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Influence of a high vertical magnetic field on Te dopant segregation in InSb grown by the vertical gradient freeze method
CRYSTAL GROWTH Journal ofCrystal Growth 140 (1994) 435—438
ELSEVIER
Letter to the Editors
Influence of a high vertical magnetic field on Te dopant segregation in InSb grown by the vertical gradient freeze method Junyong Kang
a,b,*
Yasunori Okano
a
Keigo Hoshikawa
a
Tsuguo Fukuda
a
Institute for Materials Research, Tohoku University, Sendai 980, Japan of Physics, Xiamen University, Xiamen 361005, People’s Republic of China
‘~
h Department
(Received 26 November 1993; manuscript received in final form 8 April 1994)
Abstract A vertical gradient freeze apparatus was set up to investigate the influence of a vertical magnetic field on Te dopant segregation in InSb. Te-doped InSb crystals were grown in the presence and absence of an 80.0 kG magnetic field. The axial profile of the Te concentration in the crystal grown in the magnetic field was observed to be more uniform than that grown without magnetic field, which was attributed to the influence of the high magnetic field on Te dopant segregation by reducing convection in the melt.
Application of a magnetic field to an electrically conductive melt experiencing convection establishes Lorentz forces which tend to reduce the convection intensity in the melt. A low magnetic field was applied successfully to damp out timedependent temperature fluctuations in the melt [1,2]. Elimination of the temperature fluctuations was reported to influence growth striations and defects [3—5]. Application of a high magnetic field during crystal growth is a potential method for elimination of convective interference with preferential solute partitioning at the solidification front, which was predicted to grow compositionally uniform materials [6]. An axial magnetic field of 30 kG was applied to Ga-doped germanium and HgMnTe semiconductor growths in a
_______
*
Corresponding author,
vertical Bridgman—Stockbarger system [7,81. Axial composition of the Ga-doped Ge exhibited an initial exponential rise, which was considered to result from the reduction or elimination of convective interference with segregation. Radial compositional uniformity of HgMnTe was observed to improve, but its axial compositional profile was not influenced by the magnetic field. The Lorentz force is proportional to the product of flow velocity and the square of magnetic field strength (if these are mutually perpendicular). The influence of a high magnetic field is significant for melts with high convective velocity. According to a recently derived model of the effective segregation coefficient [91,Te-doped InSb is one of the melts with high convective velocity where the elimination of convective interference with segregation is more readily achieved. In order to understand the influence of a high magnetic field, InSb : Te was selected to be grown
0022-0248/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0022-0248(94)00058-T
436
J. Kang et al. /Journal of Crystal Growth 140 (1994) 435—438
in the presence and absence of an 80.0 kG high magnetic field, and Te concentration distributions in the grown crystals were analyzed. A schematic diagram of our vertical gradient freeze apparatus is shown in Fig. 1. A solenoidal superconducting magnet was used to generate a magnetic field of 80.0 kG at maximum in the central region of the room temperature bore. A water-cooled stainless steel chamber was put into the inner bore of the superconducting magnet. In the chamber graphite felt, contained in a graphite container, was put on to act as a thermal shield. Two graphite electrodes were electrically insulated by quartz glass and passed through the bottom part of the thermal shield to connect a high stability direct current power supply with a heater. The heater was thinned down to 1.5 mm by adopting pyrolytic BN as a base material on which was evaporated a thin graphite film on its outer surface. A temperature gradient was estab-
~________
lished by carving a helical ribbon out of the graphite film with different width. A graphite outer crucible was put into the heater bore and held at both ends. In a cylindrical quartz inner crucible, presynthesized InSb Te polycrystals were loaded. The solidification positions of InSb crystals were investigated at different monitored temperatures. The data on the solidification positions as a function of the monitor temperature were fitted by a polynomial. The relationship between the solidification position and the monitor temperature was used to control the crystal growth rate. The influence of the high magnetic field on the temperature field was investigated by measuring the temperature profiles in the presence and absence of the 80.0 kG magnetic field. The temperature profiles are shown in Fig. 2. The temperature gradients were nearly the same in the presence and in the absence of the magnetic field. In order to increase the growth dy-
Superconducting magnet
_______
________ ________
_________
Crucible
—
_______
_______
____________ -
Water cooled chamber
____________________
Thermal shield
____________
Pyrolytic BN graphite film heater
_______
Melt
_________________________
Electrode Quartz glass
M Fig. 1. Schematic diagram of apparatus for vertical gradient freeze growth in high magnetic field.
