Apparatus and method for modulating light source wavelength - Patents.com

Abstract

An apparatus and method for controlling a laser system can generate bursts of pulses of laser radiation having multiple alternative wavelengths. An element controlling the wavelength is pre-positioned between positions for generating one wavelength and another wavelength during the bursts. Also disclosed is a system for determining optimal control waveforms for moving the element between multiple positions using quadratic programming, dynamic programming, inverse feedforward control, or iterative learning control. A data storage device, such as a pre-populated lookup table or a field programmable gate array, can be used to store at least one optimal control parameter for each of multiple repetition rates.

Description

[Technical field]

[0001] (CROSS REFERENCE TO RELATED APPLICATIONS)

[0001] This application claims priority to U.S. Patent Application No. 62 / 847,464, entitled "APPARATUS FOR AND METHOD OF MODULATING A LIGHT SOURCE WAVELENGTH," filed May 14, 2019, which is hereby incorporated by reference in its entirety.

[0002] The present disclosure relates to systems and methods for generating multiple laser beams, for use, for example, in a lithographic apparatus. [Background technology]

[0003]

[0003] A lithographic apparatus applies a desired pattern onto a substrate, such as a wafer of semiconductor material, usually onto a target portion of the substrate. Alternatively, a patterning device, referred to as a mask or reticle, may be used to generate the circuit pattern to be formed on an individual layer of the wafer. Transfer of the pattern is typically by imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. Generally, a single substrate will contain adjacent target portions that are successively patterned.

[0004]

[0004] Lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing the entire pattern onto the target portion in one go, and so-called scanners, in which each target portion is irradiated by scanning the pattern with a radiation beam in a given direction (the "scan" direction) while synchronously scanning the substrate parallel or anti-parallel to the given direction (the "scan" direction). It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate. For simplicity, both steppers and scanners will be referred to herein simply as scanners.

[0005]

[0005] The light source used to illuminate and project the pattern onto the substrate can be any one of a number of configurations. Deep UV excimer lasers commonly used in lithography systems include krypton fluoride (KrF) lasers with a wavelength of 248 nm and argon fluoride (ArF) lasers with a wavelength of 193 nm. Excimer lasers are typically designed to operate with specific gas mixtures, and therefore changing the wavelength can be complicated. In particular, changing the central wavelength from discharge to discharge ("shot-to-shot") is difficult.

[0006]

[0006] However, it may be desirable to have the ability to change the wavelength. For example, in 3D NAND layers of memory (i.e., memory with structures similar to NAND (not AND) gates stacked on top of each other). Moving from 2D to 3D NAND architecture requires major changes in the manufacturing process. The problems in 3D NAND manufacturing are mainly caused by the extreme aspect ratio (ratio of hole diameter to depth) etching and deposition processes. The creation of complex 3D structures with extremely high-aspect-ratio (HAR) features is complex and requires extremely high precision, and ultimately process uniformity and repeatability to achieve large scale. Furthermore, as the height of the multi-layer stack increases, the difficulty of obtaining consistent etching and deposition results at the top and bottom of the stack, such as a memory array, also increases.

[0007]

[0007] These considerations lead to the need to increase the depth of focus. The depth of focus (DOF) in lithography is defined by the relationship DOF=±m2λ / (NA) 2 where λ is the wavelength of the illumination light, NA is the numerical aperture, and m1 and m2 are practical factors that depend on the resist process. Due to the need for large depth of focus in 3D NAND lithography, two or more exposure passes are performed on the wafer, and each pass may use a different laser wavelength.

[0008]

[0008] Furthermore, the materials that make up the lenses that focus the laser radiation are dispersive, so different wavelengths are focused at different depths, another reason why it is desirable to have the ability to change the wavelength.

[0009]

[0009] DUV light sources include systems for controlling the wavelength of the DUV light. Typically, these wavelength control systems include feedback and feedforward compensators to promote wavelength stability. Characteristically, the target or reference wavelength, i.e., the wavelength required by the wavelength control system, is not expected to change rapidly during laser operation. Thus, the controller is primarily responsible for removing transient disturbances. The feedforward compensator also compensates for required changes in the wavelength target, i.e., wavelength change events that are not expected to occur frequently. When such an event occurs to achieve, for example, a 600 fm wavelength setpoint change, a settling time on the order of typically about 100 ms must be allowed for the system to stably settle to the new wavelength. Typically, this exceeds the time between pulses, so that in applications where the target wavelength setpoint is changed by about 500 fm between pulses, such a control system cannot provide the desired wavelength tracking performance.

