WO2005124468A1

WO2005124468A1 - A photolitography apparatus and mask for nano meter scale patterning of some arbitrary shapes

Info

Publication number: WO2005124468A1
Application number: PCT/KR2004/002724
Authority: WO
Inventors: Chinsoo Hong; Chang Kyo Kim
Original assignee: Chinsoo Hong; Chang Kyo Kim
Priority date: 2004-06-16
Filing date: 2004-10-26
Publication date: 2005-12-29
Also published as: KR100476819B1

Abstract

An exposure apparatus for patterning an arbitrary shape on a nanometer scale and a method for manufacturing a mask in which a Fourier-transformed pattern is formed. The exposure apparatus a light source unit, a mask unit, a lens unit, and a photoresist. The light source unit is provided with a lamp for providing light. The mask unit is equipped with the mask through which light from the light source unit is passed and in which the Fourie-transformed pattern is formed. The lens unit is provided with at least one lens for performing Fourier transform on the light passed through the mask unit. The photoresist unit is equipped with a wafer on which a photoresist is applied.

Description

A PHOTOLITHOGRAPHY APPARATUS AND MASK FOR NANO METER SCALE PATTERNING OF SOME ARBITRARY SHAPES

Background of Invention Technical Field The present invention relates, in general, to an exposure apparatus for patterning an arbitrary shape on a nanometer scale and a method for manufacturing a mask in which a Fourier-traiTsformed pattern is formed and, more particularly, to an exposure apparatus for patterning an arbitrary shape on a nanometer scale and a method for manufacttiring a mask in which a Fourier-transformed pattern is formed, which are capable of patterning the arbitrary shape on a nanometer scale by changing a lens arrangement for performing Fourier transform in a conventional exposure apparatus using the mask in which the pattern is formed in such a way as to make an arbitrary shape symmetrical with respect to an origin, Fourier-transform the arbitrary shape and then eliminate negative numbers, so that the price of the apparatus is low, the manipulation of the apparatus is easy and only the change of a Fourier-transformed pattern

is required at the time of fabricating a new circuit, thus being capable of drastically reducing the unit price of chips in a semiconductor process and facilitating research and production in all the fields r^uiring nanometer scale processing.

BackgroundArt

Modem society is rapidly changing to such a degree that new technology appears every day. The appearance of such new technology creates new demand, and such new demand requires newer technology. For example, in the case of Dynamic Random Access

Memory (DRAM), the degree of integration has increased by 50 % every year, and in the case of microprocessors, the degree of integration has increased by 35 % every year. Accordingly, the yield of chips has continually increased so that a unit cost per chip has trended downward

continuously. Technologies required for the manufacture of a Large Scale Integrated (LSI) circuit and a system-on-a-chip have been continually developed. Of the technologies, exposure

technologies have been most actively developed. An excellent exposure apparatus allows an image to be formed on a photoresist (PR) to have a miriimum feature size while mamtaining the image without a diffraction phenomenon and reducing only the size of the image. The diffraction phenomenon refers to a phenomenon that, when light passes through the vicinity of the boundary of a mask, the path of the light is changed so that the light travels along a direction different from an incident direction d ending on a distance apart from the boundary, and the minimum feature size refers to the minimum width of a line that can be formed on a silicon chip. However, as a wavelength decreases, the diffraction phenomenon cannot be avoided, and the minimum

feature size is also limited. A conventional exposure apparatus is described with reference to

FIG. 1 below. FIG. 1 is a diagram showing the optical system of a conventional exposure

apparatus. As shown in FIG. 1, the conventional exposure apparatus includes a light source 11

required for pattering, the light source 11 being one of optical light sources, such as G-line, H- line and F lasers and extreme ultraviolet light, or one of non-optical light sources, such as an electron beam, an ion beam and an X-ray, a silicon wafer 16 coated with a PR using the light

source 11, a typical mask 13 having a shape to be formed on the silicon wafer 16 using the light source 11, a condenser 12 for condensing the light onto the mask 13, projection lenses 14 and 15 for forming on the silicon wafer 16 the shape of the mask 13 fabricated using light condensed by the condenser 12, a filter (not shown) that is an additional device for canceling a ώffraction phenomenon that cannot be avoided when using an optical system, and a means for

improving a nririimum feature size. In the above-described construction, the spatial filter may or may not be used, and, if used, is positioned between the projection lenses 14 and 15. Such conventional exposure apparatuses maybe classified into exposure apparatuses using an optical system and exposure apparatuses using a non-optical system. The non- optical exposure apparatuses include an electron beam exposure apparatus, an ion beam exposure apparatus, an X-ray exposure apparatus, and an exposure apparatus using an accelerator such as synchrotron. An electron beam exposure technology is a scheme of exposing a PR using the kinetic energy of electrons that are emitted from a cathode and irradiated onto a wafer through

focusing, acceleration and deflection using an electromagnetic field. Since the wavelength of the electron beam is about several angstroms, a high resolution may be realized. However, the electron beam technology is disadvantageous in that direct writing is performed by controlling the path of an electron beam so that the productivity thereof decreases significantly. The ion beam exposure apparatus exhibits excellent characteristics as an exposure technology for hyperfine patterning, compared to the electron beam exposure and the X-ray exposure apparatus. However, the ion beam exposure apparatus has the same disadvantage

as the electron beam exposure technology, and additionally has a disadvantage in that since ions are relatively heavy, a substrate maybe damaged.