J. Kang et aL /Journal of Crystal Growth 140 (1994) 435—438
namics, the crystals were selected to grow in the higher temperature gradient region marked in Fig.2. InSb : Te polycrystals were charged into a cylindrical quartz crucible of 9 mm diameter. The growth system was pumped out, purged with high purity argon and maintained at 1 atm. The furnace was heated to a monitored temperature within 2 h and kept at the temperature for 3 h in which the charges were tested to have melted to the relevant solidification position for about 1 h. The solidification rate was controlled to be 10 mm/h on the basis of the relationship between the solidification position and the monitored temof perature. InSb : Te was solidified in two procedures. One was the conventionally vertical gradient freeze process. The other was initial solidification in the absence of a magnetic field. After an about 5 mm long crystal had been solidified, a magnetic field of 80.0 kG was applied until the melt was totally solidified. Then, the furnace ternperature was programmed to decreased slowly to room temperature. The grown crystals were polycrystals. As-grown ingots were sliced transversely, and then mechanically and chemically polished. The samples were investigated by atomic absorption spectrochemical analysis and Hall effect measurement. Axial profiles of Te concentration in the crystals grown 18
14
U
1
10
~
~l
•
—
_L.~— -2 500
540
580
•.a~s’~~•x X
B = 80.0 kG 10~ 0.0
0.2
0.4 0.6 0.8 1.0 Solidification fraction g Fig. 3. Axial profile of the Te concentration along the center the crystal grown in the presence (solid symbols) and absence (x) of an 80.0 kG magnetic field: (U), (x) determined by Hall effect measurement; (s) determined by atomic absorption spectrochemical analysis.
in the presence and absence of the magnetic field are shown in Fig. 3. The values of the Te concentration determined by atomic absorption spectrochemical analysis were close to those of the donor carrier concentration measured at room temperature by the Van der Pauw method. This indicates that most of electron carriers originate from Te atoms. In the crystal grown in the latter procedure, the Te concentration in the initial part grown without the magnetic field was close to that solidified in the conventional procedure and increased distinctly after the magnetic field was turned on. Then the Te concentration increased gradually in most parts of the crystal. In particular, the Te concentration was about 4 times lower than that solidified by the conventional procedure at the top end of the crystal for the relevant solidified fraction. Overall, the Te distribution in the crystal solidified in the magnetic field was more homogeneous than with the conventional procedure. The axial profile of the Te concentration in the conventionally solidified crystal was relatively close to the curve in Fig. 3 calculated for corn-
6
2
°
~
437
620
660
700
Temperature (°C) Fig. 2. Temperature profile of crucible center in the presence (•)and absence (x) of an 80.0 kG magnetic field,
plete mixing segregation equilibrium distribution coefficient of with k0 = an 0.5 [10]. However, the axial profile of the Te concentration in the magnetic-field-grown crystal cannot be fitted well with the curve. The convection in the InSb Te
438
J. Kang et al. /Journal of Crystal Growth 140 (1994) 435—438
melt was considered to be lowered in the presence of the 80.0 kG magnetic field. In the model of the effective segregation coefficient under low convection, the effective segregation coefficient keff is a function of convective velocity and is given by [9]: VD/(R2L/D) keff 11 ++ V 2L/D)’ (1) 0(k0R =
where VD is the convective velocity at the edge of the diffusion boundary layer, and R, L and D are growth rate, growth interface length and diffusion coefficient, respectively. The decrease of the convective velocity at the edge of the diffusion boundary layer induces an increase of the effective Te dopant segregation coefficient in InSb. Thus, the Te concentration increased distinctly after the magnetic field was turned on and was more homogeneous than that grown by the conventional method, particularly near the top of the crystal. However, the axial profile of the Te concentration in the crystal grown in the magnetic field could not be described by a constant effective segregation coefficient of keff 1. Theoretical investigation showed that the effective segregation coefficient can only reach a value of keff 0.95 for segregation without convective interference [91.Furthermore, the effective segregation coefficient was influenced by the high magnetic field generating a Lorentz force to reduce convection velocity. Its action decreases with decreasing flow velocity, so that it is difficult to further damp very weak flows. Therefore, the axial profile of the Te concentration can only be described by the low convection model with an =
=
effective segregation coefficient smaller than 0.95 though the uniformity has been improved in InSb : Te grown in the 80.0 kG magnetic field. The authors would like to thank S. Tozawa of the Institute for Materials Research of Tohoku University for and his crystal helpfulgrowth, cooperation apparatus setup and S.during Chichibu, T. Wakiyama and Professor S. Matsurnoto of the Department of Electrical Engineering of the Faculty of Science and Technology, Keio University, for their help in Hall effect measurements. We are indebted to Shin Etsu Company for cooperation during preparation of the pyrolytic BN-graphite film heater. This study was cooperated with the Center for High Magnetic Field, the Institute for Materials Research, Tohoku University.
