Method for thermomechanical control of a heat sensitive element and apparatus for a lithographic production process

Abstract

The present invention provides a method for thermomechanical control of a thermistor (MI) subjected to heat load, comprising: - providing a nonlinear thermomechanical model of the thermistor, the nonlinear thermomechanical model describing the dynamic relationship between the characteristics of the heat load and the deformation of the thermistor; - calculating a control signal based on optimization calculation of the nonlinear model; - providing an actuation signal to a heater (HE), wherein the actuation signal is at least partially based on the control signal; - heating the thermistor through the heater based on the actuation signal.

Description

[0001] Cross-references to related applications

[0002] This application claims priority to EP application 20183453.8, filed on July 1, 2020, the entire contents of which are incorporated herein by reference. Technical Field

[0003] This invention relates to a method for thermomechanical control of thermal elements and equipment for photolithography production processes. Background Technology

[0004] A photolithography apparatus is a machine configured to apply a desired pattern to a substrate. Photolithography apparatuses can be used, for example, in the manufacture of integrated circuits (ICs). A photolithography apparatus can, for example, project a pattern (often referred to as a “design layout” or “design”) from a patterning device (such as a mask) onto a layer of radiation-sensitive material (resist) disposed on a substrate (such as a wafer).

[0005] As semiconductor manufacturing processes continue to advance, the size of circuit components continues to shrink, while the number of functional elements (such as transistors) in each device has steadily increased over the decades, following a trend commonly known as "Moore's Law." To keep pace with Moore's Law, the semiconductor industry is pursuing technologies capable of creating increasingly smaller features. To project patterns onto a substrate, photolithography apparatuses can use electromagnetic radiation. The wavelength of this radiation determines the minimum size of the feature that can be patterned on the substrate. Currently used conventional wavelengths are 365 nm (i-line), 248 nm, 193 nm, and 13.5 nm. Compared to photolithography apparatuses using radiation with a wavelength of, for example, 193 nm, extreme ultraviolet (EUV) radiation in the range of 4 nm to 20 nm, such as 6.7 nm or 13.5 nm, can be used to form even smaller features on the substrate.

[0006] During wafer exposure, objects in a photolithography apparatus may be subjected to considerable thermal loads, especially those arranged to transmit or reflect electromagnetic radiation beams. This thermal load can negatively impact the performance of the corresponding elements within the photolithography process.

[0007] For example, mirrors are used to reflect radiation beams in so-called projection optics boxes (POBs). These mirrors absorb heat from the DUV, EUV, and / or infrared light originating from the light source, causing undesirable deformation of the optical surfaces. This latter phenomenon is also known as mirror / lens heating. Mirror heating can have a significant impact on the overall coverage, focal length, and projection performance of the photolithography process. This effect can be partially compensated for by adjusting the mirrors and / or the stage. The compensation mechanism is called a driven lens model (DLM). However, the self-correcting capability of the DLM is insufficient to achieve the desired performance.

[0008] In known embodiments of photolithography apparatuses, the thermal load is compensated by a mirror heater arranged to heat the mirror to a predetermined temperature. This predetermined temperature is typically chosen to be a temperature at which the mirror material exhibits relatively low thermal sensitivity. The temperature at which the derivative of the strain-temperature curve equals zero is called the zero-crossing temperature (ZCT). Typically, this ZCT is a suitable temperature for the predetermined temperature, thereby the heater is configured to hold the mirror at or near the ZCT.

[0009] Because the reflective surface of the mirror requires a considerable amount of time to reach a steady-state temperature distribution after each change in the patterning equipment and corresponding lighting settings, an active feedback control strategy is used to ensure proper adjustment of the mirror heater power during transient responses. Known control strategies for mirror heating are temperature-based, where the average temperature of the mirror is adjusted to a fixed setpoint. This setpoint is obtained from a worst-case steady-state analysis under a finite set of load conditions. Therefore, temperature-based control strategies are generally conservative and do not necessarily improve projection performance under transient conditions, as the setpoint design is based solely on a worst-case steady-state analysis. Summary of the Invention

[0010] The purpose of this invention is to provide a method for thermomechanical control of a thermistor, such as a reflector in the projection optics of a photolithography apparatus, which bears the heat of a radiation beam irradiating the thermistor. This method provides more precise control over the effects caused by the radiation beam heating the thermistor.

[0011] Another object of the present invention is to provide an apparatus, such as a lithography device or metrology tool, for use in a photolithography production process, which is capable of improving the thermomechanical control of thermal elements (such as mirrors) in the apparatus, such as mirrors heated by radiation beams used in the apparatus.

[0012] According to one aspect of the present invention, a method for thermomechanical control of a thermistor subjected to a heat load is provided, comprising:

[0013] A nonlinear thermomechanical model is provided for the thermistor, which describes the dynamic relationship between the characteristics of the heat load and the deformation of the thermistor.

[0014] The control signal is calculated based on the optimization calculation of the nonlinear model.

[0015] An actuation signal is provided to the heater, wherein the actuation signal is at least partially based on a control signal.

[0016] The thermistor is heated by a heater according to the actuation signal.

[0017] According to one aspect of the present invention, an apparatus for a photolithography production process is provided, comprising:

[0018] The light source is arranged to provide a radiation beam.

[0019] Thermistor, which is arranged to be irradiated by a radiation beam,

[0020] A heater, which is arranged to heat the thermistor to control the temperature of the thermistor.

