Modeling of the angular distribution of the emitted molecular flux from a cylindrical nozzle in a free molecular flow

In the linear source of a thermal evaporation system, the thickness of the deposited molecules depends on the angular distribution of the emitted molecular flux from the nozzle. According to Knudsen in 1907, for a cylindrical nozzle, the angular distribution of the emitted molecular flux can be expressed in the form of cos(n)(theta). The actual angular distribution, however, does not precisely match the form of cos(n)(theta) by Knudsen. Therefore, various theoretical methods have been studied in an effort to express the angular distribution of the emitted molecular flux mathematically. Using these conventional methods can allow one to determine the accurate angular distribution of the emitted molecular flux, but the same calculation should be repeated whenever the shape of the nozzle changes, as the angular distribution acquired by these methods is not an "analytical solution" but a "numerical solution." In this paper, an analytical model of the accurate angular distribution determined via an approximation method is proposed to make the nozzle array optimization processes of linear sources faster and more accurate for a cylindrical nozzle. The model is verified through a comparison involving the direct simulation Monte Carlo method and an experiment with a point evaporation source.