Patent Publication Number: US-2009219969-A1

Title: Substrate surface temperature measurement method, substrate processing apparatus using the same, and semiconductor device manufacturing method

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates, in an apparatus that heats and cools a substrate in a process of manufacturing an electronic device such as a semiconductor integrated circuit and a display device electron source, to a substrate surface temperature measurement method which measures the substrate surface temperature in-situ, a substrate processing apparatus which uses this method, and a semiconductor device manufacturing method. 
     2. Description of the Related Art 
     A semiconductor integrated circuit manufacturing process includes various types of annealing processes such as baking in photolithography, film formation, and ashing. In such an annealing process, conventionally, a target substrate is heated using a halogen lamp arranged to oppose the target substrate, or a heater incorporated in a support body that supports the target substrate. 
     In this case, a radiation thermometer is arranged on a side opposite to the halogen lamp across the target substrate and measures the temperature of the target substrate in noncontact with it. The light quantity of the halogen lamp is adjusted on the basis of the measurement result, thus controlling the heating temperature for the target substrate. 
     Regarding measurement of the substrate surface temperature, a heat flux meter and temperature sensor are arranged near the lower surface of the target substrate and measure the surface temperature using the heat resistance from their positions to the upper surface of the substrate (see Japanese Patent Laid-Open No. 2002-170775). 
     Alternatively, a window is formed in part of the wall of a chamber serving as a vacuum processing chamber for the target substrate. The surface temperature of the target substrate is measured outside the wall of the chamber using a radiation thermometer (see Japanese Patent Laid-Open No. 60-253939). 
     Alternatively, a contact type sensor such as a thermocouple is brought into direct contact with the surface of the substrate and measures the surface temperature. 
     Alternatively, a contact type distance sensor is set on the side surface of the substrate. The average temperature of the substrate is obtained by measuring the expansion amount of the substrate, and the obtained average temperature is used as the surface temperature (see Japanese Patent Laid-Open No. 7-27634). 
     A radiation thermometer used for temperature measurement is advantageous in that it can measure the surface temperature of an object in noncontact with it by measuring light having a wavelength distribution and radiated from the object surface using a sensor such as a thermopile. 
     When measuring the substrate surface using the radiation thermometer, however, the emissivity changes depending on the composition and surface state of the substrate. To accurately measure the surface temperature of the substrate, the obtained temperature must be calibrated for each composition and each surface state of the substrate. An error may occur in measurement when an observation window to observe the substrate is contaminated with a film forming gas. Also, as the radiation thermometer itself is expensive, it increases the cost of the substrate processing apparatus itself. 
     In particular, when using the radiation thermometer in a film formation apparatus, the calibration parameter must be changed in accordance with a change in film formation state that changes constantly. It is, however, very difficult to accurately obtain the thickness of the film during formation and the composition of the film. Therefore, it is difficult to set the calibration parameter correctly. 
     A prior art employing a radiation thermometer will be described with reference to  FIG. 9 . 
     Referring to  FIG. 9 , reference numeral  101  denotes a vacuum vessel;  102 , a source gas supply device which supplies gas as a film forming material;  103 , a valve;  104 , a vacuum pump;  105 , a flow controller which adjusts the concentration of the source gas; and  106 , a substrate as a processing target. Reference numeral  107  denotes an electrostatic chuck which fixes the substrate  106  at a predetermined position;  108 , a substrate stage which suppresses deformation of the electrostatic chuck  107 ; and  109 , an attaching member which connects the substrate stage  108  to the vacuum vessel  101 . Reference numeral  111  denotes a halogen heater which heats the surface of the substrate  106  with radiation heat;  112 , an attaching member which connects the heater  111  to the vacuum vessel  101 ; and  113 , a halogen heater controller. Also, reference numeral  301  denotes a radiation thermometer set outside the vacuum vessel  101 ; and  302 , an extraction window which transmits radiation from the substrate  106 . The radiation thermometer  301  can measure the radiation transmitted through the extraction window  302 . 
     When the radiation thermometer is used in this manner, generally, even if the surface temperature of the substrate  106  stays the same, the radiant quantity measured by the radiation thermometer  301  changes in accordance with a change in composition of the film formed on the surface of the substrate  106 . 
