Patent Publication Number: US-7897896-B2

Title: Temperature setting method of thermal processing plate, computer-readable recording medium recording program thereon, and temperature setting apparatus for thermal processing plate

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a temperature setting method of a thermal processing plate, a computer-readable recording medium recording a program thereon, and a temperature setting apparatus for a thermal processing plate. 
     2. Description of the Related Art 
     In a photolithography process in manufacturing, for example, a semiconductor device, for example, a resist coating treatment of applying a resist solution onto a wafer to form a resist film, exposure processing of exposing the resist film into a predetermined pattern, heating processing of accelerating the chemical reaction in the resist film after exposure (post-exposure baking), and developing treatment of developing the exposed resist film are performed in sequence, so that the series of wafer processing forms a predetermined resist pattern on the wafer. 
     For example, the heating processing such as the above-described post-exposure baking is usually performed in a heating processing apparatus. The heating processing apparatus includes a thermal plate for mounting and heating the wafer thereon. The thermal plate has a heater embedded therein which generates heat by power feeding, and the heat generated by the heater adjusts the thermal plate to a predetermined temperature. 
     The thermal processing temperature in the above-described heating processing greatly affects the line width of the resist pattern to be finally formed on the wafer. Hence, to strictly control the temperature within the wafer during heating, the thermal plate of the above-described heating processing apparatus is divided into a plurality of regions, and an independent heater is embedded in each of the regions to adjust the temperature for each of the regions. 
     It is known that if the temperature adjustment for all of the regions of the above-described thermal plate is performed at the same set temperature, the temperature may vary within the wafer on the thermal plate, for example, due to the difference in thermal resistance between the regions, resulting in variations in the line width of the resist pattern. For this reason, a temperature correction value (a temperature offset value) is set for each of the regions of the thermal plate to finely adjust the in-plane temperature of the thermal plate (see Japanese Patent Application Laid-open No. 2001-143850). 
     For setting the above-described temperature correction value, usually, the current line widths within the wafer are first measured, and an operator sets appropriate temperature correction values according to his/her experience and knowledge in consideration of measurement results. Thereafter, the line widths within the wafer are measured again, and the operator changes the temperature correction values in consideration of the line width measurement results. After operations of the line width measurement and the change of the temperature correction values are repeated through a try and error process, the operator ends the setting of the temperature correction values at a point in time when the operator judges that an appropriate line width have been obtained. 
     However, it is difficult to judge whether or not the temperature correction values at a point in time are appropriate values to provide appropriate line widths halfway through the temperature setting operation in the above-described temperature setting, and therefore the operator ends the temperature setting operation at the point in time when the operator judges that the line widths have become appropriate by his/her subjectivity. As a result, an appropriate temperature setting may not have been made, thus causing variations, among operators, in line width within the wafer after the temperature setting. Further, since an appropriate line width to be converged is not correctly known, the operator sometimes performs change of the temperature setting a number of times through a try and error process, thus taking a long time for the temperature setting operation. 
     SUMMARY OF THE INVENTION 
     The present invention has been developed in consideration of the above points, and its object is to accurately estimate processing states of a substrate such as a wafer after change of temperature setting in temperature setting of a thermal processing plate such as a thermal plate, and perform the temperature setting of the thermal processing plate in a short time and properly. 
     The present invention is a temperature setting method of a thermal processing plate for mounting and thermally processing a substrate thereon, the thermal processing plate being divided into a plurality of regions, a temperature being settable for each of the regions, and a temperature correction value for adjusting an in-plane temperature being settable for each of the regions, the method including the following steps. 
     The method includes the steps of measuring processing states within the substrate for the substrate which has been subjected to a series of substrate processing including the thermal processing, and calculating, from an in-plane tendency of the substrate of the measured processing states, an in-plane tendency improvable by changing the temperature correction value for each of the regions of the thermal processing plate and an unimprovable in-plane tendency; and adding an average remaining tendency of the improvable in-plane tendency after improvement to the calculated unimprovable in-plane tendency to estimate an in-plane tendency of the processing states after change of the temperature correction values for the thermal processing plate. 
     The average remaining tendency is calculated through the following first to fifth steps. 
     A first step: measuring processing states within the substrate for the substrate which has been subjected to substrate processing, and calculating, from an in-plane tendency of the substrate of the measured processing states, an in-plane tendency improvable by changing the temperature correction value for each of the regions of the thermal processing plate. 
     A second step: calculating, from the calculated improvable in-plane tendency, the temperature correction value for each of the regions of the thermal processing plate to bring the improvable in-plane tendency to 0 (ZERO) using a calculation model obtained in advance from a correlation between the improvable in-plane tendency and the temperature correction values. 
     A third step: changing a set temperature of each of the regions of the thermal processing plate to the calculated temperature correction value. 
     A fourth step: calculating a remaining tendency of the improvable in-plane tendency after improvement by changing the set temperature to the temperature correction value. 
     A fifth step: averaging the remaining tendencies calculated in a plurality of number of times of performance of the first to fourth steps. 
     According to the present invention, the improvable in-plane tendency and the unimprovable in-plane tendency are calculated from the measured in-plane tendency of the substrate, and the average remaining tendency of the improvable in-plane tendency after improvement obtained in advance is added to the unimprovable in-plane tendency to estimate the in-plane tendency after the temperature setting. If the improvable in-plane tendency can be completely brought to 0 (ZERO) by the change of the temperature setting of the thermal processing plate, the remaining unimprovable in-plane tendency is the in-plane tendency after improvement by the change of the temperature setting. Actually, however, the improvable in-plane tendency cannot be completely brought to 0 (ZERO) even if the change of the temperature setting is performed. The remaining tendency of the improvable in-plane tendency remaining after improvement is averaged, and the average remaining tendency is added to the unimprovable in-plane tendency, thus making it possible to extremely accurately estimate the in-plane tendency of the processing states of the substrate after change of the temperature setting. As a result, the temperature setting of the thermal processing plate can be performed in a short time and properly. 
