Methods and apparatus for determining optimum exposure threshold for a given photolithographic model

Abstract

A system and method for enhancing process latitude (tolerances) in the fabrication of devices and integrated circuits. A measuring point is selected corresponding to a feature of critical dimension. Then the pattern is convolved with the model, and its value and rate of change are calculated over a range of corresponding values of a first process parameter. Next, an optimum threshold having the largest rate of change, or contrast, is selected. Finally, proximity correction is performed using relevant parameters.

We claim:  
     
         1 . A method, in a computer, for determining the optimum process point for fabricating a device feature of a critical dimension, comprising the steps of: 
 selecting a measuring point on a computer representation of a wafer corresponding to the feature of the critical dimension;    calculating modeled behavior values and their rates of change over a range of corresponding values of a first process parameter;    selecting an optimum threshold value having the largest rate of change around said measuring point; and    determining the first process parameter value corresponding to the optimum threshold value.    
     
     
         2 . The method of  claim 1 , wherein the step of calculating model values comprises the step of calculating the model values and their rates of change over a range of corresponding values of a first process parameter representative of mask material edge position.  
     
     
         3 . The method of  claim 1 , wherein the step of calculating model values comprises the step of calculating the model values and their rates of change over a range of corresponding values of a first process parameter representative of focus.  
     
     
         4 . The method of  claim 1 , wherein the step of calculating model values comprises the step of calculating the model values and their rates of change over a range of corresponding values of a first process parameter representative of numerical aperture.  
     
     
         5 . The method of  claim 1 , wherein the step of calculating comprises the steps of: 
 selecting a point on one side of the measuring point;    calculating a value of the modeled behavior at each of the points; and    calculating a slope through each of the points, wherein the slope is a function of the values of the modeled behavior at each point.    
     
     
         6 . The method of  claim 4 , wherein the step of calculating model values further comprises selecting a second point.  
     
     
         7 . The method of  claim 1 , wherein the step of calculating threshold values and their rates of change comprises the steps of: 
 decrementing the value of the first process parameter;    calculating the value of the modeled behavior at the measuring point;    determining the value of the modeled behavior at a location offset from the measuring point in a first direction by a second value;    determining the value of the modeled behavior at a location offset from the initial position in a second direction, opposite to the first direction, by the second value; and    calculating the rate of change of the modeled behavior corresponding to the first process parameter value.    
     
     
         8 . The method of  claim 7 , wherein the step of calculating the rate of change comprises the steps of: 
 calculating a difference of the modeled behavior values ascertained during the steps of determining the values; and    dividing the difference of the modeled behavior values by twice the second value.    
     
     
         9 . A method, in a computer, for determining the optimum process point for fabricating a device feature of a critical dimension, comprising the steps of: 
 selecting a measuring point on a computer representation of a wafer corresponding to the feature of the critical dimension;    calculating modeled behavior values and their rates of change over a range of corresponding values of a first process parameter;    selecting an optimum threshold value having the largest rate of change around said measuring point;    determining the first process parameter value corresponding to the optimum threshold value; and    providing the optimum threshold value to a proximity effect correction process which modifies the mask pattern to compensate for proximity effects.    
     
     
         10 . The method of  claim 9 , wherein the step of calculating model values comprises the step of calculating the model values and their rates of change over a range of corresponding values of a first process parameter representative of a mask.  
     
     
         11 . The method of  claim 9 , wherein the step of calculating model values comprises the step of calculating the model values and their rates of change over a range of corresponding values of a first process parameter representative of mask material edge position.  
     
     
         12 . The method of  claim 9 , wherein the step of calculating model values comprises the step of calculating the model values and their rates of change over a range of corresponding values of a first process parameter representative of focus.  
     
     
         13 . The method of  claim 9 , wherein the step of calculating model values comprises the step of calculating the model values and their rates of change over a range of corresponding values of a first process parameter representative of numerical aperture.  
     
     
         14 . A method, in a computer, for determining the optimum process point for fabricating a device feature of a critical dimension, comprising the steps of: 
 selecting a measuring point on a computer representation of a wafer corresponding to the feature of the critical dimension;    calculating model values and their rates of change over a range of corresponding mask material edge positions; and    selecting an optimum threshold value having the largest rate of change around said measuring point.    
     
