- Email: [email protected]
{100} facets in pulled crystals of InSb
Solid-State Electronics Pergamon Press 1962. Vol. 5, pp. 97-110. Printed in Great Britain
NOTES {100} facets in pulled crystals of InSb
(Received 13 November 1961)
considerably less than for {111) facets. An etched cross-section through a Se-doped crystal is shown in Fig. 2. The high concentration region at the center of the crystal, which appears as a bright spot, is seen to be essentially the same size as the {100) facet in the undoped crystal of Fig. 1. The high concentration regions at the outer edges correspond to the {111} facets of Fig. 1. Resistivity measurements on the doped crystals were made at room temperature with a 4-point probe (probe spacing = 0.2 mm) in an attempt to measure the concentration ratio R100 for Te and Se. In both Cases the resistivities inside and outside the facet region were the same within the error of measurement. From this result it appears that Rloo is less than 2, compared with values of 5-10 obtained for Rill. (2-4) The fact that (100} facets are smaller than {111} facets formed under the same growth conditions shows that the degree of supercooling required to nucleate crystal growth is less for the {100} plane than for the {111) plane. (The degree of supercooling necessary for nucleation appears to be even less for the {110) plane than for the (100) plane, since several ( l l0 )-oriented crystals were grown during the present series of experiments but no central {110) facets were observed.) Therefore the lateral propagation rate of growth steps should be smaller on (100) facets than on {111} facets. According to the model of crystal growth generally adopted to account for the facet phenomenon, (7) this difference in propagation rate would tend to make Rjoo less than Rl11, as has been observed. The {100) and {111} facets might also differ in the concentration of Se or Te atoms adsorbed at the interface between the crystal and a melt of given impurity concentration. Such a difference would also be expected to contribute to the observed difference between Rxoo and Rnl.
THE EFFECT of planar {111} facets at the solidliquid interface on the impurity distribution in crystals pulled from the melt was first reported by HULME and MULLIN,(1) who observed it in InSb. DmHOFF (2) independently observed the effect in Ge; and subsequently it has been studied in InSb by several workers. (3-6) For all cases studied except Ga in Ge, the impurity concentration inside the facet region (Con) is greater than the concentration outside it (Cott). The only previous report of a facet with orientation other than {111} was made b y HULME and MULLIN,(1) who observed a {100) facet on a heavily twinned Crystal of InSb. In .the present investigation, central (100) facets have been observed on a number of InSb single crystals grown in the <100) direction. A typical case is shown in Fig. 1, which depicts the bottom of an undoped crystal which was pulled abruptly from the melt in order to reveal the shape of the solidliquid interface. The bright circular region at the center of the crystal is the (100} facet, a portion of which is covered by the usual spike formed by solidification of liquid which adhered to the interface. Two large {111) facets are also seen at the outer edges of the crystal. The {100) facets which have been observed are much smaller than the central (111) facets which are formed on ( l l l ) - o r i e n t e d InSb crystals grown in the same crystal puller under the same growth conditions. For crystals 20-25 m m in diameter, typical diameters for the {100) facets and {111} facets are 2 - 3 r a m and 8-12ram, respectively. In order to determine the effect of {100) facets on impurity distribution, (100)-oriented crystals containing Te or Se concentrations of about 1018 cm -3 were grown from suitably doped melts. Etching these crystals with dilute CP-4 revealed Acknowledgements--It is a pleasure to acknowledge the that for both Te and Se Con is greater than Colt, assistance of R. L. MAcLEAN in growing the InSb but the concentration ratio (R = Con/Cott) is crystals and of MAaY C. FINN in etching them. The 97
NOTES
98
author is also grateful to Dr. H. C. GATOSfor valuable discussions. Lincoln Laboratory* A . J . STRAUSS Massachusetts Institute of Technology, Lexington, 73, Massachusetts References
1. K. F. HULMEand J. B. MULLIN,Phil. Mag. 4, 1286 (1959). 2. It. A. M. DmHOFF, Solid-State Electron. 1, 202 (1960). 3. I- B. MULLIN and K. F. HULME,J. Phys. Chem. Solids 17, 1 (1960). 4. W. P. ALLR~D and R. T. BATE, J. Electrochem. Soc. 108, 258 (1961). 5. A. I. STRAUSSand T. C. HARMAN, Semiconductor Symposium of the Electrochemical Society, October,
1960 (unpublished). 6. M. D. BANUS and H. C. GATOS, Semiconductor Symposium of the Electrochemical Society, October,
1961 (unpublished). 7. For example, see A. TRAINORand ]3. E. BARTLETT, Solid-State Electron. 2, 106 (1961).
