RU2491594C2 - Method of obtaining three-dimensional objects - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: method of obtaining three-dimensional objects of an arbitrary shape by interference lithography involves preliminary calculation of amplitude and phase of the interfering coherent waves on a given shape of the object, illuminating a photosensitive material with a series of groups of interfering coherent waves to obtain three-dimensional distribution of density of absorbed light energy, developing the obtained photomaterial and obtaining solid three-dimensional objects.

EFFECT: synthesis of three-dimensional objects of an arbitrary shape with subwave resolution.

22 cl, 9 dwg

Description

The invention relates to processes for the formation (synthesis) of three-dimensional objects of arbitrary shape using interference lithography technology.

The prior art method for the synthesis of three-dimensional objects with submicron accuracy, characterized by scanning the volume of photosensitive material with a focal waist of the laser beam and based on two-photon absorption of light near this waist of the light beam (SU-8 for real three-dimensional subdiffraction-limit two-photon microfabrication. WH Teh, U. Durig, G. Salis, R. Harbers, U. Drechsler, RF Mahrt, CG Smith, H.-J. Guntherodt, Applied Physics Letters; Vol. 84 Issue 20, p. 4095, 2004).

The disadvantages of this method include:

- a slow synthesis process, since point-by-point scanning of photographic material is required;

- the impossibility of mass production of objects, since the products are manufactured individually, and as a result - the high cost of the products obtained;

- difficulties in synthesizing large objects due to the need to use a small focal constriction.

The prototype of the claimed invention is a method for the synthesis of microparticles of various shapes, characterized by illuminating the photosensitive material with interfering waves, the manifestation of the photographic material and obtaining objects (application WO 2008/097495, publ. 14.08.08, IPC G03F 7/004).

The disadvantage of this method is the inability to obtain objects with a predetermined shape.

The technical task of the invention is the synthesis of three-dimensional objects of arbitrary shape with sub-wave resolution.

The problem is achieved in that in the claimed method for the synthesis of three-dimensional objects of arbitrary shape by the method of interference lithography, a preliminary calculation of the amplitudes and phases of the interfering coherent waves according to the given shape of the object is performed, the photosensitive material is illuminated with a sequence of groups of interfering coherent waves to obtain a three-dimensional distribution of the density of absorbed light energy, and the obtained photographic material and get solid three-dimensional objects.

In addition, the invention provides the possibility of simultaneous synthesis of many identical objects of arbitrary shape, arranged in a two-dimensional grid, and another feature of the invention is that the direction of the interfering waves is set so that the projections of the wave vectors onto a certain plane are located in a periodic two-dimensional grid.

The invention allows the synthesis of objects when illuminating a layer of photosensitive material from two or more sides or by lighting a layer of photosensitive material on one side.

In order to obtain the absorbed light energy density corresponding to the synthesized object, the calculation of the wave amplitudes is adjusted taking into account the final absorption of the interfering waves in the layer of the photosensitive material.

In order to optimize the contrast and resolution of the method, the calculation of the amplitudes and phases of the interfering waves is carried out using a genetic optimization algorithm.

For the purpose of three-dimensional compaction of the location of identical objects, the location of simultaneously synthesized objects is carried out in a plane perpendicular to the layer of photosensitive material and / or the direction of lighting, and three-dimensional arrangement (placement) of identical objects is carried out by moving the layer of photosensitive material parallel to its plane.

To specify the calculated amplitudes and phases of the waves when illuminating a photosensitive material, a spatio-temporal light modulator based on a liquid crystal modulator or a spatio-temporal light modulator based on a microelectromechanical modulator are used.

As one of the possible options for implementing the method for the synthesis of a three-dimensional object, it is proposed to calculate the amplitudes and phases of interfering waves when calculating the diffraction of waves incident and diffracting in the directions corresponding to interfering waves, including using the fast Fourier transform.

