CN113639663B - Object three-dimensional shape measuring method based on reflected laser spatial distribution - Google Patents
Object three-dimensional shape measuring method based on reflected laser spatial distribution Download PDFInfo
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Abstract
The invention discloses a method for measuring the three-dimensional shape of an object based on the spatial distribution of reflected laser. The method comprises the steps of obtaining relevant data of two position detectors through two laser beams, calculating height information and inclination information of a measured point, and restoring the three-dimensional shape of the surface to be measured according to the height information and the inclination information of a plurality of measured points. Compared with the three-dimensional shape restored according to the height of the measured point in the prior art, the three-dimensional shape restored is more accurate, and the high-precision requirement of surface shape measurement of a semiconductor device can be met.
Description
Technical Field
The invention relates to the field of three-dimensional shape detection, in particular to a method for measuring the three-dimensional shape of an object based on the spatial distribution of reflected laser.
Background
With the development of semiconductor technology and high-precision instruments and equipment, the requirement for detecting the 3D shape of the surface of a semiconductor device in the production process is greatly improved. The optical measurement methods commonly used today are interferometric measurements and structured light measurements. The interference measurement method has high precision, but small field of view, and high requirement on environment, and is difficult to realize rapid measurement in production. The structured light method has a large measurement range and high precision, and is generally used for measuring the 3d shape of a large-size structure.
The PSD is a position-sensing photoelectric device, has the characteristics of high sensitivity and high response, and is commonly used for detecting the target space position. However, when the PSD is used as a two-dimensional measuring device to perform three-dimensional measurement of an object, coordinates of points on a surface of the object to be measured in a three-dimensional direction are usually calculated, and the topography of the surface to be measured is restored by using height information in the three-dimensional direction. But the method is not suitable for the high-precision requirement of the surface topography measurement of the semiconductor device.
In view of the above, it is necessary to develop a method for measuring the three-dimensional shape of an object to solve the above problems.
Disclosure of Invention
In order to overcome the problems of the dust filtering method, the invention aims to provide a method for measuring the three-dimensional shape of an object based on the spatial distribution of reflected laser, which solves the technical problem of low precision caused by the fact that the shape of a surface to be measured is restored by utilizing height information in the three-dimensional direction in the traditional method.
The invention aims to solve the technical problems and provides an object three-dimensional shape measuring method based on reflected laser spatial distribution, which comprises the following steps:
the first laser beam and the second laser beam respectively pass through the first focusing lens and the second focusing lens to meet the requirement of spatial orthogonality and are incident to the same point on the surface to be measured;
the first laser beam and the second laser beam are reflected by a measured point on the surface to be measured to a first imaging objective lens and a second imaging objective lens respectively, and are incident to a first position detector and a second position detector respectively after passing through the first imaging objective lens and the second imaging objective lens;
point coordinates P obtained based on the first position detector1Point coordinate P obtained by the second position detector2Object image transformation matrix of imaging lens
And a displacement matrix H between the coordinate systems1、H2To obtain a displacement matrix H1、H2And the slope information matrix S1、S2With point coordinates P obtained by the first position detector1Point coordinate P obtained by the second position detector2Object image transformation matrix of imaging lens
And formula (1) and formula (2) between coordinates W of the measured point on the measured surface:
the displacement matrix between the coordinate W of the measured point and the first imaging objective is as follows:
the displacement matrix between the coordinate W of the measured point and the second imaging objective lens is as follows:
wherein the content of the first and second substances,
，
，
respectively representing the displacement of the focusing lens relative to a coordinate system of a measured point along the X, Y and Z directions;
the object image transformation matrix of the imaging lens is as follows:
f is focal length, d is lens thickness, h1For the distance of the detection point from the front surface of the imaging lens, h2For the distance of the imaging lens from the position detector, n2Is the refractive index of the imaging lens;
wherein the content of the first and second substances,
in (A), (B)
) Is the coordinate of the measured point on the measured surface, XWAnd YWIs known;
solving S based on the formula (1) and the formula (2)1、S2W; wherein the slope information matrix S1、S2The angle ϕ of the rotation of the measured point around the X axis and the angle of the rotation around the Y axis are included in the test point
An angle theta is formed around the Z axis; z in WWRepresenting height information of a measured point;
according to height information and inclination information S of a plurality of measured points1、S2And reducing the three-dimensional appearance of the surface to be detected.
