Abstract:
A heat exchange method which uses a heat exchange unit for exchanging heat between first and second media to adjust a temperature of the first medium. The method includes (a) a detection step of detecting temperatures of the first and second media to enter the heat exchange unit, and (b) an adjustment step of adjusting a flow rate of the second medium based on the temperatures of the first and second media detected in the detection step. The adjustment step includes (i) a target heat quantity calculation step of calculating a target heat quantity based on a target temperature of the first medium and the temperature of the first medium detected in the detection step, (ii) a first temperature difference calculation step of calculating a first temperature difference based on the target temperature and the temperature of the second medium detected in the detection step, (iii) a setting step of setting a provisional target flow rate of the second medium, (iv) a second temperature difference calculation step of calculating a second temperature difference based on the target heat quantity, the provisional target flow rate, and the temperatures of the first and second media detected in the detection step, (v) an average temperature difference calculation step of calculating one of a logarithmic average temperature difference and an average temperature difference at the heat exchange unit based on the first and second temperature differences, (vi) a heat exchange quantity calculation step of calculating a heat exchange quantity at the heat exchange unit based on one of the logarithmic average temperature difference and the average temperature difference and a heat exchange gain of the heat exchange unit, and (vii) a determination step of determining a target flow rate of the second medium based on a result of a comparison between the heat exchange quantity and the target heat quantity.

