METHOD FOR DIMENSIONING A GREYSCALE LITHOGRAPH MASK

Description

TECHNICAL FIELD

[0001] The present invention relates to the field of photolithography, more specifically to grayscale lithography. The invention particularly concerns the optimization of the mask used in this technique. STATE OF THE ART

[0002] Greyscale lithography is a photolithography technique that allows the creation of three-dimensional (3D) microstructures in a single lithography and development step. It is particularly used in the fabrication of optical microelements, MEMS (microelectromechanical systems), MOEMS (microoptoelectromechanical systems), microfluidic devices, and textured surfaces.

[0003] This technique relies on varying the thickness along a dimension Z over which a photosensitive resin is exposed by modulating the dose of ultraviolet (UV) light received by the resin in space. Once the exposed portions have developed, the resin exhibits a 3D structure (seen by scanning electron microscopy (SEM) and represented in the diagram). Figures 1B And 1D ) and can, for example, serve as a mold for the fabrication of 3D microstructures.

[0004] The dose of ultraviolet radiation received locally by the resin can be modulated, in particular, by adjusting the dimensions and positioning of opaque areas present on the lithography mask ( Figures 1A And 1C ). These opaque areas are typically created by depositing chrome on a glass mask.

[0005] Greyscale lithography thus makes it possible to obtain 3D microstructures with a characteristic height ranging from tens to several hundred micrometers. However, the height at each point of the microstructure is highly dependent on manufacturing errors in the mask.

[0006] The documents US 2005 / 233228 A1, FR 2 968 780 A1, US 2021 / 255543 A1, US 2005 / 118515 A1 present methods for manufacturing greyscale lithography masks but do not allow for obtaining optimal Z-resolution at the level of microstructures manufactured using these masks.

[0007] There is therefore a need to minimize the error on the exposed thickness of the photosensitive resin in order to improve the Z resolution of 3D microstructures fabricated by greyscale lithography. SUMMARY

[0008] To achieve this objective, according to a first aspect of the invention, a method for dimensioning a grayscale lithography mask is provided. The mask extends primarily along a horizontal plane defined by a first direction and a second direction, the plane being perpendicular to a principal direction of radiation exposing a photosensitive resin through the mask. The mask comprises a plurality of areas opaque to the radiation, each opaque area being located within a region of the mask called a pixel. The plurality of opaque areas includes first opaque areas located within first pixels, the first pixels forming a first array of the mask. The method comprises the following steps: a. Establish a first target density D100* of a first surface density D100 of first opaque areas within the first grating, the first target density D100* being configured to allow the resin to be exposed to a given first target thickness e1* when the resin is exposed to radiation through the first grating of the mask, the first target thickness e1* being measured along the principal direction of the radiation, b. Obtain a first value, for the first target density D100*, of the derivative with respect to the first surface density D100 of the first thickness e1 to which the photosensitive resin is exposed when it is exposed to radiation through the first grating having the first surface density D100, said first value being denoted ∂ e 1 D 100 * ∂ D 100 c. Determine a first dimension P x,1 of the first pixels in the first direction, a first dimension P y,1 of the first pixels in the second direction, a first dimension L x,1 of the first opaque areas in the first direction, a first dimension L y,1 of the first opaque areas in the second direction, such that the value of an error on the first target thickness e 1 *, denoted MEEF(e 1 *), is less than a first given threshold, MEEF(e 1 *) being calculated from the following formula: MEEF e 1 * = ∂ e 1 D 100 * ∂ D 100 α 1 + β 1 L x , 1 P x , 1 P y , 1 With β 1 = L y , 1 L x , 1 And α 1 = δL y , 1 δL x , 1 , δL x,1 being an error on L x,1 and δL y,1 being an error on L y,1 , d. Use the dimensions obtained for the dimensioning of the first network of the mask.

[0009] These various steps allow for the optimization of pixel and opaque area sizing in the horizontal plane to minimize errors in the target thickness. Current sizing methods only constrain the choice of opaque area density. Once this density D is fixed, without any further constraints, an infinite number of pixel and opaque area sizings are possible. For example, in the specific case of square pixels with side length P and square opaque areas with side length L, any pair (L,P) satisfying L² < / P² < = D could be suitable. However, not all such pairs lead to satisfactory resolution in the principal radiation direction, at the level of the formed 3D structure.

[0010] The method according to the invention therefore makes it possible to determine pixel and opaque area dimensions leading to a satisfactory level of error.

[0011] The process thus makes it possible to obtain a significant improvement in the quality of 3D structures produced by greyscale lithography.

[0012] A second aspect of the invention relates to a method for manufacturing a greyscale lithography mask comprising the following steps: a. Dimension the mask by implementing the process according to the first aspect, b. Manufacture the mask thus dimensioned. BRIEF DESCRIPTION OF THE FIGURES