Further, the obtaining process of the formula (1) includes:
setting the world coordinate system of the first focusing lens as L1The coordinate system of the first imaging objective is I1Obtaining the coordinates of the central point of the first focusing lens as (
），
Laser is incident on the measured point from the first focusing lens and the second focusing lens, and the connecting lines of the central points of the first focusing lens and the second focusing lens and the measured point respectively satisfy a spatial orthogonal relationship, so that a relational expression (5) of the coordinate W of the measured point and the coordinate of the central point of the first focusing lens is obtained:
wherein the content of the first and second substances,
、
、
respectively displacement of the first focusing lens and the second focusing lens with the measured point in three coordinate directions;
the coordinates on the first imaging objective coordinate system are (
) Establishing a relation between two coordinate systems in a rotating and translating manner; falseLet the first imaging objective coordinate system I be rotated by an angle theta around the Z-axis1The following relation is satisfied with the coordinate system W of the measured surface:
the coordinate correspondence relationship of the above formula is satisfied when the rotation is performed around the X-axis and the Y-axis, assuming that the rotation angle around the X-axis is ϕ and the rotation angle around the Y-axis is ϕ
Thus establishing a first imaging objective coordinate system I1And the rotation matrix of the coordinate system W of the measured surface is as follows:
the first imaging objective I1The relation with the measured surface coordinate system W is expressed as:
let the two-dimensional coordinate of the plane where the measured point passes through the first imaging lens and the detector is at the first position be (
) The object image of the imaging lens is transformed into a matrix
And then:
simultaneous equations (5), (8) and (9) yield:
further, the obtaining process of the formula (2) includes:
world coordinate system L of the second focusing lens2The coordinate system of the second imaging objective is I2Obtaining the coordinates of the center point of the second focusing lens as (
) The coordinate on the second imaging objective coordinate system is (
）；
Laser is incident on the measured point from the first focusing lens and the second focusing lens, and the connecting lines of the central points of the first focusing lens and the second focusing lens and the measured point respectively satisfy the space orthogonal relationship, and the relational expression (10) of the coordinate W of the measured point and the central point coordinate of the second focusing lens is obtained
Wherein the content of the first and second substances,
、
、
respectively displacement of the first focusing lens and the second focusing lens with the measured point in three coordinate directions;
because the connecting line of the first imaging objective lens, the second imaging objective lens and the measured point has a geometrical relationship of space orthogonality in the measured surface coordinate system W, when the coordinate system is transformed, the corresponding rotation angles around the X axis and the Y axis are opposite, and the rotation angles around the Z axis are the same, so that the second imaging objective lens and the measured point have the same rotation angle around the X axis and the Y axis, and the second imaging objective lens and the measured point have the same rotation angle around the Z axisObjective lens coordinate system I2And the rotation matrix of the coordinate system W of the measured surface is as follows:
the second imaging objective I2The relation with the measured surface coordinate system W is expressed as:
the two-dimensional coordinate of the plane of the detector at the second position of the measured point passing through the second imaging lens is (
) The object image of the imaging lens is transformed into a matrix
And then:
simultaneous equations (2), (9) and (11) yield:
furthermore, the first laser beam and the second laser beam are respectively emitted by two semiconductor lasers and then enter the first focusing lens and the second focusing lens.
Furthermore, after a semiconductor laser is adopted to emit a laser beam, the laser beam is split by a beam splitter to form a first laser beam and a second laser beam, the first laser beam is incident to the first focusing lens, and the second laser beam is incident to the second focusing lens after being reflected by the reflector.
Further, the diameter of the laser beam emitted by the semiconductor laser is 0.45 mm.
Furthermore, the central wavelength of the semiconductor laser is 488-535 nm.
Further, the incident angles of the first laser beam and the second laser beam on the surface to be measured are the same.
Further, the incidence angle of the first laser beam and the second laser beam on the surface to be measured is 25-75 degrees.
Further, the spot diameter of the first laser beam and the spot diameter of the second laser beam on the surface to be measured are 2 μm.
One of the above technical solutions has the following advantages or beneficial effects: the invention provides a method for measuring the three-dimensional appearance of an object based on the spatial distribution of reflected laser, which comprises the steps of obtaining relevant data of two position detectors through two laser beams, calculating the height information and the inclination information of a measured point, and restoring the three-dimensional appearance of the surface to be measured according to the height information and the inclination information of a plurality of measured points. Compared with the prior art, the method has the advantages that the three-dimensional shape restored according to the height of the measured point is more accurate, the high-precision requirement of the surface shape measurement of the semiconductor device can be met, an angle measuring device is not added, the three-dimensional shape can be restored accurately only by adopting the existing two-dimensional PSD detector, the cost is low, and the method has higher practical value.
