Jul 6, 2004 - A dislocation structure is studied in germanium single crystals grown in a regime of minimum temperature gradients at the crystallization front ...
Russian Physics Journal, Vol. 48, No. 4, 2005
DISLOCATION GENERATION IN DISLOCATION-FREE GERMANIUM Yu. M. Smirnov, I. A. Kaplunov, and A. B. Dolmatov
UDC 548.5
A dislocation structure is studied in germanium single crystals grown in a regime of minimum temperature gradients at the crystallization front and low supercooling. The investigations show that the distortion of the flat crystallization front arising during crystal droplet detachment in the completion growth stage results in the dislocation generation in the lower parts of dislocation-free single crystals. The dislocations are generated at the phase boundary and propagate in the thermoplasticity zone.
INTRODUCTION
Single-crystal germanium is widely used in opto- and microelectronics, infrared technology, nuclear and X-ray radiation detectors, and other devices owing to its unique combination of optical, electrical, and mechanical properties. For most applications it is required that the material used should be not only highly pure and doped to a certain level but also its crystal-lattice defects should have a minimum density. Among major defects having the most pronounced effect on the optical and electrical properties of single-crystal germanium grown from the melt are dislocations, low angle boundaries, and slip bands. In spite of a great number of works [1–9] dealing with the problems of generation, multiplication, and thermoactivated and frictional motion of dislocations, a theory of crystal growth with a predetermined defect distribution has yet to be elaborated. In this connection, of special interest are growth methods for single crystals with minimal dislocation densities. In [10], the possibility of growth of dislocation-free silicon single crystals is demonstrated, the work playing a key role in the development of these methods. The method discussed in [10] resulted in the minimization of the seed crystal effect on the generation of edge dislocations in dislocation-free silicon single crystals grown in the 〈111〉 direction. One of the growth methods for dislocation-free germanium single crystals is presented in [11]. Here ingot drawing from the melt in the 〈111〉 direction was performed at a very low (less than 300 К⋅m–1) temperature gradient at the crystallization front and supercooling of about 1–3 К. Dislocation-free single crystals up to 32 mm in diameter were grown. Howevevr, it was noted that dislocations may yet be generated in the lower part of dislocation-free single crystals. This work is aimed at examining the processes of growth of dislocation-free single-crystal germanium and studying the reasons for dislocation generation in these crystals.
EXPERIMENT AND RESULTS
Germanium single crystals were grown by the Czochralski technique using the dislocation-free regimes [11]. The crystals with a 〈111〉 crystallographic orientation were grown in a vacuum furnace. Undoped crystals were grown in the form of cylindrical ingots of 16–22 mm in diameter and 240–270 mm in length. Polycrystalline zone-purified GPZ germanium was used as an initial raw material. The length and cross-section dislocation distribution was studied in the grown ingots. The dislocation density was determined using a standard procedure of selective chemical etching. Investigations of the cross sections of the grown samples show that the crystals are mostly dislocation free starting from the upper cross section, where a conical part (corresponding to the seed crystal growth up to a preset diameter)
Tver’ State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 21–24, May, 2005. Original article submitted July 6, 2004. 460
1064-8887/05/4804-0460 ©2005 Springer Science+Business Media, Inc.
a
b
c
Fig. 1. The dislocation distribution in the lower part of a dislocation-free germanium single crystal at 5 (а), 15 (b), and 25 (c) mm from the crystallization front.
transforms to a cylindrical one, down to the cross-section 30-35 mm from the crystallization front. The dislocations are yet present in the lower parts of the ingots. The typical patterns of the dislocation distribution in the lower part of the ingot (in the cross sections at 5, 15, and 25 mm from the crystallization front) are shown in Fig. 1. The dislocation density in the periphery and center of the single crystal is about (4–8)⋅103 cm–2 at a distance of 5 mm from the crystallization front (crosssection a). The slip bands are observed in the [110] direction. A certain part of this cross-section area is dislocation-free. About a half of the cross-section area is dislocation-free at a distance of 15 mm from the crystallization front (cross-section b). The dislocations with an average density of 4⋅103 cm–2 as well as slip bands are observed in the rest of this cross-section. The total number of dislocations is less than 10 at a distance of 25 mm (cross-section c), that is, the single crystal is practically dislocation-free in this cross section. Nearly the same patterns of the lengh distribution in the ingot are also observed for other samples. Dislocation-free germanium single crystals exhibit special morphological features: a flat (111) face generally occupying the whole crystallization-front area and six narrow strips on the cylindrical lateral surface of the single crystal. The strips are the {110} faces which are not revealed in single crystals containing dislocations. These faces are easily observable during single-crystal growth, which allows a control of the adequacy of the growth process and assures growth of a dislocation-free single crystal. An analysis of the formation of flat face on the crystallization front shows the following. The (111) face can arise on the crystallization front at different temperature gradients. Its size (the area of the face) decreases, while the dislocation density increases with increase in the temperature gradient. Once the (111) face occupies the whole crystallization front, no dislocations are generated during growth. The flat faces at the crystallization fronts of dislocation-free (а) and dislocationcontaining (b) single crystals are shown in Fig. 2. Figure 3 shows an experimental dependence of the (111) face diameter on the temperature gradient at the crystallization front. It is evident that a decrease in the temperature gradient leads to an increase in the diameter of the flat face formed on the whole surface of the crystallization front, that is, to an increase in the diameter of the dislocation-free single crystal. However, it is rather difficult to maintain exactly the required supercooling of the melt in the case where the temperature gradient is lower than 200 К⋅m–1. In this work, we succeeded in stable growing of dislocation-free germanium single crystals of 30-32 mm in diameter. The temperature distribution along the generatrix of a growing single crystal was measured to elucidate the reasons for dislocation generation in the lower part of the dislocation-free ingots. We have found that a dislocation-free single crystal transforms into a dislocation-containing one at temperatures above 820–870 К, that is, in the germanium thermoplasticity range. Taking into account the presence and stability of the flat crystallization front, the dislocation generation in the lower part of the single crystal can be explained in the following way. In the case where the crystal is grown by the Czochralski technique, a portion of the melt remaining at the crystallization front at rapid single crystal detachment coalesces into the so called “drop”. As a result, the temperature gradient ∆Т occurs leading to a certain temperature 461
a
b
mm
Fig. 2. Flat (111) faces at the crystallization fronts of dislocation-free (the face occupies the whole surface of the crystallization front) (а) and dislocation-containing (the flat face occupies a part of the surface) (b) germanium single crystals.
