Fast bandwidth control using adaptive gain

Abstract

A laser system configured to provide a train of optical pulses includes an oscillator configured to produce an optical pulse in a first gain medium; an amplifier optically connected to the oscillator to receive and amplify the pulse in a second gain medium during an amplification period; a bandwidth control system configured to adjust a timing delay between a production of the pulse in the oscillator and the amplification period in the amplifier based on a measured bandwidth error of light emitted from the amplifier and a control gain multiplier, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to the measured bandwidth error.

Description

FAST BANDWIDTH CONTROL USING ADAPTIVE GAINCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to US Application No. 63 / 765,290, filed February 28, 2025, titled FAST BANDWIDTH CONTROL USING ADAPTIVE GAIN, which is incorporated herein by reference in its entirety.TECHNICAL FIELD

[0002] The present disclosed subject matter relates to control of laser-generated light sources such as are used for integrated circuit photolithographic manufacturing and related processes.BACKGROUND

[0003] Laser systems are used, for example, as sources of radiation (light) in facilities that fabricate semiconductor devices, i.e., “fabs.” Laser systems, or laser-based light source systems, can be used to produce radiation for exposure of patterns in or on resists layers in photolithography processes, as well as for inspection and metrology, such as inspection and metrology of semiconductor substrates, patterns thereon, reticle properties, such as for detection of anomalies relating to these that may impact yield.

[0004] Deep ultraviolet (DUV) radiation is typically supplied as a series of pulses at a given repetition rate, for example, in the range of about 500 Hz to 6 kHz or more. DUV wavelengths can include wavelengths in a range of about 100 nanometers (nm) to about 400 nm including, for example, wavelengths of approximately 193 nanometers (nm) (ArF) and 248 nm (KrF). For any given wavelength, contrast and resulting imaging performance generally increase with reduced bandwidth. In other words, the narrower the effective bandwidth of the light, the better the contrast achievable at a given nominal center wavelength. Even small improvements in bandwidth reduction and bandwidth control can be significant.SUMMARY

[0005] The following presents a succinct summary of one or more aspects, in order to provide an introductory understanding of the presently disclosed subject matter. This summary is not an extensive overview of all contemplated implementations and is not intended to single out any elements as being key or critical. Nor is it intended to delineate the full scope of any or all implementations. Its sole purpose is to present some concepts of one or more aspects in a streamlined form as a prelude to the more detailed description that is presented later.

[0006] According to one aspect, a laser system configured to provide a train of optical pulses includes: an oscillator configured to produce an optical pulse in a first gain medium; an amplifier optically connected to the oscillator to receive the pulse from the oscillator and configured to amplifythe pulse in a second gain medium during an amplification period; a bandwidth control system configured to adjust a timing delay between a production of the pulse in the oscillator and the amplification period in the amplifier based on (1) a measured bandwidth error of light emitted from the amplifier and (2) a control gain multiplier, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to the measured bandwidth error.

[0007] Implementations can include one or more of the following.

[0008] The bandwidth control system can be configured to incrementally modify the control gain multiplier between subsequent pulses in the train of optical pulses. The bandwidth control system can be configured to recenter the timing delay within an effective control range when the timing delay is displaced from the center of the effective control range by more than a pre -specified amount of the distance to the edge of the effective control range. The bandwidth control system can be configured to recenter the timing delay within an effective control range when the timing delay is displaced from the center of the effective control range by more than 60% of the distance to the edge of the effective control range. The bandwidth control system is can be configured to recenter the timing delay by changing a parameter or parameters of the laser system, other than the timing delay, affecting a bandwidth of the light emitted from the amplifier. The parameter can include one or more of (1) the position and / or orientation a stepper-controlled optical element within the optical path of the laser system (2) a voltage used to produce electrical discharges in the first gain medium; (3) a voltage used to produce electrical discharges in the second gain medium; (4) an amount or a percentage of a halogen gas in the first gain medium; (5) an amount or a percentage of a halogen gas in the second gain medium. The bandwidth control system can be configured to modify the control gain multiplier in response to the relative position of the timing delay within the effective control range. The bandwidth control system can be configured to modify the control gain multiplier by increasing the control gain multiplier when the timing delay is sufficiently greater than a central value within the effective control range and decreasing the control gain multiplier when the timing delay is sufficiently less than a central value within the effective control range.

[0009] The bandwidth control system can be configured to increment the control gain multiplier at timepoints when the bandwidth is moving toward but not reaching the bandwidth target and decrement the control gain multiplier at timepoints when the bandwidth is moving away from the bandwidth target. The bandwidth control system is further configured to modify the control gain multiplier in response to a magnitude of the timing delay. The bandwidth control system can be configured to modify the control gain multiplier in response to a magnitude, change of magnitude, and / or change of direction of the timing delay. The bandwidth control system is further configured to modify the control gain multiplier in response to a magnitude, a change of magnitude and / or a change of direction of the bandwidth error. The bandwidth control system is further configured to increase the control gain multiplier in response to a larger magnitude of the timing delay and decrease the control gain multiplier in response to a smaller magnitude of the timing delay. The bandwidth control systemcan be configured to make changes to operating parameters of the laser system in response to requested or planned changes to the laser system and / or to the operation of the laser system. The bandwidth control system is further configured to make the changes independently of adjusting the timing delay and modifying the control gain multiplier.

[0010] According to an additional aspect, a method of operating a laser system that is configured to provide a train of optical pulses includes: producing an optical pulse in an oscillator gain medium; producing an amplification energy during an amplification period in an amplifier gain medium optically connected to the oscillator gain medium to receive and amplify the pulse from the oscillator gain medium; adjusting a timing delay between the optical pulse production and the amplification period based on (1) a measured bandwidth error of light emitted from the amplifier gain medium and (2) a control gain multiplier; and modifying the control gain multiplier in response to the measured bandwidth error.

[0011] Implementations can include one or more of the following.