pn-~3bergang erzielt, indem Arsen aus dem Germanium in die riickkristallisierte Zone eindiffundiert. Wie Versuche mit Indium reinst und Indium +0,5 % Gallium sowie der Vergleich Abb.l(a) und Abb. 2 ergeben, kann die Eindiffusion von Indium oder Gallium aus der rfickkristallisierten Schicht in das Grundmaterial gegenfiber der Diffusion von Arsen vernachl~issigt werden. Nach der Kontaktierung der Dioden und deren )ktzung wird die SperrschichtkapazitSt C des pn-i3berganges als Funktion der angelegten Sperrspannung Usp gemessen. Bei den verwendeten Arsenkonzentrationen zwischen 5.10tScm -3 und 5.1016 cm -3 l~isst sich die Erstreckung der Sperrschicht in die um mehr als zwei Zehnerpotenzen h6her dotierte Rfickkristallisationszone vernachl~issigen. Zur Berechnung des Konzentrationsverlaufes aus den gemessenen Werten C = C(Usp) l~isst sich deshalb die in (1) ver6ffentlichte Beziehung von SCHOTTKYin der Form 2 N(x~ =
dUsp
E" EO" q" F 2 d ( 1 / C 2)
(1)
Die Bestimmung des Diffusionskoeffizienten von A r s e n a n pn-t)-berg~ingen in G e r m a n i u m
mit
(Received 2 November 1961; in revised form 8 December
anwenden, wobei: x: Abstand vom pn-13bergang N¢x): Arsenkonzentration an der Stelle x F: Fl~iche des pn-fQberganges : Dielektrizit~itskonstante des Germaniums E0: Influenzkonstante q: Elementarladung.
1961) IM FOLGENDEN wird fiber die Diffusion von Arsen beim Legieren eines pn-Uberganges berichtet. Zur Untersuchung dieser Diffusion wird Indium auf eine Seite homogen arsendotierter, parallel zur (lll)-Ebene geschnittener Germaniumscheiben aufgebracht. Die Einlegierung des Indiums erfolgt zur Erzielung eines kristallografischen pn-~berganges durch langsames Aufheiz~.n gem~iss des Phasendiagrammes IndiumGermanium. Nach Erreichung der gewfinschten Maximaltemperatur wird um einige Grad Celsius abgekiihlt und so eine einige/zm dicke Rfickkristallisationszone geschaffen. Bei dieser Temperatur (580°C bzw. 650°C) werden die Dioden bis zu 20 Stunden mit einer Regelgenauigkeit von At~ ~< 1,5°C getempert. Durch Diffusion wird dabei eine Verflachung des abrupten Konzentrationssprunges der Arsenkonzentration NAs am * Operated with support from the U.S. Army, Navy and Air Force.
x = x~c) = F" ~" Eo" 1/C
(2)
Die in diese Beziehung eingehende Kapazit~it C stellt die reine, frequenzunabh~ingige Sperrschichtkapazit~it dar, die sehon von McAFEE und MITARBEITERN (2) z u r Messung von Diffusionen verwendet wurde. Eine Fehlmessung erfolgt, wenn durch die Wahl der Messparameter zus~itzliche Kapazit~iten erfasst werden. Bei Durchlass- und kleinen Sperrbelastungen des pn-I~berganges tritt als solche die temperaturund frequenzabh~ingige Injektionskapazit~it* sowie die Inversionskapazit~it auf. ~3-7) Zur Vermeidung dieser St6rkapazitSten werden die Dioden bei der Messung mit flfissigem Stickstoff gekfihlt. Die * Auch "Diffusionskapazit~it".
