Method for sizing a greyscale lithography mask
Patent Information
- Application Number
- FR2023002191
- Authority / Receiving Office
- FR · FR
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2023-03-09
- Publication Date
- 2025-03-07
- Estimated Expiration
- 2043-03-09
Smart Images
Figure 00000025_0000 
Figure 00000025_0001 
Figure 00000026_0000
Abstract
Description
Title of the invention: Method for sizing a grayscale lithography mask Technical field
[0001] The present invention relates to the field of photolithography, more precisely that of grayscale or grayscale lithography, commonly referred to by the English expression "grayscale lithography". The invention particularly relates to the optimization of the mask used in this technique. STATE OF THE ART
[0002] Grayscale lithography is a photolithography technique allowing the production of three-dimensional (3D) microstructures in a single lithographic and development step. It is particularly used in the manufacture of optical microelements, MEMS (microelectromechanical Systems), MOEMS (microoptoelectromechanical Systems), microfluidic devices or even textured surfaces.
[0003] This technique is based on varying the thickness along a dimension Z on which a photosensitive resin is exposed by modulating in space the dose of ultraviolet (UV) received by the resin. Once the exposed portions have been developed, the resin has a 3D structure (scanning electron microscope (SEM) views shown in Figures 1B and 1D) and can, for example, be used as a mold for the manufacture of 3D microstructures.
[0004] The dose of ultraviolet received locally by the resin can in particular be modulated by adjusting the dimensions and positioning of opaque zones present on the lithography mask (figures 1A and 1C). These opaque zones are typically produced by depositing chrome on a glass mask.
[0005] Gray scale lithography thus makes it possible to obtain 3D microstructures with a characteristic height ranging from around ten to several hundred micrometers. However, the height at each point of the microstructure is very dependent on manufacturing errors at the mask level.
[0006] There is therefore a need to minimize the error in the exposed thickness of the photosensitive resin in order to improve the Z resolution of 3D microstructures manufactured by grayscale lithography. SUMMARY
[0007] To achieve this objective, according to a first aspect of the invention relates to a method for sizing a grayscale lithography mask, the mask extending mainly along a horizontal plane defined by a first direction and a second direction, the plane being perpendicular to a main direction of radiation irradiating a photosensitive resin through the mask. The mask comprises a plurality of zones opaque to the radiation, each opaque zone being located in a zone of the mask called a pixel, the plurality of opaque zones comprising first opaque zones located in first pixels, the first pixels forming a first network of the mask. The method comprises the following steps: a. Establishing a first target density Di00* of a first surface density D 100 of first opaque zones within the first network, the first target density Dioo* being configured to allow the resin to be exposed to a given first target thickness ei* when the resin is exposed to radiation through the first network of the mask, the first target thickness ei* being measured along the main direction of the radiation, b. Obtaining a first value, for the first target density Dioo*, of the derivative with respect to the first surface density Dioo of the first thickness ei on which the photosensitive resin is exposed when it is exposed to radiation through the first network having the first surface density Dioo, said first value being noted 3f((D100'), c. Determine a first dimension Px i of the first pixels in the first direction, a first dimension Py>i of the first pixels in the second direction, a first dimension LXji of the first opaque zones in the first direction, a first dimension Ly>i of the first opaque zones in the second direction, so that the value of an error on the first target thickness ei*, noted MEEF(ei*), is less than a first given threshold, MEEF(ei*) being calculated from the following formula: MEEF(en=^DD''M'^^ 1 ' dD^ With o _ a and „ _ , ôLx i being an error on Lx i and ôLv i being a al~ÔLZ ' error on Ly>1, d. Use the dimensions obtained for the dimensioning of the first network of the mask.
[0008] These different steps make it possible to optimize the dimensioning of pixels and opaque zones in the horizontal plane in order to limit the error on the target thickness. Indeed, current dimensioning methods only constrain the choice of the density of opaque zones. Once this density D is fixed, without any other constraint, an infinite number of dimensionings of pixels and opaque zones are possible. By For example, in the particular case of square pixels of side P and square opaque areas of side L, any (L,P) pair satisfying L2 / P2=D could be suitable. However, not all of these pairs lead to satisfactory resolution in the main radiation direction, at the level of the 3D structure formed.
[0009] The method according to the invention therefore makes it possible to determine dimensions of pixels and opaque zones leading to a satisfactory level of error.
[0010] The method thus makes it possible to obtain a significant improvement in the quality of 3D structures produced by grayscale lithography.
[0011] A second aspect of the invention relates to a method of manufacturing a grayscale lithography mask comprising the following steps: a. Size the mask by implementing the method according to the first aspect, b. Make the mask thus sized. BRIEF DESCRIPTION OF THE FIGURES
[0012] The aims, objects, as well as the characteristics and advantages of the invention will emerge more clearly from the detailed description of an embodiment thereof which is illustrated by the following accompanying drawings in which:
[0013] [Fig. 1A] Figures 1A to 1D represent grayscale lithography masks and scanning electron microscope views of resists exposed through these masks and then developed. Figures 1A and 1B concern the fabrication of 3D structures having trays at different heights.
