Gallium oxide substrate

Abstract

The present invention provides a gallium oxide substrate having a first main surface and a second main surface facing the opposite direction to the first main surface, the gallium oxide substrate being obtained by fitting measurement data z0 (r, theta) of a height difference of the first main surface using a least square plane of the first main surface as a reference surface from z (r, theta) in formula (1) in the specification. When the second main surface and a horizontal flat surface are placed so as to face each other, the value (PV1 / D) obtained by dividing the diameter (D) of the first main surface by a first maximum height difference (PV1) of a component obtained by adding all anmznm (r, theta) for which j is 4, 9, 16, 25, 36, 49, 64, 81, by the diameter (D) of the first main surface is 0.39 * 10 <-4 > or less. When the second main surface and the flat chuck surface are completely adsorbed so as to face each other, the value (PV2 / D) obtained by dividing the diameter (D) of the first main surface by a second maximum height difference (PV2) of a component obtained by adding all anmznm (r, theta) having j of 4-81 inclusive is 0.59 * 10 <-4 > or less.

Description

[0001] This application is a divisional application of an application with application number 202080024107.3, an entry date into the national phase of September 24, 2021, and an invention title of "Gallium Oxide Substrate and Method for Manufacturing Gallium Oxide Substrate". Technical Field

[0002] The present disclosure relates to a gallium oxide substrate and a method for manufacturing a gallium oxide substrate. Background Art

[0003] In recent years, a proposal has been made to use a compound semiconductor substrate instead of a silicon semiconductor substrate. Examples of the compound semiconductor include silicon carbide, gallium nitride, and gallium oxide. Compared with a silicon semiconductor, a compound semiconductor has the advantage of having a large bandgap. The compound semiconductor substrate is polished, and an epitaxial film is formed on the polished surface.

[0004] A method for manufacturing a gallium oxide substrate is described in Patent Document 1. This manufacturing method includes using a slurry containing colloidal silica to polish only one surface of the gallium oxide substrate. The problem of Patent Document 1 is to improve the shapeability of a gallium oxide substrate having a monoclinic crystal system with poor symmetry and strong cleavage.

[0005] Patent Document 1: Japanese Unexamined Patent Application Publication No. 2016-13932

[0006] A single-sided polishing apparatus generally has a lower table, an upper table, and a nozzle. The lower table is arranged horizontally, and a polishing pad is adhered to the upper surface of the lower table. The upper table is arranged horizontally, and a gallium oxide substrate is fixed to the lower surface of the upper table. The gallium oxide substrate has a first main surface and a second main surface facing the opposite direction of the first main surface. The upper table holds the gallium oxide substrate horizontally and presses the first main surface of the gallium oxide substrate against the polishing pad. The lower table rotates about its vertical rotation center line. The upper table rotates passively along with the rotation of the lower table. The nozzle supplies a polishing slurry to the polishing pad from above. The polishing slurry is supplied between the gallium oxide substrate and the polishing pad to polish the first main surface of the gallium oxide substrate flat. Since the second main surface of the gallium oxide substrate is fixed to the lower surface of the upper table, the unevenness of the lower surface of the upper table is transferred to the second main surface.

[0007] Since the single-sided polishing apparatus polishes only the first main surface, a residual stress difference is generated between the first main surface and the second main surface after polishing. As a result, warping occurs due to the Twyman Effect. In addition, if the second main surface of the gallium oxide substrate is removed from the upper table and is adsorbed entirely with respect to a flat chuck surface, the first main surface is deformed into the same shape as the lower surface of the upper table, and the unevenness of the lower surface of the upper table appears on the first main surface.

[0008] In the past, the flatness of gallium oxide substrates was poor, and the transfer accuracy of the exposure pattern relative to the gallium oxide substrate was poor. SUMMARY OF THE INVENTION

[0009] One aspect of the present disclosure provides a technique capable of improving the flatness of a gallium oxide substrate and capable of transferring an exposure pattern to the gallium oxide substrate with high precision.

[0010] The gallium oxide substrate according to one aspect of the present disclosure has a first main surface and a second main surface facing in the opposite direction to the first main surface.

[0011] If the measurement data z0(r, θ) of the height difference of the first main surface with the least-squares plane of the first main surface as the reference plane is fitted by z(r, θ) of the following formula (1),

[0012] then, when the second main surface is placed opposite to a horizontal flat surface, for all a where j is 4, 9, 16, 25, 36, 49, 64, 81, nm z nm (r, θ), the value (PV1 / D) obtained by dividing the first maximum height difference (PV1) of the component obtained by adding them by the diameter (D) of the first main surface is 0.39×10 －4 Hereinafter,

[0013] When the second main surface is fully adsorbed opposite to a flat chuck surface, for all a where j is 4 or more and 81 or less, nm z nm (r, θ), the value (PV2 / D) obtained by dividing the second maximum height difference (PV2) of the component obtained by adding them by the diameter (D) of the first main surface is 0.59×10 －4 Hereinafter.

