METHOD OF PROCESSING WORKPIECE

Description

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to a method of processing a workpiece such as a semiconductor wafer by holding the workpiece on a holding table and processing the workpiece held on the holding table to thin down the workpiece.

Description of the Related Art

Device chips that incorporate devices such as integrated circuits (ICs) and large-scale-integration (LSI) circuits are fabricated from wafers shaped as circular plates. Specifically, a plurality of devices are constructed on a face side of a wafer, then the wafer is thinned down by having its reverse side ground and polished, after which the wafer is divided into individual device chips including the respective devices. Alternatively, device chips are fabricated from a packaged substrate where a plurality of devices are encapsulated by resin. Specifically, a packaged substrate is thinned down by having its encapsulated side ground and polished, after which the wafer is divided into individual device chips including the respective devices.

A workpiece such as a wafer is ground by a grinding apparatus and polished by a polishing apparatus. A processing apparatus such as a grinding apparatus or a polishing apparatus includes a holding table known as a chuck table for holding a workpiece thereon and a processing unit for processing the workpiece held on the holding table with a processing tool such as a grinding wheel or a polishing pad. The processing apparatus further includes a measuring instrument for measuring thicknesses of various portions of the workpiece. A thickness distribution of the workpiece while the workpiece is being processed or after it has been processed is acquired from data obtained from the measuring instrument, and then a positional relation between the processing tool and the holding table is adjusted on the basis of the thickness distribution. Thereafter, a next processing step is performed on the workpiece (see, for example, Japanese Patent Laid-open Nos. H10-112493, H2-274459, 2013-119123, and 2022-133006). There has been known in the art a non-contact thickness measuring instrument for measuring a thickness of a workpiece by applying light or ultrasonic waves to the workpiece as the measuring instrument of the processing apparatus.

SUMMARY OF THE INVENTION

A processing apparatus is sometimes used to process a workpiece where a plurality of regions, i.e., layers or structures, having respective properties different from each other are layered together. For example, the processing apparatus may process a wafer having a plurality of stacked layers having respective functions and shapes different from each other. Moreover, a processing apparatus is sometimes used to process a layered assembly of wafers such as wafer-level chip-size (scale) packages (WLCSPs), for example. In a case where such a workpiece is to be thinned down, it is necessary for the processing apparatus to thin down the workpiece such that a thickness of the entire workpiece, i.e., a total thickness of the workpiece, rather than a thickness of each of regions of the workpiece, reaches a predetermined thickness. If the entire workpiece is not finished uniformly to the predetermined thickness, then when a plurality of such workpieces are affixed together, air bubbles tend to be trapped between the affixed surfaces of the workpieces. Further, a processing apparatus is sometimes used to thin down a workpiece such as a wafer or a chip encapsulated by an encapsulating material such as SiO₂ or resin. When the encapsulating material is thinned down to expose electrodes and the like of the chip or when the encapsulating material is processed, thinned down, and left on the workpiece, it is desirable that the overall workpiece be of a uniform predetermined thickness.

A thickness measuring instrument is used to measure a thickness of a workpiece in a vicinity of a processed point thereon while the workpiece is being processed or after it has been processed. As described above, the thickness measuring instrument used in this case is a non-contact thickness measuring instrument for measuring a thickness of a workpiece by applying light or ultrasonic waves to the workpiece in order to prevent the workpiece from being damaged. However, in a case where the workpiece has a plurality of regions, i.e., layers or structures, layered together, if light or ultrasonic waves emitted from the non-contact thickness measuring instrument are not well transmitted through particular ones of the regions, then the thickness measuring instrument as it is used alone is unable to measure the total thickness of the workpiece. Stated otherwise, the thickness measuring instrument cannot be used alone to measure the total thickness of the workpiece, and a positional relation between a processing tool and a holding table cannot be adjusted using a thickness distribution of the workpiece based on data from the thickness measuring instrument. As a result, the workpiece cannot be processed to a predetermined configuration.

It is therefore an object of the present invention to provide a method of processing a workpiece where a plurality of regions, i.e., layers or structures, are layered together while acquiring the total thickness of the workpiece.

In accordance with an aspect of the present invention, there is provided a method of processing a workpiece having a first region and a second region that are layered together to thin down the workpiece, the metho including acquiring a thickness of the first region, thinning down the second region by bringing a processing tool into contact with the workpiece held on a holding table, measuring and acquiring a thickness of the second region of the workpiece that has been thinned down, adjusting a positional relation between the processing tool and the holding table by referring to a total thickness of the workpiece that includes the acquired thickness of the first region and the acquired thickness of the second region, and thinning down the workpiece by bringing the processing tool into contact with the workpiece held on the holding table after the positional relation between the processing tool and the holding table has been adjusted.

Preferably, the measuring and acquiring the thickness of the second region includes measuring the thickness of the second region of the workpiece with a thickness measuring instrument that performs thickness measurement while out of contact with the workpiece.

Preferably, the measuring and acquiring the thickness of the second region includes measuring the thickness of the second region of the workpiece with a thickness measuring instrument that performs thickness measurement using light or ultrasonic waves while out of contact with the workpiece, and the second region of the workpiece is more transmissive of the light or ultrasonic waves used by the thickness measuring instrument than the first region of the workpiece.

Preferably, the acquiring the thickness of the first region includes acquiring thicknesses of the first region at a position spaced from a center of the workpiece by a first distance and a position spaced from the center of the workpiece by a second distance different from the first distance, and the measuring and acquiring the thickness of the second region includes acquiring thicknesses of the second region at the position spaced from the center of the workpiece by the first distance and the position spaced from the center of the workpiece by the second distance.

Preferably, the measuring and acquiring the thickness of the second region is carried out while the processing tool is not being in contact with the workpiece after the thinning down the second region but before the thinning down the workpiece.

Preferably, the measuring and acquiring the thickness of the second region is carried out while the thinning down the second region is being carried out or while the processing tool is being in contact with the workpiece after the thinning down the second region.

Preferably, the acquired thickness of the first region is calculated by subtracting the thickness of the second region from the total thickness of the workpiece.

Preferably, the acquiring the thickness of the first region is carried out while the workpiece is not being held on the holding table.

In the method of processing a workpiece according to the aspect of the present invention, in the thinning down the second region, the processing tool is brought into abrasive contact with the workpiece held on the holding table to thin down the workpiece. Thereafter, the positional relation between the processing tool and the holding table is adjusted by referring to the total thickness of the workpiece. In the thinning down the workpiece, after the positional relation between the processing tool and the holding table has been adjusted, the workpiece is further thinned down.

The total thickness of the workpiece that is referred to for adjusting the positional relation between the processing tool and the holding table includes the thickness of the first region of the workpiece and the thickness of the second region thereof. The thickness of the second region is acquired in the measuring and acquiring the thickness of the second region, by measuring the workpiece thinned down in the thinning down the second region. Meanwhile, the thickness of the first region is acquired in the acquiring the thickness of the first region different from the measuring and acquiring the thickness of the second region. In other words, the thickness of the first region and the thickness of the second region are individually acquired. Consequently, even if the thickness of the first region is not obtained by way of measurement in the measuring and acquiring the thickness of the second region, the total thickness of the workpiece can be referred to at the time of adjusting the positional relation between the processing tool and the holding table. In other words, positional adjustments can be made in order to thin down the workpiece into a predetermined configuration thereafter.

Consequently, in accordance with the present invention, there is provided a method of processing a workpiece where a plurality of regions, i.e., layers or structures, are layered together, while acquiring the total thickness of the workpiece.

The above and other objects, features and advantages of the present invention and the manner of realizing them will become more apparent, and the invention itself will best be understood from a study of the following description and appended claims with reference to the attached drawings showing a preferred embodiment of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view, partly in block form, schematically illustrating a processing apparatus and a workpiece by way of example;

FIG. 2A is an enlarged fragmentary cross-sectional view schematically illustrating the workpiece;

FIG. 2B is an enlarged fragmentary cross-sectional view schematically illustrating the workpiece as simplified;

FIG. 3 is a cross-sectional view, partly in side elevation, schematically illustrating a processing unit and a holding table of the processing apparatus;

FIG. 4 is a plan view schematically illustrating a positional relation between the holding table and a grinding wheel;

FIG. 5A is a graph schematically illustrating a thickness distribution of the workpiece by way of example;

FIG. 5B is a graph schematically illustrating another thickness distribution of the workpiece by way of example;

FIG. 6 is a cross-sectional view, partly in side elevation, schematically illustrating a thickness measuring unit;

FIG. 7 is a cross-sectional view schematically illustrating a thickness measuring unit according to a modification;

FIG. 8 is a plan view schematically illustrating a reverse side of the workpiece;

FIG. 9A is a cross-sectional view schematically illustrating the workpiece before it is processed;

FIG. 9B is a cross-sectional view schematically illustrating the workpiece after a first processing step has been carried out thereon;

FIG. 9C is a cross-sectional view schematically illustrating the workpiece that has been thinned down to a predetermined thickness;

FIG. 10A is a flowchart illustrating a sequence of steps of a method of processing a workpiece; and

FIG. 10B is a flowchart illustrating a sequence of steps of a method of processing a workpiece according to a modification.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

A preferred embodiment of the present invention will be described below with reference to the accompanying drawings. A method of processing a workpiece according to the present embodiment thins down a workpiece. First, the workpiece will be described below. FIG. 1 includes illustration in perspective, partly in block form, of the workpiece, denoted by 1, by way of example. FIG. 2A schematically illustrates a workpiece 5 by way of example in enlarged fragmentary cross section. FIG. 2B schematically illustrates the workpiece 1 or 5 as simplified by way of example in enlarged cross section. The workpiece 1 is a wafer shaped as a circular plate and made of silicon (Si), silicon carbide (SiC), gallium nitride (GaN), or gallium arsenide (GaAs), or another semiconductor material, for example. A plurality of devices are constructed in a matrix pattern on a face side 1a of the workpiece 1, and then the workpiece 1 is divided into a plurality of pieces that include the respective devices as individual device chips. By thinning down the workpiece 1 in advance, thin device chips are finally obtained from the workpiece 1.

