JP2009124088A - Method of setting manufacturing condition of resist pattern, and method of manufacturing semiconductor device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a means for precisely determining manufacturing conditions of a resist pattern. <P>SOLUTION: A method of setting the manufacturing conditions of a resist pattern includes a step of measuring a plurality of sets of dimension measurement data of the resist pattern when the position of the focal point and exposure are changed independently; a step of measuring the variation of a projection exposure apparatus based on the position of the focal point of the apparatus and the normal distribution of the exposure; a step of performing a two-variable multiple regression analysis using an explanation function with the position of the focal point and the exposure as variables based on the dimension measurement data to determine an approximate expression for a multiple regression curve; a step of comparing a determination coefficient adjusted for the degree of freedom and a predetermined regression accuracy determination value; a step of generating distribution calculation points which are normally distributed about the designed point as a mean when the determination coefficient adjusted for the degree of freedom is equal to or larger than the predetermined regression accuracy determination value; a step of calculating dimension calculation data; and a step of determining the predetermined designed point as the manufacturing condition when a value three times of the standard deviation of the calculated dimension calculation data is within an allowable dimension range on both sides of the mean value. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a resist pattern manufacturing condition setting method and a semiconductor device manufacturing method in a photolithography process when manufacturing a semiconductor device.

In the photolithography process at the time of manufacturing the semiconductor device, in order to obtain the desired characteristics of the semiconductor device, manufacturing at the time of actual resist pattern formation so that the variation is smaller than the allowable range of dimensions such as line width. It is necessary to determine the conditions.
The dimensional variation factors are roughly divided into exposure amount fluctuations and focal point position fluctuations. The exposure amount fluctuation factors are the distribution of resist coating film thickness within the surface of the semiconductor wafer and the resist baking process. Temperature distribution, photomask dimensional error, illuminance distribution within the exposure area, developer liquid volume distribution within the surface of the semiconductor wafer, variation in substrate reflectivity, and the like.

Further, the fluctuation factors of the focal position include the aberration of the projection exposure apparatus and the change of the focus setting over time, the flatness of the semiconductor wafer, the unevenness of the elements formed on the semiconductor wafer, and the like.
In order to know the dimensional variation in one photolithography process, the photolithography process is actually performed, and the dimensions of the resist pattern obtained by the same photomask on a single semiconductor wafer are measured at many points. There are a method for evaluating variation and a method using process margin as an index instead of dimensional variation.

  The conventional method for calculating the process margin is to measure the dimension measurement data of the line width of the resist pattern formed when the exposure amount and the focus position are changed independently, and to measure the dimension measurement data. Approximate the dependence of the line width on the exposure amount for each focus position with a regression curve by regression analysis, and calculate the line width calculation data for each exposure amount and focus position in a matrix using this approximate expression. Using the calculated line width calculation data, the focus position dependence of the line width is approximated by a regression curve by regression analysis for each exposure dose, and each exposure amount and focus position are arranged in a matrix using this approximate expression. The line width calculation data at is calculated.

Then, the line width calculation data calculated by the two approximations is compared with the measured dimension measurement data, the dimension measurement data that is extremely different is deleted, or the best approximation is performed while changing the order of the polynomial Until the best approximation is obtained, the line width calculation data at each exposure amount and focal position is calculated in a matrix form using the approximate expression, and the calculated line is obtained. The width calculation data is used to approximate the exposure dose dependency of the line width for each focal position with a regression curve by regression analysis to obtain a final approximate expression, which is the lower limit dimension of the allowable dimension range at each focal position. The exposure amount and the exposure amount that is the upper limit dimension are calculated to determine the resist pattern manufacturing conditions in one photolithography process (see, for example, Patent Document 1).
Japanese Patent Laid-Open No. 10-199787 (page 4, paragraph 0023 to page 5, paragraph 0028, FIGS. 1 and 4)

  However, in the above-described conventional technology, a final approximate expression for calculating the dependency of the line width on the exposure amount is obtained for each focal position, and an upper limit for obtaining the line width of the allowable dimension range at each focal position using this is calculated. Since the lower limit exposure amount is obtained, the upper and lower exposure amounts at the focus position other than the focus position where the dimension measurement data is measured, that is, between the two adjacent focus positions for which the final approximate expression is obtained, are immediately obtained. If it is not possible to obtain this, it will be necessary to solve by numerical analysis using the final approximate expression obtained, which will require calculation time and reduce the calculation accuracy of the calculated dimensions There's a problem.

For this reason, if the dimension measurement data of the line width including the intermediate focus position to be set is measured again and then the above regression analysis is performed from the beginning to determine the manufacturing conditions, it takes time to determine the manufacturing conditions. There's a problem.
In addition, the dimensional variation in the photolithography process is also caused by variations caused by the projection exposure apparatus used in the process, for example, variations in exposure amount and focus position setting, changes with time, etc. If the manufacturing conditions are set without taking the variation into consideration, there is a problem that the setting accuracy is lowered, an unexpected manufacturing variation occurs, and the yield of the semiconductor device to be manufactured is reduced.

  The present invention has been made to solve the above-described problems, and an object of the present invention is to provide means for accurately determining the manufacturing conditions of a resist pattern in a photolithography process.

