Abstract:
A crucible has a first resistance heater is disposed in spaced relation above the top of the crucible and a second resistance heater with a first resistive section disposed in spaced relation beneath the bottom of the crucible and with a second resistive section disposed in spaced relation around the outside of the side of the crucible. The crucible is charged with a seed crystal at the top of an interior of the crucible and a source material in the interior of the crucible in spaced relation between the seed crystal and the bottom of the crucible. Electrical power of a sufficient extent is applied to the first and second resistance heaters to create in the interior of the crucible a temperature gradient of sufficient temperature to cause the source material to sublimate and condense on the seed crystal thereby forming a growing crystal.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims priority from U.S. Provisional Patent Application No. 61/120,556, filed Dec. 8, 2008, entitled “Axial Gradient Transport Growth Process and Apparatus Utilizing Resistive Heating”, which is incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to growing industrial-size SiC single crystals by sublimation and, more specifically, to such growth by the technique of Axial Gradient Transport (AGT). 
     2. Description of Related Art 
     Wafers of silicon carbide of hexagonal 4H and 6H polytypes serve as lattice-matched substrates to grow epitaxial layers of SiC and GaN, which are used for the fabrication of SiC- and GaN-based semiconductor devices utilized in power and microwave electronic applications. 
     Large SiC single crystals are grown conventionally by sublimation using the technique of Physical Vapor Transport (PVT). A schematic diagram of a common PVT arrangement is shown in  FIG. 1 . PVT growth is carried out in vertical crucible  11 , which is generally made of graphite. Sublimation source material  13  is disposed at the bottom of the crucible, while a growing crystal (or boule)  15  grows on a seed crystal  14  disposed at the crucible top, for instance, attached to the interior of the crucible lid  12 . Most commonly, inductive heating with a single RF coil is utilized for PVT growth. This heating arrangement is shown in  FIG. 1  which includes a cylindrical RF coil  19  positioned coaxially with growth crucible  11 . 
     PVT growth is carried out at temperatures generally between 2000° C. and 2400° C. In order to control the vapor transport rate, PVT growth is carried out under a small pressure of inert gas (e.g., helium and/or argon), generally between 1 Torr and 100 Torr. 
     At these temperatures and pressures, source material  13  vaporizes and fills the interior of crucible  11  with volatile molecular species, such as Si, Si 2 C and SiC 2 . During the growth of growing crystal  15  on seed crystal  14 , the temperature of source material  13  is maintained higher than that of the seed crystal  14 , typically by 10 to 200° C. This temperature difference forces the vapors to migrate and condense on seed crystal  14  causing the growth of growing crystal  15 . 
     The quality of PVT-grown SiC crystals depends on growth conditions, such as the sign and value of radial temperature gradients in the upper part of crucible  11  where the growth of growing crystal  15  occurs. Strong temperature gradients in growing crystal  15 , especially radial ones, cause thermo-elastic stress and the generation of defects and cracking in growing crystal  15 . 
     It is known in the art of SiC sublimation growth that the crystal growth interface closely follows the shape of isotherms in the crystal and its vicinity. Positive radial gradients (where the temperature inside of the growth crucible increases in the radial direction from the crucible axis toward the crucible wall) produce a convex (toward source material  13 ) growth interface. Negative radial gradients (where the temperature decreases in the radial direction from the crucible axis toward the crucible wall) produce a concave (toward source material  13 ) growth interface. Zero radial gradient (where the temperature does not change in the radial direction from the crucible axis toward the crucible wall) produces a flat growth interface. 
     Curved growth interfaces, convex or concave, can lead to the appearance of crude macrosteps on the growth interface causing polytype instability and generation of defects. Accordingly, it is generally believed that a flat growth interface is the most conducive to the growth of high quality crystals, such as growing crystal  15 . 
     Generally, the conventional PVT heating geometry shown in  FIG. 1  creates an axisymmetric thermal field in crucible  11  with strong radial temperature gradients which are difficult to control. 
     Another problem of single-RF coil PVT heating shown in  FIG. 1  is that it is difficult to scale up for the growth of larger-diameter crystals. With increase in the crucible diameter and the coil diameter, radial gradients become steeper, while electromagnetic coupling between the coil and crucible becomes less efficient. 