The X-ray light source, known as a soft X-ray, has a wavelength of 40 to 50 A, and is advantageous in that it is excellent in permeability to carbon, that is, the main constituent of dust, and, therefore, can nrinimize the generation of defects caused by dust or organic pollutants existing on a mask. However, it is less sensitive to a photoresist, including organic material as its main constituent, and has a long exposure time compared to the intensity of light,

thus resulting in low productivity. Finally, the synchrotron radiation accelerator is a device for performing exposure using an electromagnetic wave (having a wavelength of about 1 nm) emitted along the tangential direction of a circle along which electrons move. The synchrotron radiation accelerator is most suitable for an exposure light because it has directionality along the tangential direction of the circle and high luminance. However, the synchrotron radiation accelerator has a disadvantage in that it is excessively expensive. As described above, notΛwthstencling that the non-optical exposure apparatus is advantageous in that its miriimum feature size is very small, it is not suitable for mass

production because it has disadvantages in that it is expensive and its production yield is. low. The optical exposure apparatus using an optical system is described below. FIG. 2 is a graph showing the annual trend toward the improvement of a minimum feature size with respect to the exposure wavelength of the light source of an optical system. The light sources shown in FIG. 2 are the light sources of an optical exposure apparatus, and the discontinuous spectra of mercury and the wavelengths of lasers are illustrated in yearly order. As shown in FIG.2, in order to improve the nrinimum feature size, development trends from a normal light source to a laser and from a long wavelength to a short wavelength. The reason why the laser is used is that it can realize brighter light than the normal light. However, in the case of material whose exposure can be achieved by weak

light, the normal light having a wide range of wavelengths may be used. For a target of miriimum feature size of 100 nm or less, a light source having a wavelength of 200 nm or less

should be used. According to current size reduction trend, no progress from a nrinimum feature size of 60 nm will be made before 2010. A conventional minimum feature size is 100 nm or less, and the nrinimum feature size R has a relationship with wavelength as following:

² (1)

Accordingly, it is known that as the wavelength of a light source decreases in the exposure apparatus, the rrrinimum feature size becomes smaller. Hence, the use of the lasers has been recently researched. Fuitliermore, extreme ultraviolet (EUV) light falls wiftiin a wavelength range of 11 to 13 nm that is slightly larger than that of the soft X-ray. The EUV light is attracting attention as a light source capable of being used to obtain a rrrinimum feature size that is equal to or smaller than 70 nm. For the EUV light, a reflection type optical exposure apparatus must be used, and a normal mirror is unsuitable due to its excessively low reflectance, so that it is preferable to increase reflectance using a mirror that has a relatively high refractive index and is formed in a multi-film shape by deposition. When the optical

exposure apparatus is constructed, it is preferable to reduce the number of mirrors to 6 or less and to use aspheric mirrors with the surface roughness thereof set to approximately 0.1 to 0.2 nm. However, an exposure apparatus using EUV light may reduce a miriimum feature size and allows the size of an entire exposure apparatus product to decrease, but is not widely popularized because it is disadvantageous in that the price thereof is expensive. The minimum feature size R (resolution) and Depth Of Focus (DOF) of the conventional optical exposure apparatus can be represented as follows:

The DOF corresponds to a longitudinal focal length and, to achieve the exposure of a PR by only one exposure, the thickness of the PR must be thinner than the DOF. In Equation

2, λ is the wavelength and NA is the numerical aperture of a projection lens system. The λ

and NA are useful parameters that can be defined in the case where light is converged or

diverged at a specific rate, as in a lens or an optical fiber. FIG. 3 is a diagram illustrating an equation for calculating the numerical aperture of a lens. In FIG. 3, when D is the diameter of a lens, f is a focal length and n is the refractive index of a material surrounding the lens, the numerical aperture is defined as follows:

where the angle is half of a total angle at which light diverges. The number of lenses is f/#= f/D .