[0014] [Fig.lB]
[0015] [Fig.1C] Figures 1C and 1D relate to the fabrication of 3D microlenses having a dome shape.
[0016] [Fig.lD]
[0017] [Fig.2A] [Fig.2A] represents a grayscale lithography mask.
[0018] [Fig.2B] [Fig.2B] is a sectional view of a lithography mask on a scale of gray being used for the exposure of a photosensitive resin
[0019] [Fig.3] [Fig.3] illustrates the profile of a layer of resin exposed in different regions to light radiation passed through masks or regions of the same mask having different densities of opaque zones.
[0020] [Fig.4] [Fig.4] is a graph illustrating the evolution of the height of resin remaining after exposure to radiation through the lithography mask and then development, as a function of the density of opaque zones at the level of said lithography mask.
[0021] [Fig.5] [Fig.5] is a graph illustrating the evolution of the error on 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.
[0022] [Fig.6] [Fig.6] is a graph illustrating the evolution of the error on the height of the remaining resin after exposure as a function of the pixel dimensions, at fixed density of opaque zones.
[0023] [Fig.7A] Figures 7A and 7B illustrate the resizing of a mask according to the method according to the invention.
[0024] [Fig.7B]
[0025] [Fig.8A] Figures 8A to 8F illustrate a sequence of steps for establishing a contrast curve between the height of the resin after development and the density of opaque areas, without a test mask.
[0026] [Fig.8B]
[0027] [Fig.8C]
[0028] [Fig.8D]
[0029] [Fig.8E]
[0030] [Fig. 8F]
[0031] [Fig.9A] [Fig.9A] is a flowchart showing a sequence of steps enabling the implementation of the method according to the invention for a pixel array.
[0032] [Fig.9B] [Fig.9B] is a flowchart showing a sequence of steps enabling the implementation of the method according to the invention for a plurality of pixel arrays.
[0033] The drawings are given as examples and are not limiting of the invention. They constitute schematic representations of principle intended to facilitate the understanding of the invention and are not necessarily on the scale of practical applications. In particular, the dimensions are not representative of reality. DETAILED DESCRIPTION
[0034] Before beginning a detailed review of embodiments of the invention, optional features which may possibly be used in combination or alternatively are set out below:
[0035] According to an advantageous embodiment, a is between 0.8 and 1.2, preferably a is equal to 1.
[0036] According to one 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. Insolating a plurality of regions of the secondary resin with radiation, each region being insolated with a distinct dose of radiation, c. For each region of the secondary resin, determine, according to the main direction of radiation, a thickness of insolation of the radiation in said region, d. Establish, for each region of the secondary resin, a theoretical density of theoretical opaque areas on a theoretical mask, which, when exposing 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 from the insolation thickness and theoretical density data obtained for each of the regions.
[0037] According to one example, the step of establishing, for each region of the secondary resin, the theoretical density of theoretical opaque zones, is done at least by applying the following formula: / > — [ with i indexing the different regions of the secondary resin, D; the Quai theoretical density associated with region i, Q; the radiation dose to which region i is exposed and Qmax=max(Qi).
[0038] According to one example, the step of obtaining the first value of the derivative comprises the following steps: a. Providing a test mask having a plurality of test networks each having a distinct density of opaque test areas, b. Provide a test resin of the same type as the photosensitive resin, c. Insulating a plurality of regions of the test resin with radiation at through the test mask, the exposure of each region being done through a separate test network, d. Determine, for each region of the test resin, a thickness of insolation of the radiation in said region, e. Establish a model linking the insolation thickness of the test resin layer to the density of opaque test zones from the insolation thickness data obtained for each of the regions.
[0039] Advantageously, the first dimension PXji of the first pixels along the first direction and the first dimension Py>i of the first pixels along the second direction are each less than a main wavelength of the radiation.
[0040] Preferably, the first pixels have a square shape in the horizontal plane and in which Px i=Py i=P.
[0041] Preferably, the first opaque zones have a square shape in the horizontal plane and in which Lx i=Ly i=L.
[0042] According to one example, ( '
[0043] According to a preferred embodiment, the plurality of opaque zones comprises at least less than second opaque areas located in second pixels, the second pixels forming a second array of the mask, the method further comprising the following steps: a. Establishing a second target density D200* of a second surface density D200 of second opaque zones within the second network, 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 network of the mask, the second target thickness e2* being measured along the main direction of the radiation, the second target thickness e2* being distinct from the first target thickness ei*, b. Obtain a second value, for the second target density D200*, of the derivative with respect to the second surface density D2Oo of the second thickness e2 on which the photosensitive resin is exposed when it is exposed to radiation through the second network (200) having the second surface density D2Oo, noted ^7(^200), 9¾ 00 c. Determine a second dimension Px2 of the second pixels in the first direction, a second dimension Py 2 of the second pixels in the second direction, a second dimension Lx>2 of the second opaque areas in the first direction, a second dimension Ly>2 of the second opaque areas in the second direction, so that the value of an error on the second target thickness e2*, noted MEEF(e2*) is less than a second given threshold, MEEF(e2*) being calculated from the following formula: meef^ = ^^ With 0 _ Ç2 and ~ _ SL>2 , ôLx2 being an error on Lx2 and ôLv2 being a error on Ly>2, d. Use the dimensions obtained for the dimensioning of the second mask network.
