Existence and static stability of the meniscus in horizontal ribbon growth

• We develop an analytical model to find the hydrostatically feasible configurations in the horizontal ribbon growth process.
• We find an analytical solution to the governing Young–Laplace equation for the HRG process.
• Theoretical solution matches the computer results previously reported in the literature.
• Analytical solution gives the relationship between the melt level and the shape of the meniscus.
• We prove that the meniscus shapes described by the analytical solution are statically stable.

We present existence and stability conditions of the meniscus in the horizontal ribbon growth process. Assuming that the existence of the meniscus is defined by capillarity, we determine analytically the shape of the meniscus and an explicit expression for the equilibrium height. We then calculate the stability of the feasible curves using a variational approach, as well as the conditions under which the meniscus remained pinned to the corner of the crucible. We find that the single-valued curves describing the menisci are stable with respect to weak variations, and that for a given ribbon geometry, the existence of the meniscus depends on the use of operating parameters (such as the pulling angle and the melt height) that enhances the conditions under which the meniscus stays pinned to the corner of the crucible. The hydrostatically feasible configurations place a part or the entire meniscus above the melt level.