[0013] The aims, objects, features and advantages of the invention will become clearer from the detailed description of an embodiment thereof, which is illustrated by the following accompanying drawings in which: THE Figures 1A to 1D They represent greyscale lithography masks and scanning electron microscope views of resins exposed through these masks and then developed. Figures 1A and 1BThey concern the fabrication of 3D structures with platforms at different heights. Figures 1C and 1D concern the fabrication of 3D microlenses with a dome shape. figure 2A represents a grayscale lithography mask. figure 2B is a cross-sectional view of a greyscale lithography mask being used for exposing a photosensitive resin. figure 3 This illustrates the profile of a resin layer exposed in different regions to light radiation passing through masks or regions of the same mask exhibiting varying densities of opaque areas. figure 4 is a graph illustrating the evolution of the remaining resin height after exposure to radiation through the lithography mask and subsequent development, as a function of the density of opaque areas within said lithography mask. figure 5is a graph illustrating the evolution of the error in the height of the remaining resin after exposure as a function of the density of opaque areas and the slope of the contrast curve for fixed pixel dimensions. figure 6 is a graph illustrating the evolution of the error in the height of the remaining resin after exposure as a function of pixel dimensions, with a fixed density of opaque areas. The Figures 7A and 7B illustrate the resizing of a mask according to the method of the invention. figures 8A to 8F illustrate a sequence of steps for establishing a contrast curve between the resin height after development and the density of opaque areas, without a test mask. figure 9A is a flowchart showing a sequence of steps enabling the implementation of the method according to the invention for a pixel array. figure 9Bis a flowchart presenting a sequence of steps enabling the implementation of the method according to the invention for a plurality of pixel networks.

[0014] The drawings are provided as examples and are not intended to limit the scope of the invention. They are schematic representations of the principle intended to facilitate understanding of the invention and are not necessarily to scale with practical applications. In particular, the dimensions are not representative of reality. DETAILED DESCRIPTION

[0015] Before proceeding with a detailed review of embodiments of the invention, optional features that may be used in combination or alternatively are listed below: According to an advantageous embodiment, a is between 0.8 and 1.2, preferably a is equal to 1. According to an example, the step of obtaining the first value of the derivative comprises the following steps: a. Providing a secondary resin of the same nature as the photosensitive resin, b. Isolating a plurality of regions of the secondary resin with radiation, each region being illuminated with a distinct radiation dose, c. For each region of the secondary resin, determining, along the principal direction of the radiation, an illumination thickness of the radiation in said region, d. Establishing, for each region of the secondary resin, a theoretical density of theoretical opaque areas on a theoretical mask, which, upon exposure of said region to radiation through the theoretical mask, would have allowed said region to be exposed to the radiation dose to which said region is exposed, e.Establish a model linking the insolation thickness of the secondary resin layer to the density of opaque zones based on the insolation thickness and theoretical density data obtained for each region. As an example, the step of establishing the theoretical density of theoretical opaque zones for each region of the secondary resin is done at least by applying the following formula: D i = 1 − Q i Q max with i indexing the different regions of the secondary resin, D i the theoretical density associated with region i, Q i the radiation dose to which region i is exposed, and Q max = max(Q i). As an example, the step of obtaining the first value of the derivative comprises the following steps: a. Providing a test mask with a plurality of test gratings, each with a distinct density of opaque test areas; b. Providing a test resin of the same nature as the photosensitive resin; c. Isolating a plurality of regions of the test resin with radiation through the test mask, each region being illuminated through a distinct test grating; d. Determining, for each region of the test resin, an irradiation thickness in said region; e. Establishing a model relating the irradiation thickness of the test resin layer to the density of opaque test areas from the irradiation thickness data obtained for each of the regions.

[0016] Advantageously, the first dimension P x,1 of the first pixels along the first direction and the first dimension P y,1 of the first pixels along the second direction are each less than a principal wavelength of the radiation.

[0017] Preferably, the first pixels have a square shape in the horizontal plane and in which P x,1 =P y,1 =P.

[0018] Preferably, the first opaque areas have a square shape in the horizontal plane and in which L x,1 =L y,1 =L.

[0019] For example, MEEF e 1 * = ∂ e 1 D 100 * ∂ D 100 2 D 100 * P .

[0020] According to a preferred embodiment, the plurality of opaque areas includes at least some second opaque areas located in second pixels, the second pixels forming a second mask array, the method further comprising the following steps: a. Establish a second target density D200* of a second surface density D200 of second opaque zones within the second grating, the second target density D200* being configured to allow the resin to be exposed to a given second target thickness e2* when the resin is exposed to radiation through the second grating of the mask, the second target thickness e2* being measured along the principal direction of the radiation, the second target thickness e2* being distinct from the first target thickness e1*, b. Obtain a second value, for the second target density D200*, of the derivative with respect to the second surface density D200 of the second thickness e2 on which the photosensitive resin is exposed when it is exposed to radiation through the second grating (200) having the second surface density D200, denoted ∂ e 2 D 200 * ∂ D 200 c. Determine a second dimension P x,2 of the second pixels in the first direction, a second dimension P y,2 of the second pixels in the second direction, a second dimension L x,2 of the second opaque areas in the first direction, a second dimension L y,2 of the second opaque areas in the second direction, such that the value of an error on the second target thickness e 2 *, denoted MEEF(e 2 *) is less than a given second threshold, MEEF(e 2 *) being calculated from the following formula: MEEF e 2 * = ∂ e 2 D 200 * ∂ D 200 α 2 + β 2 L x , 2 P x , 2 P y , 2 With β 2 = L y , 2 L x , 2 And α 2 = δL y , 2 δL x , 2 , δL x,2 being an error on L x,2 and δL y,2 being an error on L y,2 , d. Use the dimensions obtained for the dimensioning of the second network of the mask.

[0021] According to an advantageous example, the second network forms a closed contour in the horizontal plane in which the first network is located.

[0022] According to a preferred example, the closed contour formed by the second grating is substantially circular. This example is particularly advantageous in microlens fabrication. In another example, the second threshold for the error on the second target thickness e2* is lower than the first threshold for the error on the first target thickness e1*.

[0023] In the context of the present invention, a resin is defined as an organic or organo-mineral material that can be shaped by exposure to an electron beam, photons, X-rays, a beam of light in the ultraviolet, extreme ultraviolet (EUV) or deep ultraviolet (Deep UV) range, typically in the wavelength range of 193 nm to 248 nm, the emission lines of a mercury lamp, i.e.: 365 nm for the l line, 435 nm for the G line and 404 nm for the H line.

