Correction of heat expansion in lithography drawing method

Abstract

To address a local heating of and a deformation caused by heating of a target during a drawing processing in an electric charge particle lithography device.SOLUTION: A pattern drawing method contains steps of: determining an exposure position where a beam is entered into a substrate and a power of the beam at the exposure position; calculating a heat diffusion and a radiation cooling in a plurality of portions over a front surface of the substrate by calculating a heating of the substrate at the exposure position; calculating a position deviation of the substrate as a result of the heat expansion in a portion on the substrate which is the same number, or the declined number; and drawing a structure updated onto the substrate by the beam by determining a deviation distance for compensating a position deviation at the exposure position, and updating a structure which as to be drawn by shifting the exposure position of the beam by the deviation distance. Those steps are repeated as a function of the exposure position of which a time and / or a beam substrate position are / is changed.SELECTED DRAWING: Figure 7

Description

[Technical Field]

[0001] This application claims the benefit of priority under the Paris Convention for European Patent Application No. 22163287.0, filed on 21 March 2022, the entire contents of said application incorporated herein by reference.

[0002] This invention relates to a pattern drawing method used in a charged particle lithography apparatus. [Background technology]

[0003] This type of method is used in reticle manufacturing or maskless direct writing lithography. The applicant has described such methods and apparatus, for example, in US9,520,268, US6,768,125, US8,222,621 and US8,378,320. Not all aspects of the above-mentioned patent disclosures are necessary for using the present invention. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] US9,520,268 [Patent Document 2] US6,768,125 [Patent Document 3] US8,222,621 [Patent Document 4] US8,378,320 [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] This invention relates to the correction of pattern position errors due to thermal expansion of a target (also referred to as a substrate) during a drawing process, wherein the target is continuously heated by a charged particle beam used in the drawing process. The generated heat diffuses during the exposure process and gradually dissipates through convection and thermal radiation, causing various deformations of the target. The inventors have found that the heating of the target and the resulting thermal expansion exhibit strong spatial inhomogeneity, which leads to serious consequences such as target deformation, degrading the quality and positional accuracy of the features generated by the drawing process, especially since the deformation changes rapidly over time.

[0006] A typical embodiment of the present invention uses a charged particle exposure apparatus as shown in Figure 10 (not to scale), which includes a charged particle irradiation system 91 that generates a charged particle beam 92, a projection optical system 93, and a beam shaping or aperture array apparatus 94 that modifies the shape of the beam or the pattern transferred to the substrate. Furthermore, the apparatus includes an exposure chamber 90 that houses a target 95 to be exposed (e.g., a resist-coated quartz photomask or silicon wafer), which is mechanically fixed to a moving stage 97 by a clamp 96 (or other type of mount). The exposure apparatus is controlled by a processing system 98. Further details of the charged particle exposure apparatus can be found in the published patent documents mentioned above. The processes of thermal diffusion, convection, and thermal radiation are symbolically represented in Figure 10 by dashed lines and dashed arrows.

[0007] From the above perspective, one objective of this application is to provide an approach to address the problems of localized heating of a target and deformation caused by heating during the drawing process in a charged particle lithography apparatus. [Means for solving the problem]

[0008] From one perspective of the present invention, a method for drawing a pattern on a substrate in a charged particle lithography apparatus using scan exposure with a charged particle beam, A method is provided in which a charged particle beam is directed to a series of exposure locations on the surface of a substrate, and at each exposure location, the charged particle beam is used to draw a structure on the substrate within a beam range around each exposure location, according to each pattern portion representing a corresponding sub-region of the pattern to be drawn. The above method involves the following steps performed for each exposure position: Based on the exposure position, determine the power of the charged particle beam applied to the substrate at that exposure position; - Calculate the heating of the substrate generated by the charged particle beam during the exposure duration associated with the exposure position, and calculate the amount of radiative cooling due to thermal diffusion and heat emission from the substrate for multiple locations defined in a predetermined array across the surface of the substrate; • Calculating the positional changes of the substrate resulting from thermal expansion based on the results of the preceding steps, for multiple locations defined in a predetermined array across the surface of the substrate; • Calculate the displacement distance, where the displacement distance represents the change in position at the exposure location; - Applying a correction to the exposure position and / or the pattern portion associated with the exposure position using the displacement distance; and, • Continue drawing the structure on the substrate with a charged particle beam according to the corrected exposure position and pattern area. Includes, The above step(s) is performed for each of a series of exposure durations(s), each of which covers a time interval associated with one or more subsequent exposure positions. The calculation of each time interval is performed using the results obtained from the calculation of the time interval preceding each time interval. It is characterized by (Form 1). [Modes for carrying out the invention]

