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Sublimation growth of silicon carbide bulk crystals: experimental and theoretical studies on defect formation and growth rate augmentation
Journal of Crystal Growth 198/199 (1999) 1005—1010
Sublimation growth of silicon carbide bulk crystals: experimental and theoretical studies on defect formation and growth rate augmentation D. Hofmann *, M. Bickermann , R. Eckstein, M. Ko¨lbl, St.G. Mu¨ller , E. Schmitt, A. Weber, A. Winnacker Department of Materials Science, WW 6, University of Erlangen-Nu( rnberg, Martensstr. 7, D-91058 Erlangen, Germany SiCrystal AG, Heinrich-Hertz-Platz 2, D-92275 Eschenfelden, Germany
Abstract SiC crystals of 30—40 mm diameter were grown by physical vapor transport (PVT). The defect generation during seeding and subsequent growth was investigated. The main origin of micropipes in crystals grown on micropipe free/reduced seeds is correlated with second-phase formation, especially with the occurrence of C inclusions. Stress and micropipe densities are found to depend on the axial temperature gradients. Radial and axial temperature gradients were determined by the application of numerical modelling. Finally, the growth rate during PVT processing of SiC crystals was studied theoretically and experimentally. Both, a better control of vapor composition and a time-dependent variation of thermal boundary conditions are proposed for an augmentation of the crystallization rate. 1999 Elsevier Science B.V. All rights reserved. PACS: 81.10.Bk; 44.90.#c; 61.70.Ph Keywords: SiC bulk crystal growth; Physical vapor transport; Micropipe formation; Modelling of SiC sublimation growth
1. Introduction Recent research and development results on the wide band-gap semiconductor silicon carbide (SiC) * Corresponding author. Tel.: #49 9131 852 7634; fax: #49 9131 852 8495; e-mail: [email protected]. Present address: CREE Research Inc., 4600 Silicon Drive, Durham NC 27703, USA.
has now reached a critical mass which pushes the commercial application of SiC-based devices for high-power/high-temperature electronics and blue optoelectronics. A key prerequisite to future SiC device production will be the availability of lowdefect SiC substrate wafers of large diameter (d*2 in.). The present status of the SiC sublimation growth technology is unsatisfactory. Crystals contain several kinds of defects with laterally and
0022-0248/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 1 2 1 2 - 3
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D. Hofmann et al. / Journal of Crystal Growth 198/199 (1999) 1005–1010
longitudinally varying densities and distributions, e.g. micropipes, dislocations, mosaic structures, stress fields and dopant inhomogeneities [1,2]. The technological origin of defect generation, e.g. micropipe formation, is still under discussion. Further deficiencies exist concerning size of crystals (small diameters )35—50 mm and short length) and magnitude of crystallization rates. SiC boules are grown from the vapor with considerably lower velocities as compared to conventional semiconductors prepared from the melt. In this paper studies on the effect of thermal and compositional process conditions during SiC PVT growth on crystal quality were conducted. The grown crystals were investigated to reveal defects, e.g. second phases, micropipes and stress fields, and possible mechanisms of their generation. The thermal growth conditions were also investigated using numerical modelling. Implications for process conditions are elaborated which should lead to defect reduction in SiC crystals. The growth rate is finally analyzed experimentally and theoretically. Strategies for growth rate augmentation are proposed.
Fig. 1. 1.5 SiC single crystal of 4H modification and respective wafers grown by the physical vapor transport technique at the University of Erlangen-Nu¨rnberg.
