foot on one side where the intensity of a point spread function of the objective lens is sufficiently small to a foot on the other side. In this case, d′ is approximately 1.6 times as large as a Rayleigh limit often used in general as a resolution limit. If d is larger than d′, when d·tan 2θ≧λ/2 Expression 1, attenuation of the interference effect occurs. If d is smaller than d′, replacing d of Expression 1 with d′, when d′·tan 2θ≧λ/2 Expression 2, attenuation of the interference effect occurs. In both the cases, to prevent the interference effect from being attenuated, the expression has to be d·tan 2θ≧λ/2 Expression 3. When θ exceeds a range in which Expression 3 is satisfied, surface profile measurement is difficult. When visible light is used as the illumination light, the center wavelength of the visible light is approximately λ=600 nm. In an objective lens having a large working distance suitable for the surface profile measurement, since a numerical aperture (NA) is as large as approximately NA=0.55, d′ is equal to or larger than approximately 1.06 micrometers. At this point, when the inclination angle of the sample surface increases and θ≧7.9°, Expression 3 is not satisfied. The surface profile measurement making use of the interference effect is difficult. 
         [0010]    On the other hand, the technique disclosed in JP-A-2006-242853 (Patent Literature 2) includes a mechanism for adjusting the surface orientation of the standard plane. It is taken into account that the interference effect in a place with a large inclination angle on the sample surface is secured. However, the mechanism is used to optimize, on the entire sample surface, alignment between an optical axis in the dual beam interferometer and optical elements before height distribution measurement of the sample is started. The technique is based on the premise that the sample surface and the standard plane have substantially equal surface profile distributions. Therefore, a situation in which the surface geometries of the sample surface and the standard plane are locally different is not taken into account. The alignment is only performed for the entire sample surface. Therefore, in the technique, the height distribution itself of the sample surface cannot be directly obtained. Only a distribution of a deviation of the height of the sample surface with respect to a height distribution of the reference object surface set as the standard plane can be measured. A technique for measuring information concerning the tilt angle distribution of the sample surface is not included either. In this way, in the technique, a surface profile of a sample having any surface profile cannot be measured. 
         [0011]    On the other hand, in the surface profile measurement technique for measuring a tilt angle distribution of a sample surface using the autocollimator described in pp. 306 to 307 of NPL 2, a measurement range of a high-precision autocollimator is approximately ± several ten seconds to ± several hundred seconds. A surface profile set as a measurement target is limited to a plane or a gentle curved surface. When the inclination angle of the sample surface increases, surface profile measurement is difficult. 
         [0012]    The present invention has been devised in view of the above and it is an object of the present invention to provide a technique that can measure a surface profile of any test object in a nondestructive manner and noncontact manner, highly accurately, and in a wide tilt angle dynamic range. 
       Solution to Problem 
       [0013]    In order to attain the object, the present invention provides, in white light interference method using a dual beam interferometer, a technique for configuring a surface orientation of a standard plane to be changed with respect to an incident optical axis on the standard plane, acquiring, while relatively changing the surface orientation of the standard plane with respect to a local surface orientation in any position on a test surface, a plurality of interferograms generated by interference of reflected light from the test surface and reflected light from the standard plane, and calculating the local surface orientation on the test surface from the interferograms to thereby measure a surface profile of the test surface. 
       Advantageous Effect of Invention 
       [0014]    In the present invention, it is possible to not only measure a surface profile of any test object in a nondestructive and noncontact manner using light but also measure the surface profile highly accurately and in a wide tilt angle dynamic range. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]      FIG. 1  is a diagram showing the configuration of a surface profile measurement device according to a first embodiment of the present invention. 
           [0016]      FIG. 2(   a ) is a diagram showing an example of an interferogram according to the first embodiment of the present invention (in the case of a monochromatic light source). 
           [0017]      FIG. 2(   b ) is a diagram showing an example of an interferogram according to the first embodiment of the present invention (in the case of a broad spectral band light source). 