Description:
This application claims priority from Japanese Patent Application No. 2004-205061, filed on Jul. 12, 2004, the entire contents of which are hereby incorporated by reference herein. 
   FIELD OF THE INVENTION 
   The present invention relates to a heat exchange method and apparatus, which use a heat exchange unit for exchanging heat between first and second media, to adjust the temperature of the first medium, an apparatus including the heat exchange apparatus and an exposure system, and a device manufacturing method using the apparatus including the exposure system. 
   BACKGROUND OF THE INVENTION 
   Recent semiconductor integrated circuits, such as ICs and LSIs, require high productivity, and accordingly, the power consumption of a semiconductor exposure apparatus tends to increase. The feature size of a circuit pattern shrinks more and more, and the environment in the exposure apparatus must be maintained more stably. In particular, as the power consumption increases, an efficient cooling apparatus or heat recovery apparatus, which has a very high temperature stability, is needed. 
   As a cooling or heat recovery apparatus, one using a refrigerating cycle, which includes a compressor, a condenser, and an evaporator is known (for example, see Japanese Patent Laid-Open No. 2002-48381). According to a cooling apparatus having this arrangement, load heat in an exposure apparatus is recovered by a circulating medium. The recovered heat is shifted to factory cooling water, which is supplied from a factory, has a comparatively high temperature, to perform cooling and heat recovery. 
   In general, when load fluctuations occur, the rotational speed of the compressor is controlled by an inverter. After heat is recovered by the refrigerating cycle when necessary, the circulating medium is heated again by an electrical heater, or the like, to improve the temperature stability. 
   In an old-fashioned semiconductor manufacturing factory, the factory cooling water often has a comparatively high temperature of 20° C. to 30° C. In a recent high-productivity factory for semiconductor devices having very small feature sizes, the factory cooling water often has a low temperature of about 10° C. to 18° C. 
   In the prior art described above, a compressor or reheating electrical heater is used, even when low-temperature factory cooling water is supplied, as in the recent semiconductor manufacturing factory. The power increases to lead to a cooling apparatus poor in efficiency. Also, inverter control and electrical heater control are performed to improve the temperature stability. Accordingly, the number of constituent components increases, the cost increases, and the apparatus becomes bulky. 
   When the load fluctuates sharply, or the temperature of the factory cooling water fluctuates, sufficient temperature stability cannot be obtained. In some cases, exposure of finer circuit patterns is adversely affected. 
   SUMMARY OF THE INVENTION 
   The present invention has been made in view of the above disadvantages, and has as its exemplified object to provide a heat exchange technique capable of stable fluid temperature adjustment. 
   According to the present invention, the foregoing object is attained by providing a heat exchange method, which uses a heat exchange unit for exchanging heat between first and second media, to adjust a temperature of the first media, comprising: 
   a detection step of detecting temperatures of the first and second media input to the heat exchange unit; and 
   an adjustment step of adjusting a flow amount of the second medium on the basis of the temperatures of the first and second media detected in the detection step. 
   In a preferred embodiment, the adjustment step includes: 
   a target heat quantity calculation step of calculating a target heat quantity on the basis of the target temperature of the first medium and the temperature of the first medium detected in the detection step, 
   an average temperature calculation step of calculating an average temperature difference at the heat exchange unit, on the basis of the target heat quantity calculated in the target heat quantity calculation step and a heat exchange gain of the heat exchange unit, and 
   a flow amount calculation step of calculating the flow amount of the second medium, which is necessary for heat exchange of the target heat quantity, on the basis of the average temperature difference calculated in the average temperature calculation step, the target temperature, and the temperature of the first and second media detected in the detection step. 
   In a preferred embodiment, the adjustment step includes: 
   a target heat quantity calculation step of calculating a target heat quantity, on the basis of the target temperature of the first medium and the temperature of the first medium detected in the detection step, a first temperature difference calculation step of calculating a first temperature difference on the basis of the target temperature and the temperature of the second medium detected in the detection step, 
   an assuming step of assuming a target flow amount of the second medium, 
   a second temperature difference calculation step of calculating a second temperature difference on the basis of the target heat quantity, the assumed target flow amount, and the temperatures of the first and second media detected in the detection step, 
   an average temperature difference calculation step of calculating one of a logarithmic average temperature difference and an average temperature difference at the heat exchange unit, on the basis of the first and second temperature differences, 
   a heat exchange quantity calculation step of calculating a heat exchange quantity at the heat exchange unit, on the basis of one of the logarithmic average temperature difference and a heat exchange gain of the heat exchange unit and an average temperature difference, and 
   a determination step of determining the target flow amount of the second medium, on the basis of a result of a comparison between the heat exchange quantity and the target heat quantity. 
   In the adjustment step, the flow amount of the second medium is adjusted so as to compensate for a fluctuation of the heat exchange gain of the heat exchange unit, the fluctuation being caused by the flow amount of the second medium. 
   In a preferred embodiment, the flow amount of the second medium is adjusted so as to compensate for the fluctuation of the gain on the basis of one of the logarithmic average temperature difference and the average temperature difference. 
   According to the present invention, the foregoing object is achieved by providing a heat exchange apparatus, which uses a heat exchange unit for exchanging heat between first and second media, to adjust a temperature of the first medium, the apparatus comprising: 
   a first sensor which detects a temperature of the first medium input to the heat exchange unit; 
   a second sensor which detects a temperature of the second medium input to the heat exchange unit; and 
   an adjustment system which adjusts a flow amount of the second medium on the basis of outputs from the first and second sensors. 
   In a preferred embodiment, the adjustment system: 
   calculates a target heat quantity on the basis of a target temperature of the first medium and the output from the first sensor, 
   calculates an average temperature difference at the heat exchange unit, on the basis of the target heat quantity and a heat exchange gain of the heat exchange unit, and 
   calculates a flow amount of the second medium, which is necessary for heat exchange of the target heat quantity, on the basis of the average temperature difference, the target temperature, and the outputs from the first and second sensors. 
   In a preferred embodiment, the adjustment system: 
   calculates a target heat quantity on the basis of a target temperature of the first medium and the output from the first sensor, 
   calculates a first temperature difference on the basis of the target temperature and the output from the second sensor, 
   assumes a target flow amount of the second medium, 
   calculates a second temperature difference on the basis of the target heat quantity, the assumed target flow amount, and the outputs from the first and second sensors, 
   calculates one of a logarithmic average temperature difference and an average temperature difference at the heat exchange unit, on the basis of the first and second temperature differences, 
   calculates a heat exchange quantity at the heat exchange unit on the basis of a heat exchange gain of the heat exchange unit and one of the logarithmic average temperature difference and the average temperature difference, and 
   determines a target flow amount of the second medium, on the basis of a result of a comparison between the heat exchange quantity and the target heat quantity. 
   In a preferred embodiment, the adjustment system adjusts the flow amount of the second medium, so as to compensate for a fluctuation of the heat exchange gain of the heat exchange unit, the fluctuation being caused by the flow amount of the second medium. 
   In a preferred embodiment, the flow amount of the second medium is adjusted so as to compensate for the fluctuation of the gain, on the basis of one of the logarithmic average temperature difference and the average temperature difference. 
   According to the present invention, the foregoing object is attained by providing an apparatus comprising: 
