Step coverage in contacts may be improved by forming a tapered hole through a dielectric layer by:a) plasma (RIE) etching through a "contact" mask the dielectric for a depth shorter than the thickness of the layer leaving a residual thickness of dielectric on the bottom of the etch;b) removing the residual masking material;c) conformally depositing a TEOS layer;d) etching the conformally deposited TEOS layer without a mask in (RIE) plasma until exposing the underlying silicon or polysilicon with which the contact must be established.The anisotropic etching of the TEOS layer, conformally deposited on the partially pre-etched dielectric layer, determines a "self-aligned" exposition of the underlying silicon or polysilicon and leaves a tapered TEOS residue on the vertical pre-etched hole's walls, thus providing a desired tapering of the contact hole. Photolithographic definition is no longer a critical factor.