In the method of processing a workpiece according to the present embodiment, a reverse side 1b of the workpiece 1 that is opposite the face side 1a is processed to be thinned down. A tape-shaped protective member 3 is affixed to the face side 1a of the workpiece 1 to protect the devices on the face side 1a.

The workpiece 1 to be processed by a processing apparatus has various stacked layers including an inorganic insulative film, an organic insulative film, a conductive film, and a semiconductor film, for example, that make up devices such as ICs or LSI circuits and have different functions and shapes. The processing apparatus may process a layered assembly of wafers such as a WLCSP, for example. The processing apparatus may also process the workpiece 5 (see FIG. 2A) or a substrate that includes chips 11 cut out of wafers and encapsulated by SiO₂ or resin. However, the workpiece 1 is not limited to any of these structures.

The processing apparatus processes any of the various workpieces 1 and 5 to thin it down. Generally, the workpieces 1 and 5 can be generalized and simplified as a layered assembly including a first region 7, i.e., a layer or a structure, and a second region 9, i.e., a layer or a structure. FIG. 2B schematically illustrates a typical simplified example of the workpieces 1 and 5. In the typical simplified example of the workpieces 1 and 5, the first region 7 may include a plurality of layers or structures or a single layer or structure, and the second region 9 may include a plurality of layers or structures or a single layer or structure. The first region 7 may not necessarily be uniform in thickness and shape throughout the workpiece 1 or 5, and the second region 9 may not necessarily be uniform in thickness and shape throughout the workpiece 1 or 5. The first region 7 and the second region 9 may be patterned into predetermined shapes.

The processing apparatus processes one of surfaces of the workpiece 1 or 5 to thin it down. The structure that is exposed on the processed surface, i.e., the reverse side 1b, of the workpiece 1 is referred to as the second region 9. The processing apparatus includes a processing tool for contacting the second region 9 to remove all of the second region 9 or part of the second region 9 to reach a thickness where the devices are exposed, for example. As described later, the second region 9 is a region whose thickness can be measured by a thickness measuring instrument. Of the workpiece 1, all the regions not belonging to the second region 9 may be referred to as the first region 7. Alternatively, for example, the first region 7 may represent a region whose thickness is relatively difficult to measure with the thickness measuring instrument to be described later.

The processing apparatus thins down the workpiece 1 or 5 into a predetermined configuration. For example, the processing apparatus thins down the workpiece 1 or 5 to reach a predetermined uniform thickness in their entirety. Alternatively, the processing apparatus thins down the workpiece 1 or 5 such that a thickness distribution of each of portions of the workpiece 1 or 5 becomes a predetermined thickness distribution. The processing apparatus for thinning down the workpiece 1 or 5 is, for example, a grinding apparatus for grinding the workpiece 1 with a grinding wheel that includes an annular array of grindstones or a polishing apparatus for polishing the workpiece 1 by holding a polishing pad in abrasive contact with the workpiece 1. Alternatively, the processing apparatus for thinning down the workpiece 1 or 5 may be a surface planer for cutting the workpiece 1 or 5 with a cutter movable along an annular path.

The processing apparatus for thinning down the workpiece 1 or 5 in the method of processing a workpiece according to the present embodiment includes a holding table, i.e., a chuck table, for holding the workpiece 1 or 5 and a processing tool for thinning down the workpiece 1 or 5 by contacting the workpiece 1 or 5. The processing apparatus for use in the method of processing a workpiece according to the present embodiment will be described below as a grinding apparatus for grinding the workpiece 1 or 5 to thin it down, for example. However, the processing apparatus should not be interpreted as being limited to a grinding apparatus.

As illustrated in FIG. 1, the grinding apparatus, i.e., the processing apparatus, 2 includes a base 4 that supports various components thereon. Two cassette rest bases 26a and 26b are fixed to a front end of the base 4. Two cassettes 28a and 28b each housing a plurality of workpieces 1 are placed on the respective cassette rest bases 26a and 26b. When the grinding apparatus 2 is in operation, workpieces 1 are pulled one by one out of the cassettes 28a and 28b and ground or thinned down, after which the ground workpieces 1 are stored one by one back into the cassettes 28a and 28b. A wafer delivery robot 30 is installed on the base 4 at a position adjacent to the cassette rest bases 26a and 26b. The wafer delivery robot 30 unloads workpieces 1 one by one from the cassettes 28a and 28b on the cassette rest bases 26a and 26b and delivers the unloaded workpieces 1 one by one onto a positioning table 32 disposed on the base 4 at a position adjacent to the wafer delivery robot 30.

The positioning table 32 has an annular array of radially movable positioning pins. When a workpiece 1 is placed on a central rest area of the positioning table 32, the positioning pins are moved in unison radially inwardly into contact with an outer circumferential edge of the workpiece 1, thereby centering the workpiece 1 in a predetermined position on the positioning table 32. A loading arm 34 and an unloading arm 36 are disposed on an upper surface of the base 4 at a position adjacent to the positioning table 32. The workpiece 1 set in the predetermined position on the positioning table 32 is delivered from the positioning table 32 by the loading arm 34.

A turntable 6 shaped as a circular plate is rotatably mounted on a central upper surface of the base 4 for rotation in a horizontal plane. The turntable 6 supports on its upper surface three holding tables or chuck tables 8 for holding respective workpieces 1 thereon. The holding tables 8 are angularly spaced from each other by 120 degrees circumferentially around the center of the turntable 6. When the turntable 6 is rotated about its central axis, the holding tables 8 can be moved while holding respective workpieces 1 thereon.

FIG. 3 schematically illustrates in cross-section, partly in side elevation, one of the holding tables 8 and other components associated therewith. Since the three holding tables 8 are structurally identical to each other, one of the holding tables 8 will be described in detail below. The holding table 8 includes a porous member 8c shaped as a circular plate that is of the same diameter as the workpiece 1 and a frame 8b made of stainless steel and having an upwardly open recess in which the porous member 8c is fitted. The frame 8b has a suction channel, not depicted, defined therein that has an end joined to a bottom of the recess in the frame 8b and an opposite end fluidly connected to a suction source, not depicted. When the workpiece 1 is placed on the porous member 8c of the holding table 8 and the suction source is actuated, the suction source generates and transmits a negative pressure through the suction channel to the porous member 8c, attracting the workpiece 1 under suction on the holding table 8. That is, the holding table 8 has an upper surface acting as a holding surface 8a for holding the workpiece 1 thereon. The holding surface 8a is shaped as an upwardly protruding conical surface that is slanted gradually as will be described later.

The holding table 8 has its bottom 54 coupled to a rotary actuator 56 such as an electric motor. When the rotary actuator 56 is energized, it rotates the holding table 8 about a table axis 58 extending through a center of the holding surface 8a. The bottom 54 of the holding table 8 is supported on the turntable 6 by a plurality of support shafts that are of a structure allowing the holding table 8 to rotate about the table axis 58. One or more of the support shafts is extensible and contractible along their axes. For example, in the grinding apparatus 2, the support shafts include a fixed shaft 60 and two adjustable shafts 62 and 64 that are extensible and contractible along their axes. The adjustable shafts 62 and 64 are adjustable or variable in length to change a tilt of the holding surface 8a, i.e., a tilt of the table axis 58, with respect to the turntable 6. Consequently, the adjustable shafts 62 and 64 function as a tilt adjusting unit for adjusting the tilt of the table axis 58.

As illustrated in FIG. 1, workpieces 1 can be delivered onto and away from the holding tables 8 in a wafer loading and unloading area. In the wafer loading and unloading area, the loading arm 34 loads a workpiece 1 onto one of the holding tables 8, and the unloading arm 36 unloads a workpiece 1 from one of the holding tables 8. After the loading arm 34 has delivered a workpiece 1 onto the holding table 8 located in the wafer loading and unloading area, the turntable 6 is turned to move the holding table 8 from the wafer loading and unloading area to a next rough grinding area disposed adjacent thereto.

The grinding apparatus 2 includes a first grinding unit, i.e., processing unit, 10a for rough-grinding the reverse side 1b of the workpiece 1 held on the holding table 8 that is located in the rough grinding area. The first grinding unit 10a is disposed radially outwardly of the turntable 6 on a rear portion of the upper surface of the base 4. After the workpiece 1 held on the holding table 8 that is located in the rough grinding area has been rough-ground by the first grinding unit 10a, the turntable 6 is turned 120 degrees to move the holding table 8 from the rough grinding area to a next finish grinding area disposed adjacent thereto.

The grinding apparatus 2 includes a second grinding unit, i.e., processing unit, 10b for finish-grinding the reverse side 1b of the workpiece 1 held on the holding table 8 that is located in the finish grinding area. The second grinding unit 10b is disposed radially outwardly of the turntable 6 on a rear portion of the upper surface of the base 4 adjacent to the first grinding unit 10a. After the workpiece 1 held on the holding table 8 that is located in the finish grinding area has been finish-ground by the second grinding unit 10b, the turntable 6 is turned 120 degrees to move the holding table 8 from the finish grinding area back to the wafer loading and unloading area where the unloading arm 36 unloads the finish-ground workpiece 1 from the holding table 8.