[0044] According to an advantageous example, the second network forms in the horizontal plane a closed contour in which the first network is located.
[0045] According to a preferred example, the closed contour formed by the second network is substantially circular. This example is particularly advantageous in the manufacture of microlenses.
[0046] According to one 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 ei*.
[0047]
[0048]
[0049]
[0050]
[0051]
[0052] 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 a beam of electrons, photons, X-rays, a beam of light in the ultraviolet, extreme ultraviolet (UEV) or deep ultraviolet (Deep UV) range, typically in the wavelength range from 193 nm to 248 nm, the emission lines of a mercury lamp, i.e.: 365 nm for the I line, 435 nm for the G line and 404 nm for the H line. The invention applies both to positive resins, that is to say, the exposed part of which becomes soluble in the developer and the unexposed part remains insoluble, and to negative resins, that is to say, the unexposed part of which becomes soluble in the developer and the exposed part remains insoluble. The contrast of a resin, commonly noted y, reflects the effectiveness of the behavior referred to in the literature as "threshold" of the resin. The greater the contrast, the smaller a dose variation is required for the resin to go from a state in which it cannot be developed to a state in which it can be developed (or vice versa for a negative resin). The value of the contrast y of a resin, whether positive or negative tone, is generally determined by the slope of the curve according to the following equation: e_ — vin( 31 \, where e is the thickness of the resin film after exposure and development development, e0 is the thickness of the initial resin film, D is the exposure dose applied and Do is the dose at which the entire thickness of the film is developed. 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. In this description, a dose is defined as a quantity 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 Watt / m2) and the exposure time (expressed in seconds). The dose is then usually expressed in Joules per m2, or more often in milli Joules (mJ) per cm 2 (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 micro Coulombs (pC) per cm 2 (10 2 m2) or in pC / m2. A parameter "substantially equal / greater / less than" a given value means that this parameter is equal / greater / less than the given value, plus or minus minus 20%, or even 10%, near this value. A parameter "substantially between" two given values is understood to mean that this parameter is at least equal to the smallest given value, plus or minus 20%, or even 10%, near this value, and at most equal to the largest given value, plus or minus 20%, or even 10%, near this value.
[0053] In the present patent application, we will preferentially speak of thickness for a layer and of height for a structure or a device. The thickness is taken in a direction normal to the main extension plane of the layer, and the height is taken perpendicular to the horizontal plane XY. Thus, a layer typically has a thickness in the so-called vertical direction Z, when it extends mainly along the horizontal plane XY. The relative terms “on”, “under”, “underlying” preferentially refer to positions taken in the vertical direction Z.
[0054] A first object of the present invention relates to a method for dimensioning a grayscale lithography mask 1. The mask 1 dimensioned using the method according to the invention may be designated “optimized mask” or “resized mask”.
[0055] The mask 1 is shown in Figures 2A and 2B. It 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 an upper face 11 and a lower face 12 each extending substantially parallel to the horizontal plane XY.
[0056] When using the mask 1, its lower face 12 is placed opposite an upper face 21 of a resin layer 20, which may also be designated 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.
[0057] When using the mask 1, the resin layer 20 is exposed to radiation 50 through the mask 1. This radiation 50 has a main direction substantially perpendicular to the horizontal plane XY. The radiation 50 is typically UV radiation (for ultraviolet); it can thus be radiation emitting in a wavelength range from approximately 100 nm to approximately 400 nm, for example 365 nm. However, it can also be radiation having wavelengths outside this range. In general, it is possible to envisage, without limitation, radiation emitting in a wavelength range from approximately 90 nm to approximately 500 nm.
[0058] Ideally, the resin 20 used has at least one of the following characteristics: a. A substantially linear response between the radiation dose to which it is exposed and the thickness over which it is exposed. b. A contrast low enough, for example less than 2, to allow the implementation of grayscale lithography, but high enough, 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.
[0059] Examples of resins that can be used in the context of the invention include, in particular, the resins produced by the company Micro Resist Technology bearing the commercial references ma-P 1215G, ma-P 1225G and ma-P 1275G.
[0060] The following paragraphs aim to describe mask 1 more precisely with reference to [Fig.2A].
[0061] As is commonly done when designing a lithography mask, the mask 1 is divided into a plurality of pixels, sometimes referred to as cells. These pixels or cells serve as reference points in the horizontal XY plane and have no physical reality other than an area of the mask including one, and only one, opaque area. Each pixel defines a theoretical closed contour in the horizontal XY plane in which there is an opaque area and a transparent area. The opaque areas and the transparent areas have a physical reality. The transparent areas correspond to regions of the mask 1 whose composition is transparent to the 50 radiation, while the opaque areas correspond to regions of the mask 1 whose composition is opaque to the 50 radiation. A zone is for example considered opaque when it stops at least 90% of the incident 50 radiation.An area is considered transparent when it transmits at least 60% of the incident radiation.
