Grating and method for manufacturing grating

Abstract

Provided is a grating comprising linear ridges of a plurality of second materials arranged at a period p in a first direction on a flat surface of a member of a first material, wherein p is 0.3-1 micrometer, and, in a cross section perpendicular to the flat surface and the first direction, the shape of each ridge is a trapezoid having a line segment corresponding to the flat surface as a lower base, the height d of the trapezoid is 0.83 × p or less, a first side and a second side of the trapezoid other than the lower base and the upper base are defined as a first side and a second side, the interior angle α formed by the first side and the lower base is 60 degrees or less, the interior angle β formed by the second side with the lower base is 75 degrees or more, and the ratio of w1 and (w1 + w2) is 0.20-0.80, where w1 is the length of the upper base and w2 is the difference between p and the length of the lower base.

Description

Grating and method for manufacturing the same

[0001] The present invention relates to a grating and a method for manufacturing a grating.

[0002] Augmented reality technology provides a synthesized image by overlaying a computer-generated image on a user's field of view of the real world using devices such as glasses or a head-mounted display. In order to deliver the computer-generated image to the wearer's eyes in such devices, a method for controlling and transmitting the direction of light using a diffraction grating has been developed (see, for example, Patent Documents 1 and 2). To improve the light utilization efficiency of devices using a diffraction grating, it is necessary to improve the diffraction efficiency of the diffraction grating. Therefore, there is a need for a grating with high diffraction efficiency and easy manufacturing, and a manufacturing method thereof.

[0003] WO2023 / 021804A1US20210294014A1

[0004] A technical object of the present invention is to provide a grating that has high diffraction efficiency and is easy to manufacture, and a method for manufacturing the same.

[0005] A grating according to a first aspect of the present invention comprises a plurality of linear ridges of a second material arranged at a period p in a first direction on a plane of a member of a first material, where p is between 0.3 micrometers and 1 micrometer, and in a cross section perpendicular to the plane and the first direction, each ridge has a trapezoidal shape with a line segment corresponding to the plane as its lower base, the height d of the trapezoid is 0.83 × p or less, sides of the trapezoid other than the lower and upper bases are defined as first and second sides, the interior angle α between the first side and the lower base is 60 degrees or less, the interior angle β between the second side and the lower base is 75 degrees or more, and the ratio of w1 to (w1 + w2) is between 0.20 and 0.80, where w1 is the length of the upper base and w2 is the difference between p and the length of the lower base.

[0006] By adopting the above-described cross-sectional shape, the grating of this embodiment has high diffraction efficiency when used as a diffraction grating and is easy to manufacture.

[0007] In the grating of the first embodiment of the first aspect of the present invention, the corner R of the vertex of the interior angle formed by the first side and the upper base or the corner R of the vertex of the supplementary angle of the interior angle formed by the first side and the lower base is 20 nanometers or less.

[0008] The grating of this embodiment has even higher diffraction efficiency when used as a diffraction grating.

[0009] A second aspect of the present invention relates to a method for manufacturing a grating, which comprises a plurality of linear ridges of a second material, each having a height d, arranged with a period p in a first direction on the plane of a member made of a first material, and in a cross section perpendicular to the plane and the first direction, each ridge has a trapezoidal shape with a line segment corresponding to the plane as its base. p is between 0.3 micrometers and 1 micrometer, and the height d of the trapezoid is 0.83 × p or less. In this manufacturing method, a layer of a second material having a thickness d is formed on the plane of the member made of the first material, a resist film is formed on the layer of the second material, and the resist film is patterned so that the cross section perpendicular to the plane has a blazed shape with a period p. The second material is then etched. The first and second materials are selected such that the etching rate of the first material is 10% or less of the etching rate of the second material under the etching conditions for the second material.

[0010] According to the manufacturing method of this aspect, by selecting the first and second materials such that the etching rate of the first material is 10 percent or less of the etching rate of the second material under the etching conditions of the second material, the cross-sectional shape of the ridges and the spacing between the ridges can be easily changed without changing the period p or the ridge height. Also, by reducing the corner R of the vertices of the trapezoidal corners of the ridge cross section, the diffraction efficiency can be improved.

[0011] In the method for manufacturing a grating according to the first embodiment of the second aspect of the present invention, when etching the second material, the length of the upper base of the trapezoid is w1, the difference between p and the length of the lower base is w2, and the etching time is changed to adjust the ratio of w1 to (w1 + w2) without changing the period p and the thickness d.

[0012] According to the method for manufacturing a grating of this embodiment, the blaze angle of the trapezoid remains constant after etching even if the etching time is changed, so it is easy to obtain the desired trapezoid shape.

