The Role of Inner And Internal Radiation on The Melt Growth of Sapphire Crystal

In this paper, for an inductively heated Czochralski furnace used to grow sapphire single crystal, influence of the inner (wall-to-wall) and crystal internal (bulk) radiation on the characteristics of the growth process such as temperature and flow fields, structure of heat transfer and crystal-melt interface has been studied numerically using the 2D quasi-steady state finite element method. The obtained results of global analysis demonstrate a strong dependence of thermal field, heat transport structure and crystal-melt interface on both types of radiative heat transfer within the growth furnace.

The well-defined and repeatable electrical properties of single-crystal sapphire make it an attractive substrate material for microstrip, but its dielectric anisotropy constitutes an important design complication. This paper describes investigations into the quasi-static characteristics of single microstrip lines on sapphire substrates cut with a specified orientation. To account for anisotropy, a new permittivity parameter epsilonreq is introduced, which is a function of the Iinewidth to substrate-height ratio W/h. The variation of epsilonreq with W/h is derived by finite-difference methods. Universal curves for microstrip on correctly orientated sapphire are presented, showing 1) Epsilonreq, 2)The low-frequency limit of effective microstrip permittivity epsilone0, and 3)The characteristic impedance of the line Z0, all as functions of W/h.


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