[0021] A control device that provides an actuation signal to a heater, wherein the control device includes a controller arranged to provide a control signal as part of the actuation signal, wherein the controller includes a nonlinear thermomechanical model of a thermistor, the nonlinear thermomechanical model describing the dynamic relationship between the heat load on the thermistor and the deformation of the thermistor, and wherein the controller is arranged to calculate the control signal based on optimization calculations of the nonlinear model. Attached Figure Description

[0022] Embodiments of the invention will now be described by way of example only with reference to the accompanying schematic diagrams, in which:

[0023] Figure 1 A schematic diagram of the photolithography apparatus is shown;

[0024] Figure 2 An embodiment of a projection optics box according to an embodiment of the present invention is shown; and Figure 1 Detailed views of parts of the photolithography apparatus; and

[0025] Figure 3 The control scheme of an embodiment of the control strategy of the present invention is illustrated schematically.

[0026] Figure 4 A schematic diagram of an EUV lithography apparatus is shown. Detailed Implementation

[0027] In this document, the terms “radiation” and “beam” are used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., with wavelengths of 365, 248, 193, 157, or 126 nm) and EUV (extreme ultraviolet radiation, e.g., with wavelengths in the range of about 5–100 nm).

[0028] The terms “marker,” “mask,” or “patterning apparatus” as used herein can be broadly interpreted as any general patterning apparatus that can be used to impart a patterned cross-section to an incident radiation beam, corresponding to a pattern to be created in a target portion of a substrate. The term “optical valve” may also be used herein. Examples of such patterning apparatuses, besides traditional masks (transmission or reflection, binary, phase-shifting, hybrid, etc.), include programmable mirror arrays and programmable LCD arrays.

[0029] Figure 1 A lithography apparatus LA is schematically illustrated. The lithography apparatus LA includes an illumination system (also referred to as an illuminator) IL configured to modulate a radiation beam B (e.g., UV radiation, DUV radiation, or EUV radiation), a mask support (e.g., a mask stage) MT configured to support a patterning apparatus (e.g., a mask) MA and connected to a first positioner PM configured to precisely position the patterning apparatus MA according to certain parameters, a substrate support (e.g., a wafer stage) WT configured to hold a substrate (e.g., a wafer coated with resist) W and connected to a second positioner PW configured to precisely position the substrate support according to certain parameters, and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted by the radiation beam B by the patterning apparatus MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0030] In operation, the illumination system IL receives a radiation beam from the radiation source SO, for example via the beam delivery system BD. The illumination system IL may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic, and / or other types of optical components, or any combination thereof, for guiding, shaping, and / or controlling the radiation. The illuminator IL can be used to adjust the radiation beam B to have a desired spatial and angular intensity distribution in a cross-section at the plane of the patterning device MA.

[0031] As used herein, the term "projection system" PS should be interpreted broadly to include all types of projection systems, including refractive, reflective, antirefractive, distorting, magnetic, electromagnetic, and / or electrostatic optical systems, or any combination thereof, suitable for the exposure radiation used, and / or suitable for other factors such as the use of immersion liquids or the use of vacuum. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system" PS.

[0032] A lithography apparatus LA can be a type in which at least a portion of the substrate can be covered by a liquid (e.g., water) with a relatively high refractive index to fill the space between the projection system PS and the substrate W; this is also known as immersion lithography. More information on immersion techniques is given in US 6952253, which is incorporated herein by reference.

[0033] The lithography apparatus LA can also be of the type having two or more substrate supports WT (also known as "bipolar"). In such a "multi-stage" machine, the substrate supports WT can be used in parallel, and / or subsequent exposure steps for preparing the substrate W can be performed on the substrate W located on one of the substrate supports WT, while another substrate W on another substrate support WT is used to expose a pattern on another substrate W.

[0034] In addition to the substrate support WT, the lithography apparatus LA may include a measurement stage. The measurement stage is arranged to hold sensors and / or cleaning equipment. Sensors may be arranged to measure characteristics of the projection system PS or the radiation beam B. The measurement stage may accommodate multiple sensors. The cleaning equipment may be arranged to clean part of the lithography apparatus, such as a portion of the projection system PS or a portion of a system providing immersion liquid. The measurement stage may move below the projection system PS as the substrate support WT moves away from the projection system PS.

[0035] In operation, a radiation beam B is incident on a pattern forming apparatus (e.g., a mask) MA held on a mask support MT, and a pattern is formed using the pattern (design layout) present on the pattern forming apparatus MA. After passing through the pattern forming apparatus MA, the radiation beam B passes through a projection system PS, which focuses the radiation beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position measurement system PMS, the substrate support WT can be moved precisely, for example, to position different target portions C in the path of the radiation beam B at focal length and alignment. Similarly, a first positioner PM and possibly another position sensor ( Figure 1 (Not explicitly shown) can be used to precisely position the patterning apparatus MA relative to the path of the radiation beam B. The patterning apparatus MA and the substrate W can be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks P1, P2 shown occupy dedicated target portions, they can be located in the space between target portions. When located between target portions C, substrate alignment marks P1, P2 are referred to as scribing alignment marks.

[0036] To illustrate the invention, a Cartesian coordinate system is used. A Cartesian coordinate system has three axes: the x-axis, the y-axis, and the z-axis. Each of the three axes is orthogonal to the other two axes. A rotation about the x-axis is called an Rx rotation. A rotation about the y-axis is called an Ry rotation. A rotation about the z-axis is called an Rz rotation. The x-axis and y-axis define the horizontal plane, while the z-axis is in the vertical direction. The Cartesian coordinate system is not limiting of the invention and is only used for illustration. Instead, another coordinate system, such as a cylindrical coordinate system, can be used to illustrate the invention. The orientation of the Cartesian coordinate system can be different, for example, such that the z-axis has a component along the horizontal plane.

[0037] Figure 4 Another example of a lithography system including a radiation source SO and a lithography apparatus LA is shown. The radiation source SO is configured to generate an EUV radiation beam B and provide the EUV radiation beam B to the lithography apparatus LA. The lithography apparatus LA includes an illumination system IL, a support structure MT configured to support a patterning device MA (e.g., a mask), a projection system PS, and a substrate stage WT configured to support a substrate W.

