JP2000011938A - Simulation method in charged particle optical system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To exactly obtain a charged particle track which is remote from the optical axis with a short calculation time by describing an axial lens field in the form fitted to a C∞-class function, and describing the lens field outside an optical axis in the differential form of a function of the axial lens field for solving the track equation of charged particles. SOLUTION: An axial lens field of a charged particle optical system is calculated discretely to fit the discrete calculated axial lens field to a C∞-class function. Subsequently, the lens field outside the optical axis is expressed by the differential form of a function of the axial lens field, and the axial lens field fitted to C∞-class function, the lens field outside the optical axis expressed by a differential form of the function of the axial lens field, and the other given conditions are input to solve the trajectory equation of the charged particles. A means for solving the calculation of the axial lens field of the charged particle optical system discretely and a means for solving the trajectory equation of charged particles can use known means.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a charged particle beam optical system simulation method used in designing a charged particle optical system.

[0002]

2. Description of the Related Art Charged particle optics has evolved from correspondence with geometric optics. That is, the trajectory of the charged particle is described as a deviation (aberration) from the ideal trajectory. As a specific method, we write down the equation of motion of the charged particle and replace the time derivative with the total derivative in the optical axis direction (z) from the assumption that it is in a steady state (d / dt = (dz / dt) d / dz
= v _z d / dz), so-called orbit equation is obtained. It was common to consider this orbit equation as a Taylor-expanded equation, assuming that r (the distance from the optical axis) is sufficiently small.

That is, the trajectory equation is described by X. Zhu and E.
As shown in the Munro literature,

[0004]

(Equation 1) It is. Where * is a complex conjugate and 'is an optical axis direction ((x,
y, z) position derivative with respect to the z-axis direction in an orthogonal coordinate system), B is a magnetic flux density distribution, E is an electric field distribution, Φ is an electrostatic potential, η = e / m, e is the charge of a charged particle, and m is It is the mass of the charged particles. Also, w = x + iy. The subscript indicates its axial component. (same as below)

When considering an electromagnetic lens system, there is no electrostatic potential distribution.

(Equation 2) I can write Here, C = (η / (2Φ)) ^1/2 (3). Rewrite equation (3) in a form that can be solved by a computer,
If equation (2) is divided into a real part and an imaginary part to form an equation,

[0006]

(Equation 3)

(Equation 4) Becomes By solving this equation, a desired trajectory is obtained.

In solving this equation, the so-called paraxial trajectory equation is a solution of an ideal optical system having no aberration, which is a second-order linear ordinary differential equation, taking the first-order expansion into consideration. If the external field has cylindrical symmetry (only the lens field and no deflection field), this differential equation becomes a homogeneous equation and has two independent solutions. Any solution to this differential equation can be written as a linear combination of the two independent solutions.

Document Numerical Analysis of electron bea
m lithography systems.HC Chuand E. Munro, Optik
61, the 121 (1982), and these independent solutions to w _a track respectively, called w _b trajectory. In w _a trajectory object plane, track for emitting at 1 slope on the optical axis, w _b trajectory is a trajectory which is emitted by the gradient from 0 point away 1 from the optical axis on the object plane. The above documents, the discussion of the absence of the aperture, when there is a aperture, w _b trajectory emitted so as to pass through the aperture from the point spaced 1 (unit amount) from the optical axis on the object plane Orbit.

[0009] In deployable up to the third order, the differential equation becomes inhomogeneous equation, using the solution w _a and w _b of the aforementioned homogeneous equations, including analytically (integral form by some method of approximating ) Can be solved. This integration is called so-called aberration integration. In this method, on the image plane, ideally, the above-mentioned aberration integral called an aberration coefficient is calculated by a cubic expression relating to α and B by how much the trajectory to reach the position B with the inclination α is shifted from the ideal position. It can be expressed in a multiplied form. This shift is a so-called third-order aberration.

Similarly, the deviation from the ideal trajectory when the expansion equation up to the fifth order is taken into the above-mentioned ordinary differential equation is the aberration up to the fifth order, and the deviation from the ideal trajectory when the expansion equation up to the seventh order is fetched. Are referred to as aberrations up to the seventh order. In the present specification, the nth-order aberration trajectory is the trajectory of a charged particle when the expansion formula up to the nth order is taken in these conventional methods.

FIG. 13 shows an example of the procedure of the above-described aberration calculation.
It is shown in (A). First, in step S21, calculation conditions are read. That is, image plane position, object plane position,
Conditions such as aperture position, beam energy, lens data, aperture angle, image plane position of paraxial trajectory, energy spread, etc. are input.

Next, in step S22, an on-axis lens field is calculated discretely, and the lens field at a point not calculated is interpolated by an m-order spline function. Then, step S2
In step 3, the m-th derivative of the on-axis lens field interpolated by the spline function is obtained. Next, in step S24, the excitation current of the lens given as a precondition is adjusted so that the focal position is adjusted to the image plane. Thereafter, in step 25, the paraxial trajectory is calculated using the on-axis lens field and its first derivative. Then, in step 27, the m-th order aberration coefficient is calculated, and in step 28, the result is output.

On the other hand, a method of directly solving an orbit equation is also known. This is a method of directly solving an orbit equation using a finite element method or the like. This example is shown in FIG. In the procedure shown in FIG. 12B, first, in step S31, calculation conditions are read. That is, conditions such as an image plane position, an object plane position, an aperture position, a beam energy, a lens field, an opening angle, an image plane position of a paraxial trajectory, and energy spread are input. At this time, for the lens field, data for each mesh point is input. The lens fields other than the mesh points are obtained by interpolation in step S32.

Next, in step S33, the initial condition of the trajectory is derived, and based on this, the exact trajectory is obtained by directly solving the trajectory equation in step S34.
Output is performed at 35.

[0015]

However, in the method of performing the above-described aberration calculation, it is considered that fifth-order or higher aberrations will be required when considering a large-area batch exposure or the like. It is estimated that the calculation of the coefficient by a computer and the meaning of the aberration can be theoretically given up to about the 7th order (actually, there is only the fifth order aberration coefficient calculation software on the market). Further, when an aberration of a certain order is obtained, it is difficult to determine whether the aberration has a satisfactory accuracy or whether it is necessary to consider aberrations up to a higher order.

Further, as can be seen from the procedure shown in FIG. 13A, the on-axis lens field is interpolated by an m-th order spline function, and the m-th order of the on-axis lens field required for subsequent calculations is calculated. , The accuracy becomes worse as the derivative gets closer to the mth order.

Although the conventional method of solving the direct trajectory equation does not have such a problem, it is necessary to obtain the off-axis lens field with a considerably high accuracy. In other words, there is another problem that an accurate lens field at a large number of mesh points is required, which is extremely disadvantageous in terms of calculation time and the like.

The present invention has been made in view of such circumstances, and provides a method of simulating a charged particle optical system that can shorten the calculation time and can accurately evaluate the trajectory reaching a position far from the optical axis. An object of the present invention is to provide a method of simulating a charged particle optical system that determines which order to take in when performing a calculation incorporating a conventional expansion equation up to a specific order.

