A differential pressure sensor device, comprising a multi-layer substrate comprising at least three sub-layers (211, 212, 213), the at least three sublayers comprising a top sub-layer and a bottom sub-layer; another layer formed on a main surface of the top sub-layer of the multi-layer substrate; an Application Specific Integrated Circuit, ASIC, formed over said other layer and a microelectromechanical system, MEMS,, formed over said other layer, wherein the MEMS is configured to output electrical signals indicative of pressure variations sensed by a membrane formed on or by a top surface of the MEMS to the ASIC and the ASIC is configured to process the electrical signals by amplification and/or analog-to-digital conversion and/or noise filtering; a housing formed on said other layer and housing the MEMS and the ASIC; a first cavity (C 1) formed by the MEMS and a second cavity (C 2) partially formed by the housing, said other layer and the membrane and wherein the first cavity (C 1) and the second cavity (C 2) are separated from each other by the membrane; wherein the first cavity (C 1) is in fluid communication with a channel via an inlet formed in the multi-layer substrate and wherein the channel is in fluid communication with a vent hole such that atmospheric pressure or a reference pressure can be built up in the first cavity (C 1) by gas entering through the vent hole, the channel and the inlet; and wherein the channel is formed in one of the plurality of sub-layers (211, 212, 213) of the multi-layer substrate between the top sub-layer and the bottom sub-layer and extends in a plane that is substantially parallel to the main surface of the top sub-layer of the substrate. a multi-layer substrate comprising at least three sub-layers (211, 212, 213), the at least three sublayers comprising a top sub-layer and a bottom sub-layer; another layer formed on a main surface of the top sub-layer of the multi-layer substrate; an Application Specific Integrated Circuit, ASIC, formed over said other layer and a microelectromechanical system, MEMS,, formed over said other layer, wherein the MEMS is configured to output electrical signals indicative of pressure variations sensed by a membrane formed on or by a top surface of the MEMS to the ASIC and the ASIC is configured to process the electrical signals by amplification and/or analog-to-digital conversion and/or noise filtering; a housing formed on said other layer and housing the MEMS and the ASIC; a first cavity (C 1) formed by the MEMS and a second cavity (C 2) partially formed by the housing, said other layer and the membrane and wherein the first cavity (C 1) and the second cavity (C 2) are separated from each other by the membrane; wherein the first cavity (C 1) is in fluid communication with a channel via an inlet formed in the multi-layer substrate and wherein the channel is in fluid communication with a vent hole such that atmospheric pressure or a reference pressure can be built up in the first cavity (C 1) by gas entering through the vent hole, the channel and the inlet; and wherein the channel is formed in one of the plurality of sub-layers (211, 212, 213) of the multi-layer substrate between the top sub-layer and the bottom sub-layer and extends in a plane that is substantially parallel to the main surface of the top sub-layer of the substrate.