Drawings
In order to more clearly illustrate the technical solution of the embodiments of the present invention, the drawings of the embodiments will be briefly described below, and it is apparent that the drawings in the following description relate only to some embodiments of the present invention and are not limiting thereof, wherein:
FIG. 1 is an optical schematic diagram of a method for measuring the three-dimensional shape of an object based on the spatial distribution of reflected laser light according to one embodiment of the present invention;
FIG. 2 is an optical schematic diagram of a method for measuring three-dimensional topography of an object based on spatial distribution of reflected laser light according to a second embodiment of the present invention;
FIG. 3 is a schematic view of the present invention when the surface to be measured is a plane;
FIG. 4 is a schematic view of the present invention when the surface to be measured is an irregular curved surface;
FIG. 5 is another schematic view of the present invention when the surface to be measured is an irregular curved surface;
fig. 6 is a comparison between the conventional restored image and the restored image of the present invention.
The figure is marked with: 111. a first semiconductor laser; 112. a second semiconductor laser; 121. a first collimating lens; 122. a second collimating lens; 13. a beam splitter; 14. a first focusing lens; 15. a first reflector; 16. a second reflector; 17. a second focusing lens; 18. a second imaging objective lens; 19. a first imaging objective lens; 10. a first position detector; 20. a second position detector; 30. and (6) a surface to be measured.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
In the drawings, the shape and size may be exaggerated for clarity, and the same reference numerals will be used throughout the drawings to designate the same or similar components.
Unless defined otherwise, technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs. The use of "first," "second," and similar terms in the description and claims of the present application do not denote any order, quantity, or importance, but rather the terms are used to distinguish one element from another. Also, the use of the terms "a," "an," or "the" and similar referents do not denote a limitation of quantity, but rather denote the presence of at least one. The word "comprise" or "comprises", and the like, means that the element or item listed before "comprises" or "comprising" covers the element or item listed after "comprising" or "comprises" and its equivalents, and does not exclude other elements or items. "upper", "lower", "left", "right", and the like are used merely to indicate relative positional relationships, and when the absolute position of the object being described is changed, the relative positional relationships may also be changed accordingly.
In the following description, terms such as center, thickness, height, length, front, back, rear, left, right, top, bottom, upper, lower, etc., are defined with respect to the configurations shown in the respective drawings, and in particular, "height" corresponds to a dimension from top to bottom, "width" corresponds to a dimension from left to right, "depth" corresponds to a dimension from front to rear, which are relative concepts, and thus may be varied accordingly depending on the position in which it is used, and thus these or other orientations should not be construed as limiting terms.
Terms concerning attachments, coupling and the like (e.g., "connected" and "attached") refer to a relationship wherein structures are secured or attached, either directly or indirectly, to one another through intervening structures, as well as both movable or rigid attachments or relationships, unless expressly described otherwise.
Example one
Referring to fig. 1 and 3 to 6, a method for measuring the three-dimensional shape of an object based on the spatial distribution of reflected laser light includes the following steps:
the first laser beam and the second laser beam respectively pass through the first focusing lens 14 and the second focusing lens 17, meet the spatial orthogonality and are incident to the same point on the surface to be measured 30;
a measured point on the surface to be measured 30 reflects a first laser beam and a second laser beam to a first imaging objective lens 19 and a second imaging objective lens 18 respectively, and the first laser beam and the second laser beam are incident on a first position detector 10 and a second position detector 20 respectively after passing through the first imaging objective lens 19 and the second imaging objective lens 18;
based on the point coordinates P obtained by the first position detector 101Point coordinates P obtained by the second position detector 202Object image transformation matrix of imaging lens
And a displacement matrix H between the coordinate systems1、H2To obtain a displacement matrix H1、H2And the slope information matrix S1、S2With point coordinates P obtained by the first position detector1Point coordinate P obtained by the second position detector2Object image transformation matrix of imaging lens
And formula (1) and formula (2) between coordinates W of the measured point on the measured surface:
the displacement matrix between the coordinate W of the measured point and the first imaging objective is as follows:
the displacement matrix between the coordinate W of the measured point and the second imaging objective lens is as follows:
wherein the content of the first and second substances,
，
，
respectively representing the displacement of the focusing lens relative to a coordinate system of a measured point along the X, Y and Z directions;
the object image transformation matrix of the imaging lens is as follows:
f is focal length, d is lens thickness, h1For the distance of the detection point from the front surface of the imaging lens, h2For the distance of the imaging lens from the position detector, n2Is the refractive index of the imaging lens;
wherein the content of the first and second substances,
in (A), (B)
) Is the coordinate of the measured point on the measured surface, XWAnd YWIs known;
solving S based on formula (1) and formula (2)1、S2W; wherein the slope information matrix S1、S2The angle ϕ of the rotation of the measured point around the X axis and the angle of the rotation around the Y axis are included in the test point
An angle theta is formed around the Z axis; z in WWRepresenting height information of a measured point;
according to height information and inclination information S of a plurality of measured points1、S2And reducing the three-dimensional appearance of the surface to be detected.