           [0018]      FIG. 3  is a diagram showing an operation flow of the surface profile measurement device according to the first embodiment of the present invention. 
           [0019]      FIG. 4  is a diagram showing an effect at the time when a surface orientation of a standard plane is changed by the surface profile measurement device according to the first embodiment of the present invention. 
           [0020]      FIG. 5  is a diagram showing the configuration of a surface profile measurement device according to a second embodiment of the present invention. 
       
    
    
     DESCRIPTION OF EMBODIMENTS  
       [0021]    Embodiments of the present invention are explained below with reference to the drawings. 
       First Embodiment 
       [0022]      FIG. 1  is a diagram showing the configuration of a surface profile measurement device according to a first embodiment of the present invention. As a light source  1 , a broad spectral band light source that generates light having a continuous wavelength such as a halogen lamp, a Xe lamp, or an LED is used. A light beam emitted from the light source  1  changes to a parallel beam  30  through an illumination optical system  2  including a lens or a reflection mirror for condensing and light beam parallelization and is made incident on a beam splitter  4  in a dual beam interferometer  3 . The parallel beam  30  is divided into two light beams by the beam splitter  4 . One divided light beam is reflected after being made incident on an illumination region  41  on the surface of a sample  40  through a sample-side objective lens  5 , changes to a sample-side reflected light beam  31 , and returns to the beam splitter  4  through the sample-side objective lens  5  again. The sample  40  is mounted on a sample moving stage  11  and is movable in orthogonal two axial directions (an X axis and a Y axis) and an optical axis direction (a Z axis) with respect to an optical axis of the sample-side objective lens  5 . The X axis and the Y axis are used to move the position of the illumination region  41  on the sample  40 . An X-coordinate value and a Y-coordinate value are controlled by an X-Y driving/control unit  12 . The Z axis is driven by a piezo actuator  13  (not shown in the figure). A Z-coordinate value can be controlled by a Z-axis control unit  14  at resolution of approximately 1 nanometer. The other of the two light beams divided by the beam splitter  4  is made incident on a standard plane  7  through a reference-side objective lens  6  and thereafter changes to a reference-side reflected light beam  32  and returns to the beam splitter  4  through the reference-side objective lens  6  again. The sample-side objective lens  5  and the reference-side objective lens  6  are set such that distances from the beam splitter  4  are equal to each other. The standard plane  7  is set in a focusing position of the reference-side objective lens  6 . An inclination angle of the standard plane  7  can be changed with respect to two axes orthogonal to an optical axis and corresponding to X and Y axes of the sample moving stage  11  by a two-axis inclining mechanism  15 . In the following explanation, an inclination angle in a direction corresponding to the X axis is represented as θx and an inclination angle in a direction corresponding to the Y axis is represented as θy. θx and θy are respectively driven by piezo actuators  16  and  17  (not shown in the figure). Angle control can be performed by an inclination-angle control unit  18  at resolution of approximately 5 micro-radians. The sample-side reflected light beam  31  and the reference-side reflected light beam  32  returning to the beam splitter  4  in this way are wave-optically combined to generate an interference light beam  33 . After the interference light beam  33  is made incident on a focusing lens  8 , a part of the interference light beam  33  passes through a field stop  9  set on a focusing surface of the focusing lens. The focusing lens  8  is adjusted to focus an image of the illumination region  41  on the focusing surface in a state in which the illumination region  41  is placed in a focusing position of the sample-side objective lens  5 . The interference light beam  33  passed through the field stop  9  is lead to a photodetector  10 . The light intensity of the interference light beam  33  is converted into an electric signal. The interference light beam  33  changes to an interference light intensity signal  34 . The interference light intensity signal  34  is captured into the computer  21  through an A/D converter  20  and subjected to arithmetic processing. The computer  21  gives commands to the X-Y driving/control unit  12 , the Z-axis control unit  14 , and the inclination-angle control unit  18  and causes the units to change the X-coordinate value, the Y-coordinate value, the Z-coordinate value, and values of θx and θy. 
