Patent Publication Number: US-2016238636-A1

Title: Method for estimating lifetime of cathode in electron beam lithography apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority from Japanese Patent Applications No. 2015-027431, filed on Feb. 16, 2015, the entire contents of which are incorporated herein by reference. 
     FIELD OF THE INVENTION 
     Embodiments described herein relate generally to a method for estimating a lifetime of a cathode in an electron beam lithography apparatus. The embodiment relates to a method for estimating a lifetime of a cathode, for example, used for an electron beam lithography apparatus that irradiates a target object with a predetermined dose of an electron beam so as to write a pattern. 
     BACKGROUND OF THE INVENTION 
     A lithography technique leads development of miniaturization of semiconductor devices. The lithography technique is an important process that generates a pattern, such as a circuit pattern. Recently, as LSIs have been highly integrated, a circuit pattern linewidth required for the semiconductor devices has been miniaturized year by year. A high-precision original pattern (also referred to as a “reticle” or a “mask”) is required in order to form a desired circuit pattern to the semiconductor devices. A lithography technique with a charged particle beam (charged particle ray) using charged particles, such as electrons, has essentially excellent resolution. The lithography technique is used so as to manufacture high-precision original patterns. 
       FIG. 11  is a schematic view for describing operation of a variable-shaped electron beam lithography apparatus. Note that, the variable-shaped electron beam lithography apparatus is an example of charged particle beam lithography apparatuses. The variable-shaped electron beam (EB: Electron beam) lithography apparatus operates as follows: Firstly, a quadrilateral, for example, a rectangular opening  411  for forming an electron beam  330  is formed on a first aperture plate  410 . A variable-shaped opening  421  is formed on a second aperture plate  420 . The variable-shaped opening  421  forms the electron beam  330  that has passed through the opening  411 , into a desired quadrilateral shape. A deflector deflects the electron beam  330  that has been emitted from a charged particle source  430  and that has passed through the opening  411 . A target object  340  mounted on a stage is irradiated with the electron beam  330  after passing through a part of the variable-shaped opening  421 . The stage continuously moves in a predetermined direction (for example, an X direction) during writing. As described above, a quadrilateral shape that can pass through both the opening  411  and the variable-shaped opening  421 , is written in a writing region of the target object  340 . A method for forming an arbitrary shape by causing the electron beam  330  to pass through both of the opening  411  and the variable-shaped opening  421 , is referred to as a variable-shaped method. 
     It is necessary to increase current density of the beam in order to improve throughput of the electron beam lithography apparatus. It is necessary to set a cathode temperature of an electron gun assembly to a high temperature in order to achieve the large current density. However, if the cathode is set to the high temperature, since an evaporation speed of a cathode material increases, a top end shape of the cathode varies while writing. Therefore, a lifetime of the cathode can be preferably estimated in order to perform writing with high-precision. 
     SUMMARY OF THE INVENTION 
     A method for estimating a lifetime of a cathode in an electron beam lithography apparatus according to an embodiment, includes: calculating emittance of the cathode by using a lifetime reference value of the cathode; calculating an emitter lifetime diameter of the cathode by using the emittance; writing a pattern on a target object by using an electron beam emitted from the cathode; measuring emission current of the electron beam; calculating an emitter diameter by using the emission current; determining a regression formula of a change with time of the emitter diameter; and estimating the lifetime of the cathode by using the regression formula and the emitter lifetime diameter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a conceptual diagram of a configuration of a variable-shaped electron beam lithography apparatus according to the present embodiment; 
         FIG. 2  is a conceptual diagram for describing a method for adjusting current density of an electron beam according to the present embodiment; 
         FIG. 3  is a flow chart of a series of main processes of the method for adjusting current density of an electron beam according to the present embodiment; 
         FIGS. 4A and 4B  are exemplary graphical representations of current density J and a target value of emission current I e  according to the present embodiment, respectively; 
         FIG. 5  is a schematic view of the electron beam according to the present embodiment; 
         FIGS. 6A and 6B  are schematic views of an emitter according to the present embodiment; 
         FIGS. 7A to 7C  are schematic views of distributions of the electron beam on a target object according to the present embodiment; 
         FIG. 8  is a graphical representation of the relationship between emittance of a cathode and an actual measured emitter diameter according to the present embodiment; 
