Thermal effusion source modeling for control in molecular beam epitaxy applications

A comprehensive model is derived to describe the flux received by a substrate through a molecular beam produced in conical or cylindrical thermal effusion sources with a free evaporating surface. The model appropriately describes the dependence of the flux to the melt height and temperature. Improved computational efficiency is obtained by the introduction of analytical solutions to the integrals that have been previously solved by numerical methods, and by the adoption of a table look-up and interpolation method for calculating fluxes at any melt-height and temperature. The entries of the look-up table are calculated only once for a given crucible geometry using a finite number of reference melt heights. Fast flux calculations are then possible, permitting the utilization of the model in real-time control applications. The model is illustrated with a conical crucible source. The results are generic for any material and only depend on the geometry of the crucible and the orientation of the substrate with respect to the source.