  In order to solve the above-described problems, the present invention provides a resist pattern manufacturing condition setting method for measuring a plurality of dimensions of a resist pattern when a focal position and an exposure amount are independently changed in one photolithography process. A step of measuring data, a step of measuring apparatus variation data in a normal distribution of a focal position and an exposure amount of a projection exposure apparatus used in the photolithography process, and a focal position and an exposure amount based on the dimension measurement data. Using the explanatory function as a variable, performing a multiple regression analysis of two variables to determine an approximate expression of a multiple regression curve, a determination coefficient adjusted for the degree of freedom of the multiple regression curve determined by the multiple regression analysis, A step of comparing with a predetermined regression accuracy judgment value, and when the degree of freedom adjusted determination coefficient is not less than the predetermined regression accuracy judgment value Generating distribution calculation points having a normal distribution with the design point as an average value based on the apparatus variation data, a focal position and an exposure amount of a predetermined design point; and for each distribution calculation point A step of calculating dimension calculation data using an approximate expression of the determined multiple regression curve, a step of calculating an average value and a standard deviation in a normal distribution of the dimension calculation data, and the calculated dimension calculation data Determining the predetermined design point as a resist pattern manufacturing condition in the photolithography process when three times the standard deviation of the average value is within an allowable dimension range on both sides of the average value. And

  As a result, the present invention can obtain an approximate expression of a multiple regression curve based on dimensional measurement data, and by substituting an arbitrary combination of focus position and exposure amount into the approximate expression of the multiple regression curve, a single calculation can be performed. The dimension calculation data W can be easily calculated, the calculation accuracy of the calculated dimension can be improved, and the calculation time of the dimension calculation data at a large number of distribution calculation points for considering the variation of the projection exposure apparatus can be reduced. It is possible to shorten the time, and the effect that the manufacturing conditions of the resist pattern can be determined accurately and quickly is obtained.

  Embodiments of a resist pattern manufacturing condition setting method according to the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram showing an arithmetic unit according to the first embodiment, and FIG. 2 is a flowchart showing manufacturing condition setting processing according to the first embodiment.
The analysis in setting the manufacturing conditions of the resist pattern of this embodiment is performed using the arithmetic unit 1 such as a personal computer.
In FIG. 1, reference numeral 2 denotes a control unit of the arithmetic device 1, which has a function of controlling each part in the arithmetic device 1 and executing manufacturing condition setting processing and the like.

A storage unit 3 stores a program executed by the control unit 2, various data used for the program, a processing result by the control unit 2, and the like.
A display unit 4 includes a display screen such as an LCD and has a function of displaying various input screens, analysis result screens, and the like.
An input unit 5 includes a keyboard, a mouse, and the like, and has a function of accepting input of various measurement data and setting values from a person in charge of process design.

The storage unit 3 of the arithmetic device 1 stores the line width measurement data L as dimension measurement data obtained by measuring the line width as the dimension of the resist pattern when the focal position f and the exposure amount d are independently changed. Multiple regression having a function of performing multiple regression analysis using a predetermined explanatory function W (f, d) of two variables (refers to a function consisting of a plurality of terms describing a multiple regression curve in multiple regression analysis) Analysis program, function of generating a distribution calculation point T (f, d) having a two-dimensional distribution form from the average value and standard deviation of the normal distributions indicating the apparatus variation of the focal position f and exposure dose d in the projection exposure apparatus distribution calculation point generator program having a degree of freedom adjusted coefficient of determination R ² _ad is compared with a predetermined regression accuracy determination value freedom adjusted coefficient of determination regression curve obtained by multiple regression analysis R ² _{When ad} is equal to or greater than the regression accuracy determination value, the convergence of the multiple regression curve is determined, and the dimension calculation data for each distribution calculation point T (f, d) is determined using the multiple regression curve described by the determined approximate expression. The line width calculation data W is calculated, and the average value and standard deviation in the normal distribution of these line width calculation data W are calculated, and when the standard deviation is within the allowable dimension range on both sides of the average value A manufacturing condition setting processing program including an application program having a function for determining the determination of manufacturing conditions is stored in advance, and the operation of the arithmetic device 1 according to the present embodiment is performed according to the steps of the manufacturing condition setting processing program executed by the control unit 2. Each functional means as hardware is formed.

Further, the storage unit 3 stores the regression accuracy determination value for determining the convergence of the multiple regression curve based on the determination coefficient R ² _ad adjusted for the degree of freedom of the multiple regression curve, and the measurement data associated with the deletion of the measurement data. Residual rate lower limit value that is the lower limit value of the residual rate (referred to as data residual rate), the separation rate from the determined multiple regression curve of the line width measurement data Lij (difference between the line width calculation data Wij and the line width measurement data Lij) The separation data determination value, which is a predetermined ratio for selecting the line width measurement data Lij used in the multiple regression analysis, is calculated in advance based on the ratio of the difference obtained by dividing the absolute value of (2) by the line width measurement data Lij. In addition to being set and stored, a measurement number count area for counting the number of line width measurement data L used for multiple regression analysis is secured.