In Equation 2, since k_\ and k₂ are values that depend on the material of a PR, an exposure processing technology and an image forming technology to improve a nrinimum feature size, they are values that must be experimentally determined. A generally used image fonrώig technology includes the usage of a phase sMfting mask, off-axis ifrumination, optical proximity correction, degree of coherence, intensity distribution in the aperture plane, lens aberration and geometrical shape (or spatial frequencies). Theoretically, it is known that k_\ is at least 0.25, and about 0.8 in the best system. In the ideal case where a non-coherence source

is used, ki=0.6, in the case of R ≥θ.5μm, ki-1, and in the case of R~0.5μm, ^-0.8. An ideal condition for an exposure apparatus corresponds to the case where a

minimum feature size decreases while DOF increases. The reason for this is because when DOF increases, the smoothness of the plane of a PR does not need to be excellent and the distance between a projection lens and the PR does not need to be strictly maintained. hi Equation 2, a reduction in nrinimum feature size is achieved by reducing the wavelength of light, increasing the numerical aperture of a projection lens system, and

reducing k_\ using a technique, such as a filter. If the numerical aperture is reduced, a njjnimum feature size is reduced and DOF is much reduced, so that a precise process for

coating an exposure material is required and, therefore, the precision between the lens and the exposure material must increase. If the reduction of a wavelength imports the use of an ultraviolet ray, an extreme ultraviolet ray or an X-ray in place of a visible ray in an exposure process, a nririimum feature size is considerably reduced according to the R~λ/2 principle, but the cost of a corresponding exposure apparatus increases exponentially. In particular, since in the case of an F? laser, the wavelengtli thereof is absorbed by oxygen molecules and moisture in the air, all the exposure equipment must be basically included in a vacuum chamber. However, a relatively high cost is required to make and maintain an extraordinary vacuum space, so that it is unsuitable for practical use. The DOF is represented using the miriimum feature size of FIG.2 as follows: DOF =-^ K —R² .2 (4) k 1² λ When a method of increasing DOF is thought over with reference to FIG. 4, the

DOF can be increased by reducing the wavelength, or k] using a phase shift filter. However, there is a limitation in reducing k_\ . The majority of articles published in relation to an exposure apparatus are related to

the technologies for reducing k_ls and the technologies may be classified into technologies for adjusting the light source of an optical system shown in FIG. 1 and technologies using a filter in a projection lens system. If DOF is larger than a minimum required exposure thickness, a problem does not occur. In contrast, if the DOF is smaller than the nrinimum required exposure thickness, a problem may occur. The exposure thickness must endure in an etching process and must be equal to or larger than a predetermined nrinimal thickness to perform the mtrinsic function of

PR Such conventional technologies include an illumination optical system (Korean

Patent No. 10-0049064-0000) in which a grating having a 1/2 period is fabricated using a dual spatial frequency system and resolution is increased two or more times by allowing +1- and -

1 -order diffracted beams to interfere with each other, an apparatus (Korean Patent No. 10- 0114334-0000) improving the MTF characteristics and image contrast of the exposure apparatus using a phase shift mask, and a method using a filter other than a mask after a mask shape is put on the mask. In order to reduce a minimum feature size, an EUV, electron beam, ion beam, or X-ray exposure apparatus or an exposure apparatus using a radiation accelerator must be used as a next generation exposure apparatus. However, such methods are disadvantageous in that the methods require expensive equipment, so that an excessively expensive cost is incurred and a production yield is low, thus being unsuitable for mass

production.

Disclosure of the Invention The present invention has been made keeping in mind the above problems occurring in the prior art, and an object of the present invention is to provide an exposure apparatus capable of performing nanometer scale patterning using only one mask without the addition of

a filter, is easy to manipulate due to the simplicity thereof, and can pattern an arbitrary shape at

low cost. hi order to accomplish the above object, the present invention provides an exposure apparatus using a mask in which a Fourier-transformed pattern is formed, including a light

source unit provided with a lamp for providing light; a mask unit equipped with the mask through which light from the light source unit is passed and in which the Fourier-transformed

pattern is formed; a lens unit provided with at least one lens for performing Fourier transform on the light passed through the mask unit; and a photoresist unit equipped with a wafer on

which a photoresist is applied. Additionally, the present invention provides a method for manufaclrjring a Fourier- transformed pattern, including the steps of fabricating an arbitrary shape using a unit pixel having a predetermined size; fabricating a -file corresponding to the arbitrary shape by evaluating the manufactured arbitrary shape and other portions; fabricating an arbitrary symmetrical shape file, including the arbitrary shape file that is symmetrical to the arbitrary shape file with respect to an origin, a horizontal line or a vertical line; performing Fourier transform on the arbitrary symmetrical shape file; and el rmating negative numbers from the

Fourier-transfoπned file.