         FIG. 9  is a flow chart of a series of main processes of a method for estimating a lifetime of the cathode in the electron beam lithography apparatus according to the present embodiment; 
         FIG. 10  is a graphical representation of a change with time of the emitter diameter of the electron beam lithography apparatus according to the present embodiment; and 
         FIG. 11  is a schematic view for describing operation of a variable-shaped electron beam lithography apparatus in the related art. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     An embodiment of the present disclosure will be described with reference to the drawings. 
     Note that, in the following descriptions, “on a target object” represents on-a-surface of the target object, the surface being irradiated with an electron beam. 
     Embodiment 
     A method for estimating a lifetime of a cathode in an electron beam lithography apparatus according to the present embodiment, includes: calculating emittance of the cathode by using a lifetime reference value of the cathode; calculating an emitter lifetime diameter of the cathode by using the emittance; writing a pattern on a target object by using an electron beam emitted from the cathode; measuring emission current of the electron beam; calculating an emitter diameter by using the emission current; determining a regression formula of a change with time of the emitter diameter; and estimating the lifetime of the cathode by using the regression formula and the emitter lifetime diameter. 
     According to the following embodiment, a variable-shaped electron beam lithography apparatus will be described as an exemplary electron beam lithography apparatus. 
       FIG. 1  is a conceptual diagram of a configuration of the variable-shaped electron beam lithography apparatus according to the present embodiment. The variable-shaped electron beam lithography apparatus  100  includes a pattern writing mechanism  150  and a first controller  160 . The pattern writing mechanism  150  includes an electron optical column  102  and a pattern writing chamber  103 . The electron optical column  102  includes an electron gun assembly  201 , an illumination lens  202 , a first forming aperture plate  203 , a forming lens  204 , a forming deflector  205 , a second forming aperture plate  206 , an objective lens  207 , a sub-deflector  212 , a main deflector  214 , a reducing lens  216 , a blanking (BLK) deflector  218 , and a blanking (BLK) aperture plate  219  disposed therein. A beam absorbing electrode (Faraday cup  209 ) for measuring current of an electron beam  200 , is disposed on an XY stage  105 . The electron gun assembly  201  has a cathode  220  and an anode  226 . The cathode  220  has an emitter  222  and a Wehnelt electrode  224 . The anode  226  is grounded (earth fault). The XY stage  105  is disposed in the pattern writing chamber  103 . A target object  340 , such as a mask, is disposed on the XY stage  105  (refer to  FIG. 11 ). The target object is an object to be written during writing. The target object  340  includes an exposure mask used upon manufacturing of a semiconductor device. The target object  340  includes a mask blank on which nothing is written. The mask blank includes a light shielding film, such as chromium (Cr), formed on a glass substrate, and coated with resist. The electron optical column  102  is detachable, for example, from the pattern writing chamber  103 . 
     The first controller  160  has an electron gun assembly power source  230  and a pattern writing control circuit  240 . A constant current source  231  supplies a predetermined heating current to both poles of the emitter  222  inside the electron gun assembly power source  230 . A variable voltage source  234  applies a predetermined bias voltage (Wehnelt voltage) between the Wehnelt electrode  224  and an intermediate voltage between the poles of the emitter  222 . One end of a predetermined direct current power source is disposed at the intermediate voltage between the poles of the emitter  222 , in parallel with the variable voltage source  234 . The other end of the direct current power source is grounded through an ammeter  238 . A voltmeter  236  is disposed in parallel with the variable voltage source  234 . A current density measuring unit  242  and a proportional-integral-derivative (PID) controller  244  are disposed in the pattern writing control circuit  240 . The PID control is control based on the amount of correction proportional to deviation from a target value, the amount of correction acquired by integrating deviation from a previous target value, and the amount of correction acquired by differentiating time variation of the deviation from the target value. In  FIG. 1 , components necessary for describing the present embodiment, are illustrated. Needless to say, the lithography apparatus  100  includes typically necessary other components. 
     Inside the electron gun assembly power source  230 , a second controller  232  detects, by the voltmeter  236 , and performs variable control to the bias voltage (Wehnelt voltage) applied from the variable voltage source  234  so as to control to acquire emission current to be targeted. The ammeter  238  can detect a value of the emission current. 