[0019]

First means for solving the problems To achieve the above object, according to a method of simulating a charged particle optical system, in a form to fit the axial lens field in the C ^∞ class function A method for simulating a charged particle optical system, comprising a step of describing a lens field off the optical axis in a differential form of a function of the on-axis lens field and solving a trajectory equation of the charged particle. It is solved by 1).

In the present means, we obtain the axial lens field in discrete form, to describe it in a format fit to C ^∞ class functions. The off-axis lens field is described in a differential form of the function of the on-axis lens field.

Conventional calculation methods (for example, ABER and AB manufactured by MEBS)
In ER5), the calculation of the on-axis lens field is performed by the finite element method,
Discrete values obtained by this method were interpolated by spline interpolation to obtain an on-axis lens field, but a cubic spline (Cubi
c spline) in C ³ primary, the fifth-order spline is C ⁵ primary, high-order differential impossible. In contrast, in the present means, since the axial lens field is described in a format to fit a function of C ^∞ grade, it is possible to perform the derivative of any rank, the accuracy is improved.

Therefore, by substituting the on-axis lens field and the off-axis lens field described above into the charged particle trajectory equation and solving the trajectory equation, the charged particle trajectory far away from the optical axis is obtained. Can also be determined exactly.
Since the lens field is represented by a ^C∞ class function and its differential form, the calculation time can be significantly reduced as compared with the conventional method of directly solving the trajectory equation.

The apparatus for performing such a simulation, the means for fitting and means for discretely calculate axial lens field of charged particle optical system, the discretely calculated axial lens field in the C ^∞ class function Means for expressing the off-axis lens field in a differential form of the function of the on-axis lens field, an on-axis lens field fitted to a ^C∞ class function, and a differential form of the function of the on-axis lens field It can be configured by having means for solving the trajectory equation of the charged particle with the input off-axis lens field and other given conditions as inputs. As means for discretely calculating the on-axis lens field of the charged particle optical system and means for solving the trajectory equation of charged particles, conventionally known means can be used.

A second means for solving the above-mentioned problem is as follows.
The first means, wherein the function of the ^C∞ class is a Fourier series (Claim 2).

By making the function a Fourier series, it is possible to easily obtain a function of class ^C∞ .

An apparatus for performing such a simulation is obtained by converting a discretely calculated on-axis lens field of the apparatus for performing a simulation described in the first means into C ^∞.
The means for fitting to the class function can be realized by Fourier transforming the on-axis lens field.

A third means for solving the above-mentioned problem is as follows.
A method for simulating a charged particle optical system, comprising:
The process of solving the orbit equation of a charged particle by describing the on-axis lens field in a form fitted to a function of the C ⁿ class and describing the off-axis lens field in a differential form of the function of the on-axis lens field is described. A method for simulating a charged particle optical system (claim 3).

[0028] This means is to use a function of C ⁿ class instead of a function of C ^∞ class in the first means.
In practice, the order of differentiation required cannot be infinite, so that n is appropriately determined, the on-axis lens field is described in a form fitted to a function of the C ⁿ class, and the off-axis lens field is described. Is described in a differential form of the function of the on-axis lens field,
By solving the orbit equation of the charged particles on the basis thereof, it is possible to obtain the same accuracy as in the first means, and it is possible to shorten the calculation time as compared with the first means. Practically, n is about 11 to 19.

The apparatus for performing such a simulation, the means for fitting and means for discretely calculate axial lens field of charged particle optical system, the discretely calculated axial lens field in C ⁿ class function If, means for representing the off-axis of the lens field in differential form of the function of the on-axis lens field, C ⁿ class functions axial lens field which is fitted to the table in the derivative form of a function of the axial lens field It can be configured by having means for solving the trajectory equation of the charged particle with the input off-axis lens field and other given conditions as inputs. As means for discretely calculating the on-axis lens field of the charged particle optical system and means for solving the trajectory equation of charged particles, conventionally known means can be used.

A fourth means for solving the above-mentioned problem is:
The third means is characterized in that the C ⁿ class function is a power series (claim 4).

By using a power series, a function of class C ⁿ can be easily obtained. The apparatus for performing such a simulation includes a means for fitting the discretely calculated on-axis lens field to a function of the C ⁿ class of the apparatus for performing the simulation described in the third means. This can be realized by fitting to a power series.

A fifth means for solving the above problem is as follows.
The fourth means is characterized in that the method for obtaining the power series is obtained by fitting original discrete data by a least squares method (claim 5).

The power series can be easily obtained by fitting the power series by the least square method.
An apparatus for performing such a simulation is an apparatus for performing the simulation described in the fourth means,
The operation of the means for fitting a discretely calculated on-axis lens field to a power series can be realized by performing fitting by the least square method.

A sixth means for solving the above-mentioned problem is:
Using the on-axis lens field and the off-axis lens field described using any one of the first to fifth means, the trajectory of the charged particle is directly solved by solving the trajectory equation of the charged particle. A method of simulating a charged particle optical system, which comprises a step of obtaining a charged particle optical system.

[0035] In the above either from the first means fifth means, the axial lens field is fit to a function or C ⁿ class functions C ^∞ grade, off-axis of the lens field, these axes Since the differential equation of the upper lens field is expressed, the calculation time can be shortened even if the orbit equation of the charged particle is directly solved, that is, solved without being approximated by expansion or the like. By directly solving the charged particle trajectory equation, the charged particle trajectory can be accurately obtained.

As in the conventional case, when the deviation from the ideal orbit (so-called aberration) is obtained by using the lens field in a developed form, the number of aberrations which appear as the degree of development increases becomes enormous. The meaning of itself is also sadly complicated. Accordingly, the frequency of mistakes (bugs) in creating the numerical calculation program also increases. With the method of directly solving the equation of motion as described above, it is not possible to obtain a specific value as the aberration coefficient, but the trajectory that has left the object surface under certain conditions is
At the image plane, it is possible to exactly obtain the position and angle at which the light is incident.

The apparatus for performing such a simulation includes a means for solving the trajectory equation of the charged particles of the apparatus for performing the simulation described in the first to fifth means, and the trajectory equation for the charged particles directly. It can be realized by solving it.

A seventh means for solving the above-mentioned problem is as follows.
The trajectory of a representative charged particle emitted from the object surface under the same initial conditions is obtained by any one of the first to sixth means and the method of obtaining the m-th order aberration trajectory. The position of the obtained trajectory on the image plane is R _、, the position of the trajectory obtained on the image plane by the latter method is R _m ,
The determined by any of the methods from the first means sixth means, the position of the image plane of the orbit of the charged particles emitted by the opening angle 0 the object plane when the R _{∞ 0,} | R _m - R _∞ | / | R _∞ −
A charged particle optical system characterized by including a step of obtaining an order of aberration required for calculation in accordance with R _{∞ 0} | and performing subsequent trajectory calculation by obtaining an aberration trajectory according to the required order of aberration. This is a simulation method (claim 7).
(However, | R _m -R _∞ | is the distance between R _m and R _、, | R _∞ -R
_{∞ 0} | is the distance between R _∞ and R _{∞ 0} . FIG. 1 shows a spot diagram of the charged particle trajectory on the image plane. The spot diagram is a diagram illustrating a position at which a charged particle that has protruded in all directions from a certain point on the image plane at a specific opening angle reaches the image plane. In FIG. 1, the image plane is shown as the xy plane, and the optical axis is shown as the origin.