[0012] Modifying the control gain multiplier can include incrementally modifying the control gain multiplier between subsequent pulses in the train of optical pulses. Modifying the control gain multiplier can include modifying the control gain multiplier in response to the relative position of the timing delay within the effective control range. Modifying the control gain multiplier can include modifying the control gain multiplier by increasing the control gain multiplier when the timing delay is greater than a central value within the effective control range and decreasing the control gain multiplier when the timing delay is less than a central value within the effective control range.

[0013] Modifying the control gain multiplier can include incrementing the control gain multiplier when the bandwidth is moving toward but not reaching the bandwidth target and decrement the control gain multiplier when the bandwidth is moving away from the bandwidth target. Modifying the control gain multiplier can include modifying the control gain multiplier in response to a magnitude of the timing delay. Modifying the control gain multiplier can include modifying the control gain multiplier in response to a magnitude, change of magnitude, and / or change of direction of the timing delay.

[0014] Modifying the control gain multiplier can include modifying the control gain multiplier in response to a magnitude, a change of magnitude and / or a change of direction of the bandwidth error. Modifying the control gain multiplier can include increasing the control gain multiplier in response to a larger magnitude of the timing delay and decreasing the control gain multiplier in response to a smaller magnitude of the timing delay.

[0015] In an additional aspect, a laser system configured to provide a train of optical pulses includes: an oscillator configured to produce an optical pulse in a first gain medium; an amplifier optically connected to the oscillator to receive the pulse from the oscillator and configured to amplify the pulse in a second gain medium during an amplification period; a bandwidth control system configured toadjust a timing delay between a production of the pulse in the oscillator and the amplification period in the amplifier based on (1) a measured bandwidth error of light emitted from the amplifier and (2) a control gain multiplier, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to a measured bandwidth of light emitted from the amplifier, a target bandwidth, or a combination thereof.

[0016] Implementations can include one or more of the following.

[0017] The bandwidth control system can be configured to modify the control gain multiplier by using as the control gain multiplier or a part thereof a value proportional to an inverse slope of a nonlinear bandwidth vs timing delay curve or an approximation thereof, at the measured bandwidth of light emitted from the amplifier, the target bandwidth, or a value therebetween. The bandwidth control system can be further configured to modify the control gain multiplier in response to the measured bandwidth error.

[0018] In an additional aspect, a method of operating a laser system that is configured to provide a train of optical pulses includes: producing an optical pulse in an oscillator gain medium; producing an amplification energy during an amplification period in an amplifier gain medium optically connected to the oscillator gain medium to receive and amplify the pulse from the oscillator gain medium; adjusting a timing delay between production of the optical pulse and the amplification period based on (1) a measured bandwidth error of light emitted from the amplifier gain medium and (2) a control gain multiplier; and modifying the control gain multiplier in response to a measured bandwidth of light emitted from the amplifier, a target bandwidth, or a combination thereof.

[0019] Implementations can include one or more of the following.

[0020] Modifying the control gain multiplier in response to a measured bandwidth of light emitted from the amplifier, a target bandwidth, or a combination thereof can include using as the control gain multiplier or a part thereof a value proportional to an inverse slope of a nonlinear bandwidth vs timing delay curve or an approximation thereof, at the measured bandwidth of light emitted from the amplifier, the target bandwidth, or a value therebetween. Modifying the control gain multiplier can further include modifying the control gain multiplier in response to the measured bandwidth error.

[0021] Further aspects, implementations, features, and advantages of the subject matter of the present disclosure, as well as the structure and operation of the various implementations, are described in detail below with reference to the accompanying drawings.BRIEF DESCRIPTION OF DRAWINGS

[0022] The accompanying drawings, which are incorporated herein and form part of the specification, illustrate the presently disclosed subject matter and, together with the description, further serve to explain the principles of the presently disclosed subject matter and to enable a person skilled in the relevant art to make and use the presently disclosed subject matter.

[0023] FIG. 1 is a diagram of an exposure system in which or with which certain aspects of the present disclosure can be implemented.

[0024] FIG. 2 is a diagram of a light source for an exposure system in which or with which certain aspects of the present disclosure can be implemented.

[0025] FIGS. 3A and 3B are graphs illustrating a delay between a discharge in an oscillator and a discharge in an associated amplifier.

[0026] FIG. 4 is a graph illustrating a variation of a laser bandwidth as a function of a delay between a discharge in an oscillator and a discharge in an associated amplifier.

[0027] FIG. 5 is a flow diagram process or method illustrating one or more aspects the present disclosure.

[0028] FIG. 6 is a graph of a simulated performance of an implementation a method and / or apparatus of the present disclosure.

[0029] Further features and advantages of the presently disclosed subject matter, as well as the structure and operation of various implementations of the presently disclosed subject matter, are described in detail below with reference to the accompanying drawings. It is noted that the scope of this disclosure is not limited to the specific implementations explicitly described herein. Such implementations are included herein for illustrative purposes only. Additional implementations will be apparent to persons skilled in the relevant art based on the teachings presented herein.DESCRIPTION

[0030] Various implementations are now described with reference to the drawings, wherein like reference numerals are used to refer to like elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to promote a thorough understanding of one or more implementations. It may be evident after reviewing this disclosure that in some or all instances any implementation described below can be practiced without adopting the specific design details described below. In some instances, well-known structures and devices are shown in block diagram form in order to facilitate description of one or more implementations.

[0031] Systems such as those described herein may render benefits in a wide range of applications and implementations. For the sake of having a specific nonlimiting example to facilitate description, one such application is in semiconductor photolithography. Also, the following examples are in terms of a system for producing radiation in the deep ultraviolet (DUV) portion of the electromagnetic spectrum that is, light having a wavelength in a range of about 100 nanometers (nm) to about 400 nm. It will be apparent, however, that the principles elucidated herein may also be applied to systems that produce radiation in other portions of the spectrum, for example, the extreme ultraviolet (EUV) portion of the spectrum, that is, having a wavelength in a range of about 5 nm to 20 nm.