[0038] The illumination system IL is configured to adjust the EUV radiation beam B before it is incident on the patterning apparatus MA. Furthermore, the illumination system IL may include a multifaceted field mirror device 10 and a multifaceted pupil mirror device 11. Together, the multifaceted field mirror device 10 and the multifaceted pupil mirror device 11 provide the EUV radiation beam B with a desired cross-sectional shape and a desired intensity distribution. In addition to, or in place of, the multifaceted field mirror device 10 and the multifaceted pupil mirror device 11, the illumination system IL may include other mirrors or devices.

[0039] After such adjustment, the EUV radiation beam B interacts with the patterning apparatus MA. As a result of this interaction, a patterned EUV radiation beam B' is generated. The projection system PS is configured to project the patterned EUV radiation beam B' onto the substrate W. For this purpose, the projection system PS may include a plurality of mirrors 13, 14, configured to project the patterned EUV radiation beam B' onto the substrate W held by the substrate stage WT. The projection system PS can apply a reduction factor to the patterned EUV radiation beam B' to form an image with features smaller than the corresponding features on the patterning apparatus MA. For example, a reduction factor of 4 or 8 can be applied. Although in Figure 4 The projection system PS is shown as having only two mirror elements 13, 14, but the projection system PS may include a different number of mirrors (e.g., six or eight mirrors).

[0040] The substrate W may include a previously formed pattern. In this case, the photolithography apparatus LA aligns the image formed by the patterned EUV radiation beam B' with the pattern previously formed on the substrate W.

[0041] A relative vacuum can be provided in the radiation source SO, the lighting system IL, and / or the projection system PS, i.e., a small amount of gas (e.g., hydrogen) at a pressure much lower than atmospheric pressure.

[0042] The radiation source SO can be a laser-generated plasma (LPP) source, a discharge-generated plasma (DPP) source, a free-electron laser (FEL) or any other radiation source capable of generating EUV radiation.

[0043] Figure 4 The projection system PS of the lithography apparatus LA includes a mirror element 14 to reflect a patterned radiation beam to guide the patterned radiation beam along the projection path. This reflection of the patterned radiation beam causes a considerable thermal load on the mirror element ME. This thermal load can induce thermal stress within the mirror element ME, and as a result of these thermal stresses, deformation occurs. Deformation of the mirror element ME can have a significant negative impact on the focal length and coverage performance of the lithography apparatus, and therefore should be avoided.

[0044] Figure 2 Schematic illustration of as Figure 1 The projection optics box (POB) is a portion of the projection system PS of the photolithography apparatus LA shown. The projection optics box (POB) includes multiple mirrors to guide the radiation beam B from the patterning device onto the substrate W.

[0045] In other embodiments, the projection optics box (POB) can be as follows: Figure 4 The projection system PS of the photolithography apparatus LA shown is illustrated. For example, the reflector MI can be any one of the plurality of reflectors 13 and 14.

[0046] The reflector MI is shown as an example of such a reflector in a projection optics box (POB). A radiation beam B entering the POB is reflected by the first reflector MI1 and strikes the reflector MI, specifically guiding the radiation beam B onto its reflective surface. The radiation beam is then reflected by the reflector MI and exits the POB. In practice, the POB may include more than two reflectors to guide the radiation beam B.

[0047] The mirror MI is subjected to heat caused by the DUV, EUV, and / or infrared light from the radiation beam B. This heating caused by the radiation beam B irradiating the mirror MI is called mirror heating. This mirror heating can cause undesirable deformation of the reflective surface of the mirror MI, which can have a significant impact on the coverage, focal length, and projection performance of the photolithography process.

[0048] The mirrors of the projection optics box (POB), such as the mirror MI, can be made of ultra-low expansion glass with low thermal sensitivity to reduce the effects of mirror heating. Despite relatively low thermal sensitivity, the relatively high power of the radiation beam B illuminating the mirror MI can still cause unacceptable deformation of the mirror MI. This is generally undesirable. The effects of mirror heating can be partially compensated for by adjusting the mirror and / or the substrate support. This compensation mechanism is called a driven lens model (DLM). However, the correction capability of the DLM itself is insufficient to achieve the desired mirror performance in more demanding lithography processes. Uncorrectable errors still exist, i.e., errors that cannot be compensated for by adjusting the mirrors of the projection optics box (POB) and / or by positioning the substrate support by the DLM.

[0049] To further reduce the impact of mirror heating, the temperature of mirror MI can be influenced by heater HE, which is arranged to provide heat to mirror MI without contacting it. In the example shown, heater HE is configured to provide heat on one side of mirror MI. In other embodiments, the heater may be arranged to provide heat on the opposite reflecting side of mirror MI or on both sides of mirror MI. This heat can provide additional heat, which can be modulated to provide heat from the radiation beam B to create a controlled thermal load on mirror MI.

[0050] In an alternative embodiment, a heater (such as an electric wire) in contact with the thermistor (here, the mirror MI) can be used to provide controlled heat to the thermistor.

[0051] A control device CON is provided to control the deformation of the mirror MI, thereby maintaining the deformation of the mirror MI at a predetermined level by heating it with a heater HE. This heating may also be referred to as supplemental heating or preheating. The predetermined deformation is, for example, based on a temperature at which the thermal sensitivity of the mirror MI is minimized. For example, the thermal sensitivity of ultra-low expansion glass includes a minimum value where the derivative of the strain-temperature curve is zero, i.e., the zero-crossing temperature (ZCT). The temperature associated with this minimum value is a suitable temperature used as the basis for determining the predetermined deformation, and the control device CON is controlled with this predetermined deformation as the target.

[0052] Other parameters, such as temperature, mechanical and / or optical parameters, can also be used as control targets for control strategies applied in control devices CON.