[0010]

[0010] As a specific example, in an application generating DUV light at two different wavelengths, the reference wavelength has two set points during the exposure: a first set point for the first wavelength and a second set point for the second wavelength. Thus, the reference wavelength is modulated between these two set points. Any wavelength target change requires a certain settling time. This limits the speed at which the reference wavelength can be modulated. Furthermore, the wavelength during the transient settling period is essentially uncontrolled. This places a constraint on the acceptable waiting time between wavelength target changes.

[0011]

[0011] It is desirable to have the ability to change the reference wavelength between pulses, i.e., on a pulse-by-pulse basis. This can be achieved by reducing the transient settling period. It is also desirable to reduce or eliminate the wait time between reference wavelength changes. Summary of the Invention

[0012]

[0012] The following presents a simplified summary of one or more embodiments in order to provide a basic understanding of such embodiments. This summary is not an extensive overview of all contemplated embodiments, is not intended to identify key or critical elements of all embodiments, and is not intended to delineate the scope of any or all embodiments. Its sole purpose is to present some concepts of one or more embodiments in a simplified form as a prelude to the more detailed description that is presented later.

[0013]

[0013] According to one aspect of the embodiment, in order to shorten the transient period caused by changing the reference wavelength, the actuator is prepared by pre-positioning the actuator between bursts to achieve the next new target wavelength between bursts.

[0014]

[0014] According to another aspect, wavelength control is achieved by using an actuator, such as a piezo actuator, in the line narrowing module. Based on a dynamic model of the actuator, an optimal control waveform is calculated for actuating the actuator to minimize the difference between the actual wavelength and the wavelength target. The optimal control waveform can be calculated using any one of several methods. For example, the optimal control waveform may be calculated using quadratic programming with constraints and / or dynamic programming that generates an optimal control signal for a given wavelength target. A pre-populated look-up table may be used that contains optimal control parameters for at least some of the different repetition rates at which the radiation source can be operated.

[0015]

[0015] As another example, optimal control waveforms can be determined using model inversion feedforward control. This method uses an actuator dynamic model to build a digital filter to invert the actuator dynamics. By passing the waveform of the desired actuator trajectory through this filter, optimal control waveforms can be generated in real time to achieve steady-state error-free tracking. Here and elsewhere, the term "trajectory" is used to refer to the characteristics of the actuator movement, including acceleration.

[0016]

[0016] As another example, the optimal solution for achieving two separate wavelengths is achieved using a learning algorithm to converge the error through several learning iterations. The proposed method can achieve two separate wavelengths separated by 1000 fm with a separation error of less than 20 fm.

[0017] According to another aspect, optimal control waveforms can be delivered to the actuators at extremely high rates using a field programmable gate array (FPGA).

[0018]

[0018] Further features and advantages of the present invention, as well as the structure and operation of various embodiments of the present invention, are described in detail below with reference to the accompanying drawings. It should be noted that the present invention is not limited to the specific embodiments described herein. Such embodiments are described herein for illustrative purposes only. Based on the teachings contained herein, a person skilled in the art will be able to easily conceive further embodiments. [Brief description of the drawings]

[0019]

[0019] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate by way of example, and not by way of limitation, methods and systems of embodiments of the present invention. The drawings, together with the detailed description, further serve to explain the principles of the methods and systems presented herein and to enable one skilled in the art to make and use the methods and systems. In the drawings, like reference numbers represent identical or functionally similar elements.

[0020] [Figure 1]

[0020] A schematic diagram, not to scale, showing the overall broad concept of a photolithography system according to one aspect of the disclosed subject matter. [Diagram 2]

[0021] FIG. 1 is a schematic diagram, not to scale, illustrating the overall broad concept of a lighting system in accordance with one aspect of the disclosed subject matter. [Diagram 3]

[0022] FIG. 1 is a functional block diagram of a two-chamber laser system according to an aspect of an embodiment. [Figure 4]

[0023] FIG. 13 is a diagram of relative discharge timing that may occur in two laser chambers in accordance with an aspect of an embodiment. [Diagram 5]

[0024] FIG. 13 is a diagram of another relative discharge timing that may occur in two laser chambers in accordance with an aspect of an embodiment.