2. Experimental procedure
3. Results and discussion
SiC crystals of 4H- and 6H-modification have been prepared by the physical vapor transport technique (PVT). The boules had diameters of 30)d)40 mm. Fig. 1 shows a typical 1.5 4HSiC single crystal and respective wafers. The temperatures at the seed and source were monitored by optical pyrometers and varied between 2100—2200°C and 2150—2300°C, respectively. Seed crystals grown by PVT in our laboratory having different micropipe densities and from the Acheson process (micropipe free) have been used. The source material was synthesized from elemental highpurity Si and C. The system pressure p was chosen between 40 and 5 mbar. The crystals have been highly doped by nitrogen which resulted in a carrier concentration n of 5;10 cm\) n)3;10 cm\. The magnitude of the crystallization rate was determined quantitatively by introducing nitrogen intermittendly during growth at defined times demarcating the interface. For the evaluation of defect generation versus crystal
3.1. Defect formation and growth conditions
length and time dependence of growth rate the crystals have been cut parallel to the [0 0 0 1] or [0 0 0 1] growth direction, respectively. These sam been investigated by optical transmission ples have microscopy. The micropipe and dislocation densities have been determined on wafers cut perpendicular to the [0 0 0 1]/[0 0 0 1] direction by optical microscopy after etching in KOH at ¹+500°C.
First the results of the influence of seeding conditions on defect generation will be presented. As starting point crystal seeds with and without micropipes have been employed in growth experiments. Besides seed quality a further parameter was the pumping rate during seeding which has been varied systematically. In first order the temporal dependence of the system pressure p can be described according to p"(p !p ) exp[!t/q]#p . We used experimentally a starting pressure p "800 mbar, an end pressure p "5—40 mbar and a time constant q"120—2400 s. This should establish conditions of different supersaturation. Fig. 2 shows representative transition layers between seed and growing crystal. It can be seen in Fig. 2a that micropipes present in the seed crystal penetrate into the adjacent layer. In contrast growth on micropipe free seeds proceeds without micropipe generation in the initial periods
D. Hofmann et al. / Journal of Crystal Growth 198/199 (1999) 1005–1010
1007
Fig. 2. (a) Axial cut (in growth direction) through a 4H SiC crystal showing the transition from the seed to the subsequent grown layers. Micropipes present in the seed penetrate into the growing crystal. (b) Axial cut (in growth direction) through a 4H SiC crystal showing the transition from the seed to the subsequent grown layers. No defect formation is visible.
(Fig. 2b). Besides micropipes originating from the seed no other defects have been observed optically at the seed/crystal interfaces. Several authors consider the sublimation etching procedure prior to growth as mandatory for low-defect growth [3]. According to our results this process step seems not to be necessary under the used boundary conditions. The variations in pumping rate showed no significant effect on the defect generation in the initial growth period. In the subsequent crystal layers second phases of different morphology and size (ranging from 2 to 50 lm) were detected. Fig. 3a shows an inclusion which is attributed to the formation of carbon (graphitization) [1]. It is visible that a micropipe is generated at this defect. Many of the found micropipes originate from these carbon inclusions. Fig. 3b shows a different type of parasitic second phase which can be characterized as round, oval or isotropic inclusion. These inclusions are attributed in the literature to the formation of silicon droplets [1] (studies for the final chemical identification of the inclusions are presently under way by Auger analysis). They can appear as a single inclusion, can form chains and act as starting or ending point of micropipes. C and Si inclusions can be present in the same crystal although the density of C inclusions is considerably higher. The micropipe density during these experiments using micropipe free/reduced seeds has been determined to range from 100 to 300 cm\. Ac-
cording to our analysis this number of micropipes should mainly originate from second phases. But there exists no direct correlation between the density of inclusions and density of micropipes. A multitude of inclusions does not act as micropipe source. Of great importance now is the knowledge about the origin of second-phase formation during PVT growth of SiC and its prevention. It is generally accepted that the Si vapor pressure is considerably higher than the pressure of other gas species and that the vapor composition alters during SiCgrowth due to Si losses from the system. There exist principally two starting points for further discussion. On the one side a thermodynamic approach can be used for the description of the formation of the minority component C which has been developed by Karpov et al. [4]. It was shown to predict reasonably well the second-phase formation of carbon in the SiC/C or SiC/Si system during molecular beam epitaxy at low temperatures. The model was also elaborated for small sized growth geometries of the sublimation sandwhich method under low-pressure conditions. From their results, graphitization effects seem to be also probable under our growth conditions due to a Si deficiency. But a quantitative analysis is not possible due to the lack of equations and material data in this publication. According to their model the Si content at the interface must be increased considerably
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D. Hofmann et al. / Journal of Crystal Growth 198/199 (1999) 1005–1010
Fig. 3. (a) Axial cut (in growth direction) through a 4H SiC crystal showing inclusions which are attributed to the secondphase formation of carbon. (b) Axial cut (in growth direction) through a 4H SiC crystal showing inclusions which are attributed to the formation of silicon droplets. In (a) and (b) second phases act as micropipe source.
