A support structure for use with a semiconductor substrate in thinning, or backgrinding, thereof, as well as during post-thinning processing of the semiconductor substrate includes a portion that extends substantially along and around an outer periphery of the semiconductor substrate to impart the thinned semiconductor substrate with rigidity. The support structure may be configured as a ring or as a member that substantially covers an active surface of the semiconductor substrate and forms a protective structure over each semiconductor device carried by the active surface.