Brief Description of Drawings FIG. 1 is a diagram showing the optical system of a conventional exposure paratus; FIG. 2 is a graph showing the annual trend toward the improvement of a minimum

feature size with respect to the exposure wavelength of the light source of an optical system; FIG. 3 is a diagram ifrustrating an equation for calculating the numerical aperture of a

lens; FIG.4 is a diagram mustrating the principle of a convex lens that is used as a Fourier

transformer, FIG. 5 is a three-dimensional graph that simulates the intensity distribution of light

Fourier-transformed at a focal point; FIG. 6 is a three-dimensional graph that simulates the intensity distribution of

partially Fourier-transfomied light at location midway between a lens and its focal lens; FIG. 7 is a diagram showing the schematic optical system of an exposure apparatus

according to the present invention; FIG. 8 is a example drawing of a shape that is wanted to be finally fabricated with the

exposure apparatus of the present invention; FIG. 9 is a view illustrating converted data in which FIG. 8 is evaluated using 0 and

1; FIGS. 10a and 10b are views to illustrate the method of making symmetrical shape

with respect to its original shape; FIGS. 1 la and 1 lb are views showing four objects to illustrate the method of making symmetrical shapes with respect to its original shape; FIG. 12 is a graph illustrating a method of eliminating imaginary numbers from a

Fourier-transformed result using two masks in the exposure apparatus of the present invention; FIG. 13 is a view illustrating the shape of a pattern depending on black and white grades or grey grades; FIG. 14 is a view showing the shape of an object; FIG. 15 is a view showing a Fourier-transformed pattern, mask; FIG. 16 is a diagram illustrating an exposure apparatus having a single lens, one of

simplest apparatuses, in accordance with the present invention; FIG. 17 is a view illustrating an exposure apparatus having three lenses in

accordance with the present invention; and FIG. 18 is a graph showing a feature size in the x-axis direction according to zi of

FIG. 8.

Best Mode for Carrying Out the Invention The present invention relates to Fourier optics and structurally pertains to an exposure apparatus, wherein Fourier optics refers to an entire process of focusing the image of a mask using Fourier transform and inverse Fourier transform. Fourier optics using a plurality of lenses requires four fundamental operators, that is, a quadratic phase operator, a scaling operator, a Fourier transform operator and a free space propagation operator according to the arrangement of the lenses, such as the distances between the lenses, and a method of combining these operators and describing Fourier optics is referred to as a Nazarathy and

Shamir's method.

The Fourier transform G(f_x, f ) of a function g(x, y) is given as following: _o l_∞ g(^x _> y) expH^'2 (/ + f_yy)]dxdy (5)

In the above Equation, 3 refers to Fourier transform, and fx and fy are referred to as spatial frequencies and are a Fourier pair corresponding to spatial coordinates x and y.

Equation 5 is used to calculate Fourier transform G(f_x, f ) when the function g(x, y) is

known. In the inverse case, inverse Fourier transform must be used. g(x,y) = y¹G(f_x,f_y) = _{∞ ∞} G(f_x,f_y) x_P[i2π(f_xx + f_yy)]df_xdf_y (6)

In Equation 6, 3^_1 refers to inverse Fourier transform. If Equations 5 and 6 are combined together, seven theorems useful for Fourier transform may be obtained. A

representative theorem is one in which two operations 3 and 3^_1 are consecutively applied. Z-¹3g(x,y) = g(-x,-y) (7)

Equation 7 indicates that a function symmetrical to an original function with respect to an origin can be obtained by consecutively applying Fourier transform and inverse Fourier

transform. In optics, a convex lens functions as a Fourier transformer, as in FIG.7. FIG.4 is a diagram illustrating the principle of a convex lens that is used as a Fourier transformer. In FIG. 4, when the optical axis direction of a lens is z, a plane on which the lens is placed is an xy-plane, the thickness of a convex lens is Δ₀ , the refractive index of a medium

constituting the convex lens is n, and phase changes according to the thickness of the lens are considered, light incident from the center of the lens to (x, y) undergoes phase changes as

following: k t_l (x, y) = exp[ϊfoιΔ₀ ] exp[-ι— (x² +y²)] (8)

In Equation 8, k is a wave number, that is, k = 2π I λ , and f is the focal length of a

convex lens. The phase changes given in FIG. 8 are the phase differences between a back plane and a front plane through which light is input to the lens and output from the lens, respectively, and the resulting equation obtained by combining Equation 8 and four

fundamental operators at the focus of a convex lens is as following:

U(x,y) (9)

It can be understood that in FIG. 9, an integral equation is Fourier-transformed when variables are properly substituted in comparison with Equation 5. In the case where

collirnated light is incident on a lens, the back plane of a lens is precisely Fourier-transformed on a focal plane in accordance with Equation 9. Now, an example in which Fourier transform is performed through a convex lens is described.