References [1] HA. Chedzey and D.T.J. Hurle, Nature 210 (1966) 933. [2] H.P. Utech and MC. Flemings, J. AppI Phys. 37 (1966) 2021. [3] A.F. Witt, C.J. Herman and H.C. Gatos, J. Mater. Sci. 5 (1970) 882. [4] K. Hoshikawa, Jap. J. Appl. Phys. 21(1982) L545. [5] K. Terashima, T. Katsumata, F. Onto, T. Kikuda and T. Fukuda, Jap. J. AppI. Phys. 22 (1983) L325. [6] WA. Tiller, K.A. Jackson, J.W. Rutter and B. Chalmers, Acta Met. 1 (1953) 428. [7] D.H. Matthiesen, M.J. Wargo, S. Motakef, D.J. Carlson, J.S. Nakos and A.F. Witt, J. Crystal Growth 85 (1987) 557 [8] P. Becla, J.-C. Han and S. Motakef, J. Crystal Growth 121 (1992) 394. [9] AG. Ostrogorsky and G. Muller, J. Crystal Growth 128 (1993) 207. [10] W.G. Pfann, Zone Melting (Wiley, New York, 1966).
ELSEVIER
Letter to the Editors
Influence of a high vertical magnetic field on Te dopant segregation in InSb grown by the vertical gradient freeze method Junyong Kang
a,b,*
Yasunori Okano
a
Keigo Hoshikawa
a
Tsuguo Fukuda
a
Institute for Materials Research, Tohoku University, Sendai 980, Japan of Physics, Xiamen University, Xiamen 361005, People’s Republic of China
‘~
h Department
(Received 26 November 1993; manuscript received in final form 8 April 1994)
Abstract A vertical gradient freeze apparatus was set up to investigate the influence of a vertical magnetic field on Te dopant segregation in InSb. Te-doped InSb crystals were grown in the presence and absence of an 80.0 kG magnetic field. The axial profile of the Te concentration in the crystal grown in the magnetic field was observed to be more uniform than that grown without magnetic field, which was attributed to the influence of the high magnetic field on Te dopant segregation by reducing convection in the melt.
