Exposure system and exposure method

An exposure system and exposure method able to obtain a transfer pattern matching to a high precision an offset of an underlying pattern of an exposed member and improving an overlay accuracy of the underlying pattern and transfer pattern. The system and method swing an electron beam back and forth for periodically repeated forward direction correction and reverse direction correction for distortion of an underlying pattern, where “forward direction correction” means making a position over the offset of the underlying pattern an electron beam target position and “reverse direction correction” means making a position not reaching the offset of the underlying pattern the electron beam target position. Electron beam sub-deflection correction is performed to control an incidence angle of the electron beam to a mask so as to be irradiated at these positions. The desired transfer pattern is obtained by overlaying exposure by the forward direction correction and exposure by the reverse direction correction.

RELATED APPLICATION DATA

The present application claims priority to Japanese Application(s) No(s). P2003-194460 filed Jul. 9, 2003, and P2004-020202 filed Jan. 28, 2004, which application(s) is/are incorporated herein by reference to the extent permitted by law.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an exposure system and an exposure method, more particularly to an exposure system and exposure method controlling an incidence angle of charged particles to a mask arranged facing a wafer to correct a position of a transfer patter in accordance with distortion of an underlying pattern of the wafer.

2. Description of the Related Art

Japanese Unexamined Patent Publication (Kokai) No. 11-135423 discloses low energy electron beam proximity projection lithography (LEEPL), which brings a stencil mask into proximity with a wafer for exposure, using an electron beam sub deflection function to control the direction of an electron beam (EB) to correct offset between a pattern of the mask and an underlying pattern on the wafer.

Japanese Unexamined Patent Publication (Kokai) No. 2003-59819 discloses complementary exposure enabling exposure of a donut shaped pattern or a leaf pattern by a stencil mask by dividing that pattern of the mask into two or more parts. To perform complementary exposure efficiently, the complementary patterns are formed adjacent to each other on the mask and exposed at one time.

If an underlying pattern of a wafer has drastic distortion at an area narrower than the EB diameter, when correcting distortion between the underlying pattern and a transfer pattern by electron beam sub-deflection, a low pass filter effect caused by the electron beam intensity distribution causes insufficient correction and residual distortions. Such drastic distortion occurs due to the magnification, rotation, or offset of the center of gravity of the chip and has to be corrected by electron beam sub-deflection. In complementary exposure, insufficient correction is caused by the electron beam being simultaneously focused on the chips at the two sides of a strut.

For decreasing the residual distortion remaining even with the electron beam sub-deflection function, it is effect to make the EB diameter smaller. However, due to following reasons, the EB diameter is difficult to make smaller.

LEEPL uses as a current source a cathode formed by LaB6. The electrons emitted from the cathode radiate from points on the surface of the cathode with a spreading angle. If the amount of current emitted from a unit area of the surface of the cathode to a unit solid angle is defined as the luminance, the electron beam optical system emitting the electron beam to the mask is maintained at a constant luminance if ignoring Coulomb interaction. Therefore, since the luminance is not increased due to Coulomb interaction, if focusing the electron beam finely, the convergence angle of the electron beam is increased.

However, if the electron beam convergence angle increases, the resolution of a transfer pattern drops. On the other hand, if maintaining the resolution constant and making the electron beam smaller in diameter, the amount of current drops. The exposure time is an important factor determining LEEPL performance. If the electron beam is made low in current, the exposure time becomes longer, so becomes a primary factor behind the drop in throughput. Further, the luminance of a cathode is limited by its material, so making the cathode higher in luminance so as to make up for amount of current and maintain resolution is difficult.

The above discussion concerned the theoretical limits. However, even within the theoretical limits, for maintaining the resolution and the exposure time while making the EB diameter smaller, the electron beam optical system has to be made higher in performance, so the cost increases. If making the cathode larger in size and larger in current to shorten the exposure time and improve the throughput of the exposure system, the EB diameter ends up becoming large due to the unchanging luminance. Therefore, there are limits to the reduction of the EB diameter.

SUMMARY OF THE INVENTION

An object of the present invention is to provide an exposure system and exposure method able to obtain a transfer pattern matching with a high precision the distortion of an underlying pattern of an exposed member and able to improve an overlay accuracy of the underlying pattern and the transfer pattern.