[0032] One system for generating laser radiation at frequencies useful for semiconductor photolithography (deep-ultraviolet (DUV) wavelengths) involves use of a Master Oscillator PowerAmplifier (MOPA) dual -gas-discharge-chamber configuration. In such architectures, a pulse of light is generated in a laser oscillator component, the master oscillator (MO), that is configured to provide a high degree of control over spectral characteristics of the pulse. The pulse is then transmitted to a laser amplifier component, the power amplifier (PA), that is configured to provide efficient amplification of the pulse. Bandwidth in such a configuration is often managed in part by using a fast bandwidth actuator that adjusts the relative timing of electrical discharges in the power amplifier and electrical discharges in the master oscillator. This adjustment of the relative discharge timing can be used to control bandwidth of the amplified pulse. This relative timing is often variously referred to as MOPA timing, AtMOPA, or DtMOPA. These shorthand notations are used herein as a shorthand for any differential timing control of the firing of the discharges in an oscillator or seed laser, such as the MO, and an amplifier, such as the PA or a power oscillator (PO), or other amplifier configuration, and are not necessarily limited to a specific configuration such as a MOPA configuration. Such a fast bandwidth actuator is disclosed, for example, in U. S. Patent No. 7,822,084, issued October 26, 2010 and titled “Method and Apparatus for Stabilizing and Tuning the Bandwidth of Laser Light,” and in U. S. Patent No. 7,830,934, issued November 9, 2010 and titled “Multi-chamber gas discharge laser bandwidth control through discharge timing,” both of which are herein incorporated by reference. A fast bandwidth actuator employing DtMOPA is generally implemented as a feedback -based controller to control for bandwidth disturbances of whatever source or cause, including random and / or unknown-cause fluctuations, preferably at a high repetition rate, such as repeating with every individual pulse of the laser within a burst of pulses.

[0033] Some changes to laser operating conditions, such as changes to pulse repetition rate, pulse energy target, bandwidth target, wavelength and / or others, can in some cases temporarily drive laser bandwidth out of desired limits even with feedback -based DtMOPA control in operation. Also, some known or intentional changes to laser operating conditions can also shift the DtMOPA feedback-based control process or system out of its effective control window. Changes to operating conditions such as these can be handled by feed-forward techniques that pre-adapt or pre-adjust the laser system and the for known or planned system changes. Feed-forward techniques for such known changes can operate in cooperation and / or in parallel with bandwidth control or stabilization through feedback -based control of DtMOPA. An example of a feed-forward system and method used for compensating bandwidth (and / or other) effects of known or planned system changes is disclosed, for example, in U. S. Patent No. 10,833,471, issued November 10, 2020, and titled “Lithography System Bandwidth Control”, the entire specification of which is hereby incorporated by reference. Control of bandwidth through DtMOPA feedback can also drift over time out of the effective control window. Changes such as, among others, changes to positions of optical elements, changes to discharge voltages, changes to gas composition in the discharge chamber, can bring a target bandwidth back into the control window. Changes to the position of one or more optical elements are often used for this purpose.

[0034] In the present disclosure, bandwidth control or stabilization through feedback -based control of DtMOPA (the timing delay between an electrical discharge in the oscillator and an electrical discharge in the amplifier) is provided using a non-constant gain (gain multiplier), or a gain (gain multiplier) that is modified based on a bandwidth error. Use of the non-constant gain as described in more detail below allows a faster recovery from random departures of the laser system from a target bandwidth, resulting in improved bandwidth control and in a narrower average bandwidth over time (due to reduction in the duration of excursions away from the bandwidth target). Before describing specific techniques of the present disclosure in more detail, an example environment will be described in which embodiments of the present disclosure may be implemented.

[0035] Referring to FIG. 1, an exposure system 100 includes a system controller 118, an output apparatus or exposure apparatus controller 116, and a light source system 102, such as a laser system, that produces a pulsed light beam 104. The pulsed light beam 104 may is directed to an exposure apparatus 106 such as stepper / scanner and / or a metrology tool that measures and analyzes critical dimensions on a wafer 110 with high precision. The exposure apparatus 106 operates to pattern features and / or precisely measure features on the wafer 110 using the pulsed light beam 104. In the exposure system 100, the components within the light source system 102 (as discussed and shown in FIG. 2 below), in combination with the components of an optical system 108 of the exposure apparatus 106, will determine the parameters of the light beam 104 at the wafer 110, and thereby influence the parameters of the features patterned, and / or the capabilities of the inspections performed, on the wafer 110 by the exposure apparatus 106.

[0036] FIG. 2 is a functional block diagram of an example configuration of a light source system 202 that can be used as the light source system 102 of FIG. 1. FIG. 2 shows a DUV light source 202 in the form of a DUV gas-discharge pulsed laser system. In some embodiments, the DUV light source 202 produces a pulsed beam 204 that can serve as the light beam 104 of FIG. 1. FIG. 2 shows a two-chamber laser system including a seed laser stage 220, such as a solid state or gas discharge master oscillator, and a power amplification stage 240, such as a single-pass power amplifier (“PA”), a power ring amplifier (“PRA”), or a power oscillator (“PO”). Single chamber systems and systems with three or more chambers can also be used. The DUV light source 202 further includes relay optics 230, and an output subsystem 250.

[0037] The seed laser stage 220 may include, e.g., a master oscillator (“MO”) chamber 224 which includes a pair of electrodes 223 and 225. The seed laser stage 220 may also include a master oscillator output coupler (“OC”) 228, which may comprise a partially reflective mirror (not shown), that forms, together with a reflective grating (not shown) in a line narrowing module (“LNM”) 222, an oscillator (optical cavity) in which a beam oscillates to form a seed laser output pulse. The seed laser stage 220 may also include a first spectrum analysis module 226. The relay optics 230 may include an MO wavefront engineering box (“WEB”) 232 that may serve to redirect the output of theseed laser stage 220 toward the power amplification stage 240, and may include a multi prism beam expander (not shown) and an optical delay path (not shown).