[0014] [Formula 1]

[0015]

[0016] [Formula 2]

[0017]

[0018] [Formula 3]

[0019]

[0020] [Formula 4]

[0021]

[0022] [Formula 5]

[0023]

[0024] In the above formulas (1) to (5), (r, θ) are polar coordinates on a reference plane, n is a natural number greater than or equal to 0 and less than or equal to k, k is 16, when n is even, m is only an even number in the range from -n to +n, when n is odd, m is only an odd number in the range from -n to +n, j is an exponent representing the combination of n and k, and a nm is a coefficient.

[0025] According to one aspect of the present disclosure, the flatness of the gallium oxide substrate can be improved, and an exposure pattern can be transferred to the gallium oxide substrate with high precision. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a flowchart showing a method for manufacturing a gallium oxide substrate according to an embodiment.

[0027] Figure 2 is a perspective view showing an example of a single-sided grinding apparatus for single-sided grinding in the implementation Figure 1 of.

[0028] Figure 3 is a sectional view showing an example of a single-sided grinding apparatus for single-sided grinding in the implementation Figure 1 of.

[0029] Figure 4 is a perspective view showing an example of a double-sided grinding apparatus for double-sided grinding in the implementation Figure 1 of.

[0030] Figure 5 is a sectional view showing an example of a double-sided grinding apparatus for double-sided grinding in the implementation Figure 1 of.

[0031] Figure 6 is a sectional view showing an example of the state of the gallium oxide substrate when measuring the first maximum height difference (PV1).

[0032] Figure 7 is a graph showing z for each of j = 1 (n = 0, m = 0), j = 2 (n = 1, m = 1), j = 4 (n = 2, m = 0), and j = 9 (n = 4, m = 0) nm (r, θ).

[0033] Figure 8 is a sectional view showing an example of the state of the gallium oxide substrate when measuring the second maximum height difference (PV2). DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. In addition, in the crystallographic descriptions in this specification, individual orientations are represented by [], collective orientations are represented by <>, individual planes are represented by (), and collective planes are represented by {}. The case where a crystallographic index is negative is usually represented by a bar above the number, but in this specification, a negative sign is prefixed to the number to represent a negative crystallographic index.

[0035] Figure 1 is a flowchart showing a method for manufacturing a gallium oxide substrate according to an embodiment. As Figure 1 shown, the method for manufacturing a gallium oxide substrate includes performing single-sided grinding (S1) on the gallium oxide substrate once. As the gallium oxide substrate, for example, a substrate obtained by previously cutting a β-Ga2O3 single crystal into a plate shape using a wire saw or the like and then grinding it to a predetermined thickness using a grinding device or the like is used. The gallium oxide substrate may contain a dopant or may not contain a dopant. As the dopant, for example, Si, Sn, Al, or In is used.

[0036] Figure 2 is a representation of the implementation Figure 1 of a perspective view of an example of a single-sided grinding device for single-sided grinding. Figure 3 is a representation of the implementation Figure 1 of a cross-sectional view of an example of a single-sided grinding device for single-sided grinding. In Figure 3 the unevenness of the lower surface 121 of the upper platform 120 is exaggeratedly shown. In addition, the single-sided grinding device for performing the secondary single-sided grinding (S2) of Figure 1 is the same as the single-sided grinding device 100 shown in Figure 2 and Figure 3 so illustration thereof is omitted.

[0037] The single-sided grinding device 100 includes a lower platen 110, an upper platen 120, and a nozzle 130. The lower platen 110 is configured to be horizontal, and a lower grinding pad 112 is adhered to the upper surface 111 of the lower platen 110. The upper platen 120 is configured to be horizontal, and a gallium oxide substrate 10 is fixed to the lower surface 121 of the upper platen 120. The upper platen 120 holds the gallium oxide substrate 10 horizontally and presses the gallium oxide substrate 10 against the lower grinding pad 112. In addition, the lower grinding pad 112 may be absent, and in this case, the upper platen 120 presses the gallium oxide substrate 10 against the lower platen 110. The diameter of the upper platen 120 is smaller than the radius of the lower platen 110, and the upper platen 120 is disposed at a position radially outside the rotation center line C1 of the lower platen 110. The rotation center line C2 of the upper platen 120 is configured to be parallel and offset from the rotation center line C1 of the lower platen 110. The lower platen 110 rotates about its vertical rotation center line C1. The upper platen 120 rotates passively as the lower platen 110 rotates. In addition, the upper platen 120 and the lower platen 110 may rotate independently or may rotate by respective rotation motors.

[0038] The gallium oxide substrate 10 has a circular first main surface 11 and a circular second main surface 12 opposite to the first main surface 11. Notches (not shown) indicating the crystal orientation of gallium oxide are formed on the outer periphery of the gallium oxide substrate 10. Instead of the notches, an orientation flat may be formed. The first main surface 11 is, for example, the {001} plane. The {001} plane is a crystal plane perpendicular to the <001> direction and may be either the (001) plane or the (00-1) plane.

[0039] In addition, the first main surface 11 may also be a crystal plane other than the {001} plane. Additionally, the first main surface 11 may have a so-called off angle with respect to a preset crystal plane. The off angle improves the crystallinity of the epitaxial film formed on the ground first main surface 11.