NOTES {100} facets in pulled crystals of InSb
(Received 13 November 1961)
considerably less than for {111) facets. An etched cross-section through a Se-doped crystal is shown in Fig. 2. The high concentration region at the center of the crystal, which appears as a bright spot, is seen to be essentially the same size as the {100) facet in the undoped crystal of Fig. 1. The high concentration regions at the outer edges correspond to the {111} facets of Fig. 1. Resistivity measurements on the doped crystals were made at room temperature with a 4-point probe (probe spacing = 0.2 mm) in an attempt to measure the concentration ratio R100 for Te and Se. In both Cases the resistivities inside and outside the facet region were the same within the error of measurement. From this result it appears that Rloo is less than 2, compared with values of 5-10 obtained for Rill. (2-4) The fact that (100} facets are smaller than {111} facets formed under the same growth conditions shows that the degree of supercooling required to nucleate crystal growth is less for the {100} plane than for the {111) plane. (The degree of supercooling necessary for nucleation appears to be even less for the {110) plane than for the (100) plane, since several ( l l0 )-oriented crystals were grown during the present series of experiments but no central {110) facets were observed.) Therefore the lateral propagation rate of growth steps should be smaller on (100) facets than on {111} facets. According to the model of crystal growth generally adopted to account for the facet phenomenon, (7) this difference in propagation rate would tend to make Rjoo less than Rl11, as has been observed. The {100) and {111} facets might also differ in the concentration of Se or Te atoms adsorbed at the interface between the crystal and a melt of given impurity concentration. Such a difference would also be expected to contribute to the observed difference between Rxoo and Rnl.
THE EFFECT of planar {111} facets at the solidliquid interface on the impurity distribution in crystals pulled from the melt was first reported by HULME and MULLIN,(1) who observed it in InSb. DmHOFF (2) independently observed the effect in Ge; and subsequently it has been studied in InSb by several workers. (3-6) For all cases studied except Ga in Ge, the impurity concentration inside the facet region (Con) is greater than the concentration outside it (Cott). The only previous report of a facet with orientation other than {111} was made b y HULME and MULLIN,(1) who observed a {100) facet on a heavily twinned Crystal of InSb. In .the present investigation, central (100) facets have been observed on a number of InSb single crystals grown in the <100) direction. A typical case is shown in Fig. 1, which depicts the bottom of an undoped crystal which was pulled abruptly from the melt in order to reveal the shape of the solidliquid interface. The bright circular region at the center of the crystal is the (100} facet, a portion of which is covered by the usual spike formed by solidification of liquid which adhered to the interface. Two large {111) facets are also seen at the outer edges of the crystal. The {100) facets which have been observed are much smaller than the central (111) facets which are formed on ( l l l ) - o r i e n t e d InSb crystals grown in the same crystal puller under the same growth conditions. For crystals 20-25 m m in diameter, typical diameters for the {100) facets and {111} facets are 2 - 3 r a m and 8-12ram, respectively. In order to determine the effect of {100) facets on impurity distribution, (100)-oriented crystals containing Te or Se concentrations of about 1018 cm -3 were grown from suitably doped melts. Etching these crystals with dilute CP-4 revealed Acknowledgements--It is a pleasure to acknowledge the that for both Te and Se Con is greater than Colt, assistance of R. L. MAcLEAN in growing the InSb but the concentration ratio (R = Con/Cott) is crystals and of MAaY C. FINN in etching them. The 97
NOTES
98
author is also grateful to Dr. H. C. GATOSfor valuable discussions. Lincoln Laboratory* A . J . STRAUSS Massachusetts Institute of Technology, Lexington, 73, Massachusetts References
1. K. F. HULMEand J. B. MULLIN,Phil. Mag. 4, 1286 (1959). 2. It. A. M. DmHOFF, Solid-State Electron. 1, 202 (1960). 3. I- B. MULLIN and K. F. HULME,J. Phys. Chem. Solids 17, 1 (1960). 4. W. P. ALLR~D and R. T. BATE, J. Electrochem. Soc. 108, 258 (1961). 5. A. I. STRAUSSand T. C. HARMAN, Semiconductor Symposium of the Electrochemical Society, October,
1960 (unpublished). 6. M. D. BANUS and H. C. GATOS, Semiconductor Symposium of the Electrochemical Society, October,
1961 (unpublished). 7. For example, see A. TRAINORand ]3. E. BARTLETT, Solid-State Electron. 2, 106 (1961).