[0013] In the method for manufacturing a grating according to the second embodiment of the second aspect of the present invention, the sides of the trapezoid other than the lower base and upper base are defined as the first side and the second side, the interior angle α between the first side and the lower base is 60 degrees or less, the interior angle β between the second side and the lower base is 75 degrees or more, the length of the upper base is w1, the difference between p and the length of the lower base is w2, and the ratio of w1 to (w1 + w2) is 0.20 or more and 0.80 or less.

[0014] In the method for manufacturing a grating according to the third embodiment of the second aspect of the present invention, the corner R of the vertex of the interior angle formed by the first side and the upper base or the corner R of the vertex of the supplementary angle of the interior angle formed by the first side and the lower base is 20 nanometers or less.

[0015] In the method of manufacturing a grating according to a fourth embodiment of the second aspect of the present invention, the combination of the first material and the second material is any one of chromium (Cr) or nickel (Ni) and silicon (Si), chromium (Cr), nickel (Ni) or silicon dioxide (SiO2) and silicon carbide (SiC), chromium (Cr) or nickel (Ni) and aluminum oxide (Al2O3), chromium (Cr), nickel (Ni) or chromium (Cr), nickel (Ni) or glass with a silicon dioxide content of less than 50 percent and silicon dioxide (SiO2).

[0016] In the method for manufacturing a grating according to the fifth embodiment of the second aspect of the present invention, the smaller of the two interior angles formed by the base and the other two sides of the triangle of the blazed shape of the resist in the cross section is defined as α', and the ratio of the etching rate of the second layer to the etching rate of the resist is defined as δ, where α' is determined by tan α' = tan α / δ.

[0017] In the method for manufacturing a grating according to the sixth embodiment of the second aspect of the present invention, the plane is divided into a plurality of regions, and the patterning or etching conditions are changed so as to change the ratio of w1 to (w1+w2) in each region.

[0018] In the method for manufacturing a grating according to the seventh embodiment of the second aspect of the present invention, the shape of a grating formed on a flat surface by the method for manufacturing a grating according to the second aspect is transferred to a flexible material by electroforming, and the flexible material is then attached to the curved surface, thereby forming a grating on the curved surface. According to this embodiment, a grating with high diffraction efficiency can be easily manufactured on a curved surface such as a spectacle lens.

[0019] 6A is a diagram showing the cross-sectional shape of a binary grating. FIG. 6B is a diagram showing the cross-sectional shape of a blazed grating. FIG. 6C is a diagram showing the cross-sectional shape of a slanted grating. FIG. 6D is a diagram showing the cross-sectional shape of an asymmetric trapezoidal grating. FIG. 6E is a diagram showing the relationship between wavelength and first-order diffraction efficiency for each type of grating. FIG. 6F is a diagram explaining the parameters of an asymmetric trapezoidal grating. FIG. 6G is a diagram showing the relationship between depth d and normalized average efficiency. FIG. 6H is a diagram showing the relationship between corner R and normalized average efficiency. FIG. 6I is a diagram showing the relationship between the duty ratio and normalized average efficiency of an asymmetric trapezoidal grating. FIG. 6I is a flow chart explaining a method for manufacturing an asymmetric trapezoidal grating. FIG. 6I is a diagram showing a first layer M1. FIG. 6I is a diagram showing a first layer M1 and a second layer M2 formed thereon. FIG. 6J is a diagram showing a state in which a resist film M3 is formed on the second layer M2. FIG. 6J is a diagram showing a state in which the resist film on the second layer is patterned into a blazed shape. FIG. 6F is a diagram showing a state after etching is performed. FIG. 6G is a diagram showing a state after the resist is removed. FIG. 6H is a diagram showing a state in which the resist film M3 on the second layer M2 is patterned into a blazed shape, similar to FIG. 6D. FIG. 6I is a diagram showing a state after a relatively short etching time. 7B shows the state after etching for a longer time than in FIG. 7B. FIG. 7C shows the state after etching for an even longer time than in FIG. 7C. FIG. 7D shows the layer M2 of grating material. FIG. 7E shows the state where a resist film M3 is formed on the layer M2 of grating material. FIG. 7F shows the state where the resist film M3 on the layer M2 of grating material has been patterned into a blazed shape. FIG. 7G shows the state after etching has been performed. FIG. 7H shows the state after the resist has been removed. FIG. 7H shows the state where a resist film M3 is formed on the layer M2 of etching that is formed on the layer M1 that is resistant to etching. FIG. 7I shows the state where a binary grating is formed by etching. FIG. 7J shows the state after further etching. FIG. 7J shows the state where a resist film M3 is formed on the layer M2 of etching that is resistant to etching. FIG. 7I shows the state where a slanted grating is formed by etching. FIG. 7J shows the state after further etching. FIG. 7F shows images showing the cross-sectional shape of the resist after patterning and the cross-sectional shape of the second layer after etching.6A shows a cross-sectional shape after etching by a manufacturing method of the present invention using an etching-resistant layer, and FIG. 6B shows a cross-sectional shape after etching by a manufacturing method not using an etching-resistant layer.