[0021]

[0025] Further features and advantages of the present invention, as well as the structure and operation of various embodiments of the present invention, are described in detail below with reference to the accompanying drawings. It should be noted that the present invention is not limited to the specific embodiments described herein. Such embodiments are described herein for illustrative purposes only. Further embodiments will be readily envisioned by those skilled in the art based on the teachings contained herein. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022]

[0026] This specification discloses one or more embodiments incorporating the features of the present invention. The disclosed embodiment or embodiments are merely exemplary of the present invention. The scope of the present invention is not limited to the disclosed embodiment or embodiments. The present invention is defined by the claims appended hereto.

[0023]

[0027] References to the described embodiments, and to "one embodiment," "an embodiment," "exemplary embodiment," and the like, herein indicate that the described embodiment may include a particular feature, structure, or characteristic, but each embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases do not necessarily refer to the same embodiment. Furthermore, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is understood that it is within the knowledge of one of ordinary skill in the art to implement such feature, structure, or characteristic in connection with other embodiments, whether or not explicitly described.

[0024]

[0028] Before describing the embodiments in detail, it is useful to illustrate an exemplary environment in which embodiments of the present invention may be practiced. With reference to FIG. 1, a photolithography system 100 includes an illumination system 105. As described more fully below, the illumination system 105 includes a light source that generates and directs a pulsed light beam 110 to a photolithography exposure apparatus or scanner 115. The photolithography exposure apparatus or scanner 115 patterns microelectronic features on a wafer 120. The wafer 120 is disposed on a wafer table 125. The wafer table 125 is constructed to hold the wafer 120 and is connected to a positioner configured to accurately position the wafer 120 according to certain parameters.

[0025]

[0029] The photolithography system 100 uses a light beam 110 having a wavelength in the deep ultraviolet (DUV) range, such as a wavelength of 248 nanometers (nm) or 193 nm. The minimum size of a microelectronic feature that can be patterned on the wafer 120 depends on the wavelength of the light beam 110, with shorter wavelengths allowing smaller minimum feature sizes. If the wavelength of the light beam 110 is 248 nm or 193 nm, the minimum size of the microelectronic feature can be, for example, 50 nm or less. The bandwidth of the light beam 110 can be the actual instantaneous bandwidth of the light spectrum (or emission spectrum), which contains information about how the light energy of the light beam 110 is distributed across various wavelengths. The scanner 115 includes an optical mechanism having, for example, one or more condenser lenses, a mask, and an objective mechanism. The mask can be moved along one or more directions, for example along the optical axis of the light beam 110 or in a plane perpendicular to the optical axis. The objective mechanism includes a projection lens and allows image transfer from the mask to the photoresist on the wafer 120. The illumination system 105 adjusts the angular range of the light beam 110 incident on the mask and also homogenizes (makes uniform) the intensity distribution of the light beam 110 on the mask.

[0026]

[0030] The scanner 115 may include, among other features, a lithography controller 130, an air conditioning device, and a power supply for various electrical components. The lithography controller 130 controls how layers are printed on the wafer 120. The lithography controller 130 includes a memory that stores information such as a process recipe. The process program or recipe determines the length of exposure to the wafer 120 based on, for example, the mask used and other factors that affect the exposure. During lithography, multiple pulses of the light beam 110 illuminate the same area of ​​the wafer 120 to constitute an illumination dose.

[0027]

[0031] Photolithography system 100 also preferably includes a control system 135. Generally, control system 135 includes one or more of digital electronic circuitry, computer hardware, firmware, and software. Control system 135 also includes memory, which may be read-only memory and / or random access memory. Suitable storage devices for tangibly embodying computer program instructions and data include all forms of non-volatile memory, by way of example only, semiconductor memory devices such as EPROM, EEPROM, and flash memory devices, magnetic disks such as internal hard disks and removable disks, magneto-optical disks, and CD-ROM disks.