In the present embodiment, the first laser beam and the second laser beam are emitted by two semiconductor lasers, and then enter the first focusing lens 14 and the second focusing lens 17. The two semiconductor lasers are a first semiconductor laser 111 and a second semiconductor laser 112, respectively. Wherein, the diameter of the laser beams emitted by the two semiconductor lasers is 0.45 mm. The central wavelength of the semiconductor laser is 488-535 nm.
Specifically, laser beams emitted by the first semiconductor laser 111 and the second semiconductor laser 112 are collimated by the first collimating lens 121 and the second collimating lens 122, respectively, and then enter the first focusing lens 14 and the second focusing lens 17, and after being focused by the first focusing lens 14 and the second focusing lens 17, two laser beams satisfy spatial orthogonality and enter the same point on the surface to be measured 30. At this time, the spot diameter of the measurement laser on the surface to be measured was 2 μm, and the incident angles of the two beams on the surface to be measured were the same. Specifically, the incidence angle of the first laser beam and the second laser beam on the surface to be measured is 25-75 degrees. Multiple tests show that the quality of light spots is good when the incident angles of the two beams of light are both 60 degrees. The two laser beams incident on the surface to be measured 30 are reflected to the first imaging objective lens 19 and the second imaging objective lens 18, focused and incident to the first position detector 10 and the second position detector 20, respectively.
The topography on the surface 30 to be measured can be decomposed into the relative height of the measurement area and the spatial tilt direction of the measurement plane. Referring to fig. 5, the change of the topography feature on the surface to be measured 30 may cause the change of the center of gravity of the light spot on the position detector PSD, but the change of the light spot position of the position detector PSD is a result of the combined action of the height feature and the slope feature, but the prior art only uses one semiconductor laser to measure the height feature to restore the topography of the surface to be measured, and the restoring accuracy is low. The invention uses two beams of orthogonal laser to measure the feature information of the same position at the same time, and two characteristic parameters of the height of the feature and the inclination direction of the measuring surface are calculated and separated, so that the feature of the surface to be measured is restored, and the restoring precision is higher.
Specifically, the obtaining process of formula (1) includes:
setting the world coordinate system of the first focusing lens as L1The coordinate system of the first imaging objective is I1Obtaining the coordinates of the central point of the first focusing lens as (
）。
Laser is incident on the measured point from the first focusing lens and the second focusing lens, and the connecting lines of the central points of the first focusing lens and the second focusing lens and the measured point respectively satisfy a spatial orthogonal relationship, so that a relational expression (5) of the coordinate W of the measured point and the coordinate of the central point of the first focusing lens is obtained:
wherein the content of the first and second substances,
、
、
respectively displacement of the first focusing lens and the second focusing lens with the measured point in three coordinate directions;
the coordinates on the first imaging objective coordinate system are (
) Establishing a relation between two coordinate systems in a rotating and translating manner; assuming a first imaging objective coordinate system I when rotated around the Z-axis by an angle theta1The following relation is satisfied with the coordinate system W of the measured surface:
the coordinate correspondence relationship of the above formula is satisfied when the rotation is performed around the X-axis and the Y-axis, assuming that the rotation angle around the X-axis is ϕ and the rotation angle around the Y-axis is ϕ
Thus establishing a first imaging objective coordinate system I1And the rotation matrix of the coordinate system W of the measured surface is as follows:
the first imaging objective I1The relation with the measured surface coordinate system W is expressed as:
let the two-dimensional coordinate of the plane where the measured point passes through the first imaging lens and the detector is at the first position be (
) The object image of the imaging lens is transformed into a matrix
And then:
simultaneous equations (5), (8) and (9) yield:
specifically, the obtaining process of formula (2) includes:
world coordinate system L of the second focusing lens2The coordinate system of the second imaging objective is I2Obtaining the coordinates of the center point of the second focusing lens as (
) The coordinate on the second imaging objective coordinate system is (
）；