     In calculating the remaining tendency after improvement in the present invention, the processing states within the substrate may be measured for a substrate which has been subjected to substrate processing after improvement, and, from the in-plane tendency of the substrate of the measured processing states, an improvable in-plane tendency may be calculated and regarded as the remaining tendency after improvement. 
     Further, in calculating the improvable in-plane tendency in the present invention, the in-plane tendency of the substrate of the measured processing states may be decomposed to a plurality of in-plane tendency components using a Zernike polynomial, and in-plane tendency components improvable by changing the temperature correction value for each of the regions of the thermal processing plate of the plurality of in-plane tendency components may be added to calculate the improvable in-plane tendency. 
     Further, the unimprovable in-plane tendency may be calculated by subtracting the calculated improvable in-plane tendency from the in-plane tendency of the substrate of the measured processing states. 
     In calculating the temperature correction value for each of the regions of the thermal processing plate in the present invention, the temperature correction value for each of the regions of the thermal processing plate to bring each of the improvable in-plane tendency components to 0 (ZERO) may be calculated using a calculation model indicating a correlation between change amounts of the plurality of in-plane tendency components within the substrate and the temperature correction values. 
     The series of substrate processing is, for example, processing of forming a resist pattern on the substrate in a photolithography process. Further, the processing states within the substrate are, for example, line widths of the resist pattern. Further, the thermal processing is heating processing performed after exposure processing and before developing treatment. 
     The above-described temperature setting method of a thermal processing plate may be, for example, computer-programmed and stored in a computer-readable recording medium 
     The present invention according to another aspect is a temperature setting apparatus for a thermal processing plate for mounting and thermally processing a substrate thereon, the thermal processing plate being divided into a plurality of regions, a temperature being settable for each of the regions, and a temperature correction value for adjusting an in-plane temperature of the thermal processing plate being settable for each of the regions of the thermal processing plate, and the temperature setting apparatus may include a computing unit for performing the following processes. 
     Specifically, the computing unit measures processing states within the substrate for the substrate which has been subjected to a series of substrate processing including the thermal processing, and calculates, from an in-plane tendency of the substrate of the measured processing states, an in-plane tendency improvable by changing the temperature correction value for each of the regions of the thermal processing plate and an unimprovable in-plane tendency; and adds an average remaining tendency of the improvable in-plane tendency after improvement to the calculated unimprovable in-plane tendency to estimate an in-plane tendency of the processing states after change of the temperature correction values for the thermal processing plate. 
     When calculating the average remaining tendency, a first step of measuring processing states within the substrate for the substrate which has been subjected to substrate processing, and calculating, from an in-plane tendency of the substrate of the measured processing states, an in-plane tendency improvable by changing the temperature correction value for each of the regions of the thermal processing plate; a second step of calculating, from the calculated improvable in-plane tendency, the temperature correction value for each of the regions of the thermal processing plate to bring the improvable in-plane tendency to 0 (ZERO) using a calculation model obtained in advance from a correlation between the improvable in-plane tendency and the temperature correction values; a third step of changing a set temperature of each of the regions of the thermal processing plate to the calculated temperature correction value; a fourth step of calculating a remaining tendency of the improvable in-plane tendency after improvement by changing the set temperature to the temperature correction value; and a fifth step of averaging the remaining tendencies calculated in a plurality of number of times of performance of the first to fourth steps, are performed. 
     According to the present invention, the processing states of a substrate after change of temperature setting of a thermal processing plate can be accurately estimated, so that the temperature setting of a thermal processing plate can be performed in a short time and properly. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a plan view showing the outline of a configuration of a coating and developing treatment system; 
         FIG. 2  is a front view of the coating and developing treatment system in  FIG. 1 ; 
         FIG. 3  is a rear view of the coating and developing treatment system in  FIG. 1 ; 
         FIG. 4  is a plan view showing a configuration of a thermal plate in a PEB unit; 
         FIG. 5  is an explanatory view showing the outline of a configuration of a line width measuring unit; 
         FIG. 6  is a block diagram showing a configuration of a temperature setting apparatus; 
         FIG. 7  is an explanatory view showing a state in which the in-plane tendency of line widths by the line width measurements is decomposed into a plurality of in-plane tendency components using a Zernike polynomial; 
         FIG. 8  is an explanatory view showing contents to calculate an improvable in-plane tendency by adding up improvable in-plane tendency components; 
         FIG. 9  is a determinant showing an example of a calculation model; 
         FIG. 10  is an explanatory showing contents to calculate an average remaining tendency by averaging a plurality of remaining tendencies; 
         FIG. 11  is an explanatory view showing contents to calculate an unimprovable in-plane tendency by subtracting an improvable in-plane tendency from a current measured in-plane tendency; 
         FIG. 12  is an explanatory view showing contents to estimate an in-plane tendency after change of temperature setting by adding the average remaining tendency to the unimprovable in-plane tendency; 
         FIG. 13  is a flowchart showing a process of calculating the average remaining tendency of a temperature setting process; 
         FIG. 14  is an explanatory view showing measurement points of the line widths within the wafer; 
         FIG. 15  is a relational expression of the calculation model into which the adjustment amounts for the in-plane tendency components and temperature correction values are substituted; 
         FIG. 16  is a flowchart showing a process of estimating the in-plane tendency after the change of temperature setting of the temperature setting process; 
         FIG. 17  is an explanatory view showing a variation tendency of line width measured values; 
         FIG. 18  is an explanatory view showing a gradient component in an X-direction of the variation tendency of the line width measured values; 
         FIG. 19  is an explanatory view showing a gradient component in a Y-direction of the variation tendency of the line width measured values; 
         FIG. 20  is an explanatory view showing a curvature component of the variation tendency of the line width measured values; and 
         FIG. 21  is a graph showing a case when 3σ of the improvable in-plane tendency exceeds a threshold value and a case when it does not exceed. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Hereinafter, a preferred embodiment of the present invention will be described.  FIG. 1  is a plan view showing the outline of a configuration of a coating and developing treatment system  1  incorporating a temperature setting apparatus for a thermal processing plate according to the embodiment,  FIG. 2  is a front view of the coating and developing treatment system  1 , and  FIG. 3  is a rear view of the coating and developing treatment system  1 . 