To achieve the above object, according to a first aspect of the present invention, there is provided an exposure system having a mask arranged at a position facing to an exposed member having an underlying pattern and formed with a pattern to be transferred to the exposed member, a charged particle beam scanning means for scanning the mask by a charged particle beam, and an incidence angle controlling means for controlling an incidence angle of the charged particle beam to the mask so as to make forward direction correction and reverse direction correction of the position of the transfer pattern with respect to distortion of the underlying pattern.

In the exposure system of the present invention, the charged particle beam used for the scanning by the charged particle beam scanning means is controlled in its incidence angle to the mask by the incidence angle controlling means and irradiated to the exposed member. The incidence angle controlling means controls the incidence angle of the charged particle beam to make forward direction correction and reverse direction correction for the distortion of an underlying pattern of the exposed member the required number of times. Note that, in the present invention, “forward direction correction” means making a position over the distortion (offset) of the underlying pattern the electron beam target position, while “reverse direction correction” means making a position not reaching the offset of the underlying pattern the electron beam target position. Due to this, latent images to the exposed member are overlaid in the forward direction correction and the reverse direction correction and, as a result, a transfer pattern distorted to match with the distortion of its underlying pattern can be obtained.

According to a second aspect of the present invention, there is provided an exposure method for arranging a mask facing an exposed member having an underlying pattern and forming a transfer pattern on the exposed member by a charged particle beam passing an aperture pattern formed in the mask, comprising a step of scanning the mask by the charged particle beam controlled an incidence angle of that to the mask so as to make forward direction correction and reverse direction correction of the position of the transfer pattern and forming the transfer pattern at the exposed member.

In the exposure method of the present invention, the incidence angle of the charged particle beam is controlled so as to make forward direction correction and reverse direction correction for distortion of the underlying pattern caused by the warping of the exposed member. Due to this, latent images to the exposed member are overlaid in the forward direction correction and the reverse direction correction and, as a result, a transfer pattern distorted to match with the distortion of its underlying pattern can be obtained.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, preferred embodiments of an exposure system and exposure method of the present invention will be explained with reference to the attached drawings.

First Embodiment

FIG. 1is a view of the general configuration of an exposure system according to a first embodiment of the present invention. An exposure system shown inFIG. 1is an equal magnification proximity exposure system using a low acceleration voltage electron beam.

The exposure system has an electron gun2for emitting an electron beam EB, a condenser lens3for making the electron beam EB parallel, an aperture4for restricting the electron beam EB, a pair of main deflectors5and6for deflecting the electron beam EB so that it strikes a stencil mask SM perpendicularly in a raster or vector scan mode while remaining parallel, and a pair of sub-deflectors7and B for deflecting the electron beam so as to adjust an incidence angle to the stencil mask.

The main deflectors5and6and the sub-deflectors7and8are connected to a control unit10outputting a signal for controlling the deflection of the electron beam by the deflectors5to8. Note that while not shown, the control unit10is also connected to the electron gun2etc. and controls operation of the entire system. The main deflectors5and6and the control unit10correspond to the electron beam scanning means of the present invention, while the sub-deflectors7and8and the control unit10correspond to the incidence angle controlling means of the present invention. The control unit10corresponds to a compensation signal generating means of the present invention, while the sub-deflectors7to8correspond to the deflecting means.

The exposure system uses low energy electrons, so uses a stencil mask SM formed with patterns comprising apertures.FIG. 2Ais a perspective view of an example of the stencil mask, whileFIG. 2Bis a cross-sectional view of the stencil mask shown in FIG.2A.

As shown inFIG. 2A, the stencil mask is comprised of an about 10 nm to 10 μm thin film22of silicon etc. formed with not shown patterns comprised of apertures and is partitioned by lattice-like struts (beams)23for reinforcing the thin film.

As shown inFIG. 2B, the stencil mask is formed for example by an SOI substrate, and, is comprised of a silicon substrate20, an etching stopper film21made of silicon oxide etc., and a thin film22formed by an SOI layer. The silicon substrate20and the etching stopper film21are processed to form the struts23. The thin film22partitioned by the struts23is formed with patterns P comprising apertures. Note that the stencil mask is not limited in its material and may be formed without utilizing an SOI substrate.

