WO2003027769A2

WO2003027769A2 - Method for producing a two-dimensional photomask

Info

Publication number: WO2003027769A2
Application number: PCT/EP2002/010610
Authority: WO
Inventors: Jörn HOPF
Original assignee: Hopf Joern
Priority date: 2001-09-21
Filing date: 2002-09-20
Publication date: 2003-04-03
Also published as: WO2003027769A3; DE10146619C2; DE10146619A1; AU2002342731A1

Abstract

The invention relates to a method for producing a two-dimensional photomask. Said photomask comprises a plurality of transparent zones with one or more mask elements each that are disposed in such a manner that, when a target is exposed through the photomask, an exposure image is produced on the target, said image being adapted to a defined halftone image. The number, geometry and/or positions of the mask elements are determined by means of an evolutionary selection procedure that comprises a multitude of mutation steps. Starting from an initial distribution of mask elements a distribution of mask elements is successively produced, until a termination criterion is fulfilled, by using an operator that is selected from a group of statistical operators. For every actual distribution, the respective exposure image is determined that would result from the exposure of the target through a photomask with the actual distribution. The termination criterion is fulfilled when an approximative quality that is characteristic for the adaptation of the exposure image to the halftone image, reaches a threshold value or does not improve over a number of mutation steps.

Description

Process for the generation of a two-dimensional photomask

The present invention relates to a method for generating a two-dimensional photomask, in particular a method for generating a photomask which is set up to generate an exposure image corresponding to a predetermined gray-scale image on a target. The invention also relates to a two-dimensional photomask produced using such a method.

The generally known photolithographic structuring of semiconductor surfaces is based on the exposure of a light-sensitive lacquer (resist) on the semiconductor surface with a specific exposure image, a subsequent structuring of the lacquer layer in accordance with the exposed and unexposed partial areas of the exposure image, so that parts of the semiconductor surface are exposed, and finally processing the exposed parts of the semiconductor surface z. B. by wet chemical etching, by sputter etching, by doping or the like. After detaching the structured lacquer layer, the correspondingly structured semiconductor surface is given.

The generation of the exposure image 20, illustrated schematically in FIG. 1, takes place using a photomask 10. This is formed, for example, by a thin glass or quartz pane 11 with an opaque masking layer 12, which has openings or translucent areas 13 in accordance with the desired exposure image the photomask is translucent. The translucent areas 13 are produced using a structuring method in the production of the photomask. In conventional chip production, photomasks are used whose translucent areas reflect the two-dimensional design of the chip surface to be processed, e.g. B. with conductor tracks or doping areas for an electronic circuit. In the case of photolithographic processing of semiconductor surfaces, various lithography methods are known which, depending on the number of photomasks (or "layers") and the number of exposure wavelengths used, are known as 1-step (one-step), multi-step (multistep) or Multi-wave (multi-wave) lithography. However, multi-wave multiwave lithography has so far only been a theoretical model and is said to not yet exist in practice, since the wave steppers are always optimized for a certain wavelength. In the future, however, this would be conceivable as soon as you have recognized the advantages and can implement it technologically. If the surface is irradiated with electron beams or X-rays, the method is accordingly referred to as electron beam or X-ray lithography.

In microsystem technology and so-called nanotechnology, non-electronic components are also formed on chip surfaces, which include, for example, sensors, mechanical actuators, fluidic elements, motors, and optical components (see, for example, BB Wagner in "End. Surg.", Vol. 3, 1995, pp. 204 to 209). These components have three-dimensional structures, such as. B. curvatures, pits, steps, webs, spherical surfaces or the like .. Three-dimensional structures can be produced lithographically analogously to the above-mentioned method, the exposure images generated on the resist with the photomask specifically having gray values or shades of gray. As a result of the processing the chip surface is removed to different extents depending on the locally given gray values.

Exposure images with relative exposures in the interval [0, 1] are generated using interference phenomena as well as reflection and scattering conditions when exposing the chip surface through the photomask. The transparent elements include, for example, geometric elements (pixels) in the masking layer of the photomask. Light is diffracted at each pixel, and there is also interference with the light that passes through neighboring pixels. The exposure image on a target (e.g. chip surface that is to be processed), produced with a given photomask, can be calculated optically in good approximation.

In contrast to the two-dimensional chip structuring, an exact image of the three-dimensional design of the chip surface to be processed cannot be represented with a photomask. The photomask is generated in such a way that the exposure image on the target approximates as well as possible an ideal gray value image, the gray value of which corresponds to the height profile of the desired three-dimensional structure.

