Single crystal silicon carbide substrate having asymmetric geometry and method of making same

Abstract

A single crystal silicon carbide substrate having an asymmetric shape for enhancing the stiffness of the substrate against thermal induced deformation, the substrate comprising: a main region, and an asymmetric region located at a peripheral region of the substrate and adjacent to the main region, wherein the asymmetric region is tilted inwardly with respect to the main region, thereby providing the substrate with an asymmetric shape. A method of producing one or more substrates having an asymmetric shape, the method comprising: performing a multi-wire sawing process in which one or more substrates are cut from a boule placed on a table using a wire saw web; and cutting one or more substrates having an asymmetric shape by controlling the relative movement between the wire saw web and the table such that the wire saw web traces a non-linear sawing path across the boule to cut the asymmetric shape.

Description

Technical Field

[0001] This invention relates to a single-crystal silicon carbide substrate having an asymmetric geometry for improving the substrate’s stiffness against thermally induced internal stress, and a method for manufacturing the same. Background Technology

[0002] Silicon carbide (SiC) substrates are commonly used in the fabrication of electronic components. The standard practice is to grow silicon carbide single crystals (also known as silicon carbide ingots) using physical vapor deposition (PVT) with appropriate source materials. Silicon carbide substrates are then fabricated from the grown single crystals using tools such as multi-wire saws, followed by surface finishing using multi-stage polishing steps. In subsequent epitaxial processes, thin single-crystal layers (e.g., silicon carbide, gallium nitride) are first deposited on the silicon carbide substrate. The properties of these layers and the components fabricated from them are highly dependent on the quality of the silicon carbide substrate.

[0003] Silicon carbide crystals can be produced using standard methods such as physical vapor deposition (PVT) as described in U.S. Patent No. 8,865,324 B2. The orientation of the raw silicon carbide crystals obtained in this manner is then arranged using X-rays or the like, such that the lattice planes have the orientation required for further processing.

[0004] Subsequently, the substrate diameter is set on the single-crystal silicon carbide semi-finished product through various surface treatment steps (e.g., by grinding), one or more oriented edges are attached, and the end face of the crystal cylinder treated in this way is prepared for the separation process, for example using a multi-wire saw.

[0005] The silicon carbide semi-finished product prepared in this way is then separated into individual raw substrates using, for example, a multi-wire sawing process. After quality control, the raw single-crystal silicon carbide substrates undergo further machining. For example, after machining the edges of the raw substrates, a single-stage or multi-stage grinding or polishing process is used to remove the interfering layer introduced by the separation process and gradually reduce the roughness. The final surface is then set using a single-sided or double-sided chemical mechanical polishing (CMP) process.

[0006] Then, in the subsequent epitaxial process, single-crystal layers of semiconductor materials (e.g., silicon carbide, gallium nitride) are deposited on the silicon carbide substrate. The properties of these epitaxial layers and the devices made from them are highly dependent on the quality of the underlying silicon carbide substrate. The geometry of the substrate is particularly important for the generation of epitaxial (EPI) layers. For example, only glass plates that do not exhibit any significant curvature can guarantee the thermal coupling that occurs in the EPI reactor (which is crucial for uniform, high-quality layer growth).

[0007] For this reason, particular attention is needed to characterize the flatness of the manufactured semiconductor substrate, such as bending and warping. As a standard definition used in silicon wafers, bending measurement represents the deviation of the center point of the midface of a free, unclamped wafer from a reference plane of the midface, defined by three equidistant points on a circle, such as a three-point plane defined around the edge of the wafer. Bow (BOW) can be negative or positive, depending on whether the center point is below or above the reference plane. Warping measurement indicates the difference between the maximum and minimum distances between the midface and the reference plane by considering the entire midface of the substrate, rather than just the center point as in the case of bending measurement. Another important parameter of the manufactured semiconductor substrate is the total thickness variation (TTV), which is the difference between the maximum and minimum thickness of the substrate. The midface can be defined as the trajectory of equidistant points between the front and back sides of the wafer. In semiconductor epitaxy, silicon carbide substrates are typically placed on a flat plate or support plate with the back side of the substrate facing the plate (i.e., the substrate surface opposite the front side where epitaxial growth will take place). The plate carrying the silicon carbide substrate is then placed in a reactor for an epitaxial process, typically reaching temperatures of 1500°C or higher. Silanes and light hydrocarbons (e.g., propane or ethylene) diluted in hydrogen are usually used as carrier gases to deposit a semiconductor layer (e.g., a silicon carbide layer) onto the front of the silicon carbide substrate.

[0008] Therefore, if the silicon carbide substrate warps across its entire surface, there will be a back-side region of the substrate in contact with the plate and a back-side region separated from the plate by a gap. Furthermore, the (radial and axial) thermal gradients established within the reactor for epitaxial growth result in a non-uniform in-plane temperature distribution across the entire silicon carbide substrate. This can lead to substrate warping due to thermally induced internal stress across the entire substrate, ultimately resulting in an increased gap between the substrate and the substrate support. Consequently, the carrier gas used during the epitaxial process can also enter this gap, leading to uneven deposition of semiconductor material on the back-side region of the substrate that is not in close contact with the support. Due to back-side growth, deviations from the ideal planar geometry (e.g., warpage and total thickness variation (TTV)) become worse after the epitaxial process, causing defocusing in subsequent photolithography processes and reducing the yield of silicon carbide devices produced from such epitaxial substrates. Figure 1 An exemplary case is illustrated after a silicon carbide substrate 100 has undergone an epitaxial process for growing an epitaxial layer 120 on the front side of the substrate, in which an undesirable material layer 130 is grown on the back side 140 of the substrate 100 due to warping of the substrate 100.

[0009] exist Figure 2In the ideal scenario illustrated, the silicon carbide substrate 200 is initially flat and does not deform due to heating during the epitaxial process. As a result, there is no gap between the silicon carbide substrate 200 and the plate 110 during the epitaxial process, and therefore no material deposition / growth occurs on the back side of the silicon carbide wafer. However, in reality, this ideal situation where the flat silicon carbide substrate 200 remains flat during heating is not observed. Under actual conditions, the silicon carbide substrate may have warped before the epitaxial process and / or experience additional warping due to the (axial and radial) thermal gradients applied during the epitaxial process. Therefore, backside growth of silicon carbide is frequently observed.