FIG. 3is a view for explaining an exposure operation using the above exposure system. Note that the struts of the stencil mask are not shown inFIG. 3is.

Electron beam EB passing through an aperture of the stencil mask SM exposes a not shown resist on a wafer W. The exposure system shown inFIG. 1employs equal magnification exposure, so the stencil mask SM and the wafer W are arranged in proximity.

In exposure, the control unit10controls the main deflectors5and6to scan the stencil mask SM by the electron beam EB so as to transfer patterns of the stencil mask to the wafer W. Further, the control unit10outputs a signal for controlling the deflection angle of electron beam to the sub-deflectors7and8. The sub-deflector7and8tilt the direction of the electron beam EB slightly to a normal V of the mask. Due to this, a transfer pattern is transferred displaced in position (distorted) so as to overlap an underlying pattern WP warped from its accurate position on the wafer W. In the present specification, “correction of distortion” means forming a transfer pattern distorted to match the distortion of its underlying pattern.

In LEEPL alignment, correction of distortion of an underlying pattern caused by system error is indispensable for achieving overlay accuracy. In the related art, as shown inFIG. 3, the electron beam EB was deflected by the electron beam sub-deflection function so that the center of the electron beam passing through the stencil mask SM overlapped the underlying pattern WP formed by a scanner etc.

[Examination of Characteristics of Electron Beam Sub-Deflection Correction]

FIG. 4Ais a view for explaining characteristics of electron beam sub-deflection correction. The changes in position of a transfer pattern due to a electron beam sub-deflection function were examined in detail. As a result, it was found that distortion G(x) of a transfer pattern after electron beam sub-deflection correction may be expressed by the following equation:
G(x)=g(x)*K(x)  (1)

where, “g(x)” is the offset of the underlying pattern on the wafer with reference to the mask pattern (distortion of the underlying pattern), “K(x)” is the electron beam intensity distribution before passing through the mask, an “*” is convolution. “G(x)” is the offset of the transfer pattern with reference to the mask pattern after exposure (distortion of transfer pattern).

In equation (1), the distortion “G” of the transfer pattern after electron beam sub-deflection correction can be considered the distortion obtained by applying a Fourier transform E of the electron beam intensity distribution K(x) as a filter to the distortion g of the underlying pattern.

FIG. 4Bis a view showing the value E obtained after a Fourier transform of the electron beam intensity distribution K(x). As clear by applying a Fourier transform to equation (1), the value E indicates the correction efficiency for each frequency of distortion when correcting distortion of an underlying pattern. InFIG. 4B, the “f” of the abscissa corresponds to the spatial frequency of the distortion of the underlying pattern.FIG. 4Bshows an example in the case of calculation assuming the electron beam intensity distribution K(x) is a Gaussian distribution of a full width at half maximum of 500 μm.

As shown inFIG. 4B, when using electron beams having the same EB diameter, the larger the spatial frequency f of distortion of an underlying pattern, the smaller the distortion compensation efficiency. Therefore, the value E of the Fourier transform of the electron beam intensity distribution K(x) can be used as a low pass filter.

From equation (1), to obtain a transfer pattern having a distortion accurately matching distortion of an underlying pattern of the wafer by electron beam sub-deflection correction, it is sufficient that the EB diameter be made smaller. However, as explained above, the EB diameter is limited by the current density of the cathode or the cathode material, so if making the EB diameter smaller, the amount of the current falls. Therefore, the throughput falls and the productivity drops. Accordingly, the EB diameter is difficult to make smaller.

In this way, when there is drastic distortion at an underlying pattern on the wafer, if performing sub-deflection correction so that the center of the electron beam overlaps the underlying pattern, the obtained transfer pattern will not accurately match with the underlying pattern and residual distortion G(x)−g(x) will occur. If making the EB diameter smaller, the distortion correction efficiency will rise, but there are limits to the reduction of the EB diameter.

FIGS. 5A,5B, and5C are graphs for explaining an example of occurrence of residual distortion in the case of correcting drastic distortion of an underlying pattern by electron beam sub-deflection correction of the related art.

