Abstract:
A position measurement unit measures the position of an object to be position controlled. A microprocessor performs a plurality of types of operations on the basis of the obtained position signal and outputs the operation result as a control signal that pertains to position control of the object to be position controlled. The microprocessor performs a difference operation, which calculates the difference signal of the position signal at the first sampling frequency and performs operations other than difference operation at the second sampling frequency lower than the first sampling frequency.

Description:
CLAIM OF PRIORITY 
   This application claims priority from Japanese Patent Application No. 2003 330402 filed on Sep. 22, 2003, the entire contents of which are hereby incorporated by reference herein. 
   FIELD OF THE INVENTION 
   The present invention relates to an alignment apparatus comprising a measuring instrument, which measures the position of an object to be position controlled and a processor, which performs a plurality of types of operations on the basis of a position signal obtained by the measuring instrument and outputs the operation result as a control signal that pertains to position control of the object to be position controlled, an exposure apparatus having the alignment apparatus, and a device manufacturing method of manufacturing a semiconductor device using the exposure apparatus. 
   BACKGROUND OF THE INVENTION 
   As a conventional technique, stage control of a stage which moves a wafer or reticle in a semiconductor exposure apparatus (to be referred to in abbreviated form as an exposure apparatus hereinafter) will be exemplified. 
   Performance characteristics required for the stage of a semiconductor exposure apparatus are: 
   1. quick response (responsiveness); 
   2. stability; and 
   3. good control accuracy (steady state error). 
   In stage control, PID compensation is used to improve these performance characteristics. Along with a recent decrease in exposure line width, an exposure apparatus stage is required to have position control accuracy on the order of several nanometers. For the purpose of increasing the productivity, the stage moving acceleration and velocity are increasing year by year. 
   To realize high speed, high precision position control, a wafer stage position control system needs to have a high servo band. For this reason, analog control using an analog device such as an operational amplifier is being replaced by digital control using a microprocessor which performs high speed digital signal processing typified by DSP. Many exposure apparatuses adopt this method. 
   An example of a control system of an exposure apparatus which performs conventional digital control using a microprocessor will be described with reference to  FIG. 11 . 
     FIG. 11  is a diagram for explaining the control system of a conventional exposure apparatus. 
   For the sake of descriptive simplicity, the controller of a single stage will be described here. The basic arrangement of the control system of each of various stages (e.g., a wafer stage, reticle stage, and the like) in the exposure apparatus is not different from that of this example. 
   Reference numeral  11  denotes a stage to be position controlled in the exposure apparatus. A position measurement unit  13  measures a position signal y(t) of the stage  11 . The position signal y(t) is converted by an A/D converter  19  to a digital signal y(n). 
   Reference symbol t denotes time; and n, the sample number. That is, the position signal y(t) is a position signal at time t. The digital signal y(n) is a digital signal whose sample number is n. 
   A control command value (control signal) u(n) is calculated within a microprocessor  18 . The control signal u(n) is converted by a D/A converter  15  to a continuous time signal u(t) and is amplified by a current amplifier  12  to a signal i(t). With the signal, a linear motor  11   a  drives the stage  11 . 
   The position of the stage  11  thus controlled is measured again by the position measurement unit  13 . A similar control operation is repeated, and the stage  11  reaches a position target value. 
   In the microprocessor  18 , the following calculation processes are performed. 
   1. An adder  903  calculates an error signal e p (n), which is a difference between the digital signal y(n) and a position target value r p (n) generated by a position target value generator  17   a.    
   2. A difference operation unit  16   b  calculates an error difference signal e d (n) of the error signals e p (n). 
   3. A sum operation unit  16   a  calculates an error sum signal e i (n) of the error signals e p (n). 
   4. The product of the error signal e p (n) and a proportional gain  14   a , the product of the error sum signal e i (n) and an integral gain  14   b , and the product of the error difference signal e d (n) and a derivative gain  14   c , are calculated. An adder  902  calculates the sum of the products as the control signal u(n). These calculation processes are performed for every predetermined sampling period. 
