Systems and methods for inspection and metrology of vertical interconnect access in semiconductor substrates

A system comprising:

• a light source configured to emit partially coherent or coherent light split into a reference beam and an object beam;
• a stage configured to support a workpiece in a path of the object beam, such that the object beam is transmitted through the workpiece, wherein the workpiece includes at least one vertical interconnect access (VIA) extending from a first side of the workpiece to a second side of the workpiece;
• a first beam splitter configured to combine the reference beam with the object beam transmitted through the workpiece into a combined beam;
• a camera configured to detect the combined beam received from the first beam splitter;
• and
• a processor in electronic communication with the camera, wherein the processor is configured to:
• generate an interference image of the workpiece based on the combined beam detected by the camera;
• determine amplitude and phase information of the object beam based on the interference image;
• generate, using numerical propagation, a plurality of depth images of the workpiece based on the amplitude and phase information of the object beam;
• and
• determine a critical dimension (CD) of the at least one VIA based on the plurality of depth images of the workpiece.