Silica-containing substrates with vias having an axially variable sidewall taper and methods for forming the same

A method for processing a substrate comprising silica content of greater than or equal to 90 mol %, a first surface, and a second surface opposite the first surface, the method comprising:

• forming, using a laser beam with a substantially uniform intensity, a damage track through the substrate from the first surface to the second surface, the laser beam comprising a pulsed laser beam focused into a laser beam focal line that is positioned through the substrate, the laser beam focal line producing a material modification within the substrate along the laser beam focal line, thereby forming the damage track, wherein a level of modification of the substrate along the damage track decreases in a first direction starting from the first surface toward a bulk of the substrate, and the level of modification along the damage track decreases in a second direction starting from the second surface toward a bulk of the substrate such that the damage track comprises:
• a first highly modified segment proximate the first surface,
• a second highly modified segment proximate the second surface,
• a minimally modified segment disposed between the first highly modified segment and the second highly modified segment,
• etching, using an etching solution, the substrate such that the first highly modified segment and the second highly modified segment are each etched ata faster rate than a minimally modified segment,
• wherein etching forms a via comprising a first diameter at the first surface, a second diameter at a second surface, and a via waist having a water diameter between the first surface and the second surface, wherein the waist diameter is about 55% or less of each of the first diameter and the second diameter.