[0062] For example, mask 1 may be a glass mask with chrome deposits. The opaque areas then correspond to the areas of mask 1 where chrome has been deposited, while the transparent areas correspond to the areas that have remained free of chrome.
[0063] According to the principle of grayscale lithography, for a given region of the mask 1, the surface density D of the opaque zones within this 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 the radiation 50. This density D is typically modulated from one region to another of the mask so as to spatially modulate the exposed thickness in the resin layer 20.
[0064] For a given region of the mask 1, the surface density D of the opaque zones is the ratio between the surface area of the region occupied by the opaque zones and the total surface area of the region. These surfaces can for example be evaluated at the level of the lower face 12 of the mask 1, on which the deposits of material (for example of chromium) forming the opaque zones are typically made.
[0065] [Fig.2A] illustrates the case of pixels arranged in square networks, but it is conceivable that these are of another type. For example, they may be network shapes among a triangular network or a hexagonal network.
[0066] [Fig.2A] also illustrates the case of opaque areas of square shape in the horizontal plane XY, but it is understood that other shapes are possible. The opaque areas can for example be rectangular, circular, triangular or even hexagonal.
[0067] The type of network according to which the pixels are arranged and the shape of the opaque zones are chosen so as to obtain the desired density within each region of the mask 1.
[0068] As illustrated in [Fig.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 marked by first pixels 110. The first pixels 110 together form a first network 100 of the mask 1. This first network 100 corresponds to a region of the mask 1 as described previously. The first network 100 typically comprises more than four first pixels 110.
[0069] The network 100 is preferably in one piece. In other words, preferably, all the pixels 110 of the network 100 are in one piece. The network 100 may optionally have a hollow shape in projection in the horizontal plane XY.
[0070] Each first pixel 110 defines a closed contour in which there is a first opaque zone 120 and a first transparent zone 130.
[0071] Within the first network 100, the first pixels 110 all have the same shape and the same dimensions. In the first direction X, the first pixels 110 have a first dimension Px4 and the first opaque zones 120 have a first dimension Lx4. In the second direction Y, the first pixels 110 have a second dimension Py i and the first opaque zones 120 have a second dimension Ly>i. Furthermore, within the first network 100, the first opaque zones 120 are all located at the same position relative to the pixel 110 which surrounds them. Preferably, the first opaque zones 120 are centered in the pixels 110.
[0072] The mask 1 advantageously has a second network 200 of second pixels 210 each comprising a second opaque zone 220 and a second zone transparent 230. Within the second network 200, the second pixels 210 all have the same shape and the same dimensions. In the first direction X, the second pixels 210 have a first dimension Px2 and the second opaque zones 220 a first dimension Lx>2. In the second direction Y, the second pixels 210 have a second dimension Py 2 and the second opaque zones 220 a second dimension Ly>2.
[0073] The relative positions of the first grating 100 and the second grating depend on the shape of the 3D structure that one wishes to manufacture. According to an embodiment finding numerous applications, the second grating 200 forms a closed contour in the horizontal plane XY and the first grating 100 is contained in this closed contour. Advantageously, this closed contour has a substantially circular shape. For example, the second grating 200 may have in the horizontal plane XY the shape of a circular crown and the first grating 100 that of a disc, the first grating 100 and the second grating 200 preferably being concentric. This latter case makes it possible in particular to form a microlens. Preferably, more than two gratings are used to form a microlens.
[0074] It should be noted that since pixels typically have straight edges, it is impossible for the networks to have perfectly curved shapes, and in particular perfectly circular ones. The shapes described for the mask networks are therefore understood as general shapes whose pixelation must be neglected.
[0075] It is understood that the mask 1 can have as many pixel arrays and opaque zones as the intended applications require. All the characteristics described for the first array apply mutatis mutandis to the second array and to any other additional array. What will distinguish one array from another will typically be the density of opaque zones within it and therefore the thickness of resin which will be insolated when the latter is exposed to radiation through the array. In other words, the different arrays of the mask 1 will typically make it possible to form regions of different heights within the 3D structure produced in the resin 20. It is not excluded, however, that two arrays have the same density of opaque zones and therefore make it possible to form regions of the same height in the resin 20. Arrays having the same density of opaque zones may be juxtaposed or not, depending on the 3D structures to be formed.
[0076] As stated in the introductory part, an objective of the invention is to propose a solution for improving the resolution along the vertical Z direction of the formed 3D structures. The following paragraphs aim first of all to show how the error on the thickness of 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.
