A method for manufacturing a fingerprint sensor device. The method comprises providing a fingerprint sensor chip, arranging the fingerprint sensor chip on a carrier, depositing a cover layer on the fingerprint sensor chip, the cover layer comprising a polarizable material; moving a top electrode into contact with a top surface of the cover layer; and applying a voltage between the top electrode and a bottom electrode located below the cover layer and comprised in a material stack between the bottom of the carrier and the cover layer, creating an electric field in the cover layer, thereby poling the cover layer such that a dielectric constant of the cover layer in a direction perpendicular to the sensing array is higher than a dielectric constant in a direction parallel to the sensing array, thereby forming a cover layer having an anisotropic dielectric constant.