Methods and apparatus of determining a stress-related characteristic of a substrate

An apparatus for determining at least one stress-related characteristic of a substrate, the apparatus comprising:

• a sample holder comprising a cavity configured to receive the substrate, the sample holder comprising a viewing aperture;
• a prism positioned such that a measurement beam is configured to impinge the prism and the viewing aperture, the prism comprising a first surface, a second surface, an end surface, and a coupling surface, the coupling surface facing the viewing aperture;
• a light-scattering polarimetry sub-system comprising a first beam source and a first detector, the first beam source configured to transmit a first beam of the measurement beam that impinges the end surface of the prism and the viewing aperture, the first detector configured to detect at least a portion of the first beam, and the at least a portion of the first beam configured to impinge the first surface of the prism;
• and
• an evanescent prism coupling spectroscopy sub-system comprising a second beam source and a second detector, the second beam source configured to transmit a second beam of the measurement beam that impinges the first surface of the prism and the viewing aperture, the second detector of the evanescent prism coupling spectroscopy sub-system is configured to detect at least a portion of the second beam, and the at least a portion of the second beam configured to impinge the second surface of the prism.

A method of determining at least one stress-related characteristic of a curved substrate comprising:

• disposing the curved substrate on a sample holder, the sample holder positioned in a first configuration, the sample holder further holding a curvature of the curved substrate in a fixed configuration with a plurality of devices, a coupling liquid positioned between a first coupling surface of a first prism and a first surface of the curved substrate in a viewing aperture of the sample holder;
• transmitting a first beam from a first beam source that impinges the first prism, the coupling liquid, and the first surface of the curved substrate at a measurement location;
• detecting at least a portion of the first beam with a first detector to generate a first signal;
• translating the sample holder from the first configuration to the second configuration in a first direction, the coupling liquid positioned between a second coupling surface of a second prism and the first surface of the curved substrate;
• transmitting a second beam from a second beam source that impinges the second prism, the coupling liquid, and the first surface of the curved substrate at the measurement location;
• detecting at least a portion of the second beam with a second detector to generate a second signal;
• and
• determining the at least one stress-related characteristic based on at least one of the first signal or the second signal.

A method of determining at least one stress-related characteristic of a substrate comprising:

• disposing the substrate on a sample holder, a coupling liquid positioned between a coupling surface of a prism and a first surface of the curved substrate in a viewing aperture of the sample holder;
• transmitting a first beam from a first beam source that impinges an end surface of the prism, the coupling liquid, and the first surface of the substrate at a measurement location;
• detecting at least a portion of the first beam with a first detector to generate a first signal, the at least a portion of the first beam impinges a first surface of the prism in traveling from the first surface of the substrate to the first detector;
• transmitting a second beam from a second beam source that impinges the first surface of the prism, the coupling liquid, and the first surface of the substrate at the measurement location;
• detecting at least a portion of the second beam with a second detector to generate a second signal, the at least a portion of the second beam impinges a second surface of the prism in travelling from the first surface of the substrate to the second detector;
• and
• determining the at least one stress-related characteristic based on at least one of the first signal or the second signal.