   Note that the error difference signal e d (n) specifically means an error signal difference obtained by the immediately preceding sampling, i.e., e d (n)=e p (n)−e p (n−1). 
   As described above, the microprocessor  18 , which calculates the control signal u(n), conventionally operates at a single sampling frequency. 
   One of the factors which lowers the control band in an alignment apparatus having a digital alignment compensator is a delay time which may appear in an error difference signal due to a difference operation of error signals. As the delay time becomes longer, the control band becomes lower, and the alignment precision decreases. 
   A delay time caused by a difference operation depends on the sampling frequency at which a difference operation is performed. The delay time becomes longer with a decrease in sampling frequency. 
   The frequency characteristic of a difference operation will be described with reference to  FIG. 12 . 
     FIG. 12  shows graphs of the frequency characteristics of a difference operation at sampling frequencies of 10 kHz and 40 MHz. 
   The upper half of  FIG. 12  is a level graph showing the relationship between the sampling frequency and its frequency level while the lower half is a phase graph showing the relationship between the sampling frequency and the phase. 
   In the lower phase graph, a solid line A indicates a case of the sampling frequency of 10 kHz while a dotted line B indicates a case of the sampling frequency of 40 MHz. 
   In an ideal difference operation in which the sampling frequency is infinite, the phase remains 90° even if the frequency infinitely increases. However, as seen from the phase graph, a delay increases with a decrease in sampling frequency. The delay at the sampling frequency of 10 kHz is larger than that at the sampling frequency of 40 MHz. The phase is delayed more at the sampling frequency of 10 kHz. 
   A PID compensator outputs the sum of an error signal, error sum signal, and error difference signal as a control signal. If the error difference signal suffers a delay, the control signal output from the PID compensator suffers a delay. 
   The frequency characteristic of the PID compensator will be described with reference to  FIG. 13 . 
     FIG. 13  shows graphs of the frequency characteristics of the PID compensator at the sampling frequencies of 10 kHz and 40 MHz. 
   The upper half of  FIG. 13  is a level graph showing the relationship between the sampling frequency and its frequency level while the lower half is a phase graph showing the relationship between the sampling frequency and the phase. 
   In the lower phase graph, a solid line A indicates a case of the sampling frequency of 10 kHz, and a dotted line B indicates a case of the sampling frequency of 40 MHz. According to the phase graph, a signal output from the PID compensator is delayed more at the sampling frequency of 10 kHz. This delay decreases a phase margin. 
   The open-loop transfer characteristics when a digital alignment compensator controls, at the sampling frequencies of 10 kHz and 40 MHz, an object to be controlled two-dimensionally, i.e., in the X and Y directions (or three-dimensionally, i.e., in the X, Y, and Z directions), such as an exposure apparatus stage, will be described with reference to  FIG. 14 . 
     FIG. 14  shows graphs of the frequency characteristics of the open loop transfer function in the alignment compensator at the sampling frequencies of 10 kHz and 40 MHz. 
   The upper half of  FIG. 14  is a level graph showing the relationship between the sampling frequency and its gain level while the lower half is a phase graph showing the relationship between the sampling frequency and the phase. 
   In the lower phase graph, a solid line A indicates a case of the sampling frequency of 10 kHz, and a dotted line B indicates a case of the sampling frequency of 40 MHz. 
   As for the alignment compensator phases at sampling frequencies whose gains are below 0 [dB] (zero-crossing frequency), there is hardly any phase margin at the sampling frequency of 10 kHz, while there is a sufficient phase margin at the sampling frequency of 40 MHz. When this phase margin decreases, the control system becomes unstable, and the alignment precision decreases. To increase the control performance, the sampling frequency must be increased as much as possible. 