   an exposure system which includes a heating element and exposes a substrate to a pattern of an original; and 
   a heat exchange apparatus as discussed above. 
   According to the present invention, the foregoing object is attained by providing a method of manufacturing a device, the method comprising steps of: 
   exposing a substrate to a pattern using an apparatus as discussed above; developing the exposed substrate; and 
   processing the developed substrate to manufacture the device. 
   Other features and advantages of the present invention will be apparent from the following description, taken in conjunction with the accompanying drawings, in which like reference characters designate the same or similar parts throughout the figures thereof. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the invention, and together with the description, serve to explain the principles of the invention. 
       FIG. 1  is a view showing the structure of a general exposure apparatus; 
       FIG. 2  is a block diagram of a cooling apparatus in an exposure apparatus according to the first embodiment of the present invention; 
       FIG. 3  is a block diagram showing an example of the structure of a control valve according to the first embodiment of the present invention; 
       FIG. 4  is a graph showing an example of the temperature characteristics of a heat exchange unit according to the first embodiment of the present invention; 
       FIG. 5  is an operation flowchart of a flow amount operation unit according to the first embodiment of the present invention; 
       FIG. 6  is a graph showing an example of the temperature characteristics of the heat exchange unit according to the first embodiment of the present invention; 
       FIG. 7  is a graph showing an example of the flow amount characteristics of the control valve according to the first embodiment of the present invention; 
       FIG. 8  is an operation flowchart of a flow amount operation unit according to the second embodiment of the present invention; 
       FIG. 9  is a block diagram of a cooling apparatus in an exposure apparatus according to the second embodiment of the present invention; 
       FIG. 10  is a block diagram showing examples of the flow amount operation unit, a temperature controller, and a flow amount controller according to the second embodiment of the present invention; 
       FIG. 11  is a graph showing an example of the heat passing ratio characteristics of a heat exchange unit according to the second embodiment of the present invention; 
       FIG. 12  is an operation flowchart of a flow amount operation unit according to the third embodiment of the present invention; 
       FIG. 13  is a graph showing an example of the heat exchange characteristics of a heat exchange unit according to the third embodiment of the present invention; 
       FIG. 14  is a flowchart showing the flow of an entire semiconductor device manufacturing process; and 
       FIG. 15  is a flowchart showing the detailed flow of the wafer process of  FIG. 14 . 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Preferred embodiments of the present invention will be described in detail in accordance with the accompanying drawings. 
   First Embodiment 
   The structure of an exposure apparatus, to which the heat exchange apparatus and method according to the present invention can be applied, will be described with reference to  FIG. 1 . 
     FIG. 1  is a view showing the structure of a general exposure apparatus. 
   Exposure light emitted from an exposure light source (not shown) irradiates a reticle  110  set on a reticle stage  120  by an illumination optical system  100 . Light transmitted through the reticle  110  is transmitted through a projection optical system  130  to reach a wafer  150  placed on a wafer stage  140 , to print a fine pattern drawn on the reticle  110  onto the respective shots on the wafer  150 . As the exposure light source, a KrF laser source or a short-wavelength ArF laser source for further micropatterning is used often. 
   In an exposure apparatus called a stepper, the reticle stage  120  is set still. The wafer stage  140  is set still during exposure, and is stepped for exposure of the next shot when the exposure is ended. In an exposure apparatus called a scanning stepper, the reticle stage  120  and wafer stage  140  are scanned in the opposite directions in synchronism with each other. Exposure is performed during sync scanning. When the exposure is ended, the wafer stage  140  is stepped for exposure of the next shot. 
   In the scanning stepper, to further improve the productivity, both the reticle stage  120  and wafer stage  140  are accelerated by higher accelerations and sync-scanned, and exposed at higher speeds. In general, assume that reduction exposure is performed with an exposure reduction ratio of the reticle  110  to wafer  150  being 4:1. The ratios of the accelerations and speeds of the reticle stage  120  to wafer stage  140  are also 4:1. Thus, the acceleration and speed of the reticle stage  120  are four times higher than those of the wafer stage  140 . 
   To improve the productivity, the acceleration and speed of each stage increase more and more. The acceleration and speed of the wafer stage  140  are increased to about 1 G to about 1.5 G and about 300 mm/s to about 500 mm/s, respectively. 
   In this manner, both the reticle stage  120  and wafer stage  140  must be driven very fast to improve the productivity, and their positions or speeds must be controlled very accurately to realize micropattern exposure. 
   In general, stages are often levitated by a pneumatic pressure or a magnetic force and are sync-scanned or stepped by linear motors employing the principle of the Lorentz force or, depending on the case, actuators, such as planar motors. In this case, a frictional force in the horizontal direction is very small. Hence, a thrust which is generated by the actuator, as it is necessary for sync scanning or stepping, is proportional to the acceleration and mass of the stage. 
   For example, the thrust generated by the linear motor is proportional to the driving current, and heat generated by the linear motor is equal to the product of the resistance of the motor winding and the square of the driving current. Accordingly, heat generated in the linear motor increases in proportion to the generated thrust, i.e., in proportion to the square of the acceleration of the stage. In other words, when the acceleration is doubled, heat generated by the linear motor becomes multiplied by four. 
   The stage positions of the reticle stage  120  and wafer stage  140  are controlled precisely on the order of a nanometer. For this purpose, generally, the stage positions are constantly monitored by laser interferometers and feedback-controlled. If, however, large heat is generated by stage driving, the heat quantity disturbs the optical paths of the laser interferometers. Consequently, the refractive indices of air in the optical paths fluctuate to cause a large error in position measurement of the stages. Therefore, to control the stages on the order of a nanometer, the temperature fluctuations of the optical paths of the interferometers must be 0.01° C. or less. 
   To realize very fine micropattern exposure with high productivity, a cooling apparatus, which removes the large amount of generated heat more accurately, to recover the heat, is necessary. 
   Each stage of the reticle stage  120  and wafer stage  140  generates a very large amount of heat during exposure. When the wafer  150  or reticle  110  is to be changed, the reticle stage  120  and wafer stage  140  are stopped and, accordingly, heat generated by them becomes almost zero. In other words, to the cooling apparatus, the load fluctuates very sharply with a very large width. 
   The exposure apparatus contains many precision measurement systems in addition to the stage. To realize very fine micropattern exposure, a cooling apparatus, which cools more accurately to recover heat, is necessary. 
   In the old-fashioned semiconductor manufacturing factory, the factory cooling water often has a comparatively high temperature of 20° C. to 30° C. In the recent high-productivity factory for semiconductor devices having very small feature sizes, the factory cooling water often has a low temperature of about 10° C. to 18° C., which is lower than the temperature of factory cooling water used in the old-fashioned semiconductor manufacturing factory. For this reason, a cooling apparatus employing a refrigerating cycle, which uses a compressor and an inverter, is becoming unnecessary. 
   Although the temperature of the factory cooling water is low, it sometimes fluctuates by 1° C. to 2° C., and with very sharp rate fluctuations. 
   Other than energy conservation, the semiconductor manufacturing factory seeks to optimize many other features, such as improvement of the space efficiency of the manufacturing line, feature size shrinkage, and the like. 
   Hence, there is required a power-saving, high-efficiency, low-cost, and compact cooling apparatus in an exposure apparatus for performing cooling or heat recovery, which can control temperature very stably against load fluctuations and factory cooling water fluctuations, when low-temperature factory cooling water is supplied. 
   A cooling apparatus in an exposure apparatus according to the first embodiment will be described with reference to  FIG. 2 . 