The generation of a photo mask for three-dimensional structuring represents an optimization task. In this optimization, process-related and physical conditions must be taken into account (so-called constraints), which are generally referred to below as process conditions. The process-related conditions include, for example, that the translucent elements must have a certain minimum size and edges that correspond to a process-related grid or grid. So the machines for the production of Only generate tomasks of translucent pixels with a certain grid dimension s (e.g. s = 0.1 μm), which determines the lateral resolution of the structuring process for the production of the photomask. A translucent pixel has a certain minimum size or minimum edge length, which corresponds, for example, to β times the grid dimension. In particular, the course of the ideal grayscale image, the laws of wave optics and the reflection and scattering conditions in the chip-resist composite are to be taken into account as physical conditions.

The reflections and scatterings in the composite of the substrate 31 and the lacquer layer 32 are illustrated schematically in FIG. 2. The primary exposure 21 is expanded in the lacquer layer 32 by scattering, so that an exposure profile 22 results. Particularly when using electron or X-rays, there is an entry into the substrate 31, from which backscatter, which influences the profile 22, and an emission 23 of Auger electrons or X-ray quanta take place. The scattering effects occurring in a specific system depend in particular on the characteristics of the primary exposure 21, the type of radiation, the materials and the geometry of the composite of substrate and lacquer layer. The radiation dose effective in one spatial point of the lacquer layer 32 can be calculated using the laws of wave optics.

It is generally known in practice to solve tasks that are not accessible to an analytical solution by linear optimization. A linear mask optimization would, however, require numerous variables and thus a high computing effort. It would therefore only be possible to optimize mask areas that are too small for practical requirements. Besides that would be linear optimization itself is poorly suited for the optimization task at hand, since non-linear phenomena occur during mask imaging. FIG. 10 shows an example of a linearly optimized photomask 10 '(left partial image, the light dots correspond to the translucent areas) for producing a quarter-sphere-shaped surface and the structure produced with this photomask (right partial image). There is only a rough approximation to the desired spherical shape with a high surface roughness.

A non-linear optimization method is also generally known which takes account of the non-linearities in the exposure. The photomask is composed of a plurality of cells 14 ', each of which represents predetermined permissible element shapes 15'. Each cell has a side length corresponding to, for example, 18 times the value of the production-related grid dimension a. In general, the element shapes meet the given process conditions. Some element shapes 15 'of the cells used in this method are illustrated by way of example in FIG. 11.

The non-linear method has the disadvantage of a limited spatial resolution. The element shapes allow only a limited range of shapes. The granularization introduced to reduce complexity results in poor surface approximation and a large surface roughness of the processed structure. For example, smooth curvatures, such as. B. round structures can not be produced satisfactorily. Instead of a desired ramp shape, a staircase structure results.

Another disadvantage of conventional methods for producing photomasks for three-dimensional structuring is is that only one mask can be calculated at a time. A simultaneous optimization of several masks, e.g. B. for a multi-step lithography is excluded.

There is an interest in photomasks whose exposure images are adapted as well as possible to the desired gray value images in order to be able to produce the three-dimensional structures with high accuracy (in particular high surface approximation, low surface roughness) and reproducibility.

It is known to use evolutionary algorithms (or: evolution strategies) to solve optimization problems. In contrast to calculation methods, in which the optimum as the extremum of a feature function is determined analytically, and search methods, in which all possible solutions are checked sequentially or according to a randomly based selection principle, the evolutionary algorithm considers non-random parts of the solution space. The search for an optimal solution is carried out by applying so-called evolutionary operators to a solution already found and by checking whether the application of the operator has improved the solution. Details of the evolutionary algorithms known per se are described, for example, by T. Back et al. in "Evolutionary Computation 1", Volume 1, 1993, pages 1-23. The use of evolutionary algorithms to solve practical optimization tasks has so far often been difficult in practice and therefore limited because there are no generally applicable rules for the construction of the genetic operators.

Evolutionary algorithms have so far been used to optimize production processes such as B. when planning material rivers or the control of complex machines or transport processes.

The object of the invention is to provide an improved method for the generation of photomasks with which the disadvantages of conventional techniques are overcome. The method is said to be particularly suitable for delivering photomasks for gray-tone lithography with high effectiveness and practical computing time, with which three-dimensional structures can be produced with great accuracy in the context of industrial applications, in particular in microtechnology. The object of the invention is also to provide photomasks for gray-tone lithography, with which exposure images can be generated on substrates with an improved adaptation to the desired gray-scale image.

These objects are achieved by a method for the generation of photomasks and photomasks with the features according to patent claims 1 or 8. Advantageous embodiments and applications of the invention result from the dependent claims.

The basic idea of the invention is, in particular, to provide a method for generating a two-dimensional photomask with translucent areas, which each consist of individual or a multiplicity of mask elements and are arranged in such a way that an exposure image is generated on the target when the target is exposed through the photomask , which is adapted to a predetermined gray-scale image, the number, geometry and positions of the mask elements being determined using an evolutionary selection procedure. The evolutionary selection procedure is characterized by the successive and / or parallel generation of changed Partitions from mask elements until the exposure image is adequately matched to the gray-scale image. The evolutionary selection procedure implements an optimization principle used for the first time for the generation of photomasks, which advantageously represents a non-deterministic search for the optimal distribution of mask elements. The photomask advantageously results from an effective search in a solution space which, in its combinatorial variety, was not accessible to the conventional methods.