[0053] Multiple temperature sensors (TSEs) can be provided on or within the reflector MI to measure a temperature signal representing the temperature of the reflector MI at the location of the respective temperature sensor (TSE). This temperature signal is then fed to the control device CON. Figure 2Three temperature sensors (TSEs) are shown. In practice, more or fewer temperature sensors (TESs) can also be provided.

[0054] The control device CON is configured to provide an actuation signal to the heater HE. Figure 2 The heater HE in one embodiment includes a plurality of heater segments HES, wherein each heater segment HES is arranged to heat a selected portion of the reflector MI. Each heater segment HES receives its individual actuation signal, such that the heater segment HES can be individually controlled to heat the associated portion of the reflector MI to obtain a predetermined temperature distribution and / or deformation in the reflector MI. The number of heater segments HES will be selected according to the desired distribution of the individually controlled portions of the reflector MI.

[0055] In existing embodiments, only one heater is used to heat the corresponding mirror, thereby controlling the heater via a single actuation signal based on the average temperature measured in the mirror MI. Since it takes a long time for the reflective surface of the mirror to reach a steady-state temperature distribution after each patterning device variation and a corresponding change in the characteristics of the radiation beam (such as the power of the radiation beam B and its spatial distribution), active feedback control strategies, possibly combined with transient feedforward signals, have been used to adjust the heater power during the transient response according to changes in the radiation beam setup.

[0056] As the performance requirements for lithography equipment increase, the power of radiation beam B can also be significantly increased. This also brings additional challenges to controlling the heating of the mirrors.

[0057] Providing multiple heater segments (HES), each associated with a corresponding portion of the mirror MI, allows for more explicit control over the deformation of the mirror MI. However, known control strategies for mirror preheating based on the average temperature of the mirror MI are generally conservative and do not necessarily improve projection performance in transient situations between subsequent uses of two pattern forming devices with different radiation characteristics, because the setpoint of this control strategy is typically based only on a worst-case steady-state analysis.

[0058] Therefore, there is a need to provide a control strategy that allows for more precise control of the deformation of the mirror MI in order to reduce the negative impact of mirror heating on overlay, focal length and projection performance.

[0059] This novel control strategy is based on a feedforward controller, which is arranged to provide a feedforward signal as part of the actuation signal fed to the heater HE, for example, a separate actuation signal fed to the heater section HES. The feedforward controller includes a nonlinear thermomechanical 3D model of the reflector MI, which describes the dynamic relationship between the thermal load on the reflector MI and the deformation of the reflector MI. The feedforward controller is arranged to calculate the feedforward signal based on optimization calculations of the nonlinear model. Temperature signals from multiple temperature sensors TSE can be used as inputs to the nonlinear model in the feedforward controller to calculate the feedforward signal.

[0060] In nonlinear thermomechanical 3D models, heat load can be described by well-predictable heating power and spatial distribution that may vary over time.

[0061] The optimization calculations include time-series optimization of the control variables to optimize surface deformation across the entire prediction range, while considering the constraints of the actuation limits of the heater HE. The actuation limits of the heater HE include, for example, that the heater can only provide heat (i.e., it has no cooling capacity) and that the heater has a maximum heating capacity.

[0062] The model used in model predictive control methods can be a high-order thermomechanical 3D model with, for example, 10,000 to 1,000,000 states, which describes the dynamic relationship between the thermal load on the mirror MI and the deformation of the mirror MI (e.g., the deformation of the reflective surface of the mirror MI). This model can be, for example, a finite element model of the mirror MI, which describes the geometry of the mirror MI and its thermal, mechanical, and optical dynamic characteristics.

[0063] To allow optimization calculations to be performed in a sufficiently short time for real-time control, multi-stage solvers can be applied. Multi-stage solvers can, for example, leverage the speed of approximation solvers (such as Jacobi-based solvers), parallelization on graphics processing units (GPUs), warm-start, etc.

[0064] Optimization computations can be performed, for example, on parallel processors such as GPUs, for real-time control. Parallel processors can be configured, for example, to run a full optimization every 1, 10, or 100 seconds. Parallel processing can also be performed using application-specific integrated circuits (ASICs), such as Tensor Processing Units (TPUs), or by using field-programmable gate arrays (FPGAs).

[0065] Inputs that can be used in this embodiment of the control strategy include, for example, the power level and / or spatial distribution of the power of the radiation beam B. Furthermore, adjustment parameters, such as the heat transfer coefficient of the medium (e.g., gas or cooling water), ambient temperature, and / or other parameters affecting the optical path of the radiation beam, can be added as inputs to the optimization calculations of the nonlinear model.

[0066] Alternatively or additionally, the spatial non-uniformity of the zero-crossing temperature, simulated by the power spectral density function, can be further used as input to the control strategy. This implementation can be used to ensure that the preheating control strategy for the photothermal-mechanical mirror is robust against ZCT non-uniformity, i.e., by evaluating the cost function in the model predictive control scheme over multiple (unique) implementations rather than over only one nominal case (uniform ZCT).

[0067] In one embodiment, the nonlinear model can be updated based on system setup data and / or system calibration data (e.g., setup data for a lighting system).

[0068] Based on the relevant projection characteristics closely related to overlay, focal length, and projection performance, a novel model predictive control strategy can be used to directly minimize errors in the radiation beam that cannot be corrected by DLM, such as wavefront errors. This control strategy, particularly when combined with a separately controllable heated segment (HES), has been found to provide significant improvements in control performance to compensate for the effects of mirror heating on overlay, focal length, and projection performance in the lithography process.

[0069] In addition to the temperature sensor TSE, or as an alternative, one or more sensors can be provided to measure aberration signals representing the wavefront aberrations of the radiation beam, wherein the control device CON is arranged to receive the aberration signals and use the aberration signals to calculate the feedforward signal.