R ₀ is a paraxial trajectory, and each ellipse is a spot diagram obtained by any of the first to sixth means (referred to as a direct trajectory spot diagram; A trajectory of a charged particle obtained by any of the sixth means is referred to as a direct trajectory), a spot diagram obtained by considering a third-order expansion formula by a conventional method (referred to as a third-order aberration trajectory spot diagram),
A spot diagram (referred to as a fifth-order aberration orbit spot diagram) obtained in consideration of the expansion formula up to the fifth order is shown. R _{∞ 0,} in direct trajectory, the charged particles flying out in the opening angle 0 is the point which reaches the image plane. R _∞ , R ₃ , R ₅
Are obtained by calculating the points at which charged particles, which have jumped out of the same point at the same opening angle from the same point and reach the image plane, on the object surface. r is R ₀ and R _∞
The distance between the, r _t is the distance between the R _{∞ 0} and R _∞, r ₃ is R ₃ and R _∞
And r ₅ indicates the distance between R ₅ and R _∞ .

Of these, the direct orbit spot diagram indicates the most accurate position. Therefore, the accuracy of the spot diagram calculated by the conventional method is represented by the distance from the direct orbit spot diagram. In this means, normalization is performed based on the distance between R _∞ and R _{∞ 0} . _{That, r 3 / r t, r} 5 / r t (| R m -R ∞ | / | R ∞ -R ∞
₀ |, m = 3, 5), and the order of the conventional method used in subsequent calculations is calculated according to the magnitude.

In the conventional method, the above-mentioned non-homogeneous equation is obtained. If the solutions w _a and w _{b of} the above-mentioned homogeneous equation are calculated once, the positions of various charged particles on the image plane can be solved by the equations. Even if they are not, the calculation can be easily performed from the aberration coefficient, the opening angle, and the arrival position of the paraxial trajectory on the image plane. Therefore, it is preferable to use the conventional method from the viewpoint of saving calculation time. Therefore, in this means, regarding the representative point, the first
If an exact solution is obtained by any of the means from the means of the sixth to the sixth and the order of the conventional method is considered,
Determine whether there is a great difference from the exact solution. After the order is determined, the trajectory calculation is performed using the conventional method. This enables accurate trajectory calculation while taking advantage of the feature of the conventional method that the calculation time is short.

The apparatus for performing such a simulation, in addition to the means for apparatus for simulating described has the sixth means from the first means, and means for determining the m-th order aberration orbit, the R _∞, R _m, and each of the means for obtaining the _{R ∞ 0, | R m -R} ∞ | / | R ∞ -R ∞ 0 |
Accordingly, there is provided a means for obtaining the order of the aberration required for the calculation and a means for performing the subsequent trajectory calculation by obtaining the aberration trajectory based on the required order of the aberration. As the means for obtaining the m-th order aberration trajectory, a conventionally known means can be used.

Eighth means for solving the above-mentioned problem is:
The seventh means, wherein | R _m -R _∞ | / | R _∞ -R _{∞ 0} |
The minimum order m of aberration that satisfies ≦ A (A is a value determined from required accuracy and is a number of 0.3 or less) is set as the order of aberration required for calculation (claim 8). It is.

By keeping | R _m -R _∞ | / | R _∞ -R _{∞ 0} | within this range, the spot diagram obtained by the simulation does not greatly deviate from the actual spot diagram, and the accuracy that can be used as a simulation is temporarily reduced. can get. The value of A is determined from the precision required in the design, but | R _m -R _∞ | / | R _∞ -R _{∞ 0} |
If it exceeds 3, the deviation of the spot diagram will increase, and the simulation accuracy will deteriorate, making it impractical.

The apparatus for performing such a simulation is different from the apparatus for performing the simulation described in the seventh means in that the calculation is necessary in accordance with | R _m −R _∞ | / | R _∞ −R _{∞ 0} |. The function of the means for determining the order of aberration is
| R _m −R _∞ | / | R _∞ −R _{∞ 0} | ≦ A can be realized by setting the minimum order of aberration to be the order of aberration required for calculation.

A ninth means for solving the above-mentioned problem is:
The trajectory of a representative charged particle emitted from the object surface under the same initial condition is obtained by the method according to any one of claims 1 to 6 and the method of obtaining an m-th order aberration trajectory, respectively. Is the position on the image plane of the orbit determined by the method
_を , the position on the image plane of the trajectory obtained by the latter method is R
_m , when the position of the charged particle on the image plane of the paraxial trajectory is R ₀ , the aberration required for calculation depends on the magnitude of | R _m −R _∞ | / | R _∞ −R ₀ | A method for simulating a charged particle optical system, comprising a step of obtaining an order and performing subsequent trajectory calculation by obtaining an aberration trajectory according to a required order of aberration. (However, | R _m -R
_∞ | is the distance between R _m and R _、, and | R _∞ -R ₀ | is the distance between R _∞ and R _0. )

Here, the position R ₀ of the charged particle on the image plane of the paraxial trajectory is determined by solving the so-called paraxial trajectory equation obtained by considering the trajectory equation up to the first order of expansion as described above. Required by

In an optical system having a small opening angle, it is not necessary to match the shapes of the spot diagrams, and only the position of the charged particle beam becomes important. In such a case, as a value for normalizing the distance R _m and R _∞, | R _∞ -R
_It is appropriate to use ₀ |. As a result, the order required for the calculation by the conventional method can be estimated without excess or deficiency. The reason that the subsequent calculation is preferably performed by the conventional method is the same as the reason described in the description of the eighth means.

The apparatus for performing such a simulation, in addition to the means for apparatus for performing the simulation described in the sixth means from said first means having, means for determining the m-th order aberration orbit, the R _∞, Means for obtaining R _m and R ₀ , means for obtaining the order of aberration required for calculation according to the magnitude of | R _m -R _∞ | / | R _∞ -R ₀ |, and subsequent trajectory calculation Is obtained by obtaining an aberration trajectory according to the required order of aberration. As the means for obtaining the m-th order aberration trajectory, a conventionally known means can be used.

A tenth means for solving the above-mentioned problem is the ninth means, wherein | R _m -R _∞ | / | R _∞ -R
₀ | ≤ B (B is a value determined from the required accuracy, 0.1
The minimum order of the aberration that satisfies the following number) is set as the order of the aberration required for calculation (claim 10).
It is.