In the evolutionary selection procedure, in particular starting from a start distribution of mask elements with an operator selected from a group of predetermined statistical operators, a modified distribution of mask elements will be generated in succession until a predetermined termination criterion is met. Each generation of a modified distribution is called a mutation step. A new mutation step is preferably carried out on the current distribution obtained in the previous mutation step. Alternatively, it is also possible to carry out several mutation steps in succession and to temporarily store the distributions obtained, the result obtained after several steps being regarded as the current distribution. For each current distribution, the associated exposure image, which would result if the target was exposed through a photomask with the current distribution, and an approximation quality, which is characteristic of the adaptation of the exposure image to the gray-scale image, are determined. The termination criterion is met when the approximation quality has reached a predetermined limit value or does not improve significantly over a predetermined number of mutation steps. The evolutionary selection procedure advantageously makes it possible to check at each mutation step whether the current distribution of mask elements fulfills predetermined process conditions. As a result, the method according to the invention automatically leads to a photomask which fulfills the process-related and physical conditions for its manufacture.

The termination criterion is preferably checked by comparing the current approximation quality with a so-called progress interval. The progress interval is a range of admissible values of the approximation quality, which is selected depending on the current phase of the selection procedure. In an initialization phase and an ambition phase in which predetermined statistical operators are carried out, the approximation quality must be improved or at least remain the same with each mutation step. In an optimization phase, the approximation quality for each mutation step must be better than a predetermined reference value of an optimization curve. Carrying out the selection process in different phases, which are explained in detail below, has the particular advantage of high process effectiveness.

The approximation quality is preferably the average deviation between the current exposure image and the gray scale image and / or a surface roughness parameter that is characteristic of the surface roughness that would result when using a photomask with the current exposure image. These parameters have the advantage of being compatible with the practical idea of the optimization process. The method according to the invention has a wide range of uses. It can be used for various lithographic processes, in particular 1-step, multi-step or multi-wave lithography, without restriction to certain structures, taking into account the specific process conditions. The mask generated according to the invention can be used for structuring, in particular, semiconductor (in particular silicon) or plastic surfaces in accordance with a procedure of photo, UV, electron beam or X-ray lithography.

Generation of a two-dimensional photomask is primarily the provision of a binary distribution of translucent mask elements and opaque areas, e.g. B. understood in the form of a listing, matrix, functional representation or the like, which would result in the desired exposure image as a mask or mask pattern when a target is exposed. In the broader sense, however, the generation of a photomask is also understood to mean a structuring process for the material production of the photomask, in which the said distribution is, for example, embossed or applied in a layer on a support or in a self-supporting layer. Structuring methods for mask production are known per se and are therefore not explained in detail here.

The invention also relates to a photomask for gray-tone lithography which, in accordance with the desired exposure image, has mask elements which form translucent regions. The edge course and / or the arrangement of the translucent areas is formed such that steps are formed on the edges of translucent areas and / or between edges of different translucent areas there are rich vertical distances that are smaller than a minimum edge length of the mask elements. According to an important feature, in a photomask according to the invention two adjacent mask elements can touch each other in such a way that they only have one common corner point. The photomask according to the invention has the advantage of a variability in the arrangement of the mask elements which is considerably expanded compared to conventional photomasks. The granularization of the exposure images is reduced.

The mask elements are arranged in accordance with a grid with predetermined grid dimensions which are equal to predetermined minimum lengths which correspond to the lateral resolution of the structuring method used to produce the photomask. The mask elements are preferably produced using a structuring method using the generation method according to the invention. The mask elements form a statistically irregular edge profile of the translucent elements. The photomask according to the invention is formed by a carrier, in particular a thin glass or quartz pane, on which the opaque masking layer is arranged, or by the opaque masking layer itself.

The invention has the following further advantages. A so-called "free-floating" of the mask elements is realized. This means that mask elements can be arranged on the mask without a fixed placement grid. This is a prerequisite so that rectangular, round and irregular surface geometries can be approximated equally well. Even complex surface structures such as microstructured Fresnel lenses can be used with a photomask according to the invention with the smallest edge length of the mask elements of approx. 0.7 μm with a surface approximation of less than 2% deviation and a surface roughness of less than 2% at the respective measuring points. With a structure height of z. B. 16 μm, this corresponds to an approximation accuracy of less than 320 nm, which is usually below the light wavelength used.

In particular, the problem of photo mask optimization with consistent consideration of the production-related and physical boundary conditions (constraints) is solved. This is advantageous if conventional methods used in mask and chip production are to be used accordingly for the production of three-dimensional chip surfaces without conversion.