[0010] Figure 3-5 Different cases are shown where material carried by a carrier gas is deposited on the back side of a silicon carbide substrate during the epitaxial process used to grow an epitaxial layer on the front side.

[0011] Figure 3 This illustrates a case where a silicon carbide wafer 300, which is flat before the heating process, acquires a convex shape (i.e., the front surface of the silicon carbide wafer 300 bends outward) due to internal stress caused by epitaxial growth conditions during the heating process, while a gap 320 is formed between the central region of the wafer 300 and the plate 110. As a result, back-side growth of a material layer 330 transported by a carrier gas occurs during the epitaxial process.

[0012] Figure 4 and Figure 5 Examples of silicon carbide wafers 400 and 500 are shown, having a concave shape (i.e., the front of the silicon carbide wafer where epitaxial growth will occur is bent inward) and thus having a negative bending degree (BOW). Figure 4 In the example shown, if the silicon carbide wafer 400 does not deform during heating and already has a non-planar shape (substrate bending (BOW) greater than 30 micrometers) before heating, then a gap 420 exists between the silicon carbide wafer 400 and the planar plate 110 during the epitaxial process. As a result, the carrier gas also causes material deposition 430 on the back side of the silicon carbide wafer 400. Please refer to... Figure 5 For example, if the silicon carbide wafer 500 is not flat before heating (substrate bending (BOW) greater than 30 micrometers) and also undergoes thermally induced deformation (increased substrate bending (BOW)) under epitaxial growth conditions, then the gap 520 between the silicon carbide wafer 500 and the plate 110 will cause backside growth 530 to occur during the epitaxial process. In particular, the development of bending of the silicon carbide substrate 500 under heating conditions is important for backside growth. Even if the bending (BOW) is less than 30 micrometers at room temperature, the substrate will deform due to heating.

[0013] Therefore, for silicon carbide wafers that have a non-planar shape before or during epitaxial growth, backside growth is expected, regardless of whether the front side is predominantly convex (positive BOW) or predominantly concave (negative BOW). As mentioned above, backside growth exacerbates substrate warpage and TTV, leading to defocusing of the photolithographic pattern during subsequent silicon carbide device fabrication processes, thus reducing the yield of silicon carbide devices produced from it. These disadvantages associated with backside growth of silicon carbide are well-recognized in the art because no solution to this problem has been provided to date.

[0014] Therefore, there is a need for a solution that can prevent or at least mitigate the disadvantages associated with backside growth on a silicon carbide substrate during the epitaxial process and thereby increase the yield of silicon carbide devices fabricated from silicon carbide substrates. Summary of the Invention

[0015] In view of the shortcomings and deficiencies of the prior art, the present invention is proposed, the purpose of which is to provide a single-crystal silicon carbide substrate with an asymmetric shape and a method for manufacturing the same, which eliminates or at least mitigates the aforementioned shortcomings and deficiencies of the related prior art.

[0016] According to the present invention, a single-crystal silicon carbide substrate having an asymmetric shape for enhancing the stiffness of the substrate against thermal deformation is provided, the substrate comprising: a main region; and an asymmetric region located in a peripheral region of the substrate and adjacent to the main region, wherein the asymmetric region is inclined inward relative to the main region, thereby providing an asymmetric shape to the substrate.

[0017] In a further improvement, the asymmetric region is defined between the substrate periphery and the main region, and the asymmetric region is joined to the main region in a continuous manner, the inclination between the asymmetric region and the main region defining an elbow or shoulder in the asymmetric shape of the substrate.

[0018] In a further improvement, the size and inward tilt of the asymmetric region relative to the main region are such that the maximum height of the substrate periphery defining the asymmetric region relative to the reference plane of the main region is in the range of 15 micrometers to 60 micrometers, preferably 25 micrometers.

[0019] In a further improvement, the maximum height corresponds to the maximum height relative to the reference plane of the main region at the intersection of the reference plane of the asymmetric region and the substrate periphery defining the asymmetric region.

[0020] In a further improvement, the size and inward tilt of the asymmetric region relative to the main region are such that the maximum distance between the projection of the substrate periphery defining the asymmetric region onto the reference plane of the main region and the main region is in the range of 5 mm to 30 mm, preferably 15 mm.

[0021] In a further improvement, the reference plane of the main region corresponds to the mid-plane of the substrate without a substrate peripheral region, and / or the reference plane of the asymmetric region corresponds to the mid-plane of the asymmetric region.

[0022] In a further improvement, the asymmetric region is located on a peripheral region of the substrate opposite to an orientation edge or notch in the substrate, and the angular displacement of the asymmetric region relative to the orientation edge or notch is between ±90°, preferably between ±60°.

[0023] In a further improvement, the size and inward tilt of the asymmetric region relative to the main region are such that the maximum height of the substrate periphery defining the asymmetric region relative to the silicon side of the substrate at the main region is a positive height.

[0024] In a further improvement, the substrate formed by the main region and the asymmetric region is characterized by a bend (BOW) value in the range of -40 micrometers to 0 micrometers, preferably in the range of -35 micrometers to 0 micrometers, and / or a warp (WARP) value of less than 70 micrometers, preferably 45 micrometers.

[0025] In a further improvement, the thickness of the asymmetric region and the main region is in the range of 200 micrometers to 1000 micrometers, preferably in the range of 250 micrometers to 500 micrometers, and / or the substrate has a local cylindrical shape in the main region, the diameter d of which is greater than 149.5 millimeters, and / or the substrate has a total thickness variation of less than 5 micrometers, and / or the asymmetric region and the main region of the substrate are formed by a monolithic silicon carbide single crystal of one of the variants 4H-SiC, 6H-SiC and 15R-SiC, and / or the silicon carbide crystal structure in the main region has an α° off-axis orientation of the basal plane (1000), the α° off-axis orientation being 0.5° and 8°, preferably 4° off-axis orientation.

[0026] In a further improvement, the main region has a substantially flat surface, and / or the asymmetric region has a shape of a circular segment defined between an adjacent main region and the periphery of the substrate; and / or the asymmetric region has a substantially flat shape or a non-flat shape with convex or concave curvature.

[0027] The present invention also provides a method for producing one or more substrates having an asymmetrical shape, the method comprising: performing a multi-wire sawing process in which one or more substrates are cut from an ingot placed on a worktable using a wire saw; and cutting one or more substrates having an asymmetrical shape by controlling the relative movement between the wire saw and the worktable, said relative movement causing the wire saw to trace a non-linear sawing path across the ingot to cut the asymmetrical shape.