Laser is incident on the measured point from the first focusing lens and the second focusing lens, and the connecting lines of the central points of the first focusing lens and the second focusing lens and the measured point respectively satisfy the space orthogonal relationship, and the relational expression (10) of the coordinate W of the measured point and the central point coordinate of the second focusing lens is obtained
Wherein the content of the first and second substances,
、
、
respectively displacement of the first focusing lens and the second focusing lens with the measured point in three coordinate directions;
because the connecting line of the first imaging objective lens, the second imaging objective lens and the measured point has a geometrical relationship of space orthogonality in the measured surface coordinate system W, when the coordinate system is transformed, the corresponding rotation angles around the X axis and the Y axis are opposite, and the rotation angles around the Z axis are the same, so that the coordinate system I of the second imaging objective lens is the same2And the rotation matrix of the coordinate system W of the measured surface is as follows:
the second imaging objective I2The relation with the measured surface coordinate system W is expressed as:
the two-dimensional coordinate of the plane of the detector at the second position of the measured point passing through the second imaging lens is (
) The object image of the imaging lens is transformed into a matrix
And then:
simultaneous equations (10), (12) and (13) yield:
the above equation (1) can also be expressed as:
the above equation (2) can also be expressed as:
the inclination information matrixes S1 and S2 include the rotation angle ϕ of the measured point around the X axis and the rotation angle around the Y axis
An angle theta is formed around the Z axis; z in WWAnd representing the height information of the measured point. In particular, ZWAnd Z1、
And (4) correlating.
Referring to FIG. 6, the dashed line is a prior art 3D topography measured from height information obtained from a beam of light on a PSD. The solid line is a 3D topography map drawn using the measured height information and the slope information of the plane in which the measurement points lie in the present invention. Therefore, compared with the prior art, the 3D topography map drawn by using the measured height information and the inclination information of the plane where the measuring point is located can more accurately restore the three-dimensional topography.
Example two
Referring to fig. 2 to 6, a method for measuring the three-dimensional shape of an object based on the spatial distribution of reflected laser includes the following steps:
the first laser beam and the second laser beam respectively pass through the first focusing lens 14 and the second focusing lens 17, meet the spatial orthogonality and are incident to the same point on the surface to be measured 30;
a measured point on the surface to be measured 30 reflects a first laser beam and a second laser beam to a first imaging objective lens 19 and a second imaging objective lens 18 respectively, and the first laser beam and the second laser beam are incident on a first position detector 10 and a second position detector 20 respectively after passing through the first imaging objective lens 19 and the second imaging objective lens 18;
based on the point coordinates P obtained by the first position detector 101Point coordinates P obtained by the second position detector 202Object image transformation matrix of imaging lens
And a displacement matrix H1、H2To obtain a displacement matrix H1、H2And the slope information matrix S1、S2With point coordinates P obtained by the first position detector1Point coordinate P obtained by the second position detector2Object image transformation matrix of imaging lens
And formula (1) and formula (2) between coordinates W of the measured point on the measured surface:
the displacement matrix between the coordinate W of the measured point and the first imaging objective lens is as follows:
the displacement matrix between the coordinate W of the measured point and the second imaging objective lens is as follows:
wherein the content of the first and second substances,
，
，
respectively representing the displacement of the focusing lens relative to a coordinate system of a measured point along the X, Y and Z directions;
the object image transformation matrix of the imaging lens is as follows:
f is focal length, d is lens thickness, h1For the distance of the detection point from the front surface of the imaging lens, h2For the distance of the imaging lens from the position detector, n2Is the refractive index of the imaging lens;
wherein the content of the first and second substances,
in (A), (B)
) Is the coordinate of the measured point on the measured surface, XWAnd YWIs known;
solving S based on formula (1) and formula (2)1、S2W; wherein the slope information matrix S1、S2The angle ϕ of the rotation of the measured point around the X axis and the angle of the rotation around the Y axis are included in the test point
An angle theta is formed around the Z axis; z in WWRepresenting height information of a measured point;
according to height information and inclination information S of a plurality of measured points1、S2And reducing the three-dimensional appearance of the surface to be detected.