A spinner cleaning unit 38 for cleaning and spin-drying the workpiece 1 that has been ground is disposed on the upper surface of the base 4 in a vicinity of the unloading arm 36 and the wafer delivery robot 30. After the workpiece 1 has been cleaned and spin-dried by the spinner cleaning unit 38, the workpiece 1 is delivered from the spinner cleaning unit 38 by the wafer delivery robot 30 and stored into one of the cassettes 28a and 28b on the cassette rest bases 26a and 26b.

Two columns 22a and 22b that are spaced from each other are erected on the respective rear portions of the upper surface of the base 4. The first grinding unit 10a is vertically movably mounted on a front face of the column 22a, whereas the second grinding unit 10b is vertically movably mounted on a front face of the column 22b. The first grinding unit 10a includes a first spindle 14a extending vertically and a first spindle motor 12a coupled to an upper end of the first spindle 14a. The second grinding unit 10b includes a second spindle 14b extending vertically and a second spindle motor 12b coupled to an upper end of the second spindle 14b.

The first grinding unit 10a includes a first raising and lowering mechanism 24a that supports and vertically moves components of the first grinding unit 10a including the first spindle 14a. Similarly, the second grinding unit 10b includes a second raising and lowering mechanism 24b that supports and vertically moves components of the second grinding unit 10b including the second spindle 14b. The spindles 14a and 14b may have their axial orientations adjustable.

FIGS. 1 and 3 schematically illustrate the second raising and lowering mechanism 24b. Since the first raising and lowering mechanism 24a is structurally identical to the second raising and lowering mechanism 24b, only the second raising and lowering mechanism 24b will be described in detail below. The second raising and lowering mechanism 24b includes a pair of guide rails 24c extending vertically and mounted on the front face of the column 22b, a raising and lowering plate 50 vertically slidably supported on the guide rails 24c, and a ball screw 44 disposed between and extending parallel to the guide rails 24c. The components of the second grinding unit 10b are supported on a face side of the raising and lowering plate 50. A nut 46 is mounted on a reverse side of the raising and lowering plate 50 and operatively threaded over the ball screw 44. The ball screw 44 has an upper end coupled to a stepping motor 48 mounted on an upper end of the column 22b. When the stepping motor 48 is energized, it rotates the ball screw 44 about its vertical central axis, raising or lowering the raising and lowering plate 50.

A wheel mount 16a shaped as a circular plate is mounted on a lower end of the first spindle 14a, and a first grinding wheel, i.e., processing tool, 18a is fixed to a lower surface of the wheel mount 16a. In other words, the first grinding wheel 18a is fixed to the lower end of the first spindle 14a. The first grinding wheel 18a has a lower surface facing the holding surface 8a of the holding table 8 located in the rough grinding area. An annular array of first grindstones 20a is mounted on the lower surface of the first grinding wheel 18a. A wheel mount 16b shaped as a circular plate is mounted on a lower end of the second spindle 14b, and a second grinding wheel, i.e., processing tool, 18b is fixed to a lower surface of the wheel mount 16b. In other words, the second grinding wheel 18b is fixed to the lower end of the second spindle 14b. The second grinding wheel 18b has a lower surface facing the holding surface 8a of the holding table 8 located in the finish grinding area. An annular array of second grindstones 20b is mounted on the lower surface of the second grinding wheel 18b.

When the first spindle motor 12a is energized, it rotates the first spindle 14a about its longitudinal axis. The first grinding wheel 18a is also rotated to cause the first grindstones 20a to move along a first annular path, not depicted. Then, the first raising and lowering mechanism 24a is actuated to lower the first spindle 14a and hence the first grindstones 20a into abrasive contact with an upper surface of the workpiece 1 held on the holding table 8 in the rough grinding area, thereby rough-grinding the workpiece 1. When the second spindle motor 12b is energized, it rotates the second spindle 14b about its longitudinal axis. The second grinding wheel 18b is also rotated to cause the second grindstones 20b to move along a second annular path, not depicted. Then, the second raising and lowering mechanism 24b is actuated to lower the second spindle 14b and hence the second grindstones 20b into abrasive contact with an upper surface of the workpiece 1 held on the holding table 8 in the finish grinding area, thereby finish-grinding the workpiece 1.

In the first grinding unit 10a, the first raising and lowering mechanism 24a lowers, i.e., grinding-feeds, the first grindstones 20a at a relatively high speed, enabling the first grindstones 20a to rough-grind the workpiece 1. The first grinding unit 10a rough-grinds the workpiece 1 to a depth that takes up most of a total depth to which the workpiece 1 has to be ground by the first grinding unit 10a and the second grinding unit 10b until the workpiece 1 reaches a finished thickness. In the second grinding unit 10b, the second raising and lowering mechanism 24b lowers, i.e., grinding-feeds, the second grindstones 20b at a relatively low speed, enabling the second grindstones 20b to finish-grind the workpiece 1. The second grinding unit 10b finish-grinds the workpiece 1 until the workpiece 1 is ground to the total depth to reach the finished thickness, removing surface irregularities from the reverse side 1b of the workpiece 1. Each of the first grindstones 20a and the second grindstones 20b contains abrasive grains of diamond, for example, and a binder that binds the abrasive grains in a dispersed manner. It is preferable that the abrasive grains contained in the second grindstones 20b used for finish grinding be smaller in particle diameter than the abrasive grains contained in the first grindstones 20a used for rough grinding. With the preferable abrasive grain sizes, the first grindstones 20a are able to rough-grind the workpiece 1 relatively quickly, and the second grindstones 20b are able to finish-grind the workpiece 1 with high quality.

A first thickness measuring instrument 40 for measuring the thickness of the workpiece 1 that is rough-ground by the first grinding unit 10a is disposed on the upper surface of the base 4 near the first grinding unit 10a. A second thickness measuring instrument 42 for measuring the thickness of the workpiece 1 that is finish-ground by the second grinding unit 10b is disposed on the upper surface of the base 4 near the second grinding unit 10b.

The first thickness measuring instrument 40 is a contact-type thickness measuring instrument for measuring the thickness of the workpiece 1 while being kept in physical contact with the reverse side 1b of the workpiece 1. The contact-type first thickness measuring instrument 40 includes two probes extending over the holding table 8 in the rough grinding area, for example. Each of the probes includes an arm extending horizontally and a contact finger extending downwardly from a distal end of the arm. One of the probes measures a height of the reverse side 1b of the workpiece 1 by keeping a lower end of the contact finger in contact with the reverse side 1b of the workpiece 1. The other probe measures a height of the holding surface 8a of the holding table 8 by keeping a lower end of the contact finger in contact with the holding surface 8a. The workpiece 1 is placed and held on the holding surface 8a of the holding table 8 with the protective member 3 interposed therebetween. Therefore, the contact-type first thickness measuring instrument 40 is able to calculate a total thickness of the workpiece 1 and the protective member 3 from a difference between the measured height of the reverse side 1b of the workpiece 1 and the measured height of the holding surface 8a of the holding table 8.

The second thickness measuring instrument 42 is a non-contact-type thickness measuring instrument for measuring the thickness of the workpiece 1 while being kept out of physical contact with the reverse side 1b of the workpiece 1, for example. The non-contact-type second thickness measuring instrument 42 includes a measuring unit 42a disposed immediately above the reverse side 1b of the workpiece 1. The measuring unit 42a emits ultrasonic waves or light to the reverse side 1b of the workpiece 1, detects a reflection of the ultrasonic waves or light from the reverse side 1b, and measures the thickness of the workpiece 1 by analyzing the detected reflection of the ultrasonic waves or light.

The non-contact-type second thickness measuring instrument 42 includes a pivotable shaft 42b extending vertically upwardly from the upper surface of the base 4 and an arm 42c extending horizontally from an upper end of the shaft 42b in overhanging relation to the holding surface 8a of the holding table 8 in the finish grinding area. The measuring unit 42a is fixed to a distal end of the arm 42c. The shaft 42b has a lower end coupled to a rotating mechanism, not depicted, such as a piston or an electric motor for rotating the shaft 42b about its vertical central axis. When the rotating mechanism rotates the shaft 42b about its vertical central axis, the measuring unit 42a moves along an arcuate measurement path about the shaft 42b. In other words, the grinding apparatus 2 includes a measuring unit moving mechanism for reciprocally moving the measuring unit 42a along the measurement path above the workpiece 1 held on the holding table 8 in the finish grinding area. While the reverse side 1b of the workpiece 1 is being ground by the second grinding unit 10b, the measuring unit 42a is movable over the reverse side 1b to measure thicknesses of various portions of the workpiece 1.

The grinding apparatus 2 further includes a controller or control unit 90 for controlling the various components thereof. For example, the controller 90 controls the turntable 6, the holding tables 8, the grinding units 10a and 10b, the wafer delivery robot 30, the positioning table 32, the loading arm 34, the unloading arm 36, and the spinner cleaning unit 38. The controller 90 is configured, for example, by a computer including a processing unit such as a central processing unit (CPU) or a microprocessor and a storage unit such as a flash memory or a hard disk drive. The controller 90 functions as specific means implemented by a cooperation between software and hardware by operating the processing unit, i.e., a hardware resource, according to programs, i.e., a software resource, stored in the storage unit.