     The electron gun assembly  201  emits the electron beam  200 . The entire first forming aperture plate  203  having a quadrilateral, for example, a rectangular hole, is illuminated, through the illumination lens  202 , by the electron beam  200  emitted from the electron gun assembly  201 . The electron beam  200  is formed so as to be quadrilateral, for example, rectangular. The forming lens  204  projects the electron beam  200  of a first aperture plate image that has passed through the first forming aperture plate  203 , on the second forming aperture plate  206 . The forming deflector  205  performs deflection control to a position of the first aperture plate image on the second forming aperture plate  206 . Therefore, a shape and dimensions of the beam can be varied. As a result, the electron beam  200  is formed. The electron beam  200  of a second aperture plate image that has passed through the second forming aperture plate  206 , is reduced through the reducing lens  216 . Then, the electron beam  200  is focused through the objective lens  207  so as to be deflected by the main deflector  214  and the sub-deflector  212 . As a result, a desired position on the target object  340  on the XY stage  105  that continuously moves is irradiated with the electron beam  200 . 
     In a case where the electron beam  200  on the target object  340  satisfies beam irradiation time Δt during which a desired dose is incident on the target object  340 , blanking is performed as follows: In order to prevent the target object  340  from being irradiated with the electron beam  200  more than necessary, for example, the electrostatic BLK deflector  218  deflects the electron beam  200  and also the BLK aperture plate  219  cuts off the electron beam  200 . Accordingly, the electron beam  200  is prevented from reaching the surface of the target object  340 . The pattern writing control circuit  240  controls a deflecting voltage of the BLK deflector  218 . A vacuum pump (not illustrated) forms vacuums inside the electron optical column  102  and inside the pattern writing chamber  103 . Thus, vacuum atmosphere in which pressure is lower than the atmospheric pressure, is provided. 
     Next, a mechanism for controlling current density J of the electron beam so as to be substantially constant during writing, and a method for controlling the current density J of the electron beam so as to be substantially constant during the writing, included in the electron beam lithography apparatus according to the present embodiment, will be described. First, while a desired pattern is written on the target object  340 , the current density J is measured a plurality of times. A target value of the emission current I e  for correcting and converging a variation of the current density J into a desired constant value, is calculated each of the plurality of times. The target value is output to the electron gun assembly power source  230 . The variable control is performed to the bias voltage in the electron gun assembly power source  230  during the writing so that the emission current I e  comes close to the target value. With this configuration, during the writing, the current density J can be maintained so as to be substantially constant. 
       FIG. 2  is a conceptual diagram for describing a method for adjusting the current density of the electron beam according to the present embodiment. In  FIG. 2 , the electron gun assembly power source  230  performs feedback control to a value of the bias voltage V B  so that the emission current I e , is set to the target value of the emission current. The electron gun assembly  201  emits the electron beam  200  of the emission current I e . The Faraday cup  209  receives the entire beam that has passed through the first forming aperture plate  203  having a constant opening size. A first forming aperture plate current value acquired from current intensity received by the Faraday cup  209 , is output to the current density measuring unit  242 . Here, beam current of the entire beam that has passed through the first forming aperture plate  203  is defined as the first forming aperture plate current. In the current density measuring unit  242 , the first forming aperture plate current value is divided by an opening area of the first forming aperture plate  203  so that the current density J is measured. The current density J is output to the PID controller  244 . The PID controller  244  calculates the target value of the emission current I e  for converging the current density J in set current density J. The target value is output to the electron gun assembly power source  230 . The electron gun assembly power source  230  performs feedback control to the bias voltage V B  so that the emission current I e  is set to the target value. The loop operation is performed a plurality of times during the writing on the target object  340 . 
       FIG. 3  is a flow chart of a series of main processes of the method for adjusting the current density of the electron beam according to the present embodiment. Firstly, an initial value of the emission current I e  is set in the second controller  232  of the electron gun assembly power source  230 . The second controller  232  performs the variable control while performing the feedback control to the value of the bias voltage V B  so that the emission current I e , comes close to the initial value to be the first target value of the emission current I e . The writing of a predetermined pattern is started on the target object  340 . During the writing, current density adjustment to be described below of the electron beam is performed a plurality of times during the writing. For example, the current density adjustment of the electron beam is performed every 10 to 30 minutes. The current density adjustment may be performed together in a beam position correction sequence periodically performed during the writing. As described above, there is no need for arranging additional time for the current density adjustment of the electron beam. Thus, degradation of throughput can be inhibited. The series of main processes of the method for adjusting the current density of the electron beam, will be described below. 
