j. . . . . . . .
CRYSTAL G R O W T H
Journal of Crystal Growth 174 (1997) 182-186
Czochralski growth of Si- and Ge-rich SiGe single crystals N . V . A b r o s i m o v l'a'*, S.N. R o s s o l e n k o l'a, W . T h i e m e b, A. G e r h a r d t b, W . S c h r 6 d e r b alnstitute o[ Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russian Federation b Institute of Crystal Growth, Rudower Chaussee 6, D-12489 Berlin, Germany
Sil -xGex single crystals (0 < x < 0.15) with diameter up to 2 in were grown by conventional Czochralski technique. The method for the growth of Gel xSix crystals using continuous feeding the melt with a number of Si rods was developed and the Gel -xSix crystals (0 < x < 0.3) were grown. The growth process both Sil _~Gex and Gel ;,Six crystals was carried out using the automated control system based on the crystal weighing. The peculiarities of weight control at the stage of conical part formation are considered. PACS: 81.05.Hd; 81.10.Fq; 81.10.- h Keywords: SiGe; Czochralski technique; Automated control; Weight technique
The Czochralski (CZ) growth in the binary system Si Ge is sufficiently difficult because of the strong segregation of the components during the pulling process which leads, as a result, to constitutional supercooling in the melt near the front of crystallization. Constitutional supercooling is the main reason of the transition from monocrystalline to polycrystalline growth. But monocrystalline growth is possible under allowed pulling rates and thermal conditions. The allowed crystal pulling
* Corresponding author. 1present address: Institute of Crystal Growth, Rudower Chaussee 6, Geb. 18.46D-12489 Berlin, Germany.
rate depends on the melt composition and on the temperature gradient at the growth interface and can be evaluated by the Tiller criterion . Another problem of the growth of SiGe single crystals is the absence of adequate seed rods, which are necessary for the initialization of single crystalline growth from highly concentrated solutions. Mismatch of the lattices parameters at the seed melt interface and resulting mechanical stresses in the contact area may exclude monocrystalline growth. The problem of the initialization of the Sil_xGex single crystal growth may be solved by different ways. In the case of small concentration of Ge in the melt it is possible to begin the pulling with pure Si seed. After that the SiGe seeds prepared from these as-grown SiGe crystals are used for the growth of crystals with higher Ge concentration.
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N.V. Abrosimov et al. / Journal of C~stal Growth 174 (1997) 182-- 186
This step-by-step approach has been developed for pulling Sil ~Ge~ single crystals [2, 3]. It is more difficult to start the growth of highly concentrated Gel_~Si~ single crystals. The use of Ge seeds is practically impossible because the melting temperature of Ge is the least in the binary Si-Ge system. Further, the temperature gradient at the crystal-melt interface is not sufficient for preventing the seed melting. The application of pure Si seeds does not provide usually the growth of single crystals at the Ge side of the phase diagram , although the growth of small single crystals Gel-~Six (0 < x < 0.64) started with pure Si seeds  was reported recently. A method is known  in which one component is charged continuously into the melt during the pulling process. The quantity of the feeding component increases smoothly until the needed concentration is reached. Then the composition of the melt is kept up constant, and the homogeneous crystal of the solid solution is pulled. In the case of the Gel ~Si~ crystal growth this process has been realized by the authors of . At the very beginning a Ge crystal has been pulled. Then a polycrystalline GeSi rod is dipped into a small melt volume and the growing Ge crystal changes into a GeSi crystal with the same diameter and composition as the feeding GeSi rod. But the preparation of such a homogeneous polycrystalline GeSi feeding rod of the required composition is problematical. This paper reports the results of the CZ growth of large Sil_xGe~ and Gel_xSi~ single crystals. Our approach in Ge~_~Si~ crystal growth is based on the use of a Ge seed for starting the single crystalline growth of the Ge crystal followed by continuous feeding the melt with solid Si rods.
2. Experimental procedure Both Si 1- xGex and Ge 1_ xSix single crystals have been grown by the CZ technique using the same equipment with resistance heating. The main facilities of the equipment supplied with a weight sensor and flexible controlling software have been described in Ref. .
