RAMO4 substrate and method of manufacture thereof, and group III nitride semiconductor

A RAMO4 substrate comprising a single crystal represented by general formula RAMO4, wherein R represents one or more trivalent elements selected from the group consisting of Sc, In, Y, and lanthanoid elements, A represents one or more trivalent elements selected from the group consisting of Fe(III), Ga, and Al, and M represents one or more divalent elements selected from the group consisting of Mg, Mn, Fe(II), Co, Cu, Zn, and Cd,

• the RAMO4 substrate having a crystal plane with an absolute value of a curvature radius r of 52 m or more, and a square value of correlation coefficient p of 0.81 or more,
• wherein the curvature radius r is calculated from a regression line obtained from a relationship between X-ray peak position wi and position Xi after the X-ray peak position wi is specified in a diffraction spectrum of an X-ray rocking curve measured at each of a plurality of positions Xi (i=1, 2, 3, . . . , n) lying on a straight line passing through a center of a surface of the RAMO4 substrate,
• wherein the X-ray peak position wi is expressed as an angular position,
• wherein the relationship between the X-ray peak position wi and the position Xi is determined by plotting the X-ray peak position wi versus the position Xi in a graph,
• wherein each of the plurality of positions Xi lies on a different point on the straight line,
• wherein the square value of correlation coefficient p is calculated from the X-ray peak position ωi, the position Xi, and the number n of the positions Xi, using the following formula,
• ρ
• =
• 1
• n
• ⁢
• ∑
• i
• =
• 1
• n
• ⁢
• (
• Xi
• -
• X
• _
• )
• ⁢
• (
• ω
• ⁢
• ⁢
• i
• -
• ω
• _
• )
• 1
• n
• ⁢
• ∑
• i
• =
• 1
• n
• ⁢
• (
• Xi
• -
• X
• _
• )
• 2
• ⁢
• 1
• n
• ⁢
• ∑
• i
• =
• 1
• n
• ⁢
• (
• ω
• ⁢
• ⁢
• i
• -
• ω
• _
• )
• 2
• wherein ω represents a mean value of wi expressed as
• ω
• _
• =
• ∑
• i
• =
• 1
• n
• ⁢
• ω
• ⁢
• ⁢
• i
• n
• ,
• X represents a mean value of Xi expressed as
• X
• _
• =
• ∑
• i
• =
• 1
• n
• ⁢
• Xi
• n
• ,
• and n represents a natural number larger than or equal to 2,
• wherein, when the regression line is represented by ω=aX+b, a and b are represented by the following formulae,
• a
• =
• ∑
• i
• =
• 1
• n
• ⁢
• {
• (
• Xi
• -
• X
• _
• )
• ⁢
• (
• ω
• ⁢
• ⁢
• i
• -
• ω
• _
• )
• }
• ∑
• i
• =
• 1
• n
• ⁢
• (
• Xi
• -
• X
• _
• )
• 2
• b
• =
• ω
• _
• -
• a
• ⁢
• ⁢
• X
• _
• where ω represents the mean value of ωi, X represents the mean value of Xi, and n represents the number of the positions Xi, and
• wherein the curvature radius r is represented by the following formula,
• r
• =
• a
• ⁢
• 180
• π
• .