     The inner side of the extraction window  302  is constantly contaminated by the source gas and the cleaning is required. Accordingly, the measured radiant quantity must be corrected in accordance with the light transmittance of the extraction window  302 . 
     Beams transmitted through the extraction window  302  include radiation from the substrate  106  as well as light reflected by the wall of the vacuum vessel  101 . Also, light from the halogen heater  111  may be directly reflected by the substrate  106 , reach the extraction window  302  in the form of stray light, and be transmitted through the extraction window  302 . A countermeasure for this problem is also necessary. 
     In this manner, although measurement using the radiation thermometer is advantageous in that it allows noncontact observation, the accuracy may be degraded by various measurement errors, and the radiation thermometer itself is expensive. 
     As another technique, a method of obtaining the substrate temperature by conversion from the expansion amount of the substrate is also available. With this method, the average temperature of the substrate can be calculated. If, however, a temperature distribution exists in the substrate, the temperature difference between the average temperature and surface temperature of the substrate increases, thus increasing the error. 
     The conventional technique of obtaining the substrate temperature by conversion from the expansion amount of the substrate will be described with reference to  FIG. 10 . 
     Referring to  FIG. 10 , reference numeral  401  denotes a lamp;  402 , a substrate;  403 , a movable quartz pin;  404 , an optical micrometer; and  405 , a support pin. Reference numeral  406  denotes a process chamber;  407 , a lamp power control unit;  408 , a displacement/temperature converter; and  409 , a process recipe.  FIG. 10  is a plan view of the substrate surface. 
     In the apparatus of  FIG. 10 , light emitted by the lamp  401  heats the substrate  402  placed in the process chamber  406 . When the substrate  402  is heated, it expands. As the support pin  405  restricts one side of the substrate  402 , the expansion amount of the substrate  402  appears as the moving amount itself of the movable quartz pin  403  provided to the substrate  402 . The expansion amount of the substrate  402  is calculated by reading the moving amount of the movable quartz pin  403  by the optical micrometer  404 . Upon reception of the calculated expansion amount, the displacement/temperature converter  408  calculates the temperature of the substrate  402  and sends it to the lamp power control unit  407 . The lamp power control unit  407  controls the lamp  401  by referring to the received substrate temperature and the process recipe  409 . 
     As the movable quartz pin  403  is in contact with the substrate  402 , however, heat of the substrate  402  drifts to the movable quartz pin  403  and heats it, and accordingly the movable quartz pin  403  itself expands. As a result, the moving amount of that surface of the movable quartz pin  403  which faces the optical micrometer  404  differs from the moving amount of the end face of the substrate  402  which is not in contact with the movable quartz pin  403 . This causes an error in temperature measurement. 
     When a temperature distribution exists in the substrate  402 , it is the average temperature of the entire substrate that can be calculated from the expansion amount of the substrate, and the surface temperature of the substrate cannot always be measured. For example, as shown in  FIG. 10 , when heating the substrate  402  using the lamp from the upper surface side, the heat drifts to the lower surface of the substrate  402 . 
     Alternatively, when heating the substrate  402  using the lamp from the lower surface side, the heat drifts to the upper surface side. Consequently, a temperature difference occurs between the upper and lower surfaces of the substrate  402 . It is thus difficult to accurately measure the surface temperature of the substrate only from the expansion amount of the substrate. 
     As another technique, a method is available which measures by bringing a contact type sensor such as a thermocouple in direct contact with the substrate. When bringing the sensor into contact with the substrate surface in this manner, or when the substrate expands by a temperature change in the substrate, it is difficult to maintain the contact state of the sensor with the substrate. Also, as the thermocouple itself is heated by the heater, an error may occur. Since the film is not formed on that portion of the substrate which is in contact with the sensor, the substrate is partly wasted. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide a surface temperature measurement method that can solve one of the problems described above, and a substrate processing apparatus which utilizes this method. It is another object of the present invention to improve the measurement accuracy of the substrate surface temperature. 
     According to one aspect of the present invention, there is provided a substrate surface temperature measurement method comprising: 