For the synthesis of three-dimensional objects, dry films of negative and positive photoresists or liquid photopolymer media are used as a photosensitive material.

In order to increase the resolution of the method when illuminating a photosensitive material with interfering waves, nonlinear effects are used, in particular two-photon absorption.

As a tool equipment for illuminating a photosensitive material with interfering waves, a Fourier lens or a micro lens are used, in which the spatio-temporal light modulator is placed in the front focal plane.

In order to increase resolution and increase the angle of illumination when illuminating a photosensitive material with interfering waves, various types of immersion are used.

When illuminating a photosensitive material with interfering waves, circular polarization of interfering waves or linear polarization of interfering waves or elliptical polarization of interfering waves are used.

To improve the quality of the products obtained, to increase the contrast of lighting, the polarization of each of the interfering waves is optimized and set separately.

The applicant considers it necessary to note that this method can be used to synthesize objects of 2.5 dimensions (two-dimensional, with a thickness of a comparable or larger part in the plane of the photoresist).

In order to obtain a three-dimensional object by the method of interference lithography, it is necessary to create a corresponding three-dimensional distribution of the density of the absorbed radiation dose in the photosensitive material. For example, for a negative type of photopolymer inside the boundaries of the object, the density of the absorbed radiation dose must exceed its threshold value to achieve the polymerization of the material, and outside the boundaries be below this value. The greater the difference between the density of absorbed energy outside and inside the object, that is, the greater the contrast of the resulting picture, the higher the quality of the transmission of the boundaries of the object, the resolution, the lower the requirements for non-linear response of the photographic material, the larger the window of permissible synthesis process parameters.

As noted above, an object of arbitrary shape is associated with a three-dimensional distribution of the density of absorbed energy. This distribution can be represented as the sum of spatial harmonics calculated by the three-dimensional Fourier transform of this distribution.

The most direct way to obtain such a distribution is to sequentially expose the photographic material with interference patterns of different periods and orientations obtained from two waves. At each exposure, one spatial harmonic is obtained in the distribution of the absorbed radiation energy. Typically, the response of the photographic material at each point is proportional to the total density of absorbed energy received from all exposures in their sequence. However, such a straightforward approach has fundamental shortcomings. One of them is that the exposure process will consist of a huge number of exposures, approximately equal to the number of bills of the synthesized object. That is, the advantage of interference lithography is lost, consisting in accelerating the process due to the parallel exposure of the entire volume.

The problem of a long illumination (exposure) time can be solved by illuminating the material simultaneously with many mutually incoherent pairs of waves. However, in addition to being technically difficult to implement, this will not solve another problem. If the illumination by different harmonics is spread out in time or is carried out by incoherent waves, the summation of harmonics occurs in intensity, and not in field strength. Since the intensity cannot take negative values, in this case, with each illumination, the Fourier harmonic is added only together with the constant component. The contrast of the density distribution of the absorbed energy obtained in this way will be too low to support the synthesis process.

The method consists of a preliminary calculation of the amplitudes and phases of the waves, exposure of the photographic material and processing of the photographic material (baking, development, etc.). Processing of photographic material is carried out, as with other lithography methods, by a method corresponding to this type of photographic material. Photoresists designed for the synthesis of three-dimensional objects (thick layer photoresists) are preferred. Also preferred are photoresists with a chemical amplification mechanism, with a cationic polymerization mechanism, which makes it possible to accumulate a dose of absorbed radiation from several exposures.

Of particular importance is the method of exposure of a photoresist to groups of waves whose directions cover the entire solid angle (4th steradian) or half of it (2nd steradian).

The invention is illustrated by drawings, where figure 1 shows a diagram of the exposure of a photoresist from one half-plane; figure 2 - scheme of exposure of the photoresist from two sides (half-planes); figure 3 - synthesized part; figure 4 - the result of computer simulation of six beams; figure 5 - the result of computer simulation - turbine; 6 is a distribution of the density of absorbed energy in the XY plane during computer simulation of the turbine; 7 is an example of the orientation of wave vectors in the two-dimensional case; Fig. 8 — orientation of wave vectors and their projections, providing simultaneous synthesis of many three-dimensional objects located in the nodes of a square grid.