The controller 90 stores processing conditions under which various workpieces 1 are to be ground by the first and second grinding units 10a and 10b and various pieces of information in the storage unit. The processing conditions stored in the storage unit represent information regarding a type and size of the workpieces 1 to be processed, workpiece thicknesses to be achieved by rough grinding and finish grinding, and speeds at which the first and second spindles 14a and 14b are to be rotated, for example. Further configurational and functional details of the controller 90 will be described later.

As illustrated in FIG. 3, the holding surface 8a of the holding table 8 is shaped as an upwardly protruding conical surface that is slanted gradually from a central apex. Since the holding surface 8a is conical in shape, when the holding table 8 holds the workpiece 1 under suction thereon, the workpiece 1 is slightly elastically deformed into a conical shape complementary to the conical shape of the holding surface 8a. The workpiece 1, the holding table 8, and other parts are depicted as exaggerated for illustrative purposes in various figures. Finish grinding carried out by the second grinding unit 10b illustrated in FIG. 3 will be described below.

For grinding the workpiece 1, the holding table 8 that is holding the workpiece 1 on the holding surface 8a is rotated about the table axis 58, and while the second spindle 14b is being rotated about its longitudinal axis, the second raising and lowering mechanism 24b lowers the second spindle 14b to bring the second grindstones 20b into abrasive contact with the reverse side 1b of the workpiece 1. As the second grindstones 20b are grinding an arcuate region of the workpiece 1 from its center to an outer circumferential potion thereof, the workpiece 1 on the holding table 8 is rotated to cause the second grindstones 20b to grind the entire reverse side 1b of the workpiece 1. The tilt of the table axis 58 is adjusted in order to make one of generatrices of the conical holding surface 8a that is closest to a rotational plane including the second annular path followed by the second grindstones 20b parallel to the rotational plane, so that the ground reverse side 1b of the workpiece 1 and the face side 1a thereof will lie parallel to each other. The second thickness measuring instrument 42 monitors the thickness of the workpiece 1. When the workpiece 1 is ground to the predetermined thickness, the second raising and lowering mechanism 24b stops lowering the second spindle 14b, thereby completing the grinding of the workpiece 1.

The controller 90 includes a grinding controlling section 92 for controlling the components of the grinding apparatus 2 to grind the workpiece 1. For grinding the workpiece 1, the grinding controlling section 92 causes the holding table 8 that is holding the workpiece 1 thereon to rotate about the table axis 58 and also causes the first and second grinding wheels 18a and 18b of the first and second grinding units 10a and 10b to rotate about the respective longitudinal axes of the first and second spindles 14a and 14b. The grinding controlling section 92 controls the first and second raising and lowering mechanisms 24a and 24b to lower the first and second spindles 14a and 14b and cause the first and second grindstones 20a and 20b to grind the workpiece 1 in abrasive contact with the upper surface, i.e., the reverse side 1b, thereof. The grinding controlling section 92 controls the components according to the processing conditions, i.e., grinding conditions, stored in the storage unit of the controller 90. While the workpiece 1 is being ground, the grinding controlling section 92 monitors the thickness of the workpiece 1 with the first and second thickness measuring instruments 40 and 42. When the workpiece 1 is ground to the predetermined thicknesses, the grinding controlling section 92 causes the first and second raising and lowering mechanisms 24a and 24b to stop lowering the first and second spindles 14 and 14b, bringing the grinding of the workpiece 1 to an end.

If the tilt of the table axis 58 of the holding table 8 is inappropriate, then the workpiece 1 does not have a uniform thickness distribution and suffers a thickness deviation, so that the face side 1a and the reverse side 1b of the workpiece 1 do not lie parallel to each other. This difficulty is dealt with as follows: While the workpiece 1 is being ground, the measuring unit 42a of the second thickness measuring instrument 42 is moved to measure the thicknesses of various portions of the workpiece 1. The thickness distribution of the workpiece 1 based on the thicknesses thus measured by the second thickness measuring instrument 42 is monitored. In a case where the monitored thickness distribution suffers a problem, the tilt adjusting unit is actuated to adjust the tilt of the table axis 58. Specifically, the controller 90 monitors the thickness distribution of the workpiece 1 with the first and second thickness measuring instruments 40 and 42. If a large thickness deviation is detected from the workpiece 1, then the controller 90 controls the tilt adjusting unit to adjust the tilt of the table axis 58.

For adjusting the tilt of the table axis 58, the controller 90 refers to a cross-sectional shape, i.e., a thickness distribution, of the workpiece 1. Specifically, the controller 90 includes a thickness distribution specifying section 94 for measuring the thicknesses of the workpiece 1 at various points with the measuring unit 42a while moving the measuring unit 42a along the measurement path with the measuring unit moving mechanism, and specifying a thickness distribution of the workpiece 1 based on the measured thicknesses. Further, the controller 90 calculates, for example, an adjustment variable for adjusting the tilt of the table axis 58 with the tilt adjusting unit so as to bring the workpiece 1 ground by the first and second grindstones 20a and 20b closer to the predetermined configuration, on the basis of the specified thickness distribution. More specifically, the controller 90 includes a positional relation adjusting section 96 for adjusting a positional relation between the second grinding wheel, i.e., processing tool, 18b and the holding table 8.

The thickness distribution specifying section 94 and the positional relation adjusting section 96 will be described in detail in connection with an adjusting step S40 of the method of processing a workpiece according to the present embodiment. The grinding controlling section 92 of the controller 90 controls the tilt adjusting unit and the like by referring to the calculated adjustment variable of the positional relation to adjust the tilt of the table axis 58 and the like and continues grinding, i.e., thinning down, the workpiece 1.

A relation between a deviation in the thickness distribution of the workpiece 1 and the tilt of the table axis 58 while the workpiece 1 is being ground will be described in detail below. The relation will be described with respect to finish grinding in which the second grinding unit 10b finish-grinds the workpiece 1 by way of example. However, the same relation applies to rough grinding in which the first grinding unit 10a rough-grinds the workpiece 1.

FIG. 4 schematically illustrates in plan the positional relation between the holding surface 8a of the holding table 8 and the annular path, denoted by 20c, that is followed by the second grindstones 20b as they are rotated by the second spindle 14b. In FIG. 4, a contour of the conical holding surface 8a of the holding table 8 and the annular path 20c are schematically illustrated as circles. The annular path 20c is of a circular shape that is equal in diameter to the circular holding surface 8a. The table axis 58 of the holding table 8 extends through the center, denoted by 68, of the holding surface 8a. FIG. 4 also illustrates the fixed shaft 60 and the two adjustable shafts 62 and 64 by which the holding table 8 is supported from below. The fixed shaft 60 is positioned generally beneath a center of the second grinding wheel 18b. The fixed shaft 60 and the two adjustable shafts 62 and 64 are disposed at respective vertexes of an equilateral triangle. The holding table 8 is supported on the turntable 6 by the fixed shaft 60 and the adjustable shafts 62 and 64, and the adjustable shafts 62 and 64 function as the tilt adjusting unit.

When the adjustable shaft 62 is neither extended nor contracted but the adjustable shaft 64 is extended or contracted, the holding table 8 varies its tilt by being turned about a first axis 74 interconnecting the fixed shaft 60 and the adjustable shaft 62. When the adjustable shaft 64 is neither extended nor contracted but the adjustable shaft 62 is extended or contracted, the holding table 8 varies its tilt by being turned about a second axis 76 interconnecting the fixed shaft 60 and the adjustable shaft 64. In other words, the tilt of the table axis 58 can be varied when one or both of the adjustable shafts 62 and 64 are extended or contracted.

For grinding the workpiece 1, the tilt adjusting unit adjusts the tilt of the table axis 58 in order to make a generatrix interconnecting the center 68 of the holding surface 8a and an outer circumferential point 66 thereof parallel to the annular path 20c, the center 68 and the outer circumferential point 66 being aligned with the annular path 20c. The second grindstones 20b that move along the annular path 20c abrasively contact the reverse side 1b of the workpiece 1 in a grinding zone 72 between a position above the center 68 of the holding surface 8a and a position above the outer circumferential point 66 of the holding surface 8a, thereby grinding the workpiece 1. In a zone between the position above the center 68 of the holding surface 8a and a position above another outer circumferential point 70 of the holding surface 8a, the center 68 and the outer circumferential point 70 being aligned with the annular path 20c, the second grindstones 20b that move along the annular path 20c are kept out of abrasive contact with the reverse side 1b of the workpiece 1.

FIGS. 5A and 5B are graphs illustrative of thickness distributions of the workpiece 1 that occur as a result of grinding when the tilt of the table axis 58 is inappropriate. In each of the graphs, a horizontal axis represents a distance from the center of the workpiece 1, and a vertical axis represents an amount of a thickness deviation of the workpiece 1. When the workpiece 1 is ground, the holding table 8 is rotated about the table axis 58, and the second grinding wheel 18b is rotated about the longitudinal axis of the second spindle 14b. At this time, since a circular area of the workpiece 1 that is spaced a certain distance from the center of the workpiece 1 is similarly ground, the workpiece 1 has an essentially constant thickness distribution in the circular area. As indicated by the graphs of FIGS. 5A and 5B, therefore, the thickness distribution of the workpiece 1 can be assessed from a relation between the distance from the center of the workpiece 1 and the amount of a thickness deviation of the workpiece 1.