[0038] The power amplification stage 240 may include, for example, a power amplifier discharge chamber 244. The power amplifier discharge chamber 244 may include a pair of electrodes 243 and 245. The power amplifier discharge chamber 244 may be part of an oscillator. The oscillator may be formed or defined by (1) seed-beam injection and output coupling optics (not shown) that may be incorporated into a PRA wavefront engineering box (“PRA WEB”) 248 and (2) a beam reverser (“BR”) 242. The PRA WEB 248 may incorporate a partially reflective input / output coupler (not shown) and a maximally reflective mirror for the nominal operating wavelength (e.g., at around 193 nm for an ArF system) and one or more prisms. The PRA WEB 248 passes a portion of the power it receives to the output subsystem 250 as a beam 249.

[0039] In the output subsystem 250, a second spectrum analysis module 252 may receive the light beam and pick off a portion of the light beam for metrology purposes, e.g., to measure the output bandwidth and pulse energy. The laser light beam 249 of pulses then passes to an optical pulse stretcher (“OPuS”) 254, and then to an autoshutter, both within the output subsystem 250. In the implementation of the output subsystem 250 shown in FIG. 2, the autoshutter is in the form of, or included within, a combined autoshutter metrology module (“CASMM”) 256, which may also include a pulse energy meter. Alternatively, a separate pulse energy meter (not shown) may be provided separately from, or in the absence of, the CASMM 256.

[0040] The power amplifier discharge chamber 244 and the MO discharge chamber 224 are configured as chambers in which electrical discharges between the electrodes create an inverted population of high energy molecules, for example, excimers or exciplexes of Ar, Kr, F2, and / or Xe to produce a relatively broad-band light amplification potential. The wavelength(s) that are permitted to oscillate, and accordingly receive significant amplification, can be line-narrowed to a relatively very narrow bandwidth around a center wavelength selected by adjustments made in the LNM 222. In addition to selecting a center wavelength, adjustments made in the LNM can provide fine- and coarse-step bandwidth adjustments to “de-saturate” or restore flexibility to the bandwidth control system when adjustments to DtMOPA are near a limit of adjustability.

[0041] FIGS. 3A and 3B are diagrammatic graphical representations showing the effective temporal overlap of the energy 358 of an oscillator-produced light pulse and an amplification energy 360 in an amplifier optically connected downstream of the oscillator, over time. (Energy E and time t are represented in arbitrary units, and the curves are for illustration purposes and are not to scale or relative scale, nor intended as representative of specific energy profiles.) In FIG. 3A, a short DTMOPA or short amplifier timing delay essentially matches the time of travel of light from the oscillator to the amplifier, effectively shifting the time envelope or amplification period of the amplification energy from a hypothetical temporal position with no delay (360o, dotted curve) to the position shown in the energy curve 360, essentially temporally overlapping with the energy 358 of theoscillator pulse. In the case of energy curve 360 of FIG. 3 A, all or most of the energy 358 of the optical pulse produced by the oscillator will be subject to amplification in the amplifier. In contrast, FIG. 3B shows a larger (longer) DtMOPA or larger (longer) amplifier timing delay, resulting in a temporal offset in the amplifier of light pulse from the oscillator, or the energy 358 of the light pulse from the oscillator, and the energy 360 in the amplifier during the amplification period. The effect of the longer DtMOPA, by displacing or delaying in time the amplification period when the energy 360 is present in the amplifier, relative pulse from the oscillator or the energy 358 of the pulse from the oscillator, is that only the portion of a light pulse from the oscillator in the temporal overlap region 362 is present in the amplifier during a time when the amplifier amplifies incoming light. Thus, only the trailing portion of the light pulse from the oscillator will be amplified.

[0042] Light produced in the latter part of the oscillator discharge (light in the latter part or trailing part of the pulse) experiences on average a proportionally higher number passages through a linewidth-controlling or line-width narrowing device, such as LNM 222 of FIG. 2, before exiting the oscillator. Accordingly, the light produced by the oscillator during a relatively latter part of the oscillator discharge has relatively narrower bandwidth compared to light produced in a relatively earlier part of the oscillator discharge. Adjusting DtMOPA selects the temporal portion of the light pulse from the oscillator that will be amplified to produce light emitted from the amplifier. Thus bandwidth B of a pulse emerging from the amplifier varies with DtMOPA — generally as illustrated in FIG. 4. FIG. 4 represents a smoothed approximation of atypical bandwidth as a function of DtMOPA curve, with bandwidth measured as the wavelength range containing 95% of the total energy of the measured light, referred to as E95 bandwidth or E95. As shown in FIG. 4, E95 bandwidth as a function of DtMOPA is nonlinear, with a decreasing negative slope as DtMOPA increases. Other measures of bandwidth can also be used, if desired, such as FWHM (full width at half maximum) and CBW (convolved bandwidth, see, e.g., W02023101807A2, “Determination of a Property of an Exposure Light Beam,” published on June 8, 2023, for reference). Note that use of CBW for bandwidth measurement or estimation can also result in a nonlinear variation of bandwidth as a function of DtMOPA, and the curve and its nonlinearities may differ from FIG. 4.

[0043] A bandwidth control system according to the present disclosure can be implemented, for example, in a controller such as the system controller 118 of FIG. 1 or in another controller of or associated with the laser system 202 of FIG. 2. The bandwidth control system adjusts the timing delay (DtMOPA) between production of a pulse in the oscillator and the amplification period in the amplifier. This can be performed by adjusting the time period between an electrical discharge in a gaseous medium in the oscillator and an electrical discharge in a gaseous medium in the amplifier. More generally, such as in implementations where one or more of the stages uses a gain excitation system other than electrical discharge, the bandwidth control system adjusts the timing delay between a timing trigger in the oscillator triggering pulse production in the oscillator and a timing trigger in the in the amplifier triggering the amplification period in the amplifier. The delay is adjusted based on ameasured bandwidth error of light emitted from the amplifier and a control gain multiplier. The bandwidth control system is further configured to modify the control gain multiplier in response to the measured bandwidth error. The bandwidth of the light emitted from the amplifier is measured, for example, by a measurement device such as the spectrum analysis module 252 of FIG. 2, and compared to target value to determine the measured bandwidth error.