[0070] As a further supplement or alternative, one or more strain sensors can be provided to measure one or more strain signals at one or more measurement locations of the thermal element, wherein the control device CON is arranged to receive the strain signals and use the strain signals to calculate the feedforward signal. Instead of using temperature measurements as input for calculating the local deformation of the reflector MI, direct deformation measurements can also be used as input signals for calculating the feedforward signal.

[0071] In one embodiment, the feedforward controller can be combined with a feedback controller to further improve control over the deformation of the mirror MI. The feedback control can be, for example, based on wavefront measurements of the radiation beam B, temperature measurements within the mirror MI using a temperature sensor TES, and / or based on an explicit state observer that combines model predictions with measurements such as wavefront measurements, temperature measurements, and / or strain measurements.

[0072] Figure 3An embodiment of a model predictive control (MPC) scheme is shown, which can be used to control... Figure 3 The diagram shows the heating of the reflector MI, which is combined with a heater HE and a temperature sensor TES in the reflector system MIS. The control scheme uses a thermomechanical nonlinear model of the deformation within the reflector MI. This nonlinear model is also included in the state estimator SES of the control device CON. The input to the state estimator SES is the temperature signal Temp from the temperature sensor TES. The output of the state estimator SES is the estimated disturbance Dist of the radiation beam B. est The estimated interference of radiation beam B (Dist) est The signal is fed to the control unit CU, which provides an actuation signal ACT to each heater section in the heater section HES to heat the reflector MI (in Figure 3 (represented by MIS in Chinese).

[0073] Optimization calculations are performed at each time step. The goal of these calculations is to find an input sequence over a finite time span that minimizes a given cost function while adhering to relevant constraints, such as the maximum power of the heater segment HES and the inability of the heater HE to be cooled. The cost function can be tailored to different performance metrics. For example, the root mean square cost function can be used to optimize deformation, the Zernike function can be used to optimize projection performance, and / or pattern shift, optimal focal length, and critical dimensional uniformity can be used to optimize imaging parameters.

[0074] Since the temperature signal Temp, which is based on the most recently measured temperature sensor, is updated and optimized at each time step, only the first entry of the result input sequence can be implemented on the actual system MIS.

[0075] In this embodiment of the control strategy, the cost function of the control scheme represents the relevant radiation characteristics taking into account the correction capability of the DLM. More specifically, the portion of the radiation beam error that can be corrected by the DLM, i.e., the projection / wavefront error, is estimated based on the predicted mirror deformation and will not be included in the cost function because this portion of the radiation beam error can be effectively corrected by the DLM. Figure 3 In the control scheme, this is shown where the mirror deformation DEF is determined by the DLM based on the reference deformation DEF that causes uncorrectable image distortion IMD. ref It needs to be corrected.

[0076] Because the temperature-strain relationship of the ultra-low expansion glass of the reflector MI is nonlinear, finite-range optimization calculations are typically non-convex. To ensure that the closed-loop system converges to the desired steady state and to avoid unwanted oscillations in the closed-loop response, a reference ref is fed to the control unit CU. This reference ref includes the desired input signal and the uncorrectable radiation beam error in the steady state, which can be obtained via a separate optimization calculation performed before the radiation beam is actually exposed to the substrate.

[0077] Alternatively or additionally, the control unit CU can be further fed with the spatial non-uniformity of the zero-crossing temperature, simulated by the power spectral density function. This implementation can be used to ensure that the preheating control strategy for the photothermal-mechanical mirror is robust against ZCT non-uniformity, i.e., by evaluating the cost function in the model predictive control scheme over multiple (unique) implementations rather than over only one nominal case (uniform ZCT).

[0078] One of the challenges of using nonlinear model predictive control schemes is managing computational complexity, as optimization calculations need to be performed within a reasonable timeframe at each time step. This problem is typically addressed through model reduction techniques. A key assumption in model reduction is that the number of possible inputs is significantly smaller than the number of states in the original model. This assumption does not hold for mirror heating control, as many different radiation beam setups / use cases are possible, for example, as a consequence of possible setups for an illumination system. While only one use case is active at this point, and therefore other use cases can be ignored for each exposure, calculating the reduced model itself is often a computationally expensive process. Therefore, it is of interest to use a full-order model, such as a full-order finite element model, in the control scheme. Model reduction techniques are not used in the optimization calculations.

[0079] By applying the null space method, the size of the optimization computation required to solve at each time step can be significantly reduced in terms of the number of variables. As a result, the optimization computation itself can be solved in milliseconds. However, this method does require online computation of a specific system response. This specific system response can be obtained efficiently using a multi-stage solver. Due to the size of the full-order model, efficiently computing the specific response is not trivial. Fortunately, the sparsity of the full-order model can be utilized to efficiently obtain the solution using iterative methods (e.g., the preconditioned conjugate gradient method).

[0080] The efficiency of this iterative method depends on the choice of pre-conditioner. Adaptive contraction is a suitable pre-conditioner because it allows the utilization of the advantages of parallel / GPU computation. In adaptive contraction, the solution to the full-order system is accelerated by correcting the full-order iteration with solutions from lower-dimensional problems, which can be computed relatively quickly. These lower-dimensional problems can be obtained, for example, by projection onto an appropriate orthogonal decomposition (POD) basis. For the proposed model predictive control strategy, the POD basis can be derived from information contained in the pre-computed null space matrix and previously obtained solutions, such as solutions at previous time steps when solving the time-domain solution of the dynamic system, or solutions at previous frequency points when solving the frequency-domain solution of the dynamic system. Using this unique choice of the POD basis, and by starting the solver with a solution obtained at a previous time step, only one iteration is needed to obtain a specific response. As a result, the computational workload can approach the theoretical minimum required to obtain the solution to the full-order finite element model.