     At S (step)  102 , as a beam irradiating process, the electron gun assembly  201  emits the electron beam  200  in which the emission current I e  is set to the target value. The electron gun assembly  201  is an example of irradiation sources. 
     At S 104 , as a current density measuring process, the current density measuring unit  242  measures the current density J of the electron beam  200  every time steps illustrated in  FIG. 3  is repeated. That is, the current density J of the electron beam  200  is measured a plurality of times while the writing on the target object  340  is performed using the electron beam  200 . As described above, in the method, the Faraday cup  209  receives the entire beam that has passed through the first forming aperture plate  203  having the constant opening size. More specifically, the electron beam  200  emitted from the electron gun assembly  201  is illuminated on the first forming aperture plate  203  through the illumination lens  202 . In order to prevent an image of the first forming aperture plate  203  that has passed through the first forming aperture plate  203 , from being shielded by the second forming aperture plate  206 , the forming deflector  205  deflects the electron beam  200 . The Faraday cup  209  measures beam current of the entire beam that has passed through the second forming aperture plate  206 . Output of the Faraday cup  209  is transmitted to the current density measuring unit  242 . In the current density measuring unit  242 , the first forming aperture plate current value is divided by the opening area of the first forming aperture plate  203  so that the current density J is calculated. Measuring the first forming aperture plate current can prevent variations of the forming lens  204  and the forming deflector  205  (noises) from giving a harmful effect to current density calculating accuracy. 
     In the above example, the current density J is calculated from the entire beam that has been passed through the first forming aperture plate  203 . The present disclosure is not limited to this. For example, the first forming aperture plate  203  and the second forming aperture plate  206  form a beam, for example, having an area of 1 square μm. Then, the Faraday cup  209  may measure the beam that has been formed. The current density J can be acquired by dividing a beam current value by the area that has been formed. As described above, determining the area to be formed in advance can measure the current density J. 
     At S 106 , as a target emission current calculating process, every time the current density J of the electron beam  200  is measured, the PID controller  244  calculates the target value of the emission current I e  that varies depending on the current density J of the electron beam  200  that has been measured, so that the current density J of the electron beam  200  becomes substantially constant. Every time the calculation is performed, the target value of the emission current I e  is output to the second controller  232 . The PID controller  244  uses a PID method and calculates the target value of the emission current I e  so that the current density J converges in a constant value. 
       FIGS. 4A and 4B  are graphical representations of examples of the current density J and the target value of the emission current I e  according to the present embodiment, respectively.  FIG. 4A  illustrates that the current density J converges as time passes. In order to achieve the convergence illustrated in  FIG. 4A , the PID controller  244  uses the PID method so as to calculate the target value of the emission current I e  illustrated in  FIG. 4B . 
     At S 108 , as a target emission current setting process, the second controller  232  inputs the target value of the emission current I e  so as to reset instead of a value that has been set. 
     At S 110 , as a bias voltage variable control process, the second controller  232  controls the electron gun assembly  201  based on the new target value of the emission current I e . 
     At S 112 , as a determining process, it is determined whether the writing has been completed. In a case where the writing is still performed, the processing goes back to S 102 . As described above, for example, every 10 to 30 minutes, the series of processes from S 102  to S 112  is repeated. Accordingly, while the writing is performed on the target object  340  by using the electron beam  200 , the current density J of the electron beam  200  is measured a plurality of times. Every time the measurement is performed, the target value of the emission current I e  is varied. When the writing is completed, the processing is completed. Otherwise, the above current density adjustment is preferably periodically performed for writing on a next target object  340  even when the writing is not performed. Accordingly, the current density J can be continuously kept substantially constant. 