     a measurement step of measuring an expansion amount of a substrate; and 
     a surface temperature calculation step of calculating a temperature of a neutral plane of the substrate using the expansion amount of the substrate, calculating a temperature difference between the neutral plane and an upper surface of the substrate from a heat flux and heat resistance of the substrate, and obtaining a temperature of the upper surface of the substrate using the temperature difference and the temperature of the neutral plane of the substrate. 
     According to another aspect of the present invention, there is provided a substrate processing apparatus comprising: 
     heating means for heating a substrate; 
     control means for controlling the heating means; 
     expansion amount measurement means for measuring an expansion amount of the substrate; and 
     heat flux measurement means for measuring a heat flux in the substrate, 
     wherein the control means calculates a temperature of a neutral plane of the substrate using the expansion amount measured by the expansion amount measurement means, calculates a temperature difference between the neutral plane and an upper surface of the substrate from the heat flux measured by the heat flux measurement means and a heat resistance, obtaining a temperature of the upper surface of the substrate using the temperature difference and the temperature of the neutral plane of the substrate, and controls the heating means on the basis of the temperature of the upper surface. 
     According to still another aspect of the present invention, there is provided a substrate processing apparatus comprising: 
     a substrate support body which supports a substrate; 
     substrate heating means provided to the substrate support body; 
     heat-insulating means for covering the substrate support body; 
     control means for controlling the substrate heating means; and 
     expansion amount measurement means for measuring an expansion amount of the substrate, 
     wherein the control means 
     calculates a temperature of a neutral plane of the substrate using the expansion amount measured by the expansion amount measurement means, 
     calculates a heat flux in the substrate from an energy supplied to the heating means, and 
     calculates a temperature difference between the neutral plane and an upper surface of the substrate from the calculated heat flux and a heat resistance, obtains a temperature of the upper surface of the substrate using the temperature difference and the temperature of the neutral plane of the substrate, and controls the heating means on the basis of the temperature of the upper surface. 
     According to yet another aspect of the present invention, there is provided a semiconductor device manufacturing method comprising a step of measuring a surface temperature of a substrate using a substrate surface temperature measurement method according to one aspect of the present invention. 
     According to the present invention, the measurement accuracy of the substrate surface temperature can improve. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a view schematically showing the arrangement of an apparatus according to the first embodiment of the present invention; 
         FIG. 2  is a view for explaining how to obtain the surface temperature of a substrate according to the first embodiment; 
         FIG. 3  is a graph for explaining the temperature gradient in the substrate; 
         FIG. 4  is a schematic view showing an arrangement of a heat flux sensor employed in the apparatus of the present invention; 
         FIG. 5  is a view schematically showing the arrangement of an apparatus according to the second embodiment of the present invention; 
         FIG. 6  is a view schematically showing the arrangement of an apparatus according to the third embodiment of the present invention; 
         FIG. 7  is a view for schematically explaining alignment marks formed on the substrate as the alignment marks are observed by an alignment scope in the third embodiment; 
         FIG. 8  is a view schematically showing the arrangement of an apparatus according to the fourth embodiment of the present invention; 
         FIG. 9  is a view schematically showing the arrangement of the first apparatus of the background art; and 
         FIG. 10  is a view schematically showing the arrangement of the second apparatus of the background art. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     In the present invention, the surface temperature of a substrate is measured using the expansion amount of the substrate, the heat flux flowing through the substrate, and the heat resistance of the substrate. In this specification, the upper surface of the substrate refers to a surface which is to undergo a process such as film formation, the lower surface of the substrate refers to a surface on a side opposite to the upper surface, and the edge surface of the substrate refers to any other surface of the substrate than the upper and lower surfaces. 
