A thermal conductivity estimation method includes: measuring temperature distribution of a measurement sample surface in a steady state by partially heating the measurement sample under predetermined heating conditions; calculating temperature distribution of a sample model surface by performing a heat-transfer simulation on the sample model of the same shape as the measurement sample for a plurality of combinations of provisional thermal conductivities and heating conditions; making a regression model, whose input is temperature distribution of the measurement sample surface and whose output is a thermal conductivity of the measurement sample, by a machine learning technique using training data in a form of a calculation result of the plurality of combinations and the temperature distribution obtained from the plurality of combinations; and estimating the thermal conductivity of the measurement sample by inputting a measurement result of the temperature distribution of the measurement sample surface into the regression model.

A low-resistance p-type SiC single crystal containing no inclusions is provided. This is achieved by a method for producing a SiC single crystal wherein a SiC seed crystal substrate 14 is contacted with a Si—C solution 24 having a temperature gradient in which the temperature falls from the interior toward the surface, to grow a SiC single crystal, and wherein the method comprises: using, as the Si—C solution, a Si—C solution containing Si, Cr and Al, wherein the Al content is 3 at % or greater based on the total of Si, Cr and Al, and making the temperature gradient y (° C./cm) in the surface region of the Si—C solution 24 satisfy the following formula (1): y≧0.15789x+21.52632 (1) wherein x represents the Al content (at %) of the Si—C solution.

A low-resistance p-type SiC single crystal containing no inclusions is provided. This is achieved by a method for producing a SiC single crystal wherein a SiC seed crystal substrate 14 is contacted with a Si—C solution 24 having a temperature gradient in which the temperature falls from the interior toward the surface, to grow a SiC single crystal, and wherein the method comprises: using, as the Si—C solution, a Si—C solution containing Si, Cr and Al, wherein the Al content is 3 at % or greater based on the total of Si, Cr and Al, and making the temperature gradient y (° C./cm) in the surface region of the Si—C solution 24 satisfy the following formula (1): y≧0.15789x+21.52632 (1) wherein x represents the Al content (at %) of the Si—C solution.

A method and apparatus for manufacturing an SiC single crystal includes a graphite crucible for receiving an SiC solution with first and second induction heating coils wound around it. The first induction heating coil is located higher than the surface of the SiC solution. The second induction heating coil is located lower than the first induction heating coil. A power supply supplies a first alternating current to the first induction heating coil and supplies, to the second induction heating coil, a second alternating current having the same frequency as the first alternating current and flowing in the direction opposite to that of the first alternating current. The distance between the surface of the SiC solution and the position in the portion of the side wall of the crucible in contact with the SiC solution with the strength of a magnetic field at its maximum satisfies a predetermined equation.

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.

In a bismuth-substituted rare earth iron garnet single crystal film production method, the bismuth-substituted rare earth iron garnet single crystal film expressed by the composition formula (Ln.sub.3-aBi.sub.a)(Fe.sub.5-bA.sub.b)O.sub.12 is grown using a substrate of paramagnetic garnet with a lattice constant of Ls. The method includes forming a buffer layer with an average lattice constant of Lb (where Lb > Ls) on the surface of the substrate with a thickness of 5 to 30 .Math.m, and growing a target bismuth-substituted rare earth iron garnet crystal film with an average lattice constant of Lf (where Lf > Lb) with a thickness of 100 .Math.m or more overlaid on the buffer layer. The rate of lattice constant change in the buffer layer is steeper than the rate of lattice constant change in the bismuth-substituted rare earth iron garnet crystal film.

In a bismuth-substituted rare earth iron garnet single crystal film production method, the bismuth-substituted rare earth iron garnet single crystal film expressed by the composition formula (Ln.sub.3-aBi.sub.a)(Fe.sub.5-bA.sub.b)O.sub.12 is grown using a substrate of paramagnetic garnet with a lattice constant of Ls. The method includes forming a buffer layer with an average lattice constant of Lb (where Lb > Ls) on the surface of the substrate with a thickness of 5 to 30 .Math.m, and growing a target bismuth-substituted rare earth iron garnet crystal film with an average lattice constant of Lf (where Lf > Lb) with a thickness of 100 .Math.m or more overlaid on the buffer layer. The rate of lattice constant change in the buffer layer is steeper than the rate of lattice constant change in the bismuth-substituted rare earth iron garnet crystal film.

It is provided a method of growing a group 13 nitride crystal layer, on an underlying substrate including a seed crystal layer composed of a group 13 nitride. The underlying substrate is immersed in a melt containing a flux to grow a group 13 nitride crystal layer two-dimensionally on a nitrogen polar surface of the seed crystal layer by flux method.

It is provided a method of growing a group 13 nitride crystal layer, on an underlying substrate including a seed crystal layer composed of a group 13 nitride. The underlying substrate is immersed in a melt containing a flux to grow a group 13 nitride crystal layer two-dimensionally on a nitrogen polar surface of the seed crystal layer by flux method.

There is provided a semiconductor substrate including: a sapphire substrate; an intermediate layer formed of gallium nitride with random crystal directions and provided on the sapphire substrate; and at least one or more semiconductor layers each of which is formed of a gallium nitride single crystal and that are provided on the intermediate layer.