[0077] In the generic case of a mask 1 comprising N opaque zones of dimensions L x>i, Ly>i (i varying from 1 to N), each opaque zone being located within a pixel of dimensions Px, Py, the theoretical density (Dmask> theoretical) of opaque zones within the mask is given by the following formula:
[0078] [Math.l] y A' n _ 2^ A.Au ^theoreticalmask ^pp
[0079] This formula does not take into account potential manufacturing errors of the mask 1. Such errors can indeed result in variations in the dimensions of the opaque zones compared to the target values. On the other hand, since the pixels have no physical reality, it is reasonable to consider that they cannot be subject to manufacturing errors. By noting ôLx i and ôLy the errors on the first dimension Lx ; and the second dimension Ly>i respectively of the opaque zones, the real density of opaque zones within the mask is given by the following formula:
[0080] [Math.2] F) , _ ' mask, real jq pp
[0081] Furthermore, it is common to estimate that the error ôLxi on the dimension Lx>i along X of the opaque zones and the error ôLy>i on the dimension Ly>i along Y of the opaque zones are proportional:
[0082] [Math.3] 1 XJ
[0083] Making this assumption, the relation Math 2 can be rewritten as follows:
[0084] [Math.4] ~ „ J^fîL^ajLyj+Lyj) U maskj-éel ^maskjtheoretical. "E ?qp p
[0085] Thus, the error in the density of opaque zones within the mask 1 can be calculated as follows, considering that the error ôLx>is on the first dimension Lx>ides opaque zones is the same for all opaque zones:
[0086] [Math.5] SDmask masquafheorique " mayqite real NPyPy
[0087] In the case of opaque zones all having the same dimensions (Lx>i=Lx and Ly>i =Ly for all i, and therefore a;=a for all i), it is possible to establish a proportionality link between their dimension in the first direction and their dimension in the second direction:
[0088] [Math.6] Ly = pLx
[0089] In this case, the MEEFZ error along the vertical direction Z on the height h of resin remaining after development is given by the following formula:
[0090] [Math.7] mfff —
[0091] If we consider that the pixels all have in the XY plane the shape of a square with side P (Px=Py=P) and that the opaque zones all have in the XY plane the shape of a square with side L (Lx=Ly=L), then the error MEEFZ in the vertical direction Z on the height h of resin remaining after development is given by the following formula:
[0092] [Math. 8] AJ £7 T7T- ()h MEE1 2 - Ô5 p ^Lymasc't-te. 1
[0093] Because then, [3=1.
[0094] The Math 8 formula shows that it is possible to modulate the MEEFZ error by varying the dimensions of the network pixels.
[0095] Furthermore, assuming that a=l (i.e. that the error ôLXji on the first dimension L Xji of the opaque zones and the error ôLy>i on the second dimension Ly>i of the opaque zones are equal), we can further simplify the formula Math 8:
[0096] [Math.9] A / EEF _ dDmasque
[0097] It should be noted that to characterize the impact of insolation on the resin, two complementary dimensions can be considered, both measured along the vertical Z directions: a. The thickness e on which the resin is exposed, before development, b. The height h of the remaining resin after development of the exposed portion.
[0098] e and h are linked very directly by the relationship h=h2o,initiale-e, with 1¾initiale the height of the resin 20 before the development step. Thus, "determining e" can involve measuring h, and vice versa. Furthermore, given the relationship between h and e, the error on e is substantially equal to the error on h. We will thus denote indifferently MEEFZ, MEEF(h) or MEEF(e).
[0099] [Fig.5] illustrates the evolution of the value of MEEFZ as a function of the parameter ôh / ôD mask and the density of opaque zones at the mask level, for fixed pixel dimensions. The plotted curve corresponds to the values of MEEFZ obtained for a given structure. It is observed that MEEFZ increases when the density of opaque zones decreases. It is therefore particularly crucial to find a solution to reduce MEEFZ that can be applied for low density values.
[0100] [Fig.6] illustrates the evolution of the value of MEEFZ as a function of the length of the side of the pixels (here the pixels are square), and this for a fixed density of opaque zones. We observe that the larger the side of the pixels, the lower MEEFZ. We therefore deduce that to improve the Z resolution of 3D structures, increasing the dimensions of the pixels is an effective solution. This solution appears all the more interesting as it is applicable for any density value, and in particular for low density values, which pose a particular problem (see [Fig.5]).
[0101] Thus, a minimum threshold is typically defined for MEEFZ, corresponding to a minimum dimension of the pixels, in order to guarantee good resolution in the vertical direction Z.
[0102] It is noted that too large an increase in the pixel dimensions can cause a decrease in the resolution in the horizontal XY plane beyond acceptable levels. Thus, a maximum threshold for MEEFZ can be used in addition to the minimum threshold to satisfy a satisfactory resolution in the first X direction and a resolution in the second Y direction.
[0103] In particular, if a dimension of the opaque zones (along the first direction X or the second direction Y) is greater than or equal to the main wavelength of the radiation 50, then the opaque zones risk being resolved and their shape risk being transferred to the 3D structure formed by grayscale lithography using the mask 1. Thus, advantageously, Px and Py (P in the case of square pixels) are less than the main wavelength of the radiation 50. The maximum threshold for MEEFZ may correspond to a value guaranteeing this.
[0104] In the case of monochromatic radiation, the main wavelength is understood to be the only wavelength represented. In the case of polychromatic radiation covering an interval of wavelengths, the main wavelength may be the wavelength located in the middle of this interval.
[0105] Method for developing an abacus linking density of opaque zones and exposed thickness using a test mask
[0106] The paragraphs below present a first method by which it is possible to obtain a chart linking density of opaque zones and thickness exposed in the resin (or height of the resin after development). This method is preferred when a lithography mask called a “test mask” is available which can be used to carry out tests with a view to sizing the mask optimized using the method according to the invention. It is understood that any other method can be implemented to obtain the same data.
