JP2006351622A - Magnetic shield analysis method, magnetic shield analysis program and design method of charged particle beam exposure apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an analysis method of magnetic shield, with which a high-accuracy solution can be acquired at high speed, by considering time variations of the excitation condition and the movement of an object. <P>SOLUTION: The method has an analysis routine, formed of a first step for setting a magnetic field state of sub-regions obtained by dividing an analysis object into a plurality of regions, a second step for acquiring a boundary condition by using an integral equation from the magnetic field state, and a third step for acquiring the magnetic field state in the sub-regions by a finite element method by using the boundary condition. The analysis routine is repeated and the magnetic shield is analyzed, while temporal variation of the condition is given from initial time (t=0), and time is made to elapse by each prescribed time step. The first to third steps are performed again, by considering the influence of eddy current so as to acquire the magnetic field state in the sub-regions. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a charged particle beam exposure apparatus used for lithography in a manufacturing process of a semiconductor device, in order to keep the magnetic field in the optical path of the charged particle beam exposure apparatus in a target state with respect to an external magnetic field or a magnetic field flowing through the outer casing of a lens barrel. The present invention relates to a magnetic shield analysis method, a magnetic shield analysis program, and a charged particle beam exposure apparatus design method using the analysis method.

  The operating wavelength of the semiconductor reduced projection exposure apparatus tends to become shorter year by year as the density of semiconductor elements increases and the target line width decreases. The wavelength of the light used shifts from the i-line (wavelength 365.015 nm) of a mercury lamp to a KrF excimer laser (wavelength 248 nm), and a reduction projection exposure apparatus using an ArF excimer laser (wavelength 193 nm) as a light source has entered the stage of practical application. Yes. However, in recent years, the demand for pattern miniaturization has further increased, and in addition to the use of light having a shorter wavelength such as an F2 excimer laser (wavelength 157 nm), a circuit pattern using a charged particle beam (electron beam) is used. A method for drawing a film on a wafer has been studied as an effective means for next-generation semiconductor lithography.

  In the case of a reduction projection exposure apparatus using charged particle beams, the optical characteristics of the electron optical system may be affected by the external magnetic field or the variable magnetic field of the elements constituting the apparatus and may deteriorate. A computer-based magnetic field analysis program is used for designing and taking measures against magnetic field effects. In this magnetic field analysis, a linear equation was created based on Maxwell's equations, basic equations representing electromagnetic phenomena, Coulomb's law and Bio-Savart's law, and the target space was modeled for analysis. This analysis method is roughly divided into those using a finite element method and an integral equation method.

  Further, a method as described in Patent Document 1 having both the advantages of the finite element method and the integral equation method has been proposed. This method divides the object of analysis into multiple sub-regions and calculates the strength of the magnetic field between each sub-region by calculating each sub-region using the finite element method while maintaining the correlation between each sub-region using the integral equation method. Regardless, it is a technique that can calculate each with an accuracy corresponding to its strength and enables modeling with higher shape accuracy, and can calculate the influence of the static magnetic field of the elements constituting the outside or the apparatus.

  In the method in Patent Document 1, the influence due to the static magnetic field can be calculated, but the calculation of the influence due to the variable magnetic field of the elements constituting the outside or the apparatus is not taken into consideration. The main factors in the calculation of the varying magnetic field can be broadly divided into temporal variations in excitation conditions and movement of objects such as excitation sources, conductors, and magnetic bodies. In the charged particle beam exposure apparatus, for example, the temporal variation of the excitation condition includes a change in the amount of energization to the coil in the apparatus, a change with time in the environmental magnetic field of the building including the geomagnetism, and the like. Examples of the movement of the object include the movement of the stage in the apparatus and the influence of conveyance in the surrounding environment.

  In the unsteady magnetic field phenomenon, an eddy current is generated on the surface of the conductor so as to prevent the fluctuation of the magnetic field due to the relative displacement in the state of the magnetic field with the passage of time and the conductivity according to the physical properties. The effect of the generated magnetic field will appear. The depth of the surface where eddy currents are generated is called the skin depth.

  Aside from the case where the object does not contain a conductor, not only the excitation conditions vary, but also the movement of the object, the movement of the excitation source and the magnetic body, the partial magnetic field in the spatial distribution due to the change of the magnetic circuit. An increase / decrease occurs, and eddy current is unavoidably generated in a conductor unless it moves within a uniform magnetic field, and dynamic magnetic field analysis is necessary.

