Well, in both cases a path is added, the visible differences are:
1- When internal connection is selected this path is metal1, for external connection is metal2 with vias to metal 1, and
2- For internal connection this path is always under one of the inductor ports, while for external connection its orientation can be selected
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This is taken from IBM’s doc, where explicitly suggests that shield must be connected to one port, specifically to the center:
“In many applications for integrated inductors, one end of the spiral will be at AC ground potential. When using the M1 groundplane inductor in an application of this type, it is suggested that the center of the spiral be placed at AC ground with the same connection that is used to ground the M1 groundplane”.
And is also added:
“If external connection is removed, the M1 groundplane’s central M1 connection should be connected directly to the innermost turn of the spiral through a low impedance via array”.
Now the same initial question, where to put this via array? Inside the inductor?