[0034] FIG. 6B shows an image of a cross-section of a mold with an asymmetric trapezoidal grating manufactured by a grating manufacturing method of the present invention.

[0035] FIG. 6C shows a single grating formed on one surface.

[0036] FIG. 6D shows a plurality of gratings with different duty ratios formed in multiple regions on one surface.

[0037] FIG. 6D shows a cross-sectional shape of a resist corresponding to FIG. 6D and a cross-sectional shape of a grating corresponding to FIG. 6F for duty ratios of 0.58, 0.46, and 0.39.

[0038] FIG. 6C shows a grating 200 formed on a substrate 110 by the method shown in FIG. 5.

[0039] FIG. 6D shows a state in which a film 300 made of ultraviolet-curable resin or thermosetting resin with an adhesive sheet 400 attached thereto is pressed onto the grating 20 ...E shows a cross-sectional view of the film 300 with the adhesive sheet 400 attached thereto removed from the grating 200. 1 is a diagram showing a state in which a film 300 with an adhesive sheet 400 attached thereto is attached to the curved surface of a substrate 120. FIG. 1 is a diagram showing a state in which a nickel film 500 with a shape 200′ of the film 300 is electroformed. FIG. 2 is a diagram showing a state in which a nickel film 500 with a lattice shape 200″ is attached to the curved surface of a matrix 130. FIG. 3 is a diagram showing a grating 200 formed on a substrate 110 by the method shown in FIG. 5. FIG. 4 is a diagram showing a state in which a film 300 made of ultraviolet curing resin or thermosetting resin with a glass film 450 attached thereto is pressed onto the grating 200. FIG. 5 is a diagram showing a film 300 with a glass film 450 attached thereto that has been removed from the grating 200. FIG. 6 is a diagram showing a state in which a nickel film 550 with a shape 200′ of the film 300 is electroformed. FIG. 7 is a diagram showing a state in which a nickel film 550 with a lattice shape 200″ is attached to the curved surface of a matrix 130. FIG. 7 is a diagram for explaining how to determine the blaze angle α and taper angle β of the cross section of an actual grating.

[0020] A diffraction grating is composed of a plurality of linear grooves formed at a regular interval in one direction on a plane. The linear grooves can also be considered to be formed by a plurality of linear ridges formed at a regular interval in one direction on a plane. The height of the ridges from the plane corresponds to the depth of the grooves.

[0021] 1A to 1D are diagrams showing the cross-sectional shapes of various types of diffraction gratings, and the cross sections shown in Fig. 1A to 1D are cross sections perpendicular to the above-mentioned plane and the above-mentioned one direction.

[0022] 1A is a diagram showing the cross-sectional shape of a binary grating. In the cross-section, the ridges of the binary grating are rectangular, and one side of the rectangle coincides with the straight line corresponding to the plane.

[0023] 1B is a diagram showing the cross-sectional shape of a blazed grating. In the cross-section, the ridges of the blazed grating are triangular, and one side of the triangle coincides with a straight line corresponding to the plane.

[0024] 1C is a diagram showing the cross-sectional shape of a slanted grating. In the cross-section, the ridges of the slanted grating are parallelograms, and one side of the parallelogram coincides with a straight line corresponding to the plane.

[0025] 1D is a diagram showing the cross-sectional shape of an asymmetric trapezoidal lattice. In the cross section, the ridges of the asymmetric trapezoidal lattice are asymmetric trapezoids, and the bottom of the trapezoid coincides with a straight line corresponding to the plane.

[0026] In the above cross section, the period of the ridges of each type of grating is p, the height (groove depth) of the ridges of each type of grating is d, the width of the top surface of the ridges of the binary grating, slanted grating, and asymmetrical trapezoidal grating is w1, the width between the ridges, i.e., the width of the valleys, of the binary grating, slanted grating, and asymmetrical trapezoidal grating is w2, and the smaller of the two interior angles formed by the base of the ridge and the other two sides of the blazed grating and asymmetrical trapezoidal grating is α. The ridge period p is also called the grating period or grating pitch. The angle α is called the blaze angle. The acute angle formed by the above plane and two sides of the slanted grating is called γ. Each γ is called a tilt angle.