  In the method of dynamic magnetic field analysis, it is the integral equation method that can easily move an object without the need for a spatial mesh, but for dynamic magnetic field analysis, the finite element method is also from the viewpoint of shape accuracy. It is generally considered suitable. In addition, when moving an object, a method is employed in which the element is crushed so as not to be crushed, or the space mesh is re-meshed with the movement of the object.

  The calculation at this time is generally difficult to converge because a nonlinear component called eddy current is added to the convergence calculation of the static magnetic field analysis in one time step. In addition, since unsteady calculation is performed for the time step, the analysis time is taken as many times as the number of time steps. The analysis data is added to the previous analysis data + current analysis data used for the convergence calculation, and the time step. Requires analysis data from the previous time. Moreover, if it is assumed that all points are calculated, the analysis result will be output that is times the number of time steps.

JP 2004-79603 A

  Conventionally, analysis has been performed using the method described above. However, when using the finite element method, it is necessary to make the element thickness on the surface side smaller than the skin depth in order to ensure accuracy. Analysis, the scale of the analysis model increases, model creation time, analysis time, etc. increase and the required analysis environment must be augmented, leading to problems in terms of delivery time and cost. There was a problem that an analysis result could not be obtained and a device with sufficient performance could not be developed.

  In addition, when the object moves, since the eddy current is calculated from the difference of the magnetic field state between the remeshing time and the old and new meshes, there is an error due to data processing such as mapping, etc. This was a factor in the deterioration of accuracy. In particular, it is very difficult to perform analysis in the design of a shield that depends on the shape of a large-scale apparatus having a complicated configuration such as a charged particle beam exposure apparatus and having many elements having different magnetic field strengths.

  The present invention has been made in view of such a problem. In a shield design of a large-sized apparatus in which a complicated shape is accurately analyzed as a model and a large number of elements having different magnetic field strengths exist, temporal fluctuations of excitation conditions and A magnetic shield analysis method, a magnetic shield analysis program, and a design method for a charged particle beam exposure apparatus using this analysis method, which can obtain a high-accuracy solution at high speed while taking into account unsteady phenomena such as object movement The purpose is to provide.

  In order to solve the above problem, the magnetic shield analysis method according to the present invention divides a region to be analyzed into a plurality of sub-regions and sets the magnetic field state of these sub-regions, and the magnetic field obtained in the first step. The second step of obtaining the boundary condition of the magnetic field in the sub-region in consideration of the correlation between the sub-regions by solving using the integral equation from the state, and the boundary condition obtained in the second step for each sub-region It has an analysis routine consisting of a third step for determining the state of the magnetic field in the sub-region by the finite element method, and the time elapses by a predetermined time step while giving temporal condition fluctuations from the initial time (t = 0) The magnetic shield analysis is performed by repeatedly performing this analysis routine. Further, in the analysis routine at the initial time, the initial state of the magnetic field in the sub-region is input in the first first step, the second and third steps are performed, and then the magnetic field state obtained in the immediately preceding third step. Is set in the next first step, and the second and third steps are performed. In the analysis routine after the second time step, the state of the magnetic field obtained in the immediately preceding third step is set in the next first step. Then, the second and third steps are performed, and based on the difference between the magnetic field state calculated in the analysis routine at the previous time step and the magnetic field state calculated by performing the first to third steps at the current time step. The eddy current is calculated, and the first to third steps are performed again in consideration of the influence of the eddy current calculated in this way to determine the state of the magnetic field in the sub-region. That.

  Each analysis routine is configured to repeat the first to third steps until it is determined that the state of the magnetic field in the sub-region has converged. At this time, in the analysis routine, it is preferable that the analysis of the remaining sub-regions is continued while the analysis of the sub-regions determined to have converged is stopped.

  It should be noted that the temporal condition fluctuation factors include the temporal fluctuation of the excitation condition, the movement of the object located in the sub-region, and the like, and it is preferable to be able to cope with these. At this time, it is preferable to move the object by moving the sub-region.

  It is desirable to be able to select a technique for obtaining the magnetic field state of the sub-region in the first step, and it is desirable to be able to select a matrix calculation technique for solving the partial differential equation in this technique technique.

  It is desirable that a static magnetic field analysis module that does not calculate eddy currents can be selected depending on the presence or absence of a conductor in the sub-region. It is desirable that the sub-region includes an area including only the coil element, and the RSP method is employed when calculating the influence of the area including only the coil element.

