Modeling for the Laser Materials
Practical applications of modeling in YAG growth:
- Hot zone optimization to reduce energy costs
- Control of faceting
- Doping uniformity
- Cracking of large crystals and residual stress
Modeling can be used to obtain information on temperature distribution and thermal fluxes throughout the hot zone. Thus, it can be used to investigate the effect of furnace modifications such as the shape of the crucible, thermal shields or position of the inductor coils on the the thermal profile. For prediction of more subtle effects such as the shape of crystallization front it is crucial to have accurate account of radiant heat inside the crystal. The following models are deployed inside the transparent crystal:
- Multi-band heat absorption to account for wavelength dependent optical properties;
- Internal reflection in the crystal;
- Refraction at the crystal/gas interface;
Since CGSim has detailed heat transfer modeling in place, it can be used to study the effect of furnace design and recipe on the shape of melt-crystal interface. In software it will be defined by local temperature gradients: balance of heating by the circulating melt and heat removal through the crystal body. Both heating and cooling depend on the furnace design and melt convection. Convection, in turn, will be governed by thermal fields, crystal rotation and pulling rates.
Example of modeling as an instrument for analysis of hot zone design: thermal fluxes visualized as vectors help with detection of thermal losses and finding ways of furnace optimization
Modeling can be applied to address faceting and increase the amount of harvestable material. Models of convection are accurate enough to study the balance of rotation-driven forces and buoyancy in the melt, such as, the domain inversion and associated changes in faceting. This allows to mitigate the negative effects of faceting by either adjusting the recipe aiming for a narrower defect core or by favoring the alternative scenario when the facets are pushed to the crystal periphery. Finally, extending he same capabilities, it is possible to account for the effect of faceting on the radial uniformity of dopant distribution.
Combination of predictive strength with total data accessibility makes modeling a good tool for designing the cooling process. At each time step, you can calculate expected stress and then examine the stress distribution throughout the crystal in terms of reaching critical values that would pose the risk of cracking and adjust the ramp-down schedule to avoid it. The same modeling results will provide information on the residual stress upon the cooling completion. Also, models used in CGSim enable prediction of dislocation behavior. Working with the software allows the user to develop a successful cooling regime that would reasonably satisfy these three criteria (risk of cracking, residual stress, dislocation density) in the shortest possible cooling time.