JP2012506634A - Method and apparatus for laser control in a two-chamber gas discharge laser - Google Patents

Abstract

The laser control system contains an oscillator gas chamber and an amplifier gas chamber. The first voltage input is operatively connected to deliver an electrical pulse to a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber. The output of the gas chamber is the energy dose calculated by the trapezoidal window. The control circuit is connected to the first voltage input to change the first voltage input. The feedback control loop communicates the gas chamber output to the control circuit to change the first voltage input.
[Selection] Figure 1

Description

  The disclosed subject matter relates generally to laser systems, and more specifically to laser control systems for two-chamber gas discharge lasers.

  FIG. 1 is an illustration of a block diagram of a MOPA (Master Oscillator / Power Amplifier) laser system 10 known in the prior art. The MOPA laser system 10 is used, for example, in the field of integrated circuit lithography. In one embodiment of the MOPA laser system 10, the 193 nm ultraviolet laser beam is input to a lithography machine / scanner 2 such as a stepper or scanner machine supplied by Canon or Nikon at a facility in Japan or by ASML at a facility in the Netherlands. Supplied at the port. The MOPA laser system 10 includes a laser energy control system 4 that controls both the pulse energy and stored dose energy output of the system at a pulse repetition rate of, for example, 4,000 Hz or greater. The MOPA laser system 10 provides a very accurate trigger of discharge relative to each other in two laser chambers using both pulse and dose energy feedback and feedforward control.

  The main components of the laser system 4 are often provided below the deck / floor 5 on which the scanner 2 is provided. However, the MOPA laser system 10 includes a beam delivery unit 6 that provides an enclosed beam path for delivering a laser beam to the input port of the scanner 2. The light source is a seed laser generator, such as a main oscillator 11, and an amplifier laser portion, such as a power amplifier 12 described in more detail below, and an oscillator, such as a power ring oscillator (also described in more detail below). PRA) can also be included. For convenience throughout this application, the seed laser may be referred to as an MO, and the amplifier laser may be referred to as a power amplifier or simply PA, together with other forms of seed laser configurations and in fact an oscillator, ie, a power oscillator, that form MOPO. (PO) is intended to include amplifier laser configurations such as power ring amplifiers (PRA), and unless expressly stated otherwise, these terms are intended to be defined in a very broad sense. Yes. The light source also includes a pulse stretcher 22.

  Each of the main oscillator 11 and the power amplifier / power oscillator 12 includes a discharge chamber 11A, 12A) that is similar to the discharge chamber of a single chamber lithography laser system. These chambers 11A, 12A contain two electrodes, laser gas, and a tangential that circulates the gas between the electrodes and the water-cooled finned heat exchanger. The main oscillator 11 oscillates in two passes through the power amplifier 12 in the PA configuration or in the PO / PRA in the PO / PRA configuration to generate the second laser beam 14B as shown in FIG. To generate a first laser beam 14A to be amplified. The main oscillator 11 includes a resonant cavity formed by the output coupler 11C and the line narrowing package 11B. The gain medium for the master oscillator 11 is generated between two elongated electrodes housed in the master oscillator discharge chamber 11A. The power amplifier 12 is basically a discharge chamber 12A, which in this preferred embodiment is almost exactly the same as the master oscillator discharge chamber 11A that provides a gain medium between the two electrodes, Unlike PO / PRA, it cannot have a resonant cavity. With this MOPRA configuration, the master oscillator 11 can be designed and operated to maximize beam quality parameters such as wavelength stability and ultra-narrow bandwidth, while the power ring amplifier 12 maximizes the power output. Designed and operated to do. For this reason, the MOPA laser system 10 represents a much higher quality and much higher power laser source than a single chamber system.

  As described above, the amplifier portion may be configured for oscillation, for example, for the passage of two beams through the discharge region of the amplifier discharge chamber or within the cavity that houses the amplifier discharge chamber as shown in FIG. it can. The beam oscillates in a cavity containing the main oscillating chamber 11A between the LNP 11B of the MO 11 and the output coupler 11C (having 30 percent reflectivity) and is strongly narrowed by passing through the LNP 10C. The wavelength of the laser beam emitted from the output coupler 11 </ b> C is measured by the line center portion analysis module 7. The line-narrowed seed beam is reflected downward by the mirror in the MO wavelength engineering box (MO WEB) 24 and is reflected horizontally and obliquely in a slightly distorted state (relative to the electrode orientation). (PA WEB) 26 to the amplifier chamber 12. At the rear end of the amplifier, the beam inverter 28 reflects the back of the beam horizontally in line with the electrode orientation for a second pass through the PA chamber 12 or towards oscillation in the PO / PRA chamber. The bandwidth of the laser emitted from the discharge chamber 12A is measured by the spectrum analysis module 9, but the laser bandwidth can be measured by the bandwidth analysis module instead.