[0027] Figure 2 shows the relationship between wavelength and first-order diffraction efficiency for each type of grating. The horizontal axis in Figure 2 represents wavelength, measured in nanometers. The vertical axis in Figure 2 represents average efficiency, which is the average value of the TE mode efficiency and the TM mode efficiency. The efficiencies in Figure 2 were calculated by simulation using optical software such as VirtualLab.

[0028] The shape of each grating type was determined to maximize efficiency at a wavelength of 530 nanometers, although the groove depth of the slanted grating was set to the same as that of the asymmetric trapezoidal grating, taking into account the difficulty of manufacturing.

[0029] Table 1 shows numerical data of parameters related to the shape of each type of grating.

[0030] As shown in FIG. 2, the diffraction efficiency of the asymmetric trapezoidal grating and the blazed grating is relatively high, and the efficiency at a wavelength of 530 nanometers is more than twice that of the binary grating.

[0031] The inventors have focused on and investigated asymmetric trapezoidal gratings, which have relatively high diffraction efficiency and a greater number of shape-related parameters than blazed gratings, giving them greater freedom in design.

[0032] FIG. 3 is a diagram illustrating the parameters of an asymmetric trapezoidal lattice. p, d, w1, w2, and α have already been explained. Angle β is the larger of the two interior angles formed by the lower base of the trapezoid and another side, and is also called the taper angle. In the simulation, taper angle β was set to 80 degrees. Corner R in FIG. 3 is the radius of curvature of the vertex of the interior angle formed by the upper base and the side that forms the blaze angle with the lower base. A trapezoid is asymmetric if angle α and angle β are different.

[0033] 4A to 4C are diagrams showing the relationship between each of the three parameters and the normalized average efficiency.

[0034] Figure 4A shows the relationship between depth d and normalized average efficiency when only depth d is changed without changing other parameters. The horizontal axis of Figure 4A represents depth d, which is measured in nanometers. The vertical axis of Figure 4A represents normalized average efficiency, which reaches a maximum value of 1 when depth d is 100 nanometers.

[0035] FIG. 4B is a graph showing the relationship between the corner R and the normalized average efficiency when only the corner R is changed without changing other parameters. The horizontal axis of FIG. 4B represents the corner R. The unit of the corner R is nanometers. The vertical axis of FIG. 4B represents the normalized average efficiency. The normalized average efficiency has a maximum value of 1 when the corner R is 0.

[0036] Figure 4C shows the relationship between the duty ratio and normalized average efficiency of an asymmetric trapezoidal grating when only the duty ratio is changed without changing other parameters. The duty ratio of an asymmetric trapezoidal grating is the ratio of w1 to (w1 + w2). The horizontal axis of Figure 4C represents the duty ratio. The vertical axis of Figure 4C represents the normalized average efficiency. The normalized average efficiency reaches its maximum value of 1 when the duty ratio is 0.5.

[0037] 4A and 4C, deviations in the depth d or duty ratio from the target values ​​that maximize average efficiency result in a significant decrease in average efficiency. Therefore, it is important to maintain the depth d and duty ratio at their target values. For the duty ratio, the decrease in average efficiency is significant when it is less than the target value of 0.5. As shown in FIG. 4B, the average efficiency decreases as the corner radius increases, with a particularly steep decrease occurring in the range of 50 nanometers or greater. Therefore, it is preferable to minimize the corner radius.

[0038] Table 2 shows the range of parameters of an asymmetric trapezoidal grating as a diffraction grating. The method for measuring the blaze angle α and taper angle β of an actual grating will be explained later.

[0039] A method for manufacturing an asymmetric trapezoidal grating will be described below.

[0040] FIG. 5 is a flow chart illustrating a method for manufacturing an asymmetric trapezoidal grating.

[0041] 6A to 6F are diagrams showing the steps of a method for manufacturing an asymmetric trapezoidal lattice. The cross sections shown in Figures 6A to 6F are cross sections perpendicular to the plane on which the ridges are arranged and the direction in which the ridges extend, as in Figures 1A to 1D.

[0042] In step S1010 of FIG. 5, design values ​​of the parameters in Table 2 are determined.

[0043] In step S1020 of FIG. 5, the materials of the first and second layers are determined.

[0044] Table 3A shows combinations of materials for the first and second layers when forming a grating on a mold substrate. The mold on which the grating is formed can be used to manufacture a diffraction grating, for example, by injection molding. In Table 3A, for example, "Cr, Ni" means that the material of the first layer is chromium (Cr) or nickel (Ni).

