A single-crystal diamond, wherein the single-crystal diamond has a nitrogen content based on the number of atoms of more than 0.1 ppm and 50 ppm or less, the single-crystal diamond has a boron content based on the number of atoms of 0.1 ppm or less, the single-crystal diamond has an average of a phase difference per unit thickness of 20 nm/mm or less, and the phase difference has a standard deviation of 10 nm/mm or less.

A single crystal diamond having a half width of an x-ray diffraction rocking curve of 20 seconds or less, a half width of a peak at a Raman shift of 1332 cm.sup.?1 to 1333 cm.sup.?1 (inclusive) in a Raman spectroscopic spectrum of 2.0 cm.sup.?1 or less, an etch pit density of 10,000/cm.sup.2 or less, a content of nitrogen based on number of atoms of 0.0001-0.1 ppm (inclusive), and a content of .sup.13C based on number of atoms of 0.01-1.0% (inclusive).

An alumina substrate wherein an AlN layer is formed on a surface of the alumina substrate and a rare earth elements-containing layer and/or rare earth elements-containing regions is/are formed in the interior of the AlN layer or in the interface between the AlN layer and the alumina substrate.

An alumina substrate wherein an AlN layer is formed on a surface of the alumina substrate and a rare earth elements-containing layer and/or rare earth elements-containing regions is/are formed in the interior of the AlN layer or in the interface between the AlN layer and the alumina substrate.

Disclosed is a nonlinear optical (NLO) material for use in deep-UV applications, and methods of fabrication thereof. The NLO is fabricated from a plurality of components according to the formula A.sub.qB.sub.yC.sub.z and a crystallographic non-centrosymmetric (NCS) structure. The NLO material may be fabricated as a polycrystalline or a single crystal material. In an embodiment, the material may be according to a formula Ba.sub.3ZnB.sub.5PO.sub.14.

A large Group III nitride crystal of high quality with few defects such as a distortion, a dislocation, and warping is produced by vapor phase epitaxy. A method for producing a Group III nitride crystal includes: a first Group III nitride crystal production process of producing a first Group III nitride crystal 1003 by liquid phase epitaxy; and a second Group III nitride crystal production process of producing a second Group III nitride crystal 1004 on the first crystal 1003 by vapor phase epitaxy. In the first Group III nitride crystal production process, the surfaces of seed crystals 1003a (preliminarily provided Group III nitride) are brought into contact with an alkali metal melt, a Group III element and nitrogen are cause to react with each other in a nitrogen-containing atmosphere in the alkali metal melt, and the Group III nitride crystals are bound together by growth of the Group III nitride crystals grown from the seed crystals 1003a to produce a first crystal 1003.

A large Group III nitride crystal of high quality with few defects such as a distortion, a dislocation, and warping is produced by vapor phase epitaxy. A method for producing a Group III nitride crystal includes: a first Group III nitride crystal production process of producing a first Group III nitride crystal 1003 by liquid phase epitaxy; and a second Group III nitride crystal production process of producing a second Group III nitride crystal 1004 on the first crystal 1003 by vapor phase epitaxy. In the first Group III nitride crystal production process, the surfaces of seed crystals 1003a (preliminarily provided Group III nitride) are brought into contact with an alkali metal melt, a Group III element and nitrogen are cause to react with each other in a nitrogen-containing atmosphere in the alkali metal melt, and the Group III nitride crystals are bound together by growth of the Group III nitride crystals grown from the seed crystals 1003a to produce a first crystal 1003.

There is provided a method for manufacturing a nitride crystal substrate, including: arranging a plurality of seed crystal substrates made of a nitride crystal in a planar appearance, so that their main surfaces are parallel to each other and their lateral surfaces are in contact with each other; growing a first crystal film using a vapor-phase growth method on a surface of the plurality of seed crystal substrates arranged in the planar appearance, and preparing a combined substrate formed by combining the adjacent seed crystal substrates each other by the first crystal film; growing a second crystal film using a liquid-phase growth method on a main surface of the combined substrate so as to be embedded in a groove that exists at a combined part of the seed crystal substrates, and preparing a substrate for crystal growth having a smoothened main surface; and growing a third crystal film using the vapor-phase growth method, on the smoothed main surface of the substrate for crystal growth.

There is provided a method for manufacturing a nitride crystal substrate, including: arranging a plurality of seed crystal substrates made of a nitride crystal in a planar appearance, so that their main surfaces are parallel to each other and their lateral surfaces are in contact with each other; growing a first crystal film using a vapor-phase growth method on a surface of the plurality of seed crystal substrates arranged in the planar appearance, and preparing a combined substrate formed by combining the adjacent seed crystal substrates each other by the first crystal film; growing a second crystal film using a liquid-phase growth method on a main surface of the combined substrate so as to be embedded in a groove that exists at a combined part of the seed crystal substrates, and preparing a substrate for crystal growth having a smoothened main surface; and growing a third crystal film using the vapor-phase growth method, on the smoothed main surface of the substrate for crystal growth.

A self-supporting substrate includes a first nitride layer grown by a hydride vapor deposition method or ammonothermal method and comprising a nitride of one or more elements selected from the group consisting of gallium, aluminum and indium; and a second nitride layer grown by a sodium flux method on the first nitride layer and comprising a nitride of one or more elements selected from the group consisting of gallium, aluminum and indium. The first nitride layer includes a plurality of single crystal grains arranged therein and extending between a pair of main faces of the first nitride layer. The second nitride layer includes a plurality of single crystal grains arranged therein and extending between a pair of main faces of the second nitride layer. The first nitride layer has a thickness larger than a thickness of the second nitride layer.