         [0023]    In general, the dual beam interferometer represented by a Michelson interferometer artificially gives a change in a phase difference to between divided light beams and thereafter recombines the light beams, causes the light beams to interfere, and records a change in interference light intensity involved in the change in the phase difference. Numerical value data of the change in the interference light intensity involved in the change in the phase difference, a figure obtained by graphing the numerical value data, or an optical image obtained by spatially generating the change in the interference light intensity as a light amount distribution of light and shade is called interferogram (interference figure). The phase difference depends on an optical path difference between optical paths of tracing of the two light beams from the division to the recombination, that is, a difference between optical lengths and the wavelength of light in use. In the optical system in this embodiment, the optical path difference between the two light beams is a difference of an optical path of the beam splitter  4 →the sample-side objective lens  5 →the illumination region  41  on the sample  40 →the sample-side objective lens  5 →the beam splitter  4 →and an optical length of an optical path of the beam splitter  4 →the reference-side objective lens  6 →the standard plane  7 →the reference-side objective lens  6 →the beam splitter  4 . When the phase difference is represented as φ radians, the optical path difference between the two divided light beams is represented as ΔL micrometers, and a wavelength in use is represented as λ micrometers, 
         [0000]      φ=2πΔ L/λ   Expression 4
 
         [0000]    is obtained. Therefore, the dual beam interferometer is often configured to place a reflection mirror in the optical path of one of the two light beams and translate the position of the reflection mirror to thereby change the optical length and record an interferogram. When a light source in use is a monochromatic light source that emits only light having a single wavelength, an equal interference light intensity change repeatedly occurs every time the optical path difference becomes twice as large as the wavelength of the light source. Therefore, an interferogram consisting of a single COS waveform shown in  FIG. 2   a  is obtained. On the other hand, when a broad spectral band light source that generates light having a continuous wavelength is used, interference between two light beams is so-called white light interference. It is well known that, as shown in  FIG. 2   b , light intensity takes a maximum value in an optical path difference (a zero optical path difference) at which phase differences are substantially zero in common at wavelengths included in the light source and a vibration waveform is observed only around the optical path difference. 
         [0024]    The operation of the computer  21  after the sample  40  is mounted on the sample moving stage  11  is explained using an operation flow in  FIG. 3 . Processing of the operation flow in  FIG. 3  is incorporated in the computer  21  as an inclination-angle measuring function  50 . 
         [0025]    In this embodiment, as shown in Step  9  to Step  12 , the computer  21  gives a command to the Z-axis control unit  14  and causes the Z-axis control unit  14  to move the Z-coordinate value from a predetermined initial position to an end position and captures the interference light intensity signal  34  to thereby record one interferogram. The initial position and the end position are determined to include the zero optical path difference. The shape of the interferogram obtained at this point is generally as shown in  FIG. 2   b . An amount serving as an interference contrast C is defined. When a light source in use is a monochromatic light source, the interference contrast C is generally defined by the following expression. In the expression, the Z coordinate is changed to Z0, Z1, . . . , and Zn at a fixed interval, interference light intensity in Zi is represented as Ji, max{Ji} represents a maximum value among J0, J1, . . . , and Jn, and min{Ji} represents a minimum value. 
         [0000]        C =[max{ Ji }−min{ Ji }]/[max{ Ji }+min{ Ji}]   Expression 5
 
         [0000]    However, when a white light source is used, since the vibration waveform of the interference intensity is observed only around the zero optical path difference as shown in  FIG. 2   b  and an envelope of vibration is attenuated as the optical path difference is further away from the zero optical path difference, the definition by the above expression is inappropriate. Therefore, in the present invention, the interference contrast C is defined by the following expression when a z coordinate of a zero optical path difference position is represented as Zc, the vibration waveform of the interference intensity is observed in a range of Za to Zb, and an average of the interference intensity {Ji} in a range of a≦i≦b is represented as J0. 