[0009] (Mode 1) Refer to one perspective of the present invention described above. (Form 2) In the method described in Form 1, The step of applying a correction to the pattern portion associated with the exposure position using the displacement distance is: (i) To obtain an updated exposure position, the exposure position of the charged particle beam is shifted by a first displacement, and (ii) Recalculating the pattern portion by shifting the structure included in the pattern portion by a second displacement in order to obtain the updated pattern portion. Perform at least one of the following, wherein the displacement distance is obtained by combining the first displacement and the second displacement. Next, a structure is drawn on the substrate with a charged particle beam according to the exposure position and pattern portion updated in this manner. It is preferable that it includes. (Form 3) In the method described in Form 1 or 2, In the step of calculating the heating of a substrate generated by a charged particle beam on the substrate, the energy deposited by the charged particle beam during a time interval associated with one or more subsequent exposure positions is modeled as being deposited by a series of heated spots. Each heating spot has a heat insertion distribution that follows a predetermined spatial distribution and is located at the center of a series of deposition positions that represent the average beam position over each sub-interval of the time interval. The aforementioned predetermined spatial distribution has a width that is significantly (significantly) larger than the actual beam region on the substrate. The aforementioned predetermined spatial distribution is preferably a Gaussian distribution. (Form 4) In the method described in any of Forms 1 to 3, The difference between the fourth power of the substrate temperature and the fourth power of the ambient temperature, and The difference between the substrate temperature and the ambient temperature. Preferably, heat diffusion is calculated using a non-uniform heat equation that includes a source-sink function including thermal radiation that is calculated as being proportional by a common proportionality constant to one of them. (Form 5) In the method according to Form 4, The common proportionality constant of the thermal radiation is preferably determined in advance by drawing markers on a test substrate at a plurality of different stages of the drawing process, measuring the deformation positions of the drawn markers, and performing a best-fit calculation of the proportionality constant with respect to the deformation positions measured in this way. (Form 6) In the method according to Form 4, The proportionality constant is determined by fitting to substrate temperature measurements (plural) that are pre-executed on a test substrate that undergoes a test drawing process in the same charged particle lithography apparatus in which the pattern is subsequently drawn on the substrate, and the test substrate and the test drawing process are preferably representative of the substrate and the pattern drawn on the substrate, respectively. (Form 7) In the method according to any one of Forms 1 to 6, In the step of calculating the heating of the substrate by the charged particle beam, the heating rate is preferably calculated as being proportional to a predetermined beam power by a proportionality constant. (Form 8) In the method according to Form 7, The proportionality constant is preferably determined in advance by drawing markers on a test substrate at a plurality of different stages of the drawing process, measuring the deformation positions of the drawn markers, and performing a best-fit calculation of the proportionality constant with respect to the deformation positions measured in this way. (Form 9) In the method according to Form 7, Preferably, the proportionality constant is determined by fitting it to a plurality of substrate temperature measurements performed in advance on a test substrate that undergoes a test drawing process in the same charged particle lithography apparatus on which the pattern is subsequently drawn, and the test substrate and the test drawing process are representative of the substrate and the pattern drawn on the substrate, respectively. (Form 10) In the method described in any of Forms 1 to 9, Preferably, at least one parameter relating to the mechanical or thermomechanical properties of the substrate is determined by using a test substrate and performing a test drawing process in the same charged particle lithography apparatus in which a pattern is subsequently drawn on the substrate, provided that the test substrate and the test drawing process are representative of the substrate and the pattern drawn on the substrate, by measuring a quantity that enables the determination of the at least one parameter, and by calculating the at least one parameter from the quantity thus measured. (Form 11) In the method described in any of Forms 1 to 10, The steps(s) described in Embodiment 1 are preferably performed in real time during the process of drawing a pattern on a substrate using the actual exposure positions(s), patterns, and current density values(s) recorded by the exposure control device. (Form 12) In the method described in any of Forms 1 to 11, Preferably, the substrate is exposed using a stripe scan drawing method that draws a structure on the substrate strip by stripe, and the calculation steps(s) described in Embodiment 1 are performed for multiple consecutive durations, with each duration corresponding to the respective part of each stripe before drawing the structure of the pattern portion belonging to each stripe or part of the stripe. (Form 13) In the method described in any of Forms 1 to 12, The step of calculating the heating of the substrate generated by the charged particle beam at the exposure position of the substrate preferably also includes the preheating of the substrate generated by the charged particle beam during the exposure path (elapsed time) on the substrate preceding the exposure position. (Form 14) In the method described in any of Forms 1 to 13, The step of calculating the amount of radiative cooling due to thermal diffusion and heat release from the substrate is preferably repeated for a series of exposure durations, and each exposure duration preferably includes a plurality of subsequent exposure positions extending at least over a first distance greater than the width of the beam region on the substrate surface. (Form 15) In the method described in Form 14, The step of calculating the change in the position of the substrate is repeated for a series of secondary durations that are less sparse than the series of exposure durations. Preferably, each of the series of secondary durations includes a plurality of subsequent exposure positions that extend at least over a second distance greater than the first distance. (Form 16) In the method described in any of Forms 1 to 15, The step of calculating mechanical strain preferably includes, as additional mechanical constraints, the action of mechanical stress introduced by external forces, including holding forces, applied to the substrate at a predetermined number of mounting positions, and / or the action of multiple fixed mounting positions of the substrate, where the magnitude of the position change at each of these positions is a predetermined value, such as a zero position change value.

[0010] The above objective is to provide a method for drawing a pattern on a substrate in a charged particle lithography apparatus using scan exposure with a charged particle beam, in accordance with the present invention, wherein the charged particle beam is directed to a series of (defined) exposure positions on the surface of the substrate, and at each exposure position, the charged particle beam is directed to draw a structure on the substrate within the beam region around each exposure position according to the respective pattern portion representing the corresponding sub-region of the pattern to be drawn. This method involves the following steps for each exposure position: Based on the exposure position, determine the power of the charged particle beam applied to the substrate at that exposure position; - Calculate the heating of the substrate generated by the charged particle beam during the exposure duration associated with the exposure position, and calculate the amount of radiative cooling due to thermal diffusion and heat emission from the substrate for multiple locations defined in a predetermined array across the surface of the substrate; • Calculate the change in position of the substrate as a result of thermal expansion (generated by substrate heating and thermal effects calculated in the previous step) at multiple locations defined in a predetermined array across the surface of the substrate; • Calculate the displacement distance, where the displacement distance represents the change in position at the exposure location; - Applying a correction to the exposure position and / or the pattern portion associated with the exposure position using the displacement distance; and, • Continue drawing structures(s) on the substrate with a charged particle beam according to the corrected exposure position and pattern areas. Includes, The aforementioned steps are performed for each of a series of exposure durations, each of which covers a time interval associated with one or more subsequent exposure positions, and the calculation of each time interval is performed for the results of calculations obtained for the time intervals preceding each time interval. Here, the term “subsequent exposure positions” is used for a series of defined regions where the beam is considered a function of time, and is intended to mean multiple exposure positions that are located immediately following each other; in other words, one pass through the above steps is performed for one exposure duration and one set of subsequent exposure positions associated with it, and multiple passes through the steps are repeated for a series of exposure durations. Furthermore, “beam range” means the beam spot generated by the entire beam on the substrate at a given time, based on the fact that the beam spot has a clearly defined finite size on the target (this finite size can often be constant (uniform) across a series of exposure positions). Furthermore, it should be noted that the exposure duration may include not just one exposure location, but multiple (generally quite a number) subsequent exposure locations, as will be explained further below.

[0011] This approach provides an efficient method for calculating and compensating for the effects of heating during the drawing process in charged particle lithography equipment. In particular, the handling of thermal effects and mechanical strain in separate steps provides reduced computation time and improved accuracy during the drawing process.

[0012] The step of calculating the position change of the substrate may include calculating the mechanical strain resulting from thermal expansion (caused by heating / cooling / diffusion of the substrate, which is calculated in each preceding step) and optionally additional mechanical constraints. Optional mechanical constraints may be used to account for additional mechanical forces applied externally to the substrate or the fixing of the substrate at defined points. Thus, calculating the mechanical strain may include, as additional mechanical constraints, the action of mechanical stress introduced by external forces, including holding forces applied to the substrate at a predetermined number of mounting positions, and / or the action of multiple fixed mounting positions of the substrate where the magnitude of the position change at each of them is a predetermined value, such as a zero position change value.

[0013] As a simple and efficient approach to calculating thermal diffusion, many embodiments may use an inhomogeneous heat equation that includes a source-sink function and includes thermal radiation calculated as proportional to the difference between the fourth power of the substrate temperature and the fourth power of the ambient temperature (according to the Stefan-Boltzmann law), by a common proportionality constant; as a simplified alternative, particularly when the amplitude of the temperature change is small enough to be linearizable, it may instead be calculated as proportional to the difference between the substrate temperature and the ambient temperature. In this approach, the proportionality constant for thermal radiation may be determined, for example, by drawing markers on a test substrate at several different stages of the drawing process, measuring the deformation locations of the drawn markers, and performing a best-fit calculation of the proportionality constant for the thus measured deformation locations. Alternatively, the proportionality constant may be determined by fitting to in-situ substrate temperature measurements. Here, the term "in situ" is used to mean that the measurement is performed beforehand on a test substrate that will be processed in a test drawing process in the same charged particle lithography apparatus on which a pattern will subsequently be drawn, where the test substrate and the test drawing process represent (each) the substrate (typically the substrate and the test substrate are of the same type) and the pattern drawn on the substrate.