[0024] The invention applies equally to positive resins, i.e., those in which the exposed part becomes soluble in the developer and the unexposed part remains insoluble, and to negative resins, i.e., those in which the unexposed part becomes soluble in the developer and the exposed part remains insoluble.

[0025] The contrast of a resin, commonly denoted γ, reflects the effectiveness of the behavior referred to in the literature as the resin's "threshold" behavior. The greater the contrast, the smaller the dose variation required for the resin to transition from a state in which it cannot be developed to a state in which it can be developed (or vice versa for a negatively saturated resin). The contrast value γ of a resin, whether positive or negative in saturated, is generally determined by the slope of the curve according to the following equation: e e 0 = γln D 0 D , where e is the thickness of the resin film after exposure and development, e 0 is the initial thickness of the resin film, D is the applied exposure dose and D 0 is the dose at which the entire thickness of the film is developed.

[0026] The "nature" of a material such as a resin refers to its chemical composition, that is, the nature and proportion of the species constituting the material. Two layers are considered to be made of the same resin if they have the same chemical composition.

[0027] In this description, the dose is defined as the amount of energy received by a resin per unit area. This energy can be in the form of photons (photolithography) for a photosensitive resin. It is then the product of the intensity of the incident light radiation (generally expressed in Watts / m²) and the exposure time (expressed in seconds). The dose is then usually expressed in Joules per m², or more often in millijoules (mJ) per cm² (10⁻⁴ m²), or even in mJ / m². This energy can also be in the form of electrons (electron lithography) for an electrosensitive resin. The dose is then usually expressed in coulombs per m², or more often in microcoulombs (µC) per cm² (10⁻² m²), or in µC / m².

[0028] A parameter that is "approximately equal to / greater than / less than" a given value means that the parameter is equal to / greater than / less than the given value, within 20% or 10% of that value. A parameter that is "approximately between" two given values ​​means that the parameter is at least equal to the smaller of the two given values, within 20% or 10% of that value, and at most equal to the larger of the two given values, within 20% or 10% of that value.

[0029] In this patent application, the terms thickness for a layer and height for a structure or device will be preferred. Thickness is measured along a direction normal to the principal plane of extension of the layer, and height is measured perpendicular to the horizontal XY plane. Thus, a layer typically has a thickness along the so-called vertical Z direction when it extends primarily along the horizontal XY plane. The relative terms "on," "under," and "below" preferentially refer to positions measured along the vertical Z direction.

[0030] A first object of the present invention relates to a method for sizing a grayscale lithography mask 1. The mask 1 sized using the method according to the invention may be designated as an "optimized mask" or a "resized mask". The mask 1 is shown in Figure 1. Figures 2A and 2BIt extends mainly along a plane (in the horizontal example) XY defined by the first direction X and the second direction Y. More precisely, it has a top face 11 and a bottom face 12, each extending substantially parallel to the horizontal plane XY.

[0031] When using the mask 1, its lower face 12 is positioned opposite an upper face 21 of a resin layer 20, which may also be referred to as resin 20. The upper face 21 of the resin layer 20 also extends parallel to the horizontal plane XY. The resin layer 20 typically rests on a support substrate 40. A sub-layer 30 may be interposed between the support substrate 40 and the resin layer 20. When using the mask 1, the resin layer 20 is exposed to radiation 50 through the mask 1. This radiation 50 has a principal direction substantially perpendicular to the horizontal plane XY. The radiation 50 is typically UV (ultraviolet) radiation; it may thus be radiation emitted in a wavelength range from approximately 100 nm to approximately 400 nm, for example, 365 nm.However, it can also be radiation with wavelengths outside this range. Generally speaking, one can consider, but not be limited to, radiation emitting in a wavelength range from approximately 90 nm to approximately 500 nm.

[0032] Ideally, the resin used should have at least one of the following characteristics: a. A substantially linear response between the radiation dose to which it is exposed and the thickness of the surface exposed. b. A sufficiently low contrast, for example less than 2, to allow for grayscale lithography, but sufficiently high, for example greater than 1, to avoid excessively long exposure times. Advantageously, the contrast is between 1.1 and 1.5. c. Good film-forming properties, guaranteed, for example, by the presence of a film-forming agent in its composition. d. Low inhibition of dissolution.

[0033] Examples of resins that can be used in the context of the invention include resins produced by Micro Resist Technology bearing the commercial references ma-P 1215G, ma-P 1225G and ma-P 1275G.

[0034] The following paragraphs aim to describe mask 1 more precisely with reference to the figure 2A .

[0035] As is commonly done when designing a lithography mask, mask 1 is divided into a plurality of pixels, sometimes called cells. These pixels or cells serve as reference points in the horizontal XY plane and have no physical reality other than a region of the mask containing one, and only one, opaque area. Each pixel defines a theoretical closed contour in the horizontal XY plane containing an opaque area and a transparent area. The opaque and transparent areas, however, do have physical reality. The transparent areas correspond to regions of mask 1 whose composition is transparent to 50 radiation, while the opaque areas correspond to regions of mask 1 whose composition is opaque to 50 radiation. An area is considered opaque, for example, when it blocks at least 90% of the incident 50 radiation.An area is considered transparent when it transmits at least 60% of the incident radiation.

