JP2007018814A - Charged particle beam optical system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a charged particle beam optical system in which deflective chromatic aberration is suppressed. <P>SOLUTION: A deflection position on an image plane is assumed to be Woai (=Xoai+i Yoai) in complex coordinate, with the amount deflected by a deflector assumed as wdi (=xdi+i ydi). The aberration coefficient (corresponds to vector 3) of deflective chromatic aberration caused by energy width of charged particles is set to be proportional (in other words, to be vector 3') to wdi/Woai (corresponding to vector 1). <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a charged particle beam optical system.

  In the conventional charged particle beam apparatus, the charged particle beam optical system analysis software of MEBS (Munro ’s Electron Beam Software Ltd) is often used in the design. However, MEBS software can only evaluate chromatic aberration due to the energy dispersion of the charged particle source. Other chromatic aberrations are also caused by electromagnetic lenses. For axial and magnification rotational chromatic aberration, the optical system is optimized because there is a relationship Ki = -2Kv between the chromatic aberration coefficient Ki due to electromagnetic lens and the chromatic aberration coefficient Kv due to energy dispersion of the charged particle source. If the chromatic aberration due to the energy dispersion of the charged particle source is evaluated on the axis, the chromatic aberration due to the electromagnetic lens is naturally determined.

  However, in actuality, the deflection chromatic aberration coefficient is assumed that the deflection position on the image plane is Woai (= Xoai + I Yoai) in complex coordinates, and the part deflected by the deflector is wdi (= xdi + I ydi). Ki =-(wdi / Woai + 2 Kv). Therefore, since there is a term wdi / Woai, the deflection chromatic aberration due to the lens power supply noise does not become small if the deflection chromatic aberration due to energy dispersion is optimized.

  The present invention has been made in view of such circumstances, and an object of the present invention is to provide a charged particle beam optical system in which deflection chromatic aberration is suppressed to be small.

  The problem is that the deflection caused by the energy width of the charged particles when the deflection position on the image plane is Woai (= Xoai + i Yoai) in complex coordinates and the part deflected by the deflector is wdi (= xdi + i ydi) This is solved by a charged particle beam optical system characterized in that the aberration coefficient of chromatic aberration is set to be proportional to wdi / Woai.

  If the aberration coefficient of the deflection chromatic aberration is set in this way, the deflection chromatic aberration can be reduced. In addition, it is possible to determine the range of the deflection chromatic aberration coefficient due to energy dispersion that satisfies the blur and misalignment specifications due to the deflection chromatic aberration required for the apparatus.

  ADVANTAGE OF THE INVENTION According to this invention, the charged particle beam optical system which suppressed the deflection chromatic aberration small can be provided.

  Hereinafter, an example of an embodiment of the present invention will be described with reference to the drawings. The symbols described in the present specification and claims are vectors (complex numbers) unless otherwise specified or unless it is obvious that they are scalar quantities. In the following description, an electron beam will be described as an example of a charged particle beam. In addition, an xyz orthogonal coordinate system having the optical axis as the z-axis is used, and a subscript indicating the object plane is set as o and a subscript indicating the image plane is set as i. “′” Indicates a first-order differential with z, and “” ”indicates a second-order differential with z. The complex number represents an x component as a real part and a y component as an imaginary part.

  The paraxial equation of electron orbit w (z) is generally

Indicated by
Here, φ (z) is an on-axis potential and is equal to electron energy. That is, when there is an electrostatic lens, it changes with the voltage, and when there is no electrostatic lens, it becomes an acceleration voltage. B (z) is the axial magnetic field of the electromagnetic lens, d1 (z) is the deflection field of the electromagnetic deflector, I is the current of the electromagnetic deflector, f1 (z) is the deflection field of the electrostatic deflector, and v is the static field. The electric deflection voltage, e is the charge of the electrons, and m is the mass of the electrons.

  When obtaining the aberration, w (z) in the equation (1) is set to w (z) + dw (z), and the derivative and the second derivative are also changed correspondingly. In this case, φ (z) is φ (z) + dv for chromatic aberration due to energy dispersion, and B (z) is B (z) (1 + ΔNI / NI) for chromatic aberration due to an electromagnetic lens, and their differentiation changes correspondingly. Let Here, NI is the ampere turn of the electromagnetic lens, and ΔNI is the variation. In this way, the aberration term dw (z) is calculated.

  In this way, from equation (1),

Can be written.
Pc (z) is chromatic aberration due to energy dispersion,

In the case of chromatic aberration due to electromagnetic lenses,

It becomes.

  On the other hand, the chromatic aberration at the image plane is

It becomes.

  here,

Indicates the complex co-divisor of w _a (z) (in other cases, the symbol above the symbol indicates the complex co-divisor of the symbol), and w _a (z) is light on the object plane. It represents a paraxial trajectory emitted from the axis with an inclination of 1 and returning to the optical axis at the image plane. or

Is

Represents the inclination on the image plane.