  The laser system output beam pulse 14B passes from the PA / PO chamber 12A to the beam splitter 16. Beam splitter 16 reflects approximately 60 percent of power amplifier output beam 14B into the delay path created by four focusing mirrors 20A, 20B, 20C, and 20D. Forty percent of the transmitted portion of each pulse of beam 14B becomes the first hump of the corresponding stretched pulse of output beam pulse 14C. The output beam 14C is directed by the beam splitter 16 to a mirror 20A that focuses the reflected portion at point 22. The beam then expands and is reflected from mirror 20B, which converts the stretched beam into a parallel beam and directs it back to mirror 20C where it is refocused at point 22. This beam is then reflected by the mirror 20D, which, like the 20B mirror, converts the stretched beam into a light collimated beam and returns it to the beam splitter 16, where 60 percent of the first reflected light is The laser system output beam pulse is completely reflected in coincidence with the first transmitted portion of this pulse in the output beam 14C to be most of the second hump in the pulse. Forty percent of the reflected beam is transmitted through the beam splitter 16 and accurately follows the path of the first reflected beam to produce yet another smaller hump in the stretch pulse. The result is a complete output beam 14C stretched with a pulse length of about 20 ns to about 70 ns. The beam transmission unit (BDU) transmits the output beam 14C. The BDU can include two beam directing mirrors 40A, 40B, one or both of which can be controlled to provide tip and tilt correction for beam pointing variations.

  FIG. 2 is an illustration of an energy control block diagram 50 for the MOPA / MOPO laser system of FIG. 1 according to the prior art. FIG. 2 shows various control elements that control the voltage source 52 for the MOPA laser system 10. The energy control block diagram 50 includes a static controller 54 that supplies an essentially predetermined voltage that is expected to achieve the energy target 56 (no other effects to consider). If). Feedforward block 58 provides voltage adjustment based on trigger interval 60. The trigger interval 60 is used to calculate the number of iterations, number of firings, and duty cycle that affect the “voltage input-energy output” relationship. The amount of voltage adjustment is calculated as a function of these values. The energy servomechanism 62 adjusts the voltage input 52 based on the calculated voltage error 64 of the previous launch. The dither cancellation unit 66 adjusts the voltage so as to remove the energy change caused by the timing dither 68. Finally, the energy dither unit 70 provides a periodic signal that is added to the voltage input 52 that is used to estimate the effect of voltage on MO energy, output energy, and MOPA timing. These five voltage signals are added together to generate the voltage input 52. When the laser is fired, energy 72 is measured. The energy target is subtracted from the measured energy 72 to produce an energy error signal 74 scaled by dV / dE, ie, a laser estimate 76 of the derivative of the voltage with respect to energy. The resulting voltage error 64 is used to drive an adaptation algorithm 78, which adapts one of the voltage signals to minimize either energy error, dose error, energy sigma, or some combination thereof. Adjust the section.

  The MOPA laser system 10 shown in FIG. 1 is an improvement over a single chamber system that provides better beam control, beam power, and stability than a single chamber system. However, resolving system sound disturbances and further sharpening of timing and energy control can greatly improve operation.

  Aspects of embodiments of the disclosed subject matter provide systems and methods for controlling a laser system. Briefly described, in architecture, among other aspects aspects of one possible embodiment of the system can be implemented as follows. The system contains an oscillator gas chamber and an amplifier gas chamber. The first voltage input is operatively connected to deliver an electrical pulse to a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber. The output of the gas chamber is the energy dose calculated by the trapezoidal window. The control circuit is connected to the first voltage input to change the first voltage input. The feedback control loop communicates the gas chamber output to the control circuit to change the first voltage input.

  An aspect of the disclosed subject matter can also be viewed as providing a method of controlling a laser system. In this regard, an embodiment of such a method includes, among other things, a first voltage input in the form of an electrical pulse, a first pair of electrodes in an oscillator gas chamber and a second pair of electrodes in an amplifier gas chamber. , The step of calculating the energy dose at the output of the gas chamber using a trapezoidal window, the step of changing the first voltage input using a control circuit, and the changing of the first voltage input And communicating the output of the gas chamber to the control circuit using a feedback control loop to broadly summarize.

