Nitride semiconductor substrate, laminate, substrate selection program, substrate data output program, off-angle coordinate map, and methods thereof
A nitride semiconductor substrate including a group III nitride semiconductor crystal and having a main surface, wherein a low index crystal plane is (0001) plane curved in a concave spherical shape to the main surface, and the off-angle (θ m , θ a ) at a position (x, y) in the main surface approximated by x representing a coordinate in a direction along <1-100> axis, y is a coordinate in a direction along <11-20> axis, (0, 0) represents a coordinate (x, y) of the center, θ m represents a direction component along <1-100> axis in an off-angle of <0001> axis with respect to a normal, θ a represents a direction component along <11-20> axis in the off-angle, (M 1 , A 1 ) represents a rate of change in the off-angle (θ m , θ a ) with respect to the position (x, y) in the main surface, and (M 2 , A 2 ) represents the off-angle (θ m , θ a ) at the center.
1. A nitride semiconductor substrate comprising a group III nitride semiconductor crystal and having a main surface,
wherein a low index crystal plane nearest to the main surface is (0001) plane curved in a concave spherical shape with respect to the main surface, and
the off-angle (θ m , θ a ) at an arbitrary position (x, y) in the main surface is approximated by the following formula (1):
[
Formula
1
]
(
θ
m
θ
a
1
)
=
(
M
1
0
M
2
0
A
1
A
2
0
0
1
)
(
x
y
1
)
(
1
)
where x represents a coordinate in a direction along <1-100> axis of the crystal as a position in the main surface, y represents a coordinate in a direction along <11-20> axis of the crystal as a position in the main surface, (0, 0) represents a coordinate (x, y) of the center of the main surface, θ m represents a direction component along <1-100> axis in an off-angle of <0001> axis of the crystal with respect to a normal of the main surface, θ a represents a direction component along <11-20> axis in the off-angle, (M 1 , A 1 ) represents a rate of change in the off-angle (θ m , θ a ) with respect to the position (x, y) in the main surface, and (M 2 , A 2 ) represents the off-angle (θ m , θ a ) at the center of the main surface, and
wherein the off-angle (θ m , θ a ) at least at a part of positions of the main surface satisfies the following formula (2):
0.0784≤θ m 2 +θ a 2 ≤0.578 (2).
2. The nitride semiconductor substrate according to claim 1 ,
wherein an absolute value of a rate of change in the Om, 1 , is different from an absolute value of a rate of change in the θ a , |A 1 |.
3. The nitride semiconductor substrate according to claim 2 ,
wherein the absolute value of the rate of change in the θ m , |M 1 |, is smaller than the absolute value of the rate of change in the θ a , |A 1 |.
4. The nitride semiconductor substrate according to claim 1 ,
wherein the off-angle (θ m , θ a ) at least at the center of the main surface satisfies the formula (2).
5. The nitride semiconductor substrate according to claim 1 ,
wherein a proportion of an area of a region where the off-angle (θ m , θ a ) satisfies the formula (2) with respect to a total area of the main surface is more than 50%.
6. A nitride semiconductor substrate comprising a group III nitride semiconductor crystal and having a main surface,
wherein a low index crystal plane nearest to the main surface is (0001) plane curved in a concave spherical shape with respect to the main surface, and
the off-angle (θ m , θ a ) at an arbitrary position (x, y) in the main surface is approximated by the following formula (1):
[
Formula
1
]
(
θ
m
θ
a
1
)
=
(
M
1
0
M
2
0
A
1
A
2
0
0
1
)
(
x
y
1
)
(
1
)
where x represents a coordinate in a direction along <1-100> axis of the crystal as a position in the main surface, y represents a coordinate in a direction along <11-20> axis of the crystal as a position in the main surface, (0, 0) represents a coordinate (x, y) of the center of the main surface, θ m represents a direction component along <1-100> axis in an off-angle of <0001> axis of the crystal with respect to a normal of the main surface, θ a represents a direction component along <11-20> axis in the off-angle, (M 1 , A 1 ) represents a rate of change in the off-angle (θ m , θ a ) with respect to the position (x, y) in the main surface, and (M 2 , A 2 ) represents the off-angle (θ m , θ a ) at the center of the main surface, and
wherein the off-angle (θ m , θ a ) at least at a part of positions of the main surface satisfies the following formulas (3-1) and (3-2):
0.47≤θ m ≤0.71 (3-1)
−0.20≤θ a ≤0.26 (3-2).
7. The nitride semiconductor substrate according to claim 6 ,
wherein the off-angle (θ m , θ a ) at least at the center of the main surface satisfies the formulas (3-1) and (3-2).
8. The nitride semiconductor substrate according to claim 6 ,
wherein a proportion of an area of a region where the off-angle (θ m , θ a ) satisfies the formulas (3-1) and (3-2) with respect to a total area of the main surface is more than 50%.
9. The nitride semiconductor substrate according to claim 1 ,
wherein the θ m at the center of the main surface is larger than the θ a at the center of the main surface, and
a maximum absolute value of an error of the θ m actually measured with respect to the θ m obtained by the formula (1) is smaller than a maximum absolute value of an error of the θ a actually measured with respect to the θ a obtained by the formula (1).