     FIG. 2  is a block diagram of the cooling apparatus in the exposure apparatus according to the first embodiment of the present invention. 
   A broken-line portion  10  indicates the entire circuit of the first medium, a broken-line portion  30  indicates the entire circuit of the second medium, and a broken-line portion  50  indicates the entire portion of the respective types of controllers. Reference numeral  12  denotes a first medium circuit; and reference numeral  22 , a load in the exposure circuit. The load  22  corresponds to the stage and respective types of precision measurement systems in the exposure apparatus of  FIG. 1 . The first medium passes through the load  22  to recover the load heat, and shifts the heat to a second medium circuit  32  through a heat exchange unit  40 . 
   In the first medium circuit  12 , a first temperature sensor  16  is attached to an outlet  43  side circuit of the heat exchange unit  40 , and a second temperature sensor  14  is attached to an inlet  41  side circuit of the heat exchange unit  40 . The first medium forms a pump  20  to form a circulation system. The pump  20  may be attached to either the inlet  41  side or outlet  43  side of the heat exchange unit  40 . A tank  18  is attached when necessary. The tank  18  may be attached to either the inlet  41  side or outlet  43  side of the heat exchange unit  40 . 
   When necessary, a flow amount sensor  24  to measure the circulating flow amount of the first medium may be attached. Usually, the flow amount sensor  24  need not be attached, because the pressure loss of the first medium circuit  12  and the rotational speed of the pump  20  are adjusted, so that the circulating flow amount becomes a predetermined value. Even if the flow amount sensor  24  should be attached, its location is not particularly limited. 
   The first medium suffices as long as it is a fluid, and may be a liquid or a gas. As the liquid, pure water or brine, which is generally used as a refrigerant, can be employed. When gas is to be used, the pump  20  is replaced by a fan. 
   The second medium is factory cooling water  39  supplied from the factory and, generally, is often water or pure water. In the recent high-productivity factory for semiconductor devices having very small feature sizes, the factory cooling water is often about 10° C. to 18° C. The factory cooling water is branched by a control valve  34  into a main circuit  31  and a branch circuit  37 . The main circuit  31  is provided with a third temperature sensor  36  and flow amount sensor  38 . The main circuit  31  is further connected to an inlet  45  of the heat exchange unit  40 . An outlet  47  of the heat exchange unit  40  merges with the branch circuit  37 , and is connected to the factory plant. 
   The respective temperature sensors  14 ,  16  and  36  are sensors, such as thermo-couples or platinum resistors, and are selected in accordance with the required temperature accuracy. The control valve  34  is preferably one which can perform proportional control, and may include a proportional three-way valve, or two proportional three-way valves (or proportional electromagnetic valves)  33  and  35 , shown in  FIG. 3 . When the two proportional two-way valves (or proportional electromagnetic valves)  33  and  35  are to be used, they require push-pull driving. Accordingly, a controller, to be described later, is formed to generate two signals, i.e., a push signal and a pull signal, like a controller  60   b.    
   Each of the flow amount sensors  24  and  38  can be of any type, such as a Karman™ vortex sensor, an electromagnetic sensor, or an impeller sensor. When the first medium is gas, a mass-flow sensor, or the like, is used as the flow amount sensor  24 . 
   As the heat exchange unit  40 , a shell-and-tube heat exchange unit, a blazing heat exchange unit, or the like, is used. When the first medium is gas, a cooling coil, or the like, is used. According to the first embodiment, the input and output of the first medium and the input and output of the second medium are connected to oppose each other. In general, a heat exchange unit often employs heat exchange by counterflows, because it is the most efficient. The heat exchange unit can also employ parallel flows in which the inputs and outputs of the first and second media are parallel. 
   In the portion  50  (also to be referred to as a flow amount adjustment system), including the respective types of controllers, a target temperature  52  and a temperature feedback signal from the first temperature sensor  16  are input to an adder-subtractor  54 , and their difference signal is input to a temperature controller  56 . The temperature controller  56  performs a control operation with proportional/integral/derivative control, or the like, as will be described later. A temperature control signal from the temperature controller  56  is added to a flow amount signal from a flow amount operation unit  62  by an adder-subtractor  58 . When necessary, a flow amount feedback signal from the flow amount sensor  38  is input to the adder-subtractor  58  to form a flow amount control system. 
   When flow amount control is to be performed, a flow amount controller  60  performs a control operation with proportional/integral/derivative control, or the like. When the flow amount control is not to be performed, the flow amount feedback signal from the flow amount sensor  38  is not input to the adder-subtractor  58 , but proportional gain calculation or filtering is performed, when necessary, to apply a flow amount control signal to the control valve  34 . 
   The control valve  34  adjusts the channels of the main circuit  31  and branch circuit  37  in response to the applied flow amount control signal to control the flow amount flowing in the main circuit  31 . The second medium of the controlled main circuit  31  passes through the heat exchange unit  40  to recover heat from the first medium, and merges with the branch circuit  37  to shift heat to the factory plant. 
   The heat exchange unit  40  can adjust the heat recovery quantity of the first medium by the flow amount of the second medium in the main circuit  31 . With this arrangement, temperature control can be performed, such that the temperature of the first medium is equal to the target temperature  52 . 
   In this case, the load  22  fluctuates sharply and largely, as described above, and, accordingly, the temperature of the first medium at the inlet  41  of the heat exchange unit  40  fluctuates sharply and largely. When the stages of the exposure apparatus are driven, heat of several kW is generated. Even when the circulating flow amount of the first medium is several tens of L/min, temperature fluctuations of about several degrees Celsius occur. 
   When the sharp and large temperature fluctuations are to be dealt with only by the feedback control of the first temperature sensor  16 , a response delay, or the like, which is a disadvantage of the feedback control, occurs. Therefore, heat of the first medium cannot be recovered accurately, and large temperature fluctuations of about several degrees Celsius occur. 
   The temperature of the factory cooling water  39  sometimes fluctuates by about 1° C. to 2° C. If the fluctuations are to be dealt with only by the feedback control of the first temperature sensor  16  in the same manner, a response delay, or the like, which is a disadvantage of the feedback control, occurs. Therefore, heat of the first medium cannot be recovered accurately, and large temperature fluctuations of about several degrees Celsius occur. 
   To deal with the fluctuations of the load  22  and the temperature fluctuations of the factory cooling water  39 , the temperature fluctuations are detected by the second temperature sensor  14  and third temperature sensor  36 . The flow amount operation unit  62  calculates the flow amount of the second medium, which is necessary to set the first medium to the target temperature, and adjusts the control valve  34 . Thus, influences of various types of temperature fluctuations are suppressed. 
   The operation of the flow amount operation unit  62  of the first embodiment will be described with reference to  FIGS. 4 and 5 . 
     FIG. 4  is a graph showing an example of the temperature characteristics of the heat exchange unit according to the first embodiment of the present invention.  FIG. 5  is an operation flowchart of the flow amount operation unit according to the first embodiment of the present invention. 
     FIG. 4  will be described.  FIG. 4  shows the temperature characteristics of the first and second media in the counter flows, in which the temperature of the first medium of the heat exchange unit  40  at the inlet  41  is expressed as T 11 . The axis of the abscissa represents the passing position in the heat exchange unit  40 . At the outlet  43 , the heat of the first medium is recovered by the second medium, so that the temperature becomes T 12 . The temperature of the second medium at the inlet  45  is expressed as T 21 . At the outlet  47  of the heat exchange unit  40 , the second medium recovers the heat of the first medium, so that its temperature becomes T 22 . 
   In the heat exchange unit  40 , a heat quantity φ 1  recovered from the first medium and a heat quantity φ 2  recovered by the second medium are equal. Hence, the following equations are established.
 