         [0000]        b C =[{Σ( Ji−J 0)̂2}/( b−a+ 1)}]̂(½)/ J 0  i=a   Expression 6
 
         [0026]    Expression 6 is equal to a relative standard deviation of {Ji} in the range of a≦i≦b. The calculation of the interference contrast is performed in Step  13 . In this embodiment, as shown in Step  5  to Step  15 , the recording of one interferogram is performed every time the computer  21  gives a command to the inclination-angle control unit  18  and causes the inclination-angle control unit  18  to move θx and θy from predetermined initial positions to end positions by a predetermined pitch. 
         [0027]    A result of an actually performed test using a dual beam interferometer same as the configuration in this embodiment is shown in  FIG. 4 . In the test, as the sample  40 , a plane mirror  42 , to an optical axis of which a predetermined inclination angle was given in advance, was placed, an inclination angle of the standard plane  7  was changed, and a relation between the inclination angle of the standard plane  7  obtained at that point and the interference contrast C was checked. As a result of the test, it was confirmed that the interference contrast C was maximized when the inclination angle of the plane mirror  42  placed as the sample and the inclination angle of the standard plane  7  were equal to each other. In this test, as differences from the configuration in this embodiment, the field stop  9  was detachably attachable, a CCD camera was able to be placed instead of the field stop  9 , and an image formed when the interference light beam  33  was focused by the focusing lens  8  was able to be observed. As a result, it was found that, when the inclination angles of the plane mirror  42  and the standard plane  7  were different, interference fringes of light and shade appeared on an image acquired by the CCD camera, an interval of the interference fringes increased as the difference between the inclination angles decreased, and, when the inclination angles were equal and had no difference, the interference fringes were not observed. From the two test results, it is seen that, when the inclination angles of the plane mirror  42  and the standard plane  7  are equal, the optical path difference is equal in the entire region of the field stop  9  and the interference fringes of light and shade are not observed and, when the plane mirror  42  is moved in the optical axis direction, since all phases of light beams passing in the region uniformly change, the interference contrast C is maximized. In general, a surface profile of the sample  40  needs to be considered a non-plane. However, the surface profile in the illumination region  41  in a microscopic sense can be approximately regarded as being sufficiently a plane under an optical microscope. Therefore, from the test results, it is seen that an inclination angle of a local micro plane in the illumination region  41  on the sample  40  can be measured by detecting an inclination angle of the standard plane  7  at the time when the interference contrast Cis maximized. Even when the inclination angle of the plane mirror  42  increases, by also increasing the inclination angle of the standard plane  7  according to the increase in the inclination angle, the phases of the light beams passing in the region can be uniformly aligned and the interference contrast can be secured. 
         [0028]    Referring back to the operation flow in  FIG. 3 , in this embodiment, in Step  16 , a set of (θx, θy) for maximizing the interference contrast C is detected. In order to obtain a set of (θx, θy) serving as a solution at high accuracy, in Step  14  and Step  15 , it is necessary to set the pitch in moving θx and θy sufficiently fine. However, as shown in  FIG. 4 , the interference contrast C shows only an extremely gentle change with respect to a change in θx and θy near a maximum point of the interference contrast C. When a measurement result of the interference contrast C wavers because of superimposition of noise, a large error is caused. Therefore, in the present invention, in Step  16 , a predetermined fitting function F(θx, θy) is fit to numerical values of a plurality of interference contrasts C obtained in Step  5  to Step  15  by a method of least squares using a value of (θx, θy) corresponding to a vertex position as an unknown number. A set of (θx, θy) obtained as a most matching result is adopted as a solution. The set of (θx, θy) obtained at this point is measurement values of inclination angles in two axial directions of X-Y on the local micro plane in the illumination region  41  on the sample  40  mounted on the sample moving stage  11 . In order to obtain inclination angles for all surfaces on the sample  40 , as shown in Step  1  to Step  18 , the sample moving stage  11  is moved in the X-Y directions and the processing shown in Step  5  to Step  16  is repeated. In this way, in this embodiment, a tilt angle distribution (θx, θy) can be measured on the all the surfaces on the sample  40 . 