  When the optical system consists of only an electromagnetic lens and an electromagnetic deflector, in the case of chromatic aberration due to energy dispersion,

In the case of chromatic aberration due to electromagnetic lenses,

Chromatic aberration at the image plane is

It becomes.

  In the case of a trajectory that is not a deflection trajectory, clearly, in the case of chromatic aberration due to energy dispersion,

In the case of chromatic aberration due to electromagnetic lenses,

here,

far. Where dwv and dwi are chromatic aberration caused by energy dispersion and chromatic aberration caused by ampere-turn fluctuation of the electromagnetic lens, Kv and Ki are aberration coefficients of the respective deflection chromatic aberration, and wi is an opening on the image plane. Indicates the amount determined by corner or image height.
In this way, from the previous equation,

Is obtained, and Ki = −2 Kv as described above.

  On the other hand, for deflection chromatic aberration, an equation derived from a paraxial equation

In the case of chromatic aberration due to energy dispersion,

Will not change,

In the case of chromatic aberration due to electromagnetic lenses,

Chromatic aberration at the image plane is

Since the first term of the equation (19) can be partially integrated, and the portion of the conjugate complex number of w _a (z) is 0 on the object plane and the image plane, the equation (19) is

It can be expressed as.
Therefore,

At this time, if the deflection trajectory is on the axis, Wm (Z _o ) = 0.
Ki = -1-2Kv… (22)
On the other hand,

Track coming out of off-axis is the sum of the track when driving the only deflector trajectory (w _b orbits in consideration of the image height) due to the image height. Therefore,

The first term on the right side is the deflection amount of the orbit due to the image height, and the second term is the deflection amount of the deflector alone. M is the complex image magnification including magnification and rotation

It is represented by
Than this,

Here, w _m (z _i ) is written as Woai according to the terminology of MWNS software. That is, as mentioned above,
Ki =-(wdi / Woai + 2 Kv)… (26d)
FIG. 1 is a diagram showing the principle of the first embodiment of the present invention. In the following description, the deflection position on the image plane is Woai (= Xoai + i Yoai) in complex coordinates, and the part deflected by the deflector is wdi (= xdi + i ydi). The deflection chromatic aberration due to energy dispersion is Kv · Woai · ΔV / V because Wi in equation (9) is equal to woai. Further, the deflection chromatic aberration due to the lens power supply noise is Ki · Woai · ΔNI / NI because Wi in equation (10) is equal to woai. Here, Kv is a deflection chromatic aberration coefficient due to energy dispersion, Ki is a deflection chromatic aberration coefficient due to lens power supply noise, and Woai is a deflection position. All are complex numbers (vectors). ΔV represents energy dispersion, V represents acceleration voltage, ΔNI represents lens power supply noise, and NI represents lens current. These are all real numbers (scalar quantities).

  Deflection chromatic aberration due to energy dispersion is always blurred because charged particles having different energies always reach the image plane. On the other hand, the deflection chromatic aberration due to the lens power supply noise changes due to the power supply noise. If the power supply noise changes at high speed, it will be blurred, but if it changes at low speed, it will be misaligned. For example, in the case of SEM, if the noise is high speed, the beam corresponding to each pixel oscillates and blurs, but if it is slightly slower than this, it will be misaligned during one scan, and it is about the same as one screen scan. In the case of medium speed, distortion occurs in the Y direction, and when the speed is further reduced, the position changes for each screen. In SEM, when the observation position is shifted from the optical axis and observed at a high magnification, Woai becomes large, so it becomes very conspicuous.

  On the other hand, in the case of a transfer exposure apparatus, since the deflection is large, and the joining accuracy and overlay accuracy become important, the specification of positional deviation (the amount allocated from the budget regarding positional deviation) is stricter than the blur. It has become. Therefore, emphasis is placed on the fact that the deflection chromatic aberration due to the lens power supply noise corresponding to the low-speed noise satisfies the positional deviation specification. In that case, Ki is a complex coordinate radius if dpos is a position deviation allowed from the specification.

Any point inside the circle represented by At this time, the deflection chromatic aberration coefficient due to energy dispersion is derived from the equation (26d):
Kv =-(wdi / Woai + Ki) / 2
There is a relationship. In a transfer exposure apparatus, a subfield far from the optical axis is generally illuminated by a reticle surface, which is the object surface, and the charged particles transmitted therethrough expose a subfield far from the optical axis of the wafer surface, which is the image plane, through the projection optical system. become. (24) In the _formula, w m _{(z i)} is the _Woai, w d _{(z i)} corresponds to the WDI. w _m (z _o ) is the position of the exposure subfield on the reticle surface, and evaluation is performed in the subfield that is maximum deflected at the time of design. Therefore, if the subfield that is maximum deflected is determined, w _m (z _o ), w _m ( Since z _i ) is determined and the complex magnification M is determined by the projection lens, the deflection amount wdi by only the deflector is also uniquely determined.

