A wedge-shaped contact region can be employed to provide electrical contacts to multiple electrically conductive layers in a three-dimensional device structure. A cavity including a generally wedge-shaped region and a primary region is formed in a dielectric matrix layer over a support structure. An alternating stack of insulating layers and electrically conductive layers is formed by a series of conformal deposition processes in the cavity and over the dielectric matrix layer. The alternating stack can be planarized employing the top surface of the dielectric matrix layer as a stopping layer. A tip portion of each electrically conductive layer within remaining portions of the alternating stack is laterally offset from the tip of the generally wedge-shaped region by a respective lateral offset distance along a lateral protrusion direction. Contact via structures can be formed on the tip portions of the electrically conductive layers to provide electrical contact.