[0040] The nozzle 130 supplies a grinding slurry 140 to the lower grinding pad 112. The grinding slurry 140 includes, for example, particles and water. The particles are the dispersed phase, and the water is the dispersion medium. In addition, the dispersion medium may be an organic solvent. The grinding slurry 140 is supplied between the gallium oxide substrate 10 and the lower grinding pad 112 to grind the lower surface of the gallium oxide substrate 10 flatly.

[0041] In a first single-sided grinding (S1), diamond particles are used as particles, for example. The Mohs hardness of the diamond particles is 10. The D50 of the diamond particles is not particularly limited, and is, for example, 50 μm. "D50" refers to the 50% particle size of the cumulative percentage based on volume in the particle size distribution measured by the dynamic light scattering method. The dynamic light scattering method is a method of measuring the particle size distribution by irradiating the polishing slurry 140 with laser light and observing the scattered light thereof using a light detector.

[0042] In the first single-sided grinding (S1), the first major surface 11 of the gallium oxide substrate 10 is pressed against the lower polishing pad 112 and is polished flatly by the lower polishing pad 112 and the polishing slurry 140. On the other hand, the second major surface 12 of the gallium oxide substrate 10 is fixed to the lower surface 121 of the upper platform 120, and thus the unevenness of the lower surface 121 is transferred to the second major surface 12.

[0043] In addition, although the upper surface 111 of the lower platform 110 also has unevenness similar to the lower surface 121 of the upper platform 120, the unevenness is hardly transferred to the first major surface 11 of the gallium oxide substrate 10. This is because, unlike the upper platform 120, the lower platform 110 is relatively displaced with respect to the gallium oxide substrate 10.

[0044] As Figure 1 shown, the method for manufacturing a gallium oxide substrate includes performing a second single-sided grinding (S2) on the gallium oxide substrate. In the second single-sided grinding (S2), similarly to the first single-sided grinding (S1), the first major surface 11 of the gallium oxide substrate 10 is pressed against the lower polishing pad 112 and is polished flatly by the lower polishing pad 112 and the polishing slurry 140.

[0045] In the second single-sided grinding (S2), particles having a smaller D50 and a smaller Mohs hardness (i.e., softer) than those in the first single-sided grinding (S1) can be used. As the particles, silica gel is used, for example. On the other hand, since the second major surface 12 of the gallium oxide substrate 10 is fixed to the lower surface 121 of the upper platform 120, the unevenness of the lower surface 121 is transferred to the second major surface 12.

[0046] In addition, as described above, although the upper surface 111 of the lower platform 110 also has unevenness similar to the lower surface 121 of the upper platform 120, the unevenness is hardly transferred to the first major surface 11 of the gallium oxide substrate 10. This is because, unlike the upper platform 120, the lower platform 110 is relatively displaced with respect to the gallium oxide substrate 10.

[0047] However, since only the first main surface 11 is polished in the first single-sided polishing (S1) and the second single-sided polishing (S2), a residual stress difference is generated between the first main surface 11 and the second main surface 12 after polishing. As a result, warping occurs due to the Tyndall effect. In addition, if the second main surface 12 of the gallium oxide substrate 10 is removed from the upper platen 120 and is adsorbed comprehensively with respect to a flat chuck surface, the first main surface 11 is deformed into the same shape as the lower surface 121 of the upper platen 120, and the concavities and convexities of the lower surface 121 appear on the first main surface 11.

[0048] Therefore, as Figure 1 shown, the manufacturing method of the gallium oxide substrate includes double-sided polishing (S3) of the gallium oxide substrate. Different from the first single-sided polishing (S1) and the second single-sided polishing (S2), the double-sided polishing (S3) includes polishing the first main surface 11 and the second main surface 12 simultaneously.

[0049] Figure 4 is a perspective view showing an example of a double-sided polishing apparatus for performing Figure 1 the double-sided polishing. Figure 5 is a cross-sectional view showing an example of a double-sided polishing apparatus for performing Figure 1 the double-sided polishing. The double-sided polishing apparatus 200 includes a lower platen 210, an upper platen 220, a planetary gear carrier 230, a sun gear 240, and an internal gear 250. The lower platen 210 is arranged horizontally, and a lower polishing pad 212 is adhered to the upper surface 211 of the lower platen 210. The upper platen 220 is arranged horizontally, and an upper polishing pad 222 is adhered to the lower surface 221 of the upper platen 220. The planetary gear carrier 230 holds the gallium oxide substrate 10 horizontally between the lower platen 210 and the upper platen 220. The planetary gear carrier 230 is arranged radially outside the sun gear 240 and radially inside the internal gear 250. The sun gear 240 and the internal gear 250 are arranged concentrically and mesh with the outer peripheral gear 231 of the planetary gear carrier 230.