     
         15 . The method of  claim 14 , further comprising the step of determining the mask material edge position corresponding to the optimum threshold value.  
     
     
         16 . The method of  claim 14 , wherein the step of calculating comprises the steps of: 
 selecting a point on one side of the measuring point;    calculating a value of the modeled behavior at each of the points; and    calculating a slope through each of the points, wherein the slope is a function of the values of the modeled behavior at each point.    
     
     
         17 . The method of  claim 14 , wherein the step of calculating threshold values and their rates of change further compromises the steps of: 
 shifting the mask material edge position by a first value;    calculating the value of the modeled behavior at the measuring point;    determining the value of the modeled behavior at a location offset from the measuring point in a first direction by a second value;    determining the value of the modeled behavior at a location offset from the measuring point in a second direction, opposite the first direction, by the second value; and    calculating the rate of change of the threshold corresponding to the mask material edge position.    
     
     
         18 . The method of  claim 17 , wherein the step of calculating the rate of change comprises the steps of: 
 calculating a difference of the modeled behavior values ascertained during the steps of determining the values; and    dividing the difference of the modeled behavior values by twice the second value.    
     
     
         19 . The method of  claim 17 , further comprising the steps of: 
 providing the optimum threshold value to a proximity effect correction process which modifies the mask pattern to compensate for proximity effects.    
     
     
         20 . A method, in a computer, for determining the optimum process point for fabricating a device feature of a critical dimension, comprising the steps of: 
 selecting a measuring point on a computer representation of a wafer corresponding to the feature of the critical dimension;    calculating modeled behavior values and their rates of change over a range of corresponding mask material edge positions, comprising the steps of: 
 shifting the mask material edge position by a first value;  
 calculating the value of the modeled behavior at the measuring point;  
 determining the value of the modeled behavior at a location offset from the measuring point in a first direction by a second value;  
 determining the value of the modeled behavior at a location offset from the measuring point in a second direction, opposite the first direction, by the second value; and  
 calculating the rate of change of the threshold, comprising the steps of: 
 calculating a difference of the modeled behavior values ascertained during the steps of determining the values; and  
 dividing the difference of the modeled behavior values by twice the second value;  
 
   selecting an optimum threshold value having the largest rate of change; and    providing the optimum threshold value to a proximity effect correction process which modifies the mask pattern to compensate for proximity effects.    
     
     
         21 . A method, in a computer, for determining the optimum process point for fabricating a device feature of critical dimension, comprising the steps of: 
 selecting a plurality of measuring points, wherein each measuring point corresponds to the feature of the critical dimension;    calculating values and rates of change of modeled behavior over a range of values of a first process parameter for each measuring point;    selecting an optimum threshold value having the largest rate of change for each measuring point;    selecting a threshold value from the plurality of optimal threshold values; and    providing the selected threshold value to a proximity effect correction process which modifies the mask pattern to compensate for proximity effects.    
     
     
         22 . The method according to  claim 21 , wherein the step of selecting an optimum threshold value includes the step of determining the mean of the selected optimum threshold values.  
     
     
         23 . The method according to  claim 21 , wherein the step of selecting an optimum threshold value includes the step of determining the median of the selected optimum threshold values.  
     
     
         24 . A computer program product comprising a memory having computer program logic recorded thereon for enabling a processor in a computer system to determine the optimum process point for fabricating a device feature of a critical dimension, the computer program logic comprising: 
 a first calculating process enabling the processor to calculate a modeled behavior value associated with the device feature and a rate of change of the modeled behavior value over a range of corresponding values of a first process parameter;    a second calculating process enabling the processor to select an optimum threshold value; and    a determining process enabling the processor to determine the value of the first process parameter corresponding to the optimum threshold value.    
     
     
         25 . The computer program product of  claim 24 , further comprising: 
 a providing process enabling the processor to provide the optimum threshold value to a proximity effect correction process which modifies the mask pattern to compensate for proximity effects.    
     
     
         26 . The computer program according to  claim 24 , wherein the first process parameter is a mask material edge position and the rate of change of the modeled behavior value indicates the process latitude in forming the device feature associated with a particular mask material edge position.  
     