Consider one of the exposure options corresponding to the illumination of a layer of photographic material from one half-plane (Fig. 1). The following system is proposed, containing a spatio-temporal light modulator 1, a Fourier lens 2, a substrate with a photoresist 3. A Fourier lens (preferably with a large numerical aperture) is used. The output plane of the space-time light modulator, consisting of a two-dimensional array of pixels, is placed in the focal plane of this lens. When a beam passes spatial coherent light (when illuminated by a spatially coherent light beam) of such a modulator, it is possible to control the phase and light intensity at the output of each pixel (each pixel, independently of the others). Similarly, you can use a modulator that works on reflection. Thus, in the front focal plane of the Fourier lens (at its input) we have a set of light sources similar to point sources, with the intensity and phase of each source being set separately. Then, at the output of such a lens (in its rear focal plane), we obtain a set of collimated light beams with a given phase and intensity. Moreover, the propagation directions (wave vectors of these light beams) will correspond to directions that can provide simultaneous synthesis of many identical objects.

Instead of a Fourier lens, another lens or a microscope lens can be used.

As a space-time modulator, a liquid crystal light modulator or a microelectromechanical light modulator (for example, a Texas Instrument Instrument DLP digital light processor) can be used.

To reduce light loss and ensure collimation of interfering waves, a lens raster can be placed at the output of the space-time modulator - one microlens per pixel. With the help of such lenses we can form the necessary beam parameters. That is, by choosing the focal length of the microlenses, you can set the diameter of the interfering beams in the photographic material, collect all the light at the output of each pixel, and ensure that the interfering beams are collimated.

Both a two-dimensional raster of microlenses and two one-dimensional rasters (two rasters of cylindrical lenses) crossed at an angle of 90 degrees can be used.

As an embodiment of lighting from a full solid angle, a similar system can be used, but, accordingly, using two space-time modulators and two Fourier lenses, as shown in FIG. 2, where the space-time light modulator 1, the Fourier lens 2, substrate with photoresist 3, mirror 4, translucent mirror 5. In this case, it is necessary to ensure the coherence of the waves incident on the layer of photographic material from two sides.

As one of the possible options, the following method for calculating the amplitudes of waves in groups is proposed. We set N directions (wave vectors) of the interfering waves that uniformly cover the entire available solid angle (for example, the full solid angle of 4 l;). The number of exposures is also assumed to be N. The wave amplitudes in each group (corresponding to one of the exposures) are defined as the amplitudes of the waves resulting from the diffraction of one of the waves in the object in these N selected directions. Thus, for the jth group, the amplitude of the i-th wave is

$$A_{i,j}={\displaystyle \int \epsilon (r)\cdot \exp (i{k}_{i}r)\cdot \exp (i{k}_{j}r)dr,(\mathrm{one})}$$

where ε (r) = 1 inside the object,

ε (r) = 0 outside the object,

k _i - wave vector of the i-th wave in the group,

r is the radius vector.

As a result of N exposures, we obtain the following distribution of the absorbed energy density

$$E(r)={{\displaystyle \sum _{j=0}^N\left|{\displaystyle \sum _{i=0}^N{A}_{i,j}\cdot \exp (i{k}_{i}r)}\right|}}^2(2)$$

векселей объекта с разрешением порядка длины волны (двухмерному случаю соответствует N·N пикселей).It is expected that in this way in the three-dimensional case we can get about $$N\cdot \sqrt{N}$$

object bills with a resolution of the order of the wavelength (two-dimensional case corresponds to N · N pixels).