By keeping | R _m -R _∞ | / | R _∞ -R ₀ | within this range, the trajectory of the charged particles in the simulation does not greatly deviate from the actual trajectory, and the accuracy that can be used as a simulation is temporarily reduced. can get. B
Is determined from the accuracy required for design, but | R _m
If −R _∞ | / | R _∞ -R ₀ | exceeds 0.1, the deviation of the position of the charged particle trajectory becomes large, and the simulation accuracy deteriorates, which is not practical. Therefore, the maximum value is set to 0.1.

The device for performing such a simulation is the same as the device for performing the simulation described in the ninth means, except that the aberrations required for the calculation are determined in accordance with | R _m -R _∞ | / | R _∞ -R ₀ |. Function of means to find the order of
This can be realized by setting the minimum order m of the aberration that satisfies R _m −R _∞ | / | R _∞ −R ₀ | ≦ B as the order of the aberration required for calculation.

According to an eleventh means for solving the above-mentioned problem, the trajectory of a representative charged particle which has exited the object surface under the same initial condition is described in any one of claims 1 to 6. When the position on the image plane of the trajectory obtained by the former method is R _、, and the position on the image surface of the trajectory obtained by the latter method is R _m , | R _∞ −R _m |, and calculating the order of the aberration required for the calculation, and performing the subsequent trajectory calculation by obtaining the aberration trajectory according to the required order of the aberration. A simulation method of a charged particle optical system (claim 11). (However, | R _∞ -R _m
Is the distance between R _∞ and R _m ).

When it is not necessary to match the shapes of the spot diagrams and absolute accuracy of the position of the charged particle beam is required, the accuracy of the conventional method should be evaluated by the distance itself between R _∞ and R _m. Is preferred. Specifically, the minimum order of aberration such that the distance between R _∞ and R _m is equal to or less than a predetermined value obtained from design conditions may be set as the order of aberration required for calculation. As a result, the order required for the calculation by the conventional method can be estimated without excess or deficiency. The reason that it is preferable to perform the subsequent calculations by the conventional method is as follows.
The reason is the same as that described in the description of the eighth means.

[0055] device for performing such a simulation, in addition to the means for apparatus for performing the simulation described in the sixth means from said first means having, means for determining the m-th order aberration orbit, the R _∞, and each means for obtaining the _{R m, | R ∞ -R m} | depending on the size, means for determining the order of the aberration required for the calculation, the subsequent trajectory calculation, the aberration orbit by orders of required aberration This is realized by having means for performing the determination. As the means for obtaining the m-th order aberration trajectory, a conventionally known means can be used.

A twelfth means for solving the above-mentioned problem is that a trajectory of a charged particle which has exited an object surface under the same initial conditions is
The method according to any one of claims 1 to 6, and a method for calculating an m-th order aberration trajectory, respectively, wherein the position of the trajectory obtained by the former method on the image plane is _R∞ , and the latter method. Where R _m is the position of the orbit on the image plane and R ₀ is the position of the charged particle on the image plane of the paraxial orbit, the value of | R _m −R _∞ | / | R _∞ −R ₀ | The distance R _{0 (m) max} from the optical axis of the paraxial trajectory to the image plane at which the maximum value becomes a predetermined value is obtained for each m-th order aberration trajectory, and the lens barrel length (the distance between the object plane and the image plane) Is L and the field size is F
(1/2) ^1/2 · F / L is the distance R _{0 (m) max} from the optical axis on the image plane of the paraxial trajectory and the lens barrel length obtained by the method for obtaining the m-th order aberration trajectory. _Is determined to be smaller than R _{0 (m) max} / L and larger than R _{0 (m−2) max} / L, and the subsequent calculation is performed by obtaining the m-th order aberration trajectory. A method of simulating a charged particle optical system (claim 12). (However, | R _m -R
_∞ | is the distance between R _m and R _、, and | R _∞ -R ₀ | is the distance between R _∞ and R ₀ . )

Here, the field size is obtained by multiplying the distance from the optical axis of the paraxial orbit on the image plane by ^21/2 . Further, the distance R from the optical axis on the image plane of the paraxial orbit that sets the maximum value of | R _m -R _∞ | / | R _∞ -R ₀ |
_{0 (m) max} is the maximum value of | R _m −R _∞ | / | R _∞ −R ₀ | for various charged particles emitted from the same position at the same position on the object surface at different opening angles in the same direction. Is calculated as the distance from the optical axis on the image plane of the paraxial trajectory that makes 所 定 a predetermined value.

When the other conditions are the same, the distance R _{0 (m) max} from the optical axis of the paraxial orbit is normalized by the lens barrel length L. The ratio (1/2) ^1/2 · F / L of the field size F to the lens barrel length L is smaller than the calculated R _{0 (m) max} / L and larger than R _{0 (m-2) max} / L. For example, by adopting this m as the order of calculation, the aberration can be estimated without excess or deficiency. Therefore, in such a case, the calculation formula can be used. In general, the higher the degree of the expansion equation taken in the conventional method, the larger the value of R _{0 (m) max} / L under the same conditions. Therefore, (1/2) ^1/2 · F / L is the distance R _{0 (m) max} from the optical axis on the image plane of the paraxial trajectory obtained by the method of obtaining the m-th order aberration trajectory, and the lens barrel. The length m is determined to be smaller than the ratio R _{0 (m) max} / L and larger than R _{0 (m−2) max} / L, and the subsequent calculation is performed by obtaining the m-th order aberration trajectory. The simulation can be performed most efficiently. In addition, this method is effective when it is not necessary to match the shapes of the spot diagrams and only the position of the charged particle beam is important. By using this method, the trajectory of the charged particles by simulation is reduced to the actual trajectory. And the accuracy can be obtained that can be used as a simulation.

[0059] device for performing such a simulation, in addition to the means for apparatus for performing the simulation described in the sixth means from said first means having, means for determining the m-th order aberration orbit, the R _∞, R _m, and each of the means for obtaining the _{R 0, | R m -R ∞} | / | R ∞ -R 0 | distance from the optical axis on the image plane of the paraxial trajectories to the maximum value of the predetermined value R _{0 (m) ma}
means for respectively obtaining _x for each m-th order aberration trajectory;
The ratio of the field size F to the lens barrel length (distance between the object plane and the image plane) L (1/2) ^1/2 · F / L is the paraxial trajectory obtained by the method of obtaining the m-th order aberration trajectory. _Is smaller than the ratio _{R0 (m) max} / L of the distance _{R0 (m) max} from the optical axis on the image plane to the lens barrel length, and m is larger than _{R0 (m-2) max} / L. This is realized by having means for determining and means for performing subsequent calculations by obtaining the m-th order aberration trajectory. As the means for obtaining the m-th order aberration trajectory, a conventionally known means can be used.