m
Fig. 3. The dependence of the face diameter d on the temperature gradient ∇T at the crystallization front of dislocation-free germanium single crystals.
deformation. The thermoelastic stresses arise in a nonuniform temperature-deformation field. The experimental values of the critical stresses σcr, at which the dislocations are generated in materials, are conventionally used as a criterion for the maximum permissible thermal stress, above which the dislocations are generated in the growing single crystal. For germanium, the values of σcr extrapolated to the melting temperature are (15–20)×104 Pa [12]. The critical stresses relax if dislocations are generated and propagate to the boundary of the thermoplasticity zone in the lower part of the crystal adjacent to the crystallization front. It should be also taken into account that an anomalously sharp decrease in the activation energy of motion of individual dislocations can be observed in the vicinity of the melting temperature [13]. The length of the crystal part (coincident with the thermoplasticity zone), where the dislocations are present, is estimated to be 5-40 mm, which is in good agreement with experiment. Figure 4 demonstrates the dislocation-density distribution along the length of the germanium single crystal grown using a conventional “dislocation” regime (the ingot diameter was 30 mm) for comparison with the dislocation-free crystals. It is seen that the dislocation density Nd sharply increases (by about one order of magnitude) in the lower part of the crystal. 462
–4
Nd ⋅10 , cm
–2
6
4
2
0
50
100
150
200
h, mm
Fig. 4. The distribution of the dislocation density Nd along the length h of the germanium single crystal containing dislocations. The ingot diameter is 30 mm.
The length of the region with the high Nd (∼50 mm) is also close to that of the thermoplasticity zone in the dislocation-free samples. Thus, in this case, additional critical stresses arising during the detachment of crystal from the melt make their contribution to the increase in dislocation density in the part of the crystal, which is adjacent to the crystallization front. It should be noted that no increase in the dislocation density is observed for dislocation-free silicon at thermal shock [14], which seems to be due to higher values of σcr in silicon ((60–150)⋅104 Pa) as compared to those in germanium. CONCLUSION
A decrease in the temperature gradient and melt supercooling during growth of dislocation-free germanium single crystals results in an increase in the diameter of the flat (111) face over the whole area of the crystallization front, that is, in an increase in the ingot diameter. The applicability of the dislocation-free crystal growth method in a regime of minimal temperature gradient at the crystallization front and low supercooling depends on the technological possibilities to maintain the preset temperature parameters. The crystal detachment from the melt in the completion growth stage results in the dislocation generation in the lower parts of dislocation-free single crystals. The dislocations are generated due to the distortion of the crystallization front by a solidifying drop and propagate within the thermoplasticity zone. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
N. Van den Bogaert and E. Dupret, J. Cryst. Growth, 171, 77–93 (1997). D. L. Li, T. Volkmann, K. Eckler, and D. M. Herlach, J. Cryst. Growth, 152, 101–104 (1995). R. M. Keyser, T. R. Tworney, and P. Sangsingkeow, J. Radioan. Nucl. Chemistry, 244, 641–647 (2000). V. B. Shikin and Yu. V. Shikina, Uspekhi Fiz., 38, No. 8, 845–876 (1995). I. A. Kaplunov and A. I. Kolesnikov, Poverhnost’, No. 2, 14–19 (2002). S. Gan, L. Li, and R. F. Hicks, Appl. Phys. Lett., 73, Nо. 8, 1068–1070 (1998). M. G. Mil’vidskii and V. B. Osvenskii, Structural Defects in Semiconductors, Metallurgiya, Moscow, 1984. I. A. Kaplunov and A. I. Kolesnikov, Kristallografiya, 49, No. 2, 234–238 (2004). Yu. L. Iunin and V. I. Nikitenko, Scripta Materialia, 45, 1239–1246 (2001). R. K. Bagai and W. N. Borle, Progr. Cryst. Growth Charact., 6, 25–46 (1983). Yu. M. Smirnov, Non-Ferrous Metals, No. 5, 48–49 (1977).
463
12. 13. 14.
464
M. G. Mil’vidskii, Semiconductor Materials in Modern Electronics, Nauka, Moscow, 1986. B. Ya. Farber, I. E. Bondarenko, and V. I. Nikitenko, Fiz. Tverd. Tela, 23, 2192–2194 (1981). S. S. Gorelik and M. Ya. Dashevskii, Semiconductor and Dielectric Materials Science, Metallurgiya, Moscow, 1988.