FIG. 5 is a three-dimensional graph that simulates the intensity distribution of light Fourier-transformed at a focal point, and FIG. 6 is a three-dimensional graph that simulates the intensity distribution of partially Fourier-transfonned light at location midway between a lens and its focal lens. As the result of the Fourier transform of a 500 nm x 800 mn rectangular aperture via the lens, it is known that the intensity distribution of light varies according to the location spaced apart from the lens when the shape of a mask becomes similar to a wavelength. Now, with reference to FIG. 7, an embodiment of the present invention is described in detail. FIG. 7 is a diagram showing the schematic optical system of an exposure apparatus

of the present invention. The exposure apparatus of the present invention includes a light source unit 20 provided with a lamp for providing optical light, a light expanding unit 30 provided with a vacuum pump 34 for minimizing the plasma phenomena of air, a vacuum tube 39 connected to the vacuum pump 34, several lenses 36 and a spatial filter 37 so as to generate light having a predetermined sectional area by finely adjusting the focal points of the lenses 36 and the location of the spatial filter 37, a mask unit 40 adapted to control the amplitude or phase of light

passed through the light expanding unit 30 and to have the Fourier-transformed mask of a target image, a lens unit 50 provided with lenses for performing the Fourier transform of light passed through the mask unit 40, and a PR unit 60 provided with a wafer having a deposited PR and an intercepting device for intercepting light irrelevant to exposure. The exposure

apparatus further includes a regulating device for finely regulating the light source unit 20, the light expanding unit 30, the mask unit 40, the lens unit 50 and the PR unit 60 upward or downward, rightward or leftward, or forward and backward, supports 22, 32, 42, 52 and 62 for supporting the light source unit 20, the light expanding unit 30, the mask unit 40, the lens unit 50 and the PR unit 60, respectively, and an optical bench 70 connected to the supports 22, 32,

42, 52 and 62 for preventing the locations and heights of the supports 22, 32, 42, 52 and 62 from being easily changed by external impact and internal vibration. Furthermore, the optical bench 70 is mounted on an optical table 72 that can allow the optical bench 70 to be stably mounted thereon and protects against external vibration. However, in the case where a high intensity laser connected to the light expanding unit 30 via an optical fiber is used as a light source, the optical table 72 is not necessary. The respective units of the exposure apparatus will be described below. The construction of the light source unit 20 can vary with the type of light source. In the case of using a monochromatic light source, a color filter for extracting monochromatic light from a lamp and a lens and aperture for converting light into collimated light must be

provided, and in the case of using a laser light source, only the laser becomes the light source unit 20.

The light expanding unit 30 receives light emitted in the form of collimated light from the light source unit 20, but light passed through the light expanding unit 30 does not need to be collimated light. Accordingly, the light may be diverging light or converging light according to circumstances. The light expanding unit 30 uses the vacuum pump 34 to

nrinimize the plasma phenomenon of air. The plasma phenomenon refers to the phenomenon in which the collimated laser light must be focused one or more times in the path through which the collimated light enters the light expanding unit 30 and passes through the

lens system, in which case a laser beam converts air into plasma and a white flash is generated around focal points. The white flash generated as described above forms an excessively distorted final image on a nanometer scale. Although vibration used to eliminate such a plasma phenomenon and generated by the vacuum pump does not matter due to a

considerably short exposure time in the case of using a pulse laser with strong intensity, more

efficient exposure can be performed in the case of eliminating a high frequency vibration of the vacuum pump to achieve perfect exposure. It is preferable to use the light expanding unit support 32 as a method of eliminating such vibration. Furthermore, if an exposure apparatus is put into a vacuum chamber and sufficiently isolated from light, it will be an exposure apparatus that can be used under any environment. The mask unit 40 may be equipped with a mask in which a Fourier-transformed pattern having the shape of a target image is formed, and the mask unit 40 may be included in

the lens unit 50. The lens unit 50 may have one or more lenses 54 therein, and a convex lens, a concave lens, a convex mirror and a concave mirror may be properly used according to circumstances. The number of lenses 54 is selected according to the desired resolution,

which will be described in detail in a description of the operational principle of the exposure apparatus according to the present invention. Since to perform patterning using the exposure apparatus according to the present invention, a mask, which will be installed in the mask unit and in which the Fourier- transformed pattern is formed, is necessary, a method of manufacturing the mask, in which the

Fourier-transformed pattern is formed, is described below. The Fourier-transformed pattern is fabricated through a total six steps, and the first step of them is the step of drawing the shape of a target image using the exposure apparatus of

the present invention. It is assumed that the shape of FIG. 8 is an example shape that is wanted to be finally fabricated using the exposure apparatus of the present invention.