As the regression accuracy determination value of this example, 0.999 is stored as the determination value of the determination coefficient R ² _{ad after} adjusting the degree of freedom, and the lower limit of the remaining rate is set to 0. 0 as the ratio to the initial number of measurement data. 8 is stored, and 0.1 is stored as the separation data determination value.
Note that the degree-of-freedom-adjusted determination coefficient R ² _ad may be such that the line width measurement data L, the line width calculation data W calculated using the focus position f of the lattice point, and the exposure amount d match completely. It is “1”, and the degree-of-freedom-adjusted determination coefficient R ² _ad does not exceed “1” and is expressed by the square, so that it does not become a negative value.

Further, degree of freedom adjusted coefficient of determination R ² _ad is an index indicating the determined coefficient R ² and goodness of correlation coefficient R as well as the regression accuracy, the coefficient of determination R ² and term of the correlation coefficient R is described functions When the number of is increased or decreased, each value changes (apparently the regression accuracy changes), whereas in the case of the determination coefficient R ² _ad adjusted for the degree of freedom, the number of terms of the explanatory function is increased or decreased. Even if the index is adjusted, the index is adjusted so that the value does not change. Therefore, it is possible to determine whether the regression accuracy is good or not regardless of the form of the explanatory function.

  In the manufacturing condition setting process of the present embodiment, a normal projection exposure apparatus used in one photolithography process (specific photolithography process) for which manufacturing conditions are to be set in advance is used, and a predetermined focal position f and exposure amount d are used. Are set to a fixed value, and the actual exposure amount d and the focus position f are measured a plurality of times (in this embodiment, about 1000 times), and the focus position f and the exposure amount d are used as device variation data at that time. The average value md of exposure and its standard deviation σd, and the average value mf of focus position and its standard deviation σf are measured.

  In addition, as shown in FIG. 3, in a specific photolithography process, the exposure amount d and the focal position f are changed independently, that is, the exposure amount d is changed under p conditions for one focal position f. Line width measurement data L obtained by measuring the line width of a resist pattern formed on a semiconductor wafer with respect to q focal positions f (in this embodiment, p is 20 to 50 conditions and q is 20 to 50 conditions). A measurement table shown in FIG. 4 is prepared in advance, in which p × q data are collected in a matrix.

Note that the line width measurement data Lij of each lattice point shown in FIG. 4 is the line width measurement data L of the line width formed with the exposure amount dj of the jth condition at the focal position fi of the ith condition. Show.
The explanatory function W (f, d) in the multiple regression analysis of the two variables (focal position f and exposure amount d) of the present embodiment includes a first function F (f) relating to the focal position f and a second function relating to the exposure amount d. The following equation is used which is obtained by adding the function G (d) and the third function H (f, d) relating to the focal position f and the exposure amount d.

W (f, d) = Co + F (f) + G (d) + H (f, d) (Co is a constant)
(1)
here,
F (f) = a ₁ f + a ₂ f ² + a ₃ f ³ + a ₄ f ⁴ (a is a coefficient)
G (d) = b ₁ / d ² + b ₂ log ₁₀ (d) (b is a coefficient)
H (f, d) = (c ₁ f + c ₂ f ² + c ₃ f ³ + c ₄ f ⁴ ) log ₁₀ (d)
+ (H ₁ f + h ₂ f ² + h ₃ f ³ + h ₄ f ⁴ ) / d ² (c and h are coefficients)
The third function H (f, d) in Expression (1) is configured by combining the terms of the first function F (f) and the second function G (d) one by one and multiplying them. .

The explanatory function W (f, d) is input in advance by the person in charge using the input unit 5 of the arithmetic device 1 and stored in the storage unit 3.
In the following, the manufacturing condition setting process of the present embodiment will be described according to the step indicated by S using the flowchart shown in FIG.
The person in charge prepares the measurement table (FIG. 4) of the line width measurement data Lij of the photolithography process and the apparatus variation data of the projection exposure apparatus when the manufacturing process is newly set up. The start-up operation of the manufacturing condition setting processing program is performed using the input unit 5 of the arithmetic device 1.

The control unit 2 of the arithmetic device 1 that has recognized the start-up operation activates the manufacturing condition setting processing program stored in the storage unit 3.
S1, When the manufacturing condition setting processing program is started, the control unit 2 reads the explanatory function W (f, d) stored in the storage unit 3, sets it as the explanatory function of the multiple regression analysis program, and displays the display unit The line width measurement data input screen is displayed on the screen No. 4, and the person in charge inputs each line width measurement data Lij with the input unit 5 while referring to the measurement table of the line width measurement data Lij, and performs the input end operation.

The control unit 2 that has recognized the input end operation receives the input of each input line width measurement data Lij, counts the total number of the data (referred to as the total number of measurements), and counts the total number of measurements and each input line width measurement data. Lij is stored in the storage unit 3 and the total number of measurements is stored in the measurement number count area of the storage unit 3.
S2, the control unit 2 uses the explanatory function W (f, d) set based on the line width measurement data Lij stored in the storage unit 3 by the multiple regression analysis program, and uses the two-variable multiple regression. The analysis was performed, and the constant Co and the coefficients a, b, and c of each term of the first function F (f), the second function G (d), and the third function H (f, d) were obtained and obtained. An approximate expression of a multiple regression curve is determined by substituting the constant Co and each count.