The method according to the invention is known using lithography methods, for. B. compatible with chip production, which are suitable for mass production, are well mastered by years of use and work inexpensively. The invention enables the most cost-effective production of three-dimensional chip surfaces, which can also be easily adapted to the specific user requirements in terms of quality, costs and the required calculation time by the number of masks (layers) used. In principle, no change in the production process is required for the production of SD microstructured chip surfaces, since the 3D microstructuring is determined solely by the element arrangement of the photomask (s). There are therefore no changeover costs.

The method is suitable for the simultaneous, coordinated optimization of several layers to approximate a surface. Even if it is important to achieve the desired quality with as few as possible To achieve masks (goal: 1-step lithography), it is still possible to optimize any number of layers in parallel, with the application of which a correspondingly higher surface quality can be achieved. The desired number of masks is theoretically unlimited. The process conditions are simplified when several masks are generated.

The implementation of the method according to the invention requires only relatively little storage space. The storage space required for the data for the generation of the mask only plays a role insofar as it must be within the scope of what can be read in by the machines.

The method according to the invention is characterized in particular by the fact that the respectively determined distribution of mask elements for producing a photomask is converted into their properties and, when the photomask is used, into the physical properties of the solid surfaces that are to be structured. With a photomask produced according to the invention, the parallel irradiation is controlled in a device for exposing a target (e.g. wafer) in such a way that the irradiation waves produce the desired dose distribution (e.g. gray tone distribution) on the target. In the combinatorial optimization of the distribution of mask elements according to the invention, technical parameters of the specific task, in particular system-related restrictions and physical specifications, are taken into account.

Further details and advantages of the invention will become apparent from the description of the accompanying drawings. Show it: FIG. 1 shows a schematic illustration of parts of a device for target exposure,

FIG. 2 shows an illustration of the scattering processes occurring on the composite of substrate and resist,

FIGS. 3 to 7 flow diagrams to illustrate details of the method according to the invention,

Figures 8, 9 illustrations of properties of photomasks produced according to the invention, and

Figures 10, 11 illustrations of conventional optimization methods (prior art).

The invention is described below without limitation with reference to the generation of a single photomask for a single exposure of a target (eg wafer) in 1-step lithography. An implementation for the multi-step technology or the parallel generation of several photomasks intended for the production of a structure is possible in an analogous manner.

1. Basics and terms

1.1 Description of a photomask

The method according to the invention contains the solution to a combinatorial optimization problem. The question to be answered is how to arrange rectangular, translucent mask elements (holes) on a photomask as translucent areas of different shapes and / or different sizes, so that after exposure on a target A desired gray tone distribution is achieved through the surface of this photomask. The fact that different shades of gray are generated at all results from the diffraction of the preferably parallel light waves, which are sent perpendicularly and homogeneously onto the photomask, at the edges between the hole and the non-hole of the mask, and the scattering processes that occur. The light intensity generated on the target depends on the mask element size, it decreases in the vicinity of the image of the mask element with increasing distance from the center of the image.

The surface of a substrate material, e.g. B. the surface of a silicon chip should be provided with a certain three-dimensional structure. For each point (location coordinates x, y) of the surface spanned in a plane there is a height coordinate h (x, y) which corresponds to the height of the desired structure above the plane. The height of the structure extends z. B. over 16 microns. For example, for a straight ramp, h (x) is a linear and h (y) is a constant function.

For the photolithographic structuring of the surface, the resist on the chip surface must be exposed accordingly with a gray tone exposure image, the dose or gray value distribution or gray value function of which corresponds exactly to the (standardized) distribution of the height coordinates. Since the gray value distribution cannot be implemented exactly in the height coordinates, but also the peculiarities of the user system (in particular the specifically implemented process parameters and the photoresist used) affect the achieved height coordinate distribution, a correction function must also be taken into account. The correction function specifies how to correct the theoretical dose-height relationship at a coordinate, if necessary is to achieve the desired structure height. The gray value function, possibly with the correction function, form a surface function f (x, y), which represents a starting point of the method. The surface function is specified, for example, analytically or as a table of values.

The desired surface function f (x, y) and the set M = {m _x , m ₂ , ..., m _n }, ne N of all possible mask elements are given. We are looking for the theoretical set * (M * c: M) of mask elements, the arrangement and geometry of which must meet the process conditions and the best approximation g * (x, y) = ∑ _m . _eM * G _± (x, y) returns f (x, y), where Gi (x, y) represents the gray value that the mask element πii generates at the point (x, y). Since the calculation of the mask elements to be used for an optimal approximation via the function g * (x, y) is not analytically possible because of the process conditions to be taken into account, an approximation of g (x, y) = ∑ _{m ± eM} ι G _{± is made} _{according to the invention} (x, y) is delivered to f (x, y), whereby the practically searched set is M 'M. The values Gi (x, y) can be calculated using the laws of wave optics.