[0014] As a simple and efficient approach to calculating beam-induced substrate heating, many embodiments may employ the calculation of the heating rate as being proportional to a predetermined beam power, where the proportionality is determined (governed) by a proportionality constant. This proportionality constant can be determined, for example, by pre-drawing markers on a test substrate at several different stages of the drawing process, calculating the deformation positions of the drawn markers, and performing a best-fit calculation of the proportionality constant for the deformation positions thus measured. Alternatively, the proportionality constant can be determined by fitting to in-situ substrate temperature measurements. In this case as well, the term "in situ" is used to mean that the measurements are performed pre-on a test substrate undergoing a test drawing process in the same charged particle lithography apparatus on which a pattern is subsequently drawn, where the test substrate and the test drawing process represent the substrate and the pattern drawn on the substrate, respectively.

[0015] Furthermore, in many embodiments, the computational complexity is reduced when mechanical stress, strain, and distortion are calculated using linear elasticity. Additionally, gravity (acting on the substrate) may be considered when calculating mechanical stress, strain, and distortion. Furthermore, it may be advantageous to consider special constraints corresponding to one or more boundary conditions, such as: normal and shear stresses that vanish at the free boundary of the substrate; substrate distortion that vanishes at the clamp mount of the substrate; and substrate mount points that generate mechanical stress on the substrate.

[0016] Furthermore, other parameters relating to the respective mechanical or thermomechanical properties of the substrate can also be predetermined. This can be advantageously achieved by using a test substrate and performing a test drawing process in the same charged particle lithography apparatus in which a pattern is subsequently drawn on the substrate, provided that the test substrate and the test drawing process represent the substrate and the pattern drawn on the substrate, respectively; then, quantities that enable the determination of these parameters are measured, and the parameters are calculated from these quantities. The parameters thus determined can then be used in the method of the present invention to calculate, among other things, thermal heating, thermal diffusion, radiation effects, and mechanical stresses and strains and the resulting deformations.

[0017] Preferably, all or at least some of the above steps of this method may be performed in real time during the process of drawing a pattern on a substrate using the actual exposure positions, patterns, and current density values ​​recorded by the exposure control device.

[0018] The method of the present invention is particularly advantageous in relation to stripe scan drawing methods, such as the drawing method described by the applicant in US9,053,906. In such a stripe scan drawing approach, the substrate is drawn stripe by stripe, and the calculation step(s) (i.e., the steps(s) ending in "calculate" among the method steps listed above) are performed for each stripe before the corresponding stripe is exposed, preferably using the result of shifting the exposure position(s) obtained for each preceding stripe, or, more advantageously, for a number of consecutive durations, each corresponding to a corresponding portion of each stripe, before drawing the structure(s) of the pattern(s) belonging to each stripe or portion of the stripe (of the same stripe or possibly at least one more preceding stripe).

[0019] Furthermore, it is often advantageous to consider the heating effect accumulated over the course of subsequent exposure positions (multiple) of the particle beam. Therefore, in many embodiments, the step of calculating the heating of the substrate generated by the beam at the exposure position is: This may also include preheating of the substrate by the beam during the exposure path on the substrate prior to the exposure position.

[0020] To reduce the required computational power (computational load), it is desirable—and often sufficient—to perform the thermal calculation process (instances) only as many times as possible on the substrate, and in particular, at a much lower frequency than the multiple exposure positions scanned by the beam during the drawing process. Thus, the step of calculating the amounts of thermal diffusion and radiative cooling can be repeated only for a series of exposure durations, each containing multiple subsequent exposure positions extending over at least a first distance that is, for example, at least an order of magnitude (i.e., 10 times) greater than the width of the beam region on the substrate surface. Furthermore, the calculation process (instances) for calculating mechanical strain can be performed at an even lower frequency. Thus, the step of calculating the position change and / or mechanical strain of the substrate may be repeated for a series of secondary durations that are less frequent than the series of exposure durations, where each secondary duration contains multiple subsequent exposure positions extending over at least a second distance that is, for example, at least an order of magnitude greater than the first distance.

[0021] In some embodiments of the present invention, the calculation of beam-induced substrate heating may be performed with reduced accuracy in order to further reduce computational complexity and to obtain a heating model that is easy to implement. This can be done, for example, in the step of calculating the substrate heating generated by the beam on the substrate, by modeling the beam's thermal track as a series of "heating spots" on the substrate surface, each of which imparts heat to the substrate according to a predetermined spatial distribution (e.g., a Gaussian distribution). It is preferable that the spatial distribution has a width significantly larger than the actual beam region. In particular, each heating spot may be located at the center of a series of deposition positions that represent the average of the beam positions over each sub-interval of each time interval associated with one or more subsequent exposure positions.

[0022] Furthermore, there are several different possibilities for applying corrections to the pattern portion based on displacement distance. For example, the correction may be applied by shifting the beam exposure position by the displacement distance to obtain the updated exposure position, and then drawing the structure(s) on the substrate according to the pattern portion and the thus updated exposure position. Alternatively, the correction may be applied by recalculating the pattern portion by shifting the structure(s) contained within the pattern portion by the displacement distance to obtain the updated pattern portion, and then drawing the structure(s) on the substrate with the beam according to the exposure position and the thus updated pattern portion. These two approaches can also be combined to have a combination of shifting the beam exposure position by a first displacement to obtain the updated exposure position and recalculating the pattern portion by shifting the structure(s) contained within the pattern portion by a second displacement to obtain the updated pattern portion. The sum of the first and second displacements constitutes the displacement distance; and the corresponding structure(s) are exposed on the substrate according to the thus updated exposure position and pattern portion.

[0023] In the following, the present invention will be described using several embodiments or examples that are described in more detail below with reference to the accompanying drawings. It should be emphasized that the embodiments or examples shown herein are for illustrative purposes only and should not be understood as limiting the scope of the present invention. [Brief explanation of the drawing]

[0024] [Figure 1] An example of thermal expansion of a substrate due to uniform heating. [Figure 2] Thermal strain in the substrate shown in Figure 1. [Figure 3] An example of thermal expansion of a substrate that has been heated unevenly. [Figure 4] Thermal strain in the substrate shown in Figure 3. [Figure 5] An example of distortion of a circuit board mounted in three positions. (A) shows the case of three slide mounts that allow slight movement at multiple mounting positions, and (B) shows the case of clamp mounts that fix the circuit board at multiple mounting points. [Figure 6] Examples of mounts. (A) shows an example of a mount that allows for multiple lateral movements, and (B) shows an example of a clamp mount that secures the substrate at the mounting point. [Figure 7] An example of a process for calculating a correction map for thermomechanical distortion. [Figure 8] An example of a correction map acquired during the drawing process following the stripe exposure method (approach). [Figure 9] An example of a test substrate created to perform in situ measurements of multiple model parameters such as power-to-heat ratio and substrate emissivity. [Figure 10] A longitudinal cross-sectional view of an example of a conventional charged particle multibeam system. [Examples]

[0025] The detailed discussion provided herein is intended to illustrate the present invention, exemplary embodiments thereof, and further advantageous developments. It will be apparent to those skilled in the art that some or all of the embodiments and aspects discussed herein may be arbitrarily combined in any way that is deemed suitable for a particular application of the present invention. Throughout this disclosure, terms such as “advantageous,” “exemplary,” or “preferred” describe elements or dimensions that are particularly suitable (but not essential) for the present invention or one embodiment thereof, and can be modified unless expressly stated otherwise, if deemed suitable by those skilled in the art. It goes without saying that the present invention is not limited to the exemplary embodiments discussed below, which are provided for the purpose of describing the present invention and merely present preferred examples of the present invention.