The drawing of FIG. 8 is drawn using a drawing tool, such as a paper and pencil, or a computer, and is stored in a computer in the form of a graphic file. The shape may have a

symmetrical shape as shown in FIG. 8, but may have an arbitrary shape that is not symmetrical in any direction. Each small square of FIG. 8 represents a pixel, and the number of pixels in a nrinimum feature size is determined depending on the number of types of different feature

sizes in the drawing. The second step is the step of evaluating the drawing. FIG. 9 is a diagram showing converted data in which the drawing of FIG. 8 is

evaluated using 0 or 1. FIG. 8 can be represented by 0 and 1 as shown in FIG. 9. White and black pixels may be represented by 1 and 0, respectively, or by 0 and 1, respectively, depending on the type

of PR, such as intaglio or relief, or how a drawing was drawn. The evaluation of FIG. 8 can be easily converted into a file using a conventional conversion program. The third step is the step of causing the evaluated data to be symmetrical with respect to an origin. A method of making the data symmetrical with respect to an origin is descried with reference to FIGS. 10 and 11.

FIGS. 10a and 10b are views to illustrate the method of making symmetrical shape with respect to its original shape, and FIGS. 11a and 1 lb are views showing four objects to illustrate the method of making symmetrical shapes with respect to its original shape. Since an arbitrary shape other than a shape being symmetrical with respect to an origin cannot be formed in a mask when the arbitrary shape is Fourier-transformed as shown in FIG. 10a, the arbitrary shape must be converted into a shape symmetrical with respect to the origin before Fourier transform. If it is assumed that a mask to be formed on a wafer is shown in FIG. 10a, a related equation is as following: 3g(x,y) = •Loo J (-00 g(x,y)oxιp[-i2π(f_xx + f ^Jy)]dxdy (10)

When two masks are placed to be symmetrical with respect to the origin as shown in FIG. 10b, the mask in the first quadrant may be represented by g(x, y) while the mask in the third quadrant may be represented by g(-x, - y) . Accordingly, when these are substituted in

Equation 10 and the equation is arranged, the following equation is obtained.

⁼ C ^g(^χ>y)^Gχpl--^i2π(fχ^χ+fyy l^dxdy + JT [^g(-x,-y)&φ[-i2π(f_xx+f_yy)]dxdy = g x,y){e [-i²π(f_x ^χ+f_yy)] + ^G [+i2π(f_xx+f_yy)]}dxdy ^{= 2}C (^χ,y)^c∞( f_xχ+f_yy)) χdy (11)

When two masks are placed to be symmetrical as shown in FIG. 10b, Equation 11 is obtained. FIGS. 1 la and 1 lb can make shapes symmetrical with respect to an origin using a similar approach. The result obtained by Fourier-transfonriing the shape of FIG. 1 lb is as following:

3{g(^χ,y) + g(- ,y) + g(^χ -y) + g(- -y)) _j+∞ rt-∞ v - ) ^{= 2 g}(^x' ^)[^cos(²^ ) ⁺ cos(2π _yy)]dxdy

Equations 11 and 12 are substantially similar to each other, and Equation 12 may be applied to the case where one-side symmetry is possible. The fourth step is the step of performing Fourier transform. The Fourier transform is the relation between the electric field component of a mask and the electrical field component of an image. Meanwhile, the object that we measure is the intensity of light proportional to the square of the amplitude of the electric field. The problem that may occur

in the case where a mask is manufactured and used based on the intensity of light is described

below. Two functions g(x, y) and G(f_x, f ) used in FIGS. 5 and 6 are represented in

tenrns of electric field components on a mask plane and an image plane, respectively. When the intensity of light is Fourier-transformed, the following Equation is obtained,

%(g(x, y) = £ ^* £^°° (g(x, y)f Q p[-i2π(f_xx + f_yy)]dxdy = Zg(x,y) ® Zg(x,y) hi Equation 13, <8> is a symbol that represents convolution. Equation 13 indicates that the Fourier transform of the intensity of light (g(x, y))² in the mask results in the

convolution of the Fourier transforms of the electric field component. That is, the Fourier transform of the intensity of light results in the convolution of desired results. If the function g(x, y) to be Fourier-transformed is symmetrical with respect to an

origin, that is, g(x, y) = g(~x, y) = g(x, -y) = g(~x, ~ y) , the following Equation is

obtained using FIGS.5 and 6:

Accordingly, if a function to be Fourier-transformed is symmetrical with respect to

an origin, the result of its inverse Fourier transform is obtained. If an image symmetrical with respect to an origin is Fourier-transformed using a convex lens, the result of the Fourier transform of the image is equal to the result of the inverse Fourier transform of the image. Accordingly, when an equation symmetrical with respect to an origin is Fourier-transformed,

the shape of FIG. 12 is obtained. FIG. 12 is a side view of FIG.5. The fifth step is the step of eliminating negative numbers from the Fourier- transformed result. Since the mask can basically represent a number using the transrnittance of light, the mask cannot represent a negative number. Accordingly, negative numbers shown in FIG. 12 have to be eliminated. Using the concept described above, a phase mask can be manufactured to represent

the desired Fourier-transformed result of a mask. The last step is the step of manufacturing a mask using the Fourier-transformed pattern from which negative numbers have been eliminated. The mask may be formed on a transparent planar plate such as a film or a glass. For example, the step of manufacturing a

film mask by forming the pattern on the film is described below. In the conversion of a Fourier-transformed file, from which negative numbers have been eliminated, into the mask, the most ideal condition is related to a film that has a considerably large number of grades capable of being represented by black and white grades, and large spatial resolution, that is, the characteristic in which the smallest distance between adjacent points is possible. In the use of the mask, the capability of exposing a larger area as well as a miriimum feature size are important, and the capability is affected by the spatial resolution and the number of black and

white grades. FIG. 13 is a view illustrating the shape of a pattern depending on black and white

grades or grey grades. As shown in FIG. 13, the final shape of an obtained pattern varies with the number of black and white grades. As the number of black and white grades increases, the shape of the co er thereof becomes sharper.

It is important to determine how many pixels are used to draw the pattern. For

example, if an optical system using a two-inch lens and a mask having a size of 3 cm are used and 3000 pixels are determined, the interval between adjacent pixels is 10 micrometers.

However, since the pixel size is related to the American Standards Association (ASA) number of a film and cannot be infinitely small, the interval between adjacent pixels has an order substantially identical to a grain size in the film and the pixel size in the optical system is directly related to how large an image can be implemented. A film recorder or a hologram recording apparatus may be used as an apparatus for manufacturing such a film mask. The comparison between the original object and the Fourier-transformed pattern

made through the six steps described above will be described hereinafter. FIG. 14 is a view showing the shape of an object. FIG. 15 is a view showing a Fourier-transformed pattern mask.

The process for manufacturing the Fourier-transfonned pattern used in the exposure apparatus of the present invention has been described, and the operational principle of the exposure apparatus using the above-described mask is described with reference to FIGS. 16 and 17 below. FIG. 16 is a diagram ffliistrating an exposure apparatus having a single lens, one of simplest apparatuses, in accordance with the present invention.

When one lens is used, the distance between a Fourier-transformed pattern 82 and a lens 83 is d, the focal length of the lens 83 is f, a ray of light 81 incident on the lens 83 is not collimated light, and a point light source (not shown) is spaced apart from the Fourier- transformed pattern 82 by a distance Zi . The result of the Fourier transform via the lens 83 is as following:

A-∞ rt-∞ (z_λ +d)(x_Qx + y_Qy) x J I-∞ J I-00 U(x₀,y₀)exp — ik dx₀dy_Q (15) ^Zl^Z2 h the case of using two lens systems, a lens having a focal length fi is installed and a Fourier-transformed pattern is installed at a location spaced apart from the lens by a distance d. A point light source is placed at a location spaced apart from the Fourier-transfonned pattern by a distance z₁. A second lens having a focal length f₂ is spaced apart from the first lens by a

distance z and a Fourier transform is performed at a location spaced apart from the second lens by a distance z₃. The Fourier-transformed image has a shape as following:

Z_{hm lenses} {mask} = — ^{( ΛU}3 e „ 2z^* ₃ ³ α₃zf ka.

Equation 17 shows the parameters used in Equation 16. The case of using three lenses is described below.

FIG. 17 is a diagram illustrating an exposure apparatus having three lenses in

accordance with the present invention.

A ray of light 91 emitted from a light source sequentially passes through a Fourier-

transformed pattern 92, a first lens 93 having a focal length fi, a second lens 94 having a focal

length f₂ and a third lens 95 having a focal length f₃, and an image is focused on a plane 96.

The distance from the light source (not shown) to the Fourier-transformed pattern 92 is Z_\, the

distance between the first lens 93 and the second lens 94 is z₂, the distance spaced apart from

the second lens 94 to the third lens 95 is z , and the distance from the third lens 95 to a Fourier

plane 96 is Z Like the results obtained using one lens and two lenses, in case of using three

lenses, a Fourier-transformed image is focused. In FIG. 17, for convenience's sake, incident

light is collimated light and the distance d spaced apart from the mask to the first lens is 0.

Although the exposure system having three lenses has been described above, an

exposure system having three or more lenses may be also used, and the resolution on the

Fourier plane varies with the number of lenses. The following Equation represents a

resolution calculation method, and calculation considers the amplitude in the x-axis direction

on the two-dimensional plane (x-y plane) of the mask. The reason for this is that the

amplitude in the y-axis direction is handled in the same manner.