[0050] The double-sided polishing apparatus 200 is, for example, a 4-way method, and the lower platen 210, the upper platen 220, the sun gear 240, and the internal gear 250 rotate around the same vertical rotation center line. While the lower platen 210 and the upper platen 220 rotate in opposite directions, the lower polishing pad 212 is pressed against the lower surface of the gallium oxide substrate 10, and the upper polishing pad 222 is pressed against the upper surface of the gallium oxide substrate 10. In addition, at least one of the lower platen 210 and the upper platen 220 supplies polishing slurry to the gallium oxide substrate 10. The polishing slurry is supplied between the gallium oxide substrate 10 and the lower polishing pad 212 to polish the lower surface of the gallium oxide substrate 10. In addition, the polishing slurry is supplied between the gallium oxide substrate 10 and the upper polishing pad 222 to polish the upper surface of the gallium oxide substrate 10.

[0051] For example, when viewed from above, the lower platform 210, the sun gear 240, and the internal gear 250 rotate in the same direction. Their rotation direction is opposite to the rotation direction of the upper platform 220. The planet carrier 230 revolves while rotating on its own axis. The revolution direction of the planet carrier 230 is the same as the rotation direction of the sun gear 240 and the internal gear 250. On the other hand, the rotation direction of the planet carrier 230 is determined by the product of the rotational speed of the sun gear 240 and the pitch circle diameter and the product of the rotational speed of the internal gear 250 and the pitch circle diameter. If the product of the rotational speed of the internal gear 250 and the pitch circle diameter is larger than the product of the rotational speed of the sun gear 240 and the pitch circle diameter, the rotation direction of the planet carrier 230 and the revolution direction of the planet carrier 230 become the same direction. On the other hand, if the product of the rotational speed of the internal gear 250 and the pitch circle diameter is smaller than the product of the rotational speed of the sun gear 240 and the pitch circle diameter, the rotation direction of the planet carrier 230 and the revolution direction of the planet carrier 230 become opposite directions.

[0052] In addition, the double-sided grinding device 200 can also be a 3-way or 2-way method. The 3-way method can be, for example, any of the following methods: (1) the internal gear 250 is fixed, and the lower platform 210, the upper platform 220, and the sun gear 240 rotate; (2) the upper platform 220 is fixed, and the lower platform 210, the sun gear 240, and the internal gear 250 rotate. In addition, the 2-way method is, for example, a method in which the lower platform 210 and the upper platform 220 are fixed, and the sun gear 240 and the internal gear 250 rotate.

[0053] The planet carrier 230, for example, holds the gallium oxide substrate 10 horizontally with the first main surface 11 of the gallium oxide substrate 10 facing downward. In addition, the planet carrier 230 can also hold the gallium oxide substrate 10 horizontally with the first main surface 11 of the gallium oxide substrate 10 facing upward. In either case, the first main surface 11 and the second main surface 12 of the gallium oxide substrate 10 are ground simultaneously.

[0054] In double-sided grinding (S3), different from the first single-sided grinding (S1) and the second single-sided grinding (S2), the first main surface 11 and the second main surface 12 are ground simultaneously, so that the residual stress difference between the first main surface 11 and the second main surface 12 after grinding can be reduced. As a result, the warping caused by the Tyndall effect can be reduced.

[0055] The warping caused by the Tyndall effect is evaluated by the first maximum height difference (PV1) described below. Figure 6 It is a side view showing the state of the gallium oxide substrate when measuring the first maximum height difference (PV1). As Figure 6 shown, the first maximum height difference (PV1) is measured in a state where the second main surface 12 is placed relative to the horizontal flat surface 20 so that the gallium oxide substrate 10 does not deform. InFigure 6 In Figure 6 , the xy plane including the mutually orthogonal x-axis and y-axis is the least-squares plane of the first principal surface 11. The least-squares plane of the first principal surface 11 refers to the plane formed by fitting the first principal surface 11 by the least-squares method. In addition, in Figure 6 Figure 6 , the z-axis perpendicular to the x-axis and y-axis is set to pass through the center of the first principal surface 11.

[0056] The measurement data z0(r, θ) of the height difference of the first principal surface 11 with the least-squares plane of the first principal surface 11 as the reference plane 13 is fitted by z(r, θ) in the following formula (1).

[0057] [Formula 1]

[0058]

[0059] [Formula 2]

[0060]

[0061] [Formula 3]

[0062]

[0063] [Formula 4]

[0064]

[0065] [Formula 5]

[0066]

[0067] In the above formulas (1) to (5), (r, θ) are polar coordinates on the reference plane 13, n is a natural number greater than or equal to 0 and less than or equal to k, k is 16, when n is even, m is only an even number in the range from -n to +n, when n is odd, m is only an odd number in the range from -n to +n, j is an index representing the combination of n and k, a nm is a coefficient. From the above formula (4), as a method of expressing the combination of two indices n and m with one index j, a notation based on fringe is used. The above formula (2) is the Zernike Polynomials, and the Zernike Polynomials are orthogonal polynomials, so the coefficient a nm can be obtained by the above formula (5).

[0068] Figure 7 is a graph showing z nm (r, θ) for j = 1 (n = 0, m = 0), j = 2 (n = 1, m = 1), j = 4 (n = 2, m = 0), j = 9 (n = 4, m = 0).