to prevent graphitization, e.g. by the introduction of a liquid Si source into the crucible. Another option would be the use of a carbon gettering environment, e.g. tantalum container [5]. For the majority component silicon, on the other side,
the concept of constitutional supersaturation can be applied [6]. The stability diagram of SiC vapor growth with the growth rate and axial temperature gradient as parameter has been evaluated. Under moderate temperature gradients *¹/*z)30 K/cm unstable growth conditions are predicted at a process temperature of 2200°C. According to this criteria relatively high-temperature gradients *50 K/cm are necessary to achieve stable growth at reasonable growth rates of »"0.5 mm/h which in turn should influence negatively the goal to reach low dislocation density and stress reduced material. But it has to be kept in mind that the used supersaturation criterion may be taken only in a semi-quantitative way, because its final experimental verification for vapor growth is not to be forthcoming [7] (it does not include stabilizing effects, e.g. due to faceted growth). Nevertheless, there exists the conflict that the prevention of C inclusions necessitates a surplus of Si, but this would increase in turn the probability of the formation of Si droplets in the case of process instabilities or can cause polytype changes (formation of 3C SiC). The impact of axial temperature gradients on thermally induced stress and micropipe formation during PVT growth has also been investigated. Crystals have been prepared at different axial temperature gradients. The gradients were lowered by decreasing the radiative heat transfer from the backside of the seed crystal. The effect of temperature field variation was already evident from the shape of the crystals after growth. At the highest gradient a strongly convex interface could be observed which changed to a almost flat and slightly concave interface, respectively, with gradient reduction. From the results of stress birefringency analysis it can be seen that the crystal grown at the highest gradient exhibits the largest stress variations. Only the faceted area in the middle part of the crystal has a weak contrast. The contrast variations decrease with lower axial gradients. A considerable decrease in micropipe density is correlated with gradient reduction (about a factor of 2—3). Numerical modelling has also been applied to study the thermal conditions, especially axial and radial ¹-gradients, inside the crucible for the above growth situations as quantitative data are not accessible from measurement. The
D. Hofmann et al. / Journal of Crystal Growth 198/199 (1999) 1005–1010
used global code calculates the Joule heat sources due to induction heating and takes into account the occurring heat transfer mechanisms conduction, convection and radiation; for details see Refs. [8—10]. The simulation program predicts rather high temperature inhomogeneities *¹)30—50 K within the SiC source powder and *¹)30 K in the crystal. Axial temperature gradients of 50—100 K/cm are evaluated at the seed location. The large axial and radial ¹-gradients can explain the high amount of stress and dislocations (10—5;10 cm\) present in the shown crystals. A further defect reduction necessitates the optimization of thermal boundary conditions in respect to gradient minimization. The large axial and radial gradients in the powder may also explain partly second-phase formation as the vapor composition in respect to Si may degradate under this condition. 3.2. Analysis for the augmentation of growth rate In the literature SiC growth rates V are determined mainly as integral value after growth ranging from 0.1 to 1 mm/h during PVT growth. The main control parameters, which should determine the magnitude of growth rate at the beginning of growth, are system pressure, temperature and temperature difference between seed and source. According to theoretical analysis considerable higher growth rates should be attainable. Recently, it was shown experimentally by our group that V can decrease considerably with process time [10]. Fig. 4 shows in a non-dimensional form measured and calculated growth rates »/» (» :
growth rate taking into account only mass transfer) versus crystal length #¸ (#¸"Bi #Bi ; Bi : Biot numbers taking into account heat of crystallization and radiation, respectively; ¸"real crystal length) with the Regime number Rg as parameter. The Regime number Rg characterizes the degree of kinetic limitations, e.g. due to graphitization (Rg"r/[r#1] with r"R /R ; R " ) " ) represent the resistivities due to diffusional mass transfer and kinetics, respectively, for details see Ref. [6]). The underlying models take into account heat transfer, mass transport, kinetic aspects and heat of crystallization. For a fixed Rg-number the growth rate depends sensitively on the crystal
1009
Fig. 4. Calculated and measured SiC growth rate »/» (» :
growth rate taking into account only mass transfer) versus crystal length #¸ (#¸"Bi #Bi ; Bi : Biot numbers due to heat of crystallization and radiative heat transfer, ¸: real crystal length) in non-dimensional form with the Regime number Rg as parameter.