[0028]

[0032] The control system 135 may also include one or more input devices (such as a keyboard, touch screen, microphone, mouse, handheld input device, etc.) and one or more output devices (such as a speaker or monitor). The control system 135 also includes one or more programmable processors and one or more computer program products tangibly embodied in a machine-readable storage device for execution by the one or more programmable processors. Each of the one or more programmable processors can execute a program of instructions to perform a desired function by performing operations on input data and generating appropriate output. Generally, a processor receives instructions and data from a memory. Any of the foregoing may be supplemented by or incorporated in specially designed ASICs (application-specific integrated circuits). The control system 135 may be centralized or partially or wholly distributed throughout the photolithography system 100.

[0029]

[0033] Referring to Figure 2, an exemplary illumination system 105 is a pulsed laser source that generates a pulsed laser beam as light beam 110. Figure 2 illustrates an exemplary block diagram of a gas discharge laser system according to an embodiment of certain aspects of the disclosed subject matter. The gas discharge laser system can include, for example, a solid-state or gas discharge seed laser system 140, an amplification stage, such as, for example, a power ring amplifier ("PRA") stage 145, relay optics 150, and a laser system output subsystem 160. Seed system 140 can include, for example, a master oscillator ("MO") chamber 165.

[0030]

[0034] The seed laser system 140 may also include a master oscillator output coupler ("MOOC") 175. The MOOC 175 may include a partially reflective mirror and, together with a reflective grating (not shown) in a line narrowing module ("LNM") 170, form an oscillator cavity within which the seed laser 140 oscillates to form the seed laser output pulses, i.e., form the master oscillator ("MO"). The system may also include a line-center analysis module ("LAM") 180. The LAM 180 may include an etalon spectrometer and a coarse-resolution grating spectrometer for fine wavelength measurements. The MO wavefront engineering box ("WEB") 185 functions to redirect the output of the MO seed laser system 140 to the amplification stage 145 and may include beam expansion, for example by a multi-prism beam expander (not shown), and coherence busting, for example in the form of an optical delay path (not shown).

[0031]

[0035] The amplification stage 145 may include, for example, a PRA laser oscillation chamber 200. This may be an oscillator formed by seed beam injection and output coupling optics (not shown) that may be incorporated, for example, in the PRA WEB 210, and redirected back through the gain medium in the beam chamber 200 by a beam reverser 220. The PRA WEB 210 may incorporate partially reflective input / output couplers (not shown), a maximum reflecting mirror for the nominal operating wavelength (e.g., about 193 nm for an ArF system), and one or more prisms.

[0032]

[0036] A bandwidth analysis module ("BAM") 230 at the output of the amplifier stage 145 receives the output laser light beam pulse from the amplifier stage and can select a portion of the light beam for metrology purposes, e.g., to measure the output bandwidth and pulse energy. The laser output light beam pulse then passes through an optical pulse stretcher ("OPuS") 240, which can be in the position of a pulse energy meter, and an output combined autoshutter metrology module ("CASMM") 250. One purpose of the OPuS 240 is to convert, e.g., a single output laser pulse into a pulse train. Secondary pulses generated from an initial single output pulse can be delayed from each other. By dispersing the initial laser pulse energy in the secondary pulse train, the effective pulse length of the laser can be extended and the peak pulse intensity can be reduced at the same time. Thus, the OPuS 240 can receive the laser beam from the PRA WEB 210 via the BAM 230 and direct the output of the OPuS 240 to the CASMM 250. Other suitable configurations can be used in other embodiments.

[0033]

[0037] The PRA laser operation chamber 200 and MO 165 are configured as a chamber in which an electrical discharge between electrodes can create a lasing gas discharge in a lasing gas, generating a population inversion of energetic molecules including, for example, Ar, Kr, and / or Xe to produce a relatively broadband radiation that can be line narrowed in a line narrowing module ("LNM") 170 to a relatively very narrow bandwidth and center wavelength selected, as is known in the art.

[0034]

[0038] Tuning is typically performed in the LNM. A typical technique used for line narrowing and laser tuning is to provide a window at the rear of the laser discharge cavity through which a portion of the laser beam enters the LNM. A portion of the beam is then expanded by a prism beam expander and directed to a grating, which reflects a narrowly selected portion of the laser's broad spectrum back into the discharge chamber where it is amplified. Tuning of the laser is typically performed by using an actuator, for example a piezo actuator, to change the angle at which the beam illuminates the grating.