[0026] In particular, the present invention can be used in combination with almost any charged particle lithography apparatus that performs scanning exposure, but an example relating to an electron beam apparatus for lithography mask manufacturing will be discussed. A suitable apparatus for embodying the present invention will be described with reference to Figure 10. In particular, in the lithography apparatus of Figure 10, the calculation and correction methods described below can be suitably performed in the processing system 98 of the lithography apparatus and / or any other control system for processing data and controlling the drawing process on the substrate (the terms substrate and target are used interchangeably here). Further details on multibeam charged particle tools can be found in US9,520,268, US6,768,125, US8,222,621 and US8,378,320 and the references cited herein, all of which are incorporated herein by reference and constitute part of this disclosure.

[0027] Thermal expansion

[0028] It is well known from the prior art (e.g., US6,424,879, US5,847,959, US9,017,903 and US10,012,900) that the reticle undergoes thermal expansion, which can lead to significant displacement of the structure during exposure (known as registration error). For example, a recent embodiment of a typical lithography apparatus, such as the applicant's so-called MBMW, uses an electron beam reaching the target with a maximum current of approximately 1 μA and a particle energy of 50 keV for mask lithography. Assuming a pattern density of 100% and zero stage recovery cycles, the electron beam energy corresponds to a constant heating effect of 0.04 W, assuming that 80% of the electron beam energy is converted into heat in the substrate. For a typical fused silica 6" (inch) photomask, according to the Stefan-Boltzmann law, Assuming typical values ​​for the mask emissivity of TIFF2023138912000002.tif6150 and an ambient temperature of 295K, thermal equilibrium is achieved at ΔT = 0.59K. For example, Assuming that a mask with the thermal expansion coefficient of TIFF2023138912000003.tif6150 can be freely expanded, it will be approximately 3.2·10 -5 The mask expands by % and, as a result, the corners of the mask experience a maximum distortion of approximately 35 nm relative to the center of the mask. The above situation, i.e., thermal distortion for a uniform temperature rise, is shown in Figure 1 in three projection planes (where x, y, and z are the maximum values ​​within the substrate, respectively). The mask center r1 is used as the reference point, and the maximum lateral distortion is achieved at the corners, which are shown as r2. Since the photomask is typically only about 6.35 mm thick, the vertical (up and down) distortions r3 and r4 of the free-expanding mask are not significant (approximately 1.5 nm at the corners, assuming the above temperature rise). Figure 2 shows the corresponding thermal strain in the xy plane (i.e., the deformation s2 of a small element s1 at a given position), which is uniform due to the uniform heating of the substrate. The amount of deformation and mask thickness are greatly exaggerated in Figures 1 to 5 for ease of visibility and understanding.

[0029] Since the acceptable target registration error for mask manufacturing in state-of-the-art manufacturing equipment is typically on the order of 1 nm 3σ, the above distortion up to approximately 35 nm results in a registration error that requires appropriate correction.

[0030] Mechanical deformation

[0031] In actual photomasks, the temperature distribution is typically not uniform because the heat introduced at the drawing location does not dissipate sufficiently quickly throughout the entire substrate. Due to such a non-uniform temperature distribution, the precise deformation of the mask depends not only on the thermal properties of the substrate but also on its mechanical properties. A typical example is shown in Figure 3, which uses the same projection plane as Figure 1, with the mask center r1 also used as the reference point. In this case, the mask is heated only partially, i.e., only in the hatched area r3. The resulting distortion is no longer uniform, as in the case of Figure 1, but varies (different) depending on the location. Furthermore, the corresponding thermomechanical strain, shown in the xy plane in Figure 4, varies throughout the entire mask and exhibits a shear effect (i.e., a small region s1 deforms into a non-rectangular parallelepiped s2) particularly in the thermal transition area.

[0032] Furthermore, the reticle is typically mounted to the stage at a predetermined mounting point(s), and therefore cannot expand freely and equally in all directions. The effect of distortion is visualized in Figures 5(A) and 5(B), which include simulation data in the x and y planes. In Figure 5(B), the substrate is fixed at three positions c1, c2, and c3 by clamping mounts that allow only very slight movement of the mask relative to the stage. In Figure 5(A), the mask is mounted at positions s1, s2, and s3 by sliding mounts that fix the mask position by friction, allowing some degree of movement. In both cases, the mask distortion becomes more pronounced (larger) towards the right side of the mask (plane of the paper), particularly towards the upper right and lower right corners (plane of the paper), and decreases towards the left side (plane of the paper).

[0033] Thermal model

[0034] This invention proposes a model that describes both the thermal and mechanical properties of a mask. In particular, for an isotropic medium having a thermal diffusivity α(r) which can preferably be considered constant, and a source-sink function S(r,t) that describes the thermal energy supplied to and dissipated by the mask, the diffusion of the temperature distribution T at position r and time t is described by the heterogeneous thermal equation. TIFF2023138912000004.tif23156 It is described by: In a typical process implementation, the mask is placed in a vacuum with small contacts (multiple contact points / fulcrums), so the primary mode of heat dissipation is radiation (radiative). According to the Stefan-Boltzmann law, for a given ambient temperature T0 of the exposure apparatus (in a typical implementation, this would also be the so-called soaking temperature of the substrate), the heat dissipation power density is: TIFF2023138912000005.tif20156 That is the case. Here, TIFF2023138912000006.tif15153 represents the emission rate of the substrate, and σ is the Stefan-Boltzmann constant. Typically, the mask temperature is not excessively far from the ambient temperature, i.e., Since it is TIFF2023138912000007.tif17153, linearization is required, i.e., TIFF2023138912000008.tif20156 This allows for a good approximation that can be applied to computer execution (calculation).

[0035] Additionally, the mask is heated by the incident charged particle beam. Its power density is Since it is given in TIFF2023138912000009.tif16153, by introducing a coupling constant γ that determines the magnitude of the beam energy converted to heat, and neglecting conductive heat transfer across the substrate mount, the source-sink function is The filename becomes TIFF2023138912000010.tif17153.

[0036] Relative thermal strain (i.e., relative length expansion of an infinitesimal element) relative to the reference temperature T1 (which is usually equal to the ambient temperature T0). TIFF2023138912000011.tif22153) is proportional to the change in temperature, that is, The filename becomes TIFF2023138912000012.tif16153.

[0037] proportionality constant α L is the coefficient of thermal expansion, which can reasonably be considered constant in the context of this invention.