     A PVT sublimation growth technique called Axial Gradient Transport (AGT) is disclosed in U.S. Pat. No. 6,800,136 (hereinafter “the &#39;136 patent”) and has as its goal to reduce undesirable radial temperature gradients. A conceptual diagram of the AGT growth geometry from the &#39;136 patent is shown in  FIG. 2 . 
     The AGT technique utilizes two independent flat heaters, namely, a source heater and a boule heater. The heaters can be either inductive or resistive. The heaters are positioned coaxially with the crucible, with the source heater disposed below the source material and the boule heater disposed above the growing crystal. 
     The AGT technique includes means for reducing heat flow in the radial direction, desirably to zero. This means includes cylindrical thermal insulation and an additional heater disposed around the AGT growth cell. A properly adjusted combination of the cylindrical thermal insulation and the heater can reduce radial heat losses to zero. The AGT geometry shown in  FIG. 2  allegedly leads to strictly axial heat flow with essentially zero radial gradients. 
     The AGT apparatus utilizing inductive heating is described in detail in the &#39;136 patent, which is incorporated herein by reference. This inductively heated AGT arrangement is shown in  FIG. 3 . It employs two flat RF coils, namely, top coil  30   a  and bottom coil  30   b . The cylindrical crucible  31  including source material  32  and a seed crystal  33 , upon which a growing crystal  35  grows, is disposed between these coils, whereby the top and bottom of the crucible serve as flat RF susceptors. Arrows  34  signify vapor transport in the growth crucible in the direction from source to crystal. 
     A disadvantage of the AGT cell design shown in  FIG. 3  is related to the character of RF coupling between the flat coils  30   a  and  30   b  and the flat top and bottom of the crucible  31 . There are two main types of flat RF coils, commonly known as “snail” and “snake” coils. When coupled to a disk-like susceptor, a “snail” coil will deposit its RF energy mostly at the susceptor edges due to skin-effect, as shown in  FIG. 3 . This type of coupling leads to poorly controllable radial temperature gradients in the crucible. “Snake” coils offer better uniformity of energy deposition, but their overall coupling efficiency is low. 
     An AGT apparatus utilizing flat resistive heaters is also disclosed in the &#39;136 patent. At source material sublimation temperatures, radiation is the main mechanism of heat transfer from the heater to the crucible. Therefore, flat resistive heaters should be free from the disadvantages of flat RF coils. 
     A simple resistively heated AGT arrangement is shown in  FIG. 4A . The cylindrical crucible  41  is placed between two flat resistive heaters  40   a  and  40   b , which are shaped as disks with their diameters larger than that of the crucible. The upper heater  40   a  is disposed above a seed crystal  43 , upon which a growing crystal  45  grows, while the lower heater  40   b  is disposed below source material  42 . Arrows  44  denote the direction of vapor transport in the crucible. 
     The arrangement of  FIG. 4A  has the disadvantage that it creates negative radial gradients (concave isotherms) in the vicinity of the growing crystal. This is illustrated in FIG.  4 B which shows the results of finite element simulation of the AGT cell shown in  FIG. 4A . The strongly concave isotherms  46  are clearly visible. The root cause of these concave isotherms  46  is radial heat losses. 
     To some degree, concave isotherms  46  can be reduced by increasing the thickness of cylindrical thermal insulation around the AGT growth cell and/or by using additional cylindrical heater(s), as described above in connection with  FIG. 2 . However, this will make such AGT growth systems prohibitively large, complex, and expensive. 
     For SiC sublimation growth, graphite is a natural choice of heater material. In order to achieve the required temperature inside the growth crucible (up to 2400° C.), the heater temperature should be by 100-200° higher. Stability and reliability of graphite heaters at such high temperatures are poorly studied. 
     One particular problem of all resistive heaters operating at high temperatures in an inert gas atmosphere is the phenomenon of thermionic emission. At high temperatures, electron clouds form around the heater. Driven by the electric field created by electric current passing through the heater, these electrons migrate in the gas-filled space and contribute to the total current between the heater terminals. With increase in the heater voltage, the electrons can acquire enough energy for gas ionization. The produced gas ions can cause secondary (cascade) gas ionization leading to glow discharge. 
     Glow discharge alters the heating geometry and leads to the erosion of the graphite crucible, the heater, and the thermal insulation. Also, with the onset of glow discharge, the electric current across the heater becomes unstable, thus creating growth instabilities leading to stress and defects in the growing crystal. 