Application of a magnetic field to an electrically conductive melt experiencing convection establishes Lorentz forces which tend to reduce the convection intensity in the melt. A low magnetic field was applied successfully to damp out timedependent temperature fluctuations in the melt [1,2]. Elimination of the temperature fluctuations was reported to influence growth striations and defects [3—5]. Application of a high magnetic field during crystal growth is a potential method for elimination of convective interference with preferential solute partitioning at the solidification front, which was predicted to grow compositionally uniform materials [6]. An axial magnetic field of 30 kG was applied to Ga-doped germanium and HgMnTe semiconductor growths in a
_______
*
Corresponding author,
vertical Bridgman—Stockbarger system [7,81. Axial composition of the Ga-doped Ge exhibited an initial exponential rise, which was considered to result from the reduction or elimination of convective interference with segregation. Radial compositional uniformity of HgMnTe was observed to improve, but its axial compositional profile was not influenced by the magnetic field. The Lorentz force is proportional to the product of flow velocity and the square of magnetic field strength (if these are mutually perpendicular). The influence of a high magnetic field is significant for melts with high convective velocity. According to a recently derived model of the effective segregation coefficient [91,Te-doped InSb is one of the melts with high convective velocity where the elimination of convective interference with segregation is more readily achieved. In order to understand the influence of a high magnetic field, InSb : Te was selected to be grown
0022-0248/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0022-0248(94)00058-T
436
J. Kang et al. /Journal of Crystal Growth 140 (1994) 435—438
in the presence and absence of an 80.0 kG high magnetic field, and Te concentration distributions in the grown crystals were analyzed. A schematic diagram of our vertical gradient freeze apparatus is shown in Fig. 1. A solenoidal superconducting magnet was used to generate a magnetic field of 80.0 kG at maximum in the central region of the room temperature bore. A water-cooled stainless steel chamber was put into the inner bore of the superconducting magnet. In the chamber graphite felt, contained in a graphite container, was put on to act as a thermal shield. Two graphite electrodes were electrically insulated by quartz glass and passed through the bottom part of the thermal shield to connect a high stability direct current power supply with a heater. The heater was thinned down to 1.5 mm by adopting pyrolytic BN as a base material on which was evaporated a thin graphite film on its outer surface. A temperature gradient was estab-
~________
lished by carving a helical ribbon out of the graphite film with different width. A graphite outer crucible was put into the heater bore and held at both ends. In a cylindrical quartz inner crucible, presynthesized InSb Te polycrystals were loaded. The solidification positions of InSb crystals were investigated at different monitored temperatures. The data on the solidification positions as a function of the monitor temperature were fitted by a polynomial. The relationship between the solidification position and the monitor temperature was used to control the crystal growth rate. The influence of the high magnetic field on the temperature field was investigated by measuring the temperature profiles in the presence and absence of the 80.0 kG magnetic field. The temperature profiles are shown in Fig. 2. The temperature gradients were nearly the same in the presence and in the absence of the magnetic field. In order to increase the growth dy-
Superconducting magnet
_______
________ ________
_________
Crucible
—
_______
_______
____________ -
Water cooled chamber
____________________
Thermal shield
____________
Pyrolytic BN graphite film heater
_______
Melt
_________________________
Electrode Quartz glass
M Fig. 1. Schematic diagram of apparatus for vertical gradient freeze growth in high magnetic field.
J. Kang et aL /Journal of Crystal Growth 140 (1994) 435—438
namics, the crystals were selected to grow in the higher temperature gradient region marked in Fig.2. InSb : Te polycrystals were charged into a cylindrical quartz crucible of 9 mm diameter. The growth system was pumped out, purged with high purity argon and maintained at 1 atm. The furnace was heated to a monitored temperature within 2 h and kept at the temperature for 3 h in which the charges were tested to have melted to the relevant solidification position for about 1 h. The solidification rate was controlled to be 10 mm/h on the basis of the relationship between the solidification position and the monitored temof perature. InSb : Te was solidified in two procedures. One was the conventionally vertical gradient freeze process. The other was initial solidification in the absence of a magnetic field. After an about 5 mm long crystal had been solidified, a magnetic field of 80.0 kG was applied until the melt was totally solidified. Then, the furnace ternperature was programmed to decreased slowly to room temperature. The grown crystals were polycrystals. As-grown ingots were sliced transversely, and then mechanically and chemically polished. The samples were investigated by atomic absorption spectrochemical analysis and Hall effect measurement. Axial profiles of Te concentration in the crystals grown 18
14
U
1
10
~
~l
•
—
_L.~— -2 500
540
580
•.a~s’~~•x X
B = 80.0 kG 10~ 0.0
0.2
0.4 0.6 0.8 1.0 Solidification fraction g Fig. 3. Axial profile of the Te concentration along the center the crystal grown in the presence (solid symbols) and absence (x) of an 80.0 kG magnetic field: (U), (x) determined by Hall effect measurement; (s) determined by atomic absorption spectrochemical analysis.