[0045] Table 3B shows combinations of materials for the first layer and the second layer when a diffraction grating is formed on a substrate without using a mold. The second layer is a layer that undergoes etching, as will be described later, and the first layer is a layer that is resistant to etching under the etching conditions of the second layer. Typically, the material of the first layer is selected so that its etching rate under the etching conditions of the second layer is 10 percent or less of the etching rate of the material of the second layer.

[0046] In step S1030 of FIG. 5, a second layer is formed on the first layer.

[0047] 6A shows the first layer M1, which in this example is made of chromium.

[0048] 6B shows the first layer M1 and the second layer M2 formed thereon. In this example, the material of the second layer M2 is silicon. The thickness of the second layer M2 is d in Table 2.

[0049] 5, the material, film thickness, and exposure dose of the resist film to be formed on the second layer are determined from the angle α in Table 2. How to determine the resist film thickness will be explained later.

[0050] 5, a resist film is formed on the second layer and patterned into a blazed shape by an electronic writing device. The resist film may also be patterned into a blazed shape by other means, such as laser writing.

[0051] FIG. 6C is a diagram showing a state in which a resist film M3 with a thickness d' is formed on the second layer M2 with a thickness d.

[0052] 6D is a diagram showing the state in which the resist film on the second layer has been patterned into a blazed shape. The period (pitch) of the blazed shape corresponds to p in Table 2.

[0053] 5, it is determined whether the blazed shape is acceptable. If it is acceptable, the process proceeds to step S1070. If it is not acceptable, the process returns to step S1040.

[0054] 5, the etching conditions are determined from the depth d and duty ratio in Table 2. The relationship between the duty ratio and the etching time will be explained later.

[0055] In step S1080 of Figure 5, etching is performed, where the etching is performed on the second layer, while the first layer is not susceptible to etching.

[0056] FIG. 6E shows the state after etching has been performed.

[0057] The relationship between the blaze angle α' of the patterned blazed shape shown in Figure 6D and the blaze angle α shown in Figure 6E is as follows: The blaze angle α' of the blazed shape is the smaller of the two interior angles formed by the base and the other two sides of the triangle of the ridge of the blazed shape in the cross section of Figure 6D. δ = tan α / tan α' δ is the ratio of the etching rate of the second layer made of silicon to the etching rate of the resist. The resist material is selected so that δ is generally between 0.8 and 1.5. The blaze angle α' of the blazed shape can be determined from the following equation, which is derived from the above equation: tan α' = tan α / δ

[0058] The thickness d' of the resist film M3 in FIG. 6C is determined so as to satisfy the following formula.

[0059] In step S1090 of FIG. 5, the remaining resist is removed.

[0060] FIG. 6F shows the state after the resist has been removed.

[0061] 5, it is determined whether the shape of the ridges of the grating after etching is acceptable. If it is acceptable, the process ends. If it is not acceptable, the process returns to step 1070 and the etching conditions are changed.

[0062] The relationship between the duty ratio and the etching time will be explained below.

[0063] 7A to 7D are diagrams for explaining the relationship between the duty ratio and the etching time.

[0064] FIG. 7A is a diagram showing a state in which the resist film M3 on the second layer M2 has been patterned into a blazed shape, similar to FIG. 6D.

[0065] FIG. 7B shows the state after a relatively short etching time.

[0066] FIG. 7C shows the state after etching for a longer time than in FIG. 7B.

[0067] FIG. 7D shows the state after etching for an even longer time than in FIG. 7C.

[0068] 7B-7D, the duty ratio decreases as the etching time increases. In this method, d in Table 2 is determined by the thickness of the second layer, and p in Table 2 is determined by the period of the blazed shape patterned on the resist film. Therefore, this method allows the duty ratio to be controlled by the etching time without changing d and p in Table 2. Furthermore, α in Table 2 after etching is completed remains the same regardless of the etching time.

[0069] For comparison with the present method, a manufacturing method that does not use an etching-resistant layer will be described.

[0070] 8A-8E show steps in a manufacturing method that does not use an etch-resistant layer.

[0071] FIG. 8A shows a layer M2 of grating material.

[0072] FIG. 8B is a diagram showing a state in which a resist film M3 is formed on the layer M2 of grating material.

[0073] FIG. 8C shows a state in which the resist film M3 on the layer M2 of grating material has been patterned into a blazed shape.

[0074] FIG. 8D shows the state after etching has been performed.

[0075] FIG. 8E shows the state after the resist has been removed.