[0038] Mechanical model

[0039] To calculate the mechanical deformation resulting from thermal expansion, the established theory of linear elasticity is a suitable model for this invention. This is represented by the following equations. TIFF2023138912000013.tif60156 Alternatively, in exponential notation, Regarding TIFF2023138912000014.tif16153, TIFF2023138912000015.tif57156 This is determined. Here, TIFF2023138912000016.tif16153 and TIFF2023138912000017.tif16153 is a file containing secondary mechanical stress and a second-order strain tensor. TIFF2023138912000018.tif16153 is a mechanical displacement vector. TIFF2023138912000019.tif16153 is a 4th-order stiffness tensor. TIFF2023138912000020.tif16153 is an external force vector, TIFF2023138912000021.tif16153 is the material density (which can be considered constant for the purposes of this invention).

[0040] In a preferred embodiment of the present invention, the substrate is considered mechanically isotropic, which suggests that the stiffness tensor is determined by (one) set of two scalar material parameters, and Hooke's law can be simplified. In particular, TIFF2023138912000022.tif23156 However, the two scalars λ and μ are Lamé parameters, and these are related to other common material parameters, such as Young's modulus E and Poisson's ratio ν. TIFF2023138912000023.tif20153 and This is easily represented by TIFF2023138912000024.tif22153. A typical value is E=17·10 (for fused quartz (quartz glass)). 10 Pa and ν = 0.17.

[0041] In a preferred embodiment of the present invention, since the temperature changes only slowly on the mask scale, the mechanical deformation is static with respect to a given temperature distribution, i.e., It is calculated as TIFF2023138912000025.tif21153. Then, the equations of isotropic linear elasticity are combined. TIFF2023138912000026.tif23156 It is possible to form this.

[0042] Full model

[0043] Thermal distortion TIFF2023138912000027.tif19153 (this is isotropic) and mechanical strain in the strain-displacement relation When combined with TIFF2023138912000028.tif17153, TIFF2023138912000029.tif23156 Here, TIFF2023138912000030.tif17153 represents the total displacement (mechanical displacement + thermal displacement), and when combined with other equations for linear elasticity (multiple equations), (in this case, static deformation and isotropic materials are assumed), TIFF2023138912000031.tif35156 You can obtain this.

[0044] external force

[0045] The force density vector F includes all external forces acting on the substrate. Gravity is particularly important. This is TIFF2023138912000032.tif16153, which leads to a sagging mask and slightly different distortion signatures under thermal fluctuations.

[0046] Boundary conditions and mounts

[0047] To solve the above equations, boundary conditions for stress, strain, or distortion must also be provided. Free points z on the mask surface. f Regarding this, (because it can move freely inward and outward) the mask is not subjected to normal (perpendicular) stress, and therefore, using the surface normal vector n, The file TIFF2023138912000033.tif16153 is obtained.

[0048] For the remainder of the mask surface, the details of the mounts used to secure the substrate to the stage (e.g., the forces generated on the (mask) surface) need to be considered in order to accurately determine the mechanical deformation. For example, a spring or friction mount 54 (shown in Figure 6(A), with the exemplary distortion in Figure 5(A)) can move the substrate 51 slightly relative to the stage 52. The spring 53 is at a point z on the contact surface. s In this case, the defined (predetermined) traction force is obtained by adding the applied traction force T0, which is proportional to the displacement due to the spring tensor K. This generates TIFF2023138912000034.tif16153. Therefore, The file TIFF2023138912000035.tif16153 is obtained.

[0049] On the other hand, the clamping mount 55 shown in Figure 6(B) with the exemplary distortion in Figure 5(B) almost completely locks the movement of the substrate 51 relative to the stage 52 by locally creating a (small) recess in the substrate. This is a special case of the spring mount described above. This corresponds to TIFF2023138912000036.tif16153. Points z on the mask surface fixed by clamp mounts. c It is not thermally distorted, that is, The filename is TIFF2023138912000037.tif16153.

[0050] Parameter determination

[0051] Most of the material parameters appearing in the above equations (or multiple equations) are related to the beam's power-to-heat ratio (which depends on how electrons interact with the surface). TIFF2023138912000038.tif16153 and substrate emissivity (which depends on the geometry of the exposure chamber 90 and the thermal properties of the exposure apparatus near the substrate) Except for a very small number of unknown parameters in systems like TIFF2023138912000039.tif16153, the beam power density associated with each exposure position is known and readily obtainable. For the purposes of the present invention, the beam power density associated with each exposure position is known. TIFF2023138912000040.tif16153 can be determined with sufficient accuracy relative to the thermomechanical simulation grid (i.e., identified by appropriate measurements and / or calculations) from quantities (multiple) that are normally monitored during the drawing process in a charged particle lithography apparatus, such as beam position, pattern density, and beam current. In particular, the determination of the actual beam current (of the whole beam) can be adequately achieved based on reference measurements (multiple) by monitoring the actual feeding current of the particle source and its time variation. Any further arbitrary input data of interest, as may be, can be readily derived from quantities (multiple) monitored in the charged particle lithography apparatus.

[0052] In one embodiment of the present invention, the power-to-heat ratio TIFF2023138912000041.tif16153 and substrate emissivity TIFF2023138912000042.tif16153 is determined by heating a substrate with a charged particle beam of defined (predetermined) power and performing in-situ measurements of the resulting temperature change of the substrate over time. These measurements can then be used to obtain the desired parameters, for example, by least-squares fitting of the measured temporal behavior to the predicted temporal behavior.

[0053] In another embodiment of the present invention, the power-to-heat ratio TIFF2023138912000043.tif16153 and substrate emissivity TIFF2023138912000044.tif16153 is determined by heating a substrate with a charged particle beam of defined (predetermined) power and performing in situ measurements of the resulting substrate deformation. An example of the procedure is described below for the test substrate shown in Figure 9, not to scale. In the first step, one set of first reference markers 81 is drawn on the substrate at a reference temperature T1. Next, one set of low-density dummy patterns 85 is drawn, and then one set of first strain markers 82 with a given nominal offset relative to the first reference markers 81 is exposed. Next, a high-density dummy pattern 86 and one set of second strain markers 83 are exposed. The dummy patterns 85 and 86 are stripes extending across an area, for example, horizontally (widthwise) or vertically (longitudinally) across the substrate, and can have any suitable shape, such as linear stripes, a chain of individual areas (e.g., rectangular or circular in shape), or multiple areas arranged in a zigzag pattern. Finally, after a defined (predetermined) cool-down period, a set of second strain [reference] markers 84 are drawn. After the exposure process, the test strain is determined by comparing the measured offsets of the reference markers 81 and 84 with the nominal offsets of the strain markers 82 and 83 (in actual tests, more sets of markers and heating / cooling stages (steps) will be used). The thermomechanical model introduced above is then used, for example by nonlinear least-squares fitting, to determine the power-to-heat ratio from the strain determined by the above experimental procedure and the defined (predetermined) exposure parameters. TIFF2023138912000045.tif16153 and substrate emissivity TIFF2023138912000046.tif16153 can be used to determine unknown parameters (multiple) of a system, including those directly related to heating and cooling rates. The same approach can be used to determine further mechanical or thermomechanical parameters, such as the elastic modulus(rate) or thermal expansion coefficient(rate) or diffusion coefficient, for example, when using composite substrates where these parameters are not readily available; and the determination of one or more such further parameters can similarly be achieved by fitting experimental procedures and / or the parameters (one or more) in question to pre-corrected data.