A thirteenth means for solving the above-mentioned problem is that a trajectory of a charged particle which has exited an object surface under the same initial conditions is
The method according to any one of claims 1 to 6, and a method for calculating an m-th order aberration trajectory, respectively, wherein the position of the trajectory obtained by the former method on the image plane is _R∞ , and the latter method. position R _m of the image plane of the orbit determined by was determined by the former method, the position of the image plane of the orbit of the charged particles emitted by the opening angle 0 the object plane when the R _{∞ 0,} | R _m
The distance R _{0 (m) max} from the optical axis on the image plane of the paraxial trajectory that makes the maximum value of −R _∞ | / | R _∞ −R _{∞ 0} | a predetermined value is obtained for each m-th order aberration trajectory. When the lens barrel length (distance between the object plane and the image plane) is L and the field size is F (1/2)
^1/2 · F / L is the distance R from the optical axis on the image plane of the paraxial trajectory obtained by the method for obtaining the m-th order aberration trajectory.
_{0 (m) max} / L, which is smaller than the ratio _{R0 (m) max} / L
_A method for simulating a charged particle optical system, comprising a step of determining m which is larger than _{0 (m-2) max} / L and performing subsequent calculations by obtaining an m-th order aberration trajectory. 13). (However, | R _m -R _∞ | is the distance R _m and _{R ∞, | R ∞ -R ∞} 0 | is the distance R _∞ and R _{∞ 0.)}

This means differs from the twelfth means in that
In the twelfth means, R _{0 (m) max} is | R _m −R _∞ |
/ | Contrast was the distance from the optical axis on the image plane of the paraxial trajectory of the maximum value of the predetermined value, in this _{means, | | R ∞ -R 0 R} m -R ∞ | / | R _∞ -R _{∞ 0} | is that the maximum value of which the distance from the optical axis on the image plane of the paraxial trajectory to a predetermined value. In this means, the same operation and effect as those of the twelfth means can be obtained.

[0062] device for performing such a simulation, in addition to the means for apparatus for performing the simulation described in the sixth means from said first means having, means for determining the m-th order aberration orbit, the R _∞, R _m, and each of the means for obtaining the R _{∞ 0,} | distance from the optical axis of the maximum value in the image plane of paraxial trajectory of the predetermined value of _{| R m -R ∞ | / |} R ∞ -R ∞ 0 R
Means for determining _{0 (m) max} for each m-th order aberration trajectory, and the ratio of the field size F to the lens barrel length (distance between the object plane and the image plane) L (1/2) ^1/2 · F / L Is the ratio R _{0 (m) max} / of the distance R _{0 (m) max} from the optical axis on the image plane of the paraxial trajectory obtained by the method of obtaining the m-th order aberration trajectory to the lens barrel length.
M smaller than L and larger than R _{0 (m−2) max} / L
And means for performing subsequent calculations by determining the m-th order aberration trajectory. As the means for obtaining the m-th order aberration trajectory, a conventionally known means can be used.

[0063]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments of the present invention will be described. First, an on-axis lens field (field of magnetic flux density) is obtained discretely, and this is set as B _M (z). Here, z is the direction of the optical axis, z = -L indicates the object plane position, and z = L indicates the image plane position. From this, the on-axis lens field B (z)
^Is described by fitting a function of the class CＣ. Here, a Fourier series is used as a function of the ^C∞ class. (Note that
B (z) is originally a three-dimensional vector, but an x-direction component,
Since the y-direction component is 0, the z-axis component is simply expressed as B (z)
As shown. )

[0064]

(Equation 5) As to obtain a C _n by numerically integrating the equation (6). Using C _n thus obtained, B (z) is

[0065]

(Equation 6) It is expressed as Thus, the axial lens field is expressed as a function of C ^∞ class. The k-order derivative B (z) ^(k) of B (z ⁾ is

[0066]

(Equation 7) Is represented as (Hereafter, higher-order derivatives are indicated by parenthesized superscripts.)

Next, the lens field off the optical axis will be described in a differential form of the function of the on-axis lens field B (z). That is, taking an xy plane perpendicular to the z axis, the lens field B _{x, y, z} (B _x , B _y , B _z ) at the position (x, y, z) is _expressed as

[0068]

(Equation 8)

(Equation 9)

(Equation 10) It represents.

In the case of an electromagnetic system, (9), (10),
Equation (11) is substituted into equations (4) and (5) to solve the orbit equation. In solving the orbital equation, (1+
x ' ² + y' ² ) You can solve the equation after expanding ^1/2 to an appropriate order, but if you want an exact solution, (4),
Equation (5) can be solved directly. (4), even solved directly (5), B _x, B _y, since B _z is expressed in functional form,
The calculation time can be greatly reduced as compared with the conventional method in which these are obtained by the finite element method or the like.

FIG. 2 shows a simulation procedure according to an embodiment of the present invention.

First, in step S11, calculation conditions are read. That is, conditions such as an image plane position, an object plane position, an aperture position, a beam energy, lens data, an opening angle, an image plane position of a paraxial orbit, an energy spread, and the like are input. This procedure is the same as that of FIG.
(A) Same as step S21.

[0072] Then, in step S12, fitting the axial lens field in the C ^∞ class functions. In step S22 of FIG. 13A described in the related art, the on-axis lens field is discretely calculated, and the lens field at a point not calculated is interpolated by the m-th order spline function. This point is different from the prior art. Then, in step S13, the on-axis lens field is analytically differentiated to a rank (n) as required. At this time, since the axial lens field are fitted to a function of C ^∞ grade, unlike the prior art, even when high rank differential,
An accurate value is obtained.

Next, in step S14, the excitation current of the lens given as a precondition is adjusted so that the focal position is adjusted to the image plane. Thereafter, in step 15, the paraxial trajectory is calculated using the on-axis lens field and its first derivative. These steps are the same as steps S24 and S25 in FIG. Next, in step S16, initial conditions of the trajectory are derived, and based on this, the m-th order aberration trajectory is calculated in step S17. At that time, the calculation is performed in consideration of the on-axis lens field and its m-order derivative.

Then, in step S18, the trajectory is directly calculated. That is, the lens field at an arbitrary position on the axis is determined by considering the on-axis lens field and its n-th derivative, and the orbit equation is directly solved. The process of solving the orbit equation is
This is basically the same as the process in the conventional technique shown in step S34 of FIG. The orbit equation can be solved by using the Runge-Kutta method or the like. Next, the result is output in step S19.

FIG. 3 shows an example of an on-axis lens field fitted to a Fourier series by the method of the present invention. Here, electrons were used for the charged particles. Thick line indicates actually given lens field (those solved using the finite element method), thin line, the C ^∞ class of functions obtained by expanding the Fourier series by the method of the present invention the lens field Show. Although there are slight differences, the two agree very well. In this figure, the direction from the object point to the image point is positive, and the position of the image point is set as the origin. The magnification is
The energy of the electron is 100 keV, reduced by 1/4. In the actual calculation, the order of the Fourier series is from -20 to 20,
The differentiation of the on-axis lens field is up to the eleventh order.