[0028] In a further improvement, controlling the relative movement between the wire saw and the worktable includes: controlling the wire saw to move toward the worktable along a straight cutting direction; and controlling the movement of the worktable and the wire saw to move in a direction perpendicular to the cutting direction in coordination, thereby causing the wire saw to trace a non-linear cutting path across the ingot, or controlling the wire saw to move in a direction perpendicular to the cutting direction in coordination with the movement in the cutting direction, thereby causing the wire saw to trace a non-linear cutting path across the ingot.

[0029] According to a further improvement, the method includes: during multi-wire sawing, controlling the stress applied to the saw wires of the wire saw mesh by controlling the relative movement between the wire saw mesh and the worktable in a direction perpendicular to the sawing direction, so that sawing begins after the depth of the wire saw mesh's saw wires entering the ingot reaches at least half the diameter of the saw wires.

[0030] In a further improvement, the selected asymmetrical shape includes an asymmetrical region located at the periphery of the substrate, adjacent to a substantially flat main region of the substrate. The selected asymmetrical shape is cut by controlling the duration and displacement of the relative movement between the wire saw and the worktable in a direction perpendicular to the sawing direction. The duration of the relative movement in the direction perpendicular to the sawing direction determines the maximum distance along the sawing direction between the substrate periphery at the asymmetrical portion and the main region, and the displacement of the relative movement in the direction perpendicular to the sawing direction determines the maximum height of the asymmetrical region relative to the main region.

[0031] To explain the principles of the invention, the accompanying drawings are incorporated into and form a part of the specification. The drawings should not be construed as limiting the invention to examples of the methods of making and using the invention shown and illustrated. Attached Figure Description

[0032] Other features and advantages will become apparent from the more detailed description of the invention given below with reference to the accompanying drawings, in which:

[0033] Figure 1 This is a cross-sectional view of a warped single-crystal silicon carbide substrate on the support plate after the epitaxial process, in which material is grown on the back side of the substrate due to the gap between the back side of the substrate and the support plate during the epitaxial process for growing an epitaxial layer on the front side of the substrate.

[0034] Figure 2 This is a cross-sectional view of a silicon carbide substrate under ideal conditions, in which: a) the silicon carbide substrate has a substantially flat shape before the heating process; and b) the flat shape is maintained during the heating process so that no gaps appear between the back sides of the substrate due to warping.

[0035] Figure 3 This is a cross-sectional view showing the warping of a conventional silicon carbide substrate in the following cases: where a) the silicon carbide substrate is substantially flat on the support plate before the heating process; and b) the shape of the silicon carbide substrate deforms during the heating process, resulting in a gap between the back side of the substrate and the support plate, and subsequently material deposition occurs on the back side of the substrate.

[0036] Figure 4 This is a cross-sectional view showing the warping of a conventional silicon carbide substrate in the following cases: where a) the silicon carbide substrate warps before the heating process, resulting in a gap between the back side of the substrate and the support plate; and b) the shape of the silicon carbide substrate does not deform during the heating process, but back side growth still occurs;

[0037] Figure 5 This is a cross-sectional view showing the warping of a conventional silicon carbide substrate in the following cases: where a) the silicon carbide substrate warps before the heating process, resulting in a gap between the silicon carbide substrate and the support plate; and b) the initial shape of the silicon carbide substrate deforms during the heating process, resulting in back-side growth in an enlarged area that is not in direct contact with the support plate.

[0038] Figure 6 A perspective view of a silicon carbide substrate with an asymmetrical shape, according to an embodiment of the present invention, is shown schematically.

[0039] Figure 7 yes Figure 6 The cross-sectional view of the silicon carbide substrate shown shows an L-shaped cross-section with a sharp elbow, wherein: a) shows a cross-section of the silicon carbide substrate with an asymmetric shape before the heating process; and b) shows a cross-section of the silicon carbide substrate after undergoing the heating process and with the asymmetric region growing on the back side only in the region of the silicon carbide substrate.

[0040] Figure 8 A cross-sectional view of a silicon carbide substrate with an asymmetrical shape (an L-shape with a smooth elbow) according to another embodiment of the invention is shown schematically.

[0041] Figure 9 A cross-sectional view of a silicon carbide substrate with an asymmetrical shape (an L-shape with convex edges) according to another embodiment of the present invention is shown schematically.

[0042] Figure 10 A silicon carbide ingot (viewed from the front) is schematically shown on the worktable of a conventional multi-wire saw for cutting silicon carbide wafers from silicon carbide ingots.

[0043] Figure 11 schematically shown Figure 10The vertical movement of the wire saw mesh of the multi-wire sawing device shown (viewed from the side of a silicon carbide ingot) causes the silicon carbide wafer to be cut into conventional planar geometry.

[0044] Figure 12 A schematic illustration shows an embodiment of a multi-wire sawing apparatus for cutting silicon carbide wafers with asymmetrical geometry, and the controlled movement of the wire saw mesh and the worktable for placing the ingot (viewed from the side of the ingot).

[0045] Figure 13 A schematic illustration shows another embodiment of a multi-wire sawing apparatus for cutting silicon carbide wafers with asymmetrical geometry, and the two-dimensional controlled movement of the wire saw relative to a worktable on which the ingot is placed (viewed from the side of the ingot).

[0046] Figure 14 The graph illustrates the relationship between the speed of relative movement between the wire saw and the worktable in a controlled movement procedure according to an embodiment of the present invention, in a direction perpendicular to the linear movement of the wire saw towards the worktable.

[0047] Figure 15 schematically shown Figure 6 The parameters of the asymmetric shape of the silicon carbide substrate in the embodiment of the invention shown (maximum distance and maximum height of the asymmetric regions) are set by controlling the duration and amount of displacement of the relative movement between the wire saw and the worktable during the MWS process; and

[0048] Figure 16 A cross-sectional view of a silicon carbide substrate with irregular thickness and reference planes for defining the asymmetric shape (maximum distance and maximum height of the asymmetric region) is schematically shown.

[0049] It should be noted that the dimensions and relative angles shown in the accompanying drawings are for illustrative purposes only and are not drawn to scale. Detailed Implementation

[0050] The invention will now be described more fully below with reference to the accompanying drawings, which illustrate some exemplary embodiments of the invention. However, the invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to make the disclosure thorough and complete, and to fully convey the scope of the invention to those skilled in the art. The same reference numerals throughout refer to the same elements.