     The coating and developing treatment system  1  has, as shown in  FIG. 1 , a configuration in which, for example, a cassette station  2  for transferring, for example, 25 wafers W per cassette as a unit from/to the outside into/from the coating and developing treatment system  1  and transferring the wafers W into/out of a cassette C; a processing station  3  including a plurality of various kinds of processing and treatment units, which are multi-tiered, each for performing predetermined processing or treatment in a manner of single wafer processing in the photolithography process; and an interface section  4  for delivering the wafers W to/from a not-shown aligner provided adjacent to the processing station  3 , are integrally connected together. 
     In the cassette station  2 , a cassette mounting table  5  is provided and configured such that a plurality of cassettes C can be mounted thereon in a line in an X-direction (a top-to-bottom direction in  FIG. 1 ). In the cassette station  2 , a wafer transfer body  7  is provided which is movable in the X-direction on a transfer path  6 . The wafer transfer body  7  is also movable in an arrangement direction of the wafers W housed in the cassette C (a Z-direction; the vertical direction), and thus can selectively access the wafers W in each of the cassettes C arranged in the X-direction. 
     The wafer transfer body  7  is rotatable in a θ-direction around a Z-axis, and can access a temperature regulating unit  60  and a transition unit  61  included in a later-described third processing unit group G 3  on the processing station  3  side. 
     The processing station  3  adjacent to the cassette station  2  includes, for example, five processing unit groups G 1  to G 5  in each of which a plurality of processing and treatment units are multi-tiered. On the side of the negative direction in the X-direction (the downward direction in  FIG. 1 ) in the processing station  3 , the first processing unit group G 1  and the second processing unit group G 2  are placed in order from the cassette station  2  side. On the side of the positive direction in the X-direction (the upward direction in  FIG. 1 ) in the processing station  3 , the third processing unit group G 3 , the fourth processing unit group G 4 , and the fifth processing unit group G 5  are placed in order from the cassette station  2  side. Between the third processing unit group G 3  and the fourth processing unit group G 4 , a first transfer unit  10  is provided. The first transfer unit  10  can selectively access the processing and treatment units in the first processing unit group G 1 , the third processing unit group G 3 , and the fourth processing unit group G 4  and transfer the wafer W to them. Between the fourth processing unit group G 4  and the fifth processing unit group G 5 , a second transfer unit  11  is provided. The second transfer unit  11  can selectively access the processing and treatment units in the second processing unit group G 2 , the fourth processing unit group G 4 , and the fifth processing unit group G 5  and transfer the wafer W to them. 
     In the first processing unit group G 1 , as shown in  FIG. 2 , solution treatment units each for supplying a predetermined liquid to the wafer W to perform treatment, for example, resist coating units  20 ,  21 , and  22  each for applying a resist solution to the wafer W, and bottom coating units  23  and  24  each for forming an anti-reflection film that prevents reflection of light during exposure processing, are five-tiered in order from the bottom. In the second processing unit group G 2 , solution treatment units, for example, developing treatment units  30  to  34  each for supplying a developing solution to the wafer W to develop it are five-tiered in order from the bottom. Further, chemical chambers  40  and  41  for supplying various kinds of treatment solutions to the solution treatment units in the processing unit groups G 1  and G 2  are provided at the lowermost tiers of the first processing unit group G 1  and the second processing unit group G 2 , respectively. 
     As shown in  FIG. 3 , in the third processing unit group G 3 , for example, the temperature regulating unit  60 , the transition unit  61  for passing the wafer W, high-precision temperature regulating units  62  to  64  each for temperature-regulating the wafer W under a high precision temperature control, and high-temperature thermal processing units  65  to  68  each for heat-processing the wafer W at a high temperature, are nine-tiered in order from the bottom. 
     In the fourth processing unit group G 4 , for example, a high-precision temperature regulating unit  70 , pre-baking units  71  to  74  each for heat-processing the wafer W after resist coating treatment, and post-baking units  75  to  79  each for heat-processing the wafer W after developing treatment, are ten-tiered in order from the bottom. 
     In the fifth processing unit group G 5 , a plurality of thermal processing units each for thermally processing the wafer W, for example, high-precision temperature regulating units  80  to  83 , and post-exposure baking units (hereinafter, referred to as “PEB units”)  84  to  89  each for heat-processing the wafer W after exposure and before development, are ten-tiered in order from the bottom. 
     The PEB units  84  to  89  each include, for example, a thermal plate  90 , as shown in  FIG. 4 , as a thermal processing plate for mounting and heating the wafer W thereon. The thermal plate  90  has an almost disk shape with a large thickness. The thermal plate  90  is divided into a plurality of, for example, five thermal plate regions R 1 , R 2 , R 3 , R 4  and R 5 . The thermal plate  90  is divided, for example, into the circular thermal plate region R 1  which is located at the central portion as seen in plan view and the thermal plate regions R 2  to R 5  which are made by equally dividing the peripheral portion around the thermal plate region R 1  into four sectors. 