[0081] Alternatively or additionally, the pre-tuned conjugate gradient method employs a multi-level or multi-grid approach, configured to correct the iterations of the full-dimensional linear equations using solutions from low-dimensional approximations of the linear equations. The multi-level or multi-grid approach can utilize the adaptive compaction method described above.

[0082] In one embodiment, the preprocessor includes projecting the residual at each iteration into a lower-dimensional space to obtain an estimate of the difference between the current iteration and the actual solution. This estimate can be used to correct the current iteration and thus improve the convergence of the pre-regulator method. In another embodiment, the adaptive compaction method can be considered a multi-level / multi-grid method.

[0083] As an alternative to adaptive contraction methods, other model order reduction techniques can be used, such as modal truncation, balancing and truncation, or Krylov subspace methods.

[0084] exist Figure 2 In multiple simulations, the proposed photothermal mechanical model predictive control strategy has been compared with a temperature-based control strategy for heater embodiments with a single heater and heater embodiments with multiple individually controllable heater sections. For the single-heater embodiment, the temperature-based controller is a PID controller. For the embodiment with heating sections, multiple PID controllers are used for each heater section, with the aim of regulating the average temperature in each part associated with the respective heater section to the zero-crossing temperature. Simulations were performed for two load conditions, namely two different settings of the radiation beam.

[0085] Simulations show that, compared to temperature-based control strategies, the photothermal mechanical control strategy using a nonlinear photomechanical model significantly improves overlay and focal length performance, especially when combined with embodiments having multiple heater sections, as this further improves the controllability of the deformation of the mirror MI.

[0086] The above describes a control strategy for controlling the deformation of the mirror MI of the projection optics box (POB) of a lithography apparatus. This method can also be used to control the deformation in other mirrors of the POB, where the deformation of each mirror is controlled individually. Furthermore, in the control strategy, the effect of mirror heating of the first mirror of the POB can be compensated by controlling the deformation in another mirror of the POB, thereby optimizing the wavefront of the radiation beam reflected by the mirror.

[0087] Furthermore, model predictive control strategies can be used to compensate for intra-substrate effects that cannot be corrected with DLM, since DLM correction is only calculated and applied when new wavefront measurements are available. Intra-wafer effects can cause focal length errors, which can affect many mirrors, especially smaller mirrors in mirror assemblies. Intra-wafer effects can be corrected by applying individually controllable heater sections and model predictive control strategies as described above. When these mirrors are relatively small, the timescale of their thermal behavior will be relatively small. Therefore, control strategies applied to these relatively small mirrors can have significantly larger bandwidths than those for larger mirrors, making them more suitable for correcting intra-wafer effects.

[0088] The control strategy for the reflector used in the projection optics box described above can also be applied to control the deformation of other thermistors in the lithography apparatus or metering tools used in the lithography production process, which are subjected to the heat of the radiation beam irradiating the thermistors.

[0089] While specific applications of photolithography apparatus in IC manufacturing are discussed in this article, it should be understood that the photolithography apparatus described herein can have other applications. Possible other applications include the fabrication of integrated optical systems, patterning for guiding and detecting magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin-film magnetic heads, etc.

[0090] Although embodiments of the invention are specifically referred to herein in the context of a lithography apparatus, these embodiments can be used in other apparatuses. Embodiments of the invention can form part of a mask inspection apparatus, metrology apparatus, or any apparatus for measuring or processing a target such as a wafer (or other substrate) or a mask (or other patterning apparatus). These apparatuses are commonly referred to as lithography tools. Such lithography tools can use vacuum conditions or ambient (non-vacuum) conditions.

[0091] Although specific reference has been made above to the use of embodiments of the invention in the context of optical lithography, it should be understood that, where the context permits, the invention is not limited to optical lithography and can be used in other applications, such as imprint lithography.

[0092] Where the context permits, embodiments of the present invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present invention may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a machine-readable (e.g., computing device) form. For example, a machine-readable medium may include read-only memory (ROM); random access memory (RAM); magnetic storage media; optical storage media; flash memory devices; electrical, optical, acoustic, or other forms of propagation signals (e.g., carrier waves, infrared signals, digital signals, etc.). Furthermore, firmware, software, routines, and instructions may be described herein as performing certain actions. However, it should be understood that this description is merely for convenience, and such actions are actually generated by a computing device, processor, controller, or other device executing the firmware, software, routines, instructions, etc., and in doing so, enable actuators or other devices to interact with the physical world.

[0093] While specific embodiments of the invention have been described above, it should be understood that the invention can be practiced in ways other than those described. The above description is intended to illustrate and not limit. Therefore, it will be apparent to those skilled in the art that modifications can be made to the described invention without departing from the scope of the following claims.

[0094] 1. A method for thermomechanical control of a thermistor subjected to heat load, comprising:

[0095] A nonlinear thermomechanical model of the thermistor is provided, which describes the dynamic relationship between the thermal load on the thermistor and the deformation of the thermistor.

[0096] The control signal is calculated based on the optimization calculation of the nonlinear model.

[0097] An actuation signal is provided to the heater, wherein the actuation signal is at least partially based on the control signal.

[0098] The thermistor element is heated by the heater according to the actuation signal.

[0099] 2. The method according to Clause 1, wherein the control signal is a feedforward signal.

[0100] 3. The method according to Clause 1 or 2, wherein the optimization calculation includes optimization calculation of the time series of control variables to optimize the deformation of the thermistor over the entire prediction range, while taking into account constraints on the actuation limit of the heater.

[0101] 4. The method according to any one of the preceding clauses, wherein the nonlinear model includes a 3D model of the thermistor, the 3D model describing the spatially non-uniform dynamic relationship between the thermal load and the deformation of the thermistor.