[0076] In a manufacturing method that does not use a layer that is resistant to etching, if the etching time is increased, the depth of the groove corresponding to d in Table 2 changes, and therefore the duty ratio cannot be controlled by the etching time without changing d.

[0077] Also, the use of etch-resistant layers in the fabrication of binary and slanted gratings is described.

[0078] 9A-9C illustrate a method for fabricating a binary grating using an etch-resistant layer.

[0079] FIG. 9A is a diagram showing a state in which a resist film M3 is formed on a layer M2 that is susceptible to etching and that is formed on a layer M1 that is not susceptible to etching.

[0080] FIG. 9B shows the state in which a binary grating is formed by etching.

[0081] 9C shows the state after further etching, where excessive etching distorts the shape of the ridges.

[0082] 10A-10C illustrate a method for fabricating a slanted grating using an etch-resistant layer.

[0083] FIG. 10A is a diagram showing a state in which a resist film M3 is formed on a layer M2 that is susceptible to etching and that is formed on a layer M1 that is not susceptible to etching.

[0084] FIG. 10B shows the state in which a slanted grating is formed by etching.

[0085] 10C shows the state after further etching, where excessive etching distorts the shape of the ridges.

[0086] An embodiment of the present invention will be described below. In the manufacturing method of the embodiment of the present invention, a mold with a grating is manufactured, and an optical element with a grating is manufactured by injection molding using the mold. Note that the size of the grating of the mold is slightly changed from the design value of the size parameter of the grating of the optical element, taking into account the shrinkage of the element after injection molding. The material of the first layer is chromium, and the material of the second layer is silicon.

[0087] First, three examples will be described in which the thickness of the second layer is the same as that of Table 2d, 350 nanometers, 200 nanometers, and 100 nanometers.

[0088] Table 4 shows the etching conditions for three examples. Etching is performed by placing the target object in a sealed reactive etching chamber and applying a high-frequency voltage while gas is being supplied. The frequency of the high-frequency voltage is 13.56 MHz. p in Table 2 is 420 micrometers. When d is 350, 200, and 100 nanometers, α in Table 2 is 60 degrees, 53 degrees, and 26 degrees, respectively.

[0089] Figure 11 is an image showing the cross-sectional shape of the resist after patterning and the cross-sectional shape of the second layer after etching. The cross sections shown in the images in Figure 11 and the following figures are cross sections perpendicular to the plane on which the ridges are arranged and the direction in which the ridges extend, as in Figures 1A to 1D. The image of the cross-sectional shape of the resist after patterning corresponds to Figure 6D. The cross-sectional shape of the second layer after etching corresponds to Figure 6F.

[0090] FIG. 12 shows images of the cross-sectional shape after etching using a manufacturing method of the present invention that uses an etching-resistant layer (A) and a cross-sectional shape after etching using a manufacturing method that does not use an etching-resistant layer (B). In Table 2, p is 420 micrometers, d is 350 micrometers, and α is 60 degrees. In Case A, the valleys are the surface of the etching-resistant layer. Therefore, compared to Case B, the valleys are flatter, and the corner R of the vertex of the complementary angle of the blaze angle of the trapezoid of the ridge is smaller. In Case B, the corner R is approximately 70 nanometers, while in Case A, the corner R is less than 10 nanometers. Note that the corner R of the mold shown in FIG. 12B corresponds to the corner R of the optical element shown in FIG. 3. Generally, the method of the present invention can achieve a corner R of less than 20 nanometers.

[0091] Figure 13 shows images of the cross-sectional shapes after etching for etching times of 120 and 130 seconds. p in Table 2 is 420 nanometers, d in Table 2 is 200 nanometers, and α in Table 2 is 53 degrees. The duty ratio for an etching time of 120 seconds is 170 / (170 + 90) = 0.65, and the duty ratio for an etching time of 130 seconds is 130 / (130 + 130) = 0.5. According to the manufacturing method of the present invention, as described above, it is possible to change only the duty ratio without changing p in Table 2 or d in Table 2. Furthermore, α in Table 2 after etching remains the same regardless of the etching time.

[0092] A mold provided with a grating was manufactured by the grating manufacturing method of the present invention, and a waveguide device was manufactured by injection molding using the mold.

[0093] Table 5 shows design parameters of an asymmetric trapezoidal grating as a diffraction grating.

[0094] FIG. 14 is an image of a cross section of a mold with an asymmetric trapezoidal grating of the parameters in Table 5, produced by the grating manufacturing method of the present invention.

