Coupled-Domains Disturbance Matrix Generation For Fast Simulation Of Wafer Topography Proximity Effects

A method for calculating light intensity values generated in a photoresist layer disposed over an inhomogeneous substrate in response to patterned incident light passed through a modeled mask configured in accordance with a mask design, said inhomogeneous substrate including a plurality of materials forming a plurality of layers and a plurality of structures disposed in said layers, the method comprising:

• generating a disturbance matrix such that said disturbance matrix provides a total reflected electric field generated at an upper photoresist surface of said photoresist layer in response to an incident electric field directed onto said inhomogeneous substrate;
• simulating wave propagation in the photoresist layer in response to said patterned incident light;
• and
• calculating said light intensity values using said disturbance matrix and said simulated wave propagation,
• wherein generating the disturbance matrix comprises:
• generating a three-dimensional (3D) substrate description including said inhomogeneous substrate and said photoresist layer;
• dividing the 3D substrate description into a plurality of vertically arranged domains separated by horizontal planar domain boundaries, each said domain defined by optical properties of one or more materials of said plurality of materials corresponding to at least one of a corresponding said modeled structure and a corresponding said modeled layer disposed in said each domain;
• utilizing Fourier-space representations to determine discrete electrical field components and discrete magnetic field components at the top domain boundary and the bottom domain boundary of at least one of said domains;
• numerically integrating the discrete electrical field components and discrete magnetic field components of said each domain to obtain a corresponding domain-specific matrix for said at least one domain;
• generating a domain transfer matrix for said at least one domain based on said corresponding domain-specific matrix such that each said domain transfer matrix defines a first pair of forward and backward propagating wave values occurring at the top domain boundary of said at least one domain in response to a corresponding second pair of forward and backward propagating wave values simultaneously occurring at the bottom domain boundary of said at least one domain;
• multiplying the transfer matrices of all of the plurality of domains to generate a total transfer matrix;
• and
• utilizing the total transfer matrix to determine said disturbance matrix.

A non-transitory, computer-readable medium storing computer-executable instructions for generating a disturbance matrix that describes E-field disturbances generated by optical properties of an inhomogeneous substrate defined by an integrated circuit (IC) design, said inhomogeneous substrate including a plurality of materials forming a plurality of layers and a plurality of structures disposed in said layers, the instructions when executed by a processor cause the processor to execute a process comprising:

• generating a three-dimensional (3D) substrate description based on the IC design, said 3D substrate description including a modeled inhomogeneous substrate generated in accordance with said inhomogeneous substrate such that all upward/downward-facing material interfaces formed between said pluralities of layers and structures of said inhomogeneous substrate are defined by corresponding planar horizontal interfaces between corresponding modeled layers and modeled structures of said modeled inhomogeneous substrate;
• dividing the 3D substrate description into a plurality of vertically arranged domains separated by horizontal planar domain boundaries, each said domain defined by optical properties of one or more materials of said plurality of materials corresponding to at least one of a corresponding said modeled structure and a corresponding said modeled layer disposed in said each domain;
• and
• generating said disturbance matrix such that said disturbance matrix provides a total reflected electric field generated in response to a modeled incident electric field that is directed onto said modeled inhomogeneous substrate, wherein generating the disturbance matrix comprises:
• utilizing Fourier-space representations to determine discrete electrical field components and discrete magnetic field components at the top domain boundary and the bottom domain boundary of at least one said domain;
• numerically integrating the discrete electrical field components and discrete magnetic field components of said each domain to obtain a corresponding domain-specific matrix for said at least one domain;
• generating a domain transfer matrix for said at least one domain based on said corresponding domain-specific matrix such that each said domain transfer matrix defines a first pair of forward and backward propagating wave values occurring at the top domain boundary of said at least one domain in response to a corresponding second pair of forward and backward propagating wave values simultaneously occurring at the bottom domain boundary of said at least one domain;
• multiplying the transfer matrices of all of the plurality of domains to generate a total transfer matrix;
• and
• utilizing the total transfer matrix to determine said disturbance matrix.