(one lens exposure system)

Width in x-axis direction (two lens exposure system)

(three lens exposure system) (18)

u₀ used in FIG. 18 is the length in which a first zero appears in the x-axis direction when a rectangular-shaped aperture is Fourier-transformed. FIG. 18 is a graph showing a feature size in the x-axis direction according to z_\ of

FIG.8. If collimated light is incident on the mask, it can be understood that z, ^ ∞ and

the feature size in the x-axis direction becomes 20 μm in FIG. 18. The Fourier transform described above is summarized below. The Fourier-transformed pattern and its image formed on the PR have a Fourier transform relationship tiierebetween, and the lens unit 50 performs Fourier transform. From the Fourier transform relation, it can be understood that the Fourier-transformed pattern and its image formed on the PR have features as described below. A large part expressed on the

Fourier-transformed pattern is converted into a small part on the PR, whereas a small part expressed on the mask is converted into a large part on the PR. From this fact, when the interval between pixels in the mask is small, a large image is expressed on the PR, whereas when the interval between pixels on the mask is large, a small image is expressed on the PR. Accordingly, the black and white grade and the pixel interval are very important parameters in

the present invention and appropriate ranges regarding these can be obtained through computer simulation. The exposure apparatus for patterning an arbitrary shape on a nanometer scale and the method for manufacturing a mask in which a Fourier-transformed pattern is formed in accordance with the present invention are not limited to the above-described embodiments, but can have various modifications without dφarting from the technical spirit of the present

invention. Industrial Applicability The present invention described above provides an exposure apparatus for patterning

an arbitrary shape on a nanometer scale and a method for manufacturing a mask in which a

Fourier-transformed pattern is formed, which are capable of patterning the arbitrary shape on a nanometer scale by changing a lens arrangement for performing Fourier transform in a conventional exposure apparatus using the mask in which the pattern is formed in such a way as to make an arbitrary shape symmetrical with respect to an origin, Fourier-transform the arbitrary shape and eliminate negative numbers, so that the price of the apparatus is low, the manipulation of the apparatus is easy and only the change of a Fourier-transformed pattern is required at the time of fabricating a new circuit, thus being capable of drastically reducing the unit price of chips in a semiconductor process and facilitating research and production in all the

fields requiring nanometer scale processing.

Claims

What Is Claimed Is: 1. An exposure apparatus using a mask in which a Fovmer-transformed pattern is

formed, comprising: a light source unit provided with a lamp for providing light; a mask unit equipped with the mask through which light from the light source unit is passed and in which the Fourier-transformed pattern is formed; a lens unit provided with at least one lens for performing Fourier transfonn on the light passed through the mask unit; and a photoresist unit equipped with a wafer on which a photoresist is applied.

2. The apparatus according to claim 1, wherein the Fourier-transformed pattern is a pattern that is obtained in such a way that an arbitrary shape is converted into a shape symmetrical with respect to an origin, a horizontal line or a vertical line and the symmetrical

shape is Fourier-transformed.

3. The apparatus according to claim 1, if the light source is a monochromatic light source, further comprising a color filter for extracting monochromatic tight from the lamp, and a lens system and aperture for converting the light into collimated light.

4. The apparatus according to claim 1, further comprising a light expanding unit that

placed between the light source and the mask unit and is composed of a spatial filter and at least a lens to output light having a predetermined sectional area.

5. The apparatus according to claim 1, wherein a portion or entire portion of the exposure apparatus operates in a vacuum state, and the exposure apparatus further comprises an optical table for stably supporting the exposure apparatus and preventing external vibration.

6. The apparatus according to claim 1, wherein the number of lenses of the lens unit

is one or more.

7. The apparatus according to claim 1, wherein the mask unit is contained in the lens

unit, and the mask placed in the mask unit is placed to come into close contact with a first lens of the lens unit.

8. A method for manufacturing a Fourier-transformed pattern, comprising the steps of: fabricating an arbitrary shape using a unit pixel having a predetermined size; fabricating a file corresponding to the arbitrary shape by evaluating the manufactured arbitrary shape and other portions; fabricating an arbitrary symmetrical shape file, including the arbitrary shape file that is symmetrical to the arbitrary shape file with respect to an origin, a horizontal line or a vertical line; performing Fourier transform on the arbitrary symmetrical shape file; and elinτinating negative numbers from the Fourier-transformed file.

9. The method according to claim 7, further comprising the step of fabricating a mask

in which a Fourier-transfonned pattern is formed on a transparent film or substrate.

10. A mask manufactured using the method of fabricating the Fourier-transformed

pattern according to claim 8 or 9.