Modeling and laboratory scale proof of concept of the horizontal ribbon growth process: Application to silicon wafer manufacturing
In this work we focus on the development of the Horizontal Ribbon Growth technique to produce highly pure silicon wafers for use in solar cells. We divide this preliminary work in two parts: a small scale experiment and the development of mathematical models to describe the crystallization phenomena. We begin by constructing a laboratory scale experiment to demonstrate the HRG concept using water as the working fluid. We made use of the fact that ice floats on water just like silicon would float on top of its melt. Therefore it is possible to conveniently test and analyze the operability of this technique. We find that the initial seeding process needs to be carefully controlled in order to extract a uniform wafer. Appropriate surface cooling and wall heating are necessary to guarantee the continuous formation of an ice film. We then develop simple mathematical models to predict the crystallization rate and thermal profiles of the system. We state that the driving force for crystallization is convective cooling and the film grows in one direction (downwards). Finally we propose how to validate the model using experimental data and how to extend the work to grow silicon ribbons.
Modeling and Analysis of Novel Horizontal Ribbon Growth of Silicon Crystal
We present a novel horizontal ribbon growth (HRG) process and a theoretical analysis of this method. Assuming that the existence of the meniscus is defined by diffuse growth, we determine analytically the thickness and height of the meniscus and an explicit expression for the performance of meniscus under different conditions. We then calculate the thermal profile in melt part, as well as the conditions under which the undercooling is sufficient around the solidification point. We find that diffuse growth is more sensitive to small initial thickness, and find the minimum length of the melt part to obtain undercooling. Finally, we calculate the change rule of solidification position by a variational approach, as well as the stability of the process under different conditions. We also give an expression to the instability of past HRG methods.
Theoretical analysis of heat flow in horizontal ribbon growth from a melt
A theoretical heat flow analysis for horizontal ribbon growth is presented. Equations are derived relating pull speed, ribbon thickness, thermal gradient in the melt, and melt temperature for limiting cases of heat removal by radiation only and isothermal heat removal from the solid surface over the melt. Geometrical cross sections of the growth zone are shown to be triangular and nearly parabolic for the two respective cases. Theoretical pull speed for silicon ribbon 0.01 cm thick, where the loss of latent heat of fusion is by radiation to ambient temperature (300 K) only, is shown to be 1 cm/sec for horizontal growth extending 2 cm over the melt and with no heat conduction either to or from the melt. Further enhancement of ribbon growth rate by placing cooling blocks adjacent to the top surface is shown to be theoretically possible.