2.1. Growth of Sil-xGex and Gel-xSix single crystals Sil-xGex single crystals were grown by conventional CZ technique . Recently, the crystals with x = 0.15 and 2" in diameter were obtained. Fig. 1 shows one of the grown crystals. Continuous feeding the melt with a number of Si rods was used for the growth of Gel -xSix crystals with a Si content up to x = 0.30. The scheme of the process is represented in Fig. 2. The Si rods are installed in the immovable screen-holder symmetrically in relation to the pulling axis. This provides an axial symmetry of the temperature field in the melting zone and avoids the probability of the crystal back-melting which can appear because of the inclined front of crystallization if an asymmetry of the temperature field exists. The crystal growth begins with a Ge seed which is dipped in a pure Ge melt. When a neck is formed and the crystal begins to expand the melt surface is contacted with the Si rods. The movement upwards of the crucible with the melt gives the possibility to solve the Si rods continuously in the Ge melt. The rate of the crucible movement depends on the rods position in such a way that the silicon concentration gradient at the conical part of the crystal would be maintained approximately constant. When the calculated concentration of Si in the crystal is achieved, the equilibrium between the solved Si and the crystallizing Si component is settled. It is supposed that the Si rods begin to solve from the very beginning after their first contact with the surface of the Ge melt. The solving process of Si in the Ge and the GeSi melt was investigated earlier in detail experimentally . According to these results the relative movement of the rod or the plate immersed into the melt does not influence the rate of solving. But in our experiments it was found that under overheating about 30 K in relation to the liquidus temperature (corresponding to the melt composition) the solving of Si rods finishes totally in 10-15 min. after immersing them into the melt, without a relative movement between the rods and the melt. If such a movement between the rods and the melt exists the rate of silicon solving keeps constant. Fig. 3
N. V. Abrosimov et al. / Journal of Crystal Growth 174 (1997) 182-186
shows Si rods before and after the crystal growth process.
2.2. Automatization of the Si-Ge crystal 9rowth process
Fig. l. Sio.93Geo.07 single crystal grown with automatic diameter control.
crystal •rod holder feeding rods chamber melt crucible
Fig. 2. Scheme of the growth ofGe~ _~Six crystals with continuous feeding the Ge melt with solving Si rods.
The crystal growth process consists of several stages, namely, initial cone formation, pulling of the cylindrical part and reverse cone formation. Control strategies at these stages may be different. In the present paper weight control of the conical part formation is considered. In the case of crystal pulling in the binary system Si-Ge the expansion angle at the conical part must not be too large, because strong overcooling of the melt can lead with high probability to the destruction of the single crystal growth. So, it was necessary to expand the crystal from the neck under the small angle of the slope to the pulling axis. For the use of the crystal weight control at the stage of conical part formation it is necessary for each moment of time to define a program mass which is compared then with a real mass of the crystal and meniscus measured by the weight sensor. In Ref. 1-9] the calculation procedure of the program mass has been developed for the crystal profile defined by the dependence of the expansion angle a(r) on the current crystal radius r. In the present work the program mass is calculated for the profile defined by the dependence of the current crystal radius r(I) on the current length I. As known El0], the mass m measured by the weight sensor is calculated with taking into account the assumption of the planar front of crystallization as follows: t
m(t, r, ~) = 7tpe ~ r 2 V c dr + r~per2h(r, or) o
+ xpea2r cos(e + ~),
where pc, Ps are the densities of the melt and the crystal, respectively, Vc is the crystallization rate, h(r,~) is the meniscus height, a is the capillary constant and e is the growth angle. A full time derivative of Eq. (1) is calculated as follows: t
rh = m~ + m," ~: + m=~ Fig. 3. Si rods before (left) and after the crystal growth process.
= 7tpsrZVc + m'~Vc tg ~ + m',V~'/.