  Other systems, methods, features, and advantages of the disclosed subject matter will be or will become apparent to those skilled in the art upon examination of the following drawings and detailed description. All such additional systems, methods, features, and advantages are included in this description, are within the scope of the disclosed subject matter, and are intended to be protected by the following claims.

  Many aspects of the invention can be better understood with reference to the following drawings. The components in the drawings are not necessarily drawn to scale, but instead are exaggerated in clearly illustrating the principles of the disclosed subject matter. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.

1 is a block diagram of a MOPA / MOPRA laser system. 2 is an energy control block diagram for the MOPA / MOPRA laser system of FIG. 6 is a graph representing trapezoidal windows with various repetition numbers according to a first exemplary embodiment of the disclosed subject matter. FIG. 4 is a graph of the frequency response of the dose operator of the window shown in FIG. 3 according to a first exemplary embodiment of the disclosed subject matter. FIG. 2 is an energy control block diagram for the MOPA / MOPRA laser system of FIG. 1 according to a first exemplary embodiment of the disclosed subject matter. 6 is a flow diagram illustrating a method for preparing the laser control system of FIG. 5 according to a first exemplary embodiment of the disclosed subject matter.

  The elements of the disclosed subject matter are based on the realization that square windows have been used in the past for energy dose calculations, but can benefit by adapting to other shaped windows. FIG. 3 is an illustration of a graph representing trapezoidal windows with various repetition numbers according to a first exemplary embodiment of the disclosed subject matter. 4 is an illustration of a graph of the frequency response of the window dose operator shown in FIG. 3 in accordance with aspects of the first exemplary embodiment of the disclosed subject matter. There are a different set of zeros for different window widths, but there are clearly zeros for all windows at 20% and 40% of the sampling rate. These zeros correspond to the five-pulse moving average zero. It can be seen that the trapezoidal window is a convolution of a rectangular window having a length equal to the window size smaller than the trailing edge and a 5-pulse rectangular window.

FIG. 5 is an illustration of an energy control block diagram 150 for the MOPA / MOPRA laser system of FIG. 1 according to a first exemplary embodiment of the disclosed subject matter. FIG. 5 shows various control elements that control the voltage input 152 to the MOPA / MOPRA laser system 10. The energy control block diagram 150 includes a static controller 154 that provides an essentially predetermined voltage that is expected to result in an energy target 156 (if there are no other effects to consider). To do. Part of the purpose of static control 154 is to cause the energy controller to respond to changes in energy target 156. If the user adjusts the energy target, the first voltage input 152 of the first launch should be calculated to meet the new energy setting. The static control 154 can supply the following voltage signals:
V = (dV / dE) _ref * (E _target −E _ref + ε (E _target −E _ref ) ² + V _ref
Here, E _ref is approximately set to the nominal energy of the laser system 10 and V _ref is the voltage that is approximately required to fire the laser at E _ref .

Feedforward block 158 provides voltage adjustment based on trigger interval 160. The trigger interval 160 is used to calculate the number of iterations, number of firings, and duty cycle that affect the “voltage input-energy output” relationship. The voltage adjustment amount for the trigger interval 160 is calculated as a function of these values. More specifically, the voltage signal supplied by feedforward block 158 can be represented by:
V = f ₀ (D) + f ₁ (R, n)
Here, D is the duty cycle, R is the number of repetitions, and n is the number of firings. Note that the feedforward voltage has two terms. One term, f ₀ , depends on the duty cycle and / or burst interval, and another term, f ₁ , depends on the number of firings and the number of repetitions. By design, f ₁ is completely zero at the first launch of each burst. Thus, f ₀ alone determines the feed forward voltage for the first firing of the burst. This term is intended to tune the laser for changes in efficiency that generally persist throughout the burst. The f ₁ term captures any transition shape. This law assumes that the effect of duty cycle or burst interval is to raise or lower the energy versus the number of firings by an equal amount for all firings in the burst. It is assumed that the shape of the energy transfer depends only on the number of repetitions. The shape of the energy transfer is compensated for by the f ₁ (R, n) function.