   Under the circumstances, in, e.g., a phase compensator for a servo circuit disclosed in Japanese Patent Laid-Open No. 06-165552, only a difference operation is performed by an analog differentiating circuit, thereby suppressing any delay time. The derivative compensation with this arrangement feeds back not the derivative value of a position error signal, but the derivative value of a position signal and does not compensate for any PID for an error in the position signal. In this arrangement, an analog circuit is used for a differential operation. A differential signal thus obtained may contain a noise component, which may decrease the alignment precision. 
   As described above, in a conventional technique, a microprocessor which calculates control signals operates at a single sampling frequency. For this reason, to increase the sampling frequency, a microprocessor with higher processing power is necessary. 
   However, a microprocessor with high processing power is expensive, and the product cost increases. 
   Additionally, only a difference operation needs to be performed at a high sampling frequency, and the sampling frequencies for other processes need not be high. 
   SUMMARY OF THE INVENTION 
   The present invention has been made to solve the above-mentioned problems, and has as its object to provide an alignment apparatus capable of increasing the alignment precision of an object to be position-controlled, an exposure apparatus having the alignment apparatus, and a device manufacturing method. 
   According to the present invention, the foregoing object is attained by providing an alignment apparatus comprising a measuring instrument which measures a position of an object to be position-controlled, and a processor which performs a plurality of types of operations on the basis of a position signal obtained from the measuring instrument and outputs an operation result as a control signal that pertains to position control of the object to be position controlled, 
   wherein the alignment apparatus performs a difference operation which calculates a difference signal of the position signal at a first sampling frequency and performs the operations other than the difference operation at a second sampling frequency lower than the first sampling frequency. 
   In a preferred embodiment, the first sampling frequency is an integral multiple of the second sampling frequency, and sampling periods of the sampling frequencies are in synchronism with each other. 
   In a preferred embodiment, the processor comprises: 
   a first processing region having a difference operation unit which performs the difference operation at the first sampling frequency; and 
   a second processing region which performs the operations other than the difference operation at the second sampling frequency. 
   In a preferred embodiment, the apparatus further comprises: 
   first A/D conversion means, connected between the first processing region and the measuring instrument, for A/D-converting the position signal at the first sampling frequency; and 
   second A/D conversion means, connected between the second processing region and the measuring instrument, for A/D-converting the position signal at the second sampling frequency. 
   In a preferred embodiment, the apparatus further comprises A/D conversion means, connected between the first processing region and the measuring instrument, for A/D-converting the position signal at the first sampling frequency, and 
   the second processing region comprises 
   first D/D conversion means for D/D-converting at the second sampling frequency the difference signal of the position signal calculated by the difference operation unit within the first processing region; and 
   second D/D conversion means for D/D-converting at the second sampling frequency a position signal converted by the A/D conversion means. 
   In a preferred embodiment, the processor comprises physically different first and second processors, 
   the first processor having a difference operation unit which performs the difference operation at the first sampling frequency, and 
   the second processor performing the operations other than the difference operation at the second sampling frequency. 
   In a preferred embodiment, the measuring instrument comprises calculation means for calculating the difference signal of the measured position signal of the object to be position-controlled. 
