Case 14: Lift-off Coater with Planets

Coaters for the lift-off process in semiconductor fabrication must meet a unique requirement - the vapor incident angle on the wafer must be kept within a few degrees. 

      One well-known design features a planetary rotation of spherical wafer carriers. To meet the restriction on the vapor incident angle the source is typically located at the center of the sphere, of which the wafer carriers are geometric parts. 

      In this example we analyze a model coater based on a sphere with a 100-cm radius, as shown in the diagram below. This sphere can accommodate three planetary segments, each of which measures 86.6 cm across and rotates on an axis that makes an 30-degree angle with the orbiting axis.  

      We first compute for the thickness distribution on the dome segment, omitting a center part. As shown in the result panel below, the coating is significantly thicker near the center with an overall nonuniformity of 6.9%.The thickness displayed is in unit of "nanometer per gram of source material evaporated," assuming the source material is gold with a density of 19.3 grams/cubic-centimeter. The material collection is 56.5%. 

      Note that the incident-angle histograms show that the vapor strikes the dome with zero incident angle at all points, as it should. 
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      To reduce the thickness nonuniformity we may introduce correction masks into the chamber. For convenience we install three masks at different azimuth angles and in a plane 51 cm above the source. (As the source is located at the center of the sphere, the angular locations of the masks can be arbitrary.) Through a mask-fitting process, manually first followed by the automated optimization, we obtained the mask shape shown in the mask panel below. 

      With the masks, the thickness nonuniformity is reduced to 0.94%, and the material collection is 47.4%, a considerable decrease. 
      Please note that the masks set is optimized for the planetary motion specifically. If we assume the vapor plume is isotropic with regard to the azimuth angle, in the absence of masks, it should make no difference if the wafer carriers make orbiting revolutions at all because the source is located at the center of the spherical surface. 

      Allowed by the planetary motion is the use of stationary correction mask(s) to reduce the thickness at the centers of the spherical segments, where wafers may be placed. In addition, the orbital  rotation is helpful when the source is non-ideal. The correction masks presented here are not reusable if the orbit rotation is stopped. 
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