[0102] 5. The method according to any one of the preceding clauses, wherein the heat load comprises the heat from the radiation beam impacting the thermistor and the heat provided by the heater.

[0103] 6. The method according to Clause 5, wherein the method comprises:

[0104] Measure the aberration signal representing the wavefront aberration of the radiation beam, and

[0105] The aberration signal is used to calculate the control signal.

[0106] 7. The method according to any one of the preceding clauses, wherein the method comprises:

[0107] Measure one or more temperature signals at one or more measurement locations of the thermistor, and

[0108] The temperature signal is used to calculate the control signal.

[0109] 8. The method according to any one of the preceding clauses, wherein the heater comprises a plurality of heater sections, the plurality of heater sections being individually controllable and arranged to heat different portions of the thermistor.

[0110] The step of providing the actuation signal to the heater includes providing a separate actuation signal to each heater section of the heater section.

[0111] 9. The method according to any one of the preceding clauses, wherein the heater is a non-contact heater, the non-contact heater being arranged to heat the thermistor without direct mechanical contact between the heater and the thermistor.

[0112] 10. The method according to any one of clauses 1-9, wherein the heater includes a heating element in mechanical contact with the thermistor, such as a wire mounted on or in the thermistor.

[0113] 11. The method according to any one of the preceding clauses, wherein the method comprises:

[0114] One or more strain signals are measured at one or more measurement locations of the thermistor, wherein the one or more strain signals represent the deformation of the thermistor at the one or more measurement locations, and

[0115] The control signal is calculated using the strain signal.

[0116] 12. The method according to any one of the preceding clauses, wherein the method comprises:

[0117] Measure one or more temperature signals at one or more measurement locations of the thermistor, and

[0118] A feedback signal is determined based on the temperature signal, wherein the feedback signal is part of the actuation signal provided to the heater.

[0119] 13. The method according to any one of the preceding clauses, wherein the thermal element is a mirror or lens of the projection system of the photolithography apparatus.

[0120] 14. The method according to Clause 13, wherein the optimization calculation is intended to minimize thermomechanical effects that cause wavefront errors in the radiation beam.

[0121] 15. The method according to Clause 13 or 14, wherein the optimization calculation includes optimization for scanner and imaging characteristics, such as overlay of the photolithography process, focal length, and critical dimensions.

[0122] 16. The method according to any one of the preceding clauses, wherein the method includes the step of updating the nonlinear model based on system setting data and / or system calibration data.

[0123] 17. The method according to any one of the preceding clauses, wherein the nonlinear model is a full-order model.

[0124] 18. The method according to Clause 17, wherein the optimization computation includes an iterative computation method that uses the solution of a low-dimensional problem to correct full-order computation.

[0125] 19. The method according to any one of the preceding clauses, wherein the optimization computation includes using a cost function to find an input sequence within a finite time range that minimizes the cost function.

[0126] 20. The method according to Clause 19, wherein the cost function includes any of the following functions: root mean square cost function, Zernike function, pattern offset, optimal focal length, or critical size uniformity.

[0127] 21. The method according to any one of the preceding clauses, wherein the method comprises performing the optimization computation on a parallel processor such as a GPU for real-time control.

[0128] 22. An apparatus for a photolithography manufacturing process, comprising:

[0129] A light source, the light source being arranged to provide a radiation beam

[0130] A thermistor, which is arranged to be irradiated by the radiation beam.

[0131] A heater, configured to heat the thermistor to control its temperature.

[0132] A control device that provides an actuation signal to the heater.

[0133] The control device includes a controller arranged to provide a control signal as part of the actuation signal, wherein the controller includes a nonlinear thermomechanical model of the thermistor, the nonlinear thermomechanical model describing the dynamic relationship between the thermal load on the thermistor and the deformation of the thermistor, and wherein the controller is arranged to calculate the control signal based on optimization calculations of the nonlinear model.

[0134] 23. The device according to Clause 22, wherein the control signal is a feedforward signal.

[0135] 24. The device according to clause 22 or 23, wherein the optimization calculation includes optimization calculation of the time series of control variables to optimize the deformation of the thermistor over the entire prediction range, while taking into account constraints on the actuation limits of the heater.

[0136] 25. The device according to any one of clauses 22-24, wherein the nonlinear model comprises a 3D model of the thermistor, the 3D model describing the spatially non-uniform dynamic relationship between the thermal load and the deformation of the thermistor.

[0137] 26. The device according to any one of clauses 22-25, wherein the heat load comprises the heat from the radiation beam impacting the thermistor and the heat provided by the heater.

[0138] 27. The apparatus of claim 26, wherein the apparatus includes one or more sensors to measure an aberration signal representing the wavefront aberration of the radiation beam, and wherein the control device is arranged to receive the aberration signal and use the aberration signal to calculate the control signal.

[0139] 28. The device according to any one of clauses 22-27, wherein the device includes one or more temperature sensors for measuring one or more temperature signals representing the temperature of the thermistor at one or more measurement locations of the thermistor, wherein the control means is arranged to receive the one or more temperature signals and use the one or more temperature signals to calculate the control signal.

[0140] 29. The device according to any one of Clauses 22-28, wherein the heater comprises a plurality of heater sections, the heater sections being individually controllable and arranged to heat different portions of the thermistor, wherein the control device is arranged to provide an individual actuation signal to each of the heater sections.

[0141] 30. The device according to any one of clauses 22-29, wherein the heater is a non-contact heater, the non-contact heater being arranged to heat the thermistor without direct mechanical contact between the heater and the thermistor.

[0142] 31. The device according to any one of clauses 22-30, wherein the heater comprises a heating element in mechanical contact with the thermistor, such as a wire mounted on or in the thermistor.