[0036] For example, mask 1 can be a glass mask with chromium deposits. The opaque areas then correspond to the areas of mask 1 where chromium has been deposited, while the transparent areas correspond to the areas that remain free of chromium. According to the principle of grayscale lithography, for a given region of mask 1, the surface density D of the opaque areas within that region determines the radiation dose received by the region of the underlying resin layer 20 and therefore, consequently, the thickness e over which this region of the resin layer 20 is exposed by radiation 50. This density D is typically modulated from one region of the mask to another so as to spatially modulate the exposed thickness in the resin layer 20. For a given region of mask 1, the surface density D of the opaque areas is the ratio between the area of ​​the region occupied by the opaque areas and the total area of ​​the region.These surfaces can for example be evaluated at the lower face 12 of the mask 1, on which the material deposits (for example of chrome) forming the opaque areas are typically made.

[0037] There figure 2A This illustrates the case of pixels arranged in square arrays, but it is possible that these arrays could be of another type. For example, they could be array shapes within a triangular or hexagonal array.

[0038] There figure 2A This also illustrates the case of opaque areas in a square shape in the horizontal XY plane, but it is understood that other shapes are possible. For example, opaque areas can be rectangular, circular, triangular, or even hexagonal.

[0039] The type of network in which the pixels are arranged and the shape of the opaque areas are chosen so as to obtain the desired density within each region of mask 1.

[0040] As illustrated in the figure 2A The opaque areas comprise a plurality of first opaque areas 120, and the transparent areas comprise a plurality of first transparent areas 130. The position of these first opaque areas 120 and these first transparent areas 130 is defined by first pixels 110. The first pixels 110 together form a first array 100 of mask 1. This first array 100 corresponds to a region of mask 1 as described previously. The first array 100 typically comprises more than four first pixels 110.

[0041] The 100-pixel array is preferably contiguous. In other words, ideally, all the 110 pixels of the 100-pixel array are contiguous. The 100-pixel array may optionally exhibit a hollow shape when projected onto the horizontal XY plane.

[0042] Each first pixel 110 defines a closed contour in which there is a first opaque area 120 and a first transparent area 130.

[0043] Within the first 100-pixel array, the first 110 pixels all have the same shape and dimensions. Along the first X direction, the first 110 pixels have a first dimension Px,1, and the first 120 opaque areas have a first dimension Lx,1. Along the second Y direction, the first 110 pixels have a second dimension Py,1, and the first 120 opaque areas have a second dimension Ly,1. Furthermore, within the first 100-pixel array, the first 120 opaque areas are all located in the same position relative to the surrounding 110 pixel. Preferably, the first 120 opaque areas are centered within the 110 pixels.

[0044] Mask 1 advantageously presents a second array 200 of second pixels 210, each comprising a second opaque area 220 and a second transparent area 230. Within the second array 200, the second pixels 210 all have the same shape and dimensions. Along the first direction X, the second pixels 210 have a first dimension Px,2 and the second opaque areas 220 have a first dimension Lx,2. Along the second direction Y, the second pixels 210 have a second dimension Py,2 and the second opaque areas 220 have a second dimension Ly,2.

[0045] The relative positions of the first grating 100 and the second grating depend on the shape of the desired 3D structure. In one embodiment with numerous applications, the second grating 200 forms a closed contour in the horizontal XY plane, and the first grating 100 is contained within this closed contour. Advantageously, this closed contour has a substantially circular shape. For example, the second grating 200 can have the shape of a circular ring in the horizontal XY plane, and the first grating 100 the shape of a disk, the first and second gratings 100 preferably being concentric. This latter case notably allows the formation of a microlens. Preferably, more than two gratings are used to form a microlens.

[0046] It should be noted that since pixels typically have straight edges, it is impossible for the gratings to have perfectly curved shapes, and especially perfectly circular ones. The shapes described for the mask gratings are therefore understood as general shapes whose pixelation should be neglected.

[0047] It is understood that mask 1 can have as many pixel arrays and opaque areas as the intended applications require. All the characteristics described for the first array apply mutatis mutandis to the second array and any additional arrays. What will distinguish one array from another will typically be the density of opaque areas within it, and therefore the thickness of resin that will be exposed when it is irradiated through the array. In other words, the different arrays of mask 1 will typically allow the formation of regions of different heights within the 3D structure created in resin 20. However, it is not impossible for two arrays to have the same density of opaque areas and thus allow the formation of regions of the same height in resin 20. Arrays with the same density of opaque areas may be juxtaposed or not, depending on the 3D structures to be formed.

[0048] As stated in the introduction, one objective of the invention is to provide a solution for improving the resolution along the vertical Z direction of the formed 3D structures. The following paragraphs first aim to show how the error in the thickness of the exposed resin (or the height of the resin after development), measured along the vertical Z direction, is established from the dimensions in the horizontal XY plane of the pixels and opaque areas.

[0049] In the generic case of a mask 1 comprising N opaque zones of dimensions L x,i , L y,i (i varying from 1 to N), each opaque zone being located within a pixel of dimensions P x , P y , the theoretical density (D mask, theoretical ) of opaque zones within the mask is given by the following formula: D masque , th é orique = ∑ i = 1 N L x , i L y , i NP x P y

[0050] This formula does not take into account potential manufacturing errors in mask 1. Such errors can indeed result in variations in the dimensions of the opaque areas compared to the target values. On the other hand, since pixels have no physical reality, it is reasonable to consider that they cannot be subject to manufacturing errors. Denoting δL x,i and δL y,i as the errors in the first dimension L x,i and the second dimension L y,i respectively of the opaque areas, the actual density of opaque areas within the mask is given by the following formula: D masque , r é el = ∑ i = 1 N L x , i + δL x , i L y , i + δL y , i NP x P y