In S3, the control unit 2 that has completed the multiple regression analysis calculates a determination coefficient R ² _ad that has been adjusted for the degree of freedom of the determined multiple regression curve.
The determination coefficient R ² _ad adjusted for the degree of freedom of the multiple regression curve in the first multiple regression analysis using the explanatory function W (f, d) of the present embodiment is R ² _ad = 0.99999 (line width measurement data The number of data of L is 1621).

In this case, the same line width measurement data L is used, and the explanatory function W (f, d) in which the third function H (f, d) in the above formula (1) is omitted, that is, W (f, d) = Co + F ( f) + G (d) (Co is a constant) (2)
here,
F (f) = a ₁ f + a ₂ f ² + a ₃ f ³ + a ₄ f ⁴ (a is a coefficient)
G (d) = b ₁ / d ² + b ₂ log ₁₀ (d) (b is a coefficient)
In the first case, the determination coefficient R ² _ad adjusted for the degree of freedom of the multiple regression curve in the first multiple regression analysis is R ² _ad = 0.98941.

S4, the degree of freedom adjusted coefficient of determination R control portion 2 calculates the ² _ad reads a regression accuracy determination value stored in the storage unit 3, the calculated degree of freedom adjusted coefficient of determination R ² _ad was read Regression When the accuracy determination value (0.999 in this embodiment) is equal to or greater than, the convergence of the regression accuracy of the multiple regression curve is determined, and the process proceeds to step S8.
When the degree-of-freedom-adjusted determination coefficient R ² _ad is less than the regression accuracy determination value, it is determined that the convergence of the regression accuracy is insufficient and the process proceeds to step S5.

S5, the control unit 2 having determined that the convergence is insufficient, reads the line width measurement data Lij and the separation data determination value stored in the storage unit 3, and the focal position fi of the lattice point of the line width measurement data Lij and the exposure The line width at each grid point is calculated by substituting the quantity di into the approximate expression of the determined multiple regression curve, and each line width calculation data Wij shown in FIG. 5 is calculated.
Then, the control unit 2 obtains a separation ratio obtained by dividing the absolute value of the difference between the line width calculation data Wij and the line width measurement data Lij by the line width measurement data Lij for each lattice point, and the separation ratio is read out. Line width measurement data L that is greater than or equal to the separation data determination value (0.1 in this embodiment) is specified, and the specified line width measurement data L is erased from the line width measurement data L in the storage unit 3 to measure the line width. While updating the data L, the number of line width measurement data L erased from the count number of the measurement number count area is subtracted to update the data number of the line width measurement data L used for the multiple regression analysis.

  S6, the control unit 2 that has updated the number of data reads the total number of measurements stored in the storage unit 3 and the remaining rate lower limit value, and divides the count number of the updated line width measurement data L by the total number of measurements. When the residual ratio is calculated and the calculated residual ratio is equal to or greater than the read lower limit lower limit (0.8 in this embodiment), it is determined that the multiple regression analysis can be continued and the process returns to step S2, and the updated The multiple regression analysis using the line width measurement data L is continued.

When the data remaining rate is less than the lower limit of the remaining rate, it is determined that the number of data for performing the multiple regression analysis is insufficient, and the process proceeds to step S7.
S7, the control unit 2 that has determined that the number of data for performing the multiple regression analysis is insufficient, displays a data shortage warning screen on the screen of the display unit 4 indicating that the variation of the line width measurement data L is excessive. The person in charge confirms the display content and performs a confirmation end operation using the input unit 5.

The control unit 2 that has recognized this confirmation ending operation ends the manufacturing condition setting process.
In this case, the person in charge confirms the presence / absence of erroneous input in step S1, increases the number of line width measurement data L when there is no erroneous input, or performs re-measurement, and again sets the manufacturing conditions by the manufacturing condition setting processing program. Set up.
In S8, the control unit 2 that has determined the convergence of the multiple regression curve designs the allowable distance range and the focal length f _DP and the exposure amount d _DP of the manufacturing condition (design point DP) to be set on the screen of the display unit 4. A data input screen is displayed, and the person in charge inputs the upper limit value and the lower limit value of the dimensional tolerance range of the photolithography process through the input unit 5, and refers to the line width measurement data L shown in FIG. Input DP and perform input termination operation.

Recognizing the input end operation, the control unit 2 stores the input upper limit value and lower limit value of the allowable dimension range, the focal length f _DP of the design point DP, and the exposure amount d _DP in the storage unit 3.
S9, the control unit 2 storing the dimension tolerance range displays an apparatus variation input screen on the screen of the display unit 4, and the person in charge uses the input unit 5 to determine the focal length f of the projection exposure apparatus used in the photolithography process. The apparatus variation data composed of the average values mf and md of the exposure dose d and the standard deviations σf and σd are input to complete the input operation.

The control unit 2 that has recognized the input end operation stores the input device variation data in the storage unit 3.
S10, the control unit 2 calculates the average of the focal length f _DP and the exposure amount d _{DP of} the design point DP stored in the storage unit 3 and the focal length f and the exposure amount d of the apparatus variation data by the distribution calculation point generation program. A normal distribution of the focal length f with the focal length f _DP of the design point DP as an average value for calculating an average value and a standard deviation in the normal distribution of the line width calculation data Wij based on the value and the standard deviation thereof; A plurality of distribution calculation points T (f, d) shown in FIG. 6 (about 1000 in this embodiment) are generated by two-dimensionally combining the normal distribution of the exposure dose d with the exposure dose d _DP as an average value. .

