Reducing size variations in funnel nozzles

A process for making a nozzle, the process comprising:

• forming a first opening having a first width in a top layer of a substrate, wherein the substrate includes the top layer and an underlying second layer of different material than the top layer;
• forming a patterned layer on a top surface of the substrate so that the patterned layer is on top of the top layer of the substrate, the patterned layer including a second opening spanning the first opening in the top layer, the second opening having a second width larger than the first width;
• reflowing the patterned layer to form curved side surfaces terminating on the top surface of the substrate;
• etching a second layer of the substrate through the first opening in the top layer of the substrate to form a straight-walled recess in the second layer with outer edges of the first opening in the top layer defining a boundary of the straight-walled recess, the straight-walled recess having the first width, a bottom surface, and a side surface substantially perpendicular to the top surface of the substrate;
• and
• after the straight-walled recess is formed, etching the curved side surface of the patterned layer, the top layer of the substrate, and the second layer of the substrate while interior surfaces of the straight-walled recess are exposed to the etch, where the etching transforms the straight-walled recess into a funnel-shaped recess, the funnel-shaped recess includes a curved sidewall gradually smoothly joining a straight-walled lower portion of the recess or terminating on the bottom surface,
• wherein the first opening in the patterned layer has a circular cross-sectional shape in a plane parallel to the exposed top surface of the patterned layer.

A process for making a nozzle, the process comprising:

• forming a first opening having a first width in a top layer of a substrate, wherein the substrate includes the top layer and an underlying second layer of different material than the top layer;
• forming a patterned layer on a top surface of the substrate so that the patterned layer is on top of the top layer of the substrate, the patterned layer including a second opening spanning the first opening in the top layer, the second opening having a second width larger than the first width;
• reflowing the patterned layer to form curved side surfaces terminating on the top surface of the substrate;
• etching a second layer of the substrate through the first opening in the top layer of the substrate to form a straight-walled recess in the second layer with outer edges of the first opening in the top layer defining a boundary of the straight-walled recess, the straight-walled recess having the first width, a bottom surface, and a side surface substantially perpendicular to the top surface of the substrate;
• and
• after the straight-walled recess is formed, etching the curved side surface of the patterned layer, the top layer of the substrate, and the second layer of the substrate while interior surfaces of the straight-walled recess are exposed to the etch, where the etching transforms the straight-walled recess into a funnel-shaped recess, the funnel-shaped recess includes a curved sidewall gradually smoothly joining a straight-walled lower portion of the recess or terminating on the bottom surface,
• wherein the funnel-shaped recess has a circular cross-sectional shape in a plane parallel to the top surface of the substrate.