FIG. 5Ashows an example of the intensity distribution of the electron beam used,FIG. 5Bshows distortion (offset) of an underlying pattern near a chip boundary (corresponding to a strut in a mask), andFIG. 5Cshows the residual distortion after transfer by sub-deflection correction.

As shown inFIG. 5A, it is assumed that the electron beam intensity follows a Gaussian distribution and assumed that an electron beam having a full width at half maximum of 350 μm is used. Further, the case of using this electron beam to correct offset (distortion) of ±10 nm at chips adjoining each other across a distance of 250 μm as shown inFIG. 5Bis assumed.

When correcting distortion under these conditions, from equation (1), the result is the residual distortion shown in FIG.5C. The drastic distortion shown inFIG. 5Boccurs in magnification, rotation, or offset in the underlying pattern of a chip. As shown inFIG. 5C, it is learned that a 40% residual distortion is present for an pattern offset of ±10 mm. This cannot be neglected.

[Electron Beam Sub-deflection Correction Method According to First Embodiment]

Therefore, the present embodiment generates a compensation signal to be output to the sub deflectors7and8for correcting an underlying pattern WP on the wafer as follows.

As explained above, the electron beam deflection correction method of the related art cannot completely correct finely fluctuating high frequency components in distortion of an underlying pattern due to a low pass filter effect of the value E after Fourier transform of the electron beam intensity distribution K (serving as the distortion correction efficiency) and residual distortion occurs. Therefore, to reduce the residual distortion after correction, it is sufficient to apply a compensation filter T of equation (2) for canceling out the filter value E to an electron beam deflection signal.
T=1/E(2)

Here, the “electron beam deflection signal” is a signal of the EB deflection angle in the case of setting a target position so that the center of the electron beam overlays a distorted underlying pattern. The compensation filter T is a reciprocal of the value E at each frequency and increases as the frequency becomes higher. That is, it is a high pass filter. Therefore, it emphasizes offset compensation of a transfer pattern.

The compensation filter T diverges exponentially, so even at a high frequency where it becomes so small that the Fourier transform F(g) of the distortion g of an underlying pattern can be neglected, the value obtained by applying the compensation filter T to F(g) diverges. Therefore, the filtered signal TF(g) also diverges.

For avoiding such divergence, it is necessary to cut off the compensation filter T at a finite frequency region ft (cutoff frequency). However, when making the chip interval (corresponding to the strut width at a mask) Wb and the frequency fb=1/(2Wb), if ft<fb, pattern distortion near the chip boundaries cannot be resolved, so a sufficient compensation effect cannot be obtained. The “fb” substantially matches with the center frequency of a spectrum obtained by applying a Fourier transform to distortion of a transfer pattern. Therefore, it is necessary that Ft>fb. The result of calculation for ft=2fb and ft=1.2fb will be explained next.

(1) Case of Cutoff Frequency ft=2fb

FIG. 6Ais a graph of the compensation filter T1in the case of a cutoff frequency ft=2fb,FIG. 6Bis a graph of the electron beam correction target position CV1based on a compensation signal generated by application of the compensation filter T1, whileFIG. 6Cis a graph of residual distortion comprised of the difference between the transfer pattern and the underlying pattern after correction. Note that “Wb” is 250 μm as an example.

When applying the compensation filter T1to the deflection signal at a broad frequency area 2fb as shown inFIG. 6A, the residual distortion decreases until around ±0.5 nm as shown in FIG.6C. However, as shown inFIG. 6B, due to the divergence effect of the compensation filter T1, the amplitude of the compensation signal also diverges. The electron beam correction target position CV1is the position of irradiation targeted by the electron beam sub-deflection performance and corresponds to the compensation signal. The compensation signal is generated and output by the control unit10. Further,FIG. 6Balso shows the distortion G of an actual transfer pattern exposed by the electron beam correction target position CV1.

FIG. 6Bshows that by swinging back and forth the electron beam targeting the electron beam correction target position CV1, the latent images are overlaid and as a result finally the transfer pattern shown by G is obtained. However, the swing of the electron beam is too much larger than the pattern to be resolved, so it is impossible to overlap the images to obtain a transfer pattern in practice. Therefore, the problem arises that resolution of the transfer pattern cannot be obtained.