In this embodiment, a first semiconductor laser 111 is used to emit a laser beam, and then the laser beam is split by the beam splitter 13 to form a first laser beam and a second laser beam. The diameter of the laser beam emitted by the semiconductor laser is 0.45 mm. The central wavelength of the semiconductor laser is 488-535 nm.
Specifically, a first semiconductor laser 111 is used to emit a laser beam, which is collimated by a first collimating lens 121 and split by a beam splitter 13 to form a first laser beam and a second laser beam, where the first laser beam is incident on a first focusing lens 14, and the second laser beam is reflected by a first reflector 15 and a second reflector 16 and then incident on a second focusing lens 17. The two laser beams after being focused by the first focusing lens 14 and the second focusing lens 17 satisfy spatial orthogonality and are incident to the same point on the surface to be measured 30. At this time, the spot diameter of the measurement laser on the surface to be measured is 2 μm, and the incident angles of the first laser beam and the second laser beam on the surface to be measured are the same. Specifically, the incidence angle of the first laser beam and the second laser beam on the surface to be measured is 25-75 degrees. Multiple tests show that the quality of light spots is good when the incident angles of the two beams of light are both 60 degrees. The two laser beams incident on the surface to be measured 30 are reflected to the first imaging objective lens 19 and the second imaging objective lens 18, focused and incident to the first position detector 10 and the second position detector 20, respectively.
The topography on the surface 30 to be measured can be decomposed into the relative height of the measurement area and the spatial tilt direction of the measurement plane. Referring to fig. 5, the change of the topography feature on the surface to be measured 30 may cause the change of the center of gravity of the light spot on the position detector PSD, but the change of the light spot position of the position detector PSD is a result of the combined action of the height feature and the slope feature, but the prior art only uses one semiconductor laser to measure the height feature to restore the topography of the surface to be measured, and the restoring accuracy is low. The invention uses two beams of orthogonal laser to measure the feature information of the same position at the same time, and two characteristic parameters of the height of the feature and the inclination direction of the measuring surface are calculated and separated, so that the feature of the surface to be measured is restored, and the restoring precision is higher.
In addition, the three-dimensional shape measurement in the method can be realized by adopting one semiconductor laser, and compared with the first embodiment, the manufacturing cost is lower.
Specifically, the obtaining process of formula (1) includes:
setting the world coordinate system of the first focusing lens as L1The cross-sectional coordinate system of the first imaging objective is I1Obtaining the coordinates of the central point of the first focusing lens as
。
Laser is incident on the measured point from the first focusing lens and the second focusing lens, and the connection between the central points of the first focusing lens and the second focusing lens and the measured point respectively meets the space orthogonal relationship, so that a relational expression (5) of the coordinate W of the measured point and the coordinate of the central point of the first focusing lens is obtained:
wherein the content of the first and second substances,
、
、
respectively displacement of the first focusing lens and the second focusing lens with the measured point in three coordinate directions;
the coordinates on the first imaging objective coordinate system are
Establishing a relation between two coordinate systems in a rotating and translating manner; assuming a first imaging objective coordinate system I when rotated around the Z-axis by an angle theta1The following relation is satisfied with the coordinate system W of the measured surface:
the coordinate correspondence relationship of the above formula is satisfied when the rotation is performed around the X-axis and the Y-axis, assuming that the rotation angle around the X-axis is ϕ and the rotation angle around the Y-axis is ϕ
Thus establishing a first imaging objective coordinate system I1And the rotation matrix of the coordinate system W of the measured surface is as follows:
the first imaging objective I1The relation with the measured surface coordinate system W is expressed as:
the two-dimensional coordinate of a measured point passing through a first image lens on the plane where the detector is located at the first position is set as
The object image of the imaging lens is transformed into a matrix
And then:
simultaneous equations (5), (8) and (9) yield:
specifically, the obtaining process of formula (2) includes:
world coordinate system L of the second focusing lens2The coordinate system of the second imaging objective is I2Obtaining the coordinates of the center point of the second focusing lens as
The coordinates on the second imaging objective coordinate system are
；
Laser is incident on the measured point from the first focusing lens and the second focusing lens, and the connecting lines of the central points of the first focusing lens and the second focusing lens and the measured point respectively satisfy the space orthogonal relationship, and the relational expression (10) of the coordinate W of the measured point and the central point coordinate of the second focusing lens is obtained
Wherein the content of the first and second substances,
、
、
respectively displacement of the first focusing lens and the second focusing lens with the measured point in three coordinate directions;
because the connecting line of the first imaging objective lens, the second imaging objective lens and the measured point has a geometrical relationship of space orthogonality in the measured surface coordinate system W, when the coordinate system is transformed, the corresponding rotation angles around the X axis and the Y axis are opposite, and the rotation angles around the Z axis are the same, so that the coordinate system I of the second imaging objective lens is the same2And the rotation matrix of the coordinate system W of the measured surface is as follows:
the second imaging objective I2The relation with the measured surface coordinate system W is expressed as:
the two-dimensional coordinate of the plane of the detector at the second position of the measured point passing through the second imaging lens is
The object image of the imaging lens is transformed into a matrix
And then:
simultaneous equations (10), (12) and (13) yield:
the above equation (1) can also be expressed as:
the above equation (2) can also be expressed as:
wherein the slope information matrix S1、S2The angle ϕ of the rotation of the measured point around the X axis and the angle of the rotation around the Y axis are included in the test point
An angle theta is formed around the Z axis; z in WWAnd representing the height information of the measured point. In particular, ZWAnd Z1、
And (4) correlating.