     The expansion amount of the substrate can be measured by detecting the edge surface of the substrate by a noncontact sensor, e.g., a distance measuring sensor using light, or by detecting a mark formed on the substrate by an alignment scope having a mark image recognition function. 
     At this time, when expansion of a scope stage on which the alignment mark is to be placed influences the measurement accuracy, the coefficient of linear expansion of the scope stage may be obtained in advance, and the temperature may be measured whenever necessary, thus canceling the influence of expansion of the scope stage. 
     In this case, it is significant that the coefficient of linear expansion of the target substrate rarely changes during the process of the substrate. In general, the substrate has a thickness of approximately 1 mm, whereas the thickness of a layer formed on the substrate is as small as approximately several μm. Even when the coefficient of linear expansion of the entire substrate is substituted by the coefficient of linear expansion of the substrate outsides the layer, the error is very small. 
     Therefore, the average temperature of the substrate can be calculated from the expansion amount and the coefficient of linear expansion of the substrate. In addition, the coefficient of linear expansion of the substrate is determined by the physical properties of the substrate, which is very convenient in obtaining the absolute temperature. This alone, however, does not enable calculation of the surface temperature of the surface when a heat flux exists in the substrate to form a temperature distribution. For this reason, the temperature gradient in the substrate is calculated by measuring the heat flux that forms the temperature distribution in the substrate. When the quantity of heat dissipating from the edge portion of the substrate is negligibly small, the temperature gradient in the substrate can be regarded constant. Thus, the average temperature of the substrate coincides with the temperature of the neutral plane of the substrate. The present invention is aimed at determining, by utilizing this fact, the absolute temperature of the substrate surface through addition and subtraction of the average temperature of the substrate (that is, the temperature of the neutral plane of the substrate) obtained from the expansion amount of the substrate and the temperature gradient calculated from the heat flux (that is, the relative temperature difference between the neutral plane and upper surface of the substrate). 
     At this time, the substrate may be heated using a halogen heater or the like from its upper surface side, or using a heater from its lower surface. Since the substrate as a whole forms a thin plate, heat dissipating from the edge surface of the substrate is negligible. Therefore, in any case, the heat flux flowing through the substrate can be approximately regarded to be equal to the heat flux flowing through a stage that supports the substrate, or through an electrostatic chuck. 
     In this manner, the temperature distribution (temperature gradient) in the substrate can be calculated from the magnitude of the measured heat flux and the heat resistance of the substrate. The surface temperature of the substrate can be obtained through addition or subtraction of the temperature gradient and the average temperature of the substrate calculated from the expansion amount. 
     Note that the “neutral plane” of the substrate refers to a virtual plane which is at the equal distance from the upper and lower surfaces of the substrate. 
     The embodiments of the present invention will now be described with reference to the accompanying drawings. 
     First Embodiment 
       FIG. 1  schematically shows the arrangement of a thermal CVD apparatus according to the first embodiment of the present invention. 
     A substrate processing apparatus employed as the thermal CVD apparatus of this embodiment includes a vacuum vessel  101  and forms a film on a substrate  106  in the vacuum vessel  101 . A source gas supply device  102  and vacuum pump  104  are provided to the vacuum vessel  101 . The source gas supply device  102  supplies a gas as the source of the film to the vacuum vessel  101 . A supply path for the source gas is provided with a valve  103  and a flow controller  105  which adjusts the concentration of the source gas. 
     The vacuum vessel  101  is provided with an electrostatic chuck  107  and substrate stage  108  at its inner bottom. The electrostatic chuck  107  fixes the substrate  106  at a predetermined position. The substrate stage  108  suppresses deformation of the electrostatic chuck  107 . The substrate stage  108  is connected to the vacuum vessel  101  through an attaching member  109 . The substrate stage  108  is formed of a sufficiently rigid member. Thus, even if the vacuum vessel  101  is deformed by heat or a change in vacuum degree, the deformation will not influence the electrostatic chuck  107 . A structure utilizing spring elasticity is interposed between the substrate stage  108  and attaching member  109 . 
     A halogen heater  111  which heats the substrate  106  is located at that portion of the inner ceiling of the vacuum vessel  101  which opposes the surface of the substrate  106 . The halogen heater  111  is connected to the vacuum vessel  101  through an attaching member  112 . A heater controller  113  controls the temperature of the halogen heater  111  and the quantity of heat to be supplied. The heater controller  113  is connected to a main controller  114 . 