   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 diagram showing the arrangement of an alignment apparatus of an exposure apparatus according to the present invention; 
       FIG. 2  is a chart showing a difference signal when a sampling frequency B or a difference operation is not an integral multiple of a sampling frequency A for control operations other than difference operation; 
       FIG. 3  is a chart showing the difference signal when the sampling frequency B for a difference operation is an integral multiple of the sampling frequency A for control operations other than difference operation, and their sampling periods are shifted from each other; 
       FIG. 4  is a chart showing the difference signal when the sampling frequency B for a difference operation is an integral multiple of the sampling frequency A for control operations other than difference operation, and their sampling periods are not shifted from each other; 
       FIG. 5  is a diagram showing the arrangement of an alignment apparatus for an exposure apparatus according to the first embodiment of the present invention; 
       FIG. 6  is a diagram showing a modification of the arrangement of the alignment apparatus for the exposure apparatus according to the first embodiment of the present invention; 
       FIG. 7  is a diagram showing another modification of the arrangement of the alignment apparatus for the exposure apparatus according to the first embodiment of the present invention; 
       FIG. 8  is a diagram showing the arrangement of an alignment compensator of an exposure apparatus according to the second embodiment of the present invention; 
       FIG. 9  is a flowchart showing the flow of the whole manufacturing process of a semiconductor device; 
       FIG. 10  is a flowchart showing the detailed flow of the wafer process; 
       FIG. 11  is a diagram for explaining the control system of a conventional exposure apparatus; 
       FIG. 12  shows graphs of the frequency characteristics of a difference operation at sampling frequencies of 10 kHz and 40 MHz; 
       FIG. 13  shows graphs of the frequency characteristics of a PID compensator at sampling frequencies of 10 kHz and 40 MHz; and 
       FIG. 14  shows graphs of the frequency characteristics of the open-loop transfer function in an alignment compensator at sampling frequencies of 10 kHz and 40 MHz. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Preferred embodiments of the present invention will be described in detail in accordance with the accompanying drawings. 
   The present invention performs a difference operation for an error signal at a position where a delay time occurs at a higher frequency than that for control operations other than the difference operation, particularly, in an alignment apparatus that pertains to alignment control of a stage for an exposure apparatus. This increases a phase margin in the alignment apparatus with an alignment compensator (PID compensator) and then realizes an increase in alignment performance. 
     FIG. 1  is a diagram showing the arrangement of an alignment apparatus of an exposure apparatus according to the present invention. 
   Note that reference numerals  1  to  3 ,  1   a ,  4   a  to  4   c ,  5 ,  6   a ,  6   b , and  7   a  in  FIG. 1  correspond to reference numerals  11  to  13 ,  11   a ,  14   a  to  14   c ,  15 ,  16   a ,  16   b , and  17   a , respectively, in  FIG. 11 . Reference numerals  200  to  202  in  FIG. 1  denote adders. 
   First and second A/D converters  9   a  and  9   b  convert a position signal y(t) of the stage  1  measured by the position measurement unit  3  to digital signals y 1 (n) and y 2 (m) at sampling frequencies A [Hz] and B [Hz], respectively. First and second digital signal processing regions  8   a  and  8   b  receive the digital signals. 
   Reference symbol t denotes time; n, the sample number at the sampling frequency A; and m, the sample number at the sampling frequency B. That is, the position signal y(t) is a position signal at time t. A digital signal y(n) is a digital signal whose sample number is n, and a digital signal y(m) is a digital signal whose sample number is m. 
   In the second digital signal processing region  8   b , the difference operation unit  6   b  performs a difference operation for the position signal y 2 (m) at the sampling frequency B [Hz]. In the first digital signal processing region  8   a , a control operation (e.g., a sum operation by the sum operation unit  6   a , a gain operation, or the like) other than a difference operation is performed at the sampling frequency A [Hz]. To perform a difference operation at a sampling frequency higher than those for control operations other than a difference operation, the sampling frequency B is made sufficiently higher than the sampling frequency A. For example, the sampling frequency A is set at 10 kHz while the sampling frequency B is set at 40 MHz. 
   If the sampling frequency B cannot be made sufficiently higher than the sampling frequency A, the sampling frequency B needs to be an integral multiple of the sampling frequency A, and their sampling frequencies should not be shifted from each other (i.e., they need to be in synchronism with each other). 
   The relationship between the sampling period of the sampling frequency and the difference signal will be described with reference to  FIGS. 2 to 4 . 
   Note that each of  FIGS. 2 to 4  shows the relationship between the sampling period and the difference signal when the sampling frequency B is not sufficiently higher than the sampling frequency A. 