As an example of a specific implementation of the method, a part having the shape of six beams is taken - FIG. 3. The number of waves used to synthesize this object was taken equal to 506. Figure 4 shows the result of adding 506 exposures for six beams. Level surfaces corresponding to various values of the absorbed energy density are shown. As you can see, the boundaries of the object are visible at intensities whose ratio exceeds Imax / Imin = 300. Thus, the contrast that can be achieved by this method is not less than m = 0.95, which is quite sufficient when using existing types of photoresists.

As another example of the implementation of the method is the synthesis of a three-dimensional object - a turbine. Figure 5 presents the result of the implementation of the method for the turbine. To illustrate the contrast of the three-dimensional distribution, FIG. 6 shows the energy density distribution in the XY section for a turbine.

The simultaneous synthesis of several identical objects is possible for the case when the projections of the wave vectors of the interfering waves in some directions relate to each other as integers. In this case, for a periodic sequence of space points along these directions, the phase difference for all wave groups will be a multiple of 2π. 7 shows an example of the orientation of the wave vectors in the two-dimensional case. The projections of the wave vectors onto the X axis are located equidistantly (refer as integers). This leads to the fact that along this axis, points remote from each other by a distance of 2π / (Δk _x ) will be illuminated at any exposure with the same intensity (similar to how the inverse Fourier series transformation gives a periodic sequence).

For a three-dimensional picture of the distribution, the fulfillment of the equidistance condition for the projections of wave vectors is possible simultaneously for two directions. In this case, a synthesis of a two-dimensional array of identical objects located at the nodes of a two-dimensional grid (square, hexagonal, etc.) is possible. In this case, the wave vector of all interfering waves can be written as

$${\overrightarrow{k}}_{m,n}=\overrightarrow{a}\cdot m+\overrightarrow{b}\cdot n+{\overrightarrow{e}}_z\cdot \sqrt{{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="00000013.png,00000014.png"\; state="\{\{state\}\}">k</figure-callout>}}_0{}^2-{\left|\overrightarrow{a}\cdot m\right|}^2-{\left|\overrightarrow{b}\cdot n\right|}^2,}(3)$$

- единичный вектор, $$\overrightarrow{a}$$

, $$\overrightarrow{b}$$

- вектора, перпендикулярные вектору $$\overrightarrow{e}$$

и образующие базис двухмерной решетки в обратном пространстве, k₀ - волновой вектор света в вакууме.where m, n are integers, $$\overrightarrow{e}$$

is the unit vector $$\overrightarrow{a}$$

, $$\overrightarrow{b}$$

- vectors perpendicular to the vector $$\overrightarrow{e}$$

and forming the basis of a two-dimensional lattice in reciprocal space, k ₀ is the wave vector of light in vacuum.

On Fig presents an example of the distribution of wave vectors on the sphere of directions, corresponding to the multiplexing of objects located in the nodes of a square grid lying in the XY plane.

The resolution of the proposed method is limited by the maximum spatial frequency corresponding to the interference of counterpropagating waves. The minimum period in this case is equal to half the wavelength of the radiation used. To ensure this condition, it is necessary to illuminate the photographic material from all directions, covering the full solid angle of 4π steradian. In practice, the photographic material is usually a dry photoresist film located on a glass substrate. From a practical point of view, it is rather difficult to take into account the phase shifts of the waves incident on the photoresist from the lower and upper hemispheres. In addition, it is required to ensure the symmetry of the directions of the waves in the lower and upper hemisphere. This will be especially critical when multiplexing objects. Let us estimate what changes when using half the full solid angle, i.e. lighting photographic material from only one hemisphere of directions. As can be seen from Fig. 9, in this case, the maximum length of the lattice vector along one of the directions will be half as much, while along the other two directions we will still have the same set of lattices. This is a hi to the fact that along the direction of illumination (perpendicular to the plane of the photoresist) the resolution will be half as high as that of illumination from a full solid angle, while the lateral resolution (in the plane of the photoresist) will remain the same, approximately equal to half the radiation wavelength.