[0044] To determine a new DtMOPA value in response to the bandwidth error, instead of a fixed gain multiplier to multiply the measured bandwidth error, a variable, or modifiable, gain multiplier is used, or in other words, a non-constant gain term is used. For example, a variety of gain values or gain curves can be used model or otherwise represent or approximate the nonlinear behavior in FIG. 4, depending on factors such as one or more recently measured bandwidth error values, one or more recent values of DtMOPA used for laser pulses, a recent rate of convergence to a desired bandwidth, a previously scanned or otherwise determined and stored curve of bandwidth vs. DtMOPA, or other parameters relating to a history of preceding pulses in a laser system. This can take one or more of various forms.

[0045] In one implementation, for example, the control gain multiplier can be modified at least in part in response to a measured bandwidth of light emitted from the amplifier, a target bandwidth, or a combination thereof. This can take the form of using as or as part of the control gain multiplier the value of, or a value proportional to, an inverse slope of a (nonlinear) bandwidth vs timing delay curve or an approximation thereof, at the measured bandwidth of light emitted from the amplifier, at the target bandwidth, or a value (such as an average of the two) in between. A piecewise-linear approximation, in which various constant slope values are assigned to bandwidth subdivisions of the approximated curve, is one example approximation of a bandwidth vs timing delay curve.

[0046] In another implementation, the gain can be incremented each time the bandwidth is moving toward the bandwidth target but not yet reaching (or exceeding) it, and decremented each time the bandwidth is currently moving away from (i.e., has crossed and is going away from) the target. This effectively increases the gain when bandwidth is further from the bandwidth target and decreases the gain when bandwidth is close to the bandwidth target. An example implementation of this technique can be expressed as set forth below.

[0047] For comparison and contrast, a commonly used “plant model” or model equation for MOPA bandwidth as a function of DtMOPA is given byBWMOPA= KMOPA* DtMOPA[k] + BWoffsetEquation (1)where DtMOPA[k] is the control variable at time (or instance) k and KMOPAis the variation in bandwidth as a function of DtMOPA (i.e., the average or assumed slope of the bandwidth curve of FIG. 4). The DtMOPA controller or control variable is then commonly given byDtMOPA[k] = DtMOPA[k - 1] + (BWM0PA[k - BWt arg et)KACTKASCEquation (2)Where DtMOPA[k] is the currently assigned value of DtMOPA, DtM0PA[k — 1] is the one-step or one-instance previous value, BWM0PA[k] is the current measured bandwidth, BWtargetis the target bandwidth, KACTis the inverse of KMOPA, and KASCis a fixed positive constant < 1 moderating the control response, with the product of both together (KACTKASC) functioning as the gain multiplier for the control variable DtM0PA[k], The technique of the present disclosure, in contrast, is to use a variable gain multiplier in place of a constant one. In one implementation, this can take the form KASCM, given as follows:KAsc[k] = sign BWM0PA[k] - BWtarget) * sign(DtMOPA[k] - DtM0PA[k - 1]) * AddGain + ScaleFactor * KASC[k — 1] Equation (3)where sign(a) = 1 if a > 0, sign(a)= -1 if a < 0, and sign(a) = 0 if a =0), AddGain is a constant value (but can also be a variable value similar to KASC) added to or subtracted from the previous KASC(or not) depending on the values of the sign functions, the magnitude of AddGain also determines how quickly KASCcan adapt in real time and ScaleFactor serves as a trust weight, in this setup, a fixed value is commonly used and is <=1 (but it can also be a variable value similar to KASC). a larger value of ScaleFactor effectively means more trust is given to the previous information for KASCadaptation. A specific instance, with AddGain of 0.25 and ScaleFactor of 1 is given byKASCW = sign(BWM0PA[k - BWtarget) * sign(DtMOPA[k] - DtMOPA[k - 1]) * 0.25 + KASC[k — 1] Equation (4)Note that sign(DtMOPA[k] — DtMOPA[k — 1]) is simply the sign of the most recent change, if any, in DtMOPA, in other words, the sign of d(DtMOPA) / dt, and sign(BWMOPA[k] — BWtarget) is simply the sign of the current error in the bandwidth. Other values of AddGain are also contemplated, depending on the implementation of the procedure, such as values of 0.01, 0.05, 0.10. 0.4, 0.5, 0.7, 1.0, 2.0, 5.0, or values therebetween. Values for KASCon startup or initiation of the controller can be set at 0.2, 0.4, 0.5, 0.6, 0.8, 0.9, 0.95, 0.99, or 1.0, or values therebetween, depending on the implementation of the procedure. As indicted above, KASCis a variable whose value evolves over time, from one iteration of the control lop to the next. In the above example, with AddGain and ScaleFactor are fixed values. In other implementations of a control system, AddGain and / or ScaleFactor are variables whose values evolve overtime.

[0048] An implementation of the controller according to the present disclosure then becomes (Equation 4 into Equation 2):DtMOPA[k] = DtMOPA[k - 1] + (BWM0PA[k - BWtarget) * KACT* KASC[k]Equation (5)in which the variable value of KASC[k] results in a variable gain factor KACT*The result during operation is to increase the gain multiplier (KACT* KASC[Ar] ) when the bandwidth is further from the target (and not reaching it immediately) and to decrease the gain multiplier when the bandwidth is close to (i.e., repeatedly crossing) the target.