FIG. 4 shows an energy spr in this optical system.
ead = + 5eV, the opening half-angle at the image plane is 6mrad, and the paraxial light reaching the position of 5 × (2) ^1/2 / 2mm from the optical axis on the image plane actually shifts. It is a representation (spot diagram). The square points represent paraxial orbits,
A thin dashed line (m = 3) indicates a third-order aberration trajectory (a trajectory obtained by solving the trajectory equation by a third-order expansion formula in the conventional method), and a thick broken line (m = 5) indicates a fifth-order aberration trajectory (conventional method). Trajectory solved by expressing the trajectory equation by an expansion formula up to the fifth order. The trajectory obtained by directly solving the equation of motion according to the present invention is shown by a solid line (Trace). Thus, where the distance from the optical axis is relatively short, the aberration trajectory up to the fifth order agrees well with the method according to the present invention.

FIG. 5 shows the distance from the optical axis under the same conditions.
In the case of paraxial light reaching the position of 7 × (2) ^1/2/2 mm, FIG. 6 shows that the distance from the optical axis reaches the position of 10 × (2) ^1/2/2 mm under the same conditions. FIG. 4 shows the case of paraxial light. It can be seen that the deviation from the fifth-order aberration trajectory increases as the distance from the optical axis increases. This means that when the distance from the optical axis is large, when designing the optical system, it is not sufficient to display only the fifth-order aberrations as a performance display of the optical system. Represents.

In the above embodiment, the on-axis lens field is described by the Fourier series.
It is not limited to this. An example is shown below.

FIG. 7 shows that the diameter D expanded to infinity in the horizontal direction.
3 shows a model of a lens having a magnetic pole array in which magnetic poles surround a hollow of the magnetic pole and a space for mounting a coil is provided at the center with a space of a width S. In this case, as shown in the drawing, assuming that the z-axis is taken at the center of the cavity, the z-coordinate of the coil center is Z ₁ , and the lens field B (z) on the z-axis is represented by a ^C∞ class function,

[0080]

[Equation 11] become that way. Where J = NI (N: number of turns of coil,
I: current value), and μ ₀ is the magnetic permeability in vacuum. This even-order derivative B (z) ⁽²ⁿ⁾ is

[0081]

(Equation 12) And the odd-order derivative B (z) ^{(2n + 1)} is

(Equation 13) Becomes Here, B ₀ is a constant, and I ₀ is a first-order modified Bessel function of order 0.

[0082] In the axial lens field of known Bell-type lens field, the axial lens field B (z) as a function of C ^∞ class,

[Equation 14] It is expressed as

In the above embodiment, the on-axis lens field B (z) is fitted to a Fourier series which is a function of the ^C∞ class. However, in the actual calculation, calculation up to infinity is performed. Since it is not possible, n may be set to an appropriate number (usually 11 or more) and fitted to a C ⁿ class function. In this case, as the simplest C ⁿ class function, B (z) is a power function.

[0084]

(Equation 15) Is the simplest method. The fitting of the on-axis lens field to these power functions can be easily performed by using the least squares method.

Although the above embodiment has been described with reference to an electromagnetic lens, the present invention is not limited to this, and is also applicable to the case of an electrostatic system. In this case, by fitting the axial electrostatic potential in function of C ^∞ class and C ⁿ class may be solved (1).

In the above embodiment, electrons are used as charged particles. However, the present invention is not limited to this, and can be applied to any charged particles.

An SMD optical system is made by using a lens having the shape shown in FIG. 7 and a quarter of this lens. In this optical system, an image of a pattern on an object surface such as a reticle is reduced and projected to 1/4 times on an image surface such as a mask. Considering the eleventh derivative of this on-axis lens field,
The result of solving the direct orbit equation (hereinafter referred to as the direct orbit), the paraxial orbit, and the third and fifth order aberration orbits are calculated.
A spot diagram on the image plane as shown in FIG. 1 is obtained.

At various opening angles, r ₃ / r (| R ₃ −
_{R ∞ | / | R ∞ -R} 0 |) and _{r 5 / r (| R 5} -R ∞ | / |
R _∞ -R ₀ | paraxial trajectory distance from the optical axis on the image plane, such as the maximum value of 5% _{of) (R 0 (m) max} , m = 3,5) the calculated shape of the lens Is changed, this point is changed to the lens barrel length L.
8 and 9 are plotted after normalization. FIG.
Is the case where the ratio D / L between D (interval between N poles and between S poles in FIG. 7) and lens barrel length L is 0.3, and the horizontal axis is the distance S between the N pole and S pole in FIG. The ratio S / L of the tube length L is shown, and the vertical axis shows R _{0 (m) max} / L. FIG. 9 shows the case where D / L is 0.7, the horizontal axis shows D / L, and the vertical axis shows R _{0 (m) max} / L. In the figure, 1 mrad and the like represent the opening angle, and m = 3 and m = 5 represent the third-order and fifth-order aberration trajectories, respectively.

In these graphs, for example, when an optical system having an opening angle of 1 mrad is considered, the value obtained by dividing the field size by the lens barrel length is an area above the curve of 1 mrad (m = 5) (large field size). , The calculation up to the 5th-order aberration is not sufficient, and if it is in the region above the 1 mrad (m = 3) curve and below the 1 mrad (m = 5) curve, 5 Calculation up to the next aberration is reasonable, and 1 mrad
In the region below the curve (m = 3), it is shown that up to the third-order aberration is sufficient without considering the fifth-order aberration.

Next, let _rt be the distance on the image plane between the position on the image plane of the direct trajectory calculated under the condition that the opening angle is 0 and the direct trajectory calculated at the desired opening angle. Then, at various opening _{angle, r 3 / r t (|} R 3 -R ∞ | / | R ∞ -R ∞ 0 |) and _{r 5 / r t (| R} 5 -R ∞ | / | R ∞ - R _{∞ 0} | paraxial trajectory distance from the optical axis on the image plane, such as the maximum value of 5% _{of) (R 0 (m) max} , m = 3,5) to seek, change the shape of the lens FIG. 10 and FIG. 11 are plotted by normalizing this point with the lens barrel length L. The reference numerals in FIG.
It is the same as FIG.

Again, from this graph, the opening angle is 1 mrad.
If the value obtained by dividing the field size by the lens barrel length is in the region above the 1 mrad (m = 5) curve (large field size), calculation up to the fifth-order aberration Is not sufficient, and in the region above the 1 mrad (m = 3) curve and below the 1 mrad (m = 5) curve, the calculation up to the fifth order aberration is appropriate, and 1mra
In the region below the curve of d (m = 3), it indicates that the third-order aberration is sufficient without considering the fifth-order aberration.

Note that the on-axis lens field can be solved analytically when the lens is spread to infinity. However, as shown in FIG. 12, this model is extended to a case where the lens has a finite size. Even so, there is no problem. (1 in FIG. 12 is a coil, 2 denotes a hole piece.) In this case, by the finite element method or the like, obtains the axial lens field, it can be fit into C _∞ class functions.