  In the second step, it is preferable that the boundary condition of the magnetic field in the sub-region is obtained by using an integral equation derived by Coulomb and Bio-Saval laws.

  On the other hand, the magnetic shield analysis program according to the present invention causes the computer to execute the steps of the magnetic shield analysis method described above.

  The charged particle beam exposure apparatus design method according to the present invention is sensitive to a charged particle source, an illumination optical system that irradiates the reticle with an electron beam emitted from the charged particle source, and an image of the electron beam that has passed through the reticle. The above-described magnetic shield analysis method is applied to a charged particle beam exposure apparatus comprising an imaging optical system that forms an image on a substrate and a magnetic shield means that blocks the influence of an external magnetic field. The magnetic shield means is designed.

  The charged particle beam exposure apparatus includes a vacuum chamber including a first sub-region intended for an electron optical column provided with a charged particle source, a sensitive substrate, and a stage on which the sensitive substrate is placed. Excitation conditions are divided into a second sub-region targeted, a third sub-region targeted for a reticle loader for exchanging reticles, and a fourth sub-region targeted for a wafer loader for exchanging sensitive substrates. It can be configured to perform analysis for fluctuations in At this time, with respect to the movement of the object in the sub-region, it is preferable that the region of the object moving in each sub-region is divided and the divided regions are moved and analyzed.

  According to the present invention, it is possible to accurately analyze a complex shape by analyzing by a finite element method, and to analyze by dividing an analysis region into sub-regions by using an integral equation method together. In a magnetic shield design of a large device with many elements with different magnetic field strengths, a magnetic shield that can obtain a highly accurate solution at high speed, taking into account the effects of eddy currents due to object movement as well as excitation fluctuations Analytical techniques can be provided. In addition, a program using this analysis method can quickly respond to the design process of such a large device and obtain a high-accuracy solution. In addition, since the calculation speed is improved, the delivery time can be shortened and the cost can be reduced.

Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings. FIG. 1 shows an example of a charged particle beam exposure apparatus. This apparatus displays an electron beam (charged particle beam) pattern obtained by irradiating an electron beam emitted from an electron gun onto a circuit pattern formed on a reticle. This is an apparatus that transfers an image by reducing projection onto a semiconductor wafer using an electron lens (using the action of a magnetic field). First, the configuration of the electron optical system of the charged particle beam exposure apparatus will be described with reference to FIG.

  An electron gun 12 is disposed at the uppermost stream of the charged particle beam exposure apparatus 11. The electron gun 12 emits an electron beam downward. A condenser lens 13 and an illumination lens 14 are provided below the electron gun 12, and the electron beam IB emitted from the electron gun 12 is The reticle 15 is illuminated through these lenses 13 and 14. Although not shown, an illumination beam shaping aperture, a blanking deflector, a blanking aperture, an illumination beam deflector, etc. are disposed in the illumination optical system having the condenser lens 13 and the illumination lens 14 as main components. Has been. The illumination beam (electron beam IB) shaped in the illumination optical system is sequentially scanned on the reticle 15 to illuminate each subfield of the reticle 15 in the field of view of the illumination optical system. The reticle 15 has a large number of subfields and is placed on a movable reticle stage 16. By moving the reticle stage 16 in a plane perpendicular to the optical axis, each subfield on the reticle 15 extending over a wider range than the field of view of the illumination optical system is illuminated.

  Below the reticle 15, an imaging optical system including a first projection lens 17, a second projection lens 18, and a deflector 19 (comprising 19-1 to 19-6) used for aberration correction and image position adjustment. A system is provided. The electron beam IB that has passed through one subfield of the reticle 15 forms an image at a predetermined position on the wafer (sensitive substrate) 20 by the first and second projection lenses 17 and 18 and the deflector 19. An appropriate resist is applied on the wafer 20. The dose of the electron beam IB is given on the resist, the pattern on the reticle 15 is reduced (for example, reduced and projected to ¼), imaged and projected onto the wafer 20 and transferred.

  A crossover C.D. O. This crossover C.I. O. A contrast opening 21 is provided at the position. The contrast opening 21 blocks the electron beam IB scattered by the non-patterned portion of the reticle 15 from reaching the wafer 20.

  The wafer 20 is mounted on a wafer stage 22 that can move in a plane perpendicular to the optical axis of the imaging optical system via an electrostatic chuck. By synchronously operating the reticle stage 16 and the wafer stage 22 in opposite directions, each part of the device pattern extending on the reticle 15 beyond the field of the projection optical system can be sequentially exposed.