The set M 'is a combinatorial arrangement of mask elements at specific positions, which each form the translucent areas with a specific shape and size. Both the quantities of mask elements determined as intermediate states during the method and the sought quantity M 'can be represented as a binary function with the values 0 or 1 on the individual pixels (primary elements, smallest units), the primary elements with the value 1 being the translucent mask elements include. In general, the photomask is determined by the mask sizes in the x and y direction (X [mm], Y [mm]), the minimum edge length of the mask elements (a [μm]), the measuring point distance used (g [μm]), and the amount the process conditions (C), and the amount M of the mask elements e is determined. Furthermore, a dependency on variants F, such as. B. the inclusion of a frame, the use of a point symmetry or the generation of overhangs, and a subdivision of the mask area into S _x and S _y sectors in the x or y direction can be provided.

Depending on the lateral resolving power of the structuring method used to produce the photomask, the mask elements are arranged according to a grid. The smallest grating unit or positioning unit is 0.1 μm, for example. The minimum edge length is, for example, a = 0.6 μm or a = 0.7 μm. The maximum number of possible mask elements i _max results accordingly from the mask size and the minimum edge length. For the optimization of a mm ² mask area only around 220 MB are required to show the state of the photomask. If the minimum edge length is reduced, the memory requirement can increase to over 500 MB.

1.2 Process conditions

Process conditions must be observed when manufacturing the photomask. The process conditions are in particular:

1. The length of each edge of a translucent area, which may consist of several mask elements, is greater than or equal to the minimum length of a mask element. 2. Parallel edges of a translucent area must have a vertical distance that is greater than or equal to the minimum edge length of a mask element.

3. Parallel edges of different translucent areas must have a vertical distance that is greater than a predetermined minimum distance (the minimum distance is, for example, 0.6 μm).

4. Translucent areas may touch at a point if this is a corner point.

5. The edge of the mask surface is to be regarded as the edge of a translucent area.

6. Translucent areas must not overlap.

7. All edges of translucent areas may only be placed on a grid with a grid dimension s.

8. Each translucent area may put an edge strip of any length and width according to the grid dimension s on each of its edges.

The process conditions to be checked in the course of the process depend on the operator currently being used. As a rule, it is no longer necessary to check all process conditions by selecting a particular operator. The check is preferably carried out hierarchically, with a group of so-called inherent process conditions being checked first, then a group of so-called advanced process conditions and finally a group of so-called M conditions.

The first group is formed solely by the process condition 7 mentioned above. The checking of this process condition practically does not have to be carried out, since it is inherent in the Process flow is ensured by defining the coordinates of the mask elements.

The second group is formed by the process conditions 1. (minimum edge length) 2. (distance of parallel edges of an element) and 5. (edge of the mask surface). These process conditions are tested before the actual check. Process conditions 1. and 2. are ensured by the operators CREATE, RESIZE and SPLIT (see below). The margin must be checked when using the CREATE, MOVE and RESIZE operators.

In the third group of the so-called M process conditions are the other process conditions 3rd (distance of parallel edges of different areas), 4th (point contact), 6th (overlay) and 8th (edge strips). These process conditions are checked on the basis of the mask pattern M, which is achieved by the currently used operator.

The fourth process condition (point contact) represents an essential feature of photomasks according to the invention. Mask elements can touch at common corner points. This significantly increases the variability of gray tone generation. The shape of individual mask elements can, for example, be square or triangular.

2. Evolutionary selection process

According to the invention, the quantity sought is determined using an evolutionary selection method, which is illustrated schematically in FIG. 3, and preferably an initialization phase 100, an ambition phase 200, an optimization phase 300 and a storage and / or display phase 400 around- summarizes. It is underlined that the evolutionary selection process according to the invention can only be implemented with the optimization phase 300 without phases 100 and 200. However, the successive execution of all three phases 100 to 300 is preferred in view of an effective process flow. The phases 100 to 300 are illustrated with further details in FIGS. 4 to 6. The storage and / or display phase 400 includes storage and / or display of the mask elements determined according to the invention prior to the actual production of the binary structured photomask.

2.1 operators

In the evolutionary selection method according to the invention, one or more operators are used, which are selected from the group of operators CREATE, ERASE, RESIZE, MOVE, SPLIT and UNDO explained below. Which operators are selected depends on the one hand on the optimization phase and on the other hand on statistical selection principles.

Generally, an operator is an arithmetic operation or rule. An operator transfers a distribution of mask elements (mask pattern) at time t into a new mask pattern at time t + 1, both mask patterns having to meet the applicable process conditions. The transfer is also known as a mutation.