[0093]

As described above, according to the first aspect of the present invention, the on-axis lens field is described in a form fitted to a C ^{フ ィ ッ ト} class function, and the off-axis lens field is described. Is described in the differential form of the function of the above-described on-axis lens field to solve the charged particle trajectory equation, so that the trajectory of the charged particle far away from the optical axis can be strictly obtained in a short calculation time.

According to the second aspect of the present invention, further,
Since the function of the C ^∞ class is a Fourier series, easily C
^{関 数} class functions can be obtained.

In the invention according to claim 3, the on-axis lens field is described in a form fitted to a function of the C ⁿ class, and the off-axis lens field is described in a differential form of the function of the on-axis lens field. Since the trajectory equation of the charged particle is solved by describing, the accuracy which is not much different from that of the invention according to claim 1 can be obtained by appropriately determining n, and can be compared with the invention according to claim 1. Calculation time can be shortened.

[0096] In the invention according to claim 4, further,
Since the function of the C ⁿ class is a power series, the function of the C ⁿ class can be easily obtained.

In the invention according to claim 5, since the fitting is performed by the least squares method to obtain the power series, the power series can be easily obtained.

In the invention according to claim 6, claim 1 is
To the lens field described in the format of claim 5,
The orbit of charged particles is obtained by directly solving the orbit equation. In the present invention, the calculation time can be shortened even if the trajectory equation of the charged particle is directly solved, that is, solved without approximation by Taylor expansion or the like. By directly solving the charged particle trajectory equation, the charged particle trajectory can be accurately obtained.

According to the seventh aspect of the present invention, the trajectory of a charged particle emitted from an object surface under the same initial conditions is determined by the method according to any one of the first to sixth aspects and the method of determining an m-th order aberration trajectory. respectively obtained by the position of the image plane of the orbit determined by the former method R _∞, the position of the image plane of the orbit determined by the latter method as R _m, one of claims 6 to claim 1 Or determined by the method described in paragraph 1,
When the position of the image plane of the orbit of the charged particles emitted by the opening angle 0 the object plane and _{R ∞ 0, | R m -R} ∞ | / | R ∞ -R ∞ 0 | depending on, required for the calculation Trajectory calculation is performed by calculating the order of the various aberrations, and the subsequent trajectory calculation is performed by calculating the aberration trajectory according to the required order of aberrations. Become.

In the invention according to claim 8, further,
| R _m −R _∞ | / | R _∞ −R _{∞ 0} | ≦ A (A is a value determined from required accuracy and is a number of 0.3 or less), and the minimum order m of aberrations required for calculation is calculated. Since the order of aberration is used, the spot diagram obtained by the simulation does not greatly deviate from the actual spot diagram, and the accuracy that can be used for the simulation is obtained.

According to the ninth aspect of the present invention, the trajectory of a representative charged particle that has exited the object surface under the same initial conditions is determined by the method according to any one of the first to sixth aspects, and
Each of the following aberration trajectories is obtained by a method of obtaining the trajectory, the position of the trajectory obtained by the former method on the image plane is R _、, the position of the trajectory obtained by the latter method on the image plane is R _m , the vicinity of the charged particle When the position of the axial trajectory on the image plane is R ₀ , | R
_{m -R ∞ | / | R ∞} -R 0 | depending on the size, calculates determined the order of the aberration required for the subsequent trajectory calculation, carried out by determining the aberration orbit by orders of required aberration Since it is not necessary to match the shape of the spot diagram and only the position of the charged particle beam becomes important,
The order required for the calculation by the conventional method can be estimated without excess and deficiency.

According to the tenth aspect of the present invention, | R _m -R _∞ | / | R _∞ -R ₀ | ≦ B (B is a value determined from the required precision and is a number of 0.1 or less). Since the minimum order m of the aberration is set to the order of the aberration required for the calculation, the trajectory of the charged particles in the simulation does not greatly deviate from the actual trajectory, and the accuracy that can be used as a simulation is obtained. In such an invention, the trajectory of a representative charged particle that has exited the object surface under the same initial conditions is determined by the method according to any one of claims 1 to 6 and the method of determining an m-th order aberration trajectory. respectively obtained, the position of the image plane of the orbit determined by the former method R _∞, the position of the image plane of the orbit determined by the latter method when the _{R m, | R ∞ -R m} | size Required for calculation, depending on Since the order of the various aberrations is calculated and the subsequent trajectory calculation is performed by obtaining the aberration trajectory based on the required order of the aberrations, it is not necessary to match the shapes of the spot diagrams, and the absolute accuracy of the position of the charged particle beam is reduced. When necessary, the order required for the calculation by the conventional method can be estimated without excess or deficiency.

According to the twelfth and thirteenth aspects of the present invention, the ratio (1/2) ^1/2 · F / L of the field size F to the lens barrel length (distance between the object surface and the image surface) L is: a ratio R _{0 (m) max} / L of the distance R _{0 (m) max} from the optical axis on the image plane of the paraxial trajectory obtained by the method of obtaining the m-th aberration trajectory to the lens barrel length, Since m which is larger than R _{0 (m−2) max} / L is determined, and subsequent calculations are performed by obtaining the m-th order aberration trajectory, the simulation can be performed most efficiently.

[Brief description of the drawings]

FIG. 1 is a diagram showing a spot diagram of a charged particle trajectory on an image plane.

FIG. 2 is a flowchart illustrating a simulation process according to an example of an embodiment of the present invention.

FIG. 3 is a diagram showing a relationship between an on-axis lens field fitted to a Fourier series and an actual lens field.

FIG. 4 is a diagram illustrating an example of a spot diagram when a paraxial orbit is close to an optical axis.

FIG. 5 is a diagram showing an example of a spot diagram when a paraxial trajectory is slightly apart from an optical axis.

FIG. 6 is a diagram illustrating an example of a spot diagram when a paraxial trajectory is far away from an optical axis.

FIG. 7 is a diagram showing a model of a lens having an N pole and an S pole having an infinite two-dimensional size;

FIG. 8 is a diagram illustrating an example of a ratio of a distance of a paraxial trajectory from an optical axis to a lens barrel length when a shape of a lens is changed.

FIG. 9 is a diagram illustrating an example of the ratio of the distance of the paraxial orbit from the optical axis to the lens barrel length when the shape of the lens is changed.

FIG. 10 is a diagram illustrating an example of a ratio of a paraxial orbit distance from an optical axis to a lens barrel length when the shape of a lens is changed.

FIG. 11 is a diagram illustrating an example of the ratio of the distance of the paraxial orbit from the optical axis to the lens barrel length when the shape of the lens is changed.

FIG. 12 is a diagram illustrating an example of a coil having a finite size.

FIG. 13 is a flowchart showing steps of a conventional simulation.