  As described above, since the charged particle beam exposure apparatus 11 uses an electron beam, exposure performance may be deteriorated by being influenced by a static magnetic field or a fluctuating magnetic field of an external element or an element constituting the apparatus. Therefore, countermeasures are being taken. A configuration of a magnetic shield of a charged particle beam exposure apparatus as an example will be described.

  FIG. 2 is a schematic view showing the entire charged particle beam exposure apparatus 11 described above, and is composed of an electron optical column 23 and a vacuum chamber 24. The electron optical barrel 23 is provided with the above-described electron gun 12, reticle 15 and the like, and the vacuum chamber 24 is provided with the wafer 20 placed on the wafer stage 22. The electron optical column 23 and the vacuum chamber 24 are provided with vacuum pipes 25a and 25b, respectively. From there, the reticle 15 and the wafer 20 can be exchanged using the reticle loader 26 and the wafer loader 27. Is possible.

  Furthermore, an active vibration isolation leg 29 (consisting of 29a and 29b) for controlling the vibration of the entire apparatus is provided. A voice coil motor is built in the active vibration isolation leg 29 (29a, 29b), and the coil 29c, 29d constituting the voice vibration motor is energized to perform vibration isolation by the generated thrust.

  The electron optical column 23 and the vacuum chamber 24 are covered with a magnetic shield 28 made of a material having a high initial permeability such as permalloy, and the electron optical column 23 and the vacuum chamber 24 are relatively covered. By forming with soft iron or the like having a high magnetic permeability, the influence of the magnetic field of the elements constituting the outside or the apparatus is blocked.

  A coil capable of generating a magnetic field in an arbitrary direction is provided at a distance from the electron optical column 23 and the vacuum chamber 24, and charging is performed using an active canceller capable of canceling an external magnetic field by the magnetic field generated by the coil. There is also a method of removing an external magnetic field such as a static magnetic field and a variable magnetic field that affects the particle beam exposure apparatus 11.

  The charged particle beam exposure apparatus as described above has a mixture of members having large shapes (on the order of meters m) to members having a small shape (on the order of millimeters mm), and the magnetic shield must be designed using a computer. is there. The magnetic shield analysis method according to the present invention will be described below.

  Electromagnetic field modeling for magnetic shield analysis is expressed by the following equation. First, the electromagnetic field is expressed by Maxwell's electromagnetic equations expressed by the following equations (1) to (4).

  In addition, among B, H, D, E, and J, there exists the relationship of the basic equation showing the electromagnetic phenomenon shown by following Formula (5)-(8).

  Further, the linear equation represented by the equation (11) is derived from the Coulomb's law represented by the equation (9) and the Bio-Savart's law represented by the equation (10).

  A magnetic shield analysis method and a program to which the magnetic shield analysis method according to this embodiment is applied will be described with reference to FIG. In the following description, it is assumed that the sub-region of the charged particle beam exposure apparatus to be analyzed is divided into n.

  First, in step 0-t, an initial state at the start time step t0 of the magnetic field to be analyzed is obtained. In the initial state, the influence of other sub-regions is not considered, and the natural boundary condition (condition that the magnetic flux is parallel to the boundary surface) closed for each sub-region is finite using Maxwell's equations (1) to (4). The state of the magnetic field is obtained by the element method, and the boundary condition of each sub-region is obtained by the integral equation method using the linear equation (11) obtained from the result of Coulomb's law and Bio-Savart's law.

  Next, in the step 1-t (1-t-1, 1-t-2,... 1-tn) (where t = t0), each sub-region is divided into its sub-regions. The state of the magnetic field in the region is analyzed by the finite element method using Maxwell's equations (1) to (4). At this time, as the boundary condition, the boundary condition obtained from the initial state obtained at step 0-t (where t = t0) is used. In step 2-t (where t = t0), the magnetic field state obtained in step 0-t (where t = t0) and the magnetic field state obtained in step 1-t (where t = t0) are determined. The convergence is determined by comparison, and if it has converged (if the difference between the magnetic field states obtained in step 0-t and step 1-t is less than or equal to a predetermined threshold value), the calculation is terminated, and step The state of the magnetic field obtained by 1-t (where t = t0) is set as the state of the magnetic field at time t0 of the region to be analyzed, and the process proceeds to the next time step (analysis routine).