[0051] The fundamental principle of this invention lies in reducing the negative impact of back-side growth on silicon carbide wafer parameters (e.g., bend over (BOW), warpage (BOW), and total thickness variation (TTV)) by increasing the stiffness of the silicon carbide substrate against deformation caused by thermal gradients (e.g., (radial and axial) thermal gradients applied to the silicon carbide substrate during conventional epitaxial growth). These parameters are crucial for the quality of the epitaxial process and the fabrication of silicon carbide devices. This increased stiffness is achieved by designing a silicon carbide substrate with a specific asymmetric shape in the peripheral region of the substrate. This counteracts the development of thermally induced internal stresses on the silicon carbide substrate while confining any final back-side growth to the peripheral region of the substrate.

[0052] More specifically, substrate stiffness can be increased by using asymmetrical geometry in which the peripheral portion of the substrate slopes upward toward the front of the substrate on which epitaxial growth will take place, as referred to below. Figure 6 As stated above.

[0053] Figure 6 A schematic perspective view of a silicon carbide substrate 600 with an asymmetrical shape is shown, which improves stiffness against thermally induced deformation. Figure 6 As shown, the asymmetric shape is provided by an asymmetric region 610 located in the peripheral region of the silicon carbide substrate 600 and adjacent to the main region 620 of the substrate 600. This substrate region is inclined inward, i.e., towards the front surface 630 of the silicon carbide substrate 600 (i.e., in...). Figure 6 The main region 620 is inclined in the Y direction (as shown). The main region 620 substantially corresponds to the remainder of the silicon carbide substrate 600 without the asymmetric region 610, and is preferably flat. The asymmetric region 610 joins the main region 620 in a continuous manner, such that the asymmetric region is defined between the substrate periphery 650 and the main region 620, and the inclination between the asymmetric region 610 and the main region 620 defines an elbow or shoulder 660 in the asymmetric shape of the substrate 600. The asymmetric region 610 is inclined relative to the reference plane of the main region 620 (parallel to the Y direction). Figure 6 The out-of-plane orientation (in the X direction) introduces asymmetry in the substrate cross-section, which counteracts the thermally induced deformation of the silicon carbide substrate 600. As a result, the larger area of ​​the substrate 600 covered by the central main region 620 remains flat, and gaps between the main region 620 and the support plate are avoided during heating processes (e.g., heating processes conventionally used in semiconductor epitaxy). Therefore, since the asymmetric shape of the silicon carbide substrate 600 increases stiffness, substrate warping during heating can be reduced, and backside growth can be eliminated or significantly reduced.

[0054] Figure 7 It shows Figure 6The asymmetric silicon carbide substrate 600 shown is a cross-section before and after the substrate 600 is heated during epitaxial growth (for simplicity, in...). Figure 7 The epitaxial layer on the front 630 of substrate 600 is omitted. (For example...) Figure 7 As shown, back-side growth may occur near the substrate periphery 650 due to the separation between the asymmetric region 610 and the substrate support plate (not shown). However, the increased stiffness from the asymmetric shape prevents back-side growth from occurring in the central region of the substrate 600, since no gap is formed between the main region 620 and the substrate support plate during epitaxial growth. As a result, the negative impact of back-side growth on substrate bendability (BOW) is significantly reduced. Furthermore, the asymmetric shape of the substrate shifts back-side growth to the peripheral region of the substrate, which has less negative impact on the post-epitaxy BOW. Another advantage of confining back-side growth to the peripheral region of the substrate 600 (i.e., the asymmetric region 610) is that this region can be easily discarded after the epitaxial process. Therefore, silicon carbide devices can be fabricated from the main region 620 of the substrate 600 without the adverse effects associated with warpage, bending, and back-side deposition observed in conventional silicon carbide substrates. As a result, higher yields of silicon carbide devices fabricated from epitaxial material deposited / grown on the main region 620 of the asymmetric substrate 600 can be achieved.

[0055] The tilt of the asymmetric region 610 can be characterized as the tilt of the mid-surface of the asymmetric region 610 relative to the reference plane 690 of the main region 620, in order to compensate for the irregularity of the substrate thickness. When the substrate 600 has an orientation edge or orientation notch 670, the asymmetric region 610 is preferably located on the peripheral region of the substrate 600 opposite to the orientation edge or orientation notch 670. For example, the asymmetric region 610 may be directly opposite the orientation notch 670 (e.g., Figure 6 (as shown), or within an angular displacement range of ±90°, preferably ±60°, relative to the directional edge or directional notch 670. In the latter case, the midpoint of the asymmetric region 610 and / or the directional edge is used to define the angular displacement.

[0056] The basic principle of improving substrate stiffness through the aforementioned asymmetric shape is applicable to silicon carbide substrates of various diameters and thicknesses, specifically silicon carbide substrates characterized by one or a combination of the following parameters: a diameter d greater than 149.5 mm, a substrate thickness (in both the asymmetric and main regions) ranging from 200 μm to 1000 μm, preferably from 250 μm to 500 μm, and a total thickness variation (TTV) of less than 5 μm. The diameter d of the asymmetric silicon carbide substrate 600 can be defined as the diameter d of the (local) cylindrical shape of the main region 620 (i.e., without a circular segment corresponding to the asymmetric region 610).

[0057] In an advantageous configuration of the silicon carbide substrate 600, the front surface 630 of the main region 620 is the silicon side of the silicon carbide single crystal. Thus, the asymmetric region 610 is tilted inward relative to the front surface 630, thereby defining the maximum height of the substrate periphery 650 defining the asymmetric region 610 relative to the reference plane 690 of the main region 620 as a positive height (see, for example, [reference needed]). Figure 15 ).