[0035]

[0039] As mentioned above, in some applications it is beneficial to be able to generate a burst of one or more pulses having one wavelength and then switch to generate a burst of one or more pulses having a different wavelength. However, trying to achieve this between pulses is difficult because the settling time, i.e. the amount of time it takes for the system to stabilize after a wavelength change, is typically longer than the interval between pulses. According to one embodiment, priming the actuator by pre-positioning it between bursts to achieve the next new target wavelength between bursts reduces the transient settling time caused by a change in the reference wavelength.

[0036]

[0040] According to another aspect, a dynamic model of the actuator is used to calculate optimal control waveforms for actuating the actuator to minimize the difference between the actual wavelength and the wavelength target.

[0037]

[0041] The optimal control waveform can be calculated using any one of several methods. For example, the optimal control waveform can be calculated using dynamic programming. This method is well adapted to handle complex models including nonlinear dynamics. When an actuator model with strong nonlinear dynamics is employed, dynamic programming can be used to generate optimal control signals for a given wavelength target. However, dynamic programming suffers from the challenge of requiring significant computational resources that may not be possible to implement in real time. This can be overcome by using a data storage device such as a pre-populated look-up table or a pre-programmed field programmable gate array (FPGA) that contains optimal control parameters for at least some of the different repetition rates at which the radiation source can be operated.

[0038]

[0042] As another example, optimal control waveforms can be determined using model inversion feedforward control. This method uses an actuator dynamic model to build a digital filter to invert the actuator dynamics. By passing the desired waveform of the desired actuator trajectory through this filter, optimal control waveforms can be generated in real time to achieve steady-state error-free tracking.

[0039]

[0043] As another example, an optimal solution for stably achieving two separate wavelengths is achieved using a learning algorithm to ensure error convergence through several learning iterations. Embodiments of the systems and methods disclosed herein may be able to achieve two separate wavelengths separated by 1000 fm with a separation error of less than 20 fm.

[0040]

[0044] According to another aspect, optimal control waveforms can be delivered to the actuators at extremely high rates using an FPGA.

[0041]

[0045] The control system may include a combination of feedforward control and iterative learning control (ILC). As shown in FIG. 3, a feedforward control signal A is calculated offline by the ILC module 300 using wavelength measurements from the streaming data acquisition unit 330 and an ILC update law, as described below. A bandwidth wavelength control module (BWCM) 340 uses the feedforward control signal A to update predefined data in a data storage unit, such as an FPGA included in the BWCM 340. The BWCM 340 then activates the PZT 350, for example at 60 kHz when the laser is pulsed. The wavelength of the laser emission is measured by the line center (center wavelength) analysis module (LAM) 360 and the fire control platform or processor (FCP) 370, and the wavelength measurements are collected in the data acquisition unit 330 at 6 kHz.

[0042]

[0046] It will be appreciated that the system shown in Figure 3 can be configured to encompass multiple frequency regimes. The area within the dashed box illustrates a process that may be performed essentially offline. The PZT350 may be driven at approximately 60 kHz. Wavelength data may be acquired at approximately 6 kHz.

[0043]

[0047] To take into account constraints on the change in the PZT voltage, constrained quadratic programming can be used to assist in finding the optimal feedforward signal within the feasible operating region. Quadratic programming is a technique for finding the optimal solution to a given quadratic cost function subject to mathematical constraints.

[0044]

[0048] A standard QP solver can solve the problem with the following structure:

[0045]

number

[0046] where X is a design parameter that can be chosen freely, but must satisfy LX ≤ b. In other words, the QP solver finds the optimal X that minimizes the cost function within the feasible region defined by LX ≤ b.

[0047]

[0049] In the application described here, the objective is to find a feedforward control that satisfies the actuator constraints while minimizing the error between the actuator position and the desired control waveform. The PZT dynamics can be expressed in the following state-space form: x(k+1)=Ax(k)+Bu(k) y(k+1)=Cx(k+1) where A, B, and C are the state, input, and output matrices, respectively, describing the PZT dynamics, x is the state vector, u is the input vector, and y is the output from the PZT.