  S11, the control unit 2 that generated the distribution calculation point T (f, d) uses the focal length f and the exposure amount d of each distribution calculation point T (f, d) as an approximate expression of the determined multiple regression curve. The line width at each distribution calculation point T (f, d) is calculated by substituting into, and the line width variation data including the average value mw of the calculated line width calculation data W (f, d) and its standard deviation σw. (Referred to as line width variation data) is calculated.

  S12, the control unit that has calculated the line width variation data reads the upper and lower limit values of the allowable dimension range stored in the storage unit 3, and is the calculated line width of the input design point DP as shown in FIG. When the range (mw ± 3σw), which is 3 times the m standard deviation σw on both sides of the average value mw of the line width calculation data W, is within the read allowable dimension range (refers to the range between the lower limit value and the upper limit value). Determines that the manufacturing conditions have been determined, and proceeds to step S15.

When the mw ± 3σw range of the calculated line width calculation data W exceeds the allowable dimension range (either the lower limit side or the upper limit side of the line width calculation data W is the lower limit value or upper limit of the allowable dimension range In the case of exceeding the value), it is determined that the design point needs to be reset, and the process proceeds to step S13.
In the determination of the manufacturing conditions in this step, the median of the upper and lower limit values of the allowable dimension range and the average value mw of the line width calculation data W do not need to match, and the mw of the line width calculation data W It is sufficient if the range of ± 3σw is within the allowable dimension range.

S13, the control unit 2 that has determined that the design point needs to be reset, displays a message on the screen of the display unit 4 that prompts the user to re-enter the design point DP, an end code for ending the manufacturing condition setting process, and the like. Display the displayed design point re-input screen.
When the person in charge recalculates line width variation data at different design points _DP, he / she inputs the focal length f _DP and exposure dose d _DP of the new design point DP used for recalculation using the input unit 5, Perform input termination operation.

Further, when the manufacturing condition setting process is terminated due to the reason that both sides of the calculated line width variation data exceed the upper limit value and the lower limit value of the allowable dimension range, an end code is input.
S14, when the new design point DP is input, the control unit 2 returns to step S10 and continues to calculate the line width variation data by the new design point DP.
When the input of the end code is recognized, the manufacturing condition setting process is ended. In this case, the person in charge determines that the projection exposure apparatus to be installed in the photolithography process is inappropriate, and considers installation of another projection exposure apparatus.

In S15, the control unit 2 that has determined that the manufacturing condition has been determined displays a manufacturing condition determination screen on which the focal length f _DP and the exposure amount d _{DP of the} design point DP are displayed on the screen of the display unit 4.
The person in charge confirms the display contents and performs a confirmation operation using the input unit 5, and the control unit 2 that recognizes the confirmation operation ends the manufacturing condition setting process.
In this way, the resist pattern manufacturing condition setting process of the present embodiment in one photolithography process is executed, and the person in charge determines the manufacturing conditions in each photolithography process of the installed manufacturing process in the same manner as described above. Then, the semiconductor device is manufactured using these determined manufacturing conditions.

As described above, in the resist pattern manufacturing condition setting process according to the present embodiment, the focus position is obtained by using the line width measurement data L of the resist pattern when the focal position f and the exposure amount d are independently changed. Multiple regression analysis using two variables of f and exposure dose d is performed, and the degree-of-freedom adjustment coefficient R ² _ad adjusted for the degree of freedom of the multiple regression curve determined thereby is compared with a predetermined regression accuracy judgment value. When the adjusted determination coefficient R ² _ad is equal to or greater than the regression accuracy determination value, the convergence of the multiple regression curve is determined and the resist pattern manufacturing conditions are determined using the approximate expression of the determined multiple regression curve. If the line width calculation data W at an arbitrary focal position f other than the focal position at which the width measurement data is measured is substituted into the approximate expression of the multiple regression curve, the focal position f and the exposure amount d are substituted once without using numerical analysis. Calculation only The calculation accuracy of the calculated line width can be improved, and the calculation time of the line width calculation data W can be shortened to increase the efficiency of determining the manufacturing conditions.

Further, an approximate expression of a multiple regression curve based on the line width measurement data L can be obtained by multiple regression analysis using two variables of the focal position f and the exposure dose d. The regression accuracy for the line width measurement data L can be improved as compared with the regression analysis based on the data including.
Furthermore, when the determination coefficient R ² _ad adjusted for the degree of freedom is less than the regression accuracy determination value, the line width measurement in the line width measurement data L has a separation rate equal to or greater than a predetermined separation data determination value from the line width calculation data W. When the data L is deleted and the data remaining rate of the line width measurement data L becomes less than the predetermined remaining rate judgment value, the data shortage warning screen is displayed and the manufacturing condition setting process is terminated. The multiple regression analysis using the width measurement data L can improve the regression accuracy of the multiple regression curve and prevent the regression accuracy of the unexpected multiple regression curve from being lowered due to the insufficient number of data of the line width measurement data L. can do.