[0058] Appropriate parameters for the asymmetric shape used to improve substrate stiffness can be selected / determined based on simulation analysis and / or experiments taking into account the desired size of the silicon carbide substrate and the temperature conditions the asymmetric substrate will experience during epitaxial growth. For example, for a silicon carbide substrate 600 with a diameter greater than 149.5 mm, improved substrate stiffness can be achieved by providing an asymmetric region 610 with dimensions relative to the main region 620 and an inwardly inclined shape, such that the maximum height of the substrate periphery 650 defining the asymmetric region 610 relative to the reference plane of the main region 620 is in the range of 15 μm to 60 μm, preferably 25 μm. In this case, the maximum height can be defined as the maximum height of the reference plane 695 of the asymmetric region 610 located at the highest point of the substrate periphery 650 defining the asymmetric region 610 relative to the reference plane 690 of the main region 620. The maximum distance between the adjacent side 680 of the asymmetric region 610 and the projection of the substrate perimeter 650 defining the asymmetric region 610 onto the reference plane 690 of the main region 620 is preferably in the range of 5 mm to 30 mm, and most preferably 15 mm. The maximum distance and maximum height of the asymmetric substrate 600 can be as follows: Figure 15 As shown in the definition, the reference plane 690 of the main region 620 corresponds to the mid-plane of the substrate 600 without the asymmetric region 610. The reference plane 695 of the asymmetric region 610 can be defined as the mid-plane of the asymmetric region 610.

[0059] exist Figure 6 and Figure 7 In the asymmetric shape shown, the asymmetric region 610 and the main region 620 have substantially flat surfaces and form an L-shaped cross-section with a sharp elbow 660. The technical advantage of this L-shaped cross-section is that it results in less deformation during epitaxy due to increased stiffness. Furthermore, since the main region 620 is substantially flat and corresponds to most of the area of ​​the silicon carbide substrate 600, the L-shape prevents backside growth from occurring over a large area of ​​the silicon carbide substrate 600, as most of the backside 640 remains in contact with the support plate during epitaxial growth. Therefore, the total area of ​​the silicon carbide substrate 600 affected by backside growth during epitaxial growth is minimized.

[0060] However, other asymmetrical shapes with different geometric shapes can also be used. For example, Figure 8 and Figure 9 Possible geometries of the asymmetric regions are shown, all of which follow the common principle of being located in the peripheral region of the substrate and tilted upward relative to the front of the main region.

[0061] Figure 8 A cross-section of an asymmetric silicon carbide substrate 800 with an asymmetric region 810 is shown. This asymmetric region 810 defines a nearly flat surface near the substrate periphery, which gradually curves (concaves) near the main region 820, thereby defining an L-shaped cross-section with a rounded elbow or shoulder 860 on the back surface 840 of the asymmetric silicon carbide substrate 800. Because this asymmetric shape provides greater stiffness, the main region 820 maintains its substantially flat shape during epitaxial growth, thus limiting back surface growth 845 to the back surface 840 of the asymmetric region 810.

[0062] Figure 9 Another example of an asymmetric shape for a silicon carbide asymmetric substrate 900 used to improve substrate stiffness is shown. In this configuration, the asymmetric shape is designed to have a substantially flat main region 920 and an asymmetric region 910 that slopes upward relative to the main region 920, and the asymmetric region 910 is shaped to have a slight convex curvature. Due to the increased stiffness, the surface of the main region 920 also remains substantially flat during heating, thereby limiting back-side growth 945 to the back side 940 of the asymmetric region 910.

[0063] The parameters of the asymmetric region described above with reference to the asymmetric substrate 600 (such as the maximum height between the reference plane of the asymmetric region and the main region, the maximum distance from the periphery of the asymmetric region, etc.) also apply. Figure 8 and 9 The asymmetrical shape shown.

[0064] According to the principles of the present invention, silicon carbide wafers with asymmetric shapes can be produced from single-crystal silicon carbide crystals or ingots using wafer separation technology, for example, using a multi-wire sawing (MWS) process with a controlled movement program that coordinates the movement of the wire saw and / or the movement of the ingot stage to cut out silicon carbide wafers with the desired asymmetric shape.

[0065] Silicon carbide substrates are typically produced from silicon carbide crystals or ingots using multi-wire sawing. Figure 10 and 11The operating principle of a conventional multi-wire sawing apparatus 1000 is illustrated. In the conventional multi-wire sawing apparatus 1000, a single saw wire is wound around a guide roller 1010. Each guide roller 1010 is slotted at a constant interval, and the arrangement of the saw wires on the spaced grooves forms a wire saw mesh 1020 parallel to the horizontal. During multi-wire sawing, slurry (a suspension of abrasive particles in a coolant) is fed onto the moving saw wires, which then transport the slurry into the cutting zone. The material to be cut (e.g., a silicon carbide ingot 1030) is fixed onto a MWS worktable 1040, and the wire saw mesh 1020 is moved downward from the top of the silicon carbide ingot 1030 placed on the MWS worktable 1040 to cut wafers 1050 from the silicon carbide ingot 1030. The entire wire saw mesh 1020 is moved vertically at a constant speed. The movement of the wire saw 1020 toward the MWS stage 1040 pushes the silicon carbide ingot 1030 through the wire saw 1020, thereby simultaneously producing a large number of wafers 1050. Since the wire saw 1020 can only move in a direction transverse to the surface of the stage, the wafers 1050 are cut into a flat surface (i.e., a cross-section with a symmetrical geometry).

[0066] This invention employs a modified MWS method with a controlled movement procedure that controls the relative movement between the wire saw and the worktable in two dimensions: the straight cutting direction of the wire saw and a direction perpendicular to that cutting direction. The relative movement between the wire saw and the worktable is coordinated such that the wire saw traces a non-linear cutting path across the ingot cross-section (i.e., in both dimensions), resulting in one or more substrates being directly cut into desired asymmetric shapes. This non-linear cutting path can be achieved using two alternative controlled movement procedures, for example, by referring to... Figure 12 and 13 The description refers to the controlled movement procedure.

[0067] Figure 12 A controlled movement program is shown, in which a stage 1240, on which an ingot 1230 is placed, is controlled to move relative to a wire saw 1210, such that the wire saw 1210 traces a nonlinear asymmetric sawing path across the ingot 1230, thereby cutting a substrate 1250 with a desired asymmetric shape, for example... Figure 8 The asymmetrical shape is shown. In the controlled movement procedure, the wire saw 1210 is controlled to cut along a straight cutting direction (…). Figure 12 The direction of the vertical arrow on the left or Figure 12The wire saw 1210 moves toward the worktable 1240 in the X direction shown in the illustration on the right. Throughout the MWS process, the wire saw 1210 moves linearly along the same straight cutting direction. To make the wire saw 1210 draw a non-linear, asymmetrical cutting path across the ingot 1230, the worktable 1240 is controlled in a direction perpendicular to the direction of movement of the wire saw 1210 (X direction). Figure 12 The direction of the horizontal arrow on the left is parallel to Figure 12 The Y-direction is shown in the illustration on the right. The specific asymmetrical shape of the substrate 1250 is achieved by coordinating the movement of the worktable 1240 and the linear movement of the wire saw 1210, for example, by adjusting the movement speed (or displacement) and duration (or vice versa) of the worktable relative to the speed (preferably constant) of the wire saw 1210. Figure 12 The L-shaped substrate 1250 shown on the right can be controlled by the wire saw mesh 1210 in the straight sawing direction (i.e., in the direction of the wire saw) throughout the entire MWS process. Figure 12 The wire saw 1210 is moved at a constant speed (in the X direction shown on the right) while simultaneously controlling the worktable 1240 to move in a direction perpendicular to the direction of movement of the wire saw 1210 for a finite amount of time, sufficient to allow the wire saw 1210 to cut the beveled edge of the L-shaped shape of the substrate 1250. Then the movement of the worktable 1240 is stopped while maintaining the movement of the wire saw 1210 in the straight cutting direction to cut the straight edge of the L-shaped shape of the substrate 1250.

