Methods for preparing single crystal silicon substrates for epitaxial growth are disclosed. The methods may involve control of the (i) a growth velocity, v, and/or (ii) an axial temperature gradient, G, during the growth of an ingot segment such that v/G is less than a critical v/G and/or is less than a value of v/G that depends on the boron concentration of the ingot. Methods for preparing epitaxial wafers are also disclosed.

A silicon wafer is provided which is a Czochralski wafer formed of silicon, and a method for producing the silicon wafer are provided. The wafer includes a bulk layer having an oxygen concentration of 0.5×10.sup.18/cm.sup.3 or more; and a surface layer extending from the surface of the wafer to 300 nm in depth, and having an oxygen concentration of 2×10.sup.18/cm.sup.3 or more.

A silicon wafer having a layer of oxygen precipitates and method of manufacturing thereof wherein the wafer exhibiting robustness characterized as having a ratio of a first average density from a first treatment that to a second average density from a second treatment is between 0.74 to 1.02, wherein the first treatment includes heating the wafer or a portion of the wafer at about 1150° C. for about 2 minutes and then between about 950 to 1000° C. for about 16 hours, and the second treatment includes heating the wafer or a portion of the wafer at about 780° C. for about 3 hours and then between about 950 to 1000° C. for about 16 hours. The wafer exhibits heretofore unattainable uniformity wherein a ratio of an oxygen precipitate density determined from any one cubic centimeter in the BMD layer of the wafer to another oxygen precipitate density from any other one cubic centimeter in the BMD layer of the wafer is in a range of 0.77 to 1.30.

A method of controlling a convection pattern of a silicon melt includes: acquiring a temperature at a first measurement point not overlapping a rotation center of a quartz crucible on a surface of the silicon melt, the quartz crucible rotating in a magnetic-field-free state; determining that the temperature at the first measurement point periodically changes; and fixing a direction of a convection flow to a single direction in a plane orthogonal with an application direction of a horizontal magnetic field in the silicon melt by starting a drive of a magnetic-field applying portion to apply the horizontal magnetic field to the silicon melt when a temperature change at the first measurement point reaches a predetermined state, and subsequently raising the intensity to 0.2 tesla or more.

A method for growing a single crystal silicon ingot by the continuous Czochralski method is disclosed. The melt depth and thermal conditions are constant during growth because the silicon melt is continuously replenished as it is consumed, and the crucible location is fixed. The critical v/G is determined by the hot zone configuration, and the continuous replenishment of silicon to the melt during growth enables growth of the ingot at a constant pull rate consistent with the critical v/G during growth of a substantial portion of the main body of the ingot. The continuous replenishment of silicon is accompanied by periodic or continuous nitrogen addition to the melt to result in a nitrogen doped ingot.

A method for growing a single crystal silicon ingot by the continuous Czochralski method is disclosed. The melt depth and thermal conditions are constant during growth because the silicon melt is continuously replenished as it is consumed, and the crucible location is fixed. The critical v/G is determined by the hot zone configuration, and the continuous replenishment of silicon to the melt during growth enables growth of the ingot at a constant pull rate consistent with the critical v/G during growth of a substantial portion of the main body of the ingot. The continuous replenishment of silicon is accompanied by periodic or continuous nitrogen addition to the melt to result in a nitrogen doped ingot.

Nitrogen-doped CZ silicon crystal ingots and wafers sliced therefrom are disclosed that provide for post epitaxial thermally treated wafers having oxygen precipitate density and size that are substantially uniformly distributed radially and exhibit the lack of a significant edge effect. Methods for producing such CZ silicon crystal ingots are also provided by controlling the pull rate from molten silicon, the temperature gradient and the nitrogen concentration. Methods for simulating the radial bulk micro defect size distribution, radial bulk micro defect density distribution and oxygen precipitation density distribution of post epitaxial thermally treated wafers sliced from nitrogen-doped CZ silicon crystals are also provided.

Nitrogen-doped CZ silicon crystal ingots and wafers sliced therefrom are disclosed that provide for post epitaxial thermally treated wafers having oxygen precipitate density and size that are substantially uniformly distributed radially and exhibit the lack of a significant edge effect. Methods for producing such CZ silicon crystal ingots are also provided by controlling the pull rate from molten silicon, the temperature gradient and the nitrogen concentration. Methods for simulating the radial bulk micro defect size distribution, radial bulk micro defect density distribution and oxygen precipitation density distribution of post epitaxial thermally treated wafers sliced from nitrogen-doped CZ silicon crystals are also provided.

A crystal puller apparatus comprises a pulling assembly to pull a crystal from a silicon melt at a pull speed; a crucible that contains the silicon melt; a heat shield above a surface of the silicon melt; a lifter to change a gap between the heat shield and the surface of the silicon melt; and one or more computing devices to determine an adjustment to the gap using a Pv-Pi margin, at a given length of the crystal, in response to a change in the pull speed. The computer-implemented method by a computing device comprises determining a pull-speed command signal to control a diameter of the crystal; determining a lifter command signal to control a gap between a heat shield and a surface of a silicon melt from which the crystal is grown; and determining an adjustment to the gap, in response to a different pull-speed, using a Pv-Pi margin.

A RAMO.sub.4 substrate that does not easily crack during or after the formation of group III nitride crystal includes a single crystal represented by general formula RAMO.sub.4 (wherein R represents one or more trivalent elements selected from the group consisting of Sc, In, Y, and lanthanoid elements, A represents one or more trivalent elements selected from the group consisting of Fe(III), Ga, and Al, and M represents one or more divalent elements selected from the group consisting of Mg, Mn, Fe(II), Co, Cu, Zn, and Cd). The RAMO.sub.4 substrate has a crystal plane with a curvature radius r of 52 m or more, and a square value of correlation coefficient ρ of 0.81 or more. The curvature radius r is calculated as an absolute value from X-ray peak position ωi and measurement position Xi after the measurements of X-ray peak positions ωi at a plurality of positions Xi lying on a straight line passing through the center of the RAMO.sub.4 substrate. The correlation coefficient ρ is a measure of correlation between ω and measurement position Xi.