A differential pressure sensor device , comprising a multi-layer substrate comprising at least three sub-layers , 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 (M) 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 (M) and wherein the first cavity (C 1 ) and the second cavity (C 2 ) are separated from each other by the membrane (M); 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 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 , 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 (M) 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 (M) and wherein the first cavity (C 1 ) and the second cavity (C 2 ) are separated from each other by the membrane (M); 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 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 . <EOS>