φ 1   =F   1 *ρ 1   *c   p1 *( T   11   −T   12 )  (1)
 
φ 2   =F   2 *ρ 2   *c   p2 *( T   22   −T   21 )  (2)
 
φ 1 =φ 2   (3)
 
where
 
   φ 1  and φ 2 : heat quantities [W], 
   F 1  and F 2 : flow amounts [m 3 /s], 
   ρ 1  and ρ 2 : densities [kg/cm 3 ], and 
   c p1  and c p2 : specific heats [kJ/kg° C.]. 
   Suffixes 1 and 2 indicate the first and second media, respectively. W=J/s. 
   A temperature difference Δθ 1  of the first medium at the inlet side of the heat exchange unit  40  from the second medium and a temperature difference Δθ 2  of the first medium at the outlet side of the heat exchange unit  40  from the second medium are expressed by the following equations:
 
Δθ 1   =T   11   −T   22   (4)
 
Δθ 2   =T   12   −T   21   (5)
 
   In general, a heat exchange quantity Q [W] in the heat exchange unit  40  is expressed by the following equation:
 
Q=KAΔT m   (6)
 
where
 
K: heat passing ratio (W/m 2 ° C.),
 
A: heat transfer area [m 2 ],
 
ΔT m : logarithmic average temperature difference [° C.]
 