Referring to FIG. 6, the dashed line is a prior art 3D topography measured from height information obtained from a beam of light on a PSD. The solid line is a 3D topography map drawn using the measured height information and the slope information of the plane in which the measurement points lie in the present invention. Therefore, compared with the prior art, the 3D topography map drawn by using the measured height information and the inclination information of the plane where the measuring point is located can more accurately restore the three-dimensional topography.
The invention provides a method for measuring the three-dimensional appearance of an object based on the spatial distribution of reflected laser, which comprises the steps of obtaining relevant data of two position detectors through two laser beams, calculating the height information and the inclination information of a measured point, and restoring the three-dimensional appearance of the surface to be measured according to the height information and the inclination information of a plurality of measured points. Compared with the three-dimensional shape restored according to the height of the measured point in the prior art, the three-dimensional shape restored is more accurate, and the high-precision requirement of surface shape measurement of a semiconductor device can be met.
Applications, modifications and variations of the present invention will be apparent to those skilled in the art.
The features of the different implementations described herein may be combined to form other embodiments not specifically set forth above. The components may be omitted from the structures described herein without adversely affecting their operation. Further, various individual components may be combined into one or more individual components to perform the functions described herein.
Furthermore, while embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in a variety of fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.
Claims (8)
1. A method for measuring the three-dimensional shape of an object based on the spatial distribution of reflected laser is characterized by comprising the following steps:
the first laser beam and the second laser beam respectively pass through the first focusing lens and the second focusing lens to meet the requirement of spatial orthogonality and are incident to the same point on the surface to be measured;
the first laser beam and the second laser beam are reflected by a measured point on the surface to be measured to a first imaging objective lens and a second imaging objective lens respectively, and are incident to a first position detector and a second position detector respectively after passing through the first imaging objective lens and the second imaging objective lens;
point coordinates P obtained based on the first position detector1Point coordinate P obtained by the second position detector2Object image transformation matrix of imaging lens
And a displacement matrix H between the coordinate systems1、H2To obtain a displacement matrix H1、H2And the slope information matrix S1、S2With point coordinates P obtained by the first position detector1Point coordinate P obtained by the second position detector2Object image transformation matrix of imaging lens
And formula (1) and formula (2) between coordinates W of the measured point on the measured surface:
the displacement matrix between the coordinate W of the measured point and the first imaging objective is as follows:
the displacement matrix between the coordinate W of the measured point and the second imaging objective lens is as follows:
wherein the content of the first and second substances,
，
，
respectively representing the displacement of the focusing lens relative to a coordinate system of a measured point along the X, Y and Z directions;
the object image transformation matrix of the imaging lens is as follows:
f is focal length, d is lens thickness, h1For the distance of the detection point from the front surface of the imaging lens, h2Is the distance of the imaging lens from the position detector;
wherein, in (A), (B), (C), (B), (C), (B), (C), (B), (C)
) Is the coordinate of the measured point on the measured surface, XWAnd YWIs known;
solving S based on the formula (1) and the formula (2)1、S2W; wherein the slope information matrix S1、S2The angle ϕ of the rotation of the measured point around the X axis and the angle of the rotation around the Y axis are included in the test point
An angle theta is formed around the Z axis; z in WWRepresenting height information of a measured point;
according to height information and inclination information S of a plurality of measured points1、S2Reducing the three-dimensional appearance of the surface to be detected;
the obtaining process of the formula (1) comprises the following steps:
setting the world coordinate system of the first focusing lens as L1The coordinate system of the first imaging objective is I1Obtaining the coordinates of the central point of the first focusing lens as (
），