(2) Case of Cutoff Frequency ft=1.2fb

FIG. 7Ais a graph showing a compensation filter T2in the case of the cutoff frequency ft=1.2fb,FIG. 7Bis a graph of an electron beam correction target position CV2based on a compensation signal generated by applying the compensation filter T2, whileFIG. 7Cis a graph of the residual distortion comprised of the difference between the transfer pattern and the underlying pattern after correction, Note that “Wb” is 250 μm as an example.

When applying the compensation filter T2to the deflection signal at the frequency region 1.2fb as shown inFIG. 7A, as shown inFIG. 7B, the divergence effect of the compensation filter T2decreases and the compensation signal for swinging back and forth the electron beam at the electron beam correction target position CV2becomes about 20 nm or the same extent as the distortion g of the underlying pattern, so the resolution can be maintained. InFIG. 7B, ““G” is the distortion G of an actual transfer pattern exposed by the electron beam correction target position CV2. The residual distortion at that time is around ±1.5 nm as shown in FIG.7C.

In the above electron beam sub-deflection correction, there is a tradeoff between the residual distortion and resolution. However, the cutoff frequency of the compensation filter T may be adjusted to select the optimal conditions. From the above, the cutoff frequency ft of the compensation filter T has to be larger than “fb”. However, if too large, the electron beam correction target position will diverge and the resolution will drop. The most suitable range of the cutoff frequency is as shown in the following equation;
fb<ft<ln(μ/ρ)fb(3)

In equation (3), “μ” is the resolution dimension, and “σ” is the magnitude of offset.

As explained above, in the present embodiment, a compensation filter for canceling out the low pass filter effect of the electron beam intensity distribution (high pass filter) is generated using a Fourier transform. The compensation filter is applied to the electron beam deflection signal to generate a compensation signal.

The compensation signal obtained by the above, as shown inFIG. 7B, makes the electron beam swing back and forth so as to periodically repeat forward direction correction and reverse direction correction for the distortion g of the underlying pattern. “Forward direction correction” means to make a position over the offset of the underlying pattern the electron beam target position, while “reverse direction correction” means to make a position not reaching the offset of the underlying pattern the electron beam target position. Based on the compensation signal output from the control unit10, the sub deflectors7and8deflect the electron beam so as to control the incidence angle of the electron beam to the mask. The latent images of the forward direction correction and the latent images of the reverse direction correction can be overlaid to obtain the desired transfer pattern.

Further, as explained with reference toFIG. 7B, the forward direction correction and the reverse direction correction are preferably repeated by a period and amplitude so that overlay of latent images of forward direction correction and latent images of reverse direction correction gives the resolution of the transfer pattern. For obtaining a compensation signal of that period and amplitude, as explained above, the cutoff frequency of the compensation filter T is adjusted.

According to the exposure system and the exposure method of the present embodiment, a transfer pattern having distortion matching with a high precision the distortion of the underlayer pattern of the wafer can be obtained and the overlay accuracy of the underlying pattern and the transfer pattern can be improved. For example, if the full width at half maximum of the electron beam is 350 μm and the strut width is 250 μm, the residual distortion can be reduced to around 1 nm.

Further, even if the EB diameter of the electron beam used becomes enlarged, the residual distortion can be reduced with a high precision, so the electron beam can be made higher in current to enable reduction of the exposure time. Therefore, the throughput of the exposure system can be improved. Note however that to obtain the resolution of the transfer pattern, the EB diameter of the electron beam used is preferably made the same or smaller than the strut width.

The patterns of a semiconductor device produced by using the exposure system and the exposure method according to the present embodiment are characterized in that offsets of the transfer patterns shown by G inFIG. 7Bbecome periodic.

Second Embodiment

In the first embodiment, the compensation signal for correcting distortion of an underlying pattern was obtained by using a Fourier transform. In the second embodiment, a wavelet transform is used.