  If it is determined in step 2-t (where t = t0) that the magnetic field state of each sub-region has not converged, the process proceeds to step 3-t (where t = t0), and step 1-t ( However, the boundary condition of each sub-region is obtained by the integral equation method using the linear equation (11) obtained from the result of t = t0) and Coulomb's law and Bio-Savart's law. (However, t = t0) is applied and analyzed, and the result is subjected to convergence determination at step 2-t (where t = t0), and the above steps 1-t to until the state of the magnetic field of each sub-region converges. The process of 3-t (however, t = t0) is repeated.

  If the magnetic field state at time t0 can be calculated as described above, the analysis routine at time t0 (initial time) is completed, and the calculation in the analysis routine at the next time step shown in FIG. Move. In the case of dynamic magnetic field analysis, eddy current calculation is performed simultaneously using the relative displacement of the magnetic field between time steps and the time interval, so the next step magnetic field state result and time interval are retained as analysis data. , The time fluctuation component is changed, and steps 1-t, 2-t, 3-t (where t = t1) are repeated to calculate the state of the magnetic field at time t1. . In the same manner, the analysis routine, that is, the repetition steps 1-t, 2-t, and 3-t are repeatedly calculated until the predetermined time t = tn, as many times as the assumed time steps.

  In this example, since iterative calculation with convergence calculation requires a lot of analysis time, the calculation in the area where no conductor exists or the influence of eddy current can be ignored is the static calculation that does not calculate eddy current. By calculating with the magnetic field module, the number of unknowns is reduced and the calculation time is increased. Specifically, as shown in FIG. 5, a non-conductor flag is set for a conductor in a region where eddy currents can be ignored, and a static magnetic field analysis module and a dynamic magnetic field analysis module are selected depending on the presence or absence of the conductor flag in the physical property data. It is. The analysis module used in each sub-region can select an optimum method for the finite element method model in each sub-region, in addition to the discrimination between the static magnetic field and the dynamic magnetic field. For example, analysis modules such as the side element A-Φ method and the T-Ω method can be selected, and various general-purpose analysis modules can be used by providing a data conversion function. Accordingly, in the finite element method, a direct method, an ICCG method, a CG method, a Gauss-Seidel method, a multigrid method, or the like is used for the matrix operation, but a method that can be used in each analysis module can also be selected.

  In this embodiment, the dynamic magnetic field module has an unknown with side length and direction, and only the tangent component of the unknown vector is continuous at the element boundary, which solves the ambiguity of the gauge in the conventional nodal element method. In addition, the side element A-Φ method, which is most widely used in the field of magnetic field analysis, has been applied recently because the compatibility with the iterative solution method is good and the processing speed is fast. In addition, when applied in the static magnetic field region, it solves the three variables, so the static magnetic field module adopts the Ω method which only needs one variable.

  In the static magnetic field module, the displacement current can be made a quasi-stationary approximation that can be ignored as compared with the conduction current, so the equation (1) of Maxwell's equation becomes the equation (12). From this equation (12), the following equation (13) ) And (14) can be defined.

rotH = J (12)
H = −gradΩ (13)
div [mu] (-grad [Omega]) = 0 (14)

  In the dynamic magnetic field module, the side element A-Φ method is applied. The side element A-Φ method is formulated based on the following basic equations (15) to (20).

  Here, the basic equations to be solved are Equation (21) and Equation (22).

  When the partial integration method is applied by multiplying both sides of Equations (14) and (21) by the weight function W, Equation (23) is obtained, and the normal component of the magnetic flux density appears in the surface integral term.

  The magnetic field intensity at an arbitrary spatial point can be calculated from the equation (24) from the Coulomb's law and the Bio-Savart's law shown in the equation (11).

  In the conventional finite element method program, H · n in equation (24) is repeatedly calculated as an unknown variable. In the present invention, H · n is given as a known quantity as a boundary condition of the finite element method, Outside of the finite element method analysis, H · n of the entire region was obtained by the integral equation method as a contribution from all the magnetic materials, and the mutual relationship between the divided regions was maintained. By doing so, it is not necessary to solve the finite element method and the integral equation method simultaneously in each region, and the generation of a huge temporary file can be prevented.

  The magnetic field created by the area of only the coil element is expressed by the equation (10). However, as shown in FIG. 6, in the case where the region of only the coil element M exists inside the other sub-region S, the inside of the sub-region S is calculated simultaneously with the calculation of the boundary condition in order to prevent the deterioration of the calculation accuracy. It is also necessary to calculate and give the magnetic field in each finite element of the following equation (10). In this case, when the magnetic field calculated by the equation (10) is Hi, the external current vector potential of the equation (21) is H0 + Hi. Such a magnetic field superposition method is called an RSP method (Reduced Scalar Potential method). In the present invention, since the movement of the object is taken into consideration, it is conceivable that the region of the coil element M alone is also moved, and it is necessary to assume the case of entering another sub-region S as shown in FIG. The RSP method is introduced. However, in order to minimize the processing time, it is possible to select whether to use the RSP method for each sub-region.