  Therefore, in the previous equation, wdi / Woai is a complex constant. This relationship is illustrated in FIG. In FIG. 1, vector 1 indicates -wdi / (2Woai) as a vector, vector 2 indicates -Ki / 2 as a vector, and vector 3 indicates Kv as a vector. Since vector 2 and vector 3 are proportional to the magnitude of deflection chromatic aberration, it is necessary to make them as small as possible, but obviously, vector 2 'and vector 3', which are projections of vector 2 and vector 3 onto vector 1, Since the length of the vector is shortened, the deflection chromatic aberration can be reduced. That is, the deflection chromatic aberration coefficient Kv is preferably proportional to wdi / Woai which is a complex constant. At this time, Ki is automatically proportional to wdi / Woai. In FIG. 1, for the convenience of illustration, the positions of the vector 1 and the vectors 2 ′ and 3 ′ are drawn different from each other, but actually they overlap.

  FIG. 2 is a diagram for explaining the principle of the second embodiment and the third embodiment of the present invention. FIG. 2 shows the deflection chromatic aberration coefficient due to energy dispersion in complex coordinates when the chromatic aberration due to power supply noise is misaligned. In FIG. 2, the same components as those shown in FIG. Vector 1 represents -wdi / (2Woai), and circle 4 represents a range in which the deflection chromatic aberration due to power supply noise satisfies the positional deviation tolerance specification. As mentioned above, Ki is a complex coordinate and the radius is dpos if the position deviation allowed from the specification is dpos.

2 is drawn in the coordinates of Kv and has the relationship of Equation 26d, so that the circle 4 has a radius of this radius value around the tip of the vector 1 It is a circle.

  On the other hand, if the maximum value of the blur allowed from the specification (bokeh budget allocated to the deflection chromatic aberration due to energy dispersion) is dblur, the vector representing the deflection chromatic aberration coefficient Kv has a radius of

It only has to be inside the circle represented by. A circle 5 represents a circle whose center is the origin and whose radius is this value.

  As shown in the first embodiment, if the deflection chromatic aberration coefficient Kv is proportional to wdi / Woai which is a complex constant, the vector indicating Ki is a vector from the tip of vector 1 toward the origin. The allowable maximum value is when the tip is on the circle 4. At this time, due to the geometric relationship, the deflection chromatic aberration coefficient Ki due to the lens power supply noise is

It becomes.

  That is, from equation (27)

Because deflection chromatic aberration is proportional to wdi / Woai
Ki = ratio ・ wdi / Woai ・ (ratio is a real proportional constant)
Therefore, Ki · Woai = ratio · wdi
dpos ≧ | ratio | ・ | wdi ｜ ・ ΔNI / NI
| ratio | ≦ dpos / | wdi | ・ NI / ΔNI
When the deviation of the chromatic aberration due to the lens power supply can be increased to the specified value
| ratio | = dpos / | wdi | ・ NI / ΔNI
Since the sign is clearly negative, the deflection chromatic aberration coefficient due to lens power supply noise is

Deflection chromatic aberration coefficient due to energy dispersion

If so, the deflection chromatic aberration positional deviation specification due to power supply noise is satisfied, and the deflection chromatic aberration blur due to energy dispersion can be minimized. As a design, if energy dispersion and power supply noise are anticipated and the deflection chromatic aberration positional deviation specification due to power supply noise is determined, the above Kv value is obtained, and the optical system may be optimized to approach that value.

In the third embodiment of the present invention, the blur due to the deflection chromatic aberration is within an allowable range, and the positional deviation is minimized. From equation (28)
dblur ≧ | Kv ・ Woai | ・ ΔV / V
It becomes. Also in the present embodiment, the deflection chromatic aberration is proportional to wdi / Woai as in the first embodiment.
Kv = ratio ・ wdi / Woai (ratio is a proportional constant and a real number)
Therefore, Kv · Woai = ratio · wdi
dblur ≧ | ratio | ・ | wdi | ・ ΔV / V
| ratio | ≦ dblur / | wdi | ・ V / ΔV
When the deflection chromatic aberration position blur due to energy dispersion can be increased to the specified value
| ratio | = dblur / | wdi | ・ V / ΔV
Since the sign is clearly negative, the deflection chromatic aberration coefficient due to lens power supply noise is

Deflection chromatic aberration coefficient due to energy dispersion

By doing so, it is possible to keep the blur due to the deflection chromatic aberration within an allowable range and to minimize the positional deviation.