     In the above example, a configuration in which the PID controller  244  calculates the target value of the emission current I e  so that the current density J of the electron beam  200  becomes substantially constant, has been given. The present disclosure is not limited to this. For example, a target value of the bias voltage V B  is preferably calculated so as to be output. In this case, there may be provided a configuration in which output of the variable voltage source  234  is varied so as to be equal to the target value of the bias voltage V B  input by the second controller  232 . 
     Next, a method for estimating a lifetime of the cathode in the electron beam lithography apparatus according to the present embodiment, will be described.  FIG. 5  is a schematic view of the electron beam according to the present embodiment. The electron beam  200  emitted from the emitter  222  of the cathode  220  forms, on a crossover surface  344 , a state called a crossover due to a lens field formed by the negative pole (cathode  220 ), the Wehnelt electrode  224 , and the positive pole (anode  226 ). After that, the electron beam  200  spreads and is refracted through a collimator lens (illumination lens)  228  so as to be perpendicular to or substantially perpendicular to a target object surface  342 . Then, the target object  340  is irradiated with the electron beam  200 . 
       FIGS. 6A and 6B  are schematic views of the emitter according to the present embodiment. The emitter  222  has lanthanum hexaboride  2  and carbon  4  disposed around the lanthanum hexaboride  2 . The lanthanum hexaboride  2  has an emitter surface  6 . The electron beam  200  described above is emitted from the emitter surface  6 . A diameter d of the emitter surface  6  is referred to as an emitter diameter. For example, an emitter diameter acquired by observation of the emitter surface  6  using a microscope, such as an optical microscope, is referred to as an actual measured emitter diameter. Note that, in a case where a shape of the emitter surface  6  is elliptical, the shorter diameter and the longer diameter of the emitter surface  6  are measured. Then, an average between the shorter diameter and the longer diameter, is preferably calculated and acquired. 
     Note that, according to the embodiment of the present disclosure, materials can be used other than lanthanum hexaboride (LaB 6 ) as a material included in the emitter  222 . The material included in the emitter  222  is required to have high electric conduction, mechanical strength and chemical stability at a high temperature. A material having a high melting point can achieve the mechanical strength and the chemical stability at the high temperature. Note that, more specifically, the high melting point is defined as a high melting point higher than an operating temperature of the electron beam lithography apparatus. Materials that satisfy the above properties and that have a low work function similar to that of lanthanum hexaboride (LaB 6 ), include metal hexaboride, such as cerium hexaboride (CeB 6 ), gadolinium hexaboride (GdB 6 ), and yttrium hexaboride (YB 6 ). For example, tungsten (W) can be also used as a material included in the emitter  222 . Since tungsten (W) has a melting point higher than those of lanthanum hexaboride (LaB 6 ) and cerium hexaboride (CeB 6 ), for example, tungsten (W) can be used at, for example, a temperature of 2000 K. 
       FIGS. 7A to 7C  are schematic views of distributions of the electron beam  200  on the target object  340  according to the present embodiment.  FIG. 7A  is the schematic view of the distribution in a direction of a radius R of the electron beam  200 .  FIG. 7B  is the schematic view of the distribution in a direction of an angle A of the electron beam  200 . The angle is defined as a beam angle of the electron beam  200  with respect to an optical axis after the crossover described above. The distributions of the electron beam  200  illustrated in  FIGS. 7A and 7B  according to the present embodiment are Gaussian distributions.  FIG. 7C  is the schematic view of a shot  264  formed, by the electron beam  200 , on the target object  340 . A shape of the shot  264  illustrated in  FIG. 7C  includes a quadrilateral, such as a rectangle, having the long side (first side) with a length of W n  and the short side (second side) with a length of H n . A position of an electron beam center  262  can be the center of gravity of the shot  264 . For example, in a case where the shot  264  is rectangular, the position of an electron beam center  262  can be the center of the rectangle. An electron beam edge  260  is defined in advance as an edge of the shot  264  having the longest distance from the electron beam center  262 . Note that, in a case where W n =H n  is satisfied, the shape of the shot  264  is square. 
     As the cathode  220  is used, since a part of the material included in the cathode  220  evaporates, the diameter of the emitter surface  6  (refer to  FIGS. 6A and 6B ) decreases. Thus, uniformity of the beam degrades. Here, in a case where the uniformity of the beam is defined as n, if a distance between the electron beam center  262  and the electron beam edge  260  is defined as R n , n can be calculated by the following expression (1) using current density J (R n ) of the electron beam edge  260  and current density J (0) of the electron beam center  262 . 
         n=J ( R   n )/ J (0)   (1)
 