length at #¸'0.1 and decreases considerably. During a typical SiC growth situation this holds for a length ¸*0.5—1 mm. Our comparative study reveals that under these conditions heat transfer limitations due to the growing crystal are operative. An additional important factor which influences the magnitude of the growth rate is the kinetic limitation due to graphitization in the SiC powder material. From the above analysis the following strategies for an augmentation of the growth rate are evident: (i) Graphitization has to be prevented/reduced during the growth process. Measures to achieve these conditions are the addition of silicon to the source material, realization of tight crucibles preventing Si losses and/or the use of alternative crucible materials like tantalum [5]. (ii) The heat transfer through the growing crystal has to be controlled progressively during the process by tailoring the thermal boundary conditions. The achievement of such boundary conditions is considered as difficult. Reactors for SiC growth are heated generally by induction with a multi-turn coil. Numerical heat transfer analysis show that a time-dependent adjustment of thermal profiles is restricted. As advanced heating concept a multi-segment induction heating system is therefore under consideration.
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D. Hofmann et al. / Journal of Crystal Growth 198/199 (1999) 1005–1010
4. Conclusions Under the used process conditions the main origin of micropipes grown on micropipe free/reduced seeds is analyzed to be second-phase generation, especially the occurrence of C related inclusions. The addition of excess Si into the growth system is proposed to reduce graphitization effects. Stress pattern and number of micropipes are found to be correlated to the magnitude of axial temperature gradient. A quantitative evaluation of temperature conditions by numerical modelling reveals high axial gradients of 50—100 K/cm which explain the stress and dislocation formation in the crystals. The measures for an augmentation of growth rate have been analyzed to be the prevention of graphitization and the counteracting of heat transfer limitations by a time-dependent tailoring of thermal conditions.
Acknowledgements This work is supported by the Bavarian Research Foundation under contract nr. 176/96. The contribution of Dr. L. Kadinski and his group (Dept. Fluid Mechanics, Univ. Erlangen-Nu¨rnberg)
concerning numerical modelling of heat transfer is acknowledged. References [1] V. Tsvetkov, R. Glass, D. Henshall, D. Asbury, C.H. Carter, Mater. Sci. Forum 264—268 (1998) 3. [2] A.R. Powell, S. Wang, G. Fechko, G.R. Brandes, Mater. Sci. Forum 264—268 (1998) 13. [3] M.M. Anikin, R. Madar, A. Ronault, I. Garcon, L. Di Cioccio, J.L. Robert, J. Camassel, J.M. Bluet, Inst. Phys. Conf. Ser. 142 (1996) 33. [4] S.Yu. Karpov, Yu.N. Makarov, M.S. Ramm, Phys. Stat. Sol. A 5 (1997) 201. [5] D. Hofmann, S.Yu. Karpov, Yu.N. Makarov, E.N. Mokhov, M.G. Ramm, M.S. Ramm, A.D. Roenkov, Yu.A. Vodakov, Inst. Phys. Conf. Ser. 142 (1996) 29. [6] D. Hofmann, R. Eckstein, L. Kadinski, M. Ko¨lbl, M. Mu¨ller, St.G. Mu¨ller, E. Schmitt, A. Weber, A. Winnacker, MRS Symp. Proc. 483 (1998) 301. [7] F. Rosenberger, M.C. Delong, D.W. Greenwell, J.M. Olson, G.H. Westphal, J. Crystal Growth 29 (1975) 49. [8] D. Hofmann, M. Heinze, A. Winnacker, F. Durst, P. Kaufmann, Y. Makarov, M. Scha¨fer, J. Crystal Growth 148 (1995) 214. [9] D. Hofmann, R. Eckstein, M. Ko¨lbl, Y. Makarov, St.G. Mu¨ller, E. Schmitt, A. Winnacker, R. Rupp, R. Stein, J. Vo¨lkl, J. Crystal Growth 174 (1997) 669. [10] St.G. Mu¨ller, R. Eckstein, D. Hofmann, L. Kadinski, P. Kaufmann, M. Ko¨lbl, E. Schmitt, Mater. Sci. Forum 264—268 (1998) 57.