[0051] Furthermore, it is common to estimate that the error δL x,i on the dimension L x,i along X of the opaque areas and the error δL y,i on the dimension L y,i along Y of the opaque areas are proportional: δL y , i = a i δL x , i

[0052] By making this assumption, the Math 2 relation can be rewritten as follows: D masque , r é el = D masque , th é orique + ∑ i = 1 N δL x , i a i L x , i + L y , i NP x P y

[0053] Thus, the error in the density of opaque areas within mask 1 can be calculated as follows, considering that the error δL x,i on the first dimension L x,i of the opaque areas is the same for all opaque areas: δD masque = D masque , th é orique − D masque , r é el = δL x ∑ i = 1 N a i L x , i + L y , i NP x P y

[0054] In the case of opaque areas all having the same dimensions (L x,i =L x and L y,i =L y for all i, and therefore ai =a for all i), it is possible to establish a proportionality link between their dimension along the first direction and their dimension along the second direction: L y = βL x

[0055] In this case, the MEEF error z along the vertical direction Z on the height h of resin remaining after development is given by the following formula: MEEF Z = ∂ h ∂ D masque a + β L x P x P y

[0056] If we consider that the pixels all have the shape of a square with side P in the XY plane (Px = Py = P) and that the opaque areas all have the shape of a square with side L in the XY plane (Lx = Ly = L), then the MEEF error z along the vertical direction Z on the height h of resin remaining after development is given by the following formula: MEEF Z = ∂ h ∂ D masque a + 1 D masque , th é orique P

[0057] Because then, β=1.

[0058] The Math 8 formula shows that it is possible to modulate the MEEF error z by varying the dimensions of the pixels in the network.

[0059] Furthermore, assuming that a=1 (i.e., that the error δL x,i on the first dimension L x,i of the opaque areas and the error δL y,i on the second dimension L y,i of the opaque areas are equal), we can further simplify the formula Math 8: MEEF Z = ∂ h ∂ D masque 2 D masque , th é orique P

[0060] It should be noted that to characterize the impact of sunlight on the resin, two complementary dimensions can be considered, both measured along the vertical Z direction: a. The thickness e over which the resin is exposed, before development, b. The height h of the resin remaining after development of the exposed portion. e and h are linked very directly by the relation h=h 20, initial -e, with h 20, initial The resin height 20 before the development stage. Thus, "determining e" can be achieved by measuring h, and vice versa. Furthermore, given the relationship between h and e, the error in e is approximately equal to the error in h. Therefore, we will denote MEEF interchangeably. z , MEEF(h) or MEEF(e).

[0061] There figure 5This illustrates the evolution of the MEEF z value as a function of the mask parameter δh / δD and the density of opaque areas at the mask level, for fixed pixel dimensions. The plotted curve corresponds to the MEEF z values ​​obtained for a given structure. It can be observed that MEEF z increases as the density of opaque areas decreases. It is therefore particularly crucial to find a solution to reduce MEEF z that can be applied to low density values.

[0062] There figure 6This illustrates the evolution of the MEEF z value as a function of the pixel side length (here, the pixels are square), for a fixed opaque area density. We observe that the larger the pixel side length, the lower the MEEF z value. We can therefore deduce that increasing the pixel dimensions is an effective solution for improving the Z-resolution of 3D structures. This solution is all the more attractive as it is applicable to any density value, and particularly to low density values, which pose a significant challenge (see figure 5 ).

[0063] Thus, a minimum threshold is typically defined for MEEF z, corresponding to a minimum pixel dimension, in order to guarantee good resolution along the vertical Z direction.

[0064] Note that an excessive increase in pixel dimensions can cause a decrease in resolution in the horizontal XY plane beyond acceptable levels. Therefore, a maximum threshold for MEEF z can be used in addition to the minimum threshold to ensure satisfactory resolution in the first X direction and satisfactory resolution in the second Y direction.

[0065] In particular, if a dimension of the opaque areas (along the first X direction or the second Y direction) is greater than or equal to the main wavelength of the 50 radiation, then the opaque areas are likely to be resolved and their shape may be transferred to the 3D structure formed by grayscale lithography using mask 1. Thus, advantageously, Px and Py (P in the case of square pixels) are less than the main wavelength of the 50 radiation. The maximum threshold for MEEF z can correspond to a value guaranteeing this.

[0066] In the case of monochromatic radiation, the principal wavelength is understood to be the single wavelength represented. In the case of polychromatic radiation covering an interval of wavelengths, the principal wavelength can be the wavelength located in the middle of that interval. Method for developing a nomogram linking opaque area density and exposed thickness using a test mask

[0067] The paragraphs below present a first method for obtaining a nomogram linking opaque zone density and exposed thickness in the resin (or resin height after development). This method is preferred when a lithography mask, known as a "test mask," is available for conducting tests to optimize mask dimensions using the method according to the invention. It is understood that any other method may be used to obtain the same data.

[0068] The different steps of this method are illustrated in figures 3 and 4.

[0069] First, a test mask with several distinct gratings, called test gratings, is used to expose a layer of test resin of the same type as that which will be used in conjunction with the optimized mask (resin layer 20). Each of the different gratings in the mask has a different density of opaque areas. After development, the resin height obtained for each density of opaque areas is measured. The experimental results obtained are illustrated in figure 3 .

[0070] Next, using the experimental data obtained with the test mask, a trend curve is established linking the density D of opaque areas at the level of a theoretical mask and the resin height h after development when the resin has been exposed through this mask. The experimental data from the previous step, as well as the model established from these data points, are represented on the graph of the figure 4This trend curve, which corresponds to a contrast curve, is continuous and allows us to estimate the relationship between h and D for density values ​​not present on the test mask.