Δ T   m =(Δθ 2 −Δθ 1 )/ln(Δθ 2 /Δθ 1 )  (7)
 
   where K is the heat passing ratio of the heat exchange unit  40  and A is the heat transfer area of the heat exchange unit  40 , which are unique to each heat exchange unit  40 . 
   When Δθ 2 =Δθ 1 , equation (7) becomes indefinite. At this singular point, in place of the logarithmic average temperature difference, an arithmetic average temperature T ave  of the following equation is used:
 
 T   ave =(Δθ 2 +Δθ 1 )/2  (8)
 
     FIG. 6  shows the characteristics of the logarithmic average temperature difference and arithmetic average temperature. 
   The axis of the abscissa represents Δθ 2 −Δθ 1 , and the axis of ordinate represents the logarithmic average temperature difference and the arithmetic average temperature. 
   The zero point on the axis of abscissa is the singular point of the logarithmic average temperature difference. When the temperature difference is small, the logarithmic average temperature difference and arithmetic average temperature are obviously substantially equal. As the temperature difference increases, the logarithmic average temperature difference and arithmetic average temperature gradually differ from each other, and the arithmetic average temperature tends to be high with respect to the logarithmic average temperature difference. Therefore, when (Δθ 2 −Δθ 1 ) is small, or the error of the arithmetic average temperature from the logarithmic average temperature difference is negligible, the heat exchange quantity in the heat exchange unit  40  can be expressed by the following equation:
 
Q=KAT ave .  (9)
 
   The heat recovery quantity between the first and second media is equal to the heat exchange quantity in the heat exchange unit  40 , and, accordingly, the following equation is established:
 
φ 1 =φ 2 =KAT ave .  (10)
 
   The operation in the flow amount operation unit  62  will be described with reference to  FIG. 5 . 
   In step S 1 , a target heat quantity φ ref  is calculated from a target temperature T 1ref  from the target temperature  52  and the temperature T 11  from the second temperature sensor  14 :
 
φ ref   =F   1 *ρ 1   *c   p1 *( T   1ref   −T   11 )  (11)
 
 G   1 =ρ 1   *c   p1   (12)
 
 G   2 =ρ 2   *c   p2 .  (13)
 
   When the flow amount sensor  24  is attached, F 1  may be calculated on the basis of the value from the flow amount sensor  24 . If a regulated flow amount value is set in advance, F 1  may be calculated by substituting it. 
   In step S 2 , the average temperature T ave  is calculated form the target heat quantity φ ref  obtained by equation (11) and the heat exchange quantity in the heat exchange unit  40  obtained by equation (10):
 
 T   ave =φ ref   /G   3   (14)
 
G 3 =KA.  (15)
 
   In step S 3 , various temperatures are calculated from the target temperature T 1ref , the temperature T 21  from the third temperature sensor  36 , and the temperature T 11  from the second temperature sensor  14 :
 
Δθ 2   =T   1ref   −T   21   (16)
 
Δθ 1 =2 T   ave −Δθ 2   (17)
 
 T   22   =T   11 −Δθ 1 .  (18)
 
   In step S 4 , a target flow amount F 2ref  of the second medium is calculated from the various values obtained by calculation and equations (2), (3), and (13):
 
 F   2ref =φ ref /( T   22   −T   11 )/ G   2 .  (19)
 
   Therefore, according to the present invention, the temperature fluctuations of the first medium caused by the fluctuations of the load  22  are detected by the second temperature sensor  14 . The temperature fluctuations of the second medium caused by the temperature fluctuations of the factory cooling water  39  are detected by the third temperature sensor  36 . The average temperature in the heat exchange unit  40  is calculated by the flow amount operation unit  62 . In addition, the flow amount of the second medium, which is necessary to set the first medium to the predetermined temperature, is calculated to adjust the control valve  34 . The heat of the first medium is recovered by the heat exchange unit  40 . Then, the temperature of the first medium is controlled by the first temperature sensor  16  and temperature controller  56 . 
   Even when the load fluctuates sharply, or the temperature of the factory cooling water fluctuates, heat can be recovered quickly and appropriately, so that stable temperature control can be performed. 
   According to the first embodiment, power devices, such as a compressor or an inverter, and mechanical components, such as a condenser, an evaporator, or an expansion valve, which are used in the prior art, become unnecessary. A power-saving, high-efficiency, low-cost, and compact cooling apparatus for performing cooling or heat recovery, which can control temperature stably against load fluctuations and factory cooling water fluctuations, when factory cooling water having a temperature lower than a predetermined temperature is supplied, can be formed. 
   Desirably, the present invention is used when (Δθ 1 −Δθ 2 ) in the heat exchange unit  40  is small, or when the error of the arithmetic average temperature form the logarithmic average temperature difference is negligible. 
     FIG. 7  shows an example of the characteristics when the control valve  34  includes a proportional three-way valve. 
   Referring to  FIG. 7 , the axis of the abscissa represents a manipulated variable from the flow amount controller  60 , and the axis of the ordinate represents the flow amount of the second medium. In general, the input/output characteristics of a three-way valve are strongly nonlinear. When the three-way valve is used as the flow amount adjustment valve of a temperature control system, the control system tends to be unstable. To improve the nonlinearity of the control valve  34 , as described above, the two proportional two-way valves (or proportional electromagnetic valves)  33  and  35 , shown in  FIG. 3 , may be used. 
   The flow amount may be feedback-controlled by the flow amount sensor  38  and flow amount controller  60  of  FIG. 2 . As described above, when flow amount control is to be performed, operation of the flow amount controller  60  includes proportional/integral/derivative control, or the like. 
   As described above, according to the first embodiment, the flow amount of the second medium is controlled by the flow amount sensor  38  and flow amount controller  60  with respect to the target flow amount from the temperature controller  56  and flow amount operation unit  62 . Heat is recovered more accurately, and, accordingly, the temperature of the first medium can be controlled more stably. 
   Second Embodiment 
   The second embodiment of the present invention will be described. 
   In the second embodiment, the operation method of the flow amount operation unit  62  in the block diagram of the cooling apparatus in  FIG. 2  of the first embodiment is different. This will be described with reference to  FIG. 8 . 
     FIG. 8  is an operation flowchart of a flow amount operation unit according to the second embodiment of the present invention. 
   In step S 1 , a target heat quantity φ ref  is calculated from a target temperature T 1ref  from a target temperature  52  and a temperature T 11  from a second temperature sensor  14  (see equations (11) to (13)). 
   When a flow amount sensor  24  is attached, F 1  may be calculated on the basis of the value from the flow amount sensor  24 . If a regulated flow amount value is set in advance, F 1  may be calculated by substituting it. 
   In step S 2 , a first temperature difference Δθ 2  is calculated from the target temperature T 1ref  and a temperature T 21  from a third temperature sensor  36 :
 