[Description of Signs] 1 coil 2 hole piece R ₀ paraxial trajectory R… the position of the trajectory of the charged particle emitted at an angle of 0 with the object plane opened at the image plane R _∞ The position of the trajectory of the charged particle on the image plane obtained by the method of the present invention R ₃ ... The position of the trajectory of the charged particle on the image surface obtained by considering the expansion formula up to the third order by the conventional method R ₅ ... Of the orbit of the charged particle on the image plane obtained by considering the expansion formula up to the 5th order

──────────────────────────────────────────────────続 き Continued on the front page (51) Int.Cl. ⁷ Identification symbol FI Theme coat ゛ (Reference) G06F 15/60 680A

Claims (13)

[Claims] 1. A method of simulating a charged particle optical system, wherein an on-axis lens field is described in a form fitted to a ^C∞ class function, and an off-axis lens field is defined by the on-axis lens field. A method for simulating a charged particle optical system, comprising a step of solving a trajectory equation of a charged particle by describing in a differential form of a function. 2. A simulation method of a charged particle optical system according to claim 1, characterized in that the Fourier series of functions of the C ^∞ class. 3. A method for simulating a charged particle optical system, wherein an on-axis lens field is described in a form fitted to a C ⁿ class function, and an off-axis lens field is defined by the above-mentioned on-axis lens field. A method for simulating a charged particle optical system, comprising a step of solving a trajectory equation of a charged particle by describing in a differential form of a function. 4. The charged particle optical system simulation method according to claim 3, wherein said C ⁿ class function is a power series. 5. The power series according to claim 4, wherein the power series is obtained by fitting the original data by a least squares method.
The simulation method of the charged particle optical system according to 1. 6. A charged particle optical system comprising a step of directly solving a trajectory equation and obtaining a trajectory of a charged particle using a lens field described in the form according to claim 1. Simulation method. 7. A trajectory of a charged particle emitted from an object surface under the same initial condition is obtained by a method according to any one of claims 1 to 6 and a method of obtaining an m-th order aberration trajectory, respectively. The position on the image plane of the trajectory determined by the former method is denoted by R _、, and the position of the trajectory on the image plane determined by the latter method is denoted by R _m , wherein was determined by the method described, the position of the image plane of the orbit of the charged particles emitted by the opening angle 0 the object plane when the _{R ∞ 0, | R m -R} ∞ | / | R ∞ -R ∞ 0 | A method of simulating a charged particle optical system (including a step of obtaining an order of aberration required for calculation, and performing subsequent trajectory calculation by obtaining an aberration trajectory based on the order of required aberration). , | R _m -R _∞ | is the distance between R _m and R _、, | R _∞
−R _{∞ 0} | is the distance between R _∞ and R _{∞ 0} ). 8. | R _m −R _∞ | / | R _∞ −R _{∞ 0} | ≦ A (A is a value determined from required accuracy, and is a number of 0.3 or less)
The simulation method for a charged particle optical system according to claim 7, wherein the minimum order m of the aberration that is obtained is the order of the aberration required for the calculation. 9. The trajectory of a typical charged particle emitted from an object surface under the same initial condition is determined by the method according to any one of claims 1 to 6 and the method of obtaining an m-th order aberration trajectory. R _を is the position of the trajectory on the image plane obtained by the former method, R _m is the position of the trajectory on the image plane obtained by the latter method, and the position of the charged particle on the image plane of the paraxial trajectory is when the the _{R 0, | R m -R ∞} | / | R ∞ -R 0 | , depending on the size, determine the order of the aberration required for the calculation, the subsequent trajectory calculation, required aberration of order simulation method of a charged particle optical system which comprises a step of performing by determining the aberration trajectory by (wherein, | R _m -R _∞ | is the distance R _n and _{R ∞, | R ∞ -R 0} | is R _∞ and R ₀ ). 10. | R _m -R _∞ | / | R _∞ -R ₀ | ≦ B (B is a value determined from required accuracy, and is a number of 0.1 or less)
The method for simulating a charged particle optical system according to claim 9, wherein the minimum order m of the aberration that is obtained is the order of the aberration required for the calculation. 11. The trajectory of a typical charged particle emitted from an object surface under the same initial condition is determined by the method according to any one of claims 1 to 6 and the method of determining an m-th order aberration trajectory. respectively obtained, the position of the image plane of the orbit determined by the former method R _∞, the position of the image plane of the orbit determined by the latter method when the _{R m, | R ∞ -R m} | size A method of simulating a charged particle optical system (including a step of obtaining an order of aberration required for calculation, and performing subsequent trajectory calculation by obtaining an aberration trajectory based on the order of required aberration). , | R _∞ -R _m | is the distance R _∞ and R _m). 12. A trajectory of a charged particle emitted from an object surface under the same initial condition is obtained by a method according to any one of claims 1 to 6 and a method of obtaining an m-th order aberration trajectory, respectively. the position of the image plane of the orbit determined by the former method R _∞, the position of the image plane of the orbit determined by the latter method R _m, the position of the image plane of the paraxial trajectory of the charged particle R _0
Where R is the distance from the optical axis on the image plane of the paraxial orbit that sets the maximum value of | R _m −R _∞ | / | R _∞ −R ₀ | to a predetermined value.
_{0 (m) max is obtained} for each m-th order aberration trajectory, and when the lens barrel length (distance between the object plane and the image plane) is L and the field size is F, (1/2) ^1/2 · F / L is a ratio R _{0 (m) max} of the distance R _{0 (m) max} from the optical axis on the image plane of the paraxial orbit determined by a method of obtaining the m-th order aberration trajectory to the lens barrel length.
M smaller than L and larger than R _{0 (m−2) max} / L
And calculating the m-th order aberration trajectory. (However, | R _m -R _∞ | is the distance between R _m and R _、, and | R _∞ -R ₀ | is the distance between R _∞ and R _0. ) 13. A trajectory of a charged particle emitted from an object surface under the same initial condition is obtained by a method according to any one of claims 1 to 6 and a method of obtaining an m-th order aberration trajectory, respectively. The position on the image plane of the trajectory obtained by the former method is R _、, the position of the trajectory on the image surface obtained by the latter method is R _m , and the object plane obtained by the former method is open angle 0
In case the position of the image plane of the orbit of emitted charged particles and _{R ∞ 0, | R m -R} ∞ | / | R ∞ -R ∞ 0 | paraxial trajectory image of the maximum value of the predetermined value When the distance R _{0 (m) max} from the optical axis on the surface is determined for each m-th order aberration trajectory, the lens barrel length (the distance between the object plane and the image plane) is L, and the field size is F ( 1/2) ^1/2 · F / L is the distance R _{0 (m) max} from the optical axis on the image plane of the paraxial orbit determined by a method for obtaining the m-th order aberration trajectory, and the lens barrel length. _Is determined to be smaller than R _{0 (m) max} / L and larger than R _{0 (m−2) max} / L.
A method for simulating a charged particle optical system, comprising a step of performing subsequent calculations by determining an m-th order aberration trajectory. (However, | R _m -R _∞ | is the distance R _m and _{R ∞, | R ∞ -R ∞} 0 | is the distance R _∞ and R _{∞ 0.)}