Abstract: A method of frequency allocation in a quantum device having a plurality of qubits includes determining a plurality of frequency groups based on a configuration of the plurality of qubits; determining, for each of the plurality of qubits, a qubit frequency; assigning a frequency group from the plurality of frequency groups to each of the plurality of qubits based on each respective qubit frequency; determining for at least one qubit of the plurality of qubits whether a frequency collision exists between the at least one qubit and neighboring qubits in the plurality of qubits based on the qubit frequency of the at least one qubit and at least one qubit frequency of the neighboring qubits; and adjusting the frequency of the at least one qubit based on the determination whether a frequency collision exists between the at least one qubit and said neighboring qubits in the plurality of qubits.

Abstract: A method of frequency allocation in a quantum device having a plurality of qubits includes determining a plurality of frequency groups based on a configuration of the plurality of qubits; determining, for each of the plurality of qubits, a qubit frequency; assigning a frequency group from the plurality of frequency groups to each of the plurality of qubits based on each respective qubit frequency; determining for at least one qubit of the plurality of qubits whether a frequency collision exists between the at least one qubit and neighboring qubits in the plurality of qubits based on the qubit frequency of the at least one qubit and at least one qubit frequency of the neighboring qubits; and adjusting the frequency of the at least one qubit based on the determination whether a frequency collision exists between the at least one qubit and said neighboring qubits in the plurality of qubits.

Abstract: Disclosed are mask definition tools, apparatus, methods, systems and computer program products configured to process data representing a semiconductor fabrication mask. A non-limiting example of a method includes performing a decomposition process on a full Transmission Cross Coefficient (TCC) using coherent optimal coherent systems (OCS) kernels; isolating a residual TCC that remains after some number of coherent kernels are extracted from the full TCC; and performing at least one decomposition process on the residual TCC using at least one loxicoherent system. The loxicoherent system uses a plurality of distinct non-coherent kernel functions and is a compound system containing a paired coherent system and an incoherent system that act in sequence. An output of the coherent system is input as a self-luminous quantity to the incoherent system, and the output of the incoherent system is an output of the loxicoherent system.

Abstract: Disclosed are mask definition tools, apparatus, methods, systems and computer program products configured to process data representing a semiconductor fabrication mask. A non-limiting example of a method includes performing a decomposition process on a full Transmission Cross Coefficient (TCC) using coherent optimal coherent systems (OCS) kernels; isolating a residual TCC that remains after some number of coherent kernels are extracted from the full TCC; and performing at least one decomposition process on the residual TCC using at least one loxicoherent system. The loxicoherent system uses a plurality of distinct non-coherent kernel functions and is a compound system containing a paired coherent system and an incoherent system that act in sequence. An output of the coherent system is input as a self-luminous quantity to the incoherent system, and the output of the incoherent system is an output of the loxicoherent system.

Abstract: Disclosed are mask definition tools, apparatus, methods, systems and computer program products configured to process data representing a semiconductor fabrication mask. A non-limiting example of a method includes performing a decomposition process on a full Transmission Cross Coefficient (TCC) using coherent optimal coherent systems (OCS) kernels; isolating a residual TCC that remains after some number of coherent kernels are extracted from the full TCC; and performing at least one decomposition process on the residual TCC using at least one loxicoherent system. The loxicoherent system uses a plurality of distinct non-coherent kernel functions and is a compound system containing a paired coherent system and an incoherent system that act in sequence. An output of the coherent system is input as a self-luminous quantity to the incoherent system, and the output of the incoherent system is an output of the loxicoherent system.

Abstract: Disclosed are mask definition tools, apparatus, methods, systems and computer program products configured to process data representing a semiconductor fabrication mask. A non-limiting example of a method includes performing a decomposition process on a full Transmission Cross Coefficient (TCC) using coherent optimal coherent systems (OCS) kernels; isolating a residual TCC that remains after some number of coherent kernels are extracted from the full TCC; and performing at least one decomposition process on the residual TCC using at least one loxicoherent system. The loxicoherent system uses a plurality of distinct non-coherent kernel functions and is a compound system containing a paired coherent system and an incoherent system that act in sequence. An output of the coherent system is input as a self-luminous quantity to the incoherent system, and the output of the incoherent system is an output of the loxicoherent system.