The thickness distribution illustrated in FIG. 5B represents an example of thickness distribution that occurs on the workpiece 1 in a case where the grinding zone 72 between the position above the center 68 of the holding surface 8a and the position above the outer circumferential point 66 of the holding surface 8a is tilted in its entirety. This thickness distribution occurs when the annular path 20c followed by the second grindstones 20b and the generatrix interconnecting the center 68 of the holding surface 8a and the outer circumferential point 66 thereof are not parallel to each other. More specifically, the thickness distribution illustrated in FIG. 5B occurs when a distance between the holding surface 8a and the annular path 20c is larger at the center 68 than at the outer circumferential point 66. The difference between the thickness of the workpiece 1 at the center 68 and the thickness of the workpiece 1 at the outer circumferential point 66 is indicated as a thickness deviation “a” in FIG. 5B. If the distance between the holding surface 8a and the annular path 20c is larger at the outer circumferential point 66 than at the center 68, then the thickness deviation “a” is of a negative value.

The thickness deviation “a” may also be called “protrusion parameter” because of the cross-sectional shape of the workpiece 1 due to the thickness deviation “a.” In order to eliminate the deviation of the thickness distribution indicated by the graph of FIG. 5B, the axial length of the adjustable shaft 64 may mainly be adjusted to make the holding surface 8a and the annular path 20c parallel to each other. As illustrated in FIG. 5B, this thickness deviation can be expressed by a linear function involving the distance from the center of the workpiece 1 on the horizontal axis and the amount of the thickness deviation of the workpiece 1 on the vertical axis. The linear function indicates that, when the distance on the horizontal axis is zero, the amount of the thickness deviation on the vertical axis is “a,” and when the distance on the horizontal axis is R indicative of a value of a radius of the workpiece 1, the amount of the thickness deviation on the vertical axis is zero.

The thickness distribution illustrated in FIG. 5A represents an example of thickness distribution that occurs on the workpiece 1 in a case where the depth to which the second grindstones 20b grind the workpiece 1 is larger or smaller at a center of the grinding zone 72 between the position above the center 68 of the holding surface 8a and the position above the outer circumferential point 66 of the holding surface 8a. In order to eliminate the deviation of the thickness distribution illustrated in FIG. 5A, the adjustable shaft 62 may be mainly adjusted while at the same time the adjustable shaft 64 may be extended or contracted so as to match a change in the tilt of the entire grinding zone 72 that is caused by the adjustment of the adjustable shaft 62. More specifically, the thickness distribution illustrated in FIG. 5A occurs in a case where the depth to which the second grindstones 20b grind the workpiece 1 is smaller at the center of the grinding zone 72 between the position above the center 68 of the holding surface 8a and the position above the outer circumferential point 66 of the holding surface 8a. The difference between the thickness of the workpiece 1 at the center of the grinding zone 72 and the thickness of the workpiece 1 at the center and outer circumferential point 66 thereof is indicated as a thickness deviation “m” in FIG. 5A. If the center of the grinding zone 72 of the workpiece 1 is ground to a larger depth than the other peripheral areas thereof, then the thickness deviation “m” is of a negative value.

The thickness deviation “m” may also be called “gullwing parameter” because of the cross-sectional shape of the workpiece 1 due to the thickness deviation “m.” Adjustment variables for the adjustable shafts 62 and 64 may be determined in order to make the thickness deviation “m” zero. As illustrated in FIG. 5A, this thickness deviation “m” can be expressed by a quadratic function involving the distance from the center of the workpiece 1 on the horizontal axis and the amount of the thickness deviation of the workpiece 1 on the vertical axis. The quadratic function indicates that, when the distance on the horizontal axis is zero, the amount of the thickness deviation on the vertical axis is zero, when the distance on the horizontal axis is 0.5 R, the amount of the thickness deviation on the vertical axis is “m,” and when the distance on the horizontal axis is R, the amount of the thickness deviation on the vertical axis is zero.

If the lengths of both of the adjustable shafts 62 and 64 are appropriate, then the thickness of the workpiece 1 is uniform in its entirety. If the lengths of both of the adjustable shafts 62 and 64 are inappropriate, then a thickness distribution that represents a sum of the thickness distribution illustrated in FIG. 5A and the thickness distribution illustrated in FIG. 5B occurs on the workpiece 1. Conversely, if the tilt of the table axis 58 of the holding table 8 is inappropriate, for example, then a thickness distribution that occurs on the workpiece 1 can be divided into the thickness distribution illustrated in FIG. 5A and the thickness distribution illustrated in FIG. 5B.

The controller 50 calculates adjustment variables for the adjustable shafts 62 and 64 in order to make the thickness deviation “m” illustrated in FIG. 5A zero and also to make the thickness deviation “a” illustrated in FIG. 5B zero. The grinding controlling section 92 refers to the calculated adjustment variables and controls the tilt adjusting unit to adjust the lengths of the adjustable shafts 62 and 64, thereby adjusting the tilt of the table axis 58. In addition to or instead of adjusting the tilt of the table axis 58 for shaping the workpiece 1 into a desired configuration as a result of the processing, the controller 90 may adjust the tilt of the first and second spindles 14a and 14b. Moreover, the controller 90 may adjust the relative positional relation between the holding table 8 and the first and second grinding units 10a and 10b in directions generally parallel to the holding surface 8a of the holding table 8. By grinding or processing the workpiece 1 progressively while making these adjustments, the workpiece 1 will eventually be shaped into the desired configuration.

The contact-type first thickness measuring instrument 40 is required to bring its probes into contact with the workpiece 1 whose thickness is to be measured, possibly causing damage to the workpiece 1. In a case where the workpiece 1 has surface irregularities, the probes are liable to be damaged or vibrated greatly when they contact steps formed on the workpiece 1 by those surface irregularities. The non-contact-type second thickness measuring instrument 42 may have a higher level of measurement accuracy than the contact-type first thickness measuring instrument 40. Therefore, it is preferable to use the non-contact-type second thickness measuring instrument 42 to measure the thickness of the workpiece 1 that is being finish-ground.

Nevertheless, the non-contact-type second thickness measuring instrument 42 may not be able to measure the total thickness of the workpiece 1 depending on the makeup of the workpiece 1. As described above, the workpiece 1 includes the first region 7 and the second region 9 overlying the first region 7. The first region 7 of the workpiece 1 may be less transmissive of light or ultrasonic waves applied from the non-contact-type second thickness measuring instrument 42 to the workpiece 1 than the second region 9 of the workpiece 1. Stated otherwise, the second region 9 of the workpiece 1 may be more transmissive of light or ultrasonic waves applied from the non-contact-type second thickness measuring instrument 42 to the workpiece 1 than the first region 7 of the workpiece 1. In this case, when the measuring unit 42a detects light or ultrasonic waves applied to and emitted from the workpiece 1, though the measuring unit 42a is capable of acquiring information regarding the thickness of the structure or structures of the second region 9, the measuring unit 42a is less liable to acquire information regarding the thickness of the structure or structures of the first region 7. Consequently, when a workpiece 1 where a plurality of regions, i.e., layers or structures, are layered together is to be measured, it is difficult for a single thickness measuring instrument disposed in a vicinity of a point where the workpiece 1 is processed to measure the total thickness of the workpiece 1.

Therefore, the total thickness of the workpiece 1 cannot be measured by simply using the single thickness measuring instrument, and the positional relation between the processing tool and the holding table cannot be adjusted on the basis of the thickness distribution of the workpiece 1. This poses a problem because the workpiece 1 cannot be processed into a predetermined configuration. In the method of processing a workpiece according to the present embodiment, the workpiece 1 is processed while the total thickness of the workpiece 1 where a plurality of regions, i.e., layers or structures, having respective properties different from each other are layered together is obtained as described below.

The method of processing a workpiece according to the present embodiment will be described below with respect to an example where the grinding apparatus, i.e., the processing apparatus, 2 is mainly used. In the example, particularly, the workpiece 1 where the first region 7 and the second region 9 are layered together is ground and hence thinned down by the second grinding unit 10b. FIG. 10A is a flowchart illustrating a sequence of steps of the method of processing a workpiece.

First, a first acquiring step S10 is carried out to acquire the thickness of the first region 7 of the workpiece 1, after which a first processing step S20 is carried out to thin down the second region 9 of the workpiece 1 held on the holding table 8 by bringing the second grindstones 20b on the second grinding wheel, i.e., processing tool, 18b into abrasive contact with the workpiece 1. Then, a second acquiring step S30 is carried out to measure and acquire the thickness of the second region 9 of the workpiece 1 that has been thinned down in the first processing step S20. Thereafter, the adjusting step S40 is carried out to adjust the positional relation between the second grinding wheel, i.e., processing tool, 18b and the holding table 8 by referring to the total thickness of the workpiece 1 that includes the thickness of the first region 7 and the thickness of the second region 9. Then, after the positional relation between the second grinding wheel 18b and the holding table 8 has been adjusted, a second processing step S50 is carried out to thin down the workpiece 1 held on the holding table 8 by bringing the second grindstones 20b on the second grinding wheel 18b into abrasive contact with the workpiece 1. Each of the steps will be described in detail below.

The first acquiring step S10 will be described in detail below. The first acquiring step S10 should preferably be carried out before the second region 9 of the workpiece 1 is processed by the second grinding wheel 18b. More preferably, the first acquiring step S10 should be carried out in a standby period of time before the workpiece 1 is delivered to the holding table 8 and held on the holding table 8 or before the workpiece 1 held on the holding table 8 is processed by the second grinding wheel 18b.