     The electrostatic chuck  107  is provided with a heat flux sensor  110  serving as a heat flux detection means which detects a heat flux drifting in the electrostatic chuck  107  in a direction perpendicular to the substrate surface. Scopes  115   a  and  115   b  serving as distance measuring sensors are set at portions that respectively face the opposing edge surfaces of the substrate  106 . The scopes  115   a  and  115   b  observe the edge positions of the substrate  106  and measure the distances to the edge surfaces. The heat flux sensor  110  and scopes  115   a  and  115   b  are connected to the main controller  114  and inform the main controller  114  of their measurement information. 
     The respective scopes  115   a  and  115   b  are fixed to a scope stage (support body)  116 . The scope stage  116  is connected to the vacuum vessel  101  through an attaching member  117 . The scope stage  116  is formed of a sufficiently rigid member so deformation in shape of the vacuum vessel  101  will not influence the scope stage  116 . A structure utilizing spring elasticity is interposed between the scope stage  116  and attaching member  117 . 
     A method of measuring the surface temperature of the substrate  106  will be described in more detail with reference to  FIG. 2 .  FIG. 2  includes the main part of the apparatus of  FIG. 1  together with variables necessary in the following description. 
       0   a,    0   b,  Lscp, Xa, Xb, and Lwaf are defined as follows. Namely,  0   a  and  0   b  represent scope position references; Lscp, the distance between the position references of the scopes  115   a  and  115   b;  Xa and Xb, the amounts of displacement of the edge surfaces of the substrate  106  which are measured by the corresponding scopes  115   a  and  115   b,  respectively (an outward direction from the substrate with reference to the scope position references  0   a  and  0   b  as origins (reference points) is determined as the positive direction); and Lwaf, a substrate length. 
     At this time, by using the distance Lscp between the scope position references and the two scope measurement values Xa and Xb, the substrate length Lwaf can be expressed as: 
         Lwaf=Lscp+Xa+Xb    (1) 
     Also, variables T 0   w,  Lwaf 0 , Twaf, and ρwaf are defined as follows. Namely, 
     T 0   w:  the temperature at which the substrate reference length is measured 
     Lwaf 0 : the substrate length Lwaf at the temperature T 0   w    
     Twaf: the average substrate temperature 
     ρwaf: the coefficient of linear expansion of the substrate  106   
     At this time, the substrate length Lwaf can also similarly be expressed as: 
         Lwaf=Lwaf 0*(1+ρ waf *( Twaf−T 0 w ))   (2) 
     Thus, from the above equations (1) and (2), the substrate average temperature Twaf can be expressed as: 
         Twaf =(( Lscp+Xa+Xb )/ Lwaf 0−1)/ρ waf+T 0 w    (3) 
     Referring to  FIGS. 2 and 3 , note that 
     Jst: the heat flux [W/cm 2 ] flowing through the electrostatic chuck  107   
     Jwaf: the heat flux [W/cm 2 ] flowing through the substrate  106  (for both Jst and Jwaf, a direction from the upper surface to the lower surface of the substrate is defined as the positive direction) 
     Tb: the temperature of the lower surface (the surface on the substrate stage  108  side) of the substrate 
     Tc: the temperature of the neutral plane of the substrate 
     Tt: the temperature of the upper surface of the substrate 
     In  FIG. 2 , part of the heat supplied by the heater  111  is dissipated from the substrate  106  through the electrostatic chuck  107 . At this time, the heat flux Jst flowing through the electrostatic chuck  107  can be measured by the heat flux sensor  110 . As the substrate  106  is chucked by the electrostatic chuck  107 , the heat flux Jwaf flowing through the substrate  106  can be substituted by the measured heat flux Jst. 
     Regarding the heat flow described above, a temperature gradient is formed in the substrate  106  in accordance with the heat flux Jwaf flowing through the substrate. The heat flux in the substrate  106  can, however, be considered to be almost constant at all locations in the direction of thickness of the substrate. Hence, a linear temperature gradient is formed from the upper surface to the lower surface of the substrate. The temperature gradient can be considered to be constant as shown in  FIG. 3 . Then, the substrate average temperature Twaf is equal to the temperature Tc of the neutral plane of the substrate. 
     Hence, 
       Tc=Twaf   (4) 
     Also, the temperature difference between the neutral plane and upper surface of the substrate is given by: 
         Tt−Tc=Jwaf*R    (5) 
     where R is the heat resistance [K·cm 2 /W] from the neutral plane to the upper surface of the substrate. 
     Therefore, using the above equations (1), (2), (3), and (4), the substrate upper surface temperature Tt can be calculated as: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Tt 
                         = 
                         