     A heater  91  generating heat by power feeding is individually embedded in each of the thermal plate regions R 1  to R 5  of the thermal plate  90  and can heat each of the thermal plate regions R 1  to R 5 . The heating value of each of the heaters  91  of the thermal plate regions R 1  to R 5  is adjusted, for example, by a temperature controller  92 . The temperature controller  92  can adjust the heating value of the heater  91  to control the temperature of each of the thermal plate regions R 1  to R 5  to a predetermined set temperature. The temperature setting in the temperature controller  92  is performed, for example, by a later-described temperature setting apparatus  150 . 
     As shown in  FIG. 1 , on the positive direction side in the X-direction to the first transfer unit  10 , a plurality of processing and treatment units are arranged, for example, adhesion units  100  and  101  each for performing hydrophobic treatment on the wafer W being two-tiered in order from the bottom as shown in  FIG. 3 . As shown in  FIG. 1 , on the positive side in the X-direction to the second transfer unit  111 , for example, an edge exposure unit  102  is disposed which selectively exposes only the edge portion of the wafer W to light. 
     In the interface section  4 , for example, a wafer transfer body  111  moving on a transfer path  110  extending in the X-direction and a buffer cassette  112  are provided as shown in  FIG. 1 . The wafer transfer body  111  is movable in the vertical direction and also rotatable in the θ-direction, and thus can access the not-shown aligner adjacent to the interface section  4 , the buffer cassette  112 , and the fifth processing unit group G 5  and transfer the wafer W to them. 
     In the coating and developing treatment system  1  configured as described above, a series of wafer processing in the photolithography process as follows is performed. The unprocessed wafers W are first taken out by the wafer transfer body  7  one by one from the cassette C on the cassette mounting table  5 , and successively transferred to the temperature regulating unit  60  in the third processing unit group G 3 . The wafer W transferred to the temperature regulating unit  60  is temperature-regulated to a predetermined temperature, and is then transferred by the first transfer unit  10  to the bottom coating unit  23  where an anti-reflection film is formed. The wafer W having the anti-reflection film formed thereon is transferred by the first transfer unit  10  to the high-temperature thermal processing unit  65  and the high-precision temperature regulating unit  70  in sequence so that predetermined processing is performed in each of the units. 
     Thereafter, the wafer W is transferred to the resist coating unit  20 , where a resist film is formed on the wafer W. The wafer is then transferred by the first transfer unit  10  to the pre-baking unit  71  and subjected to pre-baking. The wafer is subsequently transferred by the second transfer unit  11  to the edge exposure unit  102  and the high-precision temperature regulating unit  83  in sequence so that the wafer W is subjected to predetermined processing in each of the units. The wafer W is then transferred by the wafer transfer body  111  in the interface section  4  to the not-shown aligner, where the wafer W is exposed to light. The wafer W for which exposure processing has been finished is transferred by the wafer transfer body  111 , for example, to the PEB unit  84 . 
     In the PEB unit  84 , the wafer W is mounted on the thermal plate  90  which has been set to a predetermined temperature for each of the thermal plate regions R 1  to R 5  in advance to thereby be subjected to post-exposure baking. 
     The wafer W for which the post-exposure baking has been completed is transferred by the second transfer unit  11  to the high-precision temperature regulating unit  81 , where the wafer W is temperature-regulated. The wafer W is then transferred to the developing treatment unit  30 , where the resist film on the wafer W is developed. The wafer W is then transferred by the second transfer unit  11  to the post-baking unit  75 , where the wafer W is subjected to post-baking. The wafer W is then transferred to the high-precision temperature regulating unit  63 , where the wafer W is temperature-regulated. The wafer W is then transferred by the first transfer unit  10  to the transition unit  61  and returned to the cassette C by the wafer transfer body  7 , thus completing the photolithography process being a series of wafer processing. 
     Incidentally, a line width measuring unit  120  for measuring the line width of a resist pattern as the processing state within the wafer is provided as shown in  FIG. 1  in the above-described coating and developing treatment system  1 . The line width measuring unit  120  is provided, for example, in the cassette station  2 . The line width measuring unit  120  includes, for example, a mounting table  121  for horizontally mounting the wafer W thereon as shown in  FIG. 5  and an optical profilometer  122 . The mounting table  121  forms, for example, an X-Y stage and can move in two dimensional directions in the horizontal directions. 
     The optical profilometer  122  includes, for example, a light irradiation unit  123  for applying light to the wafer W from an oblique direction, a light detection unit  124  for detecting the light applied from the light irradiation unit  123  and reflected by the wafer W, and a calculation unit  125  for calculating the line width of the resist pattern on the wafer W based on light reception information from the light detection unit  124 . The line width measuring unit  120  according to this embodiment is for measuring the line width of the resist pattern, for example, using the Scatterometry method, in which the line width of the resist pattern can be measured in the calculation unit  125  by checking the light intensity distribution within the wafer detected by the light detection unit  124  against a virtual light intensity distribution stored in advance and obtaining a line width of the resist pattern corresponding to the checked virtual light intensity distribution. 
     The line width measuring unit  120  can measure the line widths at a plurality of locations within the wafer by horizontally moving the wafer W relative to the light irradiation unit  123  and the light detection unit  124 . The measurement result of the line width measuring unit  120  can be outputted, for example, from the calculation unit  125  to a later-described temperature setting apparatus  150 . 
