A stack of semiconductor layers (310) forms a re-emitting semiconductor construction (RSC). The stack (310) includes an active region (316) that converts light at a first wavelength to light at a second wavelength, the active region (316) including at least one potential well. The stack (310) also includes an inactive region (318) extending from an outer surface of the stack to the active region. Depressions (326) are formed in the stack (310) that extend from the outer surface into the inactive region (318). An average depression depth is at least 50% of a thickness of the inactive region. Alternatively, the average depression depth is at least 50% of a nearest potential well distance. Still other alternative characterizations of the depressions (326) are also disclosed. The depressions (326) may have at least a 40% packing density in plan view. The depressions (326) may also have a substantial portion of their projected surface area associated with obliquely inclined surfaces.