Abstract: Disclosed are mask definition tools, apparatus, methods, systems and computer program products configured to process data representing a semiconductor fabrication mask. A non-limiting example of a method includes performing a decomposition process on a full Transmission Cross Coefficient (TCC) using coherent optimal coherent systems (OCS) kernels; isolating a residual TCC that remains after some number of coherent kernels are extracted from the full TCC; and performing at least one decomposition process on the residual TCC using at least one loxicoherent system. The loxicoherent system uses a plurality of distinct non-coherent kernel functions and is a compound system containing a paired coherent system and an incoherent system that act in sequence. An output of the coherent system is input as a self-luminous quantity to the incoherent system, and the output of the incoherent system is an output of the loxicoherent system.

Abstract: Disclosed are mask definition tools, apparatus, methods, systems and computer program products configured to process data representing a semiconductor fabrication mask. A non-limiting example of a method includes performing a decomposition process on a full Transmission Cross Coefficient (TCC) using coherent optimal coherent systems (OCS) kernels; isolating a residual TCC that remains after some number of coherent kernels are extracted from the full TCC; and performing at least one decomposition process on the residual TCC using at least one loxicoherent system. The loxicoherent system uses a plurality of distinct non-coherent kernel functions and is a compound system containing a paired coherent system and an incoherent system that act in sequence. An output of the coherent system is input as a self-luminous quantity to the incoherent system, and the output of the incoherent system is an output of the loxicoherent system.

Abstract: Disclosed are mask definition tools, apparatus, methods, systems and computer program products configured to process data representing a semiconductor fabrication mask. A non-limiting example of a method includes performing a decomposition process on a full Transmission Cross Coefficient (TCC) using coherent optimal coherent systems (OCS) kernels; isolating a residual TCC that remains after some number of coherent kernels are extracted from the full TCC; and performing at least one decomposition process on the residual TCC using at least one loxicoherent system. The loxicoherent system uses a plurality of distinct non-coherent kernel functions and is a compound system containing a paired coherent system and an incoherent system that act in sequence. An output of the coherent system is input as a self-luminous quantity to the incoherent system, and the output of the incoherent system is an output of the loxicoherent system.

Abstract: A method for correcting a lithographic pattern includes selecting, by a processor, first stage input factors for utilization with a first computer-implemented model. The processor measures pattern data from existing measured dimensions of a semiconductor to obtain values for the first stage input factors and the first model against the measured pattern data. The processor applies the calibrated first model to predict printed dimensions and the printed dimensions from applying the calibrated first model comprise residuals. The processor establishes, based on the residuals, second stage input factors for a second model and calibrates the second model against the measured pattern data to predict deviations of the printed dimensions from the printed dimensions from the first stage input factors by utilizing the second stage input factors. The method produces predicted printed dimensions of a lithographic pattern by using the second model to revise the printed dimensions of the first model.

Abstract: A method for correcting a lithographic pattern includes selecting, by a processor, first stage input factors for utilization with a first computer-implemented model. The processor measures pattern data from existing measured dimensions of a semiconductor to obtain values for the first stage input factors and the first model against the measured pattern data. The processor applies the calibrated first model to predict printed dimensions and the printed dimensions from applying the calibrated first model comprise residuals. The processor establishes, based on the residuals, second stage input factors for a second model and calibrates the second model against the measured pattern data to predict deviations of the printed dimensions from the printed dimensions from the first stage input factors by utilizing the second stage input factors. The method produces predicted printed dimensions of a lithographic pattern by using the second model to revise the printed dimensions of the first model.

Abstract: A system and method for optimizing (designing) a mask pattern, in which SMO and OPC are collaboratively used to exert a sufficient collaborative effect or are appropriately used in different manners. The method for designing a source and a mask for lithography includes a step (S1) of selecting a set of patterns; a step of performing source mask optimization (SMO) using the set of patterns, under an optical proximity correction (OPC) restriction rule which is used for selectively restricting shifting of an edge position of a polygon when OPC is applied to the set of patterns; and a step (S3, S4) of determining a layout of the mask for lithography, by applying OPC to all patterns constituting the mask for lithography using the source optimized through the SMO.

Abstract: Disclosed are mask definition tools, apparatus, methods, systems and computer program products configured to process data representing a semiconductor fabrication mask. A non-limiting example of a method includes performing a decomposition process on a full Transmission Cross Coefficient (TCC) using coherent optimal coherent systems (OCS) kernels; isolating a residual TCC that remains after some number of coherent kernels are extracted from the full TCC; and performing at least one decomposition process on the residual TCC using at least one loxicoherent system. The loxicoherent system uses a plurality of distinct non-coherent kernel functions and is a compound system containing a paired coherent system and an incoherent system that act in sequence. An output of the coherent system is input as a self-luminous quantity to the incoherent system, and the output of the incoherent system is an output of the loxicoherent system.