[0048]

[0050] Substituting the dynamic model above, the initial cost function can be rewritten as:

[0049]

number

[0050]

[0051] This fits the following standard QP form: H=P T QP f=-P T QR X=U L=D b=l P describes the PZT input / output dynamics, Q is a weighting function, R denotes the desired control waveform, D represents the actuator constraint, and l is the threshold of the actuator constraint.

[0051]

[0052] According to another embodiment, the ILC control can be described by the following equation: Uk =U k-1 +LE k-1 Here, U k is the feedforward control signal used in the kth iteration, L is the learning function that determines the convergence of the ILC algorithm, and E k is the error at the kth iteration.

[0052]

[0053] The stability and convergence properties of the ILC control can be derived by combining the ILC control method with the dynamic model of the system as follows. E k =(l-PL)E k-1

[0053]

[0054] where P is a matrix describing the input-output relationship of the system, and I is the identity matrix. Stability is guaranteed when the absolute values ​​of all eigenvalues ​​of (I-PL) are less than 1. Also, the convergence rate is determined by the matrix (I-PL). If (I-PL)=0, the error converges to zero after one iteration.

[0054]

[0055] FIG. 4 is a flow chart showing a method of controlling a radiation source according to one aspect of an embodiment. In step S100, a previous burst of pulses is terminated. In step S110, the actuator is prepared by prepositioning it to a position that is between where it must be to generate pulses having a first frequency and where it must be to generate pulses having a second frequency. In step S120, an optimal control waveform is calculated using one or more of the techniques described above. In step S130, it is determined whether a new burst has been triggered. If "yes", i.e. a new burst has been triggered, then in step S140, parameters for operating at the required repetition rate and frequency are communicated to the radiation source, for example using an FPGA. In step S150, it is determined whether the current burst has ended. If the current burst has not ended, step S140 is repeated. If the burst has ended, the process ends in step S160.

[0055]

[0056] FIG. 5 shows the method performed by the ILC to calculate the update using the initial QP feedforward control signal. In step S210, the initial feedforward control signal is generated using quadratic programming. In step S220, the feedforward control signal is used to fire the laser. In step S230, it is determined whether the error in the feedforward signal has converged. If the error has not converged, then in step S250, the control signal is updated using iterative learning. The new control signal is then used to fire the laser in step S220. If the error has converged, the process ends in step S240.

[0056]

[0057] It is recognized that the "Description of the Invention" section is intended to be used to interpret the claims, rather than the "Summary" and "Abstract" sections. The "Summary" and "Abstract" sections may describe one or more exemplary embodiments of the invention as envisioned by the inventors, but cannot describe all of those exemplary embodiments, and are therefore not intended to limit the scope of the invention and the appended claims in any manner.

[0057]

[0058] The present invention has been described above in terms of functional building blocks illustrating examples of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for convenience of description. Alternative boundaries may be defined so long as the specified functions and relationships thereof are appropriately performed.

[0058]

[0059] The foregoing description of the specific embodiments fully reveals the overall nature of the present invention, so that by applying knowledge within the art, such specific embodiments can be easily modified and / or adapted for various applications without undue experimentation and without departing from the overall concept of the present invention. Therefore, based on the teaching and guidance presented herein, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed embodiments. It will be understood that the expressions or terms in this specification are for the purpose of explanation rather than limitation, and should be interpreted in light of the teaching and guidance by those skilled in the art.

[0059]