[0054] Calculation process

[0055] The above equations form a system of coupled partial differential equations, which can be solved using appropriate conventional finite element method (FEM) software.

[0056] In a preferred embodiment of the present invention, thermal distortion is calculated in real time during mask exposure. This approach has the advantage that only information available at runtime, such as fluctuations in the current in the particle source ("gun") or delays or interruptions occurring during exposure, can be incorporated into the simulation. This can be achieved, for example, by repeating several steps shown in Figure 7 within a time interval of duration Δt, where these steps represent a complete iterative loop. In the first step 61, represented by "ES_SOURCE", the beam position and power for the current time interval [t, t+Δt] are determined or estimated (e.g., from exposure data). Next, in step 62, represented by "UD_THERMD", the temperature distribution T is updated, preferably by solving the thermal and emission equations as described above, taking into account both added heat and emissions. In step 63, represented by “UD_DISTOR”, a mechanical mask model is used to calculate the thermal distortion relative to the undistorted state at a reference temperature T1 or to the calculated distortion state obtained during the preceding iteration steps, by using thermomechanical equations, including, for example, the Navier-Cauchy equations described above. In step 64, represented by “UD_CRRMAP”, a correction map is generated from the estimated thermomechanical distortion. Next, in step 65, represented by “APCRR_WR”, the corrections identified by the correction map are applied to the drawing process, which will be described in more detail below. Advantageously, the correction map is calculated simultaneously with or immediately before (e.g., 100 ms) the actual exposure of the exposure location(s) considered in step 65. In relation to multibeam mask writing machines, the thermal distortion of the diffuse mask scale (but not the local distortion in the vicinity of the beam) is of primary importance (of interest). In this case, additional thermal distortion generated near a certain exposure position may be calculated after the exposure, and the update interval(s) can be longer if the synchronization is loose.

[0057] Preferably, the process in steps 61-64 is repeated at predetermined time intervals or for specific positions of the beam frame, after each duration in which the beam frame has traveled a predetermined distance, for example, every specific percentage of the length of the substrate (measured in the longitudinal direction of the stripe), such as 1%, 2%, 5%, 10%, 20%, 25%, or 50% of the substrate length. It should be noted that such selections of durations for time intervals will correspond to a beam travel distance that is often considerably larger than the overall size of the beam region on the target (because the beam has a defined finite size on the target surface). In some embodiments of the present invention, steps 63 and 64 are skipped for the majority of the iterative loop(s) (e.g., more than 50%, 80%, or 90%), so that the temperature distribution is updated more frequently than the strain map and correction map (this is indicated in Figure 7 by dashed arrows skipping some of the steps); thus, only a small percentage of the iterative loop(s) are complete, i.e., including the complete set of steps 61-65. This reduces computation time, because the calculation of the strain map is exceptionally large from a computational standpoint; furthermore, the strain map usually changes only slowly over time, which is why a low update frequency is sufficient, whereas it has been found (by the present invention) that rapidly (frequently) updating the temperature distribution (e.g., by using finer time steps in the thermal equation) is useful for adequately capturing thermal diffusion and radiation.

[0058] In another embodiment of the present invention, the underlying drawing method includes a stripe scanning method, such as the one described by the present applicant in US9,053,906. In this case, of course, the stripe exposure duration or a defined (predetermined) proportion (part) thereof is used as the correction map update interval [t, t+Δt]. That is, before drawing each stripe, the correction map is updated (using past or predicted exposure positions and beam power).

[0059] FIG. 8 shows an example of a correction map obtained for an update interval that is half of the exposure time during which the stripe 72 is exposed. (Note that FIG. 8 shows only a part of the target, i.e., only the part corresponding to some stripes 71, 72 that are exposed during the drawing process.) The calculation of the correction map 74 for the stripe 72 is based on the previous correction map 73 calculated for the previous stripe(s) before the exposure of the stripe 72. However, the correction map 73 (shown as a black arrow in FIG. 8) is generated based on the thermo-mechanical deformation of the substrate at time t k due to the heat applied during the drawing of the previous stripe(s) 71, and this correction map is updated at specific time point(s) within the duration of the exposure of the stripe 72; for example, it is updated at the midpoint of the exposure time as shown in FIG. 8. The correction map represents the shift in the position r in the grid of the reference position(s) at the reference temperature T1 at time t k received TIFF2023138912000047.tif16153 is included. At time t k+1 = t k + Δt (i.e., after half of the stripe exposure time has elapsed in the illustrated example), the correction map is updated to a new map 74 (shown as a gray arrow in FIG. 8), taking into account the energy applied during the drawing of the first position of the stripe 72. Note that the scales of the beam and mask distortion are greatly exaggerated from the perspective of visibility.

[0060] In a variant of the present invention, the additional (applied) heat determined in step 62 UD_THERMD is calculated with a reduced accuracy, i.e., at a lower resolution compared to the simulation grid (e.g., triangular surface elements in the implementation of FEM). Instead, a sub-interval of the update interval [t, t + Δt] TIFF2023138912000048.tif16153 (however,[[]] TIFF2023138912000049.tif16153 is a relevant (or specified :relevant) point in time within the update interval, and TIFF2023138912000050.tif16153 is a sub-interval length less than Δt, and in typical embodiments of the invention, the collected energy applied within a sub-interval (which may be significantly smaller than Δt, e.g., 10% thereof) is modeled using a Gaussian heat distribution that has a distribution significantly wider than the actual beam region 75 at the target, as applied to the average beam position in the sub-interval. Figure 8 shows the 1σ (sigma), 2σ, and 3σ level ranges of an exemplary single distribution as multiple concentric circles 76. The inventors have found that this approach is simpler while still being sufficiently accurate, and also provides more consistent thermomechanical distortion results (increased simulation stability) when the grid resolution is changed.

[0061] Application of correction

[0062] Once the distortion is determined by the mask scale, the distortion is compensated for by appropriately correcting the beam position and / or pattern in the drawing process (step 65 in Figure 7). One clear and simple approach is to move the beam exposure position to the distorted position, i.e., a local displacement. The beam is updated by shifting by a displacement distance corresponding to TIFF2023138912000051.tif16153 (black arrow in Figure 8). This beam shift can be achieved by any suitable means for correcting the drawing position of the beam at the location of the mask, for example, by using drawing multipoles in the projection optical system 93. However, for some embodiments, such as the case of a multi-beam charged particle exposure apparatus, it is expected that correction of local distortions by other modifications of the drawing process may be more efficient. In particular, a pixel-based approach, such as that described by the applicant in US9,568,907, is proposed as a favorable method for correcting distortions with significant changes across a single beam field. In particular, the pattern inside the beam region at the beam location is recalculated, for example, by dividing the pattern into multiple parts, and each part is local displacement at the location of a representative point of each part. The shift is performed according to TIFF2023138912000052.tif16153. It should be noted that the two approaches described above can be combined; that is, part of the correction for local displacement can be performed by beam shifting to the updated beam position, and the other part by recalculating the pattern portion at the updated beam position.