[0071] The derivative of the function corresponding to this trend line reflects the impact of a change in the density of opaque areas on the resin height after development. This value is used to determine the error in the resin height after development (see formula Math 7).

[0072] Thus, using simple tests with a test mask and a test resin of the same nature as resin 20 which will be used with the optimized mask, we can obtain a key parameter for the dimensioning of this optimized mask. Method for developing a nomogram linking opaque zone density and exposed thickness without requiring a test mask

[0073] The paragraphs below present a second method for obtaining a nomogram linking opaque zone density and exposed thickness in the resin (or resin height after development). This method is preferred when a lithography mask is not available for testing the dimensions of an optimized mask using the method according to the invention. It is understood that any other method can be used to obtain the same data.

[0074] The different steps of this method are illustrated in figures 8A to 8F .

[0075] There figure 8Aillustrates the provision of a stack comprising a secondary resin layer 80 of the same type as that which will be used in association with the optimized mask (resin layer 20). The secondary resin layer 80 is exposed from its upper surface to insolation radiation. Different zones 81, 82, 83, 84 of the resin 80 are insolated with different doses Q81, Q82, Q83, Q84, each inducing a certain thickness e of insolated resin. Therefore, after development ( figure 8B ) of the exposed resin, the secondary resin layer 80 has different heights h 81 , h 82 , h 82 , h 83 , at the level of the different zones 81, 82, 83, 84. We can thus associate with each dose a height of resin obtained after development.

[0076] From the experimental points thus obtained, a trend curve can then be established linking the dose applied to the resin and the height of the resin after development ( figure 8C).

[0077] It is also possible to determine, for each zone i of the resin 80, the theoretical density D i of opaque zones at the level of a theoretical mask that would have allowed the zone in question to be exposed, during its exposure through the theoretical mask, with a dose Q i that it actually received during the calibration step illustrated in the figure 8A The following formula allows us to calculate this density Di, where Qi corresponds to the radiation dose received by zone i during the calibration step ( figure 8A ), and Q max corresponding to the radiation dose received by the area of ​​secondary resin 80 that was most exposed to sunlight (in the example illustrated in the figure 8A , Q max =Q 81 ) : D i = 1 − Q i Q max

[0078] We therefore assume that for Qi = Qmax, the density of opaque areas at the theoretical mask is zero. This amounts to considering that when using this theoretical mask, for an equal exposure time texpo, the intensity I0 of the radiation before it passes through the mask corresponds to the intensity Imax required to obtain the dose Qmax (that is: I0 = Imax with Imax = Qmax / texpo).

[0079] Using the formula above and the experimental points obtained by calibration, a trend curve can be established relating the density D of opaque areas at the theoretical mask level and the height h of resin after development when the resin has been exposed through this mask ( figure 8D ). This trend curve, which corresponds to a contrast curve, is continuous and allows us to estimate the relationship between h and D for dose values ​​(and therefore theoretical densities) not tested during calibration.

[0080] The derivative of the function corresponding to this trend line reflects the impact of a change in the density of opaque areas on the resin height after development. This value is used to determine the error in the resin height after development (see formula Math 7).

[0081] Thus, using a simple calibration on a secondary resin 80 of the same nature as the resin 20 which will be used with the optimized mask, we can obtain a key parameter for the dimensioning of this optimized mask. First example of the implementation of the sizing process according to the invention

[0082] THE Figures 7A and 7B illustrate how the method according to the invention can be used to resize a greyscale lithography mask having an unsatisfactory Z resolution.

[0083] There figure 7AThis illustrates two networks R1, R2 of the same mask 1 (or possibly of two distinct masks 1) used to expose a resin layer in two distinct thicknesses, thus forming, once developed, two regions of distinct heights h1 and h2 within the resin layer. The heights h1 and h2 are obtained by sizing the masks to have the appropriate surface density of opaque areas. In the figure 7A The dimensions of the pixels and opaque areas were chosen arbitrarily, with the sole constraint being that the surface density of opaque areas must allow for the desired resin height. Both gratings have square pixels with side length P. The R1 grating, giving a resin height h1, has square opaque areas with side length L1, while the R2 grating, giving a resin height h2, has square opaque areas with side length L2. The method according to the invention makes it possible to determine the ideal dimensions of the two gratings R1, R2 to limit the error in the resin heights h1, h2. According to the results of the method, concerning grating R1, it is necessary, in order to achieve the desired levels of precision, to assign to the pixels a side P1' with P1'>P and to the opaque areas a side L1' with L1'>L1. Naturally, in order for the height h1 to be the same before and after dimensioning, we have L12< / P2< =L1'2< / P1'2<. By writing L1'=αL1 and P1'=αP1, we can establish a scale factor α.

[0084] Regarding the R2 network, application of the method according to the invention shows that the dimensions P and L2 induce a satisfactory error along z. These dimensions can therefore be retained for the dimensioning of the optimized mask 1.