[0060] Other aspects of the invention are described in the following numbered clauses. 1. A laser system comprising: an actuator having a first state that causes the laser system to generate a first burst of one or more pulses of laser radiation having a first wavelength and a second state that causes the laser system to generate a second burst of one or more pulses of laser radiation having a second wavelength different from the first wavelength; an actuator controller configured to provide a signal to the actuator to place the actuator in a third state between the bursts, the third state being intermediate the first state and the second state; A laser system comprising: 2. The laser system of clause 1, wherein the first state is a first position, the second state is a second position, and the third state is a third position between the first position and the second position. 3. A laser system comprising: an actuator having a first state that causes the laser system to generate a first burst of one or more pulses of laser radiation having a first wavelength and a second state that causes the laser system to generate a second burst of one or more pulses of laser radiation having a second wavelength different from the first wavelength; an actuator controller configured to provide a signal to the actuator to transition the actuator from a first state to a second state, the actuator controller comprising a module configured to calculate an optimal control waveform for the signal for transitioning the actuator from the first state to the second state, and transitioning the actuator from the first state to the second state along a trajectory under control of the optimal control waveform; A laser system comprising: 4. The laser system of clause 3, wherein the module is adapted to calculate the optimal control waveform using constrained quadratic programming. 5. The laser system of claim 3, wherein the module is adapted to calculate the optimal control waveform using dynamic programming. 6. The laser system of clause 3, wherein the module is adapted to calculate the optimal control waveform using model inversion feedforward control. 7. The laser system of clause 3, wherein the module is adapted to calculate the optimal control waveform using iterative learning control. 8. A laser system as described in any one of clauses 3 to 7, wherein the module further comprises means for storing at least one optimal control parameter for each of a plurality of repetition rates. 9. The laser system of claim 8, wherein the means for storing at least one optimal control parameter for each of a plurality of repetition rates includes a pre-populated look-up table. 10. The laser system of claim 8, wherein the means for storing at least one optimal control parameter for each of a plurality of repetition rates includes a field programmable gate array. 11. A method of controlling a laser system, comprising: placing an actuator in a first state that causes the laser system to generate a first burst of one or more pulses of laser radiation having a first wavelength; placing the actuator in a second state that causes the laser system to generate a second burst of one or more pulses of laser radiation having a second wavelength different from the first wavelength; The method further includes a third step between the steps of placing the actuator in the first state and placing the actuator in the second state, of placing the actuator in a third state intermediate the first state and the second state. 12. A method of controlling a laser system as described in clause 11, wherein the first state is a first position, the second state is a second position, and the third state is a third position between the first position and the second position. 13. A method of controlling a laser system, comprising: placing an actuator in a first state that causes the laser system to generate a first burst of one or more pulses of laser radiation having a first wavelength; placing the actuator in a second state that causes the laser system to generate a second burst of one or more pulses of laser radiation having a second wavelength different from the first wavelength; The method, wherein the step of placing the actuator in the second state includes calculating an optimal control waveform for the actuator to transition from the first state to the second state, and transitioning the actuator from the first state to the second state along a trajectory under control of the optimal control waveform. 14. A method of controlling a laser system as recited in claim 13, wherein calculating an optimal control waveform for transitioning the actuator from the first state to the second state includes using constrained quadratic programming. 15. The method of controlling a laser system as recited in claim 13, wherein calculating an optimal control waveform for transitioning an actuator from a first state to a second state includes using dynamic programming. 16. A method of controlling a laser system as recited in clause 13, wherein calculating an optimal control waveform for transitioning an actuator from a first state to a second state includes using model inversion feedforward control. 17. A method of controlling a laser system as described in clause 13, wherein calculating an optimal control waveform for transitioning the actuator from the first state to the second state includes using iterative learning control. 18. A method of controlling a laser system described in any one of clauses 13 to 17, wherein calculating an optimal control waveform for transitioning the actuator from a first state to a second state includes storing means for storing at least one optimal control parameter for each of a plurality of repetition rates. 19. A method of controlling a laser system as described in clause 18, wherein storing at least one optimal control parameter for each of a plurality of repetition rates is performed using a pre-populated look-up table. 20. A method of controlling a laser system as described in clause 18, wherein storing at least one optimal control parameter for each of a plurality of repetition rates includes using a field programmable gate array. 21. A method of controlling a laser system, comprising: placing an actuator in a first state that causes the laser system to generate a first burst of one or more pulses of laser radiation having a first wavelength; placing the actuator in a second state that causes the laser system to generate a second burst of one or more pulses of laser radiation having a second wavelength different from the first wavelength; further comprising a third step between the step of placing the actuator in the first state and the step of placing the actuator in the second state, of placing the actuator in a third state intermediate the first state and the second state; The method, wherein placing the actuator in the second state includes calculating an optimal control waveform for transitioning the actuator from the first state to the second state along an optimal trajectory.