  Furthermore, each focal length f of the distribution calculation point T (f, d) having a two-dimensional distribution form of a normal distribution generated from the apparatus variation data of the focal position f and the exposure dose d in the projection exposure apparatus, and the exposure dose d. Is used to calculate the line width calculation data W in the determined multiple regression curve at each distribution calculation point T, and the average value and standard deviation in the normal distribution of the line width calculation data W are calculated. 3 is less than the allowable dimension range on both sides of the average value, the determination of the manufacturing condition is judged. Therefore, the resist pattern manufacturing condition can be easily determined in consideration of the variation of the projection exposure apparatus, and is expected. The manufacturing conditions of the resist pattern can be accurately set by preventing the occurrence of manufacturing variations, and the manufacturing is performed by preventing the dimensional deviation in the photolithography process using the determined manufacturing conditions. It is possible to improve the yield of the conductor arrangement.

As described above, in this embodiment, a plurality of line width measurement data L of the resist pattern when the focal position f and the exposure dose d are independently changed in one photolithography process, and the photolithography. A device position variation data of the focal position f and the exposure amount d of the projection exposure apparatus used in the process is measured in advance, and a plurality of values using the focal position f and the exposure amount d as variables based on the measured line width measurement data L. A multiple regression analysis of two variables is performed using an explanatory function W (f, d) consisting of the following term, and a determination coefficient R ² _ad adjusted for the degree of freedom of the multiple regression curve determined by the multiple regression analysis and a predetermined regression accuracy determination by comparing the values, when the degree of freedom adjusted coefficient of determination R ² _ad is equal to or higher than the predetermined regression accuracy determination value, the device variation data measured, the focal length f _DP and the exposure of a given design point DP Based on the d _DP, generates a distribution calculation point having a distribution shape of a normal distribution with mean value design point DP, for each of these distribution calculation point, the approximate expression definitive linewidth calculation of regression curve was determined The data W is calculated, the average value mw and the standard deviation σw in the normal distribution of the width calculation data are calculated, and three times the standard deviation σw of the calculated line width calculation data W (3σw) is the average value mw When a predetermined design point DP is determined as a resist pattern manufacturing condition in the photolithography process when both sides are within the allowable line width range, an approximate expression of a multiple regression curve based on the line width measurement data is obtained. By substituting a combination of an arbitrary focal position f and exposure dose d into the approximate expression of the multiple regression curve, the line width calculation data W can be easily calculated by one calculation, and the calculated line Width calculation It is possible to increase the degree of calculation and to shorten the calculation time of the line width calculation data W at a large number of distribution calculation points T (f, d) for considering variations in the projection exposure apparatus. It is possible to accurately and quickly determine the manufacturing conditions of the resist pattern that prevents the occurrence of manufacturing variations.

The configuration of the present embodiment and the flowchart of the manufacturing condition setting process are the same as those of the first embodiment.
The storage unit 3 of the arithmetic device 1 of the present embodiment stores in advance a manufacturing condition setting processing program similar to that of the first embodiment, and this embodiment is performed according to the steps of the manufacturing condition setting processing program executed by the control unit 2. Each functional means as hardware of the arithmetic device 1 is formed.

In addition, the storage unit 3 stores a regression accuracy determination value, a remaining rate lower limit value, and a separation data determination value similar to those in the first embodiment, and stores a measurement number count area similar to that in the first embodiment. Is secured.
The explanatory function W (f, d) in the multiple regression analysis of the two variables (focal position f and exposure dose d) of this embodiment is the explanatory function W (f, d) shown in the equation (1) of the first embodiment. The following equation is used by changing the third function H (f, d).

W (f, d) = Co + F (f) + G (d) + H (f, d) (Co is a constant)
(3)
here,
F (f) = a ₁ f + a ₂ f ² + a ₃ f ³ + a ₄ f ⁴ (a is a coefficient)
G (d) = b ₁ / d ² + b ₂ log ₁₀ (d) (b is a coefficient)
H (f, d) = c ₁ f ² log ₁₀ (d) + c ₂ f ² / d ² + c ₃ f / d (c is a coefficient)
The first function F (f) and the second function G (d) are the same as those in the first embodiment.

The manufacturing condition setting process of this embodiment is the same as the manufacturing condition setting process shown in FIG.
In this case, the explanatory function W (f, d) of Expression (3) is used for the multiple regression analysis of two variables in step S2.
Further, the determination coefficient R ² _ad adjusted for the degree of freedom of the multiple regression curve in the first multiple regression analysis using the explanatory function W (f, d) of the present embodiment calculated in step S3 is R ² _ad = 0.99973 (the line width measurement data L used in the analysis is the same as in Example 1 above).

  As described above, in the present embodiment, in addition to the same effects as in the first embodiment, the number of terms of the third function H (f, d) of the explanatory function W (f, d) is reduced. Thus, it is possible to further reduce the calculation time of the line width calculation data W at a large number of distribution calculation points T (f, d) for taking into account variations in the projection exposure apparatus.