[0049] As mentioned above, the dependence of bandwidth, measured as E95 bandwidth, on DtMOPA is non-linear, as shown in FIG. 4. And this dependence can be nonlinear, but with curves different from that of FIG. 4, when bandwidth is measured by other standards or techniques. In an additional aspect or implementation of the present disclosure, feedback control using a non-constant gain can use the non-constant gain to reflect or match, or at least partially reflect or match, the nonlinearity of the bandwidth response curve, for example, with the following controller implementation:DtMOPA[k] = DtMOPA[k - 1] + (BWMOPA[k] - BWtarget) * KACT[k] * KASC[k]Equation (6)where KACT[k] is a variable or non-constant expression of the reciprocal slope of the bandwidth response curve (e.g., the reciprocal slope of the curve of FIG. 4), at the current or immediately previous DtMOPA. KACT[k] can determined or approximated in a number of ways. For example, the curve of bandwidth vs. DtMOPA or the slope thereof can be scanned and stored periodically at nonproductive times of laser operation. KACT[k] for a given DtMOPA[k] can also be approximated by be given by DtM0PA[k] — DtMOPA[k — 1] ) / (BWM0PA[k] — BWM0PA[k — 1]) for example. The effective result is that a larger gain will be applied where the bandwidth response is less sensitive (in the areas of shallow slope of FIG. 4, for example), closing the gap between the measured bandwidth and the target more quickly than otherwise, and a smaller gain will be applied where the bandwidth response is more sensitive, closing the gap between the measured bandwidth and the target more slowly than otherwise, reducing the likelihood of excessively overshooting the target.

[0050] In the implementation illustrated in Equation 6 above, the variability of the gain (KACT[k] * KASC[k]) is provided by variability in both terms, KACT[k] andl’qanother implementation, the gain factor can be given by / crlT * ASCnqwhich KASCis a constant, and the variability of the gain is provided only by KACT[fc].

[0051] FIG. 5 is a flow diagram of a process or method M500 according to an aspect of the present disclosure. The method includes producing first electrical discharges in an oscillator gain medium and second electrical discharges in an amplifier gain medium optically connected to receive light from the oscillator gain medium (S510), adjusting a timing delay between the first electrical discharges and thesecond electrical discharges based on (1) a measured bandwidth error of light emitted from the amplifier gain medium and (2) a control gain multiplier (S520), and modifying the control gain multiplier in response to the measured bandwidth error (S530).

[0052] It will be appreciated that various ways and methods of modifying the control gain multiplier have been disclosed and discussed above, including incrementally modifying the control gain multiplier between subsequent pulses in the train of optical pulses produced by the discharges.

[0053] The control gain multiplier can also be modified in response to the relative position of the timing delay within the effective control range, such as when a variable KACTis used as in Equation 6 above, or similarly by increasing the control gain multiplier when the timing delay is greater than a central value within the effective control range and decreasing the control gain multiplier when the timing delay is less than a central value within the effective control range or simply modifying the timing delay in response to the magnitude of the timing delay. These methods can compensate or partially compensate for a nonlinear bandwidth vs. timing delay relationship, as discussed above. Not only the magnitude of the timing delay, but also the change of magnitude, and / or change of direction of the timing delay can be used. Magnitude, change of magnitude, and / or change of direction of bandwidth error can also be used.

[0054] The control gain multiplier can also be modified by incrementing the control gain multiplier when the bandwidth is moving toward but not reaching the bandwidth target and decrement the control gain multiplier when the bandwidth is moving away from the bandwidth target, as reflected in Equation 4 above (and Equations 5 and 6 which incorporate the effects of Equation 4).

[0055] FIG. 6 shows traces of simulated error signals in a bandwidth control loop after a disturbance using a variable gain multiplier as disclosed herein, such as in Equations 4, 5, and / or 6 above, (trace 672) and using a constant gain multiplier (trace 670). Units on the left axis are units of measured bandwidth error relative to bandwidth target in femtometers (fin). Units on the bottom axis are in number of bandwidth measurements (one per pulse measurements, in this case). As may be seen from the traces 670 and 672, with a variable gain multiplier as disclosed herein, the bandwidth error recovers more quickly, with the difference in performance manifested by the area 674 between the initial part of the traces 670, 672. The performance after initial recovery is essentially indistinguishable, but the advantage in initial recovery, though short, is significant in that the average bandwidth over time, which involves recovering from frequent random disturbances, can be significantly reduced by the improved control evidenced in the figure.

[0056] Based on the teachings contained in this disclosure, it will be apparent to persons skilled in the relevant art(s) how to make and use implementations of this disclosure using data processing devices, computer systems and / or computer architectures other than that shown in FIG. 5. In particular, implementations may operate with software, hardware, and / or operating system implementations other than those described herein.

[0057] Although specific reference may have been made above to the use of implementations in the context of optical lithography, it will be appreciated that implementations may be used in other applications, for example imprint lithography, and where the context allows, is not limited to optical lithography.

[0058] It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by those skilled in relevant art(s) in light of the teachings herein.

[0059] It is to be appreciated that the Detailed Description section is intended to be used to interpret the claims. The Summary and Abstract sections may set forth one or more but not all exemplary contemplated implementations, and thus, are not intended to limit the implementations and the appended claims in any way.

[0060] The implementations have been described above with the aid of functional building blocks illustrating the implementation of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions are appropriately performed.

[0061] The foregoing description of the specific implementations will so fully reveal the general nature of the implementations that others can, by applying knowledge within the skill of the art, readily modify and / or adapt for various applications such specific implementations, without undue experimentation, without departing from the general concept of the implementations. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed implementations, based on the teaching and guidance presented herein.

[0062] The above description includes examples of multiple implementations. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the these implementations, but one of ordinary skill in the art may recognize that many further combinations and permutations of various implementations are possible. Accordingly, the described implementations are intended to embrace all such alterations, modifications, and variations that fall within the spirit and scope of the appended claims. Furthermore, although elements of the described aspects and / or implementations may be described or claimed in the singular, the plural is contemplated unless limitation to the singular is explicitly stated. Additionally, all or a portion of any aspect and / or implementation may be utilized with all or a portion of any other aspect and / or implementation, unless stated otherwise.