     Gas ions accelerated by the electric field bombard the heater surface and can cause secondary electron emission. This chain of surface bombardment and ionization events at high temperatures is called thermionic emission (glow discharge is, in fact, the first stage of thermionic emission). With further increase in the heater temperature and voltage, and with a sufficient supply of gas ions, glow discharge evolves into arc. Such arc can cause severe damage to the heater, crucible and power supply. Therefore, in order to realize the advantages of resistive heating in AGT growth of SiC crystals, glow discharge in the growth system is desirably avoided. 
     SUMMARY OF THE INVENTION 
     The present invention is an axial gradient transport crystal growth apparatus. The apparatus includes a crucible having a top, a bottom and a side that extends between the top of the crucible and a bottom of the crucible. The crucible is adapted to support a seed crystal at the top of an interior of the crucible and source material in the interior of the crucible in spaced relation between the seed crystal and the bottom of the crucible. The space between the source material and the bottom of the crucible defines a cavity in the interior of the crucible. A first resistance heater is disposed in spaced relation above the top of the crucible. A second resistance heater has a first section disposed in spaced relation beneath the bottom of the crucible and a second section disposed in spaced relation around the outside of the side of the crucible. 
     The first and second resistance heaters can be operative for growing on the seed crystal disposed at the top of an interior of the crucible a growth crystal having a convex growth interface, wherein a ratio of a radius of curvature of the convex growth interface over a diameter of the grown crystal is between about 2 and about 4. 
     The top and bottom of the crucible can be round. The first resistance heater can be disk-shaped. The first section of the second resistance heater can be disk-shaped. 
     The first heater and the first section of the second resistance heater can have outer diameters that are between 110% and 130%, inclusive, of the outer diameter of the respective top and bottom of the crucible. 
     The first resistance heater and the first section of the second resistance heater can have central holes with a diameter between 25% and 75% of a diameter of the crucible. 
     The side of the crucible and the second section of the second resistance heater can be cylindrical-shaped. 
     The top of the second section of the second resistance heater can be disposed at a position between 50% and 75% of the height of the crucible. 
     The inner diameter of the second section of the second resistance heater can be spaced from the exterior of the crucible by a radial distance between 10 mm and 25 mm. 
     The cavity inside the crucible between the source material and the bottom of the crucible can have a height-to-diameter ratio between 0.2 and 1. 
     The invention is also an axial gradient growth method. The method includes: (a) providing a crucible having a top, a bottom and a side that extends between the top of the crucible and a bottom of the crucible, a first resistance heater disposed in spaced relation above the top of the crucible, and a second resistance heater having a first resistive section disposed in spaced relation beneath the bottom of the crucible and a second resistive section disposed in spaced relation around the outside or exterior of the side of the crucible; (b) providing a seed crystal at the top of an interior of the crucible and a source material in the interior of the crucible in spaced relation between the seed crystal and the bottom of the crucible; (c) applying electrical power to the first and second resistance heaters of a sufficient extent to create in the interior of the crucible a temperature gradient of sufficient temperature to cause the source material to sublimate and condense on the seed crystal thereby forming a growth crystal; and (d) maintaining the electrical power to the first and second resistance heaters until the growth crystal has grown to a desired size. 
     The first resistance heater can receive between 10% and 30% of the electrical power. The second resistance heater can receive between 70% and 90% of the electrical power. 
     The voltage applied to each heater is desirably less than 30 VAC RMS and more desirably less than 25 VAC RMS. 
     An interior and an exterior of the crucible and the heaters are in the presence of between 1 Torr and 40 Torr of an inert gas during the growing of the growth crystal. The inert gas can be helium. 
