A crystal is of a non-centrosymmetric structure and belongs to the −43 m point group of the cubic crystal system. M denotes an alkaline earth metal, which can be Ba, Ca, or Sr, and RE denotes a rare earth element, which can be Y, La, Gd, or Yb. The growth method of the M.sub.3RE(PO.sub.4).sub.3 crystal comprises steps as follows: (1) polycrystalline material synthesis: MCO.sub.3, RE.sub.2O.sub.3, and phosphorous compound are used as raw materials and blended according to the stoichiometric proportions; then, the phosphorous compound is further added to be excessive; the raw materials are sintered twice to obtain the M.sub.3RE(PO.sub.4).sub.3 polycrystalline material; (2) polycrystalline material melting; (3) Czochralski crystal growth. The M.sub.3RE(PO.sub.4).sub.3 crystal prepared by the invention is a high-quality single crystal.

A crystal is of a non-centrosymmetric structure and belongs to the −43 m point group of the cubic crystal system. M denotes an alkaline earth metal, which can be Ba, Ca, or Sr, and RE denotes a rare earth element, which can be Y, La, Gd, or Yb. The growth method of the M.sub.3RE(PO.sub.4).sub.3 crystal comprises steps as follows: (1) polycrystalline material synthesis: MCO.sub.3, RE.sub.2O.sub.3, and phosphorous compound are used as raw materials and blended according to the stoichiometric proportions; then, the phosphorous compound is further added to be excessive; the raw materials are sintered twice to obtain the M.sub.3RE(PO.sub.4).sub.3 polycrystalline material; (2) polycrystalline material melting; (3) Czochralski crystal growth. The M.sub.3RE(PO.sub.4).sub.3 crystal prepared by the invention is a high-quality single crystal.

A silicon-based molten composition according to an exemplary embodiment of the present invention is used in a solution growing method for forming silicon carbide single crystal, and is expressed in Formula 1 including silicon (Si), chromium (Cr), vanadium (V), and aluminum (Al).
Si.sub.aCr.sub.bV.sub.cAl.sub.d  [Formula 1]
In Formula 1, a is equal to or greater than 0.4 and equal to or less than 0.9, b+c is equal to or greater than 0.1 and equal to or less than 0.6, c/(b+c) is equal to or greater than 0.05 and equal to or less than 0.95, and d is equal to or greater than 0.01 and equal to or less than 0.1.

A silicon-based molten composition according to an exemplary embodiment of the present invention is used in a solution growing method for forming silicon carbide single crystal, and is expressed in Formula 1 including silicon (Si), chromium (Cr), vanadium (V), and aluminum (Al).
Si.sub.aCr.sub.bV.sub.cAl.sub.d  [Formula 1]
In Formula 1, a is equal to or greater than 0.4 and equal to or less than 0.9, b+c is equal to or greater than 0.1 and equal to or less than 0.6, c/(b+c) is equal to or greater than 0.05 and equal to or less than 0.95, and d is equal to or greater than 0.01 and equal to or less than 0.1.

An embodiment provides a silicon single crystal growth method comprising the steps of: (a) allowing the shoulder of a single crystal to grow vertically; (b) allowing the shoulder to grow horizontally after the vertical growth; and (c) allowing the shoulder to grow in a downward convex shape after the horizontal growth of the shoulder, wherein the shoulder grows at a preset rate on the basis of the final diameter of the shoulder and the shoulder growth height according to steps (b) and (c).

An embodiment provides a silicon single crystal growth method comprising the steps of: (a) allowing the shoulder of a single crystal to grow vertically; (b) allowing the shoulder to grow horizontally after the vertical growth; and (c) allowing the shoulder to grow in a downward convex shape after the horizontal growth of the shoulder, wherein the shoulder grows at a preset rate on the basis of the final diameter of the shoulder and the shoulder growth height according to steps (b) and (c).

A polycrystalline silicon material for producing silicon single crystal, containing a plurality of polycrystalline silicon chunks, in which assuming that a total concentration of donor elements present inside a bulk body of the polycrystalline silicon material is Cd1 [ppta], a total concentration of acceptor elements present inside the bulk body of the polycrystalline silicon material is Ca1 [ppta], a total concentration of the donor elements present on a surface of the polycrystalline silicon material is Cd2 [ppta], and a total concentration of the acceptor elements present on the surface of the polycrystalline silicon material is Ca2 [ppta], Cd1, Ca1, Cd2, and Ca2 satisfy a relation of 2 [ppta]≤(Cd1+Cd2)−(Ca1+Ca2)≤8 [ppta].

A polycrystalline silicon material for producing silicon single crystal, containing a plurality of polycrystalline silicon chunks, in which assuming that a total concentration of donor elements present inside a bulk body of the polycrystalline silicon material is Cd1 [ppta], a total concentration of acceptor elements present inside the bulk body of the polycrystalline silicon material is Ca1 [ppta], a total concentration of the donor elements present on a surface of the polycrystalline silicon material is Cd2 [ppta], and a total concentration of the acceptor elements present on the surface of the polycrystalline silicon material is Ca2 [ppta], Cd1, Ca1, Cd2, and Ca2 satisfy a relation of 2 [ppta]≤(Cd1+Cd2)−(Ca1+Ca2)≤8 [ppta].

An embodiment provides a silicon single crystal growth method comprising the steps of: (a) allowing the shoulder of a single crystal to grow vertically; (b) allowing the shoulder to grow horizontally after the vertical growth; and (c) allowing the shoulder to grow in a downward convex shape after the horizontal growth of the shoulder, wherein the shoulder grows at a preset rate on the basis of the final diameter of the shoulder and the shoulder growth height according to steps (b) and (c).

An embodiment provides a silicon single crystal growth method comprising the steps of: (a) allowing the shoulder of a single crystal to grow vertically; (b) allowing the shoulder to grow horizontally after the vertical growth; and (c) allowing the shoulder to grow in a downward convex shape after the horizontal growth of the shoulder, wherein the shoulder grows at a preset rate on the basis of the final diameter of the shoulder and the shoulder growth height according to steps (b) and (c).