A multi-grooved interposer includes an interposer substrate containing multiple parallel grooves laterally extending along a first direction and laterally spaced among one another along a second direction, and multiple conductive strips. The multiple parallel grooves are recessed from front side surfaces of the multi-grooved interposer in a third direction toward a back side surface of the multi-grooved interposer. The multiple conductive strips continuously extend across recessed surfaces in the multiple parallel grooves and the front side surfaces along the second direction with an undulating surface profile to provide electrically conductive paths across the multiple parallel grooves. Each of the multiple parallel grooves is configured to receive an edge of a respective semiconductor chip.