     Step (c) can include controlling the electrical power applied to the first and second resistance heaters in a manner to cause a growth crystal to grow on the seed crystal, wherein the grown growth crystal has a convex growth interface, wherein a ratio of a radius of curvature of the convex growth interface over a diameter of the grown growth crystal is between about 2 and about 4. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is schematic diagram of a prior art physical vapor transport sublimation growth cell; 
         FIG. 2  is a conceptual diagram of a prior art axial gradient transport (AGT) apparatus; 
         FIG. 3  is a schematic diagram of the prior art AGT growth cell of  FIG. 2 ; 
         FIG. 4A  is a schematic diagram of a resistively heated prior art AGT growth cell; 
         FIG. 4B  is a graph of isotherms that would be realized in the interior of the resistively heated prior art AGT growth cell of  FIG. 4A  during use; 
         FIG. 5  is a schematic diagram of a resistively heated AGT growth apparatus in accordance with the present invention; 
         FIG. 6A  a schematic diagram of the resistively heated AGT growth cell of  FIG. 5 ; 
         FIG. 6B  is a graph of isotherms that would be realized in the interior of the resistively heated AGT growth cell of  FIG. 6A  during use; 
         FIG. 7  is a graph of electrical conductance versus gas (helium) pressure for the graphite heaters of the resistively heated AGT growth apparatus of  FIG. 5 ; 
         FIG. 8  is plan view of the top heater of the resistively heated AGT growth apparatus of  FIG. 5 ; 
         FIG. 9A  is plan view of the bottom heater of the resistively heated AGT growth apparatus of  FIG. 5 ; 
         FIG. 9B  is a sectional view taken along line IXB-IXB of  FIG. 9A ; 
         FIGS. 10A ,  10 B and  10 C are photographs of 100 mm SiC boules of polytype 6H SI, 6H SI and 4H n + , respectively, grown in the AGT growth apparatus of  FIG. 5 ; 
         FIGS. 11A and 11B  are x-ray diffraction graphs of the boules of  FIGS. 10B and 10C , respectively, obtained from scans performed along the &lt;1-210&gt; and &lt;10-10&gt; axes; and 
         FIGS. 12A and 12B  are micropipe density maps of the boules of  FIGS. 10B and 10C , respectively. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention is an AGT growth apparatus and process, including the geometry of the heaters, as well as measures for the reduction or elimination of glow discharge in the growth chamber. The AGT growth process described herein has a growth interface which is slightly convex toward the crucible bottom. This slightly convex growth interface can yield large SiC single crystals of 6H and 4H polytypes suitable for the manufacturing of high quality SiC substrates of 3 inches and 100 mm in diameter. 
     Herein, when temperature gradients inside of the crucible increase in the radial direction from the crucible axis toward the crucible wall, such radial temperature gradients are known as positive radial temperature gradients. Isotherms of positive radial temperature gradients inside of the crucible are convex toward the crucible bottom (i.e., toward source material  13 ). In contrast, when temperature gradients inside of the crucible decrease in the radial direction from the crucible axis toward the crucible wall, such radial temperature gradients are known as negative radial temperature gradients. Isotherms of negative radial temperature gradients inside of the crucible are concave toward the crucible bottom. Lastly, when temperature gradients inside of the crucible do not change in the radial direction from the crucible axis toward the crucible wall, such radial temperature gradients are known as zero radial temperature gradients. Isotherms of zero radial temperature gradients inside of the crucible are flat and perpendicular to the crucible axis. 
     With reference to  FIG. 5 , a resistively heated AGT growth apparatus in accordance with the present invention includes a cylindrical growth crucible  51 , having therein an SiC source material  52  and an SiC seed crystal  53 . Growth crucible  51  is positioned between two resistive heaters, which are disposed coaxially with growth crucible  51 . These heaters include top heater  50   a  and bottom heater  50   b . Growth crucible  51  and heaters  50   a  and  50   b  are surrounded by thermal insulation  57  made of light-weight fibrous graphite. Electric power is provided to heaters  50   a  and  50   b  via graphite extension electrodes  59  which extend through widows  56  in thermal insulation  57 . Desirably, growth crucible  51 , heaters  50   a  and  50   b , and thermal insulation  57  are disposed in a larger container (not shown) that can maintain crucible  51 , heaters  50   a  and  50   b , and thermal insulation  57  at a suitable pressure (discussed hereinafter) during the growth of a growing crystal  64  on seed crystal  53 . 
     Top heater  50   a  is disk-shaped with a central hole  60 . The outer diameter of top heater  50   a  is larger than that of growth crucible  51 . Desirably, the outer diameter of top heater  50   a  is between 110% and 130% the diameter of growth crucible  51 . The inner diameter of top heater  50   a  (i.e., the diameter of central hole  60 ) is smaller than that of growth crucible  51 . Desirably, the inner diameter of top heater  50   a  is between 25% and 75% the diameter of growth crucible  51 . Top heater  50   a  is disposed above growth crucible  51  at a distance from growth crucible  51  desirably between 10% and 30% the diameter of crucible  51 . 