                           Tc 
                           + 
                           
                             Jwaf 
                             * 
                             
                                 
                             
                              
                             R 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           Twaf 
                           + 
                           
                             Jwaf 
                             * 
                             
                                 
                             
                              
                             R 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     ( 
                                     
                                       Lscp 
                                       + 
                                       Xa 
                                       + 
                                       Xb 
                                     
                                     ) 
                                   
                                    
                                   
                                     / 
                                   
                                    
                                   Lwaf 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                              
                             
                               / 
                             
                              
                             ρwaf 
                           
                           + 
                           
                             T 
                              
                             
                                 
                             
                              
                             0 
                              
                             w 
                           
                           + 
                           
                             Jst 
                              
                             
                                 
                             
                             * 
                             
                                 
                             
                              
                             R 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     This will be described with reference to the apparatus in  FIG. 1 . While processing the substrate, the measurement values Xa and Xb indicating the expansion amount of the substrate  106  are obtained by the scopes  115   a  and  115   b.  The main controller  114  is informed of the measurement values Xa and Xb. Based on the expansion amount, the initial length (substrate reference length Lwaf 0 ) of the substrate  106  which is measured in advance, the temperature T 0   w  at which Lwaf 0  is measured, and the coefficient ρwaf of linear expansion of the substrate  106 , the main controller  114  calculates the temperature Tc (substrate average temperature Twaf) of the neutral plane of the substrate  106  (see equations (3) and (4)). As the substrate reference length Lwaf 0 , temperature T 0   w,  and coefficient ρwaf of linear expansion are fixed parameters, they need to be stored in the main controller  114  in advance before processing the substrate. 
     Simultaneously with the Tc calculation step, the heat flux sensor  110  measures the heat flux Jwaf in the substrate  106  (substituted by the heat flux Jst in the electrostatic chuck  107 ). The main controller  114  is informed of the heat flux Jst. Based on the measured heat flux Jst and the heat resistance R of the substrate  106  which is input in advance, the main controller  114  calculates the temperature difference (Tt−Tc) between the neutral plane and upper surface of the substrate  106  (see equation (5)). Regarding the heat resistance R of the substrate  106 , if the substrate is a wafer product to sell or the like, its heat resistance value is known. This value is stored in the main controller  114  in advance. 
     Finally, using the calculated temperature Tc of the neutral plane of the substrate  106  and the temperature difference (Tt−Tc) between the neutral plane and upper surface of the substrate  106 , the main controller  114  obtains the surface temperature Tt of the substrate. The quantity of heat of the halogen heater  111  is adjusted in accordance with this measurement result. 
     In this manner, with the apparatus of this embodiment, the substrate surface temperature Tt can be calculated using the measurement values Xa and Xb of the scopes  115   a  and  115   b  and the measurement value Jst of the heat flux sensor  110 . 
       FIG. 4  is a schematic view showing a practical example of the heat flux sensor  110 . 
     A heat flux sensor functions as follows. Thermocouples are disposed on the upper and lower surfaces, respectively, of the plate-like body of the heat flux sensor having a heat resistance. A temperature difference (T 1 −T 2 ) occurring when a heat flux flows through the thermocouples is measured, thus measuring the magnitude of the heat flux. The temperature difference (T 1 −T 2 ) measured by the thermocouples on the heat flux sensor surfaces is equal to the product of the heat flux (W/cm 2 ) and the heat resistance (K·cm 2 /W). If the heat resistance is obtained in advance, the heat flux is obtained from the measured temperature difference. As a scheme to improve the sensitivity, as shown in  FIG. 4 , thermocouples are connected in series in a heat flux sensor. 