[0085] Thus, the passage of the figure 7A to the figure 7Billustrates a resizing of mask 1 allowing to obtain the same 3D structures at the level of the photosensitive resin, but guaranteeing a lower error in the vertical direction Z. Second example of the implementation of the sizing method according to the invention

[0086] The following paragraphs describe, with reference to the flowchart presented in figure 9A , a sequence of steps allowing the dimensioning of the first network 100 of the mask 1. These sequences are described for first pixels 110 and first opaque areas 120 of square shape, but it is understood that it can be adapted to any other shape of first pixels 110 and first opaque areas 120. a. Block 1001: In this step, the first target density D100* is defined, allowing the photosensitive resin to be exposed to the first target thickness e*. A pair of values ​​(P1 i=1< , L1 i=1< ) is then chosen for the P1 side of the first pixels 110 and for the L1 side of the opaque areas 120. A counter i, tracking the pairs of values, is initialized (i=1). b. Block 1002: The error Δh on the first target thickness e* is calculated for the pair (P1 i< , L1 i< ). c. Block 1003: The error Δh obtained in the previous step is compared to a previously fixed error threshold Δh. If the error obtained is greater than this threshold, we proceed to the step described in block 1004. Otherwise, we proceed to the step described in block 1005. d.Block 1004: The error on the first target thickness e* for the pair (P 1 i< , L 1 i< ) being unsatisfactory, a new pair of values ​​(P 1 i+1< , L 1 i+1< ) is chosen for the P 1 side of the first pixels 110 and for the L 1 side of the opaque areas 120, with P 1 i+1< >P 1 i< and respecting (L 1 i< ) 2< / (P 1 i< ) 2< = (L 1 i+1< ) 2< / (P 1 i+1< ) 2< to maintain the same density of opaque areas 120. We then return to block 1002. At each passage from block 1004 to block 1002, we increment i by 1. e. Block 1005: The error on the first target thickness e* for the pair that was the subject of the last calculation in block 1002 is satisfactory. This pair can therefore be retained for the dimensioning of the first network 100 of mask 1. Third example of the implementation of the sizing process according to the invention

[0087] The following paragraphs describe, with reference to the flowchart presented in figure 9B, a sequence of steps allowing the dimensioning of mask 1 when it comprises N arrays. These sequences are described for square-shaped pixels and opaque areas, but it is understood that they can be adapted to any other shape of pixels and opaque areas. a. Block 2001: In this first step, the number N of gratings to be dimensioned within the mask is determined. A counter j, tracking these N gratings, is initialized (j=1). b. Block 2002: In this step, the target density Δj* of grating n°j is defined, enabling the exposure of the photosensitive resin to the target thickness ej*. A first pair of values ​​(Pji=1< , Lji=1< ) is then chosen for the Pj side of the pixels of grating n°j and for the Lj side of the opaque areas of grating n°j. Block 2003: The error Δh on the target thickness ej* is then calculated for the pair (Pji< , Lji< ). d. Block 2004: The error Δh obtained in the previous step is compared to a previously fixed error threshold Δh. If the error obtained is greater than this threshold, we proceed to the step described in block 2005. Otherwise, we proceed to the step described in block 2006. e.Block 2005: The error on the first target thickness ej* for the pair (P1i<, L1i<) being unsatisfactory, a new pair of values ​​(P1i+1<, L1i+1<) is chosen for the Pj side of the pixels of the grating n°j and for the Lj side of the opaque areas of the grating n°j, with Pji<i+1<>Pji< and respecting (Lji<)2< / (Pji<)2< = (Lji<i+1<)2< / (Pji<i+1<)2< to maintain the same density of opaque areas within the grating n°j. We then move on to block 2003. At each transition from block 2005 to block 2003, we increment i by 1. f. Block 2006: The error in the first target thickness ej* for the pair that was the subject of the last calculation in block 2003 is satisfactory. This pair can therefore be retained for the sizing of network no. j of mask 1. g. Block 2007: We check if j=N. If not, we increment j by 1 and return to block 2002. If it is, we proceed to block 2008. h. Block 2008: The N networks have been sized.The mask as a whole can be resized.

[0088] The invention is not limited to the embodiments described above and extends to all embodiments covered by the invention as defined in the claims below. In particular, the implementation of the process according to the invention is not limited to the fabrication of microlenses and can naturally enable the fabrication of 3D structures as diverse as pillars, cones, slanted gratings, and stepped structures.

Claims

1. Method for sizing a greyscale lithography mask (1), the mask (1) mainly extending along a horizontal plane (XY) defined by a first direction (X) and a second direction (Y), the plane being perpendicular to a main direction of a light-exposing radiation of a photosensitive resin (20) through the mask (1), the mask (1) comprising a plurality of opaque zones to the radiation, each opaque zone being located in a zone of the mask (1) called pixel, the plurality of opaque zones comprising first opaque zones (120) being located in first pixels (110), the first pixels (110) forming a first grating (100) of the mask (1), the method comprising the following steps: • Establishing a first target density D100* of a first surface density D100 of first opaque zones (120) within the first grating (100), the first target density D100* being configured to enable the resin (20) to be exposed to light over a first given target thickness e1* when the resin (20) is exposed to radiation through the first mask (1) grating (100), the first target thickness e1* being measured in the main direction of the radiation, • Obtaining a first value, for the first target density D100*, of the derivative with respect to the first surface density D100 of the first thickness e1 over which the photosensitive resin (20) is exposed to light, when it is exposed to a radiation through the first grating (100) having the first surface density D100, said first value being referenced ∂ e 1 D 100 * ∂ D 100 , • Determining a first dimension Px,1 of the first pixels (110) in the first direction (X), a first dimension Py,1 of the first pixels (110) in the second direction (Y), a first dimension Lx,1 of the first opaque zones (120) in the first direction (X), a first dimension Ly,1 of the first opaque zones (120) in the second direction (Y), such that the value of an error over the first target thickness e1*, referenced MEEF(e1*), is less than a first given threshold, MEEF(e1*) being calculated from the following formula: MEEF e 1 * = ∂ e 1 D 100 * ∂ D 100 a 1 + β 1 L x , 1 P x , 1 P y , 1 With β 1 = L y , 1 L x , 1 and a 1 = δL y , 1 δL x , 1 , δLx,1 being an error over Lx,1 and δLy,1 being an error over Ly,1, • Using the dimensions obtained for the sizing of the first mask (1) grating (100).