     Bottom heater  50   b  is cup-shaped. More specifically, bottom heater  50   b  comprises two heating sections: namely, a first, flat or disk-shaped section  61   a  and a second, cylindrically-shaped section  61   b . Bottom heater  50   b  is disposed below and around source material  52  in growth crucible  51 . Flat section  61   a  of bottom heater  50   b  has a central hole  62  with a diameter smaller than that of growth crucible  51 . Desirably, the diameter of central hole  62  of bottom heater  50   b  is between 25% and 75% of the diameter of growth crucible  51 . The flat section of bottom heater  50   b  is desirably disposed a distance from growth crucible  51  between 10% and 30% of the diameter of crucible  51 . The cylindrical section  61   b  of the bottom heater  50   b  surrounds the side of growth crucible  51 . Desirably, the height of cylindrical section  61   b  is between 50% and 75% of the height of growth crucible  51 . Desirably, the inner diameter of cylindrical section  61   b  is spaced from the outer diameter of growth crucible  51  by a radial distance between 10 mm and 25 mm. 
     Desirably, source material  52  is disposed on a structure  63  a distance from the bottom of crucible  51  to create an empty space or cavity  54  between source material  52  and the bottom of crucible  51 , wherein all of the source material is spaced from the bottom of the crucible by a gap between all of the source material and the bottom of the crucible. Structure  63  can be made of any suitable and/or desirable material, such as, without limitation, light-weight fibrous graphite. Desirably, cavity  54  has the height-to-diameter aspect ratio between 0.2 and 1. 
     Pyrometric windows  58  can be formed in the top and bottom parts of thermal insulation  57  for measuring the temperature of crucible  51  via a pyrometer. 
     A portion of the resistively heated AGT growth cell of  FIG. 5  is shown in isolation in  FIG. 6A . The result of a thermal simulation on the portion of the resistively heated AGT growth cell shown in  FIG. 6A  is shown in  FIG. 6B . The reference numbers in  FIGS. 6A and 6B  are the same as in  FIG. 5 . The heating geometry of the AGT growth cell shown in  FIG. 5  creates isotherms  55  in the vicinity of growing crystal  64  which are slightly convex towards the bottom of the crucible. 
     The AGT heating geometry shown in  FIG. 5  has the following advantages: (i) the radial temperature gradients in the vicinity of growing crystal  64  are slightly positive (i.e., slightly convex toward the bottom of growth crucible  51 ), which helps avoid a concave growth interface toward the bottom of growth crucible  51  or a flat growth interface; and (ii) the radial temperature gradients in growing crystal  64  are relatively small, which helps to avoid stress and cracking in growing crystal  64 . 
     An advantage of the AGT heating geometry shown in  FIG. 5  is that it creates relatively small and positive radial temperature gradients in the vicinity of growing SiC crystal  64 . Such gradients avoid or eliminate multiple growth centers, crude macrosteps, polytype instability, and associated defects in growing crystal  64 . 
     The AGT growth apparatus and growth process of  FIG. 5  yield SiC crystals having a convex growth interface. For SiC crystal boules capable of yielding 3″ substrates, the radius of interface curvature is desirably between 15 cm and 30 cm. For large-diameter SiC boules capable of yielding 100 mm substrates, the radius of interface curvature is desirably between 20 cm and 40 cm. For each diameter boule, the ratio of curvature of the convex growth interface radius over diameter is between about 2 and about 4, e.g., 20 cm/100 mm=2; and 40 cm/100 mm=4. 
     In the AGT growth cell shown in  FIG. 5 , bottom heater  50   b  is the main heater supplying approximately 80% of the required power, while top heater  50   a  supplies approximately 20% of power. The purpose of top heater  50   a  is to create a desired temperature distribution in the upper part of growth crucible  51 . Fine tuning of the thermal gradients in the upper part of the growth crucible  51  can be achieved by further adjustment of the shape of the upper heater  50   a , for instance, by changing the diameter of the central hole  60   a.    
     In a prior art PVT arrangement, single-coil RF heating created conditions wherein the cylindrical wall of the crucible serving as an RF susceptor was hotter than the crucible bottom. This lead to the deposition of polycrystalline SiC on the bottom of the crucible and poor utilization of the source material. 
     In the growth cell shown in  FIG. 5 , both the cup-like shape of bottom heater  50   b  and cavity  54  disposed under source material  52  serve to eliminate this shortcoming. Due to the radiative character of heat transport, the high emissivity of graphite (α=0.95−0.98), and the aforementioned height-to-diameter aspect ratio of cavity  54  of 0.2 to 1.0, the temperature distribution inside cavity  54  is spatially uniform, i.e., with low temperature gradients. Accordingly, the spacing between the isotherms inside cavity  54  in  FIG. 6B  is large. 