     FIG. 2  is a chart showing the difference signal when the sampling frequency B for a difference operation is not an integral multiple of the sampling frequency A for control operations other than a difference operation. 
     FIG. 3  is a chart showing the difference signal when the sampling frequency B for a difference operation is an integral multiple of the sampling frequency A for control operations other than a difference operation, and their sampling periods are shifted from each other. 
     FIG. 4  is a chart showing the difference signal when the sampling frequency B is an integral multiple of the sampling frequency for control operations other than a difference operation, and their sampling periods are not shifted from each other. 
   In  FIGS. 2 to 4 , the abscissa represents time ti (i=1, 2, . . . , N), while the ordinate represents the signal magnitude. Solid lines are used to represent difference signals, and dotted lines are used to represent the sampling period for control operations other than a difference operation. Each symbol • represents the value of a difference signal to be received when performing a control operation other than a difference operation. 
   In  FIG. 2 , the sampling frequency B for a difference operation is not an integral multiple of the sampling frequency A for control operations other than a difference operation. For this reason, difference signals may be held at times t 1 , t 2 , t 3 , and t 4  and may be received at times t 1  and t 3 ′. In this case, the signal received at time t 3 ′ has a value held from time t 3  and suffers a delay. This delay is undesirable. 
   In  FIG. 3 , the difference signal sampling frequency B is an integral multiple of the sampling frequency A for control operations other than a difference operation, and their sampling periods are shifted from each other. For this reason, difference signals may be held at times t 1 , t 2 , t 3 , and t 4  and may be received at times t 1 ′ and t 3 ′. In this case, the signal received at time t 1 ′ and t 3 ′ has a value held from time t 1  to t 3  and suffers a delay. This delay is undesirable. 
   In  FIG. 4 , the difference signal sampling frequency B is an integral multiple of the sampling frequency A for control operations other than a difference operation, and their sampling periods are not shifted from each other. In this case, the difference signal is held and at the same time is received as an operation target. Thus, the difference signal does not suffer a delay. 
   If the sampling frequency B is not sufficiently higher than the sampling frequency A, desirably, the sampling frequency B is an integral multiple of the sampling frequency A, and the their sampling periods are not shifted from each other. On the other hand, if the sampling frequency B is sufficiently higher than the sampling frequency A, any shift between the sampling periods produces little effect. 
   The PID compensator having the above-mentioned arrangement uses a high sampling frequency only for a difference operation. With this PID compensator, an inexpensive circuit with low processing power can output a high-precision control signal, unlike a conventional method in which all processes are performed at a high sampling frequency. In other words, when the PID compensator is used as an alignment compensator for the stage of the exposure apparatus, high-precision alignment can be realized. 
   A case will be described with reference to  FIG. 5  wherein the PID compensator of  FIG. 1  is used as the alignment apparatus for the stage of the exposure apparatus. 
   Note that the exposure apparatus comprises a light source such as an F 2  excimer laser which emits a short-wavelength laser beam as illumination light and uniformly illuminates a reticle (mask) through a proper illumination optical member. Light (exposure light) having passed through the reticle reaches, through various optical members, which constitute a projection optical system, the surface of a wafer mounted on a wafer stage. The light forms the pattern of the reticle on the wafer. 
   The wafer stage having the wafer mounted thereon is so arranged as to move three-dimensionally (in the X, Y, and Z directions). The pattern of the reticle is sequentially projected and transferred onto the wafer by repeating stepping and exposure, i.e., a so-called step and repeat method. When the present invention is applied to a scanning exposure apparatus, the exposure apparatus has almost the same arrangement. 
   A microprocessor in a main controller performs movement control, position control, and the like, for the stage having the wafer and reticle mounted thereon. These control operations are performed systematically, together with various operations such as wafer replacement, alignment operation, exposure operation, and the like. 
   First Embodiment 
     FIG. 5  is a diagram showing the arrangement of an alignment apparatus for an exposure apparatus according to the first embodiment of the present invention. 