     Next, the configuration of the temperature setting apparatus  150  for performing temperature setting of the thermal plate  90  in the above-described PEB units  84  to  89  will be described. The temperature setting apparatus  150  is composed of, for example, a general-purpose computer comprising a CPU and a memory. The temperature setting apparatus  150  is connected to the temperature controller  92  for the thermal plate  90  and the line width measuring unit  120  as shown in  FIG. 4  and  FIG. 5 . 
     The temperature setting apparatus  150  comprises, for example, as shown in  FIG. 6 , a computing unit  160  for executing various kinds of programs; an input unit  161  for inputting, for example, various kinds of information for temperature setting of the thermal plate  90 ; a data storage unit  162  for storing the various kinds of information for temperature setting of the thermal plate  90 ; a program storage unit  163  for storing the various kinds of programs for temperature setting of the thermal plate  90 ; and a communication unit  164  for communicating the various kinds of information for temperature setting of the thermal plate  90  with the temperature controller  92  and the line width measuring unit  120 . 
     The program storage unit  163  stores, for example, a program P 1  to calculate, from measurement results of the line widths within the wafer, a plurality of in-plane tendency components Z i  (where i=1 to n, and n is an integer equal to or greater than 1) of the measured line widths within the wafer. The plurality of in-plane tendency components Z i  can be calculated by decomposing an in-plane tendency Z (the variation tendency within the wafer) of the measured line widths within the wafer into a plurality of components using a Zernike polynomial as shown in  FIG. 7 . 
     Adding here explanation about the Zernike polynomial, the Zernike polynomial is a complex function on a unit circle with a radius of 1 (practically used as a real function) which is often used in the optical field, and has arguments (r, θ) of polar coordinates. The Zernike polynomial is mainly used to analyze the aberration component of a lens in the optical field, and the wavefront aberration is decomposed using the Zernike polynomial, whereby aberration components based on the shape of each independent wavefront, for example, a mount shape, a saddle shape, or the like can be known. 
     In this embodiment, the line width measured values at many points within the wafer are expressed in the height direction above the wafer surface and the points of the line width measured values are connected by a smooth curved surface so that the in-plane tendency Z of the measured line widths within the wafer is grasped as a vertically waiving wavefront. The in-plane tendency Z of the measured line widths within the wafer is then decomposed using the Zernike polynomial, for example, into a plurality of in-plane tendency components Z i , such as a deviation component in the Z-direction being the vertical direction, a gradient component in the X-direction, a gradient component in the Y-direction, and a curvature component convexly curving or concavely curving. The magnitude of each of the in-plane tendency components Z i  can be expressed by the Zernike coefficient. 
     The Zernike coefficient indicating each of the in-plane tendency components Z i  can be specifically expressed by the following expressions using the arguments (r, θ) of polar coordinates. 
     Z1 (1) 
     Z2 (r·cos θ) 
     Z3 (r·sin θ) 
     Z4 (2r 2 −1) 
     Z5 (r 2 ·cos 2θ) 
     Z6 (r 2 ·sin 2θ) 
     Z7 ((3r 3 −2r)·cos θ) 
     Z8 ((3r 3 −2r)·sin θ) 
     Z9 (6r 4 −6r 2 +1) 
     and so on. 
     The Zernike coefficient Z1 indicates the line width average value within the wafer (the deviation component in the Z-direction), the Zernike coefficient Z2 indicates the gradient component in the X-direction, the Zernike coefficient Z3 indicates the gradient component in the Y-direction, and the Zernike coefficients Z4, Z9 indicate the curvature components, for example, in this embodiment. 
     As shown in  FIG. 6 , the data storage unit  162  stores, for example, Zernike coefficient number information I on in-plane tendency components Za i  (where i is an integer between 1 and n) improvable (variable) by changing, for example, the temperature correction values for the thermal plate regions R 1  to R 5  of the in-plane tendency components Z i  decomposed from the in-plane tendency Z of the measured line widths within the wafer. For example, for the improvable in-plane tendency components Za i , the temperatures of the respective thermal plate regions R 1  to R 5  of the thermal plate  90  are individually varied and the line widths within the wafer in that case are measured. The in-plane tendency of the line widths in that case is decomposed using the Zernike polynomial and in-plane tendency components which vary depending on the variations in the set temperatures of the thermal plate regions R 1  to R 5  are identified and regarded as the improvable in-plane tendency components Za i . 
     The program storage unit  163  stores, as shown in  FIG. 8 , for example, a program P 2  to calculate an improvable in-plane tendency Za in the measured line widths within the wafer by identifying the improvable in-plane tendency components Za i  of the in-plane tendency components Z i  decomposed from the line width tendency Z of the measured line widths within the wafer and adding up them. 
     The program storage unit  163  stores a program P 3  to calculate a temperature correction value ΔT for each of the thermal plate regions R 1  to R 5  to bring each of the in-plane tendency components Za i  of the improvable in-plane tendency Za to 0 (ZERO), for example, from the following relational expression (1).
 
Δ Z=M·ΔT   (1)
 
     The calculation model M of the relational expression (1) is a correlation matrix indicating the correlation between the variation amount (the change amount of each Zernike coefficient) ΔZ of each in-plane tendency component Z i  of the line widths within the wafer and the temperature correction value ΔT. Specifically, the calculation model M is a determinant of n (the number of in-plane tendency components) rows by m (the number of thermal plate regions) columns expressed using the Zernike coefficients on a specific condition, for example, as shown in  FIG. 9 . 