Sublimation growth of silicon carbide bulk crystals: experimental and theoretical studies on defect formation and growth rate augmentation D. Hofmann *, M. Bickermann , R. Eckstein, M. Ko¨lbl, St.G. Mu¨ller , E. Schmitt, A. Weber, A. Winnacker Department of Materials Science, WW 6, University of Erlangen-Nu( rnberg, Martensstr. 7, D-91058 Erlangen, Germany SiCrystal AG, Heinrich-Hertz-Platz 2, D-92275 Eschenfelden, Germany
Abstract SiC crystals of 30—40 mm diameter were grown by physical vapor transport (PVT). The defect generation during seeding and subsequent growth was investigated. The main origin of micropipes in crystals grown on micropipe free/reduced seeds is correlated with second-phase formation, especially with the occurrence of C inclusions. Stress and micropipe densities are found to depend on the axial temperature gradients. Radial and axial temperature gradients were determined by the application of numerical modelling. Finally, the growth rate during PVT processing of SiC crystals was studied theoretically and experimentally. Both, a better control of vapor composition and a time-dependent variation of thermal boundary conditions are proposed for an augmentation of the crystallization rate. 1999 Elsevier Science B.V. All rights reserved. PACS: 81.10.Bk; 44.90.#c; 61.70.Ph Keywords: SiC bulk crystal growth; Physical vapor transport; Micropipe formation; Modelling of SiC sublimation growth
1. Introduction Recent research and development results on the wide band-gap semiconductor silicon carbide (SiC) * Corresponding author. Tel.: #49 9131 852 7634; fax: #49 9131 852 8495; e-mail: [email protected]. Present address: CREE Research Inc., 4600 Silicon Drive, Durham NC 27703, USA.
has now reached a critical mass which pushes the commercial application of SiC-based devices for high-power/high-temperature electronics and blue optoelectronics. A key prerequisite to future SiC device production will be the availability of lowdefect SiC substrate wafers of large diameter (d*2 in.). The present status of the SiC sublimation growth technology is unsatisfactory. Crystals contain several kinds of defects with laterally and
0022-0248/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 1 2 1 2 - 3
1006
D. Hofmann et al. / Journal of Crystal Growth 198/199 (1999) 1005–1010
longitudinally varying densities and distributions, e.g. micropipes, dislocations, mosaic structures, stress fields and dopant inhomogeneities [1,2]. The technological origin of defect generation, e.g. micropipe formation, is still under discussion. Further deficiencies exist concerning size of crystals (small diameters )35—50 mm and short length) and magnitude of crystallization rates. SiC boules are grown from the vapor with considerably lower velocities as compared to conventional semiconductors prepared from the melt. In this paper studies on the effect of thermal and compositional process conditions during SiC PVT growth on crystal quality were conducted. The grown crystals were investigated to reveal defects, e.g. second phases, micropipes and stress fields, and possible mechanisms of their generation. The thermal growth conditions were also investigated using numerical modelling. Implications for process conditions are elaborated which should lead to defect reduction in SiC crystals. The growth rate is finally analyzed experimentally and theoretically. Strategies for growth rate augmentation are proposed.