  In the fourth embodiment of the present invention, a vector indicating deflection chromatic aberration due to energy dispersion and a vector indicating deflection chromatic aberration due to lens power supply noise are proportional to the vector 1 in FIG. It is to be in the part where 5 overlaps. In this way, both the blur caused by the deflection chromatic aberration and the positional deviation can be within the range determined by the specifications. Such a condition is that the deflection chromatic aberration coefficient due to the lens power supply noise is determined from the description of the second embodiment and the third embodiment.

Deflection chromatic aberration coefficient due to energy dispersion

It is clear that this can be realized by setting so that. Further, if Kv enters a region where a product set of the inner side of the circle 4 and the inner side of the circle 5 is taken, the specification is satisfied with respect to the blur position deviation.

  The fifth embodiment of the present invention will be described below. When power supply noise (fluctuation in ampere-turn of electromagnetic deflector) is high frequency and deflection chromatic aberration due to power supply noise is blurred, it causes blurring regardless of deflection chromatic aberration due to energy dispersion and deflection chromatic aberration due to power supply noise. May be set to a value that minimizes the sum of squares of the blur generated by. When considering minimizing the sum of squared blurs, the Woai term is ignored because it is common to deflection chromatic aberration due to energy dispersion and deflection chromatic aberration due to power supply noise.

Solving these simultaneous equations with Kvx and Kvy differentials as 0,
The x and y components of the aberration coefficient of deflection chromatic aberration due to the energy dispersion of the charged particle source are

At this time, the minimum blur occurs. This value may be calculated and optimized so that the deflection chromatic aberration coefficient due to energy dispersion becomes the above value.

It is a figure which shows the principle of the 1st Embodiment of this invention. It is a figure for demonstrating the principle of the 2nd Embodiment of this invention, and 3rd Embodiment.

Explanation of symbols

1 ... vector representing -wdi / (2Woai), 2 ... 2 '... minimum vector vector 2 representing deflection chromatic aberration due to lens power supply noise, 3 ... vector representing deflection chromatic aberration due to energy dispersion, 3' ... vector 3 4 is a circle representing deflection chromatic aberration due to lens power supply noise corresponding to the tolerance of misalignment, and 5 is a circle representing deflection chromatic aberration due to energy dispersion corresponding to the tolerance of blurring.

Claims (6)

When the deflection position on the image plane is Woai (= Xoai + i Yoai) in complex coordinates and the part deflected by the deflector is wdi (= xdi + i ydi), the deflection chromatic aberration caused by the energy width of the charged particles A charged particle beam optical system characterized in that the aberration coefficient is set to be a real number multiple of wdi / Woai. 2. The charged particle beam optical system according to claim 1, wherein when the required beam position accuracy range is dpos, the deflection chromatic aberration coefficient due to lens power supply noise is

Deflection chromatic aberration coefficient due to energy dispersion

A charged particle beam optical system characterized by that.
Where NI is the ampere turn of the electromagnetic lens, and ΔNI is the amount of variation. The charged particle beam optical system according to claim 1, wherein a deflection chromatic aberration coefficient due to lens power supply noise when a required beam blur range is dblur,

Deflection chromatic aberration coefficient due to energy dispersion

A charged particle beam optical system characterized by that.
However, V is an acceleration voltage and ΔV is energy dispersion. 2. The charged particle beam optical system according to claim 1, wherein when the required position accuracy range is dpos and the required beam blur range is dblur, the deflection chromatic aberration coefficient due to lens power supply noise is

Deflection chromatic aberration coefficient due to energy dispersion

A charged particle beam optical system characterized by being set to be
Where NI is the ampere turn of the electromagnetic lens, ΔNI is the amount of variation thereof, V is the acceleration voltage, and ΔV is the energy dispersion. When the acceleration voltage of the charged particle source is V, the energy dispersion is ΔV, the ampere turn of the electromagnetic lens is NI, and the variation is ΔNI, the x component Kvx, y component of the aberration coefficient of deflection chromatic aberration due to the energy dispersion of the charged particle source Kvy

A charged particle beam optical system characterized by being set to be
Where NI is the ampere turn of the electromagnetic lens, ΔNI is the amount of variation thereof, V is the acceleration voltage, and ΔV is the energy dispersion. The deflection position on the image plane is Woai (= Xoai + i Yoai) in complex coordinates, the amount deflected by the deflector is wdi (= xdi + i ydi), the required beam position accuracy is dpos, and the blur accuracy is When dblur is set, the radius is centered on the origin

The inside of the circle and

A charged particle beam optical system, characterized in that a deflection chromatic aberration coefficient Kv due to energy dispersion is set at a point in a product set with the inside of a circle.
Where NI is the ampere turn of the electromagnetic lens, ΔNI is the amount of variation thereof, V is the acceleration voltage, and ΔV is the energy dispersion.

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