   First and second A/D converters  29   a  and  29   b  convert a stage position signal y(t) measured by a position measurement unit  23  to digital signals y 1 (n) and y 2 (m) at sampling frequencies A [Hz] and B [Hz], respectively. A microprocessor  30  receives the digital signals. 
   In the microprocessor  30 , two processes are in action at the sampling frequencies A [Hz] and B [Hz], respectively. To perform a difference operation by a different operation unit  26   b  at a higher sampling frequency than that for other control operations (e.g., a sum operation by a sum operation unit  26   a ), the sampling frequencies are so set as to satisfy (sampling frequency B for a difference operation)&gt;(sampling frequency A for other control operations). 
   When the sampling frequency B is not sufficiently higher than the sampling frequency A, desirably, the sampling frequency B is an integral multiple of the sampling frequency A, and their sampling periods are not shifted from each other. 
   In a digital signal processing region  28  for the sampling frequency B [Hz], the digital signal y 2 (m) is converted by the difference operation unit  26   b  to a difference signal y d (m) and is passed to a first digital signal processing region for the sampling frequency A [Hz]. 
   In the first digital signal processing region for the sampling frequency A [Hz], the following processes are performed. 
   1. An adder  102  calculates an error signal e p (n) which is a difference between the digital signal y 1 (n) and a position target value generated by a position target value generator  27   a.    
   2. The sum operation unit  26   a  calculates an error sum signal e i (n) of the error signal e p (n). 
   3. A D/D converter  29   c  converts the difference signal y d (m), which is calculated in the processing region  28  for the sampling frequency B [Hz], to a difference signal y d (n) for the sampling frequency A [Hz]. 
   4. An adder  100  calculates an error difference signal e d (n), which is a difference between the digital signal y d (n) and a speed target value r d (n) generated by a speed target value generator  27   b.    
   5. The product of the error signal e p (n) and a proportional gain  24   a (P), the product of the error sum signal e i (n) and an integral gain  24   b (I), and the product of the error difference signal e d (n) and a derivative gain  24   c (D) are calculated. An adder  101  calculates the sum of the products as a control signal u(n). 
   In short, the control signal u(n) (=Pe p (n)+Ie i (n)+De d (n)) is calculated. 
   The control signal u(n) thus calculated is converted by a D/A converter  25  to a control signal u(t) and is amplified by a current amplifier  22 . With the control signal, a linear motor  21   a  drives (aligns) a stage  21 . 
   The speed target value generator  27   b  will be described now. 
   The present invention performs digital conversion of position signals and a difference operation at the higher sampling frequency B and, thus, cannot perform a difference operation for a position error signal, unlike a conventional method. For this reason, the speed target value generator  27   b , a position target value r p (n), generated by the position target value generator  27   a , is used. The position error difference signal e d (n) is calculated by subtracting the speed target value r d (n) from the position difference signal y d (n). 
   The arrangement of  FIG. 6 , which is a modification of the arrangement of  FIG. 5 , can produce the same effect as that of  FIG. 5 . 
     FIG. 6  is a diagram showing a modification of the arrangement of the alignment apparatus for the exposure apparatus according to the first embodiment of the present invention. 
   The arrangement of  FIG. 6  is different from that of  FIG. 5  in A/D and D/D converters. 
   More specifically, the arrangement of  FIG. 6  has one A/D converter  59   b  and two D/D converters, i.e., first and second D/D converters  59   a  and  59   c.    
   The A/D converter  59   b  converts the stage position signal y(t) to the digital signal y 2 (m) at the sampling frequency A [Hz]. At the same time, a difference operation unit  56   b  performs a difference operation for the position signal y(t) at the sampling frequency B [Hz]. With this operation, the difference signal y d (m) is calculated. 
