Bandgap measurements of patterned film stacks using spectroscopic metrology

A fabrication system, comprising:

• one or more process tools for fabricating multilayer gratings based on a process recipe;
• a spectroscopic metrology tool tool;
• and
• a controller communicatively coupled to the spectroscopic metrology tool and the one or more process tools, the controller including one or more processors configured to execute program instructions configured to cause the one or more processors to:
• generate a model of a metrology target including a multilayer grating, wherein the multilayer grating is formed from a patterned substrate layer and two or more additional layers on the patterned substrate layer to form a multilayer pattern, the two or more additional layers forming a multilayer stack shaped to conform to at least a portion of the patterned substrate layer, the two or more additional layers including a test layer to be modeled, wherein at least one of a size or spacing of elements of the multilayer pattern are representative of device features to be fabricated on a common sample with the metrology target, wherein the model is parameterized with two or more parameters associated with the multilayer grating, wherein the two or more parameters include one or more geometric parameters indicative of at least a size, shape, or periodicity of the test layer within the elements of the multilayer pattern, wherein the two or more parameters include one or more dispersion parameters indicative of at least a bandgap of the test layer including dimension-dependent physical effects associated with the one or more geometric parameters;
• receive a measured spectroscopic signal of a fabricated multilayer grating from the spectroscopic metrology tool, wherein the fabricated multilayer grating is fabricated according to the model of the metrology target by the one or more process tools based on the process recipe;
• determine values of the two or more parameters of the model providing a simulated spectroscopic signal corresponding to the measured spectroscopic signal within a selected tolerance;
• calculate the bandgap of the test layer of the fabricated multilayer grating based on the determined values of the two or more parameters;
• and
• adjust the process recipe for the one or more process tools for fabricating multilayer gratings based on the calculated bandgap of the test layer.