Method of growing hexagonal single crystals and use of same as substrates for semiconductor elements

A low-stress or stress-poor hexagonal single crystal obtainable by a method comprising the steps of:

• a) dipping a single crystal in a melt of crystal raw material so that a solid-liquid phase boundary is formed while keeping the single crystal at a temperature below a melting point of the crystal raw material, said single crystal consisting of the crystal raw material in single crystal form with a hexagonal crystal structure with a crystallographic c-axis perpendicular to a [0001] surface;
• b) withdrawing said single crystal from the melt by drawing upward with an upwardly directed drawing motion along the crystallographic c-axis so that a temperature gradient of at least 30 K/cm is present in the single crystal within 1 cm of the solid-liquid phase boundary in order to grow the single crystal;
• and then
• c) subjecting the single crystal produced in step b) to a tempering treatment.

A semiconductor element comprising a hexagonal single crystal, said hexagonal single crystal being obtainable by a method comprising the steps of:

• a) dipping a single crystal in a melt of crystal raw material so that a solid-liquid phase boundary is formed while keeping the single crystal at a temperature below a melting point of the crystal raw material, said single crystal consisting of the crystal raw material in single crystal form with a hexagonal crystal structure with a crystallographic c-axis perpendicular to a [0001] surface;
• b) withdrawing said single crystal from the melt by drawing upward with an upwardly directed drawing motion along the crystallographic c-axis so that a temperature gradient of at least 30 K/cm is present in the single crystal within 1 cm of the solid-liquid phase boundary in order to grow the single crystal;
• and
• then
• c) subjecting the single crystal produced in step b) to a tempering treatment.

A method of growing a low-stress or stress-poor single crystal with a hexagonal crystal structure, which has a crystallographic c-axis perpendicular to a [0001] surface, said method comprising the steps of:

• a) providing a melt of a crystal raw material consisting of aluminum oxide;
• b) dipping a single crystal into said melt, said single crystal consisting of corundum with a hexagonal crystal structure with a crystallographic c-axis perpendicular to a [0001] surface, so that a solid-liquid phase boundary is formed while keeping the single crystal at a temperature below a melting point of the crystal raw material;
• c) withdrawing said single crystal with said hexagonal crystal structure from the melt by drawing upward with an upwardly directed drawing motion along the crystallographic c-axis at a drawing speed of 30 to 150 mm/day so that a temperature gradient of at least 30 K/cm is present in the single crystal within 1 cm of the solid-liquid phase boundary in order to grow the single crystal with the hexagonal crystal structure with said crystallographic c-axis;
• and then
• d) tempering said single crystal produced in step c) by heat-treating at a treatment temperature of at least 1850 K for at least one hour;
• and
• e) cooling down said single crystal with a cooling rate of at maximum 50 K/hr from said treatment temperature while adjusting at least one of an axial temperature gradient and radial temperature gradient to at maximum 4 K/cm during the cooling down;
• so that said low-stress or stress-poor single crystal grown in a direction of said crystallographic c-axis has lower stress values than corundum single crystals grown in an in-direction or in an r-direction from said melt.

A low-stress or stress-poor single crystal of corundum grown by a method comprising the steps of:

• a) providing a melt of a crystal raw material consisting of aluminum oxide;
• b) dipping a single crystal into said melt, said single crystal consisting of corundum with a hexagonal crystal structure with a crystallographic c-axis perpendicular to a [0001] surface, so that a solid-liquid phase boundary is formed while keeping the single crystal at a temperature below a melting point of the crystal raw material;
• c) withdrawing said single crystal from the melt by drawing upward with an upwardly directed drawing motion along the crystallographic c-axis at a drawing speed of 30 to 150 mm/day so that a temperature gradient of at least 30 K/cm is present in the single crystal within 1 cm of the solid-liquid phase boundary in order to grow the single crystal with the hexagonal crystal structure with said crystallographic c-axis;
• and then
• d) tempering said single crystal produced in step c) by heat-treating at a treatment temperature of at least 1850 K for at least one hour;
• and
• e) cooling down said single crystal with a cooling rate of at maximum 50 K/hr from said treatment temperature while adjusting at least one of an axial temperature gradient and radial temperature gradient to at maximum 4 K/cm during the cooling down;
• so that said low-stress or stress-poor hexagonal single crystal of said corundum grown by said method in a direction of said crystallographic c-axis has lower stress values than corresponding corundum single crystals grown in an in-direction or in an r-direction from said melt.