The advantages of the proposed method:

1. High speed exposure (simultaneous illumination of the entire volume of the photoresist).

2. The ability to simultaneously synthesize many identical objects (parts).

3. The use of single-photon absorption, which does not require high peak power, the possibility of using cw lasers with a long coherence length, and, accordingly, the possibility of obtaining a large number of resolved bills of synthesized objects.

4. The absence of moving parts of the circuit (no precise movements of the focal constriction or the application of many layers of photoresist are necessary).

Claims (22)

1. A method for producing three-dimensional objects of arbitrary shape by the method of interference lithography, characterized in that they carry out a preliminary calculation of the amplitudes and phases of the interfering coherent waves according to the given shape of the object, illuminate the photosensitive material with a sequence of groups of interfering coherent waves to obtain a three-dimensional distribution of the density of absorbed light energy, show the resulting photographic material and get solid three-dimensional objects. 2. The method according to claim 1, characterized in that at the same time synthesize many identical objects of arbitrary shape, ordered in a two-dimensional grid. 3. The method according to claim 2, characterized in that the direction of the interfering waves is set so that the projections of the wave vectors onto a certain plane are located in a periodic two-dimensional grid. 4. The method according to claim 1, characterized in that the layer of photosensitive material is illuminated from two sides. 5. The method according to claim 1, characterized in that they illuminate the layer of photosensitive material on one side. 6. The method according to claim 1, characterized in that the calculation of the wave amplitudes is adjusted taking into account the final absorption of interfering waves in the layer of photosensitive material. 7. The method according to claim 2, characterized in that the location of simultaneously synthesized objects is carried out in a plane perpendicular to the layer of photosensitive material and / or the direction of illumination. 8. The method according to claim 7, characterized in that the three-dimensional arrangement of identical objects is carried out by moving the layer of photosensitive material parallel to its plane. 9. The method according to claim 1, characterized in that when illuminating the photosensitive material, a spatio-temporal light modulator based on a liquid crystal modulator is used. 10. The method according to claim 1, characterized in that when illuminating the photosensitive material, a spatio-temporal light modulator based on a microelectromechanical modulator is used. 11. The method according to claim 1, characterized in that the preliminary calculation of the amplitudes and phases of the interfering waves is carried out using a genetic optimization algorithm. 12. The method according to claim 1, characterized in that the preliminary calculation of the amplitudes and phases of the interfering waves is carried out when calculating the diffraction of waves incident and diffracting in the directions corresponding to the interfering waves. 13. The method according to claim 1, characterized in that the preliminary calculation of the amplitudes and phases of the interfering waves is carried out using a fast Fourier transform. 14. The method according to claim 1, characterized in that as a photosensitive material using dry films of negative and positive photoresists. 15. The method according to claim 1, characterized in that as the photosensitive material using liquid photopolymer media. 16. The method according to claim 1, characterized in that when illuminating the photosensitive material with interfering waves, nonlinear effects are used, in particular two-photon absorption. 17. The method according to claim 1, characterized in that when illuminating the photosensitive material with interfering waves, a Fourier lens or a micro lens is used, in which the spatio-temporal light modulator is placed in the front focal plane. 18. The method according to claim 1, characterized in that when illuminating the photosensitive material with interfering waves, various types of immersion are used. 19. The method according to claim 1, characterized in that when illuminating the photosensitive material with interfering waves, circular polarization of the interfering waves is used. 20. The method according to claim 1, characterized in that when illuminating the photosensitive material with interfering waves, linear polarization of the interfering waves is used. 21. The method according to claim 1, characterized in that when illuminating the photosensitive material with interfering waves, elliptical polarization of the interfering waves is used. 22. The method according to claim 1, characterized in that when illuminating the photosensitive material with interfering waves, the polarization of each of the interfering waves is optimized and set separately.

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