Group 13 element nitride layer, free-standing substrate and functional element

A layer of a crystal of a nitride of a group 13 element, said crystal of said nitride being selected from gallium nitride, aluminum nitride, indium nitride and the mixed crystals thereof and comprising an upper surface and a bottom surface:

• wherein said upper surface consists essentially of a linear high-luminance light-emitting part and low-luminance light-emitting regions provided on both sides of said high-luminance light-emitting part, respectively;
• said linear high-luminance light-emitting part forms a continuous phase;
• said low-luminance light-emitting regions each forming a discontinuous phase divided by said linear high-luminance light-emitting part;
• said high-luminance light-emitting part comprises a portion extending along an m-plane of said crystal of said nitride of said group 13 element, said upper surface being observed by cathode luminescence;
• and
• said upper surface has an arithmetic average roughness Ra of 0.05 nm or more and 1.0 nm or less.