[0063] All or part of the above embodiments may be described as follows, but are not limited to them. [Note 1] A method for drawing a pattern on a substrate using a charged particle lithography apparatus that employs scan exposure with a charged particle beam. A charged particle beam is directed to a series of exposure locations on the surface of the substrate, and at each exposure location, the charged particle beam is used to draw a structure on the substrate within the beam region around each exposure location, according to the respective pattern portion representing the corresponding sub-region of the pattern to be drawn. The above method involves the following steps performed for each exposure position: Based on the exposure position, determine the power of the charged particle beam applied to the substrate at that exposure position; • Calculate the heating of the substrate generated by the charged particle beam during the exposure duration associated with (at least) the exposure location, and calculate the amount of radiative cooling due to thermal diffusion and thermal emission of the substrate for multiple locations defined in a predetermined array across the surface of the substrate; • Calculating the positional changes of the substrate resulting from thermal expansion based on the results of the preceding steps, for multiple locations defined in a predetermined array across the surface of the substrate; • Calculate the displacement distance, where the displacement distance represents the change in position at the exposure location; - Applying a correction to the exposure position and / or the pattern portion associated with the exposure position using the displacement distance; and, • Continue drawing the structure on the substrate with a charged particle beam according to the corrected exposure position and pattern area. Includes. The aforementioned step(s) is performed for each of a series of exposure durations(s), each of which covers a time interval associated with one or more subsequent exposure positions; The calculation of each time interval is performed using the results obtained for the time interval preceding each respective time interval. [Note 2] In the above method, in particular the method described in Note 1, The step of applying a correction to the pattern portion associated with the exposure position using the displacement distance is: (i) To obtain an updated exposure position, the exposure position of the charged particle beam is shifted by a first displacement, and (ii) Recalculating the pattern portion by shifting the structure included in the pattern portion by a second displacement in order to obtain the updated pattern portion. Perform at least one of the following, wherein the displacement distance is obtained by combining the first displacement and the second displacement. Next, a structure is drawn on the substrate with a charged particle beam according to the exposure position and pattern portion updated in this manner. Includes. [Note 3] In the above method, in particular the method described in Note 1 or 2, In the step of calculating the heating of a substrate generated by a charged particle beam on the substrate, the energy applied by the charged particle beam during a time interval associated with one or more subsequent exposure positions is modeled as being applied by a series of heating spots; Each heating spot has a heat insertion distribution that follows a predetermined spatial distribution and is located at the center of a series of deposition positions that represent the average beam position over each sub-interval of the time interval; The aforementioned predetermined spatial distribution has a width that is significantly (significantly) larger than the actual beam region on the substrate; The predetermined spatial distribution is preferably a Gaussian distribution. [Note 4] In the above method, in particular in the method described in any of Notes 1 to 3, The difference between the fourth power of the substrate temperature and the fourth power of the ambient temperature, and The difference between the substrate temperature and the ambient temperature. One method involves calculating thermal diffusion using a heterogeneous thermal equation that includes a source-sink function, which involves thermal radiation calculated as proportional to a common constant of proportionality. [Note 5] In the above method, in particular the method described in Note 4, The common proportionality constant for thermal radiation is predetermined by drawing multiple markers on a test substrate at multiple different stages of the drawing process, measuring the deformation positions of the drawn markers, and performing a best-fit calculation of the proportionality constant for the deformation positions thus measured. [Appendix 6] In the above method, in particular the method described in Appendix 4, The proportionality constant is determined by fitting to a plurality of substrate temperature measurements performed in advance on a test substrate that undergoes a test drawing process in the same charged particle lithography apparatus on which the pattern is subsequently drawn; the test substrate and the test drawing process are representative of the substrate and the pattern drawn on the substrate, respectively. [Appendix 7] In the above method, in particular in any of the methods described in Appendices 1 to 6, In the step of calculating the heating of the substrate by a charged particle beam, the heating rate is calculated to be proportional to a predetermined beam power using a proportionality constant. [Appendix 8] In the above method, in particular the method described in Appendix 7, The proportionality constant is predetermined by drawing multiple markers on a test substrate at multiple different stages of the drawing process, measuring the deformation positions of the drawn markers, and performing a best-fit calculation of the proportionality constant for the deformation positions thus measured. [Note 9] In the above method, in particular the method described in Note 7, The proportionality constant is determined by fitting to a plurality of substrate temperature measurements performed in advance on a test substrate that undergoes a test drawing process in the same charged particle lithography apparatus on which the pattern is subsequently drawn; the test substrate and the test drawing process are representative of the substrate and the pattern drawn on the substrate, respectively. [Note 10] In the above method, in particular in the method described in any of Notes 1 to 9, At least one parameter relating to the mechanical or thermomechanical properties of a substrate is determined by using a test substrate and performing a test drawing process in the same charged particle lithography apparatus in which a pattern is subsequently drawn on the substrate, provided that the test substrate and the test drawing process are representative of the substrate and the pattern drawn on the substrate, measuring quantities that enable the determination of the at least one parameter, and calculating the at least one parameter from the quantities thus measured. [Note 11] In the above method, in particular in the method described in any of Notes 1 to 10, The steps described in Appendix 1 are performed in real time during the process of drawing a pattern on the substrate, using the actual exposure positions, patterns, and current density values ​​recorded by the exposure control device. [Appendix 12] In the above method, in particular in the method described in any of Appendices 1 to 11, The substrate is exposed using a stripe scan drawing method, which draws a structure on the substrate strip by stripe, and the calculation steps(s) described in Appendix 1 are performed for multiple consecutive durations; each duration corresponds to each part of each stripe before the structure of the pattern part belonging to each stripe or part of the stripe is drawn. [Note 13] In the above method, in particular in the method described in any of the notes 1 to 12, The step of calculating the heating of the substrate generated by the charged particle beam at the exposure position of the substrate also includes the preheating of the substrate generated by the charged particle beam during the exposure path (elapsed time) on the substrate preceding the exposure position. [Appendix 14] In the above method, in particular the method described in any of Appendices 1 to 13, The step of calculating the amount of radiative cooling due to thermal diffusion and heat release from the substrate is repeated for a series of exposure durations; each exposure duration includes a plurality of subsequent exposure locations extending at least over a first distance greater than the width of the beam region on the substrate surface. [Note 15] In the above method, in particular the method described in Note 14, The step of calculating the change in the position of the substrate is repeated for a series of secondary durations that are less frequent than the series of exposure durations; Each of the aforementioned series of secondary durations includes a plurality of subsequent exposure positions that extend at least over a second distance greater than the first distance. [Note 16] In the above method, in particular in the method described in any of the notes 1 to 15, The step of calculating mechanical strain includes, as additional mechanical constraints, the action of mechanical stress introduced by external forces, including holding forces applied to the substrate at a predetermined number of mounting positions, and / or the action of multiple fixed mounting positions of the substrate, where the magnitude of the position change at each of these positions is a predetermined value, such as a zero position change value.