[0107] The different stages of this method are illustrated in Figures 3 and 4.
[0108] First, a test mask presenting several distinct networks, called networks tests, is used to expose a layer of test resin of the same nature as that which will be used in association with the optimized mask (resin layer 20). The different networks of the mask each have 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 [Fig.3].
[0109] A trend curve is then established from the experimental points obtained using the test mask, linking the density D of opaque zones at the level of a theoretical mask and the height h of resin after development when the resin has been exposed through this mask. The experimental points from the previous step as well as the model established from these points are represented on the graph in [Fig.4]. This trend curve, which corresponds to a contrast curve, is continuous and makes it possible to estimate the relationship between h and D for density values not present on the test mask.
[0110] The derivative of the function corresponding to this trend curve reflects the impact of a variation in the density of opaque areas on the height of the resin after development. This value is involved in determining the error on the height of the resin after development (see formula Math 7).
[0111] Thus, using simple tests using a test mask and a test resin of the same nature as the resin 20 which will be used with the optimized mask, it is possible to obtain a key parameter for the dimensioning of this optimized mask.
[0112] Method for developing an abacus linking density of opaque zones and exposed thickness not requiring a test mask
[0113] The paragraphs below present a second method by which it is possible to obtain a chart linking density of opaque zones and thickness exposed in the resin (or height of the resin after development). This method is preferred when a lithography mask is not available which can be used to carry out tests with a view to sizing the mask optimized using the method according to the invention. It is understood that any other method can be implemented to obtain the same data.
[0114] The different steps of this method are illustrated in Figures 8A to 8F.
[0115] [Fig.8A] illustrates the provision of a stack comprising a secondary resin layer 80 of the same nature 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 face to insolation radiation. Different zones 81, 82, 83, 84 of the resin 80 are insolated with different doses Q8[, Q82, Q83, Q84, each inducing a certain thickness e of insolated resin. As a result, after development ([Fig.8B]) of the exposed resin, the secondary resin layer 80 has different heights h8i, h82, h82, h83, at the different zones 81, 82, 83, 84. It is thus possible to associate with each dose a height of resin obtained after development.
[0116] 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 ([Fig.8C]).
[0117] It is also possible to determine, for each zone i of the resin 80, the theoretical density D; of opaque zones at the level of a theoretical mask which would have made it possible to insolate the zone in question, during its insolation through the theoretical mask, with a dose Q; which it actually received during the calibration step illustrated in [Fig.8A]. The following formula makes it possible to calculate this density D;, Q; corresponding to the radiation dose received by the zone i during the calibration step ([Fig.8A]), and Qmax corresponding to the radiation dose having been received by the zone of the secondary resin 80 having been the most insolated (in the example illustrated in [Fig.8A], Qmax=Q8i):
[0118] [Math. 10]
[0119] We therefore assume that for Qi=Qmax, the density of opaque zones at the level of the theoretical mask is zero. This amounts to considering that when using this theoretical mask, at equal exposure time texpo, the intensity Io of the radiation before its passage through the mask corresponds to the intensity Imax making it possible to obtain the dose Qmax (i.e. Io Imax with Imax Qmax / texpo)*
[0120] Using the above formula and the experimental points obtained by calibration, a trend curve can be established linking the density D of opaque zones at the level of the theoretical mask and the height h of resin after development when the resin has been exposed through this mask ([Fig.8D]). This trend curve, which corresponds to a contrast curve, is continuous and makes it possible to estimate the relationship between h and D for dose values (and therefore theoretical densities) not tested during calibration.
[0121] The derivative of the function corresponding to this trend curve reflects the impact of a variation in the density of opaque areas on the height of the resin after development. This value is involved in determining the error on the height of the resin after development (see formula Math 7).
[0122] 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, it is possible to obtain a key parameter for the dimensioning of this optimized mask.
[0123] First example of implementation of the dimensioning method according to the invention
[0124] Figures 7A and 7B illustrate how the method according to the invention can be used to resize a grayscale lithography mask having an unsatisfactory Z resolution.
[0125] [Fig.7A] illustrates two Rb R2 networks of the same mask 1 (or possibly of two distinct masks 1) used to expose a resin layer over two distinct thicknesses, and therefore to form in the resin layer, once it has been developed, two regions of distinct heights hi and h2. The heights hi and h2 are obtained by dimensioning the masks so that they have the appropriate surface density of opaque zones. In [Fig.7A], the dimensions of the pixels and opaque zones have been chosen arbitrarily, with the only constraint being that the surface density of opaque zones makes it possible to obtain the desired resin height. Both networks have square pixels with side P. The network Ri giving a resin height hi has square opaque zones with side Lb while the network R2 giving a resin height h2 has square opaque zones with side L2.