[0069] AsFigure 7 As shown by the solid line, for \(j = 1\), \(z\) nm (r, θ) is the offset plane parallel to the xy plane. For \(j = 1\), \(z\) nm (r, θ) depends neither on r nor on θ.

[0070] As Figure 7 As shown by the dashed line, for \(j = 2\), \(z\) nm (r, θ) is the inclined plane obtained by rotating the xy plane about the y-axis. In addition, for \(j = 3\) (\(n = 1, m = -1\)), \(z\) nm (r, θ) is the inclined plane obtained by rotating the xy plane about the x-axis.

[0071] As Figure 7 As shown by the dash-dotted line, for \(j = 4\), \(z\) nm (r, θ) is the surface obtained by rotating the conic curve symmetric with respect to the z-axis on the xz plane by 180° about the z-axis. For \(j = 4\), \(z\) nm (r, θ) depends only on r and not on θ.

[0072] As Figure 7 As shown by the double dash-dotted line, for \(j = 9\), \(z\) nm (r, θ) is the surface obtained by rotating the quartic curve symmetric with respect to the z-axis on the xz plane by 180° about the z-axis. For \(j = 9\), \(z\) nm (r, θ) depends only on r and not on θ.

[0073] For \(z\) where \(j\) is the square of a natural number (e.g., 4, 9, 16, 25, 36, 49, 64, 81 ···) nm (r, θ) depends only on r and not on θ. In addition, for \(j = 1\) (\(n = 0, m = 0\)), \(z\) nm (r, θ), as described above, depends neither on r nor on θ.

[0074] The warping caused by the Twyman effect is generated by the residual stress difference between the first principal surface 11 and the second principal surface 12. This residual stress difference depends only on r and not on θ.

[0075] Therefore, the warping caused by the Twyman effect is evaluated by the first maximum height difference (PV1) of the component obtained by adding all \(a\) nm for \(z\) nm (r, θ) where \(j = 4, 9, 16, 25, 36, 49, 64, 81\). The first maximum height difference (PV1) refers to the height difference between the highest point and the lowest point with respect to the reference plane 13. The smaller the warping caused by the Twyman effect, the smaller the first maximum height difference (PV1).

[0076] In addition, for \(a\) where \(j>81\), \(z\) nm for \(z\)nm (r, θ) has almost no effect on the unevenness of the first main surface 11, so it is also ignored for the sake of simplifying the calculation.

[0077] In double-sided grinding (S3), different from the first single-sided grinding (S1) and the second single-sided grinding (S2), the first main surface 11 and the second main surface 12 are ground simultaneously. Therefore, as described above, the warpage caused by the Twyman effect can be reduced. As a result, the value (PV1 / D) obtained by dividing the first maximum height difference (PV1) by the diameter (D) of the first main surface 11 can be reduced to 0.39×10 －4 as follows. In addition, the first maximum height difference (PV1) can be reduced to 2 μm or less. In addition, PV1 / D is a dimensionless quantity, and "10 －4 " in the numerical value of PV1 / D is equivalent to "μm / cm".

[0078] As described above, PV1 / D is, for example, 0.39×10 －4 as follows. If PV1 / D is 0.39×10 －4 as follows, the warpage caused by the Twyman effect can be reduced. Therefore, the flatness of the gallium oxide substrate 10 can be improved. Furthermore, an exposure pattern can be transferred to the gallium oxide substrate 10 with high precision. PV1 / D is preferably 0.2×10 －4 as follows, and more preferably 0.1×10 －4 as follows. In addition, from the viewpoint of productivity, PV1 / D is preferably 0.02×10 －4 or more.

[0079] As described above, PV1 is, for example, 2 μm or less. If PV1 is 2 μm or less, the warpage caused by the Twyman effect can be reduced. Therefore, the flatness of the gallium oxide substrate 10 can be improved. Furthermore, an exposure pattern can be transferred to the gallium oxide substrate 10 with high precision. PV1 is preferably 1 μm or less, and more preferably 0.5 μm or less. In addition, from the viewpoint of productivity, PV1 is preferably 0.1 μm or more.

[0080] D is not particularly limited. For example, it is 5 cm or more and 31 cm or less. D is preferably 10 cm or more and 21 cm or less, and more preferably 12 cm or more and 15 cm or less.

[0081] However, in double-sided grinding (S3), unlike the first single-sided grinding (S1) and the second single-sided grinding (S2), not only the lower platen 210 but also the upper platen 220 is displaced relative to the gallium oxide substrate 10. As a result, it is possible to suppress the transfer of unevenness on the lower surface 221 of the upper platen 220 to the upper surface of the gallium oxide substrate 10, and the upper surface of the gallium oxide substrate 10 can be ground parallel to the lower surface of the gallium oxide substrate 10. Therefore, when the second major surface 12 of the gallium oxide substrate 10 is entirely adsorbed relative to the flat chuck surface 30, it is possible to suppress the unevenness of the lower surface 221 of the upper platen 220 from appearing on the first major surface 11.