2. Method according to the preceding claim, wherein a1 is between 0.8 and 1.2, preferably a is equal to 1.

3. Method according to any one of the preceding claims, wherein the step of obtaining the first value of the derivative comprises the following steps: • Providing a secondary resin (80) of the same nature as the photosensitive resin (20), • Exposing a plurality of regions (81, 82, 83, 84) of the secondary resin (80) to light with a radiation, each region (81, 82, 83, 84) being exposed to light with a distinct dose (Q81, Q82, Q83, Q84) of radiation, • For each region (81, 82, 83, 84) of the secondary resin (80), determining in the main direction of the radiation, a light-exposing thickness of the radiation in said region (81, 82, 83, 84), • Establishing, for each region (81, 82, 83, 84) of the secondary resin (80), a theoretical density (D81, D82, D83, D84) of theoretical opaque zones on a theoretical mask, which, during exposure to a radiation of said region (81, 82, 83, 84) through the theoretical mask, would have made it possible to expose said region to the dose (Q81, Q82, Q83, Q84) of radiation, to which said region (81, 82, 83, 84) is exposed, • Establishing a model connecting the light-exposing thickness of the secondary resin layer (80) to the opaque zone density from light-exposing thickness and theoretical density data (D81, D82, D83, D84) obtained for each of the regions (81, 82, 83, 84).

4. Method according to the preceding claim, wherein the step of establishing, for each region (81, 82, 83, 84) of the secondary resin (80), of the theoretical density (D81, D82, D83, D84) of theoretical opaque zones, is done at least by application of the following formula: D i = 1 − Q i Q max with i indexing the different regions (81, 82, 83, 84) of the secondary resin (80), Di the theoretical density associated with the region i, Qi the dose of radiation to which the region i is exposed and Qmax=max(Qi).

5. Method according to claim 1 or claim 2, wherein the step of obtaining the first value of the derivative comprises the following steps: • Providing a test mask having a plurality of test gratings, each having a distinct density of test opaque zones, • Providing a test resin of the same nature as the photosensitive resin (20), • Exposing a plurality of regions of the test resin to light with a radiation through the test mask, the exposing to light of each region being done through a distinct test grating, • Determining, for each region of the test resin, a light-exposing thickness of the radiation in said region, • Establishing a model connecting the light-exposing thickness of the test resin layer to the density of test opaque zones from light-exposing thickness data obtained for each of the regions.

6. Method according to any one of the preceding claims, wherein the first dimension Px,1 of the first pixels (110) in the first direction (X) and the first dimension Py,1 of the first pixels (110) in the second direction (Y) are each less than a main wavelength of the radiation (50).

7. Method according to any one of the preceding claims, wherein the first pixels (110) have a square shape in the horizontal plane (XY) and wherein Px,1=Py,1=P.

8. Method according to any one of the preceding claims, wherein the first opaque zones (120) have a square shape in the horizontal plane (XY) and wherein Lx,1=Ly,1=L.

9. Method according to the two preceding claims combined, wherein: MEEF e 1 * = ∂ e 1 D 100 * ∂ D 100 2 D 100 * P 10. Method according to any one of the preceding claims, wherein the plurality of opaque zones comprises at least second opaque zones (220) being located in second pixels (210), the second pixels (210) forming a second mask (1) grating (200), the method further comprising the following steps: • Establishing a second target density D200* of a second surface density D200 of second opaque zones (220) within the second grating (200), the second target density D200* being configured to enable the resin to be exposed to light over a second given target thickness e2* when the resin is exposed to the radiation through the second mask (1) grating (200), the second target thickness e2* being measured in the main direction of the radiation, the second target thickness e2* being distinct from the first target thickness e1*, • Obtaining a second value, for the second target density D200*, of the derivative with respect to the second surface density D200 of the second thickness e2 over which the photosensitive resin is exposed to light when it is exposed to a radiation through the second grating (200) having the second surface density D200, referenced ∂ e 2 D 200 * ∂ D 200 , • Determining a second dimension Px,2 of the second pixels (210) in the first direction (X), a second dimension Py,2 of the second pixels (210) in the second direction (Y), a second dimension Lx,2 of the second opaque zones (220) in the first direction (X), a second dimension Ly,2 of the second opaque zones (220) in the second direction (Y), such that the value of an error over the second target thickness e2*, referenced MEEF(e2*) is less than a second given threshold, MEEF(e2*) being calculated from the following formula: MEEF e 2 * = ∂ e 2 D 200 * ∂ D 200 a 2 + β 2 L x , 2 P x , 2 P y , 2 With β 2 = L y , 2 L x , 2 and a 2 = δL y , 2 δL x , 2 , δLx,2 being an error over Lx,2 and δLy,2 being an error over Ly,2, • Using the dimensions obtained for the sizing of the second mask (1) grating (200).

11. Method according to the preceding claim, wherein the second grating (200) forms, in the horizontal plane (XY), a closed contour, wherein the first grating (100) is located.

12. Method according to the preceding claim, wherein the closed contour formed by the second grating (200) is substantially circular.

13. Method according to any one of the two preceding claims, wherein the second threshold for the error over the second target thickness e2* is less than the first threshold for the error over the first target thickness e1*.

14. Method for manufacturing a greyscale lithography mask (1) comprising the following steps: • Sizing the mask (1) by implementation of the method according to any one of the preceding claims, • Manufacturing the mask (1) thus sized.