The f ₁ (R, n) function is maintained as the number of table pairs and the number of firings. A single integrator is used to fit the bins. Traditionally, the bin was initialized to zero and several bursts were required before the laser control correctly reversed the transition at the number of repetitions. Instead of initializing these bins with zeros, the feed forward bin can be initialized with the value of the trained bin whose frequency is closest. Initializing the bin with a value closer to the correct value so that the shape of the energy transfer can be obtained, the transfer can be reversed at a repetition rate with laser control more quickly and accurately.

  The energy servo mechanism 162 adjusts the voltage input 152 based on the calculated voltage error 164 of the previous firing within the same firing. The amount of adjustment from the energy servomechanism 162 can be calculated in at least some different modes. First, IISquared feedback is a feedback method known to those skilled in the art. In this feedback method, one voltage (integral gain) proportional to the integral of the voltage error and another voltage (I square gain) proportional to the voltage error integrated twice are fed back. Several sets of gains, ie soft, hard, and MO, are fed into the IISquared filter. Soft gain is used for modes of operation where the objective is to minimize energy errors between launches. The soft gain is selected to minimize energy error. Hard gain is used for dose mode and sigma mode. The hard gain is intended to minimize the dose (integrated energy error) and tends to be larger than the soft gain. The MO gain is used for the MO energy control mode and is intended to minimize energy errors.

  An alternative to IISquared feedback is dose feedback. Similar to the IISquared controller with hard gain, the dose feedback controller aims to minimize the dose but uses a control method that improves performance with a non-rectangular dose window (eg, a trapezoidal dose window). Dose feedback is controlled by sizing parameters and gain vectors. The dose feedback controller is only available in dose mode and sigma mode, and a “linear quadratic regulator” can be utilized to minimize the secondary sum of energy dose and energy error 172. Tests have shown that the use of a linear secondary regulator instead of 100% integral feedback reduces the energy dose error by about 25%.

The effect of the laser system 4 is to transform the voltage input 152 into energy (evaluated by an energy measurement 172) through static gain, as shown in FIG. In addition, there is a set of disturbances that are added to the energy signal. Thus, the state of the system can be equivalent to disturbance characteristics and dose operators. The energy servomechanism 162 is directed to making a voltage adjustment in response to the behavior of the dose operator. The energy dose feedback can be calculated as the inner product of the state feedback vector K and the vector xd characterizing the state of the dose operator.
Vdose = -K xd
Here, K is calculated as the solution of the linear secondary regulator that minimizes the weighted sum of the square of the energy error and the square of the energy dose error.

The dither cancellation unit 166 adjusts the voltage so as to cancel the energy change caused by the timing dither 168. The secondary effect of this cancellation is that it is a derivative of the voltage for MOPA / MOPRA timing at constant energy, ie, MopaOpPoint180 (
Where E is the laser energy, V is the voltage, and t is the MOPA timing, ie the firing time difference between the MO chamber and the PA chamber.
u = 1 / E * dV / dt: to estimate the value used to calculate the operating point u) of the MOPA laser system, which can be defined as constant energy. For certain aspects of timing control, a local slope of the timing versus energy curve is required. This information is obtained by applying a dither signal at the differential timing commanded by the MO and PA rectifier triggers. Since timing is coupled to energy, this dither signal produces a matched dither in energy. The dither cancellation algorithm adaptively finds a voltage signal that accurately cancels the dither in the energy generated by the timing dither signal when applied to the laser. Thus, the timing dither no longer appears in the energy signal and therefore does not affect the energy sigma or energy dose.

  A byproduct of this cancellation algorithm is the derivative of the voltage with respect to constant energy timing. This by-product is gradient information to which timing dithering is applied in order to identify first. The parameter dMpopdMopa (MopaOpPoint derivative with respect to the difference between the MO chamber and PA chamber firing times) used in the laser control system for gas control is a dither cancellation change in MOPA timing (MO chamber and PA chamber firing times Can be used to respond to the difference) almost instantaneously. If this parameter is off, with a “big” (1-2 ns) change in MOPA / MOPRA timing, MopaOpPoint 180 (Mpop) will jump to a new value and then drift to a different value over the next thousands of firings. To do. During the time during which the MopaOppoint 180 estimate converges, a portion of the timing dither signal is released into energy. If the gas control parameters described above are set correctly, the MopaOpPoint 180 should jump to a new value with a “large” MOPA / OPRA timing change, then stay at that new value, and drift should be substantially reduced. is there.