  Table 1 shows a comparison result obtained by applying the method according to the present invention and the conventional method to a program, and applying to the case where there are three objects 1 to 3 in a certain region 4 'as shown in FIG. 7B. The time variation gave excitation variation (change in current value) to the coil element 1b of the object 1 in the region 4 ', and the processing time was determined as an average value of the processing time per time step. In addition, as shown to Fig.7 (a), it divides | segments into the sub area | regions 4-6 for every object 1-3 blocked | interrupted magnetically in space. Further, the boundary condition of the magnetic field in the outer circumferences 7 to 9 of the sub-regions 4 to 6 is determined by the distance from each of the objects 1 to 3, and the linear equation (11) obtained from the above-mentioned Coulomb's law and Bio-Savart's law. And the correlation equation 10 of each sub-region is determined by the integral equation method.

  In the present embodiment shown in FIG. 7, three objects having a magnetic field strength different by 5 digits (assuming a motor as the object 1, a magnetic material having a magnetic flux density of 1 [T] order, composed of a permanent magnet and a coil to be energized. The object 2 is a magnetic conductor having a magnetic flux density of the order of 1 × 10E-3 [T], and the object 3 does not have to consider the eddy current having the magnetic flux density of the order of 1 × 10E-5 [T]. Although the analysis model having a magnetic material (FIG. 7B) is used, each sub-region (sub-region 4 shown in FIG. 7A) has an accuracy of a maximum of five digits in the normal finite element method. Since the objects 1 to 3 having different orders of the magnetic field strength are divided into 6 to 6), the sub-regions 4 to 6 ensure the accuracy of 5 digits in the portion to which the finite element method is applied, and the whole boundary condition To analyze with a precision of 10 digits in the part obtained by the integral equation method I was able to. Further, by dividing the analysis model into three, the processing time and disk (memory) required for the calculation could be reduced to about one-fourth. Furthermore, the static magnetic field module is applied to the finite element method analysis of the sub-region 6 of the object 3 that does not need to consider the influence of the eddy current, and a matrix operation solver adapted to the finite element model is adopted, and the magnetic field state has converged. By stopping the analysis of the sub-region 6 of the object 3 at the time when it can be determined, the time required for the finite element analysis is reduced to about one third, and the processing time and the disk (memory) are both about 7 minutes as a whole. It was also possible to set to 1.

  Further, the relative error of the magnetic flux density was used as a determination value for the convergence determination of the finite element analysis. At the time of determination, a relative error from the previous calculation result is obtained for each of the sub-regions 4 to 6, and the maximum value is used as the determination value, thereby obtaining a converged result in consideration of eddy currents in all regions. The flow was able to be obtained, and was sequentially obtained over time. For determining whether or not the sub-regions 4 to 6 have converged, an arbitrary threshold value is set in the step of obtaining the integral boundary condition, similarly using the maximum value of the relative error of the magnetic flux density with the previous calculation result as a determination value. Judgment was carried out.

  FIG. 8 is a graph showing the relationship between the relative error and the number of convergence for each sub-region corresponding to the above embodiment. FIG. 8A shows the case where the convergence calculation of all the sub-regions is continued until all the sub-regions converge, and FIG. 8B shows the case where the analysis of the sub-region considered to have converged is stopped. is there. The total number of times of convergence is 20 times in FIG. 8 (a) × 60 in 3 areas, 41 times in FIG. 8 (b) 5 times + 16 times + 20 times, and about 2/3 of the number of times of convergence. The calculation time can be shortened.

  Next, an embodiment in which a charged particle beam exposure apparatus is designed using the magnetic shield analysis method according to the present invention will be described with reference to FIG. Here, the charged particle beam exposure apparatus 11 shown in FIG. 2 is divided into six parts of first to sixth sub-regions FEM1 to FEM6 as shown in FIG.

