Method of determining surface orientation of single crystal wafer

A method of measuring a surface orientation of a single crystal wafer in order to determine the surface orientation formed by a crystal plane normal of a single crystal and a surface normal of the wafer, comprising:

• measuring a high-resolution X-ray rocking curve of a selected diffraction plane under a Bragg diffraction condition by rotating the wafer by a predetermined azimuth angle (φ) with respect to a rotation axis of an apparatus for measuring the surface orientation,
• determining a position (ωφ) of a maximum peak of the high-resolution X-ray rocking curve by the following Equation:
• ωφ≅−δ1·cos(φ−φφ)−δ0·cos(φ−φφ)+κP(R)+θB+δ0·cos(−φφ)−κS(R)(φ=0),
• where δ1 indicates an angle (surface angle) of the crystal plane normal with respect to the surface normal, φφ indicates a direction in which the surface angle appears, δ0 indicates a misalignment angle formed by the rotation axis of the apparatus for measuring the surface orientation and the surface normal, φφ indicates a direction of a misalignment axis, κP(R) indicates a small angle component which appears as the crystal plane normal is projected on the diffraction plane at the azimuth angle (φ) in the case in which the surface normal is not parallel to the rotation axis of the apparatus for measuring the surface orientation, θB indicates a Bragg angle, and κS(R) indicates a small angle component which appears as the surface normal is projected on the diffraction plane at the azimuth angle (φ) in the case in which the surface normal is not parallel to the rotation axis of the apparatus for measuring the surface orientation,
• wherein the surface angle (δ1) of the wafer and the direction (φφ) in which the surface angle appears is determined by the following Equation:
• ω
• ϕ
• -
• ω
• ϕ
• ′
• ≅
• 2
• ⁢
• δ
• 1
• ·
• sin
• ⁢
• Δϕ
• p
• 2
• ·
• sin
• ⁡
• (
• ϕ
• -
• ϕ
• p
• -
• Δϕ
• p
• 2
• )
• ,
• where Δφφ indicates a phase change value applied at a time of designing a wafer holder, and ωφ−ω′φ indicates an angle difference between peaks of the high-resolution X-ray rocking curve each measured depending on Δφφ, and
• determining a variation (δP(S)) of the surface orientation of the wafer depending on a function of the azimuth angle (φ) by the following Equation:
• δP(S)≅δ1·cos(φ−φφ),
• wherein the high-resolution X-ray rocking curve is measured two times at φ=φ1 and φ=φ2, and Δφφ is determined by the following Equation:
• Δφφ=φ2−φ1,
• wherein an angle component (δ1·cos φφ) of the surface orientation of the wafer along a direction of 0 to 180° is determined by the following Equation:
• δ1·cos φφ=½(ω′0−ω0),
• wherein an angle component (δ1·sin φφ) of the surface orientation of the wafer along a direction of 90 to 270° is determined by the following Equation:
• δ1·sin φφ=½(ω′φ0−ωφ0), and
• wherein the surface orientation of the single crystal wafer is measured only by measuring the high-resolution X-ray rocking curve two times at an interval of 90° at each of two sample azimuth angles of Δφφ=180°.