It has been shown previously that the presence of ultrasound parallel to the pulling axis in the melt decreased growth striations in semiconductor single crystals grown by the Czochralski method. The effect of ultrasound on striations, which decrease in number and disappear in the central part of InSb, GaAs, Bi_xSb_1-x and Ga_xIn_1-xSb solid solutions pulled single crystals, was studied and reported in several publications of our group [1-4]. We showed experimentally that ultrasonic waves at frequencies from 0.15 to 5 MHz can be used for damping of convection in the melt during crystal growth. The damping of convection is attributed to forming of ultrasonic standing waves under the sold-liquid (S/L) interface. However, the behavior of convective flow under the effect of ultrasound was not studied.

In the present study, we modeled convection at the growth conditions of small Ga_xIn_1-xSb and large Si single crystals. The flow simulation for Ga_xIn_1-xSb and Si melts was conducted for quasi-steady conditions, when Raleigh number was less than 10⁵. For these conditions applied to Ga_0.03In_0.97Sb and Si single crystals, the growth parameters have the values listed in Table 1.

Table 1. Parameters of the growth crystals

The radial and axial distributions of flow in Ga_xIn_1-xSb and silicon melts were calculated. The radial velocity distribution of flow increases from the center to R_c/2 in both crucibles, and then decreases. The maximum velocity of axial flow was under the S/L interface at the axis of the crucibles. However, summary values of the radial and axial flow velocities had maximum values under the S/L interface near periphery of the crystals. The maximum velocities were 0.9 cm/s and 28 cm/s for Ga_xIn_1‑xSb and silicon melts, respectively.

The maximum calculated flow velocity was used for the calculation of the force F_c acting on Si particles in the melt. Particles of 5 nm radius and different mass for these melts were accepted for our calculations. Then, the maximal force F_C acting on the particle in convective flow was 3∙10^-21 N and 1.2∙10^-21 N for Ga_xIn_1-xSb and Si melts, respectively.

It is established that introduction of ultrasound into the liquid forms a standing wave channel under the S/L interface. The force F_US acting on the melt particle in ultrasonic standing waves was calculated according to the equation in [4]. The ultrasonic field parameters for a given system were selected at frequencies of 0.1 – 4.0 MHz. The force F_US increases with increase of the frequency in Ga_xIn_1-xSb and Si melts from 1∙10^-20 N to 7∙10^-19 N and 6.3∙10^-23 N to 4.0×10^-18 N, respectively.

The results of these calculations have shown that the ultrasound at frequencies over 0.1 MHz can be used for reduction of striations in pulled Ga_xIn_1-xSb single crystals, since the force F_US is larger than the convective force F_C by a factor of 3 – 600 in this melt. However, for striation-free Si single crystals, the ultrasound frequencies must be larger than 0.5 MHz, according to our calculations.

Therefore, we believe that ultrasound at a high frequency can be used for reduction of convection in Czochralski growth of Ga_xIn_1-xSb solid solutions and Si single crystals. The strong reduction of flow motion is associated with the formation of a standing wave channel between the S/L interface and the crucible bottom. This modeling has shown the potential of using ultrasound to damp convection in the melt and decrease striations in semiconductor single crystals. 

References

[1] G.N. Kozhemyakin,V.G. Kosushkin, S.Y. Kurochkin, J. Crystal Growth. 121, 240 (1992).

[2] G.N. Kozhemyakin,L.G. Kolodyazhnaya, J. Crystal Growth. 147, 200 (1995).

[3] G.N. Kozhemyakin, J. Crystal Growth. 149, 266 (1995).

[4] G.N. Kozhemyakin, J. Crystal Growth. 257, 237 (2003).  

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/28798 must be provided.

1. Formation of nanocrystals in Bi_0.9Sb_0.1 amorphous alloy
2. Features of semiconductor crystal growth in ultrasonic fields by Czochralski method