Aluminum nitride single crystal forming polygonal columns and a process for producing a plate-shaped

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An aluminum nitride single crystal in the form of polygonal columns, the polygonal columns having the following properties [a] to [c] : [a] the content of a metal impurity is below a detection limit, [b] the average bottom area is from 5×103 to 2×105 μm2, and [c] the average height is 50 μm to 5 mm. The above aluminum nitride single crystal is preferably obtainable in a method including the steps of sublimating an aluminum nitride starting material (A) containing 0.1 to 30% by mass of a rare earth oxide by heating the starting material at a temperature of not lower than 2000° C., depositing aluminum nitride on a hexagonal single crystal substrate and thereby growing aluminum nitride single crystal in the shape of polygonal columns.