A method of forming a scribe line having a sharp snap line entails directing a UV laser beam along a ceramic or ceramic-like substrate such that a portion of the thickness of the substrate is removed. The UV laser beam forms a scribe line in the substrate without appreciable substrate melting so that a clearly defined snap line forms a region of high stress concentration extending into the thickness of the substrate. Consequently, multiple depthwise cracks propagate into the thickness of the substrate in the region of high stress concentration in response to a breakage force applied to either side of the scribe line to effect clean fracture of the substrate into separate circuit components. The formation of this region facilitates higher precision fracture of the substrate while maintaining the integrity of the interior structure of each component during and after application of the breakage force.