[0095] Table 6 shows the brightness when a waveguide device with an asymmetric trapezoidal grating and a waveguide device with a binary grating, both manufactured using the mold shown in FIG. 14, are used with the same light source. The parameters of the binary grating are shown in Table 1. The waveguide device is, for example, that disclosed in WO2023 / 021804A1. The luminous flux of the incident light is 4.5 lumens. According to Table 6, the brightness of the waveguide device with the asymmetric trapezoidal grating is more than twice that of the waveguide device with the binary grating.

[0096] Another embodiment will now be described.

[0097] A single surface may be divided into multiple regions, and gratings with different duty ratios may be formed in each region. Such gratings may be used, for example, to improve the uniformity of an image provided by a diffraction grating.

[0098] FIG. 15A shows a single grating formed on one surface.

[0099] FIG. 15B is a diagram showing a plurality of gratings with different duty ratios formed in a plurality of regions on one surface.

[0100] A first method for producing a grating such as that shown in Figure 15B is to vary the duty cycle of the etching process by varying the etching time for different regions, and to repeat the steps of etching the regions to be etched while shielding the regions other than the regions to be etched.

[0101] Figure 16 shows images of the cross-sectional shape after etching when the etching times are 85 seconds, 75 seconds, and 67 seconds. The duty ratios are 0.40, 0.50, and 0.58, respectively. p in Table 2 is 420 nanometers, d in Table 2 is 100 nanometers, and α in Table 2 is 26 degrees.

[0102] A second method for fabricating a grating such as that shown in Figure 15B is to pattern different areas differently to create different resist shapes, and then etch all areas for the same amount of time.

[0103] 17 is an image showing the cross-sectional shape of the resist corresponding to FIG. 6D and the cross-sectional shape of the grating corresponding to FIG. 6F when the duty ratios are 0.58, 0.46, and 0.39. p in Table 2 is 420 nanometers, d in Table 2 is 200 nanometers, and α in Table 2 is 53 degrees.

[0104] As yet another embodiment, a method for forming a grating on a curved surface such as the surface of an eyeglass lens will be described.

[0105] 18A-F are diagrams illustrating a method for forming a grid on a curved surface.

[0106] Fig. 18A is a diagram showing a grating 200 formed on a substrate 110 by the method shown in Fig. 5. The grating 200 corresponds to the portions indicated by M1 and M2 in Fig. 6F.

[0107] 18B is a diagram showing a state in which a film 300 made of ultraviolet curable resin or thermosetting resin with an adhesive sheet 400 attached thereto is pressed onto the lattice 200. A lattice pattern 200' is transferred onto the film 300.

[0108] 18C is a diagram showing film 300 to which adhesive sheet 400 has been attached, having been removed from lattice 200. A lattice pattern 200' has been transferred onto film 300.

[0109] FIG. 18D is a diagram showing a state in which film 300 with adhesive sheet 400 attached thereto is attached onto the curved surface of substrate 120.

[0110] FIG. 18E shows the state where the nickel film 500 is electroformed with the shape 200′ of the film 300. The grating shape 200″ is transferred to the nickel 500.

[0111] FIG. 18F is a diagram showing a state in which a nickel film 500 having a lattice pattern 200 ″ is attached to the curved surface of the matrix 130 .

[0112] Eyeglass lenses with gratings and the like can be manufactured by injection molding using the mold shown in Figure 18F.

[0113] Another method for forming a grid on a curved surface will now be described.

[0114] 19A-E are diagrams illustrating another method for forming a grid on a curved surface.

[0115] FIG. 19A shows a grating 200 formed on a substrate 110 by the method shown in FIG.

[0116] 19B is a diagram showing a state in which a film 300 made of ultraviolet curable resin or thermosetting resin with a glass film 450 attached thereto is pressed onto the grating 200. The grating shape 200' is transferred onto the film 300.

[0117] 19C shows the film 300 to which the glass film 450 has been attached, having been removed from the grating 200. The grating shape 200' has been transferred onto the film 300.

[0118] FIG. 19D shows the electroformed nickel film 550 with the shape 200' of the film 300. The grating shape 200'' is transferred to the nickel 550. The thickness of the nickel film 550 is about 0.1 millimeters.

[0119] FIG. 19E is a diagram showing a state in which a nickel film 550 having a lattice pattern 200 ″ is attached to the curved surface of the matrix 130 .

[0120] Eyeglass lenses with gratings and the like can be manufactured by injection molding using the mold shown in Figure 19E.

[0121] By using the method shown in Figures 18A-F or 19A-E, a grating can be formed even on the curved surface of a spectacle lens with a diopter of 14 (focal length of 0.071 meters).

[0122] A method for measuring the blaze angle α and taper angle β of an actual grating will now be described.