[0126] The method according to the invention makes it possible to determine what are the ideal dimensions of the two RB R2 networks to limit the error on the resin heights hB h2. According to the results of the method, concerning the network Rbil it is necessary, to achieve the desired levels of precision, to assign to the pixels a Pf side with Pi '>P and to the opaque zones a Lf side with Li'>Lp Naturally, for the height hi to be the same before and after dimensioning, we have Li2 / P2=Li'2 / Pi'2. By writing Li '= aLi and Pi'=aPi, we can establish a scale factor a.
[0127] Concerning the network R2, it is found, by applying the method according to the invention, 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.
[0128] Thus, the transition from [Fig.7A] to [Fig.7B] illustrates a resizing of the mask 1 making it possible to obtain the same 3D structures at the level of the photosensitive resin, but guaranteeing a lower error in the vertical direction Z.
[0129] Second example of implementation of the dimensioning method according to the invention
[0130] The following paragraphs describe, with reference to the flowchart presented in [Fig.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 zones 120 of square shape, but it is understood that it can be adapted to any other shape of first pixels 110 and first opaque zones 120. a. Block 1001: In this step, the first target density Dioo* is defined to expose the photosensitive resin to the first target thickness e*. A pair of values (Pii=1, LC1) is then chosen first for the Pi side of the first pixels 110 and for the Li side of the opaque areas 120. A counter i identifying the pairs of values is initialized (i=1). b. Block 1002: We calculate the error Ah on the first target thickness e* for the pair (Pf, Lf). c. Block 1003: The error Ah obtained in the previous step is compared with a previously set error threshold Ahseuii. If the error obtained is greater than this threshold, we move on to the step described in block 1004. Otherwise, we move on to the step described in block 1005. d. Block 1004: The error on the first target thickness e* for the pair (PA LA not being satisfactory, we choose a new pair of values (Pii+1, Lii+1) for the Pi side of the first pixels 110 and for the Li side of the opaque zones 120, with PÀ^Pf and respecting (Lii)2 / (Pii)2=(Lii+1)2 / (Pii+1)2 to keep the same density of opaque zones 120. We then go back to block 1002. Each time we go 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 kept for the dimensioning of the first network 100 of mask 1.
[0131] Third example of implementation of the dimensioning method according to the invention
[0132] The following paragraphs describe, with reference to the flowchart presented in [Fig.9B], a sequence of steps allowing the dimensioning of the mask 1 when it comprises N networks. These sequences are described for pixels and opaque areas of square shape, 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, we determine the number N of networks to be dimensioned within the mask. A counter j identifying these N networks is initialized (j=l). b. Block 2002: In this step, we define the target density Dj* of the network n°j allowing the photosensitive resin to be exposed to the target thickness ej*. We then choose a first pair of values (Pji=1, LC) for the Pj side of the pixels of the network n°j and for the Lj side of the opaque zones of the network n°j. c. Block 2003: We then calculate the error Ah on the target thickness ej* for the pair (Pÿ, L / ). d. Block 2004: The error Ah obtained in the previous step is compared to a previously set error threshold Ahseuii. If the error obtained is greater than this threshold, we move on to the step described in block 2005. Otherwise, we move on to the step described in block 2006. e. Block 2005: The error on the first target thickness ej* for the pair (PA Lf ) not being satisfactory, we choose a new pair of values (Pii+1, Lii+1) for the side Pj of the pixels of network n°j and for the side Lj of the opaque zones of network n°j, with PA^P,1 and respecting (Lji)2 / (Pji)2=(Lji+1)2 / (Pji+1)2 for keep the same density of opaque zones within network n°j. We then move on to block 2003. Each time we move from block 2005 to block 2003, we increment i by 1. f. Block 2006: The error on 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 kept for the dimensioning 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 so, we go to block 2008. h. Block 2008: The N networks have been sized. The mask as a whole can be sized.
[0133] The invention is not limited to the embodiments previously described and extends to all embodiments covered by the invention. In particular, the implementation of the method according to the invention is not limited to the manufacture of microlenses and can naturally allow the manufacture of 3D structures as diverse as pillars, cones, oblique gratings ("slanted gratings" in English) and staircase structures.
Claims
1. Claims A method for sizing a grayscale lithography mask (1), the mask (1) extending mainly 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 radiation irradiating a photosensitive resin (20) through the mask (1), the mask (1) comprising a plurality of zones opaque to the radiation, each opaque zone being located in a zone of the mask (1) called a pixel, the plurality of opaque zones comprising first opaque zones (120) located in first pixels (110), the first pixels (110) forming a first network (100) of the mask (1), the method comprising the following steps: • Establishing a first target density Di00* of a first surface density DiOo of first opaque zones (120) within the first network (100), the first target density Di00* being configured to allow the resin (20) to be exposed to a given first target thickness ei* when the resin (20) is exposed to radiation through the first network (100) of the mask (1), the first target thickness ei* being measured along the main direction of the radiation, • Obtain a first value, for the first target density D ioo*, of the derivative with respect to the first surface density Dioo of the first thickness ei on which the photosensitive resin (20) is exposed when it is exposed to radiation through the first network (100) having the first surface density Dioo, said first value being noted A'j(P|on'), ^ioo • Determine a first dimension Px i of the first pixels (110) in the first direction (X), a first dimension Py i of the first pixels (110) in the second direction (Y), a first dimension LXji of the first opaque zones (120) in the first direction (X), a first dimension Ly>i of the first opaque zones (120) in the second direction (Y), so that the value of an error on the first target thickness ei*, noted MEEF(ei*), is less than a first given threshold, MEEF(ei*) being calculated from the following formula:
2.