Fig. 1. 1.5 SiC single crystal of 4H modification and respective wafers grown by the physical vapor transport technique at the University of Erlangen-Nu¨rnberg.
2. Experimental procedure
3. Results and discussion
SiC crystals of 4H- and 6H-modification have been prepared by the physical vapor transport technique (PVT). The boules had diameters of 30)d)40 mm. Fig. 1 shows a typical 1.5 4HSiC single crystal and respective wafers. The temperatures at the seed and source were monitored by optical pyrometers and varied between 2100—2200°C and 2150—2300°C, respectively. Seed crystals grown by PVT in our laboratory having different micropipe densities and from the Acheson process (micropipe free) have been used. The source material was synthesized from elemental highpurity Si and C. The system pressure p was chosen between 40 and 5 mbar. The crystals have been highly doped by nitrogen which resulted in a carrier concentration n of 5;10 cm\) n)3;10 cm\. The magnitude of the crystallization rate was determined quantitatively by introducing nitrogen intermittendly during growth at defined times demarcating the interface. For the evaluation of defect generation versus crystal
3.1. Defect formation and growth conditions
length and time dependence of growth rate the crystals have been cut parallel to the [0 0 0 1] or [0 0 0 1] growth direction, respectively. These sam been investigated by optical transmission ples have microscopy. The micropipe and dislocation densities have been determined on wafers cut perpendicular to the [0 0 0 1]/[0 0 0 1] direction by optical microscopy after etching in KOH at ¹+500°C.
First the results of the influence of seeding conditions on defect generation will be presented. As starting point crystal seeds with and without micropipes have been employed in growth experiments. Besides seed quality a further parameter was the pumping rate during seeding which has been varied systematically. In first order the temporal dependence of the system pressure p can be described according to p"(p !p ) exp[!t/q]#p . We used experimentally a starting pressure p "800 mbar, an end pressure p "5—40 mbar and a time constant q"120—2400 s. This should establish conditions of different supersaturation. Fig. 2 shows representative transition layers between seed and growing crystal. It can be seen in Fig. 2a that micropipes present in the seed crystal penetrate into the adjacent layer. In contrast growth on micropipe free seeds proceeds without micropipe generation in the initial periods
D. Hofmann et al. / Journal of Crystal Growth 198/199 (1999) 1005–1010
1007
Fig. 2. (a) Axial cut (in growth direction) through a 4H SiC crystal showing the transition from the seed to the subsequent grown layers. Micropipes present in the seed penetrate into the growing crystal. (b) Axial cut (in growth direction) through a 4H SiC crystal showing the transition from the seed to the subsequent grown layers. No defect formation is visible.
