Numerical modelling of Czochralski growth of quadratic silicon crystals by means of a travelling magnetic field

Abstract

We present 3D simulations of melt flow in a Czochralski process of Si single crystal growth with a travelling magnetic field (TMF). The choice of the TMF significantly influences the thermal field in the melt. Using a downwards TMF field the induced convection causes a thermal field with a low radial component of the temperature gradient along the melt surface and a high vertical component below the crystal. Such a thermal field allows the kinetics‐based creation of {110} side facets, which was proven in several experimental runs. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Growth of square Si single bulk crystals with large side-face widths using noncontact crucible method

“…Therefore, to obtain large square Si single bulk crystals with a large side-face width, it is important to develop a technology to maintain a small radial temperature gradient near the growth interface even when the supercooling in the melt increases. This concept appears to be consistent with that of Miller et al 13) In the present method, the radial temperature gradient near the growing interface is proportional to ¦T in . Therefore, to obtain large square Si single bulk crystals with a large side-face width, it is important to keep ¦T in small even when the low-temperature region becomes larger.…”

“…It was reported that the supercooling of the Si melt in the radial direction of an ingot and a low radial temperature gradient are important factors in obtaining Si single bulk crystals with a square top face. [10][11][12][13] The size of the square face is determined by the side-face width of the four-cornered pattern on the top surface of the ingot. Figure 6 shows the side-face widths (cm) of several bulk crystals grown by the present method as a function of 1/¦T in (K ¹1 ).…”

“…This value is comparable to previously reported values. [10][11][12][13] For circular ingots with a smaller side-face width, the radial temperature gradient was estimated to be 3-4 K/cm.…”

“…The growth of square or rectangular Si single crystals by the CZ method and the floating zone (FZ) method 8) has been reported by several researchers. [9][10][11][12][13] Rudolph and coworkers prepared rectangular Si single bulk crystals using a traveling magnetic field (TMF) to stabilize the radial temperature gradient in the Si melt. 11,12) To obtain a large square single bulk crystal for solar cell applications, the side-face width of the four-cornered pattern 12) appearing on the top surface of ingots should be much larger.…”

“…10) Miller et al used numerical modeling to report that a small radial temperature gradient near the melt surface and a large vertical temperature gradient below the crystals are both important for the growth of square crystals by forming f110g faces. 13) Rudolph and coworkers used a TMF to obtain a small radial temperature gradient for the growth of Si bulk crystals with a quadratic cross section, and they obtained an ingot with a maximum area of 9.1 © 9.1 cm 2 and a side-face width of 5.6 cm. 11,12) This side-face width was not large enough to obtain significantly larger ingots with a square shape, even though a 15 cm fused silica crucible and 2 kg of Si feedstock were used for their growth.…”