Laser is incident on the measured point from the first focusing lens and the second focusing lens, and the connecting lines of the central points of the first focusing lens and the second focusing lens and the measured point respectively satisfy a spatial orthogonal relationship, so that a relational expression (5) of the coordinate W of the measured point and the coordinate of the central point of the first focusing lens is obtained:
wherein the content of the first and second substances,
、
、
respectively displacement of the first focusing lens and the second focusing lens with the measured point in three coordinate directions;
the coordinates on the first imaging objective coordinate system are (
) Establishing a relation between two coordinate systems in a rotating and translating manner; assuming a first imaging objective coordinate system I when rotated around the Z-axis by an angle theta1The following relation is satisfied with the coordinate system W of the measured surface:
the coordinate correspondence relationship of the above formula is satisfied when the rotation is performed around the X-axis and the Y-axis, assuming that the rotation angle around the X-axis is ϕ and the rotation angle around the Y-axis is ϕ
Thus establishing a first imaging objective coordinate system I1And the rotation matrix of the coordinate system W of the measured surface is as follows:
the first imaging objective I1The relation with the measured surface coordinate system W is expressed as:
let the two-dimensional coordinate of the plane where the measured point passes through the first imaging lens and the detector is at the first position be (
) The object image of the imaging lens is transformed into a matrix
And then:
simultaneous equations (5), (8) and (9) yield:
the obtaining process of the formula (2) comprises the following steps:
world coordinate system L of the second focusing lens2The coordinate system of the second imaging objective is I2Obtaining the coordinates of the center point of the second focusing lens as (
) The coordinate on the second imaging objective coordinate system is (
）；
Laser is incident on the measured point from the first focusing lens and the second focusing lens, and the connecting lines of the central points of the first focusing lens and the second focusing lens and the measured point respectively satisfy the space orthogonal relationship, and the relational expression (10) of the coordinate W of the measured point and the central point coordinate of the second focusing lens is obtained
Wherein the content of the first and second substances,
、
、
respectively displacement of the first focusing lens and the second focusing lens with the measured point in three coordinate directions;
because the connecting line of the first imaging objective lens, the second imaging objective lens and the measured point has a geometrical relationship of space orthogonality in the measured surface coordinate system W, when the coordinate system is transformed, the corresponding rotation angles around the X axis and the Y axis are opposite, and the rotation angles around the Z axis are the same, so that the coordinate system I of the second imaging objective lens is the same2And the rotation matrix of the coordinate system W of the measured surface is as follows:
the second imaging objective I2The relation with the measured surface coordinate system W can be expressed as:
the two-dimensional coordinate of the plane of the detector at the second position of the measured point passing through the second imaging lens is (
) The object image of the imaging lens is transformed into a matrix
And then:
simultaneous equations (10), (12) and (13) yield:
2. the method according to claim 1, wherein the first laser beam and the second laser beam are emitted by two semiconductor lasers respectively and then enter the first focusing lens and the second focusing lens.
3. The method as claimed in claim 1, wherein a semiconductor laser is used to emit a laser beam, and the laser beam is split by a beam splitter to form a first laser beam and a second laser beam, wherein the first laser beam is incident on the first focusing lens, and the second laser beam is reflected by the reflector and then incident on the second focusing lens.
4. The method according to claim 2 or 3, wherein the diameter of the laser beam emitted by the semiconductor laser is 0.45 mm.
5. The method as claimed in claim 2 or 3, wherein the central wavelength of the semiconductor laser is 488-535 nm.
6. The method for measuring the three-dimensional topography of an object based on the spatial distribution of reflected laser light according to claim 1, wherein the first laser beam and the second laser beam have the same incident angle on the surface to be measured.
7. The method for measuring the three-dimensional topography of an object based on the spatial distribution of reflected laser light according to claim 1, wherein the incident angles of the first laser beam and the second laser beam on the surface to be measured are 25-75 degrees.
8. The method for measuring the three-dimensional topography of an object based on the spatial distribution of reflected laser light according to claim 1, wherein the spot diameters of the first laser beam and the second laser beam on the surface to be measured are 2 μm.
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