(Fig. 2b). Besides micropipes originating from the seed no other defects have been observed optically at the seed/crystal interfaces. Several authors consider the sublimation etching procedure prior to growth as mandatory for low-defect growth [3]. According to our results this process step seems not to be necessary under the used boundary conditions. The variations in pumping rate showed no significant effect on the defect generation in the initial growth period. In the subsequent crystal layers second phases of different morphology and size (ranging from 2 to 50 lm) were detected. Fig. 3a shows an inclusion which is attributed to the formation of carbon (graphitization) [1]. It is visible that a micropipe is generated at this defect. Many of the found micropipes originate from these carbon inclusions. Fig. 3b shows a different type of parasitic second phase which can be characterized as round, oval or isotropic inclusion. These inclusions are attributed in the literature to the formation of silicon droplets [1] (studies for the final chemical identification of the inclusions are presently under way by Auger analysis). They can appear as a single inclusion, can form chains and act as starting or ending point of micropipes. C and Si inclusions can be present in the same crystal although the density of C inclusions is considerably higher. The micropipe density during these experiments using micropipe free/reduced seeds has been determined to range from 100 to 300 cm\. Ac-
cording to our analysis this number of micropipes should mainly originate from second phases. But there exists no direct correlation between the density of inclusions and density of micropipes. A multitude of inclusions does not act as micropipe source. Of great importance now is the knowledge about the origin of second-phase formation during PVT growth of SiC and its prevention. It is generally accepted that the Si vapor pressure is considerably higher than the pressure of other gas species and that the vapor composition alters during SiCgrowth due to Si losses from the system. There exist principally two starting points for further discussion. On the one side a thermodynamic approach can be used for the description of the formation of the minority component C which has been developed by Karpov et al. [4]. It was shown to predict reasonably well the second-phase formation of carbon in the SiC/C or SiC/Si system during molecular beam epitaxy at low temperatures. The model was also elaborated for small sized growth geometries of the sublimation sandwhich method under low-pressure conditions. From their results, graphitization effects seem to be also probable under our growth conditions due to a Si deficiency. But a quantitative analysis is not possible due to the lack of equations and material data in this publication. According to their model the Si content at the interface must be increased considerably
1008
D. Hofmann et al. / Journal of Crystal Growth 198/199 (1999) 1005–1010
Fig. 3. (a) Axial cut (in growth direction) through a 4H SiC crystal showing inclusions which are attributed to the secondphase formation of carbon. (b) Axial cut (in growth direction) through a 4H SiC crystal showing inclusions which are attributed to the formation of silicon droplets. In (a) and (b) second phases act as micropipe source.
to prevent graphitization, e.g. by the introduction of a liquid Si source into the crucible. Another option would be the use of a carbon gettering environment, e.g. tantalum container [5]. For the majority component silicon, on the other side,
the concept of constitutional supersaturation can be applied [6]. The stability diagram of SiC vapor growth with the growth rate and axial temperature gradient as parameter has been evaluated. Under moderate temperature gradients *¹/*z)30 K/cm unstable growth conditions are predicted at a process temperature of 2200°C. According to this criteria relatively high-temperature gradients *50 K/cm are necessary to achieve stable growth at reasonable growth rates of »"0.5 mm/h which in turn should influence negatively the goal to reach low dislocation density and stress reduced material. But it has to be kept in mind that the used supersaturation criterion may be taken only in a semi-quantitative way, because its final experimental verification for vapor growth is not to be forthcoming [7] (it does not include stabilizing effects, e.g. due to faceted growth). Nevertheless, there exists the conflict that the prevention of C inclusions necessitates a surplus of Si, but this would increase in turn the probability of the formation of Si droplets in the case of process instabilities or can cause polytype changes (formation of 3C SiC). The impact of axial temperature gradients on thermally induced stress and micropipe formation during PVT growth has also been investigated. Crystals have been prepared at different axial temperature gradients. The gradients were lowered by decreasing the radiative heat transfer from the backside of the seed crystal. The effect of temperature field variation was already evident from the shape of the crystals after growth. At the highest gradient a strongly convex interface could be observed which changed to a almost flat and slightly concave interface, respectively, with gradient reduction. From the results of stress birefringency analysis it can be seen that the crystal grown at the highest gradient exhibits the largest stress variations. Only the faceted area in the middle part of the crystal has a weak contrast. The contrast variations decrease with lower axial gradients. A considerable decrease in micropipe density is correlated with gradient reduction (about a factor of 2—3). Numerical modelling has also been applied to study the thermal conditions, especially axial and radial ¹-gradients, inside the crucible for the above growth situations as quantitative data are not accessible from measurement. The
