A microphone sensing element and a method for making the same are disclosed. The sensing element has a diaphragm and an attached electrical lead-out arm preferably made of polysilicon that are separated by an air gap from an underlying backplate region created on a conductive silicon substrate. The backplate region has acoustic holes created by removing an oxide filling in a continuous trench that surrounds hole edges and by removing oxide to form the air gap. The diaphragm is softly constrained along its edge by an elastic element that connects to a surrounding rigid polysilicon layer. The elastic element is typically a polymer such as parylene having a Young's modulus substantially less than that of the diaphragm. First and second electrodes are connected to the diaphragm through the lead-out arm and to the substrate through polysilicon via fillings, respectively, and thereby establish a variable capacitor circuit for acoustic sensing.