[0063] The implementations can be further described using the following clauses.1. A laser system configured to provide a train of optical pulses, including: an oscillator configured to produce an optical pulse in a first gain medium; an amplifier optically connected to the oscillator to receive the pulse from the oscillator and configured to amplify the pulse in a second gain medium during an amplification period; a bandwidth control system configured to adjust a timing delaybetween a production of the pulse in the oscillator and the amplification period in the amplifier based on (1) a measured bandwidth error of light emitted from the amplifier and (2) a control gain multiplier, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to the measured bandwidth error.2. The laser system of clause 1, wherein the bandwidth control system is configured to incrementally modify the control gain multiplier between subsequent pulses in the train of optical pulses.3. The laser system of clause 1, wherein the bandwidth control system is further configured to recenter the timing delay within an effective control range when the timing delay is displaced from the center of the effective control range by more than a pre-specified amount of the distance to the edge of the effective control range.4. The laser system of clause 1, wherein the bandwidth control system is further configured to recenter the timing delay within an effective control range when the timing delay is displaced from the center of the effective control range by more than 60% of the distance to the edge of the effective control range.5. The laser system of clause 3, wherein the bandwidth control system is further configured to recenter the timing delay by changing a parameter or parameters of the laser system, other than the timing delay, affecting a bandwidth of the light emitted from the amplifier.6. The laser system of clause 5, wherein the parameter includes one or more of (1) the position and / or orientation a stepper-controlled optical element within the optical path of the laser system (2) a voltage used to produce electrical discharges in the first gain medium; (3) a voltage used to produce electrical discharges in the second gain medium; (4) an amount or a percentage of a halogen gas in the first gain medium; (5) an amount or a percentage of a halogen gas in the second gain medium.7. The laser system of clause 1, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to the relative position of the timing delay within the effective control range.8. The laser system of clause 7, wherein the bandwidth control system is further configured to modify the control gain multiplier by increasing the control gain multiplier when the timing delay is sufficiently greater than a central value within the effective control range and decreasing the control gain multiplier when the timing delay is sufficiently less than a central value within the effective control range.9. The laser system of clause 1, wherein the bandwidth control system is further configured to increment the control gain multiplier at timepoints when the bandwidth is moving toward but not reaching the bandwidth target and decrement the control gain multiplier at timepoints when the bandwidth is moving away from the bandwidth target.10. The laser system of clause 1, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to a magnitude of the timing delay.11. The laser system of clause 1, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to a magnitude, change of magnitude, and / or change of direction of the timing delay.12. The laser system of clause 1, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to a magnitude, a change of magnitude and / or a change of direction of the bandwidth error.13. The laser system of clause 1, wherein the bandwidth control system is further configured to increase the control gain multiplier in response to a larger magnitude of the timing delay and decrease the control gain multiplier in response to a smaller magnitude of the timing delay.14. The laser system of clause 1, wherein the bandwidth control system is further configured to make changes to operating parameters of the laser system in response to requested or planned changes to the laser system and / or to the operation of the laser system.15. The laser system of clause 14, wherein the bandwidth control system is further configured to make the changes independently of adjusting the timing delay and modifying the control gain multiplier. 16. A method of operating a laser system configured to provide a train of optical pulses, the method including: producing an optical pulse in an oscillator gain medium; producing an amplification energy during an amplification period in an amplifier gain medium optically connected to the oscillator gain medium to receive and amplify the pulse from the oscillator gain medium; adjusting a timing delay between the optical pulse production and the amplification period based on (1) a measured bandwidth error of light emitted from the amplifier gain medium and (2) a control gain multiplier; and modifying the control gain multiplier in response to the measured bandwidth error.17. The method of clause 16, wherein modifying the control gain multiplier includes incrementally modifying the control gain multiplier between subsequent pulses in the train of optical pulses.18. The method of clause 16, wherein modifying the control gain multiplier includes modifying the control gain multiplier in response to the relative position of the timing delay within the effective control range.19. The method of clause 18, wherein modifying the control gain multiplier includes modifying the control gain multiplier by increasing the control gain multiplier when the timing delay is greater than a central value within the effective control range and decreasing the control gain multiplier when the timing delay is less than a central value within the effective control range.20. The method of clause 16, wherein modifying the control gain multiplier includes incrementing the control gain multiplier when the bandwidth is moving toward but not reaching the bandwidth target and decrement the control gain multiplier when the bandwidth is moving away from the bandwidth target.21. The method of clause 16, wherein modifying the control gain multiplier includes modifying the control gain multiplier in response to a magnitude of the timing delay.22. The method of clause 16, wherein modifying the control gain multiplier includes modifying the control gain multiplier in response to a magnitude, change of magnitude, and / or change of direction of the timing delay.23. The method of clause 16, wherein modifying the control gain multiplier includes modifying the control gain multiplier in response to a magnitude, a change of magnitude and / or a change of direction of the bandwidth error.24. The method of clause 16, wherein modifying the control gain multiplier includes increasing the control gain multiplier in response to a larger magnitude of the timing delay and decreasing the control gain multiplier in response to a smaller magnitude of the timing delay.25. A laser system configured to provide a train of optical pulses, including: an oscillator configured to produce an optical pulse in a first gain medium; an amplifier optically connected to the oscillator to receive the pulse from the oscillator and configured to amplify the pulse in a second gain medium during an amplification period; a bandwidth control system configured to adjust a timing delay between a production of the pulse in the oscillator and the amplification period in the amplifier based on (1) a measured bandwidth error of light emitted from the amplifier and (2) a control gain multiplier, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to a measured bandwidth of light emitted from the amplifier, a target bandwidth, or a combination thereof.26. The laser system of clause 25, wherein the bandwidth control system is configured to modify the control gain multiplier by using as the control gain multiplier or a part thereof a value proportional to an inverse slope of a nonlinear bandwidth vs timing delay curve or an approximation thereof, at the measured bandwidth of light emitted from the amplifier, the target bandwidth, or a value therebetween.27. The laser system of clause 25, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to the measured bandwidth error.28. A method of operating a laser system configured to provide a train of optical pulses, the method including: producing an optical pulse in an oscillator gain medium; producing an amplification energy during an amplification period in an amplifier gain medium optically connected to the oscillator gain medium to receive and amplify the pulse from the oscillator gain medium; adjusting a timing delay between production of the optical pulse and the amplification period based on (1) a measured bandwidth error of light emitted from the amplifier gain medium and (2) a control gain multiplier; and modifying the control gain multiplier in response to a measured bandwidth of light emitted from the amplifier, a target bandwidth, or a combination thereof.29. The method clause 28, wherein modifying the control gain multiplier in response to a measured bandwidth of light emitted from the amplifier, a target bandwidth, or a combination thereof includes using as the control gain multiplier or a part thereof a value proportional to an inverse slope of anonlinear bandwidth vs timing delay curve or an approximation thereof, at the measured bandwidth of light emitted from the amplifier, the target bandwidth, or a value therebetween.30. The method of clause 28, further including modifying the control gain multiplier in response to the measured bandwidth error.