     The calculation model M is made by raising the temperature of each of the thermal plate regions R 1  to R 5  in sequence by 1° C., measuring the line width variation amounts within the wafer in each case, calculating the variation amounts of the Zernike coefficients (the variation amounts of the in-plane tendency components) corresponding to the variation amounts of the line widths, and expressing the variation amounts of the Zernike coefficients per unit temperature variation as elements M i,j  of the determinant (1≦i≦n, and 1≦j≦m (m=5 being the number of thermal plate regions in this embodiment)). Note that the in-plane tendency component that does not vary even when the temperature of the thermal plate region is raised by 1° C. creates a variation amount of the Zernike coefficient of 0 (ZERO), so that the element corresponding to that is 0 (ZERO). 
     The relational expression (1) is expressed by the following expression (2) by multiplying both sides of the relational expression (1) by an inverse matrix M −1  of the calculation model M.
 
Δ T=M   −1   ·ΔZ   (2)
 
To bring each of the in-plane tendency components Za i  of the improvable in-plane tendency Za to 0 (ZERO), a value obtained by multiplying the value of each of the improvable in-plane tendency components Za i  by −1 is substituted into the variation amount ΔZ of the in-plane tendency, and 0 (ZERO) is substituted into the other unimprovable in-plane tendency components.
 
     The program storage unit  163  stores a program P 4  to calculate a remaining tendency Zc of an improvable in-plane tendency from the in-plane tendency Z of the measured line widths within the wafer after improvement by changing the setting of the temperature correction values for the thermal plate regions R 1  to R 5 . The program storage unit  163  also stores a program P 5  to calculate an average remaining tendency Zd by obtaining a plurality of in-plane remaining tendencies Zc and averaging them as shown in  FIG. 10 . 
     The program storage unit  163  stores, as shown in  FIG. 11 , a program P 6  to calculate an unimprovable in-plane tendency Ze by subtracting the improvable in-plane tendency Za from the in-plane tendency Z of the measured line widths within the wafer. The unimprovable in-plane tendency Ze is the in-plane tendency which cannot be improved by the change of the setting of the temperature correction values for the thermal plate regions R 1  to R 5 . The program storage unit  163  further stores, as shown in  FIG. 12 , for example, a program P 7  to estimate an in-plane tendency Zf of the line widths within the wafer after change (after improvement) of the setting of the temperature correction values for the thermal plate regions R 1  to R 5  by adding the above-described average remaining tendency Zd to the unimprovable in-plane tendency Ze. 
     Note that the above-described various kinds of programs for embodying the temperature setting process by the temperature setting apparatus  150  may be ones recorded on a recording medium such as a computer-readable CD and installed from the recording medium into the temperature setting apparatus  150 . 
     Next, the temperature setting process by the temperature setting apparatus  150  configured as described above will be described. 
     First of all, a process in calculating the average remaining tendency Zd of the improvable in-plane tendency after improvement will be described.  FIG. 13  shows a flowchart showing an example of the process of calculating the average remaining tendency Zd. 
     The wafer W for which the above-described series of wafer processing has been finished in the coating and developing treatment system  1 , for example, is transferred into the line width measuring unit  120  in the cassette station  2 , where the line widths of the resist pattern within the wafer W are measured (Step S 1  in  FIG. 13 ). In this event, the line widths at a plurality of measurement points Q within the wafer as shown in  FIG. 14  are measured to measure at least the line widths in wafer regions W 1 , W 2 , W 3 , W 4 , and W 5  corresponding to the respective thermal plate regions R 1  to R 5  of the thermal plate  90 . 
     The measurement results of the line widths within the wafer are outputted to the temperature setting apparatus  150 . In the temperature setting apparatus  150 , for example, from measured values of the line widths at the plurality of measurement points Q in the wafer regions W 1  to W 5 , the in-plane tendency Z of the measured line widths within the wafer is calculated, and the plurality of in-plane tendency components Z i  (i=1 to n) are calculated from the in-plane tendency Z using the Zernike polynomial as shown in  FIG. 7  (Step S 2  in  FIG. 13 ). 
     Subsequently, the improvable in-plane tendency components Za i  obtained in advance are extracted from the plurality of in-plane tendency components Z i  as shown in  FIG. 8  and added together. Thus, the improvable in-plane tendency Za of the measured line widths within the wafer is calculated (Step S 3  in  FIG. 13 ). 
     Then, the temperature correction values ΔT for the thermal plate regions R 1  to R 5  of the thermal plate  90  are calculated. For example, the above-described value obtained by multiplying each of the in-plane tendency components Za i  of the improvable in-plane tendency Za by −1 is substituted into the term of ΔZ of the relational expression (2) as shown in  FIG. 15 . For the unimprovable in-plane tendency component, 0 (ZERO) is substituted. This relational expression (2) is used to find the temperature correction values ΔT 1 , ΔT 2 , ΔT 3 , ΔT 4 , and ΔT 5  for the thermal plate regions R 1  to R 5  to bring the components Za i  of the improvable in-plane tendency Za to 0 (ZERO) (Step S 4  in  FIG. 13 ). 
     Thereafter, the information on each of the temperature correction values ΔT 1  to ΔT 5  is outputted from the communication unit  164  to the temperature controller  92 , and the set temperatures of the thermal plate regions R 1  to R 5  of the thermal plate  90  in the temperature controller  92  are changed to new temperature correction values ΔT 1  to ΔT 5  (Step S 5  in  FIG. 13 ). 
     After the setting has been changed to the new temperature correction values ΔT 1  to ΔT 5 , a series of wafer processing is performed again in the coating and developing treatment system  1 , and the line widths of the resist pattern within the wafer are measured. From the measured line widths within the wafer, the in-plane tendency Z thereof is calculated, and the plurality of in-plane tendency components Z i  (i=1 to n) are calculated from the in-plane tendency Z using the Zernike polynomial as in the above-described Step S 2 . Subsequently, the improvable in-plane tendency components Za i  are extracted from the plurality of in-plane tendency components Z i  and added together to calculate the improvable in-plane tendency within the wafer. This in-plane tendency is the remaining tendency Zc of the improvable in-plane tendency after improvement by the above-described change of the temperature setting (Step S 6  in  FIG. 13 ). Thus, the in-plane tendency Za improvable by the above-described change of the temperature setting is not completely brought to 0 (ZERO) but a portion thereof remains as the remaining tendency Zc. This remaining tendency Zc is stored, for example, in the data storage unit  162 . 