Δθ 2   =T   1ref   −T   21 .  (20)
 
   In step S 3 , a flow amount F 2set  of the second medium is set/changed. 
   In step S 4 , a temperature T 22  of the second medium at the output is calculated from the target heat quantity φ ref  calculated in step S 2  and the flow amount F 2set  and temperature T 21  of the second medium:
 
 T   22 =φ ref   /F   2set   /G   2   +T   21 .  (21)
 
   Then, a second temperature difference Δθ 1  is calculated from the temperature T 11  and T 22 :
 
Δθ 1   =T   11   −T   22 .  (22)
 
   Then, a logarithmic average temperature difference ΔT m  or average temperature T ave  is calculated by equation (7) or (8) from the first and second temperature differences Δθ 1  and Δθ 2 . 
   In step S 5 , a heat exchange quantity Q of the heat exchange unit  40  is calculated by equation (6), when the logarithmic average temperature difference ΔT m  is used, and by equation (9), when the average temperature T ave  is used. 
   In step S 6 , the target heat quantity φ ref  calculated in step S 1  and the heat exchange quantity Q calculated in step S 5  are compared. If it is confirmed that the target heat quantity φ ref  and the heat exchange quantity Q are equal, or substantially equal, by minimum value judgment, or the like, the flow advances to step S 7 . If NO, the flow returns to step S 3  to change the flow amount of the second medium. Then, the operations of steps S 3  to S 6  are repeated. 
   In step S 7 , the flow amount of the second medium determined in step S 6  is set as a target flow amount F 2ref  of the second medium. 
   The logarithmic average temperature difference in step S 4  is a singular point when Δθ 2 =Δθ 1 , and its solution becomes indefinite. At the singular point, calculation must be performed by substituting an average temperature value. Except for this, the logarithmic average temperature difference expresses the characteristics of a heat exchange unit  40  accurately. Therefore, the flow amount of the second medium can be calculated more accurately to realize stable temperature control. 
   If an average temperature is to be employed, desirably, it is used when (Δθ 2 −Δθ 1 ) in the heat exchange unit  40  is small, or when the error of the average temperature from the logarithmic average temperature difference is negligible. 
   Therefore, according to the second embodiment, the temperature fluctuations of the first medium caused by the fluctuations of the load  22  are detected by the second temperature sensor  14 . The temperature fluctuations of the second medium caused by the temperature fluctuations of factory cooling water  39  are detected by the third temperature sensor  36 . The logarithmic average temperature difference or average temperature in the heat exchange unit  40  is calculated by a flow amount operation unit  62 . In addition, the flow amount of the second medium, which is necessary to set the first medium to the predetermined temperature, is calculated, to adjust a control valve  34 . The heat of the first medium is recovered by the heat exchange unit  40 . Then, the temperature of the first medium is controlled by a first temperature sensor  16  and temperature controller  56 . 
   Even when the load fluctuates sharply, or the temperature of the factory cooling water fluctuates, heat can be recovered quickly and appropriately, so that stable temperature control can be performed. 
   According to the second embodiment, power devices, such as a compressor or an inverter, and mechanical components, such as a condenser, an evaporator, or an expansion valve, which are used in the prior art, become unnecessary. A power-saving, high-efficiency, low-cost, and compact cooling apparatus for performing cooling or heat recovery, which can control temperature very stably against load fluctuations and factory cooling water fluctuations, when factory cooling water having a temperature lower than a predetermined temperature is supplied, can be formed. 
   In the same manner as in the first embodiment, to improve the nonlinearity of the control valve  34 , the two proportional two-way valves (or proportional electromagnetic valves)  33  and  35 , shown in  FIG. 3 , may be used. 
   The flow amount may be feedback-controlled by the flow amount sensor  38  and flow amount controller  60  of  FIG. 2 . As described above, when flow amount control is to be performed, operation of the flow amount controller  60  includes proportional/integral/derivative control, or the like. 
   Hence, according to the second embodiment, the flow amount of the second medium is controlled by the flow amount sensor  38  and flow amount controller  60 , with respect to the target flow amount from the temperature controller  56 , and a flow amount operation unit  62   a . Heat is recovered more accurately, and, accordingly, the temperature of the first medium can be controlled more stably. 
     FIG. 9  is a block diagram of a cooling apparatus, which is obtained by adding new functions to the second embodiment. 
   Portions having the same functions as their counterparts in  FIG. 2  are denoted by the same reference numerals. A description will be made of a temperature controller  56   a , flow amount controller  60   a , and flow amount operation unit  62   b , which have different functions. 
     FIG. 10  shows an example of the detailed arrangement of the temperature controller  56   a , flow amount controller  60   a , and flow amount operation unit  62   b.    
   The flow amount operation unit  62   b  includes a target flow amount calculation unit  90 , K-value correction unit  92 , and ΔT correction unit  94 . The target flow amount calculation unit  90  calculates the target flow amount by the operation flow of  FIG. 8 , described in advance. 
   The characteristics of a heat passing ratio K of a heat exchange unit  40  will be described with reference to  FIG. 1 . 
   Referring to  FIG. 11 , the axis of the abscissa represents the flow amount of the second medium in the heat exchange unit  40 , and the axis of the ordinate represents the heat passing ratio K. In general, the heat passing ratio of the heat exchange unit  40  is not constant with respect to the flow amount, but has flow amount dependence, as shown in  FIG. 11 . To obtain these characteristics, data may be acquired as the characteristics of the heat exchange unit  40 , or a characteristic equation, or the like, may be acquired from the manufacturer of the heat exchange unit. When the flow amount is decreased, the heat passing ratio K decreases often. When the heat passing ratio K decreases, the heat exchange quantity in the heat exchange unit  40 , which is obtained with equation (9), also decreases. Then, an error occurs undesirably in the calculation of the target flow amount of the second medium. 
   Referring back to  FIG. 10 , the K-value correction unit  92  has a correction table or characteristic equation for the heat passing ratio K, with respect to the flow amount of the second medium, as described above. More specifically, the heat passing ratio K is corrected with respect to the flow amount of the second medium input from the target flow amount calculation unit  90 , and the corrected ratio K is output to the target flow amount calculation unit  90 . 
   In the operation flow of  FIG. 8  described above, the K value is corrected by the K-value correction unit  92  in accordance with the preset flow amount F 2set  of the second medium. Before the heat exchange quantity Q is calculated in step S 5 , G 3  of equation (15) is changed, and calculation is performed. 
   This can suppress the influence of the heat passing ratio of the heat exchange unit  40 , which depends on the flow amount of the second medium, so that the flow amount of the second medium, which is necessary to constantly perform accurate heat exchange, can be calculated. Then, a cooling apparatus for performing cooling or heat recovery, which can control temperature more stably, can be formed. 
   The K-value correction unit  92  outputs a gain correction signal to a gain correction unit  78  in the temperature controller  56   a . The heat exchange quantity Q in the heat exchange unit  40  is expressed by equation (6) or (9). When the temperature is to be fed back by the first temperature sensor  16  to perform feedback control by the temperature controller  56   a , the heat passing ratio K of the heat exchange unit  40  forms one element of the loop again in the control loop. 
   As described above, as the heat passing ratio K is changed by the flow amount of the second medium, the loop gain of the temperature control system also changes consequently. When the loop gain changes, the response speed of the temperature control system may greatly decrease. Depending on the case, the temperature control system may undesirably oscillate or cause very large temperature fluctuations. The K-value correction unit  92  outputs the fluctuation amount of the K value to the gain correction unit  78 . The gain correction unit  78  corrects the loop gain so that the loop gain of the temperature control system constantly has a predetermined value, regardless of the fluctuation amount of the K value. 
   Furthermore, the ΔT correction unit  94  outputs a ΔT correction signal to the gain correction unit  78  in the temperature controller  56   a . The heat exchange quantity Q in the heat exchange unit  40  is expressed by equation (6) or (9). The logarithmic average temperature difference ΔT m  or average temperature T ave  becomes the gain of the heat exchange unit  40  to accordingly form one element of the loop gain in the temperature control loop. 
   The logarithmic average temperature difference ΔT m  or average temperature T ave  is changed by the fluctuations in the load  22 , the temperature fluctuations in the factory cooling water  39 , and the preset flow amount of the second medium. The ΔT correction unit  94  calculates the fluctuation amount from ΔT m  or T ave , which is predetermined as a reference value, and outputs it to the gain correction unit  78 . The gain correction unit  78  corrects the loop gain, so that the loop gain of the temperature control system constantly has a predetermined value, regardless of the fluctuation amount of ΔT. 
   A proportion unit  70 , an integration unit  72 , a derivative unit  74 , and an addition unit  76 , in the temperature controller  56   a , are control operation units, which perform proportional/integral/derivative control, or the like, described above. 