The CREATE operator creates a rectangular mask element with its coordinate vertices. The unit of measurement is, according to the minimum placement grid s z. B. 0.1 μm. The selection of the coordinates of a mask element to be generated can, if necessary, with inherent consideration the process conditions, using a random number generator.

The operator ERASE removes a mask element e at time t, the process conditions also having to be checked after using this operator.

The RESIZE operator is used to enlarge or reduce a translucent area consisting of several mask elements. The RESIZE operator has the option of shifting one or more of the edges of the translucent area in positive or negative direction by an integral multiple of the minimum edge length of a mask element.

If a mask element or a translucent area consisting of several mask elements remains unchanged in size and is to be placed at a different location, the MOVE operator is used. The MOVE operator comprises two substeps, which can be described accordingly with the CREATE operator and the ERASE operator.

Another mutation, which does not mean a structural change in the current mask element distribution, but which enables this in the further course of the evolutionary selection, is the division of translucent areas with the SPLIT operator. A translucent area is not changed in size or location. There is only a division into at least two sub-areas. The SPLIT operator advantageously opens up new degrees of freedom in the further optimization of the photomask.

The UNDO operator cancels previously performed operations. This is particularly provided if a mask pattern obtained after an operation violates a process condition or the approximation quality achieved by the previous operation lies outside the progress interval (see optimization phase). The UNDO operator corresponds to the application of the inverse operation after the previous operation.

2.2 Initialization phase 100

In the initialization phase 100, an output distribution of elements on the photomask is generated non-deterministically, which is optimized in the subsequent phases. During the initialization phase, only the CREATE and UNDO operators are used, taking the process conditions into account. The CREATE operator creates a rectangular primary element with predetermined coordinate vertices. The CREATE operator thus writes the value 1 for a specific position in the representation of the current mask element distribution. With the UNDO operator, CREATE is undone and a primary element is destroyed accordingly. H. a value of 1 is converted to a value of 0.

According to FIG. 4, the initialization phase 100 initially comprises a step 101 in which a start distribution of primary elements is applied. The start distribution includes, for example, a homogeneous distribution of translucent mask or primary elements (e.g. on 50% of the mask area). At least one primary element is provided as a start distribution. The start distribution can also be selected as a function of predetermined information about the presumably optimal mask element distribution, for example if the desired 3-dimensional structure contains certain previously known partial structures (e.g. spherical surfaces). Then will at step 102, another primary element with statistically selected coordinates is applied with the CREATE operator. The process conditions (constraints) are met in step 102 by admitting only those new elements that correspond to the process conditions. Otherwise, a separate test step can also be provided.

The conformity of the current distribution of mask elements with the process conditions is checked using the coordinates of the mask elements or by simulating the current mask state. The use of an independent mapping for checking the process conditions is preferred, since the mapping advantageously provides direct information about the current mask layout.

In step 103 it is checked whether and if so to what extent the approximation (adaptation of the approximation function g to the surface function f) has improved or not. If an improvement has been obtained, step 101 is carried out again with a further primary element. Otherwise, the primary element just created is deleted again in step 104. Each deletion 104 represents a failed attempt. The number of successive failed attempts is counted in step 105. It is used to calculate the probability that the approximation will improve when a further element is added.

The initialization phase 100 is ended after step 106 depending on the test of an abort criterion. The termination criterion includes, for example, the question of how much the approximation with the last new elements has improved and / or how many failed attempts have occurred in succession. If the adaptation of the approximation function g to the surface If function f has improved less than a predetermined limit value during a predetermined number of newly generated elements, phase 100 is ended. Likewise, if a certain number of failed attempts is exceeded, the initialization phase provides no further improvement in the current distribution of mask elements.

As a result of the randomized initialization phase 100, a distribution of mask elements is found that represents a local minimum in the solution space.

2.3 Ambition phase 200

In the ambition phase 200, the result of the initialization phase 100 is improved through the use of further operators. The ambition phase 200 is also referred to as the hill climbing phase or one-way optimization phase because of the choice of the steepest optimization increase. In addition to the CREATE and UNDO operators executed during initialization, the ERASE, MOVE and RESIZE operators are used. The ambition phase schematically illustrated in FIG. 5 is carried out with a strategy analogous to that of the initialization phase 100, so that a picture similar to that in FIG. 4 results. The only difference is that there are more operators available to change the current mask element distribution, the operator to be used being selected based on a probability assessment.

First, in step 201, a mask element is selected to which the operator is to be applied in the next step. The mask element is selected at random. At step 202, one of the operators mentioned is selected and applied to the mask element. The selection of the Opera ^¬ tors is again randomly or preferably a function of the probability that a particular operator provides an improvement of the approximation or not. This probability is determined from the previous failed attempts with the respective operator within a predetermined previous time range. Alternatively, it is also possible to use each operator once in succession to select the operative operator, to determine the approximation quality thus achieved and then to undo it again with the UNDO operator. The operator with the best approximation quality is then used for the further procedure.