  As described above with respect to FIG. 4, when using trapezoidal windows, there is clearly zero for all windows at 20% and 40% of the sampling rate (if the leading and trailing edges of the trapezoidal window are 5 pulses) . The dither amplitude can usually be set low to reduce energy dither, but this low amplitude delays the calculation of the energy dose derivative versus voltage estimate. If the dither is moved below the zero of one of the trapezoidal windows, the amplitude can be increased and adverse effects are reduced.

  Mpop compensation 182 adjusts voltage input 152 to compensate for changes in MOPA timing. This adjustment is primarily to stabilize the energy against changes in DtMopaTarget greater than about 1 nanosecond. If the laser is operating with bandwidth control enabled (ASC) and is currently operating away from resonance to keep the bandwidth from dropping, the control system will delay the delay between the MO and PA triggers. To reduce. At this point, MopaOpPoint will be a low negative value because DtMopaTarget is several ns below the value for peak efficiency. Next, the scanner 2 switches the number of repetitions to that on the bandwidth resonance. The bandwidth increases and the bandwidth controller advances DtMopaTarget by a few ns to compensate. The laser thereby approaches a peak efficiency of a few ns and the energy increases in steps. This step change in energy will affect the energy dose until the energy servomechanism 162 has the opportunity to compensate.

On the other hand, the MopaOppoint compensation 182 counters this effect. Calculate the amount that the voltage will need to change for a given change in Mopa timing, using the same value dMpopDMopa used to adjust dither cancellation for changes in Mopa timing. Can do. When the Mopa timing changes rapidly, the MopaOp Point Compensation 182 also predicts how much voltage change is needed and does not have to wait for the energy error 174 to appear, and the appropriate voltage signal at the voltage input 152 Can be supplied. The MopaOp point compensation 182 can be described as follows.
V = Eu ² / 2k
Where E is the laser energy, u is MopaOpPoint, and k is dMpopDMopa, ie the derivative of MopaOpPoint with respect to Mopa timing, ie the difference in firing time between the MO and PA chambers.

  The disturbance prediction unit 184 adjusts the voltage input 152 based on the prediction of the voltage error assuming that the disturbance acting on the energy is DC offset + several tones. Tone is a frequency that is a multiple of the MO and PA / PO blower speeds. This predicted voltage error is subtracted from the voltage input 152, thus eliminating the effects of DC offset or blower blade passage.

Finally, the energy dither unit 170 provides a periodic signal that is added to the voltage input 152 that is used to estimate the effect of voltage on MO energy, output energy, and MOPA timing. The periodic signal from the energy dither 170 is the length of n firings and can be described by the following equation:
V [k] = A cos (2πn _d k / n) k = 0,. . . , N-1
Where A is the dither amplitude and n _d is the number of cosine periods within one complete cycle of the dither.

  The dither signal is withheld for a fixed number of firings before starting with each burst. This delay is provided so that the dither cannot combine with the start of the burst effect to push the laser 4 out of specification. In order to prevent other signals at or near the dither frequency from interfering with the derivative estimate, the phase of the dither signal can be randomized. Randomization is done by randomizing the value of k in the above equation to start dithering. For the window shown in FIG. 3, the dither frequency is 1/5 of the repetition rate (5 firings of the leading and trailing edges of each trapezoidal window). This is an important frequency for lasers that use trapezoidal windows to calculate dose. For a window with a 4 pulse leading and trailing edge, 20% of the repetition rate is within zero of the dose operator. Therefore, dithering at this frequency will not affect the dose.

  These voltage signals are added together to generate a voltage input 152. When the laser is fired, energy is measured (172). The energy target is subtracted from the energy measurement to create an energy error signal 174 scaled by a laser estimate 176 of dV / dE, ie, the derivative of the voltage with respect to energy. The resulting voltage error 164 is used to drive an adaptive algorithm 178 that adjusts a portion of the voltage signal to minimize energy error, dose error, energy sigma, or some combination thereof.

  FIG. 6 is a flow diagram illustrating a method for preparing the laser control system 150 of FIG. 5 according to a first exemplary embodiment of the disclosed subject matter. Any process description or block in the flowchart should be understood to represent a stage that includes one or more instructions that perform a particular logical function in a module, segment, code portion, or process. Implementations perform functions out of the order from the illustration or description, including substantially the same or the reverse order based on the functionality involved, as will be appreciated by those skilled in the art of the disclosed subject matter. It should be noted that it is within the scope of the disclosed subject matter.