     The presence of cavity  54  under source material  52  helps to increase the temperature at the bottom of the source material  52  and crucible  51 . As a result, the deposition of polycrystalline SiC on the crucible bottom is avoided or eliminated and the utilization of source material  52  is improved. 
     The onset of glow discharge in a resistively heated system depends on the gas nature, its pressure and heater voltage, but does not depend on the material of the heater, provided that a sufficiently high temperature is reached.  FIG. 7  shows the dependence of the electrical conductance of a graphite heater on inert gas (helium) pressure at a resistive heater voltage of 25 VAC RMS and temperature of 2200° C. The sharp increase in the heater conductance at pressures between 0.1 and 40 Torr reflects the contribution of glow discharge (thermionic emission) to the total electric current flowing between the heater terminals. 
     The explanation for this phenomenon is as follows. At a low gas pressure there is a low concentration of gas ions, and the additional electronic/ionic current is small. With increase in the gas pressure the electric current increases due to thermionic emission, and the measured conductance of the heater increases. With further increase in gas pressure, scattering and energy dissipation by the gas atoms quench the emission leading to a decrease in the measured heater conductance. 
     The pressure range and magnitude of thermionic emission depends on the nature of the inert gas used. With heavy gases having low ionization potential, such as argon, thermionic emission starts at lower voltages, reaches higher amplitudes and readily progresses into arc. With light gases having high ionization potential, such as helium, thermionic emission starts at higher voltages and its amplitude is lower. Helium is a light gas which has the highest ionization potential among inert gases. Therefore, helium represents the best choice for resistively heated SiC crystal growth systems. 
     Another factor to prevent thermionic emission is the heater geometry. Glow discharge starts in areas of a heater where the temperature and electric field strength are the highest. Therefore, the design of the AGT heater of the present invention desirably avoids closely spaced terminals (extension electrodes), which are under highest potential difference. 
     Resistively heated AGT systems in accordance with the present invention, utilized for the growth of industrial size SiC crystals, have shown that SiC crystal growth can be successfully carried out in helium without glow discharge. Desirably, the He pressure is above 25 Torr and, more desirably, above 30 Torr; and the voltage applied to the heater desirably does not exceed 30 VAC RMS and, more desirably, does not exceed 25 VAC RMS. 
     The aforementioned limitation to the heater voltage determines the heater resistance. An example of a practical calculation is given below. Assume that heat losses in the AGT growth apparatus require 15 kW of power to achieve and maintain the desired SiC growth temperature. This means that the bottom heater should produce about 12 kW of power, while the top heater should produce about 3 kW. Assume further that in order to prevent glow discharge, the bottom heater voltage is limited to 20 VAC RMS and the top heater voltage is limited to 12 VAC RMS. Then, the resistance of the lower heater should be about 0.03 Ohm, and the resistance of the top heater should be about 0.05 Ohm. The electric current in the heaters will be about 660 A RMS in the bottom heater  50   b  and about 240 A RMS in the top heater  50   a.    
     Exemplary dimensions of an exemplary top heater  50   a  satisfying the above requirements are shown in  FIG. 8 . Exemplary dimensions of an exemplary bottom heater  50   b  satisfying the above requirements is shown in  FIGS. 9A and 9B . The graphite material for heaters  50   a  and  50   b  is desirably isostatically molded, fine-grain graphite of a density, desirably, between 1.73 and 1.82 g/cm 3  and resistivity, desirably, between 9 and 14 μOhm-meter at room temperature. 
     Exemplary top heater  50   a  shown in  FIG. 8  includes a plurality of internal slits (or slots)  66 , each of which extends radially outward from central hole  60  and terminates intermediate central hole  60  and the circumference of top heater  50   a . Top heater  50   a  also includes a plurality of external slits (or slots)  68 , each of which extends radially inward from the circumference of top heater  50   a  and terminates intermediate central hole  60  and the circumference of top heater  50   a . Desirably, internal slits  66  and external slits  68  are dispersed uniformly around the circumference of top heater  50   a  in an interdigitated pattern, whereupon a portion of each slit  66  resides between a pair of slits  68 , and a portion of each slit  68  resides between a pair of slits  66 . Exemplary top heater  50   a  includes twelve slits  66  and twelve slits  68 . However, this is not to be construed as limiting the invention. 