In the first acquiring step S10, the thickness of the first region 7 of the workpiece 1 is acquired. For example, the thickness of the first region 7 of the workpiece 1 is acquired by way of measurement. The thickness of the first region 7 acquired by way of measurement is stored in the storage unit of the controller 90. Alternatively, in the first acquiring step S10, the thickness of the first region 7 that has been measured and stored beforehand in the storage unit of the controller 90 is acquired by being read from the storage unit. In the case where the thickness of the first region 7 of the workpiece 1 is acquired by way of measurement or the thickness of the first region 7 is measured in advance and then stored in the storage unit of the controller 90, the measurement may be performed in the grinding apparatus 2 or outside the grinding apparatus 2. If the measurement is performed outside the grinding apparatus 2, the thickness is measured before the workpiece 1 is stored in the cassette 28a or 28b.

If the thickness of the first region 7 of the workpiece 1 is measured in the grinding apparatus 2, the thickness may be measured during a period of time after the workpiece 1 has been unloaded from the cassette 28a or 28b and before the workpiece 1 is delivered onto the holding table 8. In other words, the first acquiring step S10 may be carried out while the workpiece 1 is not being held on the holding table 8. In the case where the workpiece 1 is not held on the holding table 8, the thickness of the first region 7 of the workpiece 1 can be measured and acquired by a method that cannot be performed while the workpiece 1 is being held on the holding table 8, e.g., while at least a portion of the surface of the workpiece 1 held on the holding table 8 is being exposed. The grinding apparatus 2 may include a measuring unit for measuring the workpiece 1 that is being delivered by the wafer delivery robot 30 or the loading arm 34 or a measuring unit for measuring the workpiece 1 that is placed on the positioning table 32.

FIG. 6 schematically illustrates in cross section, partly in side elevation, a thickness measuring unit 100 that can be used in the first acquiring step S10. The thickness measuring unit 100 is disposed on the upper surface of the base 4 of the grinding apparatus 2, for example. Particularly, the thickness measuring unit 100 should preferably be incorporated in the positioning table 32. However, the thickness measuring unit 100 may be disposed outside the grinding apparatus 2. As illustrated in FIG. 6, the thickness measuring unit 100 includes a support 102 for supporting the workpiece 1 from below and a measuring section 104 for measuring the thickness of the workpiece 1 supported on the support 102. The support 102 is of a substantially hollow cylindrical shape and includes a substantially annular upper surface 106. The workpiece 1 as an object whose thickness is to be measured is placed on the support 102 such that the workpiece 1 has its outer circumferential portion lying on the upper surface 106 of the support 102. When the workpiece 1 is placed on the support 102, the workpiece 1 has its lower surface, i.e., the face side 1a, exposed downwardly almost in its entirety except for a part of the outer circumferential portion thereof.

The measuring section 104 includes a probe unit 116 for contacting the upper surface, i.e., the reverse side 1b, of the workpiece 1, a probe unit 112 for contacting the lower surface, i.e., the face side 1a, of the workpiece 1, and a support block 108 that supports the probe units 112 and 116 while allowing them to be raised and lowered. The support block 108 is disposed sideways of the support 102. The measuring section 104 further includes an arm 114 extending from the support block 108 over the workpiece 1 supported on the support 102 and an arm 110 extending from the support block 108 under the workpiece 1 supported on the support 102. The probe unit 116 is fixed to a distal end of the arm 114, and the probe unit 112 is fixed to a distal end of the arm 110. The probe unit 116 includes a probe 120 for contacting the upper surface of the workpiece 1, and the probe unit 112 includes a probe 118 for contacting the lower surface of the workpiece 1.

The support block 108 incorporates therein a raising and lowering mechanism, not depicted, that may be of a ball-screw type or a cylinder type, for example. When actuated, the raising and lowering mechanism raises and lowers the respective arms 110 and 114. The thickness measuring unit 100 detects a height of the upper surface of the workpiece 1 and a height of the lower surface of the workpiece 1 by raising and lowering the arms 110 and 114 and sensing when the probes 118 and 120 contact the workpiece 1. The thickness measuring unit 100 identifies a difference between the detected heights as the total thickness of the workpiece 1.

It is preferable that the components of the thickness measuring unit 100 have their shapes and sizes determined to keep the probes 118 and 120 in vertical alignment with each other. The probes 118 and 120 that are vertically aligned with each other make it possible to simultaneously measure the heights of the upper and lower surfaces of the workpiece 1 at one location on the workpiece 1.

The thickness measuring unit 100 allows the probes 118 and 120 to change their positions with respect to the workpiece 1 by, for example, moving the support block 108 in directions parallel to the upper surface 106 of the support 102, extending or contracting the arms 110 and 114, and/or turning one of or both the support block 108 and the workpiece 1 supported on the support 102 about respective axes perpendicular to the upper surface 106 of the support 102. The support 102 has its shape and layout determined in order to avoid colliding with the probe unit 112 held in contact with the lower surface of the workpiece 1 and the arm 110 when the positions of the probes 118 and 120 with respect to the workpiece 1 are changed.

The measuring section 104 of the thickness measuring unit 100 further includes a non-contact-type measuring head 122 for measuring the thickness of the second region 9 of the workpiece 1. The measuring head 122 acts as a non-contact-type thickness measuring instrument similar to the second thickness measuring instrument 42 described above. The measuring head 122 operates as follows: The measuring head 122 that is disposed immediately above the upper surface, i.e., the reverse side 1b, of the workpiece 1 applies light or ultrasonic waves to the workpiece 1 and detects light or ultrasonic waves reflected from the workpiece 1. The thickness measuring unit 100 measures the thickness of the second region 9 by analyzing the detected light or ultrasonic waves. The thickness measuring unit 100 can calculate the thickness of the first region 7 by subtracting the thickness of the second region 9 from the total thickness of the workpiece 1 that is measured by the measuring section 104. As with the probe units 112 and 116, the measuring head 122 can change its position with respect to the workpiece 1. By measuring the total thicknesses of the workpiece 1 and the thicknesses of the second region 9 at different portions of the workpiece 1, it is possible to acquire the thicknesses of the first region 7 at the different portions of the workpiece 1. The thickness of the first region 7 of the workpiece 1 acquired in the first acquiring step S10 may be calculated by subtracting the thickness of the second region 9 from the total thickness of the workpiece 1.

The thickness measuring unit may not necessarily be required to measure the total thickness of the workpiece 1 in the first acquiring step S10. A thickness measuring unit according to a modification for use in the first acquiring step S10 will be described below. FIG. 7 schematically illustrates in cross section, partly in side elevation, a thickness measuring unit 100a according to a modification. As illustrated in FIG. 7, the thickness measuring unit 100a includes a support 102a for supporting the workpiece 1 from below, as with the thickness measuring unit 100 illustrated in FIG. 6. The support 102a is similar in structure to the support 102 of the thickness measuring unit 100. The support 102a supports thereon the workpiece 1 with the reverse side 1b facing downwardly and the face side 1a facing upwardly.

The thickness measuring unit 100a includes a measuring head 122a for directly measuring the thickness of the first region 7 of the workpiece 1. The measuring head 122a acts as a non-contact-type thickness measuring instrument similar to the measuring head 122 illustrated in FIG. 6. However, the measuring head 122a applies to the workpiece 1 ultrasonic waves or light that can be transmitted more easily through the first region 7 than through the second region 9. The measuring head 122a detects ultrasonic waves or light reflected from the workpiece 1. The thickness measuring unit 100a then measures the thickness of the first region 7 by analyzing the detected ultrasonic waves or light. Alternatively, the thickness measuring unit 100a may measure the thickness of the second region 9. According to the alternative, the measuring head 122a applies to the workpiece 1 ultrasonic waves or light that can be transmitted more easily through the second region 9 than through the first region 7. The thickness measuring unit 100a may measure the thickness of the second region 9 and then calculate the thickness of the first region 7 by subtracting the measured thickness of the second region 9 from the total thickness of the workpiece 1.

The measuring head 122a may be disposed beneath the workpiece 1 rather than above the workpiece 1 as illustrated in FIG. 7. In the case where the measuring head 122a is disposed beneath the workpiece 1 placed on the support 102a, the workpiece 1 is placed on the support 102a with the face side 1a facing downwardly and the reverse side 1b facing upwardly.

The thickness of the first region 7 of the workpiece 1 that is acquired in the first acquiring step S10 is measured by the thickness measuring unit 100 or 100a. In the first acquiring step S10, the thickness of the first region 7 of the workpiece 1 is measured and acquired by the thickness measuring unit 100 or 100a and stored in the storage unit of the controller 90 of the grinding apparatus 2. Alternatively, in the first acquiring step S10, the thickness of the first region 7 is acquired by subtracting the measured thickness of the second region 9 from the total thickness of the workpiece 1 stored in the storage unit of the controller 90 and is then stored in the storage unit of the controller 90. Further alternatively, in the first acquiring step S10, the thickness of the first region 7 that has been stored in the storage unit of the controller 90 is read from the storage unit.