[0068] The controlled movement procedure can control the stress applied to the wire saw 1210 by moving the wire saw 1210 only toward the worktable 1240 (along the vertical sawing direction) at the start of the MWS process until the wire penetrates the ingot 1230 to a depth of at least D / 2, i.e., half the wire diameter D. After this point, the worktable 1240 can begin to move in a direction perpendicular to the vertical sawing direction, while the wire saw 1210 continues to move vertically toward the worktable 1240, preferably at a constant speed.

[0069] Figure 14 The speed of the table 1240 as a function of time (i.e., in the direction transverse to the vertical movement of the wire saw 1210) during a controlled movement process for producing a substrate 1250 with a smooth L-shaped cross-section, including the control of the saw wire stress, is illustrated by way of example. Figure 14In this process, time t0 corresponds to the time when the saw wire of the wire saw 1210 touches the ingot 1230, which can be detected by known methods, such as using a dedicated sensor. At time t0, the table 1240 remains stationary until time t1, at which time the saw wire of the wire saw 1210 has penetrated the ingot 1230 to a depth of at least D / 2. At time t1, a controlled movement program causes the table 1240 to move in a direction perpendicular to the cutting direction, and coordinates the movement of the table with the speed of the wire saw 1210 to cut a substrate 1250 with the desired asymmetrical shape. For example, as... Figure 14 As shown, the stage 1240 can initially move at a high speed, which determines the initial slope of the asymmetric region relative to the main region. Then, the speed of the stage movement can be gradually reduced while maintaining a constant speed for the wire saw 1210, resulting in a bent elbow or shoulder on the substrate 1250. Once the asymmetric region of the substrate 1250 has been cut, the controlled movement program stops the stage 1240. From this point, the controlled movement program keeps the wire saw 1210 moving only in the vertical sawing direction and stops it only when the wire saw 1210 reaches the stage 1240 to completely cut the main region of the substrate 1250 across the entire ingot 1230.

[0070] Different types of asymmetrical shapes can be achieved using the MWS method with the aforementioned controlled movement program by adjusting the function of the table's movement speed as a function of time and the speed of the wire saw 1210. For example, this can be achieved by maintaining a substantially constant relative movement of the table in the direction perpendicular to the movement of the wire saw 1210 for the time required to cut the asymmetrical region 610. Figure 6 The silicon carbide substrate 600 shown has an asymmetric shape (where both the asymmetric region 610 and the main region 620 have flat surfaces).

[0071] Therefore, the specific size, shape, and tilt of asymmetrical regions can be achieved by simply controlling the combination of the total duration and displacement of the table movement. For example... Figure 15As shown, for substrate 600, when measured along the reference plane 690 of the main region 620, the maximum distance between the substrate periphery 650 defining the asymmetric region 610 and the end of the asymmetric region 610 (which roughly corresponds to the starting point of the elbow 660 at the meeting point of the asymmetric region 610 and the main region 620 of substrate 600) is determined by the total displacement of the wire saw 1210 in the wire sawing direction within the time interval of the controlled movement of the worktable. Therefore, this maximum distance can be set by adjusting the duration of the worktable movement based on the speed of the wire saw 1210. On the other hand, the maximum height between the substrate periphery 650 at the asymmetric region 610 and the reference plane 690 of the main region of the substrate elbow 660 is determined by the total displacement of the worktable 1240. The maximum distance and the maximum height are preferably defined relative to the mid-surface of the main region 620 (i.e., the reference plane 690 of the main region 620) and the mid-surface of the asymmetric region 610 (i.e., the reference plane 695 of the asymmetric region 610). This allows for setting the maximum distance and maximum height of the controlled movement program in a uniform manner for different substrate thicknesses. It also allows for defining a reference plane that takes into account the irregularities in substrate thickness, for example... Figure 16 The reference plane 790 of the main region in the substrate 700 with an asymmetrical shape is shown.

[0072] exist Figure 13 Another example of a controlled-motion MWS method for producing silicon carbide substrates 1350 with asymmetrical cross-sections is shown. Please refer to [reference needed]. Figure 13 The MWS device 1300 executes a controlled movement procedure, which is the same as described above. Figure 12 The difference in the described procedure is that the asymmetric sawing path across the silicon carbide ingot 1330 is achieved by controlling the movement of the guide roller 1310 in the vertical and horizontal directions, while the worktable 1340 remains stationary during the MWS process. More specifically, to reduce stress on the saw wire, the movement of the wire saw mesh 1310 (i.e., the guide roller) is initially controlled to be along a straight direction (i.e., along...). Figure 13 The direction of the vertical arrow on the left, or along... Figure 13 The wire saw (in the X direction shown in the illustration on the right) moves toward the worktable 1340 until the depth of the wire entering the silicon carbide ingot 1330 reaches at least half the thickness D / 2 of the wire, in order to control the stress on the wire. After this initial stage, the movement of the wire saw 1310 is controlled to maintain movement along the vertical direction and begin to move in a second direction perpendicular to the vertical movement, i.e., in Figure 13 The direction of the horizontal arrow on the left (parallel to) Figure 13The wire saw 1310 moves in the Y direction (as shown in the illustration on the right). The combined movement of the wire saw 1310 continues until the elbow of the substrate 1350 is cut out of its asymmetrical shape. After this point, the horizontal movement of the wire saw 1310 ceases, and it continues only vertically through the remaining portion of the silicon carbide ingot 1330 until it reaches the worktable 1340, thus cutting out the main area of ​​the substrate 1350. The combined vertical and perpendicular movement of the wire saw 1310 within a selected time period, along with a selected horizontal displacement, allows the cutting of the substrate 1350 with the desired asymmetrical shape, as shown in the illustration on the right. Figure 13 As shown on the right.