Steps 203 to 206 take place analogously to steps 103 to 106 according to FIG. 4. The advantage of the ambition phase 200 is the rapid improvement of the approximation. The mask element distribution resulting from the ambition phase 200 forms the basis for the subsequent optimization phase 300.

In test 206 of the termination criterion, the adaptation of the function g to the target function f is evaluated. The evaluation is based on at least one of the following quality criteria. A first criterion is given by the average deviation in the approximation between the two functions. The approximation At at time t is calculated from the sum of the differences in the amounts from functions f and g across all measuring points.

A _t = ∑ij I f (i, j) - g (i, j) I A second criterion, which can be used optionally, is given by the surface roughness R. This is defined as the arithmetic mean between the maximum difference in amount between f and g and the minimum difference in amount between f and g for a selected target structure height.

The check of the termination criterion comprises the test as to whether the currently determined approximation quality has reached or exceeded a predetermined value in accordance with the quality criteria mentioned.

2.4 Optimization phase 300

The optimization phase is based on the use of the same operators as in the ambition phase. In contrast to step 203 (see FIG. 4), however, only operations which lead to an equally good or improved approximation are permitted. This condition generally only enables a local optimum to be found in the context of the ambition phase, but not a local optimum that meets the requirements (closer to the global optimum) or even the global optimum even among the mask element distributions available.

After a mask element has also been selected (step 301) and an operator has been selected and applied (step 302) in the optimization phase 300, analogously to the steps described above, a test is carried out in step 303 as to whether the approximation achieved lies within a predetermined progress interval or not. The progress interval of the optimization phase 300 is determined empirically and its reference variable is placed around the approximation quality achieved so far, the interval limits being greater, equal or smaller than the approximation quality achieved so far. The progress interval is continuously checked and possibly adjusted depending on the approximation quality achieved so far, so that the optimization phase implements a strategy which is based on the known "simulated annealing" method (see v. Laarhoven et al. In "Mathematics and its Applications "Dordrecht, Klüver 1987). The optimization curve or cooling function of the progress interval can also be determined from preliminary tests. Examples of cooling functions of the optimization phase 300 are illustrated in FIG. 8 (see below).

If the currently executed operator leads to an approximation that lies within the progress interval, the system jumps back to the next step 301.Otherwise, the operator is canceled at step 304, the current failed attempt is counted (step 305) and the termination criterion is checked (step 306). The termination criterion is met when the approximation quality has reached a predetermined limit value or has remained unchanged over a predetermined number of mutation steps.

The in Figs. 3 to 5 steps are carried out successively for a mask element or primary element. After the use of an operator, another use of an operator or the reversal of the previous operator is preferably provided. According to alternative embodiments of the invention, a multiple execution of the UNDO operator can also be provided, so that successively several steps are undone. Furthermore, in a departure from the procedure shown, it is also possible to change several mask elements which are arranged in mutual neighborhood. According to one embodiment of the method according to the invention, the mask area can be partitioned into several sectors. A sector comprises an area which, for example, corresponds to a predetermined partial structure of the desired 3-dimensional structuring of the target surface. The procedures according to FIGS. 3 to 5 can advantageously be run through simultaneously for several sectors, the mask distributions at the sector boundaries being taken into account as process conditions.

The subdivision of the mask area into sectors has several advantages. First, the storage space required for the individual optimization processes is reduced. In addition, the effectiveness of operator selection in the course of the process is improved.

3. Photomask

7 schematically illustrates a section of a photomask according to the invention with three translucent areas 13, 14, 19. A process-related grid is drawn in as a background, with which the lateral resolving power of the application of mask elements is defined. The grid dimension s is 0.1 μm, for example. In general, the mask elements have a minimum side length of, for example 6 ^• s. However, they can also have longer edge lengths.

The translucent area 13 is formed by a single mask element with the minimum edge length (6 ^• s). The translucent area 14, on the other hand, comprises three mask elements, of which the mask element has a greater edge length at the bottom right. The vertical distance between the adjacent areas corresponds to the minimum edge length of a mask element management. The translucent area 19 has point contact with the translucent area 14.

A special feature of photomasks produced according to the invention is that the arrangement of the translucent areas and their borders have such an irregular arrangement that no periodicity is discernible over the mask surface. A photomask according to the invention is characterized exclusively by a periodicity which corresponds to the grid (pitch s) due to the manufacture. For example, steps can occur in the element border that are smaller than the minimum edge length and, for example, correspond exactly to the minimum grid dimension s (see step 15 on the translucent area 14 in FIG. 7). Corresponding steps also occur between adjacent areas as vertical distances 18 between adjacent edges, as is illustrated by the offset of the edges 16 and 17.