     Second Embodiment 
       FIG. 5  schematically shows the arrangement of a thermal CVD apparatus according to the second embodiment of the present invention. 
     The apparatus of this embodiment is obtained by adding a scope stage temperature sensor  118  to the arrangement of  FIG. 1 . The scope stage temperature sensor  118  serves as a support body temperature detection means for detecting the temperature of a scope stage  116 . In addition, a scope stage temperature controlling pipe  119  and scope stage temperature controller  120  are added. The scope stage temperature controlling pipe  119  is laid in the scope stage  116  to adjust the temperature of the scope stage  116 . The scope stage temperature controller  120  controls the circulation of a refrigerant flowing in the pipe  119 . 
     As the refrigerant circulates in the scope stage temperature controlling pipe  119 , the temperature nonuniformities in the scope stage  116  can be decreased more than in a scope stage not provided with a scope stage temperature controlling pipe  119 . Hence, the measurement error of the scope stage temperature sensor  118  can be suppressed. 
     The scope stage temperature sensor  118  is connected to a main controller  114  and informs it of the temperature of the scope stage  116 . 
     In the above arrangement, assume that the temperature of the scope stage  116  changes due to heat exchange with the ambient atmosphere and that the length of the scope stage  116  itself changes. In this case as well, a length Lwaf of a substrate  106  and a substrate surface temperature Tt can be calculated accurately. This will be described below in detail. 
     Note that 
     T 0   s:  the temperature at which the scope reference length is measured 
     Tscp: the scope stage temperature measured by the scope stage temperature sensor  118   
     Lscp 0 : a distance Lscp between the position references of scopes  115   a  and  115   b,  respectively, at the temperature T 0   s    
     ρscp: the coefficient of linear expansion of the scope stage  116   
     Then, a distance Lscp between the scope position references can be expressed as: 
         Lscp=Lscp 0*(1+ ρscp *( Tscp−T 0 s ))   (7) 
     When equation (7) is combined with equation (6) described above, the substrate surface temperature Tt is calculated as: 
         Tt =((( Lscp 0*(1+ ρscp *( Tscp−T 0 s )))+ Xa+Xb )/ Lwaf 0−1)/ρ waf+T 0 w+Jwaf*R    (8) 
     In this manner, with the apparatus of  FIG. 5 , the substrate surface temperature Tt can be calculated using measurement values Xa and Xb of the scopes  115   a  and  115   b,  respectively, a measurement value Jst of a heat flux sensor  110 , and the scope stage temperature (Tscp). 
     Third Embodiment 
       FIG. 6  schematically shows the arrangement of a thermal CVD apparatus according to the third embodiment of the present invention. In the description of this embodiment, the same constituent components as those of the apparatuses shown in  FIGS. 1 and 5  are denoted by the same reference numerals, and a repetitive description will be omitted. 
     In the third embodiment, no halogen heater (see reference numeral  111  in  FIGS. 1 and 2 ) is provided above the substrate surface. As shown in  FIG. 6 , a heater  121  arranged in a substrate stage  108  heats a substrate  106 . The heater  121  is connected to a heater controller  122 . The heater controller  122  is connected to a main controller  114 . 
     The upper surface of the substrate  106  has alignment marks  126  at a plurality of portions. The positions of the alignment marks  126  can be detected by alignment scopes  123   a  and  123   b  above them. The alignment scopes  123   a  and  123   b  are attached to a scope stage  124 . The scope stage  124  is connected to the ceiling of a vacuum vessel  101  through an attaching member  125 . A scope stage temperature controlling pipe  119  is laid in the scope stage  124 . A scope stage temperature controller  120  controls the circulation of a refrigerant flowing in the controlling pipe  119 . 
       FIG. 7  schematically shows how the alignment marks  126  formed on the substrate  106  are observed by the alignment scopes  123   a  and  123   b.  The alignment scopes  123   a  and  123   b  can measure the amounts of displacement of the alignment marks  126 . 
     Note that 
       0   a,    0   b:  the alignment scope position references 
     Xa, Xb: the amounts of displacement of the alignment mark  126  measured by the alignment scopes  123   a  and  123   b,  respectively (an outward direction from the substrate with reference to the alignment scope position references  0   a  and  0   b  as origins is determined as the positive direction) 
     Lwaf: the distance between the alignment marks  126   
     Then, when obtaining the substrate surface temperature, the equations (1) to (6) described above can be employed in the same manner. 
     Hence, using equation (6), a substrate surface temperature Tt is calculated as: 
         Tt =(( Lscp+Xa+Xb )/ Lwaf 0−1)/ρ waf+T 0 w+Jst*R    (6) 
     In this embodiment, heat drifts in the substrate  106  in a direction opposite to that in the first and second embodiments. Therefore, although the heat fluxes Jst and Jwaf shown in  FIG. 2  become negative, equations (1) to (6) can be employed in the same manner. 