[0073] Therefore, compared with the reference Figure 12 The MWS process described is similar. Figure 13 The controlled movement procedure shown allows for setting / adjusting the size and shape of the substrate 1350 by controlling and coordinating the movement of the wire saw 1310 in both the vertical and horizontal directions. For example, the amount of vertical displacement of the wire saw 1310 during the time interval in which it also moves in the vertical direction determines the maximum distance between the substrate periphery 650 defining the asymmetric region 610 and the end of the asymmetric region 610 (roughly corresponding to the starting point of the elbow 660), as... Figure 15 As shown. On the other hand, the maximum height between the substrate periphery 650 at the asymmetric region 610 and the reference plane 690 of the main region of the substrate elbow 660 is determined by the total displacement of the wire saw 1310 in the horizontal direction. Therefore, the specific size, shape, and inclination of the asymmetric region 610 can be achieved by simply coordinating and controlling the duration and displacement of the guide roller 1310 in the transverse direction and the movement of the guide roller in the vertical direction.

[0074] Use reference Figure 12 and Figure 13 Any controlled mobile application described above can obtain the information mentioned above. Figures 7 to 9 The asymmetric shape shown is used to improve the stiffness of silicon carbide substrates. However, it is also conceivable that other... Figures 7 to 9 In addition to the asymmetric shape shown, the asymmetric shape is based on the same principle as having a substantially flat main region corresponding to the central region of the substrate and an asymmetric region located in the peripheral region of the substrate that slopes inward toward the front of the substrate (i.e., toward the plane of the main region) to improve substrate stiffness.

[0075] Figure 12 and 13 The two alternative MWS methods with controlled movement procedures shown make it possible to cut substrates with given asymmetric shapes. However, it is conceivable to have other variations / combinations of controlled movement procedures with movements performed by a stage and / or wire saw to cut the same or other asymmetric shapes. For example, the reference could be modified. Figure 12and Figure 13 The described controlled movement procedure ensures that the asymmetric region of the silicon carbide substrate is cut not at the beginning, but before the end of the MWS process. The relative movement between the table and the wire saw mesh can also be generated by a combination of linear movement of the wire saw mesh and rotational movement of the table to cut curved asymmetric regions. In any of these cases, an MWS method with a controlled movement program can be implemented by implementing an MWS device having a combination of mechanical devices and a controller. The mechanical devices are capable of generating the desired relative movement between the guide roller and the ingot stage (e.g., generating vertical movement of guide roller 1210 (or 1310) (i.e., movement in a direction perpendicular to the surface of stage 1240 (or 1340)) and movement of stage 1240 (or guide roller 1310) in a direction perpendicular to the vertical movement of the guide roller). The controller is used to control such mechanical devices to move the stage and / or guide roller according to software / routines specifying the amount, duration, and direction of movement of the stage and / or guide roller to cut a silicon carbide substrate with a desired asymmetric shape, such as... Figure 12 and 13 As shown.

[0076] The principles of this invention can be advantageously applied to improve the stiffness of silicon carbide substrates characterized by a total BOW value in the range of -40 μm to 0 μm, preferably in the range of -35 μm to 0 μm, and / or a WARP value of less than 70 μm, preferably 45 μm. Furthermore, the silicon carbide substrate of this invention with an asymmetric shape is preferably made from a single crystal of silicon carbide of one of the variants 4H-SiC, 6H-SiC, and 15R-SiC, and / or has an off-axis orientation of 0.5° to 8° at the basal plane (1000) in the main region, more preferably 4° off-axis orientation.

[0077] In summary, the silicon carbide substrate with asymmetrical geometry according to the principles of the present invention and the method for manufacturing the same make it possible to provide silicon carbide substrates with higher stiffness against thermally induced deformation (e.g., warping and / or bending). Therefore, compared to conventional flat substrates with symmetrical cross-sections, backside growth on silicon carbide substrates with asymmetrical geometry is effectively reduced and confined to the peripheral region of the substrate, thereby reducing the negative impact on substrate bending.

[0078] Finally, although some features of the exemplary embodiments described above are described using terms such as “upward,” “inward,” “vertical,” and “horizontal,” these terms are merely for the convenience of describing the asymmetrical shape of the substrate and the relative movement between the plate and the guide roller during the MWS process, and therefore should not be construed as limiting the claimed invention or any part thereof to its use in a particular spatial orientation. Furthermore, although the invention has been described above with reference to a single-crystal silicon carbide substrate, the principles of the invention can also be advantageously applied to substrates made of other semiconductor single crystals (e.g., aluminum nitride and gallium nitride).

[0079] Figure Labels

[0080] 600, 700 substrates (asymmetric)

[0081] 610, 710 asymmetric regions

[0082] 620, 720 main areas

[0083] Before 630 and 730

[0084] Back of 640 and 740

[0085] 645 Backside Growth

[0086] Peripheral of 650, 750 substrate

[0087] 660 (substrate) elbow or shoulder

[0088] 670 directional notch

[0089] 680 (adjacent sides of the asymmetric region)

[0090] Reference planes for the 690 and 790 main regions

[0091] 695 reference planes for asymmetric regions

[0092] 800 asymmetric silicon carbide substrate

[0093] 810 asymmetric region

[0094] 820 main area

[0095] 840 back

[0096] 845 back growth

[0097] shoulder of 860 substrate

[0098] 900 asymmetric substrate

[0099] 910 asymmetric region

[0100] 920 Main Area

[0101] 940 back

[0102] 945 Backside Growth

[0103] Shoulder of 960 substrate

[0104] 1000 standard multi-wire sawing equipment

[0105] 1010 guide roller

[0106] 1020 wire saw mesh

[0107] 1030 silicon carbide ingot

[0108] 1040MWS workbench

[0109] 1050 chip

[0110] 1200, 1300 multi-wire sawing equipment

[0111] 1210, 1310 wire guide rollers or wire saw mesh

[0112] 1230, 1330 silicon carbide ingots

[0113] 1240, 1340 workbench

[0114] 1250, 1350 substrates

Claims

1. A single-crystal silicon carbide substrate having an asymmetric shape for enhancing the stiffness of the substrate against thermally induced deformation, the substrate comprising: Main area; as well as The asymmetric region located on the periphery of the substrate and adjacent to the main region. The asymmetric region is tilted inward relative to the main region, thereby providing an asymmetric shape to the substrate.