FIG. 8 is a flowchart showing the manufacturing condition setting process of the third embodiment.
In addition, the same part as the said Example 1 attaches | subjects the same code | symbol, and abbreviate | omits the description.
In the storage unit 3 of the arithmetic device 1 of the present embodiment, each item of the third function H (f, d) of the explanatory function W (f, d) is added to the manufacturing condition setting processing program similar to that of the first embodiment. A manufacturing condition setting processing program in which a contribution rate is calculated, and when there is a contribution rate term less than a predetermined contribution rate judgment value, a speedup processing program is added to delete the term and speed up the process calculation Are stored in advance, and each function means as hardware of the arithmetic device 1 of the present embodiment is formed by the steps of the manufacturing condition setting processing program executed by the control unit 2.

In addition to the regression accuracy determination value, the remaining rate lower limit value, and the separation data determination value similar to those in the first embodiment, the storage unit 3 stores the third function H (f, d) of the explanatory function W (f, d). ) Is determined and stored in advance, and a measurement count area similar to that in the first embodiment is secured.
The contribution rate in this example is obtained by performing multiple regression analysis using the explanatory function W (f, d) shown in the expression (1) of Example 1 above, and using the constant Co and each coefficient determined thereby, The line width calculation data Wij under the calculation condition composed of the focal position f and the exposure dose d of each line width measurement data L is calculated, and the calculated line width calculation data Wij and the line width measurement data Lij based on the calculation condition are calculated. The line width calculation data Wk (k = 1 to N, N is calculated by excluding any one of the terms of the third function H (f, d) under the same calculation condition as the square of the difference Xo from (The number of data of the line width measurement data L) and the root mean square of the difference Xk between the line width measurement data Lij, and the contribution ratio A at that time is defined as the ratio of the root mean square of the difference Xk to the square of the difference Xo Then
A = (ΣXk ² / N) / Xo ² (4)
The contribution rate determination value is set as 0.03.

In the manufacturing condition setting process of the present embodiment, as in the first embodiment, the apparatus variation data of the projection exposure apparatus used for a specific photolithography process in advance and the line width measurement data Lij of each lattice point shown in FIG. Has been measured.
As the explanatory function W (f, d) in the multiple regression analysis of the two variables (focal position f and exposure dose d) that are the basis of the present embodiment, the expression (1) of the first embodiment is used. W (f, d) is stored in the storage unit 3 as in the first embodiment.

In the following, the manufacturing condition setting process of the present embodiment will be described according to the steps indicated by SA using the flowchart shown in FIG.
The person in charge performs the start-up operation of the manufacturing condition setting processing program in the same manner as in the first embodiment, and the control unit 2 of the arithmetic unit 1 that recognizes this starts the manufacturing condition setting processing program.
When the SA1 and manufacturing condition setting processing program is activated, the control unit 2 performs the explanation function W (f, d) that is the basis of the storage unit 3 in the same manner as in the first embodiment (formula (1) in this embodiment). Is set as an explanatory function of the multiple regression analysis program, the input of the line width measurement data Lij from the person in charge is received, the total number of measurement of the data and each line width measurement data Lij are stored in the storage unit 3, and the storage unit The total number of measurements is stored in the measurement number count area 3.

  SA2, the control unit 2 uses a multiple regression analysis program, based on the line width measurement data Lij stored in the storage unit 3, and uses a basic explanatory function W (f, d) to perform multiple regression of two variables. The analysis is performed, and the constant term Co and the coefficients a, b, and c of each term of the first function F (f), the second function G (d), and the third function H (f, d) are obtained and obtained. The approximate expression of the multiple regression curve in the basic explanatory function W (f, d) obtained by substituting the constant Co and each count is determined.

SA3, the control unit 2 that has determined the approximate expression of the basic multiple regression curve uses the expression (4) by the high-speed processing program, and uses the third function H () of the basic explanatory function W (f, d). The contribution rate A of each term of f, d) is calculated.
The control unit 2 that calculated the contribution rate A of SA4 and the third function H (f, d) reads the contribution rate determination value stored in the storage unit 3, and calculates the calculated contribution rate A and the read contribution rate. Compared with the rate judgment value (0.03 in this embodiment), the term having the contribution rate A less than the contribution rate judgment value is deleted to reduce the number of terms of the explanatory function W (f, d), and the high speed The converted new explanatory function W (f, d) is set as an explanatory function in the multiple regression analysis after step SA5.

Subsequent operations in steps SA5 to SA18 are the same as the operations in steps S2 to S15 in the first embodiment, and a description thereof will be omitted.
In this case, the new explanatory function W (f, d) set in step SA4 is used for the two-variable multiple regression analysis in step SA5.
As described above, in this embodiment, in addition to the same effects as those in the first embodiment, the contribution ratio A to the line width calculation data L of each term of the third function H (f, d) of the explanatory function is calculated in advance. When the calculated contribution rate A is less than the predetermined contribution rate determination value, the term is deleted, thereby reducing the number of terms of the explanatory function W (f, d) used for the multiple regression analysis. Thus, it is possible to further reduce the calculation time of the line width calculation data W at a number of distribution calculation points T (f, d) for taking into account variations in the projection exposure apparatus.