     Exemplary flat or disk-shaped section  61   a  of exemplary bottom heater  50   b  shown in  FIG. 9A  includes a plurality of internal slits (or slots)  70 , each of which extends radially outward from central hole  62  and terminates intermediate central hole  62  and the circumference of disk-shaped section  61   a . Disk-shaped section  61   a  also includes a plurality of external slits (or slots)  72 , each of which extends radially inward from the circumference of top heater  50   a  and terminates intermediate central hole  62  and the circumference of top heater  50   a . Desirably, internal slits  70  and external slits  72  are dispersed uniformly around the circumference of disk-shaped section  61   a  in an interdigitated pattern, whereupon a portion of each slit  70  resides between a pair of slits  72 , and a portion of each slit  72  resides between a pair of slits  70 . Exemplary disk-shaped section  61   a  includes ten slits  70  and ten slits  72 . However, this is not to be construed as limiting the invention. 
     Exemplary cylindrically-shaped section  61   b  of exemplary bottom heater  50   b  shown in  FIG. 9B  includes a plurality of upwardly extending slits (or slots)  74 , each of which extends upward from disk-shaped section  61   a  and terminates before the top edge of cylindrically-shaped section  61   b . Cylindrically-shaped section  61   b  also includes a plurality of slits (or slots)  76 , each of which extends downward from the top edge of cylindrically-shaped section  61   b  and either terminates before disk-shaped section  61   a  or extends completely to disk-shaped section  61   a . However, this is not to be construed as limiting the invention. 
     The foregoing descriptions of the slits of top heater  50   a , disk-shaped section  61   a , and cylindrically-shaped section  61   b  are not to be construed as limiting the invention since it is envisioned that each of top heater  50   a , disk-shaped section  61   a , and cylindrically-shaped section  61   b  can have any suitable and/or desirable arrangement of slits. 
     Advantages of the Present Invention Include: 
     An Axial Gradient Transport (AGT) crystal growth process and apparatus for the sublimation growth of SiC single crystals which includes a cylindrical growth crucible for supporting the SiC source material and the SiC seed in said crucible in spaced relation. The AGT growth apparatus includes two resistive heaters, one top heater and one bottom heater, disposed coaxially with the cylindrical growth crucible. The top heater is disposed above the growing crystal and the bottom heater is disposed around and below the source material. The top heater is disk-shaped with a central hole. The bottom heater is cup-shaped having two heating sections—one flat and one cylindrical. The top and bottom heaters are made of graphite. 
     The disk-shaped top heater has an outer diameter that is desirably between 10% and 30% larger than the crucible diameter and an inner (hole) diameter desirably between 25% and 75% of the diameter of the crucible. The top heater is disposed above the growth crucible at a distance from the crucible desirably between 10% and 30% of the crucible diameter. 
     The cup-shaped bottom heater includes a flat section which is disposed at a distance from the crucible desirably between 10% and 30% of the crucible diameter. The flat section has a central hole with a diameter desirably between 25% and 75% of the crucible diameter. The cylindrical section has a height desirably between 50% and 75% of the crucible height. The cylindrical section has an inner diameter desirably between 10 mm and 25 mm larger than the crucible outer diameter. 
     The heaters are desirably made of isostatically molded, fine-grain graphite of a density desirably between 1.73 and 1.82 g/cm 3  and resistivity desirably between 9 and 14 μOhm-meters at room temperature. 
     The growth crucible desirably includes a cavity separating the source material from the crucible bottom. The cavity has a height-to-diameter aspect ratio desirably between 0.2 and 1.0. 
     The AGT crystal growth process utilizes one top and one bottom heater. The bottom heater desirably provides between 70% and 90% of the electrical power required to heat the growth crucible to the required sublimation growth temperatures. The top heater desirably provides between 10% and 30% of the electrical power required to heat the growth crucible to the required sublimation growth temperatures. The top heater defines a thermal field in the upper portion of the growth crucible characterized by low and positive radial temperature gradients to produce flat or slightly convex isotherms. The voltage applied to the heaters desirably does not exceed 30 VAC RMS and, more desirably, does not exceed 25 VAC RMS. 
     The AGT crystal growth process desirably occurs in an atmosphere of inert gas, such as, without limitation, helium, at a pressure desirably above 25 Torr and, more desirably, above 30 Torr. 