2. The single-crystal silicon carbide substrate as described in claim 1, wherein: The asymmetric region is defined between the substrate periphery and the main region, and The asymmetrical regions are joined to the main region in a continuous manner, and the tilt between the asymmetrical regions and the main region defines an elbow or shoulder in the asymmetrical shape of the substrate.

3. The single-crystal silicon carbide substrate as described in claim 1, wherein: The size and inward tilt of the asymmetric region relative to the main region result in a maximum height of the substrate periphery defining the asymmetric region relative to the reference plane of the main region ranging from 15 micrometers to 60 micrometers.

4. The single-crystal silicon carbide substrate as described in claim 3, wherein: The size and inward tilt of the asymmetric region relative to the main region result in the maximum height of the substrate periphery defining the asymmetric region being 25 micrometers relative to the reference plane of the main region.

5. The single-crystal silicon carbide substrate as described in claim 3, wherein: The maximum height corresponds to the maximum height relative to the reference plane of the main region at the intersection of the reference plane of the asymmetric region and the periphery of the substrate that defines the asymmetric region.

6. The single-crystal silicon carbide substrate as described in claim 1, wherein: The size and inward tilt of the asymmetric region relative to the main region result in a maximum distance between the projection of the substrate periphery defining the asymmetric region onto the reference plane of the main region and the main region, ranging from 5 mm to 30 mm.

7. The single-crystal silicon carbide substrate as described in claim 6, wherein: The size and inward tilt of the asymmetric region relative to the main region result in a maximum distance of 15 mm between the projection of the substrate periphery defining the asymmetric region onto the reference plane of the main region and the main region.

8. The single-crystal silicon carbide substrate as described in claim 3, wherein: The reference plane of the main region corresponds to the mid-plane of the substrate without a peripheral region, and / or The reference plane of the asymmetric region corresponds to the mid-plane of the asymmetric region.

9. The single-crystal silicon carbide substrate as claimed in claim 1, wherein: The asymmetric region is located on the outer periphery of the substrate, opposite to the oriented edge or notch in the substrate, and The angular displacement of the asymmetrical region relative to the oriented edge or notch is between ±90°.

10. The single-crystal silicon carbide substrate as claimed in claim 9, wherein: The angular displacement of the asymmetrical region relative to the oriented edge or notch is between ±60°.

11. The single-crystal silicon carbide substrate as claimed in claim 1, wherein: The size and inward tilt of the asymmetric region relative to the main region make the maximum height of the substrate periphery defining the asymmetric region relative to the silicon side of the substrate in the main region a positive height.

12. The single-crystal silicon carbide substrate as claimed in claim 1, wherein, The substrate formed by the main region and the asymmetric region is characterized in that: BOW values ​​range from -40 micrometers to 0 micrometers and / or The WARP value is less than 70 micrometers.

13. The single-crystal silicon carbide substrate as described in claim 12, wherein, The substrate formed by the main region and the asymmetric region is characterized in that: The BOW value is in the range of -35 micrometers to 0 micrometers, and / or The WARP value is 45 micrometers.

14. The single-crystal silicon carbide substrate as claimed in claim 1, wherein: The thickness of the asymmetric region and the main region is in the range of 200 micrometers to 1000 micrometers, and / or The substrate has a local cylindrical shape in the main region, the diameter d of which is greater than 149.5 mm, and / or The substrate has a total thickness variation of less than 5 micrometers, and / or The asymmetric and main regions of the substrate are formed from monolithic silicon carbide single crystals of one of the variants 4H-SiC, 6H-SiC, and 15R-SiC, and / or In the main region, the silicon carbide crystal structure has an α° off-axis orientation on the basal plane (1000), which is a 0.5° to 8° off-axis orientation.

15. The single-crystal silicon carbide substrate as claimed in claim 14, wherein: The thickness of the asymmetric region and the main region is in the range of 250 micrometers to 500 micrometers, and / or The α° off-axis orientation is a 4° off-axis orientation.

16. The single-crystal silicon carbide substrate as claimed in claim 1, wherein: The main region has a substantially flat surface, and / or The asymmetric region has the shape of a circular segment defined between an adjacent main region and the periphery of the substrate; and / or The asymmetrical region has a substantially flat shape or a non-flat shape with convex or concave curvature.

17. A method for producing one or more substrates having an asymmetrical shape, the method comprising: A multi-wire sawing process is performed, in which one or more substrates are cut from an ingot placed on a worktable using a wire saw mesh. One or more substrates with asymmetrical shapes are cut by controlling the relative movement between the wire saw and the worktable. The relative movement causes the wire saw to trace a non-linear sawing path across the ingot to cut out asymmetrical shapes.

18. The method of claim 17, wherein Controlling the relative movement between the wire saw mesh and the worktable includes: Control the wire saw mesh to move towards the worktable along the straight sawing direction; as well as The control table moves in coordination with the wire saw mesh in a direction perpendicular to the sawing direction, so that the wire saw mesh traces a non-linear sawing path across the ingot, or The wire saw mesh is controlled to move in a direction perpendicular to the cutting direction in coordination with the movement in the cutting direction, thereby causing the wire saw mesh to trace a non-linear cutting path across the ingot.

19. The method of claim 17, comprising: In the multi-wire sawing process, the stress applied to the saw wires of the wire saw is controlled by controlling the relative movement between the wire saw mesh and the worktable in a direction perpendicular to the sawing direction, so that sawing begins after the depth of the saw wires of the wire saw mesh into the ingot in the sawing direction reaches at least half the diameter of the saw wire.

20. The method of claim 17, wherein: The asymmetric shape includes an asymmetric region in the peripheral region of the substrate that is adjacent to a substantially flat main region of the substrate. The asymmetrical shape is cut by controlling the duration and amount of relative movement between the wire saw mesh and the worktable in a direction perpendicular to the sawing direction. The duration of the relative movement in the direction perpendicular to the sawing direction determines the maximum distance along the sawing direction between the substrate periphery located in the asymmetric region and the main region. The amount of displacement of the relative movement in the direction perpendicular to the sawing direction determines the maximum height of the asymmetric region relative to the main region.

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