     Thereafter, the process of changing the setting of the temperature correction values (Step S 1  to Step S 5 ) are performed a plurality of number of times so that the remaining tendency Zc is calculated every time and stored in the data storage unit  162 . The plurality of remaining tendencies Zc are averaged as shown in  FIG. 10  to calculate the average remaining tendency Zd (Step S 7  in  FIG. 13 ). 
     Next, a process of estimating the in-plane tendency Zf of the line widths within the wafer after the change of the temperature setting in the temperature setting process of the temperature correction values for the thermal plate regions R 1  to R 5  will be described. 
       FIG. 16  is a flowchart showing an example of the process of estimating the in-plane tendency Zf after the change of the temperature setting. 
     First of all, the current line widths of the resist pattern within the wafer are measured for the wafer W, for example, for which a series of wafer processing has been completed in the coating and developing treatment system  1  (Step K 1  in  FIG. 16 ). Then, based on the measurement results of the line widths within the wafer, the current in-plane tendency Z of the measured line widths within the wafer is calculated, and the plurality of in-plane tendency components Z i  (i=1 to n) are calculated from the in-plane tendency Z using the Zernike polynomial as in the above-described step S 2 . Subsequently, the improvable in-plane tendency components Za i  are extracted from the plurality of in-plane tendency components Z i  and added together to calculate the improvable in-plane tendency Za within the wafer. Then, the improvable in-plane tendency Za is subtracted from the in-plane tendency Z of the measured line widths to calculate the unimprovable in-plane tendency Ze as shown in  FIG. 11 . Thus, the improvable in-plane tendency Za and the unimprovable in-plane tendency Ze are calculated from the measured line widths within the wafer (Step K 2  in  FIG. 16 ). Then, the in-plane tendency Zf of the line widths after the change of the temperature setting is calculated by adding the average remaining tendency Zd obtained in advance to the unimprovable in-plane tendency Ze as shown in  FIG. 12  (Step K 3  in  FIG. 16 ). 
     In the above embodiment, the in-plane tendency Zf of the line widths after the change of the temperature setting is estimated by subtracting the improvable in-plane tendency Za from the current in-plane tendency Z of the measured line widths within the wafer to calculate the unimprovable in-plane tendency Ze, and adding the average remaining tendency Zd obtained in advance to the unimprovable in-plane tendency Ze. If all the improvable in-plane tendency Za of the current in-plane tendency Z can be improved, the in-plane tendency Zf after the improvement matches with the unimprovable in-plane tendency Ze, but it is difficult to completely bring the improvable in-plane tendency Za after improvement to 0 (ZERO). For this reason, the average remaining tendency Zd of the remaining tendencies Zc of the improvable in-plane tendencies remaining after improvement is obtained in advance and added to the unimprovable in-plane tendency Ze for correction, so that the in-plane tendency Zf of the line widths after the change of the temperature setting can be estimated very accurately. As a result, unlike the prior art, it is not necessary to change the setting of the temperature correction values may times, making it possible to perform the temperature setting of the thermal plate  90  properly and in a short time. 
     According to the above embodiment, in calculating the improvable in-plane tendency Za, the in-plane tendency Z of the measured line widths within the wafer is decomposed into the plurality of in-plane tendency components Z i  using the Zernike polynomial, and the improvable in-plane tendency components Za i  of the plurality of in-plane tendency components Z i  are added together to calculate the improvable in-plane tendency Za, whereby the calculation of the improvable in-plane tendency Za is accurately and easily performed. 
     Since the improvable in-plane tendency Za is subtracted from the in-plane tendency Z of the line widths within the wafer to calculate the unimprovable in-plane tendency Ze in the above-described embodiment, the unimprovable in-plane tendency Ze can be accurately and easily calculated. 
     Further, since, when changing the temperature correction values ΔT of the thermal plate regions R 1  to R 5 , the calculation model M of the relational expression (1) is used to calculate the temperature correction values ΔT 1  to ΔT 5  for the thermal plate regions R 1  to R 5  to bring each of the improvable in-plane tendency components Za i  to 0 (ZERO) and the calculated temperature correction values ΔT 1  to ΔT 5  are set to the temperatures of the thermal plate regions R 1  to R 5 , the line width in-plane tendency improved as much as possible can be obtained in the wafer processing after temperature correction. Accordingly, a uniform line width within the wafer can be formed. Particularly, since the thermal processing performed in the PEB unit  84  greatly affects the line width of the finally formed resist pattern by the photolithography process, the effect by performing the temperature setting of the thermal plate  90  of the PEB unit  84  by the method is profound. 
     Though the calculation of the improvable in-plane tendency Za and the calculation of the temperature correction values ΔT for the thermal plate regions R 1  to R 5  are performed using the Zernike polynomial, they may be performed using other methods. 