Abstract: Disclosed are mask definition tools, apparatus, methods, systems and computer program products configured to process data representing a semiconductor fabrication mask. A non-limiting example of a method includes performing a decomposition process on a full Transmission Cross Coefficient (TCC) using coherent optimal coherent systems (OCS) kernels; isolating a residual TCC that remains after some number of coherent kernels are extracted from the full TCC; and performing at least one decomposition process on the residual TCC using at least one loxicoherent system. The loxicoherent system uses a plurality of distinct non-coherent kernel functions and is a compound system containing a paired coherent system and an incoherent system that act in sequence. An output of the coherent system is input as a self-luminous quantity to the incoherent system, and the output of the incoherent system is an output of the loxicoherent system.

Abstract: Disclosed are mask definition tools, apparatus, methods, systems and computer program products configured to process data representing a semiconductor fabrication mask. A non-limiting example of a method includes performing a decomposition process on a full Transmission Cross Coefficient (TCC) using coherent optimal coherent systems (OCS) kernels; isolating a residual TCC that remains after some number of coherent kernels are extracted from the full TCC; and performing at least one decomposition process on the residual TCC using at least one loxicoherent system. The loxicoherent system uses a plurality of distinct non-coherent kernel functions and is a compound system containing a paired coherent system and an incoherent system that act in sequence. An output of the coherent system is input as a self-luminous quantity to the incoherent system, and the output of the incoherent system is an output of the loxicoherent system.

Abstract: Methods and systems for determining a source shape, a mask shape and a target shape for a lithography process are disclosed. One such method includes receiving source, mask and target constraints and formulating an optimization problem that is based on the source, mask and target constraints and incorporates contour-based assessments for the target shape that are based on physical design quality of a circuit. Further, the optimization problem is solved by integrating over process condition variations to simultaneously determine the source shape, the mask shape and the target shape. In addition, the determined source shape and mask shape are output.

Abstract: In one embodiment, a source mask optimization (SMO) method is provided that includes controlling bright region efficiency during at least one optical domain step. The bright region efficiency being the proportion of the total transmitted light that is transferred to bright areas of a target pattern. The optical domain intermediate solution provided by the at least one optical domain step may then be binarized to obtain an initial spatial domain solution with a controlled MEEF (Mask Error Enhancement Factor). The MEEF is controlled during at least one spatial domain step that optimizes the initial spatial domain solution.

Abstract: Methods and systems for determining a source shape, a mask shape and a target shape for a lithography process are disclosed. One such method includes receiving source, mask and target constraints and formulating an optimization problem that is based on the source, mask and target constraints and incorporates contour-based assessments for the target shape that are based on physical design quality of a circuit. Further, the optimization problem is solved by integrating over process condition variations to simultaneously determine the source shape, the mask shape and the target shape.

Abstract: A system and method for optimizing (designing) a mask pattern, in which SMO and OPC are collaboratively used to exert a sufficient collaborative effect or are appropriately used in different manners. The method for designing a source and a mask for lithography includes a step (S1) of selecting a set of patterns; a step of performing source mask optimization (SMO) using the set of patterns, under an optical proximity correction (OPC) restriction rule which is used for selectively restricting shifting of an edge position of a polygon when OPC is applied to the set of patterns; and a step (S3, S4) of determining a layout of the mask for lithography, by applying OPC to all patterns constituting the mask for lithography using the source optimized through the SMO.

Abstract: A method includes selecting a mask blank for lithographically forming a desired pattern of main features to be printed onto a wafer by projection lithography. First locations are identified in the desired pattern, the first locations being those which would produce on the wafer images impacted by phase distortions of actinic light through openings in the desired pattern. Second locations in the desired pattern are identified for the insertion of orthoedges. The orthoedges are provided to contribute an additional amplitude of actinic light to the images impacted by phase distortions when the actinic light is projected onto the wafer. The orthoedges are then inserted into the desired pattern at the second locations at orientations such that the orthoedges provide a quadrature component to the additional amplitude of actinic light having an opposite sign to the quadrature component of the actinic light producing the phase distortions.