   The flow amount controller  60   a  may have a gain correction unit  87 . As described with reference to  FIG. 7 , the control valve  34  often has nonlinearity. Hence, the gain correction unit  87  performs gain correction to correct the nonlinearity of the control valve  34  on the basis of the flow amount feedback signal from a flow amount sensor  38 . The characteristics of the nonlinearity of the control valve  34  may be measured in advance. Alternatively, a characteristic equation may be acquired from the manufacturer, and the gain may be corrected on the basis of the acquired characteristics. 
   A proportion unit  80 , an integration unit  82 , a derivative unit  84 , and an addition unit  86 , in the flow amount controller  60   a , are control operation units, which perform proportional/integral/derivative control, or the like, described above. 
   According to the second embodiment, a change in characteristics of the heat exchange unit  40 , which depends on the flow amount of the second medium, can be corrected by the K-value correction unit  92 , the ΔT correction unit  94 , and the gain correction unit  78  in the temperature controller  56   a . As a result, a cooling apparatus for performing cooling or heat recovery, which can always control temperature very stably against load fluctuations and factory cooling water fluctuations, regardless of the flow amount of the second medium, can be formed. 
   Third Embodiment 
   The third embodiment of the present invention will be described. 
   In the third embodiment, the operation method of the flow amount operation unit  62  in the block diagram of the cooling apparatus in  FIG. 2  of the first embodiment is different. This will be described with reference to  FIG. 12 . 
     FIG. 12  is an operation flowchart of a flow amount operation unit according to the third embodiment of the present invention. 
   In step S 1 , a target heat quantity φ ref  is calculated from a target temperature T 1ref  from a target temperature  52  and a temperature T 11  from a second temperature sensor  14  (see equations (11) to (13)). 
   When a flow amount sensor  24  is attached, F 1  may be calculated on the basis of the value from the flow amount sensor  24 . If a regulated flow amount value is set in advance, F 1  may be calculated by substituting it. 
   In step S 2 , the flow amount of the second medium, which is equal to or substantially equal to the target flow amount φ ref , is calculated from the temperature T 11  from the second temperature sensor  14  and a temperature T 21  from a third temperature sensor  36 , by using a look-up table or characteristic equation, which represents the relationship between the flow amount of the second medium of the heat exchange unit  40  and the heat exchange quantity. 
   The look-up table or characteristic equation will be described with reference to  FIG. 13 . 
     FIG. 13  shows the heat exchange quantity (cooling capability) of the heat exchange unit  40  with respect to the flow amount of the second medium where the temperature T 11  is a constant temperature and the temperature T 21  serves as parameters Ta, Tb, and Tc (Ta&lt;Tb&lt;Tc). 
   Note that T 21 &lt;T 11 , and that the first medium is to be cooled by the second medium. In this case, the lower the temperature of the second medium, the higher the cooling capability, and heat exchange can be performed with a smaller flow amount. Accordingly, for the respective temperatures T 11 , a look-up table or characteristic equation, as shown in  FIG. 13 , using the temperature T 21  is obtained, which shows the characteristics of the heat exchange quantity with respect to the flow amount of the second medium. Thus, in step S 2  of  FIG. 12 , the flow amount of the second medium, which is equal to or substantially equal to the target flow amount φ ref , can be calculated 
   The characteristics of the look-up table or characteristic equation may be measured in advance. Alternatively, the characteristic equation may be acquired from the manufacturer or created on the basis of a theoretical calculation value. 
   In step S 3  of  FIG. 12 , the flow amount of the second medium, which is calculated in step S 2 , is set as a target flow amount F 2ref  of the second medium. 
   Therefore, according to the third embodiment, the temperature fluctuations of the first medium caused by the fluctuations of the load, or the like, are detected by the second temperature sensor  14 . The temperature fluctuations of the second medium are detected by the third temperature sensor  36 . The flow amount of the second medium, which is necessary to set the first medium to the predetermined temperature, is calculated from the look-up table or characteristic equation to adjust a control valve  34 . The heat of the first medium is recovered by the heat exchange unit  40 . Then, the temperature of the first medium is controlled by the first temperature sensor  16  and a temperature controller  56 . 
   Even when the load fluctuates sharply or the temperature of the factory cooling water fluctuates, heat can be recovered quickly and appropriately, so that stable temperature control can be performed. Hence, a power-saving, high-efficiency, low-cost, and compact cooling apparatus for performing cooling or heat recovery, which can control temperature stable against load fluctuations and factory cooling water fluctuations, when factory cooling water having a temperature lower than a predetermined temperature is supplied, can be formed. 
   As described above, according to a given embodiment, when the load fluctuates sharply or the temperature of the factory cooling water fluctuates, heat can be recovered quickly and appropriately, so that stable temperature control can be performed. Hence, a power-saving, high-efficiency, low-cost, and compact cooling apparatus for performing cooling or heat recovery, which can control temperature stably against load fluctuations and factory cooling water fluctuations, when factory cooling water having a low temperature is supplied, can be formed. 
   According to a given embodiment, the flow amount of the second medium is controlled by the flow amount sensor and flow amount control valve with respect to the target flow amount from the temperature controller and flow amount operation unit. Heat is recovered more accurately, and, accordingly, the temperature of the first medium can be controlled more stably. 
   According to a given embodiment, a change in characteristics of the heat exchange unit, which depends on the flow amount of the second medium, can be corrected by the heat exchange gain correction unit and temperature control gain correction unit. As a result, a cooling apparatus for performing cooling or heat recovery, which can always control temperature very stably against load fluctuations and factory cooling water fluctuations, regardless of the flow amount of the second medium, can be formed. 
   A given embodiment is not limited to a cooling apparatus not using a compressor, or the like, but can be widely applied to a cooling apparatus or heating or warming apparatus, which has a heat exchange unit. 
   According to a given embodiment, even when the load fluctuates sharply or the temperature of the second medium, which is input to the heat exchange unit, fluctuates, heat can be recovered quickly and appropriately. Thus, the temperature can be controlled very stably. 
   When the load fluctuations are small and fluctuations in temperature of the first medium at the inlet to the heat exchange unit are small, the second temperature sensor need not be included. In this case, the flow amount of the second medium, which is necessary to set the first medium to the predetermined temperature, may be calculated from the target temperature and the output from a temperature sensor, which detects the temperature of the second medium on the basis of the predetermined temperature of the first medium. When the temperature fluctuations of the second medium are small, the third temperature sensor need not be included. In this case, the flow amount of the second medium, which is necessary to set the first medium to the predetermined temperature, may be calculated from the target temperature and the output from the second temperature sensor, which detects the temperature of the first medium on the basis of the predetermined temperature of the second medium. 
   [Application of Exposure Apparatus] 
   A semiconductor device manufacturing process, which uses the exposure apparatus described above, will be described. 
     FIG. 14  shows the flow of the entire semiconductor device manufacturing process. 
   In step  101  (circuit design), the circuit of a semiconductor device is designed. In step  102  (mask fabrication), a mask is fabricated on the basis of the designed circuit pattern. In step  103  (wafer manufacture), a wafer is manufactured using a material such as silicon. 
   In step  104  (wafer process), called a preprocess, an actual circuit is formed on the wafer in accordance with lithography using the above mask and wafer. In the next step, step  105  (assembly), called a post-process, a semiconductor chip is formed from the wafer fabricated in step  104 . This step includes assembly processes, such as assembly (dicing and bonding) and packaging (chip encapsulation). In step  106  (inspection), inspections, such as an operation check and a durability test, of the semiconductor device fabricated in step  105 , are performed. A semiconductor device is finished with these steps and shipped (step  107 ). 
     FIG. 15  shows the flow of the above wafer process in detail. 
   In step  111  (oxidation), the surface of the wafer is oxidized. In step  112  (CVD), an insulating film is formed on the wafer surface. In step  113  (electrode formation), an electrode is formed on the wafer by deposition. In step  114  (ion implantation), ions are implanted in the wafer. In step  115  (resist process), a photosensitive agent is applied to the wafer. 
   In step  116  (exposure), the circuit pattern is transferred to the wafer by the above exposure apparatus. In step  117  (development), the exposed wafer is developed. In step  118  (etching), portions other than the developed resist image are removed. In step  119  (resist removal), any unnecessary resist remaining after etching is removed. These steps are repeated to form multiple circuit patterns on the wafer. 
   The present invention is not limited to the above embodiments, and various changes and modifications can be made within the spirit and scope of the present invention. Therefore, to apprise the public of the scope of the present invention, the following claims are made.