N.V. Abrosimov et al. / Journal o f Crystal Growth 174 (1997) 182 186
On the other hand, the full time derivative rh of the mass change is proportional to the rate /:/ of the melt level change in the crucible of the radius R: rh =
Generally, the radius of the crucible may be not constant along its length. The rate of crystallization depends on the pulling rates, the melt level and the meniscus height changes: V~ = V - / : / -
li = V - / : / - -
(h; tg ~ +
Using Eqs. (2)-(4) the expression for the program rate of the crystallization for the non-stationary growth should be found:
V = VI1 +
psr2 +(h,r p/R2 h'
mr' ~ ~prRZj tg ,~
rn,' .~ c~'~
m'r = r~pt(2rh + r2h'r + a 2 cos(e + :0), m'~ = rcp/(r2h'~ - a2r
sin(t; + ~)),
h',, h'~ are partial derivatives of the meniscus height over the crystal radius and the profile slope angle, respectively. They can be found by differentiating the approximate Tsivinski  or Johansen formulas . The program crystal length is found by the numerical integrating of Eq. 5. Then the current value of program mass must be calculated from the Eq. 1. The optimal conditions of the GeSi crystal expansion under a small angle of expansion (a < 20 °) was found. This provides the maintenance of the single-crystal growth at a durable time interval. The temperature of the crystallization increases with the increase of the Si concentration in Ge melt in accordance with the phase diagram of the Ge-Si system. Therefore, it is necessary to increase the heating power during the crystal growth. It was found that a small decrease of heating power leads to the formation of a dendrite net on the melt
Fig. 4. Gej _~Si~ crystal (GeSi-51) grown with the continuous feeding the Ge melt with Si rods.
surface and, as a result, to the transition into the polycrystalline growth. In the first experiments of the Gel-xSix crystal growth using the weight control a PID regulator  with limitation of the output signal was used. The same regulator using the second derivative control was applied to the processes of Sil -xGex crystal growth . Direct application of this method of control to the automated pulling the Gel_~Six crystals did not lead to positive results. To provide the automatic increase of the heating power during the whole process of the Gel_xSi~ crystal growth the application of a PID-regulator with asymmetrical control was used:
ifAP>0, ifAP < 0, k+,k_ ~(0, 1),
k+ and k_ are asymmetry coefficients of the positive and the negative semiwaves of the signal AP, respectively. The use of the asymmetrical control allows to avoid the oscillations of the heating power resulted from the anomalous change of the weight signal and, as a result, to decrease the deviations of the lateral surface of the expanding crystal. In the process of pulling the crystal shown in Fig. 4 these coefficients had the following values: k+ = 1, k_ =0.2.
N.V. Abrosimov et al. /Journal of Crystal Growth 174 (1997) 182 186
3. Summary and conclusions The CZ technique allowed the growth of Sil-xGex single crystals 2 in. in diameter with Ge content up to x = 0.15 and the growth of Gel _xSi~, crystals with x up to x = 0.3. Single crystalline growth of Gel _~Six crystals was observed up to the Si content x = 0.i. For the growth of the Ge, _xSi~,crystals the technique based on the continuous feeding the Ge melt with Si rods was developed. The choice of the movement rate of the Si rods allows to control the change of Si concentration in Gel-xSix crystals (Fig. 5). In the case of the crystal GeSi-45 growth the movement rate of rods was about 1.8 times higher then during the growth of the GeSi-51. One of the problems in the growth of Gel :,Six crystals is the absence of the model of Si transport to the solid-liquid interface during dissolution of Si rods. A delay up to some hours was observed between the first contact of Si rods with Ge melt and appearance of Si in the crystal. Therefore, to improve the growth process it is necessary to investi-
Si-Concentration [at%] A & A A &
12 10 ;,
8 6 4
4 5 Crystal-length [¢m]
Fig. 5. Longitudinal SJ distribution determined for two crystals
by the measurement of IR-transmission at the indirect absorption edge .
gate the mass transport in the system Si rodsmelt-crystal in dependence on the process parameters such as rotation rates of the crystal and the crucible, geometry of the crucible, volume of the melt, form and shape of the feeding rods.
Acknowledgements This work was carried out in the Institute of Crystal Growth, Berlin (Germany) under financial support of the European Commission in the frame MONOCHESS II project (JOU2-CT92-0140) and of the German Space Agency DARA (project 50WM9221).
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