A semiconductor device package includes: (1) a carrier; (2) a sensor element disposed on or within the carrier; and (3) a cover including a top surface, a bottom surface and an inner sidewall, the inner sidewall defining a penetrating hole extending from the top surface to the bottom surface, and the penetrating hole exposing the sensor element. The semiconductor device package is characterized such that (i) the inner sidewall is divided into an upper portion and a lower portion, the upper portion is substantially perpendicular to the top surface, and the lower portion is tilted; or (ii) the entire inner sidewall is tilted. The lower portion of the inner sidewall or the entire inner sidewall is tilted at an angle of between about 10° to less than about 90°, relative to the top surface.