[0064] Within the framework of the full disclosure of the present invention (including the claims and drawings), further modifications and adjustments to the embodiments are possible based on the fundamental technical concept. Furthermore, within the framework of the full disclosure of the present invention, various combinations or selections (including "non-selection") of various disclosed elements (including each element of each claim, each element of each embodiment, each element of each drawing, etc.) are possible. In other words, the present invention naturally includes the full disclosure, including the claims and drawings, and various modifications and alterations that a person skilled in the art could make in accordance with the technical concept of the present invention. In particular, with respect to the numerical ranges described herein, any numerical value or sub-range included within that range should be interpreted as being specifically described, even if not otherwise stated.

[0065] Furthermore, the reference numerals in the drawings included in the claims are solely for the purpose of aiding the understanding of the invention, and are not intended to limit the present invention to the embodiments and illustrated examples.

[0066] Furthermore, the full contents of each of the above-mentioned documents are incorporated into this book through reference and are included herein.

Claims

1. 1. A method of writing a pattern on a substrate in a charged particle lithography apparatus using scanning exposure with a charged particle beam, comprising: the charged particle beam is directed to a series of exposure locations on the surface of the substrate, and at each exposure location the charged particle beam is used to write structures on the substrate within a beam area around the respective exposure location according to a respective pattern portion representing a corresponding sub-area of ​​the pattern to be written; The method comprises the following steps performed for each exposure location: - determining the power of the charged particle beam applied to the substrate at the exposure position based on the exposure position; Calculating the heating of the substrate produced by the charged particle beam during the exposure duration associated with the exposure location, and calculating the amount of radiative cooling due to thermal diffusion and thermal emission of the substrate for a plurality of sites defined in a predetermined array across the surface of the substrate; - calculating, for a plurality of sites defined in a predetermined array across the surface of the substrate, the change in position of the substrate resulting from thermal expansion based on the results of the previous steps; calculating a displacement distance, wherein the displacement distance represents the position change in the exposure position; - applying a correction to the exposure position and / or the pattern portion associated with the exposure position using the displacement distance; and Continuing to write structures onto the substrate with the charged particle beam according to the thus corrected exposure positions and pattern portions. Including, the steps are performed for each of a series of exposure durations, each of the exposure durations covering a time interval associated with one or more subsequent exposure positions; The calculations for each time interval are performed on the results of the calculations obtained for the time intervals that respectively precede each time interval. A method characterized by:

2. 10. The method of claim 1, applying a correction to a pattern portion associated with an exposure position using the displacement distance, (i) shifting an exposure position of the charged particle beam by a first displacement to obtain an updated exposure position; and (ii) recalculating the pattern portion by shifting the structures included in the pattern portion by a second displacement to obtain an updated pattern portion; wherein the displacement distance is obtained by combining the first displacement and the second displacement; Then, writing a structure on the substrate by the charged particle beam according to the thus updated exposure position and pattern portion; Contains A method characterized by:

3. 10. The method of claim 1, In the step of calculating heating of the substrate produced by the charged particle beam on the substrate, the energy applied by the charged particle beam during a time interval associated with one or more subsequent exposure positions is modeled as being applied by a series of heating spots; each heating spot having a heat insertion distribution according to a predetermined spatial distribution and positioned at the center of one of a series of application positions representing an average of the beam positions over a respective subinterval of the time interval; The predetermined spatial distribution (76) has a width significantly greater than the actual beam area (75) at the substrate. A method characterized by:

4. In the method according to claim 3, the predetermined spatial distribution is a Gaussian distribution; A method characterized by:

5. 4. The method according to claim 1 or 3, the difference between the fourth power of the substrate temperature and the fourth power of the ambient temperature, and The difference between the board temperature and the ambient temperature One of these is that heat diffusion is calculated using a non-uniform heat equation with a source-sink function, with heat radiation calculated as proportional with a common proportionality constant. A method characterized by:

6. 6. The method of claim 5, the common proportionality constant for thermal radiation is predetermined by drawing markers on a test substrate at different stages of a drawing process, measuring deformation positions of the drawn markers, and performing a best-fit calculation of the proportionality constant to the deformation positions so measured. A method characterized by:

7. 6. The method of claim 5, the proportionality constant is determined by fitting to substrate temperature measurements previously performed on a test substrate that is subjected to a test writing process in the same charged particle lithography apparatus on which a pattern is subsequently written onto the substrate, the test substrate and the test writing process being representative of the substrate and the pattern to be written onto the substrate; A method characterized by:

8. 10. The method of claim 1, In the step of calculating the heating of the substrate by the charged particle beam, the rate of heating is calculated as being proportional to the predetermined beam power by a proportionality constant. A method characterized by:

9. 9. The method of claim 8, the proportionality constant is predetermined by drawing markers on a test substrate at different stages of a drawing process, measuring deformation positions of the drawn markers, and performing a best-fit calculation of the proportionality constant to the deformation positions so measured. A method characterized by:

10. 9. The method of claim 8, the proportionality constant is determined by fitting to substrate temperature measurements previously performed on a test substrate that is subjected to a test writing process in the same charged particle lithography apparatus on which a pattern is subsequently written onto the substrate, the test substrate and the test writing process being representative of the substrate and the pattern to be written onto the substrate; A method characterized by:

11. 10. The method of claim 1, At least one parameter related to a mechanical or thermomechanical property of a substrate is determined by performing a test writing process in the same charged particle lithography apparatus using a test substrate in which a pattern is subsequently written onto a substrate, the test substrate and the test writing process being representative of said substrate and said pattern to be written onto said substrate, measuring quantities that allow the determination of said at least one parameter, and calculating said at least one parameter from the quantities so measured. A method characterized by:

12. 10. The method of claim 1, 10. The steps of claim 1 are performed in real time during a process for writing a pattern on a substrate using actual exposure positions, patterns, and current density values ​​recorded by an exposure controller. A method characterized by:

13. 10. The method of claim 1, the substrate is exposed using a stripe scan writing method that writes structures on the substrate stripe by stripe, and the calculation steps of claim 1 are performed for a plurality of successive durations, each duration corresponding to a respective portion of each stripe prior to writing the structure of the pattern portion belonging to the respective stripe or stripe portion. A method characterized by:

14. 10. The method of claim 1, the step of calculating the heating of the substrate generated by the charged particle beam at the exposure position of the substrate also includes pre-heating of the substrate generated by the charged particle beam during an exposure pass on the substrate preceding the exposure position. A method characterized by:

15. 10. The method of claim 1, the step of calculating the amount of radiative cooling due to thermal diffusion and thermal emission of the substrate is repeated for a series of exposure durations, each exposure duration including a plurality of subsequent exposure positions extending over at least a first distance at the substrate surface that is greater than a width of the beam area. A method characterized by:

16. 16. The method of claim 15, the step of calculating the change in position of the substrate is repeated for a series of secondary durations sparser than said series of exposure durations; the series of secondary durations each including a plurality of subsequent exposure positions extending over at least a second distance greater than the first distance; A method characterized by:

17. 10. The method of claim 1, The step of calculating the mechanical strain may include, as additional mechanical constraints, the effect of mechanical stresses introduced by external forces including retention forces applied to the substrate at a predetermined number of mounting positions, and / or the effect of a plurality of fixed mounting positions for the substrate, each of which has a predetermined value for the magnitude of the position change, such as a value for zero position change. A method characterized by:

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