     Technical Advantage of the Invention: 
     Application of the invention to sublimation growth of silicon carbide yields SiC single crystals of high quality and low thermal stress. 
     The invention has been reduced to practice in several SiC growth runs. These runs yielded large-diameter, high-quality, semi-insulating 6H and n +  4H crystals, as described below. 
     A schematic diagram of the resistively-heated AGT growth apparatus used in these runs is shown in  FIG. 5 . The heating assembly comprised two resistive heaters similar to those shown in  FIGS. 8 ,  9 A and  9 B. That is, the bottom heater was cup-shaped, while the top heater was disk-shaped. The central holes in the heaters were 50 mm in diameter for the top heater and 75 mm in diameter for the bottom heater. The axial distances between each heater and the crucible were about 25 mm. The radial distance between the outside surface of the crucible and the inner surface of the portion of the bottom heater that surround the side of the crucible was 12 mm. 
     The heaters were made of dense, low-porosity graphite with a density of 1.75 g/cm 3 . The resistance of the heaters was 0.03 Ohm for the top heater and 0.05 Ohm for the bottom heater (measured at room temperature). During a growth cycle, the bottom heater produced 80% of the required power, while the top heater produced 20% of the required power. The voltage on the terminals of either heater did not exceed 20 VAC RMS. 
     All of the growth runs occurred in the presence of helium at a pressure of 40 Torr. Because the crucible is made from a porous graphite, the pressure of the helium inside the crucible, as well as outside the crucible and around the heaters, was approximately the same, i.e., 40 Torr. During growth, the source and seed temperatures were maintained at 2180° C. and 2130° C., respectively. 
       FIGS. 10A ,  10 B and  10 C are photographs of some SiC boules grown using the resistively-heated AGT growth apparatus shown in  FIG. 5  that reached 100 mm in diameter.  FIG. 10A  is photograph of a 6H SI boule number DC0020;  FIG. 10B  is photograph of a 6H SI boule number DE0001; and  FIG. 10C  is photograph of a 4H n +  boule number DF0001. All SiC crystal boules grown in the improved AGT growth process and apparatus, including 3″ and 100 mm boules, exhibited a slightly convex growth interface with the radius of curvature between 25 and 35 cm. The grown crystals shown in  FIGS. 10A ,  10 B and  10 C were successfully processed into wafers, including 3 inch diameter wafers and 100 mm diameter wafers. 
       FIG. 11A  shows graphs of x-ray rocking curve scans performed on the &lt;1-210&gt; and &lt;10-10&gt; axes of the 6H crystal boule (DE0001) shown in  FIG. 10B . The Full Width and Half Maximum (FWHM) of the x-ray reflection serves as a good measure of crystal quality: the narrower the reflection and the lower the FWHM value, the better is the crystal quality. To compare, the best quality 6H SiC Lely platelets measured yielded FWHM values between 20 and 40 arc-seconds. The FWHM of typical PVT-grown bulk SiC boules is usually higher—between 40 and 100 arc-seconds. As can be see in  FIG. 10A , the FWHM values for the crystal DE0001 are between 25 and 60 arc-seconds. Such low FWHM values testify to the excellent crystal quality. 
       FIG. 11B  shows graphs of x-ray rocking curve scans on performed on the &lt;1-210&gt; and &lt;10-10&gt; axes of the 4H crystal boule (DF0001) shown in  FIG. 10C . The measurement conditions were the same as in the case above. The values of FWHM measured on this 4H crystal boule were even lower, between 18 and 40 arc-seconds. Thus, for this boule as well, the x-ray analysis revealed excellent crystal quality. 
     Another measure of crystal quality is its micropipe density (MPD). Micropipes are harmful defects causing device failure, and the majority of device applications require low MPD values in the SiC substrate. While SiC substrates with zero MPD are gradually becoming available commercially, the current state of the art across the entire industry is on the order of 5 to 40 micropipes-cm −2 .  FIGS. 12A and 12B  show MPD maps measured on the AGT-grown crystals DE0001 and DF0001 of  FIGS. 10B and 10C , respectively. Both crystals show average MPD below 0.5 micropipes-cm −2 , with boule DE0001 ( FIG. 11A ) being practically micropipe-free. 
     The invention has been described with reference to the preferred embodiment. Obvious modifications and alterations will occur to those skilled in the art upon reading and understanding the preceding detailed description. It is intended that the invention be construed as including all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.