     The uniformity n of the beam is an example of a lifetime reference value of the cathode  220 . If the uniformity n of the beam falls below a certain reference value, the cathode  220  is defined so as to be the end of lifetime thereof. For example, n is preferably in a range between 0.95 and 0.99. In the following descriptions, n is defined as 0.98. 
     In a case where the distribution of the electron beam  200  is a Gaussian distribution, and in a case where R is defined as a distance from the electron beam center  262  on the target object  340  and J 0  is defined as a constant, current density J(R) of the electron beam  200  can be expressed by the following expression. 
         J ( R )= J   0 exp(− R   2   /R   e   2 )   (2)
 
     Here, R e  is defined as a radius of the electron beam  200  with which the number of electrons per unit time becomes the number of electrons per unit time at the electron beam center  262  in the electron beam  200 , multiplied by 1/e (e is defined as the base of a natural logarithm) on the target object  340  as illustrated in  FIG. 7A . The uniformity n of the beam can be expressed by the following expression (3) with expression (1) and expression (2). As the cathode  220  is used, the diameter of the emitter surface  6  (refer to  FIGS. 6A and 6B ) decreases and R e  also decreases. Accordingly, n decreases by the following expression. 
         n =exp(− R   n   2   /R   e   2 )   (3)
 
     In a case where the shape of the shot  264  is rectangular illustrated in  FIG. 7C , R n  is expressed by the following expression (4) with W n  and H n . 
         R   n =1/2( W   n   2   +H   n   2 ) 0.5    (4)
 
     Thus, R e  is expressed by the following expression (5) with expression (3) and expression (4). 
     
       
         
           
             
               
                 
                   
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                             W 
                             n 
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                             H 
                             n 
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     Next, emittance of the cathode  220  will be described. The emittance of the cathode  220  is defined as an amount of a spread of the electron beam  200  emitted from the cathode  220 . Here, a diameter of a guide of the spread of the electron beam  200  is expressed as 2R e  using the above R e . Here, A e  is defined as an angle at which the number of electrons per unit time becomes the number of electrons per unit time at the electron beam center in the electron beam  200  (A=0) 262  multiplied by 1/e (e is defined as the base of a natural logarithm) on the target object  340  as illustrated in  FIG. 7B . In this case, a guide of the spread in an angle direction of the electron beam  200  is expressed as 2A e  by the sum of a spread in a positive angle direction and a spread in a negative angle direction. The emittance of the cathode  220  is defined as the product of 2R e  and 2A e  by the following expression. 
       Emittance=4R e A e    (6)
 
     The emittance is expressed by the following expression (7) with expression (5) and expression (6). 
     