10. A nitride semiconductor substrate comprising a group III nitride semiconductor crystal and having a main surface,
wherein a low index crystal plane nearest to the main surface is (0001) plane curved in a concave spherical shape with respect to the main surface, and
the off-angle (θ m , θ a ) at an arbitrary position (x, y) in the main surface is approximated by the following formula (1):
[
Formula
1
]
(
θ
m
θ
a
1
)
=
(
M
1
0
M
2
0
A
1
A
2
0
0
1
)
(
x
y
1
)
(
1
)
where x represents a coordinate in a direction along <1-100> axis of the crystal as a position in the main surface, y represents a coordinate in a direction along <11-20> axis of the crystal as a position in the main surface, (0, 0) represents a coordinate (x, y) of the center of the main surface, θ m represents a direction component along <1-100> axis in an off-angle of <0001> axis of the crystal with respect to a normal of the main surface, θ a represents a direction component along <11-20> axis in the off-angle, (M 1 , A 1 ) represents a rate of change in the off-angle (θ m , θ a ) with respect to the position (x, y) in the main surface, and (M 2 , A 2 ) represents the off-angle (θ m , θ a ) at the center of the main surface, and
wherein the off-angle (θ m , θ a ) at least at a part of positions of the main surface satisfies the following formulas (4-1) and (4-2):
−0.05≤θ m ≤0.21 (4-1)
0.36≤θ a ≤0.65 (4-2).
11. The nitride semiconductor substrate according to claim 9 ,
wherein the off-angle (θ m , θ a ) at least at the center of the main surface satisfies the formulas (4-1) and (4-2).
12. The nitride semiconductor substrate according to claim 9 ,
wherein a proportion of an area of a region where the off-angle (θ m , θ a ) satisfies the formulas (4-1) and (4-2) with respect to a total area of the main surface is more than 50%.
13. The nitride semiconductor substrate according to claim 1 ,
wherein the θ a at the center of the main surface is larger than the θ m at the center of the main surface,
a maximum absolute value of an error of the θ a actually measured with respect to the θ a obtained by the formula (1) is smaller than a maximum absolute value of an error of the θ m actually measured with respect to the θ m obtained by the formula (1).
14. The nitride semiconductor substrate according to claim 1 ,
wherein an error of the off-angle actually measured with respect to the off-angle obtained by the formula (1) at arbitrary position in the main surface is within ±0.12°.
15. A semiconductor laminate comprising:
the nitride semiconductor substrate according to claim 1 , and
a semiconductor layer comprising a group III nitride semiconductor, provided on the nitride semiconductor substrate.
16. A manufacturing method of nitride semiconductor substrate, comprising: fabricating the nitride semiconductor substrate according to claim 1 by a VAS (Void-Assisted Separation) method.
17. A manufacturing method of a semiconductor laminate, comprising:
fabricating the nitride semiconductor substrate according to claim 1 by a VAS (Void-Assisted Separation) method, and
epitaxially growing a semiconductor layer comprising a group III nitride semiconductor on the nitride semiconductor substrate to fabricate a semiconductor laminate.
18. A manufacturing method of a semiconductor device, comprising:
fabricating a nitride semiconductor substrate comprising a group III nitride semiconductor crystal and having a main surface, and
epitaxially growing a semiconductor layer comprising a group III nitride semiconductor on the nitride semiconductor substrate to fabricate a semiconductor laminate,
cutting the semiconductor laminate to fabricate a semiconductor device, and
selecting the semiconductor device,
wherein, in the fabrication of the nitride semiconductor substrate, the nitride semiconductor substrate is fabricated so that:
a low index crystal plane nearest to the main surface is (0001) plane curved in a concave spherical shape with respect to the main surface, and
the off-angle (θ m , θ a ) at a position (x, y) in the main surface is approximated by the following formula (1):
[
Formula
9
]
(
θ
m
θ
a
1
)
=
(
M
1
0
M
2
0
A
1
A
2
0
0
1
)
(
x
y
1
)
(
1
)
where x represents a coordinate in a direction along <1-100> axis of the crystal as a position in the main surface, y represents a coordinate in a direction along <11-20> axis of the crystal as a position in the main surface, (0, 0) represents a coordinate (x, y) of the center of the main surface, θ m represents a direction component along <1-100> axis in an off-angle of <0001> axis of the crystal with respect to a normal of the main surface, θ a represents a direction component along <11-20> axis in the off-angle, (M 1 , A 1 ) represents a rate of change in the off-angle (θ m , θ a ) with respect to the position (x, y) in the main surface, and (M 2 , A 2 ) represents the off-angle (θ m , θ a ) at the center of the main surface;
in the selection of the semiconductor device, the semiconductor device is selected based on the off-angle (θ m , θ a ) at a position (x, y) in the main surface.
19. A semiconductor laminate comprising:
the nitride semiconductor substrate according to claim 6 , and
a semiconductor layer comprising a group III nitride semiconductor, provided on the nitride semiconductor substrate.
20. A semiconductor laminate comprising:
the nitride semiconductor substrate according to claim 10 , and
a semiconductor layer comprising a group III nitride semiconductor, provided on the nitride semiconductor substrate.
21. A manufacturing method of a nitride semiconductor substrate, comprising:
fabricating the nitride semiconductor substrate according to claim 6 by a VAS (Void-Assisted Separation) method.
22. A manufacturing method of a nitride semiconductor substrate, comprising:
fabricating the nitride semiconductor substrate according to claim 10 by a VAS (Void-Assisted Separation) method.
23. A manufacturing method of a semiconductor laminate, comprising:
fabricating the nitride semiconductor substrate according to claim 6 by a VAS (Void-Assisted Separation) method, and
epitaxially growing a semiconductor layer comprising a group III nitride semiconductor on the nitride semiconductor substrate to fabricate a semiconductor laminate.
24. A manufacturing method of a semiconductor laminate, comprising:
fabricating the nitride semiconductor substrate according to claim 10 by a VAS (Void-Assisted Separation) method, and
epitaxially growing a semiconductor layer comprising a group III nitride semiconductor on the nitride semiconductor substrate to fabricate a semiconductor laminate.