In the method of processing a workpiece according to the present embodiment, the first processing step S20 is carried out after the first acquiring step S10 or before the first acquiring step S10. In the first processing step S20, the workpiece 1 is delivered onto the holding table 8 and held under suction on the holding table 8. Then, the second grinding wheel, i.e., processing tool, 18b is brought into abrasive contact with the workpiece 1 held on the holding table 8 to thin down the workpiece 1. Before the workpiece 1 is ground by the second grindstones 20b on the second grinding wheel 18b, the workpiece 1 may be ground by the first grindstones 20a on the first grinding wheel 18a. FIG. 3 schematically illustrates in cross-section, partly in side elevation, a manner in which the workpiece 1 held on the holding table 8 is ground, i.e., thinned down, by the second grinding unit 10b. The second grinding unit 10b thins down the workpiece 1 by rotating the second grinding wheel 18b and the holding table 8 about their respective axes and lowering the second grinding unit 10b to bring the second grindstones 20b on the second grinding wheel 18b into abrasive contact with the reverse side 1b of the workpiece 1 on the holding table 8. At this time, the second grinding unit 10b stops being lowered before the workpiece 1 is thinned down to the finished thickness as a final target thickness.

In the method of processing a workpiece according to the present embodiment, the second acquiring step S30 is carried out to measure and acquire the thickness of the second region 9 of the workpiece 1 that has been thinned down in the first processing step S20. The second acquiring step S30 may be carried out by the second thickness measuring instrument 42 of the grinding apparatus 2. In the second acquiring step S30, the thickness of the second region 9 of the workpiece 1 may be measured by the second thickness measuring instrument 42 that performs the measurement of the thickness using light or ultrasonic waves without contacting the workpiece 1. In this case, the second region 9 of the workpiece 1 should preferably be more transmissive of light or ultrasonic waves used by the second thickness measuring instrument 42 than the first region 7 of the workpiece 1.

The thickness of the second region 9 of the workpiece 1 is measured after the first processing step S20 has been completed and before the second processing step S50 to be described later is carried out. After the first processing step S20 has been completed, the second grinding wheel, i.e., processing tool, 18b should preferably be retracted from an area above the workpiece 1. In this case, the second acquiring step S30 is carried out with the second grinding wheel 18b being kept out of contact with the workpiece 1. As the second grinding wheel 18b has been retracted from the area above the workpiece 1, the measuring unit 42a of the second thickness measuring instrument 42 can be moved to any position in the area above the workpiece 1 without physical interference with the second grinding wheel 18b.

Positions where the thickness of the second region 9 is acquired in the second acquiring step S30 will be described below. As described below, the positions where the thickness of the second region 9 is acquired have a predetermined relation to the positions where the thickness of the first region 7 is acquired in the first acquiring step S10. Therefore, the positions where the thickness of the first region 7 is acquired will also be described below.

There is no need to acquire the thickness of the first region 7 of the workpiece 1 in its entirety in the first acquiring step S10, and there is no need either to acquire the thickness of the second region 9 of the workpiece 1 in its entirety in the second acquiring step S30. As long as the positional relation can be adjusted with sufficient accuracy in the adjusting step S40 to be described later, the thickness of the workpiece 1 may be acquired in a small number of positions. For example, at least two positions on the workpiece 1 for acquiring the thickness of the first region 7 and the thickness of the second region 9 may be enough to allow sufficiently accurate adjustment in the adjusting step S40.

However, in order to calculate the total thickness of the workpiece 1 at various portions thereof in the adjusting step S40 to be described later, the thickness of the workpiece 1 should preferably be acquired in similar positions in the first acquiring step S10 and the second acquiring step S30. Stated otherwise, it is preferable to acquire the thickness of the first region 7 in the first acquiring step S10 and to acquire the thickness of the second region 9 in the second acquiring step S30 at particular positions on the workpiece 1. However, the position where the thickness of the workpiece 1 is to be acquired in the first acquiring step S10 and the position where the thickness of the workpiece 1 is to be acquired in the second acquiring step S30 do not need to be completely identical to each other. Depending on properties of the workpiece 1 and details of the thinning, there are occasions in which the thickness of the first region 7 remains alike in a particular area of the workpiece 1 on a plane parallel to the face side 1a and the reverse side 1b, and the thickness of the second region 9 before the workpiece 1 is thinned down and while the workpiece 1 is being thinned down remains alike in the particular area.

For example, the thickness of the first region 7 may remain alike in an annular area representing a set of points spaced a certain distance from the center of the workpiece 1 on the plane parallel to the face side 1a and the reverse side 1b. Moreover, in the annular area, the thickness of the second region 9 before the workpiece 1 is thinned down may remain alike, and the thickness of the second region 9 while the workpiece 1 is being thinned down may remain alike. In this case, the thickness of the first region 7 may be acquired at one of the points belonging to the annular area in the first acquiring step S10, and the thickness of the second region 9 may be acquired at the identical one or another one of the points belonging to the annular area in the second acquiring step S30. Each of the acquired thicknesses can be handled as a representative value of the thickness in the annular area. FIG. 8 schematically illustrates in plan the reverse side 1b, as a processed surface, of the workpiece 1. FIG. 8 indicates positions where the thickness of the workpiece 1 is acquired. For example, positions 13 where the thickness is to be acquired should preferably be located in a vicinity of the center of the workpiece 1, in an annular area 15 spaced from the center of the workpiece 1 by a predetermined distance equal to one half of the radius of the reverse side 1b of the workpiece 1, and in a vicinity of the outer circumferential portion of the workpiece 1.

The positions where the thickness of the first region 7 of the workpiece 1 is acquired and the positions where the thickness of the second region 9 thereof is acquired will be described from another standpoint below. In the first acquiring step S10, the thickness of the first region 7 may be acquired at positions spaced a first distance from the center of the workpiece 1 and at positions spaced a second distance, different from the first distance, from the center of the workpiece 1. In the second acquiring step S30, the thickness of the second region 9 may be acquired at positions spaced the first distance from the center of the workpiece 1 and at positions spaced the second distance from the center of the workpiece 1. By thus determining the positions 13 where the thickness of the workpiece 1 is to be acquired, a tendency of the thicknesses of the first region 7 and the second region 9 of the workpiece 1 in its entirety can fully be recognized. Consequently, adjustments can be made with sufficient accuracy in the adjusting step S40.

As described above, the thicknesses of the second region 9 of the thinned-down workpiece 1 are measured and acquired in the second acquiring step S30. The thicknesses of the second region 9 acquired in the second acquiring step S30 may be stored in the storage unit of the controller 90. In this manner, the total thickness of the workpiece 1 that has been thinned down can be derived, and adjustments can be made on the basis of the total thickness of the workpiece 1 in the adjusting step S40 to be described below.

In the method of processing a workpiece according to the present embodiment, the adjusting step S40 is carried out after the second acquiring step S30. For example, the adjusting step S40 is carried out mainly by the thickness distribution specifying section 94 and the positional relation adjusting section 96 of the controller 90. Consequently, the description of the adjusting step S40 to be given below may be referred to as the description of the functions of the thickness distribution specifying section 94 and the positional relation adjusting section 96. In the adjusting step S40, the positional relation between the second grinding wheel 18b and the holding table 8 is adjusted. The positional relation is adjusted by referring to the total thickness of the workpiece 1 that includes the thickness of the first region 7 acquired in the first acquiring step S10 and the thickness of the second region 9 acquired in the second acquiring step S30.

For carrying out the adjusting step S40, the thickness of the first region 7 stored in the storage unit of the controller 90 is acquired. In a case where the first acquiring step S10 is carried out by acquiring the thickness of the first region 7 stored in the storage unit, the first acquiring step S10 is carried out when the adjusting step S40 is carried out. In a case where the first acquiring step S10 is carried out by measuring and acquiring the thickness of the first region 7, the adjusting step S40 is carried out after the first acquiring step S10. In the adjusting step S40, the thickness of the second region 9 acquired in the second acquiring step S30 and stored in the storage unit of the controller 90 is read from the storage unit. The controller 90 calculates the total thickness of the workpiece 1 from the thickness of the first region 7 and the thickness of the second region 9 thus read from the storage unit. More specifically, the thickness distribution specifying section 94 of the controller 90 adds the thicknesses of the first region 7 and the thicknesses of the second region 9 at various portions of the workpiece 1 to calculate the total thicknesses of the workpiece 1 at the various portions thereof. In this fashion, a thickness distribution of the workpiece 1 is obtained.

In the adjusting step S40, the positional relation adjusting section 96 of the controller 90 calculates adjustment variables for the adjustment of the positional relation between the second grinding wheel 18b and the holding table 8 on the basis of the total thicknesses at the various portions of the workpiece 1, i.e., the thickness distribution. For example, the positional relation adjusting section 96 calculates a deviation “a,” i.e., a protrusion parameter, and a deviation “m,” i.e., a gullwing parameter, illustrated in FIGS. 5A and 5B, from the total thicknesses at the various portions of the workpiece 1, i.e., the thickness distribution. Then, the positional relation adjusting section 96 derives adjustment variables to make the deviation “a” and the deviation “m” closer to zero through subsequent thinning in the second processing step S50.

For example, the positional relation adjusting section 96 derives adjustment variables required with respect to the tilt of the table axis 58 and calculates adjustment variables for the lengths of the adjustable shafts 62 and 64. Then, the positional relation adjusting section 96 adjusts the lengths of the adjustable shafts 62 and 64 based on the calculated adjustment variables, thereby adjusting the tilt of the table axis 58. Alternatively, in the adjusting step S40, the positional relation adjusting section 96 may calculate an adjustment variable for the tilt of the second spindle 14b of the second grinding unit 10b, i.e., the tilt of an axis about which a processing tool is rotatable, instead of or in addition to the tilt of the table axis 58. Moreover, in the adjusting step S40, the positional relation adjusting section 96 may calculate adjustment variables for the relative positions of the second grinding wheel 18b and the holding table 8 in directions parallel to the holding surface 8a of the holding table 8. Accordingly, the positional relation between the second grinding wheel 18b and the holding table 8, for which adjustment variables are calculated in the adjusting step S40, refers to a positional relation to be adjusted on the basis of some or all of the adjustment variables described above. Then, in the adjusting step S40, the positional relation adjusting section 96 adjusts the positional relation between the second grinding wheel 18b and the holding table 8 on the basis of the calculated adjustment variables.