  In the first sub-region FEM1, the electron beam IB trajectory irradiated from the charged particle source (electron gun 12), the reticle 15, and its exchange port (vacuum pipe 25a) are provided for analysis. . In the second sub-region FEM2, the wafer 20 placed on the vacuum chamber 24 and the wafer stage 22 is the object of analysis. In the third and fourth sub-regions FEM3 and FEM4 (FEM4-1 and FEM4-2), the reticle loader 26 and the wafer loader 27 each having a driving mechanism including a magnet are set as objects of analysis. The fifth and sixth sub-regions FEM5 and FEM6 are installation legs for vibration isolation of the entire charged particle beam exposure apparatus, and have voice coil motors 29a and 29b built therein. Only the motors 29a and 29b are modeled and analyzed, and the coils 29c and 29d inside the motor are modeled in the region of the FEM5 and FEM6 as coil elements, and current values are given. As described above, the electron optical column 23 and the vacuum chamber 24 are provided with the magnetic shield 28.

  In the present embodiment, the influence on the electron optical system (illumination optical system, imaging optical system, etc.) due to the temporal change of the currents of the coils 29c and 29d of the vibration isolating voice coil motors 29a and 29b is analyzed. A design was made to reduce the influence of the coil current of the vibration isolating voice coil motor over 100 [nT]. In this embodiment, the maximum magnetic flux density of the vibration isolation voice coil motor is about 2 [T], and as a result of the analysis by the magnetic shield analysis method according to the present invention, the influence on the electron optical system is 30 [nT]. The result was obtained. When this analysis result is compared with the actually measured value, it is an error of ± 10% or less in the magnetic flux density, and the accuracy can be secured to 10 digits, and taking into account the physical property error and the influence of the simplified part of the model, The analysis was performed with sufficient accuracy.

  Finally, an embodiment that considers the movement of an object when designing a charged particle beam exposure apparatus using the magnetic shield analysis method according to the present invention will be described. Here, the wafer loader 27 in the charged particle beam exposure apparatus shown in FIG. 9 is further divided into a movable arm portion 27b and a main body 27a, and the fourth sub-region FEM4 and the fourth-sub-region FEM4-1 are respectively defined for each. The analysis is performed as the 4-2th sub-region FEM4-2.

  In this embodiment, an electron optical system (illumination optical system, imaging optical system, etc.) when the movable arm 27b of the wafer loader is moved by the transfer of a wafer or the like in the external space of the charged particle beam exposure apparatus 11 is used. It analyzes the effect on As shown in FIG. 9B, when the wafer is transferred, the movable arm portion 27b rotates with respect to the main body 27a. If the influence of the rotation of the movable arm portion 27b is 100 [nT] or less, the operation during exposure is possible. Therefore, when the movable arm portion 27b is improved depending on whether or not it is possible, the magnetic shield analysis method according to the present invention is performed. As a result of the analysis, the design result that the influence on the electron optical system is 20 [nT] was obtained. When this analysis result is compared with the actually measured value, it is an error of ± 10% or less in the magnetic flux density as in the above-described embodiment, and the accuracy can be ensured to 10 digits. Taking into account the effects of, we were able to analyze with sufficient accuracy.

It is the schematic which shows the electron optical system of the charged particle beam exposure apparatus used as the application object of the magnetic shield analysis method based on this invention. It is the schematic which shows the whole structure of the said charged particle beam exposure apparatus. It is a flowchart which shows the magnetic shield analysis method based on this invention. It is a flowchart which shows the magnetic shield analysis method based on this invention. It is a flowchart which shows the magnetic shield analysis method based on this invention. It is explanatory drawing which shows the example of a movement of the coil which applies the RSP method which concerns on this invention. In the magnetic shield analysis method concerning this invention, it is a conceptual diagram at the time of dividing | segmenting the analysis object area | region into a sub area | region including a coil element. It is a graph which shows the convergence condition at the time of applying the magnetic shield analysis method based on this invention. In the magnetic shield analysis method according to the present invention, it is a conceptual diagram when it is divided including a sub-region accompanied by the movement of an object.