3. *\_) ( <zdAKx.i e i I - ~1d^ p^T With o _ ^-i and _ , ôLx i being an error on Lx i and ôLy i being P\~La "1“ ÔLsJ an error on Lyj, • Use the dimensions obtained for the dimensioning of the first network (100) of the mask (1). Method according to the preceding claim in which ai is between 0.8 and 1.2, preferably a is equal to 1. A method according to any preceding claim wherein the step of obtaining the first value of the derivative comprises the following steps: • Provide a secondary resin (80) of the same nature as the photosensitive resin (20), • Insolating a plurality of regions (81, 82, 83, 84) of the secondary resin (80) with radiation, each region (81, 82, 83, 84) being insolated with a distinct dose (Q8B Q82, Q83, Q84) of radiation, • For each region (81, 82, 83, 84) of the secondary resin (80), determine according to the main direction of the radiation a thickness of insolation of the radiation in said region (81, 82, 83, 84), • Establish, for each region (81, 82, 83, 84) of the secondary resin (80), a theoretical density (D8b D82, D83, D84) of theoretical opaque zones on a theoretical mask, which, upon exposure to radiation of said region (81, 82, 83, 84) through the theoretical mask, would have made it possible to expose said region to the dose (Q8B Q82, Q83, Q84) of radiation to which said region (81, 82, 83, 84) is exposed, • Establish a model linking the insolation thickness of the secondary resin layer (80) to the density of opaque zones from the insolation thickness and theoretical density data (D8b D82, D83, D84) obtained for each of the regions (81, 82, 83, 84).
4. Method according to the preceding claim in which the step of establishing, for each region (81, 82, 83, 84) of the secondary resin (80), the theoretical density (D8[, D82, D83, D84) of theoretical opaque zones, is done at least by applying the following formula: Q Di ~ ]~Q~~ with i indexing the different regions (81, 82, 83, 84) of the secondary resin (80), Di the theoretical density associated with region i, Q; the radiation dose to which region i is exposed and Qmax=max(Qi).
5. Method according to claim 1 or claim 2 in which the step of obtaining the first value of the derivative comprises the following steps: • Providing a test mask having a plurality of test networks each having a distinct density of opaque test zones, • Providing a test resin of the same nature as the photosensitive resin (20), • Insolating a plurality of regions of the test resin with radiation through the test mask, the insolation of each region being done through a distinct test network, • Determining, for each region of the test resin, an insolation thickness of the radiation in said region, • Establishing a model linking the insolation thickness of the test resin layer to the density of opaque test zones from the insolation thickness data obtained for each of the regions.
6. Method according to any one of the preceding claims in which the first dimension Px i of the first pixels (110) in the first direction (X) and the first dimension Py i 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 in which the first pixels (110) have a square shape in the horizontal plane (XY) and in which Px>i=Py>i=P.
8. A method according to any preceding claim in in which the first opaque zones (120) have a square shape in the horizontal plane (XY) and in which Lx i=Ly i=L.
9. Method according to the two preceding claims taken in combination in which: MEEF(e / ) = r>^°^
10. Method according to any one of the preceding claims in which the plurality of opaque zones comprises at least second opaque zones (220) located in second pixels (210), the second pixels (210) forming a second network (200) of the mask (1), the method further comprising the following steps: • Establishing a second target density D200* of a second surface density D20o of second opaque zones (220) within the second network (200), 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 network (200) of the mask (1), the second target thickness e2* being measured along the main direction of the radiation, the second target thickness e2* being distinct from the first target thickness ei*, • Obtaining a second value, for the second target density D^o*,of the derivative with respect to the second surface density D2Oo of the second thickness e2 on which the photosensitive resin is exposed when it is exposed to radiation through the second network (200) having the second surface density D200, noted 3e2(D200 ), ^200 • Determine 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 Lx2 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), so that the value of an error on the second target thickness e2*, noted MEEF(e2*) is less than a second given threshold, MEEF(e2*) being calculated from the following formula:, With a _ Ly2 and _ , ôLx 2 being an error on Lx 2 and ôLy 2 being P 2 “ 4.2 °2 “ an error on Ly>2, • Use the dimensions obtained for the dimensioning of the second network (200) of the mask (1).
11. Method according to the preceding claim in which the second network (200) forms in the horizontal plane (XY) a closed contour in which the first network (100) is located.
12. Method according to the preceding claim in which the closed contour formed by the second network (200) is substantially circular.
13. A method according to any one of the two preceding claims wherein the second threshold for the error on the second target thickness e2* is less than the first threshold for the error on the first target thickness ei*.
14. Method for manufacturing a grayscale lithography mask (1) comprising the following steps: • Dimensioning the mask (1) by implementing the method according to any one of the preceding claims, • Manufacturing the mask (1) thus dimensioned.