[0082] The shape transfer of the upper platen 220 relative to the gallium oxide substrate 10 is evaluated by the second maximum height difference (PV2) described below. Figure 8 It is a side view showing the state of the gallium oxide substrate when measuring the second maximum height difference (PV2). As Figure 8 shown, the second maximum height difference (PV2) is measured in a state where the second major surface 12 is entirely adsorbed relative to the flat chuck surface 30. The adsorption is, for example, vacuum adsorption, and the chuck surface 30 is formed of a porous body. In Figure 8 , the xy plane including the x-axis and the y-axis orthogonal to each other is the least-squares plane of the first major surface 11. In addition, in Figure 8 , the z-axis perpendicular to the x-axis and the y-axis is set to pass through the center of the first major surface 11.

[0083] The measurement data z0(r, θ) of the height difference of the first major surface 11 with the least-squares plane of the first major surface 11 as the reference plane 13 is fitted by z(r, θ) of the above (1). z for j = 1, 2, 3 nm (r, θ) is a flat surface as described above, and thus is a component that is meaningless when measuring the second maximum height difference (PV2).

[0084] Therefore, the shape transfer of the upper platen 220 relative to the gallium oxide substrate 10 is evaluated by the second maximum height difference (PV2) of the component obtained by adding all a nm z nm (r, θ) where j is 4 or more and 81 or less. The second maximum height difference (PV2) refers to the height difference between the highest point and the lowest point relative to the reference plane 13. The smaller the shape transfer of the upper platen 220 relative to the gallium oxide substrate 10, the smaller the second maximum height difference (PV2).

[0085] In addition, a for j greater than 81 nm z nm (r, θ) has little effect on the unevenness of the first major surface 11, and thus is also ignored for simplifying the calculation.

[0086] In double-sided polishing (S3), unlike the first single-sided polishing (S1) and the second single-sided polishing (S2), the first major surface 11 and the second major surface 12 are polished simultaneously. Thus, as described above, shape transfer of the upper platen 220 with respect to the gallium oxide substrate 10 can be suppressed. As a result, the value (PV2 / D) obtained by dividing the second maximum height difference (PV2) by the diameter (D) of the first major surface 11 can be reduced to 0.59×10 －4 as follows. In addition, the second maximum height difference (PV2) can be reduced to 3 μm or less. Furthermore, PV2 / D is a dimensionless quantity, and the "10 －4 " in the numerical value of PV2 / D is equivalent to "μm / cm".

[0087] As described above, PV2 / D is, for example, 0.59×10 －4 as follows. If PV2 / D is 0.59×10 －4 as follows, shape transfer of the upper platen 220 with respect to the gallium oxide substrate 10 can be suppressed. Thus, the flatness of the gallium oxide substrate 10 can be improved, and furthermore, an exposure pattern can be transferred to the gallium oxide substrate 10 with high precision. PV2 / D is preferably 0.2×10 －4 as follows, and more preferably 0.1×10 －4 as follows. In addition, from the viewpoint of productivity, PV2 / D is preferably 0.02×10 －4 or more.

[0088] As described above, PV2 is, for example, 3 μm or less. If PV2 is 3 μm or less, shape transfer of the upper platen 220 with respect to the gallium oxide substrate 10 can be suppressed. Thus, the flatness of the gallium oxide substrate 10 can be improved, and furthermore, an exposure pattern can be transferred to the gallium oxide substrate 10 with high precision. PV2 is preferably 1 μm or less, and more preferably 0.5 μm or less. In addition, from the viewpoint of productivity, PV2 is preferably 0.1 μm or more.

[0089] Double-sided polishing (S3) includes simultaneously polishing the first major surface 11 and the second major surface 12 of the gallium oxide substrate 10, which face each other, using a polishing slurry containing particles with a Mohs hardness of 7 or less. If the Mohs hardness is 7 or less, the particles are soft, so generation of damage to the gallium oxide substrate 10 can be suppressed, and thus breakage of the gallium oxide substrate 10 can be suppressed. The Mohs hardness is preferably 6 or less, and more preferably 5 or less. From the viewpoint of polishing speed, the Mohs hardness is preferably 2 or more.

[0090] As particles with a Mohs hardness of 7 or less, silica gel is used, for example. The Mohs hardness of silica gel is 7. In addition, the material of the particles with a Mohs hardness of 7 or less is not limited to SiO2, and may also be TiO2, ZrO2, Fe2O3, ZnO, or MnO2, etc. The Mohs hardness of TiO2 is 6, the Mohs hardness of ZrO2 is 6.5, the Mohs hardness of Fe2O3 is 6, the Mohs hardness of ZnO is 4.5, and the Mohs hardness of MnO2 is 3. In the double-sided grinding (S3), the grinding slurry only needs not to contain particles with a Mohs hardness exceeding 7, and may also contain two or more kinds of particles with a Mohs hardness of 7 or less.

[0091] In the double-sided grinding (S3), the D50 of the particles contained in the grinding slurry is, for example, 1 μm or less. If the D50 is 1 μm or less, the particles are small, so that it is possible to suppress the situation where excessive stress acts locally on the gallium oxide substrate 10, and thus it is possible to suppress the cracking of the gallium oxide substrate 10. The D50 is preferably 0.7 μm or less, and more preferably 0.5 μm or less. From the viewpoint of the grinding speed, the D50 is preferably 0.01 μm or more.