pn-~3bergang erzielt, indem Arsen aus dem Germanium in die riickkristallisierte Zone eindiffundiert. Wie Versuche mit Indium reinst und Indium +0,5 % Gallium sowie der Vergleich Abb.l(a) und Abb. 2 ergeben, kann die Eindiffusion von Indium oder Gallium aus der rfickkristallisierten Schicht in das Grundmaterial gegenfiber der Diffusion von Arsen vernachl~issigt werden. Nach der Kontaktierung der Dioden und deren )ktzung wird die SperrschichtkapazitSt C des pn-i3berganges als Funktion der angelegten Sperrspannung Usp gemessen. Bei den verwendeten Arsenkonzentrationen zwischen 5.10tScm -3 und 5.1016 cm -3 l~isst sich die Erstreckung der Sperrschicht in die um mehr als zwei Zehnerpotenzen h6her dotierte Rfickkristallisationszone vernachl~issigen. Zur Berechnung des Konzentrationsverlaufes aus den gemessenen Werten C = C(Usp) l~isst sich deshalb die in (1) ver6ffentlichte Beziehung von SCHOTTKYin der Form 2 N(x~ =
dUsp
E" EO" q" F 2 d ( 1 / C 2)
(1)
Die Bestimmung des Diffusionskoeffizienten von A r s e n a n pn-t)-berg~ingen in G e r m a n i u m
mit
(Received 2 November 1961; in revised form 8 December
anwenden, wobei: x: Abstand vom pn-13bergang N¢x): Arsenkonzentration an der Stelle x F: Fl~iche des pn-fQberganges : Dielektrizit~itskonstante des Germaniums E0: Influenzkonstante q: Elementarladung.
1961) IM FOLGENDEN wird fiber die Diffusion von Arsen beim Legieren eines pn-Uberganges berichtet. Zur Untersuchung dieser Diffusion wird Indium auf eine Seite homogen arsendotierter, parallel zur (lll)-Ebene geschnittener Germaniumscheiben aufgebracht. Die Einlegierung des Indiums erfolgt zur Erzielung eines kristallografischen pn-~berganges durch langsames Aufheiz~.n gem~iss des Phasendiagrammes IndiumGermanium. Nach Erreichung der gewfinschten Maximaltemperatur wird um einige Grad Celsius abgekiihlt und so eine einige/zm dicke Rfickkristallisationszone geschaffen. Bei dieser Temperatur (580°C bzw. 650°C) werden die Dioden bis zu 20 Stunden mit einer Regelgenauigkeit von At~ ~< 1,5°C getempert. Durch Diffusion wird dabei eine Verflachung des abrupten Konzentrationssprunges der Arsenkonzentration NAs am * Operated with support from the U.S. Army, Navy and Air Force.
x = x~c) = F" ~" Eo" 1/C
(2)
Die in diese Beziehung eingehende Kapazit~it C stellt die reine, frequenzunabh~ingige Sperrschichtkapazit~it dar, die sehon von McAFEE und MITARBEITERN (2) z u r Messung von Diffusionen verwendet wurde. Eine Fehlmessung erfolgt, wenn durch die Wahl der Messparameter zus~itzliche Kapazit~iten erfasst werden. Bei Durchlass- und kleinen Sperrbelastungen des pn-I~berganges tritt als solche die temperaturund frequenzabh~ingige Injektionskapazit~it* sowie die Inversionskapazit~it auf. ~3-7) Zur Vermeidung dieser St6rkapazitSten werden die Dioden bei der Messung mit flfissigem Stickstoff gekfihlt. Die * Auch "Diffusionskapazit~it".