Rate limits in silicon sheet growth: The connections between vertical and horizontal methods

Abstract

Meniscus-defined techniques for the growth of thin silicon sheets fall into two categories: vertical and horizontal growth. The interactions of the temperature field and the crystal shape are analyzed for both methods using two-dimensional finite-element models which include heat transfer and capillarity. Heat transfer in vertical growth systems is dominated by conduction in the melt and the crystal, with almost flat melt/crystal interfaces that are perpendicular to the direction of growth. The high axial temperature gradients characteristic of vertical growth lead to high thermal stresses. The maximum growth rate is also limited by capillarity which can restrict the conduction of heat from the melt into the crystal. In horizontal growth the melt/crystal interface stretches across the surface of the melt pool many times the crystal thickness, and low growth rates are achievable with careful temperature control. With a moderate axial temperature gradient in the sheet a substantial portion of the latent heat conducts along the sheet and the surface of the melt pool becomes supercooled, leading to dendritic growth. The thermal supercooling is surpressed by lowering the axial gradient in the crystal; this configuration is the most desirable for the growth of high quality crystals. An expression derived from scaling analysis relating the growth rate and the crucible temperature is shown to be reliable for horizontal growth.