4. Examples

In Figs. 8 and 9 are illustrated by way of example of photomasks produced in accordance with the invention and associated 3-dimensional structures with measurement results. The upper two partial images of FIG. 8 show a partial mask and partial surface of the spherical surface. Because of the symmetry of the spherical surface, it is sufficient to calculate only a quarter of the mask data. The deviations from the ideal surface function and the approximation curve of the method according to the invention are illustrated in the lower partial images in FIG. 8.

A total of 3735 mask elements were placed on an area of 100 μm '100 μm with a minimum edge length of the mask elements of 0.7 μm. The method according to the invention the search for the optimal distribution of mask elements with an approximation deviation of 0.465%. The partial images of FIG. 8 (bottom right) show that an approximation deviation of around 1% was achieved within the first approximately 2.5 million mutations. The left curve shows the improvement in the deviation in the range of 0.5% to 3.5% for the first 12.5 10 ⁶ mutations. The right curve shows the further course in the range from 0.46% to 0.53% to 7.5 '10 ⁷ mutations. The final value was only achieved after around 70 million mutations. The lower left partial image of FIG. 8 shows a high approximation in the area of the spherical surface, deviations only occur at the edge and at the top of the surface (dark dotted).

The comparison of FIGS. 8 and 10 impressively show the superiority of the method according to the invention in the optimization of photomasks. The surface roughness has improved considerably compared to the spherical surface formed with the conventional method.

FIG. 9 shows two further examples of 3-dimensional structures that can be generated with a photomask generated according to the invention. In the left part a pyramid composed of four parts is shown. The right part of FIG. 9 shows the detail of a Fresnel lens which is formed by superimposing a large number of hemispheres or hemispherical shells.

Masks for lithography produced according to the invention have applications in micromechanics, microtechnology, microsystem technology, microstructure technology, including photovoltaics (solar cells, replacement of previous chemical or mechanical processes, optimization of structure for reflection), "cellular" Biotechnology, and integration of sensors and actuators in semiconductor chips.

Claims

claims

1. A method for generating a two-dimensional photomask, in particular for gray-tone lithography, the photomask having a multiplicity of translucent regions, each with one or more mask elements, which are arranged such that an exposure image is generated on the target when the target is exposed through the photomask , which is adapted to a predetermined gray-scale image, characterized in that the number, size and / or positions of the mask elements are determined using an evolutionary selection procedure with a large number of mutation steps in which

- starting from a start distribution of mask elements with an operator selected from a group of predetermined statistical operators, a modified distribution of mask elements are successively generated until a predetermined termination criterion is met, and

- For each current distribution, the associated exposure image is determined, which would result from exposure of the target through a photomask with the current distribution, whereby

- The termination criterion is met if an approximation quality, which is characteristic for the adaptation of the exposure image to the gray value image, has reached a predetermined limit value or has not been improved over a predetermined number of mutation steps.

2. The method according to claim 1, in which it is checked at each mutation step or after a plurality of mutation steps whether the current distribution of mask elements fulfills predetermined process conditions.

3. The method as claimed in claim 1, in which the operator executed in a mutation step is undone if the current distribution obtained therewith results in an exposure image whose approximation quality lies outside a predetermined progress interval.

4. The method according to claim 3, wherein the progress interval in an initialization phase (100), in which a CREATE or UNDO operator is executed, and an ambitioins phase (200), in which a CREATE, MOVE -, RESIZE, ERASE or an UNDO operator is performed, characterized in that the approximation quality is improved with each mutation step or at least remains the same.

5. The method according to claim 3, wherein the progress interval is in an optimization phase (300), in which a

CREATE, MOVE, RESIZE, ERASE or an UNDO operator operator is performed, characterized in that the approximation quality for each mutation step is better than a predetermined reference value of an optimization curve.

6. The method according to claims 3 to 5, wherein the mutation steps are carried out first in the initialization phase (100), then in the ambition phase (200) and finally in the optimization phase (300).

7. The method as claimed in claim 1, in which the approximation quality is the average deviation between the current exposure image and the gray-scale image and / or a surface roughness parameter R which is characteristic of the surface roughness would result when using a photomask with the current exposure image.

8. Photo mask, which has a plurality of translucent areas, each with one or more mask elements, characterized in that the edge profile and / or the arrangement of the translucent areas is formed such that steps (15) are formed on the edges of translucent areas and / or there are vertical distances (18) between edges of different translucent areas, the steps or vertical distances being smaller than a minimum edge length of the mask elements.

9. Photo mask according to claim 8, wherein the minimum edge length of the mask elements is equal to an integer multiple of a grid dimension (s), which corresponds to the lateral resolution of the structuring method used to produce the photo mask.

10. Photo mask according to claim 8 or 9, wherein the mask elements are arranged so that two mask elements touch each other only in a common corner point.

11. Photo mask according to one of claims 8 to 10, in which the number and arrangement of the opaque mask elements is formed by a method according to one of claims 1 to 7.