In the present embodiment, the description has been made assuming that the term having a low contribution rate A of the third function H (f, d) is deleted, but each term of the first function F (f) and the second function G (d) is deleted. For the above, the contribution rate may be obtained in the same manner as described above, and the term with a low contribution rate may be deleted. The same applies to the explanation function W (f, d) of the second embodiment.
As a result, the calculation speed can be further increased.

In each of the above embodiments, the dimension of the resist pattern is described as a line width. However, the dimension of the resist pattern is not limited to the above, and may be a gap between patterns, a vertical and horizontal length of a specific area, or the like. May be.
In each of the above embodiments, the first function F (f) has been described as being a quartic polynomial, but may be a polynomial having an order of 5 or more.

Further, in each of the above embodiments, the second function G (d) has been described as being composed of two terms, but a higher order polynomial, for example,
G (d) = b ₁ / d ² + b ₂ log ₁₀ (d) + b ₃ (log ₁₀ (d)) ² (b is a coefficient)
(5)
Etc.

  In this case, when the first function F (f) and / or the second function G (d) is a higher order polynomial, the third function H (f, d) also has a higher order term. The function that contains it will be used.

FIG. 1 is a block diagram illustrating an arithmetic device according to a first embodiment. The flowchart which shows the manufacturing condition setting process of Example 1. Explanatory drawing which shows the line submeasurement data of Example 1. Explanatory drawing which shows the structural example of the measurement table | surface of the line submeasurement data of Example 1. FIG. Explanatory drawing which shows the structural example of the calculation table of the line subcalculation data of Example 1. FIG. Explanatory drawing which shows the generation | occurrence | production state of the distribution calculation point of Example 1. Explanatory drawing which shows the decision state of the manufacturing conditions of Example 1. The flowchart which shows the manufacturing condition setting process of Example 3.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Arithmetic unit 2 Control part 3 Memory | storage part 4 Display part 5 Input part

Claims (5)

Measuring a plurality of dimension measurement data of a resist pattern when the focal position and the exposure amount are independently changed in one photolithography process;
Measuring apparatus variation data in a normal distribution of the focal position and exposure amount of the projection exposure apparatus used in the photolithography process;
Based on the dimension measurement data, using an explanatory function with the focal position and the exposure dose as variables, performing a two-variable multiple regression analysis and determining an approximate expression of a multiple regression curve;
Comparing the coefficient of determination adjusted for the degree of freedom of the multiple regression curve determined by the multiple regression analysis with a predetermined regression accuracy judgment value;
When the degree-of-freedom-adjusted determination coefficient is equal to or greater than the predetermined regression accuracy determination value, the design point is set as an average value based on the apparatus variation data, the focal position and the exposure amount of the predetermined design point. Generating a distribution calculation point having a normal distribution shape;
Calculating dimension calculation data using the approximate expression of the determined multiple regression curve for each distribution calculation point;
Calculating a mean value and a standard deviation in a normal distribution of the dimension calculation data;
Determining the predetermined design point as a resist pattern manufacturing condition in the photolithography process when three times the standard deviation of the calculated dimension calculation data is within an allowable dimension range on both sides of the average value; A method for setting a manufacturing condition of a resist pattern, comprising: In claim 1,
The focal position constituting the two variables is f, the exposure amount is d, the first function relating to the focal position f is F (f), the second function relating to the exposure amount d is G (d), the focal position f and the exposure amount d. When the third function for and is H (f, d),
The explanatory function W (f, d) used for the multiple regression analysis is
W (f, d) = Co + F (f) + G (d) + H (f, d) (Co is a constant)
here,
F (f) = a ₁ f + a ₂ f ² + a ₃ f ³ + a ₄ f ⁴ (a is a coefficient)
G (d) = b ₁ / d ² + b ₂ log ₁₀ (d) (b is a coefficient)
H (f, d) = (c ₁ f + c ₂ f ² + c ₃ f ³ + c ₄ f ⁴ ) log ₁₀ (d)
+ (H ₁ f + h ₂ f ² + h ₃ f ³ + h ₄ f ⁴ ) / d ² (c and h are coefficients)
A method for setting manufacturing conditions for a resist pattern. In claim 1,
The focal position constituting the two variables is f, the exposure amount is d, the first function relating to the focal position f is F (f), the second function relating to the exposure amount d is G (d), the focal position f and the exposure amount d. When the third function for and is H (f, d),
The explanatory function W (f, d) used for the multiple regression analysis is
W (f, d) = Co + F (f) + G (d) + H (f, d) (Co is a constant)
here,
F (f) = a ₁ f + a ₂ f ² + a ₃ f ³ + a ₄ f ⁴ (a is a coefficient)
G (d) = b ₁ / d ² + b ₂ log ₁₀ (d) (b is a coefficient)
H (f, d) = c ₁ f ² log ₁₀ (d) + c ₂ f ² / d ² + c ₃ f / d (c is a coefficient)
A method for setting manufacturing conditions for a resist pattern. In any one of Claims 1 to 3,
Calculating a contribution rate of each term of the explanatory function;
And a step of deleting the item when the contribution ratio is less than a predetermined contribution ratio determination value.   5. A method for manufacturing a semiconductor device, comprising: determining a resist pattern manufacturing condition in each photolithography step using the resist pattern manufacturing condition setting method according to claim 1.