US 2022/0028700 A1Published application

Gallium oxide substrate and method of manufacturing gallium oxide substrate

AssigneeAGC Inc.

InventorYusuke HIRABAYASHI

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Abstract

A gallium oxide substrate includes first and second main surfaces. When measured data z0(r,θ) of height differences of points (r,θ,z) on the first main surface from a least square plane of the first main surface are approximated by a function z(r,θ)=Σanmznm(r,θ), a ratio of a first maximum height difference of a component of z(r,θ) obtained by summing terms anmznm(r,θ) with an index j of 4, 9, 16, 25, 36, 49, 64, and 81, when the second main surface is placed facing a horizontal flat surface, to a diameter of the first main surface is 0.39×10−4 or less, and a ratio of a second maximum height difference of a component of z(r,θ) obtained by summing terms anmznm(r,θ) with j of from 4 to 81, when an entire surface of the second main surface is adsorbed to a flat chuck surface, to the diameter is 0.59×10−4 or less.

A gallium oxide substrate comprising:

a first main surface;
and
a second main surface which is opposite to the first main surface, wherein
when measured data z0(r, θ) of height differences of points (r, θ, z) on the first main surface from a reference plane, which is a least square plane of the first main surface, are approximated by a function z(r, θ) expressed by equation (1),
[
Math
⁢
⁢
1
]
⁢
z
⁡
(
r
,
θ
)
=
∑
n
=
0
k
⁢
∑
m
=
-
n
n
⁢
a
n
⁢
m
⁢
z
n
⁢
m
⁡
(
r
,
θ
)
(
1
)
where
[
Math
⁢
⁢
2
]
⁢
z
n
⁢
m
⁡
(
r
,
θ
)
=
{
R
n
m
⁡
(
r
)
⁢
cos
⁡
(
m
⁢
⁢
θ
)
m
≥
0
R
n
m
⁡
(
r
)
⁢
sin
⁡
(

m

⁢
θ
)
m
<
0
(
2
)
and
[
Math
⁢
⁢
3
]
⁢
R
n
m
⁡
(
r
)
=
{
∑
i
=
0
n
-
m
2
⁢
(
-
1
)
i
⁢
(
n
-
i
)
!
i
⁢
!
(
n
+
m
2
-
i
)
⁢
!
(
n
-
m
2
-
i
)
!
⁢
r
n
-
2
⁢
i
n
-
m
⁢
⁢
is
⁢
⁢
even
⁢
0
n
-
m
⁢
⁢
is
⁢
⁢
odd
(
3
)
j is an index representing a combination of n and k, expressed by equation (4),
[
Math
⁢
⁢
4
]
⁢
j
=
(
1
+
n
+

m

2
)
2
-
2
⁢

m

+
⌊
1
-
sgn
⁢
⁢
m
2
⌋
(
4
)
anm is a coefficient obtained by equation (5),
[
Math
⁢
⁢
5
]
⁢
a
n
⁢
⁢
m
=
∫
0
2
⁢
π
⁢
∫
0
D
/
2
⁢
z
0
⁡
(
r
,
θ
)
⁢
z
n
⁢
m
⁡
(
r
,
θ
)
⁢
r
⁢
d
⁢
r
⁢
d
⁢
θ
∫
0
2
⁢
π
⁢
∫
0
D
/
2
⁢
z
n
⁢
m
⁡
(
r
,
θ
)
⁢
z
n
⁢
m
⁡
(
r
,
θ
)
⁢
r
⁢
d
⁢
r
⁢
d
⁢
θ
(
5
)
parameters (r, θ) are polar coordinates on the reference plane,
n is an integer greater than or equal to 0 and less than or equal to k,
k is 16,
m is an even number within a range from −n to +n, when n is an even number, and
m is an odd number within a range from −n to +n, when n is an odd number,
a ratio (PV1/D) of a first maximum height difference (PV1) of a component of z(r, θ) obtained by summing all terms anmznm(r, θ) with j which are 4, 9, 16, 25, 36, 49, 64, and 81, when the second main surface is placed facing a horizontal flat surface, to a diameter (D) of the first main surface is less than or equal to 0.39×10−4, and
a ratio (PV2/D) of a second maximum height difference (PV2) of a component of z(r, θ) obtained by summing all terms anmznm(r, θ) with j which are greater than or equal to 4 and less than or equal to 81, when an entire surface of the second main surface is adsorbed to a flat chuck surface, to the diameter (D) of the first main surface is less than or equal to 0.59×10−4.

347 more elements

Abstract

Claims5