Experimental Verification of the Numerical Model for a CaF2 Crystal Growth Process

Abstract

Large calcium fluoride (CaF2) single crystals are required for the fabrication of lenses in so‐called wafer‐steppers of future IC‐lithography technologies operating at 193 nm and 157 nm. Numerical simulation plays an important role to design an adequate growth setup and processing conditions for the growth of high quality crystals. An important issue is the consideration of the internal heat transfer by radiation in the semitransparent CaF2 during the crystal growth process. Results of the numerical modeling of the heat transport are presented, which are obtained by using the software package CrysVUn++ with different models considering the internal heat transport in CaF2. To improve the availability of experimental data on CaF2 bulk growth, an especially designed R&D‐facility was built. This growth system is equipped with a variety of in‐situ measurement systems to detect the temperature distributions in the crystal and melt region. Calculated temperature distributions are compared with experimental data. Also first results on single crystal growth will be reported.

Challenges in modeling of bulk crystal growth

“…(c) It is common to most publications about modeling of the internal radiative heat transfer, that mainly numerical studies are performed and no direct comparison to experiments is given because model experiments are missing. One exceptional case is the study of Molchanov et al [49,50], who carried out temperature measurements in the melt and the crystal during growth of CaF 2 . They showed that the Rosseland approximation using the data published by Vizman [33] is not adequate to accurately describe the measurements (see Fig.…”

Birefringence simulations of single crystals

“…The surface temperature of a crystal ingot are calculated by taking account of the heat radiation from a furnace for ingot annealing using a computer code such as CrysUV (Kurz et al, 1999;Molchanov et al, 2002). Then the temperature distribution in the crystal ingot is obtained by a transient heat conduction analysis using the finite element code MSC Marc (MSC Software, 2003).…”

Study of the oxygen incorporation during growth of large CaF2-crystals

“…A modified Bridgman-Stockbarger furnace is used in our laboratory to grow CaF 2 -crystals with a diameter and a cylindrical length of 150 mm [5,6]. The [1 1 1]-oriented seed crystal and the synthetic, high-purity CaF 2 starting material are put into graphite crucible and then positioned in the growth chamber.…”

“…also during flushing of the crucible. Thereby the pressure in the autoclave is monitored by a pressure gauge (5).…”