  Three alternatives of the first exemplary embodiment will now each be described below with reference to FIG.

  In the first alternative, a first voltage input is actuated in the form of electrical pulses on a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber, as indicated by block 202. To send. The energy dose at the output of the gas chamber is calculated with a trapezoidal window (block 204). Changing the first voltage input at the control circuit, the frequency response to the dose operator has at least one zero (block 206). At least one of energy dither and timing dither is started below one of zeros (block 208). A feedback control loop that changes the first voltage input is used to communicate the output of the gas chamber to the control circuit (block 210).

In the second alternative, as indicated by block 202, the first voltage input is activated in the form of electrical pulses to the first pair of electrodes in the oscillator gas chamber and the second pair of electrodes in the amplifier gas chamber. To send. The energy dose at the output of the gas chamber is calculated with a trapezoidal window (block 204). The control circuit changes the first voltage input, the control circuit changes the first voltage input according to the equation V = Eu ² / 2k, where E is the laser energy and u is the MopaOpPoint. , K is the derivative of MopaOpPoint with respect to the firing time difference between the gas chambers (block 206). In this alternative, block 208 is not used. A feedback control loop that changes the first voltage input is used to communicate the output of the gas chamber to the control circuit (block 210).

In a third alternative, a first voltage input is actuated in the form of electrical pulses on a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber, as indicated by block 202. To send. The energy dose at the output of the gas chamber is calculated with a trapezoidal window (block 204). The control circuit changes the first voltage input by adding an energy dose feedback calculated as V _dose = −Kxd to the first voltage input, where K is the square of the energy error and the energy dose error. A state feedback vector calculated as the solution of the linear quadratic regulator that minimizes the weighted sum of squares, and xd is a vector characterizing the state of the dose operator (block 206). In this alternative, block 208 is not used. A feedback control loop that changes the first voltage input is used to communicate the output of the gas chamber to the control circuit (block 210).

  It should be emphasized that the above-described embodiments of the disclosed subject matter, and in particular any “preferred” embodiments, are merely possible examples of implementation, ie, illustrated so that the principles of the invention can be clearly understood. Is. Many variations and modifications may be made to the above-described embodiments of the invention without departing substantially from the spirit and principles of the invention. All such modifications and variations are intended to be included herein within the scope of the present disclosure and the disclosed subject matter and protected by the following claims.

2 Scanner 6 Beam sending unit 11 Main oscillator 12 Power amplifier

Claims (27)