     
         27 . A computer system, comprising: 
 a processor;    a memory operatively coupled to the processor;    a first calculating process enabling the processor to calculate a modeled behavior value associated with the device feature and a rate of change of the modeled behavior value over a range of corresponding values of a first process parameter;    a second calculating process enabling the processor to select the optimum threshold value; and    a determining process enabling the processor to determine the value of the first process parameter corresponding to the optimum threshold value.    
     
     
         28 . The computer system of  claim 27 , further comprising the step of providing process enabling the processor to provide the optimum threshold value to a proximity effect correction process which modifies the mask pattern to compensate for proximity effects.  
     
     
         29 . The computer system of  claim 27 , wherein the first process parameter is a mask edge position and the rate of change of the modeled value indicates the process latitude of an edge of the device feature.  
     
     
         30 . A simulation method for determining an optimum process point for fabricating a device feature of a critical dimension, comprising: 
 calculating model values over a range of mask material edge positions; and    calculating rates of change of model values over a range of the mask material edge positions.    
     
     
         31 . A simulation method for determining an optimum process point for fabricating a device feature of a critical dimension, comprising: 
 calculating model values over a range of process parameters representative of focus; and    calculating rates of change of model values over a range of the process parameters representative of focus.    
     
     
         32 . A simulation method for determining an optimum process point for fabricating a device feature of a critical dimension, comprising: 
 calculating model values over a range of process parameters representative of numerical aperture; and    calculating rates of change of model values over a range of the process parameters representative of numerical aperture.    
     
     
         33 . A simulation method, comprising: 
 simulating a processing step for a wafer;    calculating model values and their rates of change over a range of values of a processing parameter;    determining an optimum value having a largest calculated rate of change; and    determining the process parameter corresponding to the optimum value.    
     
     
         34 . The method of  claim 33 , wherein simulating the processing step includes simulating an exposure step.  
     
     
         35 . The method of  claim 33 , wherein simulating the processing step includes simulating a development step.  
     
     
         36 . The method of  claim 33 , wherein simulating the processing step includes simulating an etch step.  
     
     
         37 . The method of  claim 33 , wherein simulating the processing step includes selecting an initial position of a simulated mask material edge.  
     
     
         38 . The method of  claim 37 , wherein simulating the processing step includes defining a critical dimension of a device feature.  
     
     
         39 . The method of  claim 38 , wherein calculating the model value includes selecting a measuring point.  
     
     
         40 . The method of  claim 39 , wherein calculating the model value includes selecting a threshold to create an edge that includes the measuring point.  
     
     
         41 . The method of  claim 33 , wherein determining the process parameter includes providing the optimum value to a proximity effect correction model.  
     
     
         42 . The method of  claim 41 , wherein determining the process parameter includes modifying the process parameter to compensate for proximity effects.  
     
     
         43 . A simulation method for determining an optimum process point for fabricating a device feature of a critical dimension, comprising: 
 calculating model values over a range of attenuated phase shift mask material edge positions; and    calculating rates of change of model values over the range of the attenuated phase shift mask material edge positions.    
     
     
         44 . A simulation method for determining an optimum process point for fabricating a device feature of a critical dimension, comprising: 
 calculating model values over a range of alternating aperture phase shift mask material edge positions; and    calculating rates of change of model values over the range of the alternating aperture phase shift mask material edge positions.    
     
     
         45 . A simulation method for determining an optimum process point for fabricating a device feature of a critical dimension, comprising: 
 calculating model values over a range of chromeless phase shift mask material edge positions; and    calculating rates of change of model values over the range of the chromeless phase shift mask material edge positions.    
     
     
         46 . A simulation method, comprising: 
 simulating a lithography processing step for a substrate;    calculating model values and their rates of change over a range of values of a processing parameter;    determining an optimum value having a largest calculated rate of change; and    determining the process parameter corresponding to the optimum value.    
     
     
         47 . The method of  claim 46 , wherein determining the process parameter includes providing the optimum value to a proximity effect correction model.  
     
     
         48 . The method of  claim 47 , wherein determining the process parameter includes modifying the process parameter to compensate for proximity effects.  
     
     
         49 . The method of  claim 46 , wherein simulating a lithography processing step for a substrate includes simulating X-ray lithography.  
     
     
         50 . The method of  claim 46 , wherein simulating a lithography processing step for a substrate includes simulating ion beam lithography.  
     
     
         51 . The method of  claim 46 , wherein simulating a lithography processing step for a substrate includes simulating electron beam lithography.