[0143] 32. The device according to any one of clauses 22-31, wherein the device includes one or more strain sensors to measure one or more strain signals at one or more measurement locations of the thermosensitive element, and wherein the control device is arranged to receive the strain signals and use the strain signals to calculate the control signal.

[0144] 33. The device according to any one of clauses 22-32, wherein the device includes one or more temperature sensors for measuring one or more temperature signals representing the temperature of the thermistor at one or more measurement locations of the thermistor, wherein the control device is arranged to receive the one or more temperature signals and determine a feedback signal based on the one or more temperature signals, wherein the feedback signal is a portion of the actuation signal provided to the heater.

[0145] 34. The apparatus according to any one of clauses 22-33, wherein the apparatus is a photolithography apparatus, and wherein the thermal element is a mirror or lens of the projection system of the photolithography apparatus.

[0146] 35. The device according to Clause 34, wherein the optimization calculation is designed to minimize thermomechanical effects that cause wavefront errors in the radiation beam.

[0147] 36. The device according to clause 34 or 35, wherein the optimization calculation includes optimization of scanner and imaging characteristics, such as overlay, focal length and critical dimensions of the photolithography process.

[0148] 37. The device according to any one of clauses 22-36, wherein the control device is configured to update the nonlinear model based on system setting data and / or system calibration data.

[0149] 38. The device according to any one of clauses 22-37, wherein the nonlinear model is a full-order model.

[0150] 39. The apparatus according to Clause 38, wherein the optimization computation includes correcting full-order iterations using solutions to low-dimensional problems.

[0151] 40. The device according to any one of clauses 22-39, wherein the optimization calculation includes using a cost function to find an input sequence over a finite time range that minimizes the cost function.

[0152] 41. The device according to Clause 40, wherein the cost function includes any of the following functions: root mean square cost function, Zernike function, pattern offset, optimal focal length, or critical size uniformity.

[0153] 42. The device according to any one of clauses 22-41, wherein the control device includes a plurality of parallel processors to perform the optimization calculations for real-time control.

Claims

1. A method for thermomechanical control of a thermistor subjected to heat load, comprising: A nonlinear model of the thermomechanics of the thermistor is provided, which describes the dynamic relationship between the thermal load on the thermistor and the deformation of the thermistor; and for multiple time steps: Measure one or more temperature signals at one or more measurement locations of the thermistor. The control signal is calculated using the temperature signal and based on the optimization calculation of the nonlinear model. An actuation signal is provided to the heater, wherein the actuation signal is at least partially based on the control signal. The thermistor is heated by the heater according to the actuation signal.

2. The method according to claim 1, wherein the control signal is a feedforward signal.

3. The method according to claim 1 or 2, wherein the optimization calculation includes optimization calculation of the time series of control variables to optimize the deformation of the thermistor over the entire prediction range, while taking into account constraints on the actuation limit of the heater.

4. The method according to claim 1 or 2, wherein the nonlinear model includes a 3D model of the thermistor, the 3D model describing the spatially non-uniform dynamic relationship between the thermal load and the deformation of the thermistor.

5. The method according to claim 1 or 2, wherein the heat load comprises the heat from the radiation beam impacting the thermistor and the heat provided by the heater. The method includes: Measure the aberration signal representing the wavefront aberration of the radiation beam, and The aberration signal is used to calculate the control signal.

6. The method according to claim 1 or 2, wherein the heater comprises a plurality of heater sections, the plurality of heater sections being individually controllable and arranged to heat different portions of the thermistor. The step of providing the actuation signal to the heater includes: A separate actuation signal is provided to each of the heater sections.

7. The method according to claim 1 or 2, wherein the method comprises: At one or more measurement locations of the thermistor, one or more strain signals are measured, wherein the one or more strain signals represent the deformation of the thermistor at the one or more measurement locations, and The control signal is calculated using the strain signal.

8. The method according to claim 1 or 2, wherein the method comprises: Measure one or more temperature signals at one or more measurement locations of the thermistor, and A feedback signal is determined based on the temperature signal, wherein the feedback signal is part of the actuation signal provided to the heater.

9. The method according to claim 5, wherein the thermal element is a reflector or lens of the projection system of the photolithography apparatus. The optimization calculations described therein aim to minimize the thermomechanical effects that cause wavefront errors in the radiation beam.

10. The method of claim 1 or 2, wherein the optimization calculation includes optimization for the scanner and imaging characteristics.

11. The method of claim 10, wherein the optimization calculation includes optimization of overlay, focal length, and critical dimensions for the photolithography process.

12. The method according to claim 1 or 2, wherein the method includes the step of updating the nonlinear model based on system setting data and / or system calibration data.

13. The method according to claim 1 or 2, wherein the nonlinear model is a full-order model. The optimization computation mentioned therein includes an iterative computation method that uses the solution of a low-dimensional problem to correct the full-order computation.

14. The method of claim 1 or 2, wherein the optimization computation includes using a cost function to find an input sequence within a finite time range that minimizes the cost function.

15. The method of claim 14, wherein the cost function comprises any one of the following functions: root mean square cost function, Zernike function, pattern offset, optimal focal length, or critical size uniformity.

16. An apparatus for a photolithography production process, comprising: A light source, the light source being arranged to provide a radiation beam A thermistor, which is arranged to be irradiated by the radiation beam. A heater, configured to heat the thermistor to control its temperature. A control device for providing an actuation signal to the heater. The control device includes a controller arranged to provide a control signal as part of the actuation signal, wherein the controller includes a nonlinear model of the thermomechanical properties of the thermistor, the nonlinear model describing the dynamic relationship between the thermal load on the thermistor and the deformation of the thermistor, and wherein the controller is arranged to calculate the control signal based on an optimization calculation of the nonlinear model. The control device is configured to perform a method for thermomechanical control of a thermistor subjected to a heat load according to any one of the preceding claims.

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