   Then, the first and second D/D converters  59   a  and  59   c  are used to convert the digital signal y 2 (m) and difference signal y d (m), respectively, at the sampling frequency A [Hz], thereby obtaining a digital signal y 2 (n) and the difference signal y d (n). The subsequent control operation is performed in the same manner as that described for the arrangement of  FIG. 5 . Reference numerals for components in  FIG. 6  are different from those in  FIG. 5 . 
   More specifically, reference numerals  54   a  to  54   c ,  55 ,  56   a ,  56   b ,  57   a ,  57   b , and  500  to  502  in  FIG. 6  correspond to reference numerals  24   a  to  24   c ,  25 ,  26   a ,  26   b ,  27   a ,  27   b , and  100  to  102  in  FIG. 5 . 
   The arrangement of  FIG. 7 , which is another modification of the arrangement of  FIG. 5 , can produce the same effect as that of  FIG. 5 . 
     FIG. 7  is a diagram showing a modification of the arrangement of the alignment apparatus for the exposure apparatus according to the first embodiment of the present invention. 
   In the arrangement of  FIG. 7 , processes, which are performed by the second digital signal processing region  28  for the sampling frequency B and the first digital signal processing region for the sampling frequency A in the arrangement of  FIG. 5 , are implemented by separate microprocessors. More specifically, two microprocessors  68   a  and  68   b  are provided. A difference operation, which is performed by the second digital signal processing region  28  for the sampling frequency B in  FIG. 5 , is implemented by the microprocessor  68   b , while a process, which is performed by the first digital signal processing region for the sampling frequency A in  FIG. 5 , is implemented by the microprocessor  68   a.    
   Reference numerals  61  to  63 ,  61   a ,  64   a  to  64   c ,  65 ,  66   a ,  66   b ,  67   a ,  67   b ,  69   a ,  69   b , and  600  to  602  in  FIG. 7  correspond to reference numerals  21  to  23 ,  21   a ,  24   a  to  24   c ,  25 ,  26   a ,  26   b ,  27   a ,  27   b ,  29   a ,  29   b , and  200  to  202 , respectively, in  FIG. 5 . 
   As described above, according to the first embodiment, only a difference operation, which requires a high sampling frequency, is performed at a higher sampling frequency than the sampling frequency for control operations other than a difference operation. This makes the processing load on the microprocessor lighter and the delay time caused by a difference operation shorter, than an arrangement wherein all processes within the microprocessor are performed at a high sampling frequency to increase the precision. With this arrangement, an inexpensive alignment apparatus with high precision can be implemented. 
   Second Embodiment 
   In the first embodiment, a position difference signal or position error difference signal is calculated in the microprocessor. When the position measurement unit is arranged to input the position difference signal for the stage to the microprocessor, the microprocessor may be arranged to calculate only the position error difference signal using the position difference signal. 
   A stage for a semiconductor exposure apparatus requires an alignment precision on the order of nanometers, and its position is generally measured using a laser interferometer. A microprocessor calculates a position error difference signal using a position difference signal output from the laser interferometer. 
   A measurement board of a laser interferometer (ZMI 2004) manufactured by Zygo can output a position signal or position difference signal as a digital signal at a sampling frequency of 40 MHz. 
   The second embodiment will describe the arrangement of an alignment apparatus in an exposure apparatus having such a laser interferometer and measurement board as a position measurement unit with reference to  FIG. 8 . 
     FIG. 8  is a diagram showing the arrangement of an alignment apparatus for an exposure apparatus according to the second embodiment of the present invention. 
   Note that reference numerals  71 ,  71   a ,  72 ,  74   a  to  74   c ,  75 ,  76   a ,  77   a ,  77   b , and  700  to  702  in  FIG. 8  correspond to reference numerals  21 ,  21   a ,  22 ,  24   a  to  24   c ,  25 ,  26   a ,  27   a ,  27   b , and  200  to  202  in  FIG. 5 . 