D. Hofmann et al. / Journal of Crystal Growth 198/199 (1999) 1005–1010
used global code calculates the Joule heat sources due to induction heating and takes into account the occurring heat transfer mechanisms conduction, convection and radiation; for details see Refs. [8—10]. The simulation program predicts rather high temperature inhomogeneities *¹)30—50 K within the SiC source powder and *¹)30 K in the crystal. Axial temperature gradients of 50—100 K/cm are evaluated at the seed location. The large axial and radial ¹-gradients can explain the high amount of stress and dislocations (10—5;10 cm\) present in the shown crystals. A further defect reduction necessitates the optimization of thermal boundary conditions in respect to gradient minimization. The large axial and radial gradients in the powder may also explain partly second-phase formation as the vapor composition in respect to Si may degradate under this condition. 3.2. Analysis for the augmentation of growth rate In the literature SiC growth rates V are determined mainly as integral value after growth ranging from 0.1 to 1 mm/h during PVT growth. The main control parameters, which should determine the magnitude of growth rate at the beginning of growth, are system pressure, temperature and temperature difference between seed and source. According to theoretical analysis considerable higher growth rates should be attainable. Recently, it was shown experimentally by our group that V can decrease considerably with process time [10]. Fig. 4 shows in a non-dimensional form measured and calculated growth rates »/» (» :
growth rate taking into account only mass transfer) versus crystal length #¸ (#¸"Bi #Bi ; Bi : Biot numbers taking into account heat of crystallization and radiation, respectively; ¸"real crystal length) with the Regime number Rg as parameter. The Regime number Rg characterizes the degree of kinetic limitations, e.g. due to graphitization (Rg"r/[r#1] with r"R /R ; R " ) " ) represent the resistivities due to diffusional mass transfer and kinetics, respectively, for details see Ref. [6]). The underlying models take into account heat transfer, mass transport, kinetic aspects and heat of crystallization. For a fixed Rg-number the growth rate depends sensitively on the crystal
1009
Fig. 4. Calculated and measured SiC growth rate »/» (» :
growth rate taking into account only mass transfer) versus crystal length #¸ (#¸"Bi #Bi ; Bi : Biot numbers due to heat of crystallization and radiative heat transfer, ¸: real crystal length) in non-dimensional form with the Regime number Rg as parameter.
length at #¸'0.1 and decreases considerably. During a typical SiC growth situation this holds for a length ¸*0.5—1 mm. Our comparative study reveals that under these conditions heat transfer limitations due to the growing crystal are operative. An additional important factor which influences the magnitude of the growth rate is the kinetic limitation due to graphitization in the SiC powder material. From the above analysis the following strategies for an augmentation of the growth rate are evident: (i) Graphitization has to be prevented/reduced during the growth process. Measures to achieve these conditions are the addition of silicon to the source material, realization of tight crucibles preventing Si losses and/or the use of alternative crucible materials like tantalum [5]. (ii) The heat transfer through the growing crystal has to be controlled progressively during the process by tailoring the thermal boundary conditions. The achievement of such boundary conditions is considered as difficult. Reactors for SiC growth are heated generally by induction with a multi-turn coil. Numerical heat transfer analysis show that a time-dependent adjustment of thermal profiles is restricted. As advanced heating concept a multi-segment induction heating system is therefore under consideration.
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D. Hofmann et al. / Journal of Crystal Growth 198/199 (1999) 1005–1010
4. Conclusions Under the used process conditions the main origin of micropipes grown on micropipe free/reduced seeds is analyzed to be second-phase generation, especially the occurrence of C related inclusions. The addition of excess Si into the growth system is proposed to reduce graphitization effects. Stress pattern and number of micropipes are found to be correlated to the magnitude of axial temperature gradient. A quantitative evaluation of temperature conditions by numerical modelling reveals high axial gradients of 50—100 K/cm which explain the stress and dislocation formation in the crystals. The measures for an augmentation of growth rate have been analyzed to be the prevention of graphitization and the counteracting of heat transfer limitations by a time-dependent tailoring of thermal conditions.
Acknowledgements This work is supported by the Bavarian Research Foundation under contract nr. 176/96. The contribution of Dr. L. Kadinski and his group (Dept. Fluid Mechanics, Univ. Erlangen-Nu¨rnberg)
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