Claims

1. 1. A laser system comprising: an actuator having a first state that causes the laser system to generate a first burst of one or more pulses of laser radiation having a first wavelength and a second state that causes the laser system to generate a second burst of one or more pulses of laser radiation having a second wavelength different from the first wavelength; an actuator controller configured to provide a signal to the actuator to transition the actuator from the first state to the second state, the actuator controller comprising a module configured to calculate an optimal control waveform for the signal for transitioning the actuator from the first state to the second state, and transitioning the actuator from the first state to the second state along a trajectory under control of the optimal control waveform; Equipped with the module is adapted to calculate the optimal control waveform by updating the feedforward control signal using an iterative learning control until an error in the feedforward control signal converges; A laser system that uses the feedforward control signal to emit a laser beam.

2. 2. The laser system of claim 1 , wherein the modules comprise: a data acquisition unit configured to collect wavelength measurements of the laser radiation; and an iterative learning control module configured to calculate the feedforward control signal using the wavelength measurements and an iterative learning control update method.

3. 3. The laser system of claim 2, wherein said iterative learning control module calculates said feedforward control signal offline.

4. 3. The laser system of claim 2, wherein said iterative learning control module calculates initial feedforward control signals using constrained quadratic programming.

5. 3. The laser system of claim 2, wherein said modules further comprise a bandwidth wavelength control module configured to actuate said actuator based on said calculated feedforward control signal.

6. 10. The laser system of claim 1, wherein said module further comprises means for storing at least one optimal control parameter for each of a plurality of repetition rates.

7. 7. The laser system of claim 6, wherein said means for storing at least one optimal control parameter for each of a plurality of repetition rates comprises a pre-populated look-up table.

8. 1. A method for controlling a laser system, comprising: placing an actuator in a first state that causes the laser system to generate a first burst of one or more pulses of laser radiation having a first wavelength; placing the actuator in a second state that causes the laser system to generate a second burst of one or more pulses of laser radiation having a second wavelength different from the first wavelength; the step of placing the actuator in the second state includes calculating an optimal control waveform for the actuator to transition from the first state to the second state, and transitioning the actuator from the first state to the second state along a trajectory under control of the optimal control waveform; calculating an optimal control waveform for the actuator to transition from the first state to the second state includes updating the feedforward control signal using an iterative learning control until an error in the feedforward control signal converges; Using the feedforward control signal to effect laser emission.

9. calculating an optimal control waveform for the actuator to transition from the first state to the second state includes collecting wavelength measurements of the laser radiation; 10. The method of claim 8, wherein updating the feedforward control signal comprises calculating the feedforward control signal using the wavelength measurements and an iterative learning control update method.

10. 10. The method of claim 9, wherein calculating the feedforward control signal is performed offline.

11. 10. The method of claim 9, wherein calculating the feedforward control signal comprises calculating an initial feedforward control signal using constrained quadratic programming.

12. 10. The method of controlling a laser system of claim 9, wherein calculating an optimal control waveform for the actuator to transition from the first state to the second state includes actuating the actuator based on the calculated feedforward control signal.

13. 9. The method of controlling a laser system of claim 8, wherein calculating an optimal control waveform for said actuator to transition from said first state to said second state includes storing at least one optimal control parameter for each of a plurality of repetition rates.

14. 14. The method of controlling a laser system of claim 13, wherein storing the at least one optimal control parameter for each of a plurality of repetition rates is performed using a pre-populated look-up table.

15. 1. A method for controlling a laser system, comprising: placing an actuator in a first state that causes the laser system to generate a first burst of one or more pulses of laser radiation having a first wavelength; placing the actuator in a second state that causes the laser system to generate a second burst of one or more pulses of laser radiation having a second wavelength different from the first wavelength; further comprising, between the step of placing the actuator in the first state and the step of placing the actuator in the second state, a third step of placing the actuator in a third state intermediate the first state and the second state; the step of placing the actuator in the second state includes calculating an optimal control waveform for transitioning the actuator from the first state to the second state along an optimal trajectory; calculating an optimal control waveform for transitioning the actuator from the first state to the second state along an optimal trajectory includes updating the feedforward control signal using an iterative learning control until an error in the feedforward control signal converges; Using the feedforward control signal to effect laser emission.

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