A metrology system includes a radiation source configured to generate radiation, an optical element configured to direct the radiation toward a grating structure comprising a non-constant pitch, and a detector configured to receive radiation scattered by the grating structure and generate a measurement based on the received radiation. The metrology system is configured to generate a set of measurements corresponding to a set of locations on the grating structure along a direction of the non-constant pitch and determine a parameter of a lithographic process or a correction for the metrology system based on the set of measurements.

A sensor device provided in the disclosure includes a sensor substrate, a first transparent layer, a collimator layer, and a lens. The first transparent layer is disposed on the sensor substrate, wherein the first transparent layer defines an alignment structure. The collimator layer is disposed on the first transparent layer. The lens is disposed on the collimator layer.

An alignment system includes a light source for emitting a light. An alignment mark is disposed on a substrate for receiving the light. The alignment mark includes a first pattern and a second pattern disposed on the substrate. The first pattern includes a first region and a second region. The second pattern includes a third region and a fourth region. The first region and the third region are symmetrical with respective to a symmetrical axis. The second region and the fourth region are symmetrical with respective to the symmetrical axis. The first region includes first mark lines parallel to each other. The second region includes second mark lines parallel to each other. A first pitch is disposed between the first mark lines adjacent to each other. A second pitch is disposed between the second mark lines adjacent to each other. The first pitch is different from the second pitch.

A self-aligned multiple patterning mark is provided. The mark includes a group of patterns disposed on the substrate and a cover layer. The group of patterns includes a plurality of strip patterns extending in a first direction and arranged parallel to each other, and the ends of two adjacent strip patterns are connected to each other to form an independent ring. The cover layer is disposed on the substrate and covers the group of patterns. The cover layer has an opening extending in a second direction across the first direction, and the cover layer covers two opposite ends of each strip pattern.

Methods for manufacturing a semiconductor structure are provided. A substrate is provided. A metrology target is formed in a layer over the substrate according to a first layer mask and a second layer mask. The metrology target includes a first pattern formed by a plurality of first photonic crystals corresponding to the first layer mask and a second pattern formed by a plurality of second photonic crystals corresponding to the second layer mask. First light is provided to illuminate the metrology target. Second light is received from the metrology target in response to the first light. The second light is analyzed to detect overlay-shift between the first pattern and the second pattern. The first pattern and the second pattern are arranged to cross in one direction in the metrology target.

In an alignment apparatus, a measurement device includes an illuminator that illuminates a first original-side mark and a second original-side mark arranged in an original and a first substrate-side mark and second substrate-side mark arranged in a substrate. The measurement device performs coarse measurement based on light beams from the first original-side mark and the first substrate-side mark by causing the illuminator to illuminate the first original-side mark and the first substrate-side mark under a first condition, and performs fine measurement based on light beams from the second original-side mark and the second substrate-side mark by causing the illuminator to illuminate the second original-side mark and the second substrate-side mark under a second condition.

Two pairs of alignment targets (one aligned, one misaligned by a bias distance) are formed on different masks to produce a first pair of conjugated interference patterns. Other pairs of alignment targets are also formed on the masks to produce a second pair of conjugated interference patterns that are inverted the first. Misalignment of the dark and light regions of the first interference patterns and the second interference patterns in both pairs of conjugated interference patterns is determined when patterns formed using the masks are overlaid. A magnification factor (of the interference pattern misalignment to the target misalignment) is calculated as a ratio of the difference of misalignment of the relatively dark and relatively light regions in the pairs of interference patterns, over twice the bias distance. The interference pattern misalignment is divided by the magnification factor to produce a self-referenced and self-calibrated target misalignment amount, which is then output.

A target for use in the measurement of misregistration between layers formed on a wafer in the manufacture of semiconductor devices, the target including a first pair of periodic structures (FPPS) and a second pair of periodic structures (SPPS), each of the FPPS and the SPPS including a first edge, a second edge, a plurality of first periodic structures formed in a first area as part of a first layer and having a first pitch along a first pitch axis, the first pitch axis not being parallel to either of the first edge or second edge, and a plurality of second periodic structures formed in a second area as part of a second layer and having the first pitch along a second pitch axis, the second pitch axis being generally parallel to the first pitch axis.

A sensor device provided in the disclosure includes a sensor substrate, a first transparent layer, a collimator layer, and a lens. The first transparent layer is disposed on the sensor substrate, wherein the first transparent layer defines an alignment structure. The collimator layer is disposed on the first transparent layer. The lens is disposed on the collimator layer.

A method for determining substrate deformation includes obtaining first measurement data associated with mark positions, from measurements of a plurality of substrates; obtaining second measurement data associated with mark positions, from measurements of the plurality of substrates; determining a mapping between the first measurement data and the second measurement data; and decomposing the mapping, by calculating an eigenvalue decomposition for the mapping, to separately determine a first deformation (e.g. mark deformation) that scales differently from a second deformation (e.g. substrate deformation) in the mapping between the data. The steps of determining a mapping and decomposing the mapping may be performed together using non-linear optimization.