   In  FIG. 8 , the position of the stage  71  is measured by a laser interferometer  73 . A measurement board  73   a  of the laser interferometer  73  can output a position signal y d (m) at a sampling frequency of 40 MHz and a position difference signal y d (m) having undergone a difference operation at the sampling frequency of 40 MHz. The position signal y 1 (m) and position difference signal y d (m) are input to a microprocessor  78   a.    
   The position signal y 1 (m) and position difference signal y d (m), having been processed at the sampling frequency of 40 MHz, are converted by first and second D/D converters  79   a  and  79   b  to a position signal y 1 (n) and a position difference signal y d (n) for the sampling frequency A [Hz] of the microprocessor  78   a . The signals are received by the microprocessor  78   a.    
   By performing the same control operation as described in the first embodiment, the stage  71  can be aligned at high precision. 
   Since the sampling frequency for the microprocessor  78   a  is several tens of kHz, the position difference signal y d (m) output by the measurement board  73   a  of the laser interferometer  73  is a signal processed at a sampling frequency (40 MHz) sufficiently higher than the sampling frequency for the microprocessor  78   a.    
   The arrangement in which a position difference signal output from the measurement board  73   a  of the laser interferometer  73  is used suffers shorter delay in the position difference signal than an arrangement as described in the first embodiment, in which a difference operation is performed in a microprocessor. The phase margin of the control system increases. Therefore, the position precision can be increased without an expensive microprocessor. 
   As described above, according to the second embodiment, alignment of an exposure apparatus stage can be performed at a higher precision, in addition to the effects described in the first embodiment. 
   [Application Example of an Exposure Apparatus] 
   The manufacturing process of a semiconductor device using each of the above-mentioned exposure apparatuses will be described next. 
     FIG. 9  shows the flow of the whole manufacturing process of the semiconductor device. 
   In step  1  (circuit design), a semiconductor device circuit is designed. In step  2  (mask formation), a mask having the designed circuit pattern is formed. In step  3  (wafer manufacture), a wafer is manufactured by using a material such as silicon. In step  4  (wafer process), called a preprocess, an actual circuit is formed on the wafer by lithography using the prepared mask and wafer. 
   Step  5  (assembly), called a post-process, is the step of forming a semiconductor chip by using the wafer formed in step  4 , and includes an assembly process (dicing and bonding) and a packaging process (chip encapsulation). In step  6  (inspection), the semiconductor device manufactured in step  5  undergoes inspections such as an operation confirmation test and a durability test of the semiconductor device manufactured in step  5 . After these steps, the semiconductor device is completed and shipped (step  7 ). 
     FIG. 10  shows the detailed flow of the above-mentioned wafer process. 
   In step  11  (oxidation), the wafer surface is oxidized. In step  12  (CVD), an insulating film is formed on the wafer surface. In step  13  (electrode formation), an electrode is formed on the wafer by vapor deposition. In step  14  (ion implantation), ions are implanted in the wafer. In step  15  (resist processing), a photosensitive agent is applied to the wafer. In step  16  (exposure), the circuit pattern is transferred onto the wafer using the above-mentioned exposure apparatuses. In step  17  (development), the exposed wafer is developed. In step  18  (etching), the resist is etched except for the developed resist image. In step  19  (resist removal), an unnecessary resist after etching is removed. These steps are repeated to form multiple circuit patterns on the wafer. 
   The PID compensator in each of the above-mentioned embodiments has been described by taking as an example a case wherein the PID compensator is used as the alignment compensator of a stage alignment apparatus for an exposure apparatus. The present invention is not limited to this. The present invention can be applied to a device such as a precision machine tool or precision measuring tool, which position-controls a moving member (object to be position-controlled), such as a stage. 
   The embodiments have been described. The present invention can constitute an embodiment as, e.g., a system, an apparatus, a method, a program, a storage medium, or the like. More specifically, the present invention can be applied to a system comprising a plurality of devices or an apparatus comprising a single device. 
   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.