[0092] In the first half of 50% or more of the double-sided grinding (S3), the grinding pressure is, for example, 9.8 kPa or less. In the first half of the double-sided grinding (S3), since the first main surface 11 and the second main surface 12 are not sufficiently flattened, the unevenness is large and stress concentration is likely to occur. If the grinding pressure is 9.8 kPa or less in the first half of 50% or more of the double-sided grinding (S3), it is possible to suppress the situation where excessive stress acts locally on the gallium oxide substrate 10, and thus it is possible to suppress the cracking of the gallium oxide substrate 10. In the first half of 50% or more of the double-sided grinding (S3), the grinding pressure is preferably 8.8 kPa or less, and more preferably 7.8 kPa or less. In addition, from the viewpoint of the grinding speed, in the first half of 50% or more of the double-sided grinding (S3), the grinding pressure is preferably 3 kPa or more.

[0093] In addition, during the entire period of the double-sided grinding (S3), the grinding pressure may also be constant. In addition, in the double-sided grinding (S3), as time passes, the first main surface 11 and the second main surface 12 are gradually flattened and the unevenness becomes smaller. Therefore, in order to increase the grinding speed, the grinding pressure may be increased step by step.

[0094] In addition, the manufacturing method of the gallium oxide substrate is not limited to Figure 1 the method shown, and may be a method including double-sided grinding (S3). In addition, the manufacturing method of the gallium oxide substrate may also include Figure 1Processes other than the processes shown may also include cleaning, for example, of the adherends (such as particles) on the gallium oxide substrate 10. The cleaning is performed, for example, between the first single-sided grinding (S1) and the second single-sided grinding (S2), and between the second single-sided grinding (S2) and the double-sided grinding (S3).

[0095] Examples

[0096] Hereinafter, examples and comparative examples will be described. Examples 1 to 3 among the following Examples 1 to 7 are examples, and Examples 4 to 7 are comparative examples.

[0097] [Examples 1 to 3]

[0098] In Examples 1 to 3, a β-Ga2O3 single crystal substrate having a diameter of 50.8 mm and a thickness of 0.7 mm was Figure 1 subjected to the first single-sided grinding (S1), the second single-sided grinding (S2), and the double-sided grinding (S3) under the same conditions as shown.

[0099] In the first single-sided grinding (S1), the (001) plane of the β-Ga2O3 single crystal substrate was ground with Figure 2 the single-sided grinding device 100 shown. A tin-made lower platen 110 and diamond particles having a particle size of 0.5 μm were used for grinding. In the first single-sided grinding (S1), instead of using the lower grinding pad 112, the substrate was pressed against the lower platen 110 for grinding.

[0100] In the second single-sided grinding (S2), the (001) plane of the β-Ga2O3 single crystal substrate was ground with Figure 2 the single-sided grinding device 100 shown. In the second single-sided grinding (S2), different from the first single-sided grinding (S1), the lower grinding pad 112 was used. In the second single-sided grinding (S2), a polyurethane-made lower grinding pad 112 and silica gel particles having a particle size of 0.05 μm were used for grinding.

[0101] In the double-sided grinding (S3), with Figure 4The shown double-sided grinding device 200 grinds the (001) surface and the (00-1) surface of the β-Ga2O3 single crystal substrate simultaneously. The double-sided grinding device 200 is a product named DSM9B made by SPEEDFAM, and the lower grinding pad 212 and the upper grinding pad 222 are products named N7512 made by FILWEL. The grinding slurry is a slurry containing 20% by mass of silica gel and 80% by mass of water, and the D50 of the silica gel is 0.05 μm. During the entire period of double-sided grinding (S3), the grinding pressure is 9.8 kPa, the rotation speed of the lower platen 210 is 40 rpm, the rotation speed of the upper platen 220 is 14 rpm, the rotation speed of the sun gear 240 is 9 rpm, and the rotation speed of the internal gear 250 is 15 rpm. The pitch diameter of the sun gear 240 is 207.4 mm, and the pitch diameter of the internal gear 250 is 664.6 mm.

[0102] [Examples 4 to 6]

[0103] In Examples 4 to 6, a single-sided grinding (S1) and a double-sided single-sided grinding (S2) were performed only once on the β-Ga2O3 single crystal substrate with a diameter of 50.8 mm and a thickness of 0.7 mm under the same conditions as in Examples 1 to 3. In Examples 4 to 6, double-sided grinding (S3) was not performed.

[0104] [Example 7]

[0105] In Example 7, except for using diamond particles with a particle size of 0.5 μm as the particles for double-sided grinding (S3) and using a grinding pad made of epoxy resin as the grinding pad for diamond particles, a single-sided grinding (S1), a double-sided single-sided grinding (S2), and a double-sided grinding (S3) were performed under the same conditions as in Examples 1 to 3. As a result, the gallium oxide substrate 10 was cracked during the double-sided grinding (S3).