     The in-plane tendency of the measured line widths within the wafer is indicated by expressing line width measured values D at the plurality of measurement points Q within the wafer in the height direction above the wafer surface, for example, as shown in  FIG. 17 . The line width measured values D at the plurality of measurement points Q are projected to a vertical plane including an X-axis, for example, as shown in  FIG. 18 , and a gradient component Fx in the X-direction being one of the in-plane tendency components is calculated from the distribution of the line width measured values D using the least square method. The line width measured values D at the plurality of measurement points Q are projected to a vertical plane including a Y-axis as shown in  FIG. 18 , and a gradient component Fy in the Y-direction being one of the in-plane tendency components is calculated from the distribution of the line width measured values D using the least square method. Furthermore, a convex curvature component Fz being one of the in-plane tendency components is calculated as shown in  FIG. 20  by subtracting the gradient component Fx in the X-direction and the gradient component Fy in the Y-direction from the whole in-plane tendency of the line width measured values D. For example, these in-plane tendency components Fx, Fy, and Fz are added together to calculate an improvable in-plane tendency Fa. 
     When calculating the temperature correction values ΔT for the thermal plate regions R 1  to R 5 , the temperature correction values ΔT for the thermal plate regions R 1  to R 5  are calculated to bring each of the in-plane tendency components Fx, Fy, and Fz to 0 (ZERO) from the improvable in-plane tendency Fa, for example, by the following relational expression (3).
 
 ΔF=M·ΔT   (3)
 
     The calculation model M of the relational expression (3) is a correlation matrix indicating the correlation between the variation amount ΔF of each of the in-plane tendency components Fx, Fy, and Fz of the line widths within the wafer and the temperature correction values ΔT. 
     A value obtained by multiplying the value of each of the tendency components Fx, Fy, and Fz by −1 is substituted into the term of ΔF of the relational expression (3) to obtain the temperature correction values ΔT 1  to ΔT 5  for the thermal plate regions R 1  to R 5 . 
     Even in this case, the calculation of the improvable in-plane tendency Za and the temperature correction values ΔT is accurately performed, with the result that the in-plane tendency Zf of the line widths within the wafer after the change of the temperature setting can be accurately and properly estimated to performed the temperature setting process properly and in a short time. 
     Incidentally, the change of the temperature setting of the thermal plate  90  described in the above embodiment may be performed, for example, only when the magnitude of the improvable in-plane tendency Za calculated from the in-plane tendency Z of the measured line widths within the wafer (the degree of variations) exceeds a predetermined threshold value. 
     In this case, every several wafers W which are being successively processed in the coating and developing treatment system  1  are periodically subjected to line width measurement. From the in-plane tendency Z of the measured line widths within the wafer obtained by the line width measurement, the improvable in-plane tendency Za is calculated, and whether or not the value of 3σ (sigma) indicating the magnitude of the calculated improvable in-plane tendency Za exceeds a threshold value which has been set in advance is judged. 
     When 3σ of the improvable in-plane tendency Za is equal to or smaller than the threshold value L as shown at (a) in  FIG. 21 , the change of the temperature correction values ΔT for the thermal plate regions R 1  to R 5  is not performed, whereas when 3σ of the improvable in-plane tendency Za exceeds the threshold value L as shown at (b) in  FIG. 21 , the change of the temperature correction values ΔT for the thermal plate regions R 1  to R 5  of the thermal plate  90  is performed. 
     According to this example, whether or not 3σ of the improvable in-plane tendency Za of the in-plane tendency Z of the measured line widths within the wafer exceeds the threshold value L which has been set in advance is judged, and when it exceeds, the temperature correction values ΔT for the thermal plate regions R 1  to R 5  of the thermal plate  90  are changed, so that the timing of changing the setting of the temperature correction values ΔT can be stabilized irrespective of, for example, the experience and knowledge of an operator. Further, since the change of the temperature correction values ΔT is performed only when the improvable in-plane tendency Za is large, the temperature correction values ΔT are not changed in an unnecessary case, thus making it possible to make the timing of changing the setting of the temperature correction values ΔT appropriate. 
     Note that while the necessity of changing the temperature setting is judged depending on whether or not 3σ of the improvable in-plane tendency Za exceeds the threshold value L in this example, the necessity of changing the temperature setting may be judged by expressing the magnitude of the improvable in-plane tendency Za in a difference between the maximum value and the minimum value within the wafer and comparing the difference to its threshold value. 
     A preferred embodiment of the present invention has been described above with reference to the accompanying drawings, and the present invention is not limited to the embodiment. It should be understood that various changes and modifications within the scope of the spirit as set forth in claims are readily apparent to those skilled in the art, and those should also be covered by the technical scope of the present invention. 
     While the thermal plate  90  to be temperature-set is divided into five regions in the above embodiment, any number of divisions can be selected. The shapes of the divided regions of the thermal plate  90  can also be arbitrarily selected. While the above embodiment is an example in which the temperature setting of the thermal plate  90  of the PEB unit  84  is performed based on the line widths within the wafer, the present invention is also applicable to a case of performing the temperature setting of a thermal plate for performing other thermal processing placed in a pre-baking unit, a post-baking unit or the like and the temperature setting of a cooling plate of a cooling unit for cooling the wafer W. Further, while the temperature setting of the thermal plate is performed based on the line widths within the wafer in the above embodiment, the temperature setting of a thermal processing plate of a PEB unit, a pre-baking unit or a post-baking unit based on the processing state other than the line width within the wafer, such as the angle of the side wall in the groove of the resist pattern (the side wall angle) or the film thickness of the resist pattern. 
     Further, while the temperature setting of the thermal plate is performed based on the line width of a pattern after the photolithography process and before the etching process in the above embodiment, the temperature setting of the thermal processing plate may be performed based on the line width or the side wall angle of the pattern after the etching process. Furthermore, the present invention is also applicable to temperature setting of a thermal processing plate for thermally processing substrates other than the wafer, such as an FPD (Flat Panel Display), a mask reticle for a photomask, and the like. 
     The present invention is useful in performing the temperature setting of a thermal processing plate for mounting and thermally processing a substrate thereon.