As shown in equation (1), the distortion G of a corrected transfer pattern is expressed by a convolution of the distortion g of the correction target and the electron beam intensity distribution K. When an m-dimensional vector having as elements target positions Xi(compensation signal) for control of the electron beam deflection angle is “v” and an n-dimensional vector having as elements position xiof points of the underlying pattern to be corrected is “q”, equation (1) may be expressed by a matrix equation as shown by equation (4):
q=M·v(4)

“M” is an n×m system matrix. Its elements mijare mij=K(xi−Xj) using the normalized intensity distribution K of the electron beam. The order “m” is the number of data points when sampling by a frequency not less than 2fmaxwhere the maximum frequency of the Fourier spectrum of the electron beam intensity distribution is “fmax”. At that time, it is guaranteed that the electron beam intensity distribution can be accurately reproduced by a sampling theorem. Here, “fmax” is the frequency where the magnitude of the spectrum becomes small enough to be ignored. The system matrix is a matrix for expressing convolution of equation (1) by a matrix equation.

By finding a “v” satisfying equation (4) (solution of equation (4)), a “v” suitable for correction of the distortion of the underlying pattern (corresponding to compensation signal) is obtained. However, if solving equation (4) as it is, the disadvantage explained below occurs, so in the present embodiment, an approximate solution v″ is found using a wavelet transform.

(1) When n>m, in general “v” can be obtained by the least square method, but by using a wavelet transform, the magnitude of the frequency component contained in the approximate solution v″ (becoming the compensation signal) can be adjusted. Therefore, a compensation signal suitable for electron beam deflection correction can be obtained. As explained later, a low frequency component near the mother wavelet is extracted and used to obtain a v″, suitable for control of the electron beam sub-deflection.

(2) When n=m, “v” is unambiguously determined, bu7t this “v” may not necessarily be suitable for electron beam sub-deflection correction. Therefore, even if residual distortion remains, it is necessary to find the approximate solution v″ suitable for electron beam sub-deflection correction. Note that, the residual distortion at the time of electron beam sub-deflection correction using the approximate solution v″ has to be in the permissible range. To find this v″, a wavelet transform is effective. For the calculation method, as explained later, the same technique as in the above (1) is used.

(3) When n<m, (2) is an unsuitable linear system, so in general “v” is not determined. Therefore, for example, “v” unsuitable for control of electron beam sub-deflection correction, such as including a high frequency component, is included. However, as explained later, by using a technique similar to the case of (1), a v″ suitable for control of electron beam sub-deflection correction can be obtained.

In this way, regardless of the magnitude of the order “n” of the input vector and the order “m” of the unknown vector, equation (4) can give an approximate solution v″ by the technique explained below using a wavelet transform. Equation (4) is expressed by the following equation (5) by application of a wavelet transform:
Wn·q=(Wn·M·WmT)·(Wm·v)  (5)

In equation (5), “Wm” and “Wn” are wavelet transform matrixes. For the basis functions forming the transform matrixes, Haar basis or other orthogonal basis can be used. “WmT” expresses a transpose matrix of “Wm” and is an inverse matrix “Wm”.

Here, if expressing the operations of equation (5) by the following equations (6), equation (5) may be expressed by the following equation (7):
Q=Wn·q
Mw=Wn·M·WmT
V=Wm·v(6)
Q=Mw·V(7)

A wavelet transform by nature results in data of the system matrix M being converged near the mother wavelet (M1,1) expressing the average information of the data. Therefore, by extracting a square matrix near the mother wavelet of “Mw” after the wavelet transform of the system matrix M, obtaining its inverse matrix, and applying an inverse wavelet transform, an approximate solution vector v″ can be obtained.

Below, an example will be shown of calculation of distortion compensation for drastic distortion occurring at chip boundaries.FIG. 8Ais a graph of distortion near chip boundaries for calculation of distortion compensation and shows a case of offset of ±10 nm at chips adjoining each other across a space of 240 nm. The distortion of the underlying pattern shown inFIG. 8Acorresponds to the “q” in equation (4), while the position on the abscissa inFIG. 8Bcorresponds to the order “n”.

The full width at half maximum of the electron beam used for the electron beam sub-deflection correction is assumed to have a Gaussian distribution of 300 μm.FIG. 8Bis a contour graph of the system matrix M when the order of the input vector “q” is n=64 and the order of the approximate solution vector v″ is m=256.FIG. 8Bis shows the electron beam intensity distribution K as well.