[0106] [Grinding Results]

[0107] For the first maximum height difference (PV1) of the (001) surface as the first main surface 11, as Figure 6 shown, it was measured in a state where the (00-1) surface as the second main surface 12 was placed opposite to a horizontal flat surface 20 so that the gallium oxide substrate 10 was not deformed. As the measuring device, a product named PF-60 made by Mitaka Kohki was used.

[0108] For the second maximum height difference (PV2) of the (001) surface as the first main surface 11, as Figure 8 shown, it was measured in a state where the (00-1) surface as the second main surface 12 was fully adsorbed opposite to a flat chuck surface 30. As the measuring device, a product named PF-60 made by Mitaka Kohki was used.

[0109] Table 1 shows the polishing results of Examples 1 to 6. In addition, in Example 7, as described above, the gallium oxide substrate 10 was cracked during double-sided polishing (S3).

[0110] [Table 1]

[0111]

[0112] As can be seen from Table 1, Examples 1 to 3 are different from Examples 4 to 6. Since double-sided polishing (S3) was performed, PV1 / D is 0.39×10 －4 Hereinafter, PV1 is 2 μm or less. It can be seen that by double-sided polishing (S3), warping caused by the Tyndall effect can be reduced.

[0113] In addition, as can be seen from Table 1, Examples 1 to 3 are different from Examples 4 to 6. Since double-sided polishing (S3) was performed, PV2 / D is 0.59×10 －4 Hereinafter, PV2 is 3 μm or less. It can be seen that by double-sided polishing (S3), shape transfer of the upper platen 220 relative to the gallium oxide substrate 10 can be suppressed.

[0114] In addition, in Examples 1 to 3, the Mohs hardness of the particles used in double-sided polishing (S3) is 7 or less, the D50 of the particles is 1 μm or less, and the polishing pressure is 9.8 kPa or less during 50% or more of the first half period. Therefore, the gallium oxide substrate 10 did not crack during double-sided polishing. On the other hand, in Example 7, since the Mohs hardness of the particles used in double-sided polishing (S3) exceeds 7, the gallium oxide substrate 10 cracked during double-sided polishing.

[0115] In addition, in one-time single-sided polishing (S1), diamond particles with a Mohs hardness of 10 were used for polishing, but the gallium oxide substrate 10 did not crack. In single-sided polishing, compared with double-sided polishing, the gallium oxide substrate 10 is less likely to crack, and it can be presumed that this should be the reason why Patent Document 1 adopted single-sided polishing.

[0116] As described above, embodiments of the gallium oxide substrate and the method for manufacturing the gallium oxide substrate according to the present disclosure have been described, but the present disclosure is not limited to the above embodiments and the like. Within the scope described in the claims, various changes, corrections, substitutions, additions, deletions, and combinations can be made. These of course also fall within the technical scope of the present disclosure.

[0117] This application claims priority based on Japanese Patent Application No. 2019-073548 filed with the Japan Patent Office on April 8, 2019, and the entire contents of Japanese Patent Application No. 2019-073548 are incorporated herein by reference.

[0118] Explanation of reference numerals

[0119] 10... Gallium oxide substrate; 11... First main surface; 12... Second main surface.

Claims

1. A gallium oxide substrate, wherein, It is a gallium oxide substrate having a first major surface and a second major surface facing in the opposite direction to the first major surface, wherein the first major surface is a {001} plane or has a desired inclination angle with respect to the {001} plane. If the measurement data z0(r, θ) of the height difference of the first major surface with the least-squares plane of the first major surface as the reference plane is fitted by z(r, θ) of the following formula (1). Then, when the second major surface is placed opposite to a horizontal flat surface, all the values of a for j = 4, 9, 16, 25, 36, 49, 64, 81 nm z nm (r, θ) is added, and the value (PV1 / D) obtained by dividing the first maximum height difference (PV1) of the resulting component by the diameter (D) of the first major surface is 0.39×10 －4 Hereinafter, All a where j is 4 or more and 81 or less when the second main surface is fully adsorbed relative to the flat chuck surface nm z nm The value (PV2 / D) obtained by dividing the second maximum height difference (PV2) of the component obtained by adding (r, θ) by the diameter (D) of the first main surface is 0.59×10 －4 or less [Formula 1] [Formula 2] [Formula 3] [Formula 4] [Formula 5] In the above formulas (1) to (5), (r, θ) are polar coordinates on a reference plane, n is a natural number greater than or equal to 0 and less than or equal to k, k is 16, when n is even, m is only an even number in the range from -n to +n, when n is odd, m is only an odd number in the range from -n to +n, j is an exponent representing the combination of n and k, and a nm is a coefficient.

2. The gallium oxide substrate according to claim 1, wherein, The first maximum height difference (PV1) is 2 μm or less. The second maximum height difference (PV2) is 3 μm or less.

3. The gallium oxide substrate according to claim 1 or 2, wherein, The value (PV1 / D) obtained by dividing the first maximum height difference (PV1) by the diameter (D) of the first main surface is 0.2×10 －4 or less.

4. The gallium oxide substrate according to claim 1 or 2, wherein, The value (PV2 / D) obtained by dividing the second largest height difference (PV2) by the diameter (D) of the first main surface is 0.55×10 －4 or less.

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