       
         
           
             
               
                 
                   Emittance 
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     In a case where the shape of the shot  264  is square, namely, W n =H n  is satisfied, the emittance is expressed by the following expression (8). 
     
       
         
           
             
               
                 
                   Emittance 
                   = 
                   
                     
                       2.82 
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                         W 
                         n 
                       
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       FIG. 8  is a graphical representation of the relationship between the emittance of the cathode  220  and the actual measured emitter diameter according to the present embodiment. Here, the emittance illustrated in  FIG. 8  is an actual measured value. As illustrated in  FIG. 8 , an excellent correlation between the emittance and the actual measured emitter diameter, is observed. Therefore, an emitter lifetime diameter as the lifetime of the cathode  220  can be acquired from the uniformity n of the beam as the lifetime of the cathode  220 . According to the present embodiment, the emittance is 64 μm mrad when n=0.98 is satisfied. Therefore, it is estimated that the emitter lifetime diameter is 33 μm. When once a change with time of the emitter diameter can be measured, the lifetime of the cathode  220  can be estimated. Note that, as the emittance, a value may be used based on a value acquired by each of expression (6), expression (7), and expression (8), such as a constant multiplication of each of expression (6), expression (7), and expression (8). 
       FIG. 9  is a flow chart of a series of main processes of the method for estimating the lifetime of the cathode in the electron beam lithography apparatus according to the present embodiment. The method for estimating the lifetime of the cathode in the electron beam lithography apparatus according to the present embodiment, performs the series of processes including a beam uniformity determining process (S 202 ), an emittance calculating process (S 204 ), an emitter lifetime diameter calculating process (S 206 ), a writing process (S 208 ), an emission current measuring process (S 210 ), an emitter diameter calculating process (S 212 ), a change-with-time regression formula determining process (S 214 ), and a lifetime estimating process (S 216 ). 
     First, the first controller  160  or an operator determines the uniformity n of the electron beam  200  at the beam uniformity determining process (S 202 ). For example, a data storage unit  254  stores the uniformity n of the beam, the uniformity n having been determined. 
     Next, at the emittance calculating process (S 204 ), the operator or the first controller  160  uses a first calculator  246  so as to calculate the emittance of the cathode by, for example, expression (6), expression (7), or expression (8), using n that has been determined at the beam uniformity determining process (S 202 ). Here, for example, then that has been stored in the data storage unit  254 , can be used as the uniformity n of the beam. 
     Next, at the emitter lifetime diameter calculating process (S 206 ), the operator or the first controller  160  uses a second calculator  248  so as to calculate an emitter lifetime diameter of the cathode  220  by, for example, using the relationship illustrated in  FIG. 8 , with the emittance calculated at the emittance calculating process (S 204 ). 
     Next, at the writing process (S 208 ), the first controller  160  writes a pattern on the target object  340  using the electron beam  200  emitted from the cathode  220 . 
     Next, at the emission current measuring process (S 210 ), the operator or the first controller  160  uses the ammeter  238  so as to measure emission current I e  of the electron beam  200 . 
     Next, at the emitter diameter calculating process (S 212 ), the operator or the first controller  160  uses a third calculator  250  so as to calculate an emitter diameter d with the emission current I e  measured at the emission current measuring process (S 210 ). In the electron beam lithography apparatus according to the present embodiment, current density J can be controlled to be constant. In this case, a relationship between the emission current I e , the current density J, and the emitter diameter d, can be expressed by the following expression (9). Therefore, the emitter diameter d can be calculated. 
     