     Fourth Embodiment 
       FIG. 8  schematically shows the arrangement of a thermal CVD apparatus according to the fourth embodiment of the present invention. 
     In the fourth embodiment, a heat-insulating material  127  which covers an electrostatic chuck  107  and a substrate stage  108  is added to the arrangement of  FIG. 6 . The substrate stage  108  serves as a substrate support body and is provided with a heater  121 . Heat from the heater  121  almost entirely flows through a substrate  106 . 
     With this arrangement, a heat flux Jwaf flowing through the substrate  106  becomes sufficiently equal to the energy supplied to the heater  121 . 
     Accordingly, the heat flux Jwaf can be expressed as: 
         Jwaf=Pw/S    (9) 
     where 
     Pw: the energy [J/s] supplied to the heater  121   
     S: the area [m 2 ] of the substrate  106  Therefore, using equations (1) to (6) and (9), a substrate surface temperature Tt is calculated as: 
         Tt =(( Lscp+Xa+Xb )/ Lwaf 0−1)/ρ waf+T 0 w +( Pw/S )*R   (10) 
     As is apparent from the above equation (10), this embodiment is advantageous in that it does not require the heat flux sensor  110  which is necessary in the apparatus of  FIG. 6 . 
     Further, referring to the above embodiments, for example, when glass is used as the base material of the substrate, the coefficient of linear expansion is at least approximately 3E-6. Assuming that the substrate has a length of 1 m, if the substrate length can be measured with an error of approximately 1 μm, a temperature at this measurement can be obtained with an error of as small as approximately 0.3° C. 
     When the substrate is made of glass, the thermal conductivity is approximately 1 W/(m·K). When the substrate has a thickness of 2 mm, its heat resistance is approximately 20K·cm 2 /W. If a heat flux of 1 W/cm 2  flows at this time, a temperature difference of 20K occurs between the upper and lower surfaces of the substrate, and a temperature difference of 10K occurs between the neutral plane and upper surface of the substrate. Even in this case, the temperature distribution in the substrate can be calculated by measuring the heat flux. 
     As the material of a high-temperature polysilicon TFT substrate, silica glass is employed. When the substrate is made of silica glass, the thermal conductivity is approximately 1.4 W/(m·K). When the substrate has a thickness of 1 mm, its heat resistance is 7K·cm 2 /W; when 2 mm, 14K·cm 2 /W. If a heat flux of 1 W/cm 2  flows at this time, when the substrate thickness is 1 mm, a temperature difference of 7K occurs between the upper and lower surfaces of the substrate, and a temperature difference of 3.5K occurs between the neutral plane and upper surface of the substrate. Similarly, when the substrate thickness is 2 mm, a temperature difference of 14K occurs between the upper and lower surfaces of the substrate, and a temperature difference of 7K occurs between the neutral plane and upper surface of the substrate. 
     When the substrate is made of polyether sulfone (PES) which is expected as the material of a bendable TFT, the thermal conductivity is approximately 0.18 W/(m·K). When the substrate has a thickness of 1 mm, its heat resistance is 56K·cm 2 /W; when 0.3 mm, 17K·cm 2 /W. If a heat flux of 1 W/cm 2  flows at this time, when the substrate thickness is 1 mm, a temperature difference of 56K occurs between the upper and lower surfaces of the substrate, and a temperature difference of 28K occurs between the neutral plane and upper surface of the substrate. Similarly, when the substrate thickness is 0.3 mm, a temperature difference of 17K occurs between the upper and lower surfaces of the substrate, and a temperature difference of 8.5K occurs between the neutral plane and upper surface of the substrate. 
     The value of the heat resistance can be calculated by an equation expressed as t/C where C is the thermal conductivity (W/cm·K) and t is the thickness (cm) of the material. 
     As described above, when the average temperature of the substrate is calculated on the basis of the expansion amount of the substrate and the relative temperature difference between the neutral plane and the upper surface of the substrate is calculated on the basis of the heat flux in the substrate, the surface temperature of the substrate can be obtained accurately. 
     As described above, according to the present invention, the surface temperature of the substrate can be measured very accurately without adversely affecting the process such as film formation that should originally be performed in noncontact with the substrate. As a result, the reproducibility and stability of the process can improve. This is effective in improving the quality of the formed film and the yield, thus reducing the cost. 
     As the noncontact type sensor which is prepared in the present invention to obtain the surface temperature in the noncontact manner, a distance measuring sensor employing a general laser or an alignment scope provided with an inexpensive image processor can be used. Thus, the measurement system can be formed at a greatly lower cost than in a case that uses a radiation thermometer. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2008-051931, filed Mar. 3, 2008, which is hereby incorporated by reference herein in its entirety.