         [0029]    The inclination angles (θx, θy) in the two axial directions of X-Y on the local micro plane in the illumination region  41  on the sample  40  mounted on the sample moving stage  11  are differential values of a sample surface Z=F(X, Y) in the local plane position. That is, 
         [0000]      θ x=∂F ( X,Y )/∂ X, θy=∂F ( X,Y )/∂ Y   Expression 7
 
         [0000]    Therefore, by integrating (θx, θy) on a two-dimensional plane of X-Y by giving an appropriate initial value, conversely, it is possible to reconstruct a distribution of Z=F (X, Y). In this embodiment, the computer  21  also includes an inclination angle/height converting function  51  for converting an inclination angle into Z height according to this integration conversion. It is possible to calculate a height distribution Z=F (X, Y) from the distribution of the inclination angles (θx, θy) measured as explained above. 
         [0030]    In this way, in this embodiment, a height distribution and a tilt angle distribution can be measured as a surface profile of any test object in a nondestructive manner and noncontact manner, highly accurately, and in a wide tilt angle dynamic range using light. 
       Second Embodiment 
       [0031]    A second embodiment of the present invention is explained with reference to  FIG. 5 , which is a configuration diagram in the second embodiment. 
         [0032]    In this embodiment, a mechanism for measuring the height Z of the local micro plane in the illumination region  41  on the sample  40  is added to the first embodiment to make it possible to evaluate an up-down fluctuation characteristic of a sample moving stage. As explained above, in the first embodiment, it is possible to calculate the height distribution Z=F (X, Y) by directly measuring the distribution of the inclination angles (θx, θy). However, in addition to this, this embodiment has a function of directly measuring the height distribution Z=F (X, Y) using a dual beam interferometer. An optically directly measured height distribution is represented as Z1=F1 (X, Y) and a height distribution calculated by integrating a tilt angle distribution is represented as Z2=F2(X, Y) to distinguish the height distributions. In Z1, not only height information of the sample  40  but also undesired up-down height fluctuation of the stage surface in driving the sample moving stage  11  to move the measurement position is included as an error. On the other hand, when the stage surface moves up and down according to the driving, if fluctuation in an angle direction is sufficiently small, since inclination angle measurement is hardly affected by the fluctuation, Z2 does not involve an error. Therefore, it is possible to evaluate a height fluctuation characteristic of the sample moving stage  11  by calculating a difference of Z1−Z2. Therefore, in this embodiment, in the computer  21 , a height measuring function  52  and a height-difference detecting function  53  are provided in addition to the inclination-angle measuring function  50  and the inclination angle/height converting function  5   l . The other components are the same as the components in the first embodiment. 
         [0033]    In this embodiment configured as explained above, besides the effects obtained in the first embodiment, it is possible to evaluate the up-down fluctuation characteristic of the sample moving stage. 
       REFERENCE SIGNS LIST 
       [0000]    
       
         
           
               1  Light source 
               2  Illumination optical system 
               3  Dual beam interferometer 
               4  Beam splitter 
               5  Sample-side objective lens 
               6  Reference-side objective lens 
               7  Standard plane 
               8  Focusing lens 
               9  Field stop 
               10  Photodetector 
               11  Sample moving stage 
               12  X-Y driving/control unit 
               13 ,  16 ,  17  Piezo actuators 
               14  Z-axis control unit 
               15  Two-axis inclining mechanism 
               18  Inclination-angle control unit 
               20  A/D converter 
               21  Computer 
               30  Parallel beam 
               31  Sample-side reflected light beam 
               32  Reference-side reflected light beam 
               33  Interference light beam 
               34  Interference light intensity signal 
               35  Interferogram 
               40  Sample 
               41  Illumination region 
               50  Inclination-angle measuring function 
               51  Inclination angle/height converting function 
               52  Height measuring function 
               53  Height-difference detecting function