Explanation of symbols

1-3 objects (magnetic material, conductor, or excitation source)
1b, coil 4-6 sub-region 7-9 boundary condition 10 integral equation method 11 charged particle beam exposure apparatus 12 electron gun 13 condenser lens 14 illumination lens 15 reticle 16 reticle stage 17 first projection lens 18 second projection lens 19 deflector (19-1 to 6) 20 Wafer 22 Wafer stage 23 Electro-optical column 24 Vacuum chamber 26 Reticle loader 27 Wafer loader 27a Wafer loader body 27b Wafer loader arm 28 Magnetic shield IB Electron beam S0-t In the analysis method according to the present invention Step S1-t for setting the initial state at time t Step S2-t for determining the state of the magnetic field in the sub-region at time t in the analysis method according to the invention Convergence determination at time t in the analysis method according to the invention Step S3-t of the present invention Determining the boundary conditions of the magnetic field of the sub-region at time t in the analysis method

Claims (16)

A first step of dividing the region to be analyzed into a plurality of sub-regions and setting the magnetic field state of the sub-regions, and solving the region between the sub-regions using an integral equation from the magnetic field state obtained in the first step A second step of obtaining a boundary condition of the magnetic field in the sub-region in consideration of the correlation, and a magnetic field in the sub-region by the finite element method using the boundary condition obtained in the second step for each sub-region. An analysis routine comprising a third step for determining the state;
A method for performing a magnetic shield analysis by repeatedly performing the analysis routine while giving a change in time condition from an initial time (t = 0) while passing time by a predetermined time step,
In the analysis routine at the initial time, the initial state of the magnetic field of the sub-region is input in the first first step, the second and third steps are performed, and then the determination is performed in the immediately preceding third step. Performing the second and third steps by setting the state of the magnetic field in the next first step;
In the analysis routine after the second time step, the state of the magnetic field obtained in the immediately preceding third step is set in the next first step to perform the second and third steps, and the previous time The eddy current is calculated based on the difference between the magnetic field state calculated in the analysis routine in step and the magnetic field state calculated by performing the first to third steps in the current time step, and the eddy current calculated in this way The magnetic shield analysis method is characterized in that the state of the magnetic field in the sub-region is obtained by performing the first to third steps again in consideration of the influence of the above.   2. The magnetic shield analysis method according to claim 1, wherein in each of the analysis routines, the first to third steps are repeated until it is determined that the state of the magnetic field in the sub-region has converged.   3. The analysis routine according to claim 2, wherein the analysis of the remaining sub-region is continued while the analysis of the sub-region determined to have converged in the analysis routine is stopped. Magnetic shield analysis method.   The magnetic shield analysis method according to claim 1, wherein the temporal condition change is an excitation condition.   The magnetic shield analysis method according to claim 1, wherein the temporal condition fluctuation is a movement of an object located in the sub-region.   The magnetic shield analysis method according to claim 5, wherein the object is moved by moving the sub-region.   The magnetic shield analysis method according to claim 1, wherein a method for obtaining the magnetic field state of the sub-region in the first step can be selected.   The magnetic shield analysis method according to claim 7, wherein a matrix operation method for solving the partial differential equation in the method can be selected.   The magnetic shield analysis method according to claim 1, wherein a static magnetic field analysis module that does not calculate the eddy current can be selected according to the presence or absence of a conductor in the sub-region.   The magnetic shield analysis method according to claim 1, wherein the sub-region includes a region including only a coil element.   The magnetic shield analysis method according to claim 10, wherein an RSP method is employed when calculating an influence of a region of only the coil element.   The said 2nd step WHEREIN: It comprised so that the boundary condition of the said magnetic field of the said sub-region might be calculated | required using the integral equation derived | led-out by the law of Coulomb and Bio-Savart. The magnetic shield analysis method described.   A magnetic shield analysis program for causing a computer to execute the steps of the magnetic shield analysis method according to claim 1. A charged particle source, an illumination optical system for irradiating the reticle with an electron beam emitted from the charged particle source, an imaging optical system for forming an image of the electron beam transmitted through the reticle on a sensitive substrate, and an external In a design method of a charged particle beam exposure apparatus equipped with a magnetic shield means for blocking the influence of a magnetic field,
A charged particle beam exposure apparatus, wherein the analysis target is the charged particle beam exposure apparatus, and the magnetic shield analysis method according to any one of claims 1 to 12 is applied to design the magnetic shield means. Design method.   The charged particle beam exposure apparatus includes a vacuum chamber including a first sub-region intended for an electron optical column provided with a charged particle source, the sensitive substrate, and a stage on which the sensitive substrate is placed. Dividing into a target second sub-region, a third sub-region targeted for a reticle loader for exchanging the reticle, and a fourth sub-region targeted for a wafer loader for exchanging the sensitive substrate, The method for designing a charged particle beam exposure apparatus according to claim 14, wherein analysis is performed with respect to fluctuations in excitation conditions. The charged particle according to claim 15, wherein the movement of the object in the sub-region is analyzed by dividing the region of the object moving in each sub-region and moving the divided region. Design method for line exposure equipment.

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