[0064] The above-described implementations and other implementations are within the scope of the following claims.

Claims

CLAIMS1. A laser system configured to provide a train of optical pulses, the laser system comprising:an oscillator configured to produce an optical pulse in a first gain medium;an amplifier optically connected to the oscillator to receive the pulse from the oscillator and configured to amplify the pulse in a second gain medium during an amplification period;a bandwidth control system configured to adjust a timing delay between a production of the pulse in the oscillator and the amplification period in the amplifier based on (1) a measured bandwidth error of light emitted from the amplifier and (2) a control gain multiplier, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to the measured bandwidth error.

2. The laser system of claim 1, wherein the bandwidth control system is configured to incrementally modify the control gain multiplier between subsequent pulses in the train of optical pulses.

3. The laser system of claim 1, wherein the bandwidth control system is further configured to recenter the timing delay within an effective control range when the timing delay is displaced from the center of the effective control range by more than a pre-specified amount of the distance to the edge of the effective control range.

4. The laser system of claim 1, wherein the bandwidth control system is further configured to recenter the timing delay within an effective control range when the timing delay is displaced from the center of the effective control range by more than 60% of the distance to the edge of the effective control range.

5. The laser system of claim 3, wherein the bandwidth control system is further configured to recenter the timing delay by changing a parameter or parameters of the laser system, other than the timing delay, affecting a bandwidth of the light emitted from the amplifier.

6. The laser system of claim 5, wherein the parameter comprises one or more of (1) the position and / or orientation a stepper-controlled optical element within the optical path of the laser system (2) a voltage used to produce electrical discharges in the first gain medium; (3) a voltage used to produce electrical discharges in the second gain medium; (4) an amount or a percentage of a halogen gas in the first gain medium; (5) an amount or a percentage of a halogen gas in the second gain medium.

7. The laser system of claim 1, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to the relative position of the timing delay within the effective control range.

8. The laser system of claim 7, wherein the bandwidth control system is further configured to modify the control gain multiplier by increasing the control gain multiplier when the timing delay is sufficiently greater than a central value within the effective control range and decreasing the control gain multiplier when the timing delay is sufficiently less than a central value within the effective control range.

9. The laser system of claim 1, wherein the bandwidth control system is further configured to increment the control gain multiplier at timepoints when the bandwidth is moving toward but not reaching the bandwidth target and decrement the control gain multiplier at timepoints when the bandwidth is moving away from the bandwidth target.

10. The laser system of claim 1, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to a magnitude of the timing delay.

11. The laser system of claim 1, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to a magnitude, change of magnitude, and / or change of direction of the timing delay.

12. The laser system of claim 1, wherein the bandwidth control system is further configured to modify the control gain multiplier in response to a magnitude, a change of magnitude and / or a change of direction of the bandwidth error.

13. The laser system of claim 1, wherein the bandwidth control system is further configured to increase the control gain multiplier in response to a larger magnitude of the timing delay and decrease the control gain multiplier in response to a smaller magnitude of the timing delay.

14. The laser system of claim 1, wherein the bandwidth control system is further configured to make changes to operating parameters of the laser system in response to requested or planned changes to the laser system and / or to the operation of the laser system.

15. The laser system of claim 14, wherein the bandwidth control system is further configured to make the changes independently of adjusting the timing delay and modifying the control gain multiplier.

16. A method of operating a laser system configured to provide a train of optical pulses, the method comprising:producing an optical pulse in an oscillator gain medium;producing an amplification energy during an amplification period in an amplifier gain medium optically connected to the oscillator gain medium to receive and amplify the pulse from the oscillator gain medium;adjusting a timing delay between the optical pulse production and the amplification period based on (1) a measured bandwidth error of light emitted from the amplifier gain medium and (2) a control gain multiplier; andmodifying the control gain multiplier in response to the measured bandwidth error.

17. The method of claim 16, wherein modifying the control gain multiplier comprises incrementally modifying the control gain multiplier between subsequent pulses in the train of optical pulses.

18. The method of claim 16, wherein modifying the control gain multiplier comprises modifying the control gain multiplier in response to the relative position of the timing delay within the effective control range.

19. The method of claim 18, wherein modifying the control gain multiplier comprises modifying the control gain multiplier by increasing the control gain multiplier when the timing delay is greater than a central value within the effective control range and decreasing the control gain multiplier when the timing delay is less than a central value within the effective control range.

20. The method of claim 16, wherein modifying the control gain multiplier comprises incrementing the control gain multiplier when the bandwidth is moving toward but not reaching the bandwidth target and decrement the control gain multiplier when the bandwidth is moving away from the bandwidth target.

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