       
         
           
             
               
                 
                   
                     J 
                     × 
                     
                       
                         π 
                          
                         
                           ( 
                           
                             d 
                              
                             
                               / 
                             
                              
                             2 
                           
                           ) 
                         
                       
                       2 
                     
                   
                   = 
                   
                     I 
                     e 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Next, at the change-with-time regression formula determining process (S 214 ), the operator or the first controller  160  uses a processing unit  256  and, for example, plots a change with time of the emitter diameter d calculated at the emitter diameter calculating process (S 212 ). Then, a regression formula of the change with time is determined. 
     Next, at the lifetime estimating process (S 216 ), the operator or the first controller  160  uses a fourth calculator  252  so as to estimate the lifetime of the cathode  220  using the regression formula acquired at the change-with-time regression formula determining process (S 214 ) and the emitter lifetime diameter calculated at the emitter lifetime diameter calculating process (S 206 ). 
       FIG. 10  is a graphical representation of the change with time of the emitter diameter d of the electron beam lithography apparatus according to the present embodiment. The graphical representation illustrated in  FIG. 10  is acquired, for example, at the change-with-time regression formula determining process (S 214 ). In  FIG. 10 , the regression formula of the change with time of the emitter diameter d is, for example, a linear expression, the regression formula being acquired at the change-with-time regression formula determining process (S 214 ). In  FIG. 10 , the number of days during which the emitter diameter d becomes 33 μm, is estimated to be 260 days or 290 days in accordance with a range of days during which the emitter diameter has been measured. Note that the regression formula is not limited to a linear expression. 
     Upon operation of the electron beam lithography apparatus, estimating the lifetime of the cathode is preferable for maintenance of the electron beam lithography apparatus, including replacement of the cathode. The method for estimating the lifetime of the cathode in the electron beam lithography apparatus according to the present embodiment, can quantitatively estimate the lifetime of the cathode. In particular, as illustrated in  FIG. 10 , the change with time of the emitter diameter d is well expressed by the regression formula of a linear expression. Therefore, the lifetime can be simply estimated with high precision. As in  FIG. 8 , it is thought that an excellent linear relationship between the emittance and the emitter diameter d causes the above estimation to be possible. 
     The method for estimating the lifetime of the cathode in the electron beam lithography apparatus according to the present embodiment, can provides a method for estimating a lifetime of a cathode of an electron beam lithography apparatus, capable of performing quantitative estimation. 
     In the above descriptions, pieces of processing of functions of the first controller  160 , the second controller  232 , the current density measuring unit  242 , the PID controller  244 , the first calculator  246 , the second calculator  248 , the third calculator  250 , the fourth calculator  252 , and the processing unit  256 , may be performed by software in a control calculator including a computer. Hardware of an electrical circuit may perform the pieces of processing of functions. A combination of the hardware of an electrical circuit and the software may perform the pieces of processing of functions. A combination of the hardware and firmware may be used. With a configuration of the software, a program is stored in a recording medium (not illustrated), such as a magnetic disk drive, a magnetic tape drive, a FD, or a read only memory (ROM). In that case, the control calculator may be coupled, via a bus, to a random access memory (RAM), the ROM, the magnetic disk (HD) drive, as an example of a data storage device (data storage unit), a keyboard (K/B), a mouse, as an example of an input unit, a monitor, a printer, as an example of an output unit, an external interface (I/F), a FD, a DVD, or a CD, as an example of an input-and-output unit. 
     According to the embodiment, parts, such as configurations, that are not directly necessary for describing the present disclosure, have been omitted. For example, a necessary configuration can be appropriately selected and used. With an element according to the present disclosure, a method for estimating a lifetime of a cathode in an electron beam lithography apparatus, appropriately changed and designed by a person skilled in the art, is included in the scope of the present disclosure. The scope of the present disclosure is defined by the scope of the claims and the scope of equivalents of the claims.