[0123] 20 is a diagram illustrating a method for measuring the blaze angle α and taper angle β of an actual grating cross section. Three straight lines parallel to the upper and lower bases of the trapezoid are drawn so as to divide the height of the ridges into four equal parts. For the two sides other than the upper and lower bases, two straight lines are determined by least-squares approximation of the two parts other than the highest and lowest of the four parts divided by the three straight lines. The smaller of the interior angles formed by the two straight lines and the lower base is defined as the blaze angle α, and the larger is defined as the taper angle β.

Claims

1. A lattice consisting of a plurality of linear ridges of a second material arranged with a period p in a first direction on the plane of a component of a first material, p being 0.3 micrometers or more and 1 micrometer or less, and in a cross section perpendicular to the plane and the first direction, the shape of each ridge is a trapezoid with a line segment corresponding to the plane as its lower base, and the height d of the trapezoid is 0.83 x p or less, and the sides other than the lower base and upper base of the trapezoid are defined as first and second sides, the interior angle α between the first side and the lower base is 60 degrees or less, and the interior angle β between the second side and the lower base is 75 degrees or more, the length of the upper base is w1, the difference between p and the length of the lower base is w2, and the ratio of w1 to (w1 + w2) is 0.20 or more and 0.80 or less.

2. The grating according to claim 1, wherein the corner R of the vertex of the interior angle formed by said first side and said upper base or the corner R of the vertex of the supplementary angle of the interior angle formed by said first side and said lower base is 20 nanometers or less.

3. A molded part equipped with a grid according to claim 1.

4. An augmented reality device comprising the grid of claim 1.

5. A method for manufacturing a grating comprising a plurality of linear ridges of a second material of a first material arranged with a period p in a first direction on a plane of a member of a first material, the shape of each ridge being a trapezoid with a line segment corresponding to the plane as a base in a cross section perpendicular to the plane and the first direction, where p is between 0.3 micrometers and 1 micrometer and the height d of the trapezoid is 0.83 x p or less; forming a layer of the second material of a thickness d on the plane of the member of the first material; forming a film of resist on the layer of the second material; patterning the film of resist so that a cross section perpendicular to the plane has a blazed shape with a period p; etching the second material; and the first and second materials are selected such that the etching rate of the first material is 10 percent or less of the etching rate of the second material under the etching conditions of the second material.

6. A method for manufacturing a grating as described in claim 5, in which, when etching the second material, the length of the upper base of the trapezoid is w1 and the difference between p and the length of the lower base is w2, and the ratio of w1 to (w1+w2) is adjusted by changing the etching time without changing the period p and thickness d.

7. A method for manufacturing a grating as set forth in claim 5, wherein the sides of said trapezoid other than the upper and lower bases are defined as a first side and a second side, the interior angle α between said first side and said lower base is 60 degrees or less, the interior angle β between said second side and said lower base is 75 degrees or more, the length of said upper base is w1, the difference between p and the length of said lower base is w2, and the ratio of w1 to (w1 + w2) is 0.20 or more and 0.80 or less.

8. A method for manufacturing a grating as set forth in claim 7, wherein the corner R of the vertex of the interior angle formed by said first side and said upper base or the corner R of the vertex of the supplementary angle formed by said first side and said lower base is 20 nanometers or less.

9. The method of claim 5, wherein the combination of the first material and the second material is any of chromium (Cr) or nickel (Ni) and silicon (Si), chromium (Cr), nickel (Ni) or silicon dioxide (SiO2) and silicon carbide (SiC), chromium (Cr) or nickel (Ni) and aluminum oxide (Al2O3), chromium (Cr), nickel (Ni) or chromium (Cr), nickel (Ni) or glass with less than 50 percent silicon dioxide content and silicon dioxide (SiO2).

10. A method for manufacturing a grating as described in claim 5, wherein the smaller of the two interior angles formed by the base and the other two sides of the triangle of the blazed shape of the resist in the cross section is α', and the ratio of the etching rate of the second layer to the etching rate of the resist is δ, and the angle α' is determined by tan α' = tan α / δ.

11. The method of manufacturing a grating according to claim 5, wherein the plane is divided into a plurality of regions, and the patterning or etching conditions are changed so as to change the ratio of w1 to (w1+w2) in each region.

12. A method for forming a grating on a curved surface by transferring the shape of a grating formed on a flat surface by the grating manufacturing method described in claim 5 to a flexible material by electroforming, and then attaching the flexible material to the curved surface.

13. A method for manufacturing a molded part using a mold provided with a lattice manufactured by the method for manufacturing a lattice according to claim 5.

14. The method of making a molded part according to claim 13, wherein the molded part is an augmented reality device.

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