Crystal Growth and Evaluation of Silicon for VLSI and ULSI

79Different Techniques for Growing Single-Crystal Silicon

the body growth play a key role in the device yield [77]. It is this part of the crystal that is

used for device fabrication.

Transport phenomena within the melt are important, as they affect the quality of the

crystal. Momentum, energy, and mass transfer have been considered in the vicinity of the

crystal—in other words, in the meniscus below the crystal. Driving forces due to buoy-

ancy, crystal rotation, and thermocapillary effects have been included. Estimation of the

nondimensional parameters involved reveals that the surface tension gradient and crys-

tal rotations are important for the growth of silicon crystals. For pure thermocapillary

ow with large Peclet number (Marangoni num ...