In the method of processing a workpiece according to the present embodiment, the total thickness of the workpiece 1 can be calculated using the thickness of the first region 7 measured before the workpiece 1 is thinned down and the thickness of the second region 9 measured after the workpiece 1 has been thinned down. Therefore, even though the processing apparatus, i.e., the grinding apparatus 2, includes the thickness measuring instrument, i.e., the second thickness measuring instrument 42, not suitable for measuring the thickness of the first region 7, the processing apparatus can derive the total thickness of the workpiece 1 by using the thickness measuring instrument and can adjust the positional relation of the processing tool and the like on the basis of the total thickness. Stated otherwise, even though the workpiece 1 includes a layer or region whose thickness is difficult to measure with the thickness measuring instrument included in the processing apparatus that thins down the workpiece 1, it is possible to derive the total thickness of the workpiece 1 by using the thickness measuring instrument. Consequently, the workpiece 1 can be thinned down into a predetermined configuration while adjustments are being made on the basis of the total thickness of the workpiece 1.

In the method of processing a workpiece according to the present embodiment, the second processing step S50 is carried out after the adjusting step S40. In the second processing step S50, after the positional relation between the second grinding wheel 18b and the holding table 8 has been adjusted, the second grindstones 20b on the second grinding wheel 18b are brought into abrasive contact with the workpiece 1 held on the holding table 8 to thin down the workpiece 1. The second processing step S50 is carried out in the same manner as the first processing step S20 except that the positional relation between the second grinding wheel 18b and the holding table 8 has been adjusted. When the workpiece 1 has been thinned down to a predetermined thickness, the second grinding unit 10b stops thinning down the workpiece 1.

The method of processing a workpiece according to the present embodiment will be summed up as follows: FIG. 9A schematically illustrates in cross section the workpiece 1 before it is processed. In the method of processing a workpiece according to the present embodiment, the second grindstones 20b on the second grinding wheel 18b are brought into abrasive contact with the workpiece 1 held on the holding table 8 to thin down the workpiece 1 (first processing step S20). FIG. 9B schematically illustrates in cross section the workpiece 1 that has been thinned down in the first processing step S20. In the method of processing a workpiece according to the present embodiment, thereafter, the positional relation between the second grinding wheel 18b and the holding table 8 is adjusted by referring to the total thickness of the workpiece 1 (adjusting step S40). In the second processing step S50, after the positional relation between the second grinding wheel 18b and the holding table 8 has been adjusted, the workpiece 1 is further thinned down.

The total thickness of the workpiece 1 that is referred to for adjusting the positional relation between the second grinding wheel 18b and the holding table 8 includes the thickness of the first region 7 of the workpiece 1 and the thickness of the second region 9 thereof. The thickness of the second region 9 is acquired in the second acquiring step S30 by measuring the workpiece 1 thinned down in the first processing step S20. Meanwhile, the thickness of the first region 7 is acquired in the first acquiring step S10 different from the second acquiring step S30. In other words, the thickness of the first region 7 and the thickness of the second region 9 are individually acquired. Consequently, even if the thickness of the first region 7 is not obtained by way of measurement after the first processing step S20, the total thickness of the workpiece 1 can be referred to at the time of adjusting the positional relation between the second grinding wheel 18b and the holding table 8. In other words, positional adjustments can be made in order to thin down the workpiece 1 into a predetermined configuration thereafter.

After the positional relation between the second grinding wheel 18b and the holding table 8 has been adjusted, the workpiece 1 is further thinned down into a predetermined configuration (second processing step S50). FIG. 9C schematically illustrates in cross section the workpiece 1 that has been thinned down to a predetermined thickness. For example, even in a case where it is not easy to measure the thickness of the first region 7, the workpiece 1 can be thinned down such that the entire workpiece 1 will finally be of a uniform thickness, as illustrated in FIG. 9C.

In the method of processing a workpiece according to the present embodiment, depending on the calculated total thickness, i.e., thickness distribution, of the workpiece 1, the positional relation between the second grinding wheel 18b and the holding table 8 may not need to be adjusted in the adjusting step S40. That is, adjustment variables may be calculated as zero. Even in this case, it is confirmed that the workpiece 1 can be processed highly accurately without adjusting the positional relation. Accordingly, the adjusting step S40 includes an occasion where the positional relation is adjusted using zero adjustment variables.

The present invention is not limited to the above embodiment, and various changes and modifications may be made therein. According to the above embodiment, the second acquiring step S30 is carried out with the second grinding wheel 18b retracted from the area above the workpiece 1 after the first processing step S20. However, the present invention is not limited to such a feature.

In the method of processing a workpiece according to the present invention, the second acquiring step S30 may be carried out while the first processing step S20 is being carried out. Alternatively, providing the second acquiring step S30 is carried out after the first processing step S20, the second acquiring step S30 may be carried out while the second grindstones 20b on the second grinding wheel 18b are being held in abrasive contact with the workpiece 1. According to these alternatives, since the second grindstones 20b are held in contact with the center of the reverse side 1b, i.e., processed surface, of the workpiece 1, keeping the center of the reverse side 1b unexposed, the measuring unit 42a is unable to access the center of the reverse side 1b. In other words, the thickness of the second region 9 cannot be measured by the second thickness measuring instrument 42 at the center of the workpiece 1. One solution is to store a plurality of representative examples of the cross-sectional shape of the workpiece 1 in the storage unit of the controller 90 or the like, so that the thickness of the workpiece 1 at the center thereof can be predicted on the basis of the cross-sectional shape, obtained by way of measurement, of a portion of the workpiece 1 other than the center.

The solution will be described in detail below with reference to FIG. 8, for example. At the position 13 near the center of the workpiece 1, the thickness of the second region 9 is not measured. The thickness of the second region 9 is measured at other positions than this position 13. Specifically, the thickness of the second region 9 is measured at the position 13 spaced from the center of the workpiece 1 by a distance equal to one half of the radius of the workpiece 1 and the position 13 near the outer circumferential portion of the workpiece 1. Thereafter, the cross-sectional shape, obtained by way of measurement, of a portion of the workpiece 1 other than the center is compared with the representative examples stored in the storage unit of the controller 90, and one of the representative examples that is closest to the measured cross-sectional shape is selected. Then, a thickness distribution of the entire workpiece 1 is predicted on the basis of the selected representative example, and the tilt of the table axis 58 or the like is adjusted on the basis of the predicted thickness distribution in the adjusting step S40. In the case where the thickness of the second region 9 is not measured at the center of the workpiece 1, therefore, the second acquiring step S30 can be carried out while the first processing step S20 is being carried out. Alternatively, the second acquiring step S30 can be carried out while the second grindstones 20b on the second grinding wheel 18b are being held in abrasive contact with the workpiece 1 after the first processing step S20.

According to the above embodiment, the first acquiring step S10 is primarily carried out before the first processing step S20. However, the present invention is not limited to such a feature. For example, in a case where the thickness of the first region 7 is acquired by reading the thickness of the first region 7 stored in advance in the storage unit of the controller 90 in the first acquiring step S10, the first acquiring step S10 may be carried out after the first processing step S20 and before the adjusting step S40. FIG. 10B is a flowchart illustrating a sequence of steps of a method of processing a workpiece according to a modification where the first acquiring step S10 is carried out after the first processing step S20. The thickness of the first region 7 acquired in the first acquiring step S10 is used in the adjusting step S40. Therefore, the first acquiring step S10 may as well be completed before the adjusting step S40 is carried out.

According to the above embodiment, moreover, it has been described that the thickness of the first region 7 of the workpiece 1 acquired in the first acquiring step S10 is obtained by measuring the workpiece 1 as an object to be thinned down in the first processing step S20 and the like. However, the present invention is not limited to such a detail. In a case where the method of processing a workpiece according to the present invention is repeated to thin down a plurality of workpieces 1, not all of the workpieces 1 need to be measured for the thickness of the first region 7.

Specifically, providing the workpieces 1 are of stable quality and have their first regions 7 with similar thicknesses, the thickness of the first region 7 may be acquired by way of measurement in the first acquiring step S10 from only the workpiece 1 to be processed first. Then, the thickness of the first region 7 acquired by way of measurement may be stored in the storage unit of the controller 90. In a case where the method of processing a workpiece according to the present invention is performed on the second and succeeding workpieces 1, the thickness of the first region 7 of the workpiece 1 processed first which thickness has been stored in the storage unit of the controller 90 may be acquired in the first acquiring step S10. Since the measurement performed to acquire the thickness of the first region 7 of the workpiece 1 may be performed a minimum number of times, the workpieces 1 can efficiently be processed. The thickness of the first region 7 of the workpiece 1 acquired in the first acquiring step S10 thus does not need to be derived by the measurement performed on the workpiece 1 as an object to be thinned down in the first processing step S20 and the like.

The present invention is not limited to the details of the above described preferred embodiment. The scope of the invention is defined by the appended claims and all changes and modifications as fall within the equivalence of the scope of the claims are therefore to be embraced by the invention.