in the presence and absence of the magnetic field are shown in Fig. 3. The values of the Te concentration determined by atomic absorption spectrochemical analysis were close to those of the donor carrier concentration measured at room temperature by the Van der Pauw method. This indicates that most of electron carriers originate from Te atoms. In the crystal grown in the latter procedure, the Te concentration in the initial part grown without the magnetic field was close to that solidified in the conventional procedure and increased distinctly after the magnetic field was turned on. Then the Te concentration increased gradually in most parts of the crystal. In particular, the Te concentration was about 4 times lower than that solidified by the conventional procedure at the top end of the crystal for the relevant solidified fraction. Overall, the Te distribution in the crystal solidified in the magnetic field was more homogeneous than with the conventional procedure. The axial profile of the Te concentration in the conventionally solidified crystal was relatively close to the curve in Fig. 3 calculated for corn-
6
2
°
~
437
620
660
700
Temperature (°C) Fig. 2. Temperature profile of crucible center in the presence (•)and absence (x) of an 80.0 kG magnetic field,
plete mixing segregation equilibrium distribution coefficient of with k0 = an 0.5 [10]. However, the axial profile of the Te concentration in the magnetic-field-grown crystal cannot be fitted well with the curve. The convection in the InSb Te
438
J. Kang et al. /Journal of Crystal Growth 140 (1994) 435—438
melt was considered to be lowered in the presence of the 80.0 kG magnetic field. In the model of the effective segregation coefficient under low convection, the effective segregation coefficient keff is a function of convective velocity and is given by [9]: VD/(R2L/D) keff 11 ++ V 2L/D)’ (1) 0(k0R =
where VD is the convective velocity at the edge of the diffusion boundary layer, and R, L and D are growth rate, growth interface length and diffusion coefficient, respectively. The decrease of the convective velocity at the edge of the diffusion boundary layer induces an increase of the effective Te dopant segregation coefficient in InSb. Thus, the Te concentration increased distinctly after the magnetic field was turned on and was more homogeneous than that grown by the conventional method, particularly near the top of the crystal. However, the axial profile of the Te concentration in the crystal grown in the magnetic field could not be described by a constant effective segregation coefficient of keff 1. Theoretical investigation showed that the effective segregation coefficient can only reach a value of keff 0.95 for segregation without convective interference [91.Furthermore, the effective segregation coefficient was influenced by the high magnetic field generating a Lorentz force to reduce convection velocity. Its action decreases with decreasing flow velocity, so that it is difficult to further damp very weak flows. Therefore, the axial profile of the Te concentration can only be described by the low convection model with an =
=
effective segregation coefficient smaller than 0.95 though the uniformity has been improved in InSb : Te grown in the 80.0 kG magnetic field. The authors would like to thank S. Tozawa of the Institute for Materials Research of Tohoku University for and his crystal helpfulgrowth, cooperation apparatus setup and S.during Chichibu, T. Wakiyama and Professor S. Matsurnoto of the Department of Electrical Engineering of the Faculty of Science and Technology, Keio University, for their help in Hall effect measurements. We are indebted to Shin Etsu Company for cooperation during preparation of the pyrolytic BN-graphite film heater. This study was cooperated with the Center for High Magnetic Field, the Institute for Materials Research, Tohoku University.
References [1] HA. Chedzey and D.T.J. Hurle, Nature 210 (1966) 933. [2] H.P. Utech and MC. Flemings, J. AppI Phys. 37 (1966) 2021. [3] A.F. Witt, C.J. Herman and H.C. Gatos, J. Mater. Sci. 5 (1970) 882. [4] K. Hoshikawa, Jap. J. Appl. Phys. 21(1982) L545. [5] K. Terashima, T. Katsumata, F. Onto, T. Kikuda and T. Fukuda, Jap. J. AppI. Phys. 22 (1983) L325. [6] WA. Tiller, K.A. Jackson, J.W. Rutter and B. Chalmers, Acta Met. 1 (1953) 428. [7] D.H. Matthiesen, M.J. Wargo, S. Motakef, D.J. Carlson, J.S. Nakos and A.F. Witt, J. Crystal Growth 85 (1987) 557 [8] P. Becla, J.-C. Han and S. Motakef, J. Crystal Growth 121 (1992) 394. [9] AG. Ostrogorsky and G. Muller, J. Crystal Growth 128 (1993) 207. [10] W.G. Pfann, Zone Melting (Wiley, New York, 1966).