FIG. 9Ais a contour graph of the matrix Mwobtained by applying a two-dimensional wavelet transform to the system matrix M shown in FIG.8B. The Haar basis is an orthogonal basis, so can transform data completely similar to a Fourier transform.

A wavelet transform by nature results in data converging at a low level element near the mother wavelet (origin), so the low level element is extracted.FIG. 9Bis a view obtained by extracting a 16×16 partial matrix H shown by the square frame in FIG.9A and expresses the magnitudes of the elements of the partial matrix H by shading.

FIG. 10Ais a graph obtained by finding an inverse matrix H−1of the partial matrix H shown in FIG.9B and expressing the magnitudes of the elements of the inverse matrix H−1by shading. The 16×16 inverse matrix H−1is given an 0 element at its outside to make the 256×64 matrix shown in FIG.10B and thereby generate an approximate inverse matrix H′−1of Mw.

By applying the approximate inverse matrix H′−1from the left side of equation (7), the following equation (8) stands:
H′−1·Q=V(8)

Equation (8) may be rewritten using equations (6) to obtain the following equation (9):

If applying wavelet transforms to the two sides of equation (9), the following equation (10) is obtained:
(WmT·H′−1·Wn)·q=v  (10)

Therefore, comparing equation (4) and equation (10), the approximate inverse matrix Minvof the system matrix M is expressed by the following equation (11). As shown in equation (11), “Minv” is given by a two-dimensional wavelet transform of “H′−1”.
Minv=WmT·H′−1·Wn(11)

FIG. 11is a graph expressing the magnitudes of the elements of the approximate inverse matrix Minvshown in equation (11) by shading. Summarizing the above, an approximate solution vector v″ (which shows the electron beam correction target position and corresponds to the compensation signal) is calculated by the following equation (12):
v″=Minv·q(12)

FIG. 12Ais a graph of the distortion G of a transfer pattern predicted at the time of electron beam sub-deflection correction using the compensation signal v″ given by equation (12).FIG. 12Bis a graph of the result of calculation of the residual distortion G−g=r in the case electron beam sub-deflection correction using the compensation signal v″ and in the case of electron beam sub-deflection correction of the related art. In this figure, “r1” is the residual distortion after electron beam sub-deflection correction according to the present embodiment, and “r2” is the residual distortion after electron beam sub-deflection correction of the related art.

As shown inFIG. 12B, a residual distortion of 3 nm occurs at the chip boundaries in the related art, but the residual distortion can be suppressed to ±1 nm in the electron beam scan method according to the present embodiment. Therefore, the overlay accuracy between the underlying pattern and the transfer pattern can be improved.

Further, as shown inFIGS. 12A and 12B, the correction target position v″ and the residual distortion do not diverge at the two ends of a calculation area. That is, with the method of generating a compensation signal using a wavelet transform, the signal converges at positions away from the drastic distortion, so is suited for actual electron beam sub-deflection correction.

The compensation signal generated using the Fourier transform explained in the first embodiment covers not only the vicinity the drastic distortion, but also the entire region. On the other hand, the compensation signal generated using a wavelet transform is localized at only drastic distortion. That is, a Fourier transform transforms all positional coordinates to frequency, so positional data is lost. On the other hand, a wavelet transform transforms spanning both position and frequency, so no positional data is lost.

Summarizing the effects of the present invention, a transfer pattern matching with a high precision the distortion of the underlying pattern of an exposed member can be obtained, and the overlay accuracy between the underlying pattern and the transfer pattern can be improved.

The present invention is not limited to the method such as the first embodiment in which a compensation filter prepared using a Fourier transform is applied to the electron beam deflection signal to obtain a compensation signal or the method such as the second embodiment in which wavelet transform is used to obtain a compensation signal suitable for control. In the final analysis, it is not particularly limited so long as a transfer pattern reduced in distortion due to repeated forward direction correction and reverse direction correction and overlay of latent images can be obtained. Further, the EB diameter of the electron beam is not limited. In addition, any charged particle beam other than an electron beam, such as ion beam, can also be used.