A laser control system,
An oscillator gas chamber;
An amplifier gas chamber;
A first voltage input operatively connected to deliver an electrical pulse to a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber;
Including
The gas chamber output is the energy dose calculated by the trapezoidal window;
Laser control system
A control circuit connected to the first voltage input to change the first voltage input;
Further including
The frequency response to the dose operator has at least one zero;
Laser control system
At least one of energy dither and timing dither arranged to start under one of said zeros;
A feedback control loop that communicates the output of the gas chamber to the control circuit to change the first voltage input;
Further including
A system characterized by that. The control circuit includes the first circuit according to equation V = Eu ² / 2k, where E is the laser energy, u is MopaOpPoint, and k is the derivative of the difference in firing time between the gas chambers of MopaOpPoint. The laser control system according to claim 1, wherein the voltage input is changed.   The laser control system of claim 1, wherein the at least one of energy dither and timing dither further includes an energy dither that starts under one of the zeros. Periodic signal from the energy dithering is a length of n times of firing, has an amplitude A, and from k = 0 n-1, n _d is the cosine period within one complete cycle of the dither If the number, V [k] = Acos laser control system according to claim 3, characterized in that satisfy (2πn _d k / n).   The laser control system of claim 1, wherein the at least one of energy dither and timing dither is arranged to start under one of the zeros. The control circuit has a state feedback vector, where K is calculated as the solution of a linear quadratic regulator that minimizes the weighted sum of the square of energy error and the square of energy dose error, and xd characterizes the state of the dose operator. The laser control system of claim 1, further comprising an energy dose feedback circuit that is calculated as V _dose = -Kxd if it is a vector. The control circuit further includes a function of energy transfer;
Multiple iteration bins are initialized for non-zero values,
The laser control system according to claim 1.   8. The laser control system of claim 7, wherein the repetition rate bin is initialized to a value for a trained bin having a similar repetition rate.   The laser control system according to claim 1, wherein the control circuit further includes a linear secondary regulator that feeds back a state of a filter that approximates a dose operator. A laser control system,
An oscillator gas chamber;
An amplifier gas chamber;
A first voltage input operatively connected to deliver an electrical pulse to a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber;
Including
The gas chamber output is the energy dose calculated by the trapezoidal window;
Laser control system
A derivative of the difference in firing time between the gas chambers connected to the first voltage input to change the first voltage input, where E is the laser energy, u is MopaOpPoint, and k is MopaOpPoint. A control circuit for changing the first voltage input according to the equation pair = Eu ² / 2k when
A feedback control loop that communicates the output of the gas chamber to the control circuit to change the first voltage input;
Further including
A system characterized by that. It said first voltage input, when E _ref is, is almost set to a nominal energy of the laser system 10, and V _ref is a voltage which is substantially required to fire the laser at E _ref, V = ^{_{(dV / dE) ref * (}} E target -E ref + ε (E target -E ref) laser control system of claim 10, characterized in ^{that 2} + further comprising an input that is calculated from the energy target as V _ref.   11. The laser control system of claim 10, wherein the frequency response to the dose operator has at least one zero, and the control circuit further includes an energy dither initiated under one of the zeros. . Periodic signal from the energy dithering is a length of n times of firing, has an amplitude A, and from k = 0 n-1, n _d is the cosine period within one complete cycle of the dither If the number, V [k] = Acos laser control system according to claim 12, characterized in that satisfy (2πn _d k / n).   The laser control system of claim 10, wherein the frequency response to the dose operator has at least one zero, and the timing dither is arranged to start under one of the zeros. The control circuit has a state feedback vector, where K is calculated as the solution of a linear quadratic regulator that minimizes the weighted sum of the square of energy error and the square of energy dose error, and xd characterizes the state of the dose operator. 11. The laser control system according to claim 10, further comprising an energy dose feedback circuit that is calculated as V _dose = −Kxd if it is a vector. The control circuit further includes a function of energy transfer;
Multiple iteration bins are initialized for non-zero values,
The laser control system according to claim 10.   The laser control system of claim 16, wherein the repetition rate bin is initialized to a value of a trained bin having a similar repetition rate.   The laser control system according to claim 10, wherein the control circuit further includes a linear secondary regulator that feeds back a state of a filter that approximates a dose operator. A laser control system,
An oscillator gas chamber;
An amplifier gas chamber;
A first voltage input operatively connected to deliver an electrical pulse to a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber;
Including
The gas chamber output is the energy dose calculated by the trapezoidal window;
Laser control system
Connected to the first voltage input to change the first voltage input, K is calculated as the solution of a linear secondary regulator that minimizes the weighted sum of the square of the energy error and the square of the energy dose error. A control circuit further comprising: an energy dose feedback circuit calculated as V _dose = −Kxd, where xd is a vector characterizing the state of the dose operator;
A feedback control loop that communicates the output of the gas chamber to the control circuit to change the first voltage input;
Further including
A system characterized by that. The control circuit includes the first circuit according to equation V = Eu ² / 2k, where E is the laser energy, u is MopaOpPoint, and k is the derivative of the difference in firing time between the gas chambers of MopaOpPoint. The laser control system according to claim 19, wherein the voltage input is changed.   20. The laser control system of claim 19, wherein the frequency response to the dose operator has at least one zero, and the control circuit further includes an energy dither initiated under one of the zeros. . Periodic signal from the energy dithering is a length of n times of firing, has an amplitude A, and from k = 0 n-1, n _d is the cosine period within one complete cycle of the dither If the number, V [k] = Acos laser control system of claim 21, characterized in that satisfy (2πn _d k / n).   20. The laser control system of claim 19, wherein the frequency response to the dose operator has at least one zero and the timing dither is arranged to start under one of the zeros. It said first voltage input, when E _ref is, is almost set to a nominal energy of the laser system 10, and V _ref is a voltage which is substantially required to fire the laser at E _ref, V = ^{_{(dV / dE) ref * (}} E target -E ref + ε (E target -E ref) laser control system of claim ^19, wherein the ² + further comprising an input that is calculated from the energy target as V _ref. The control circuit further includes a function of energy transfer;
Multiple iteration bins are initialized for non-zero values,
The laser control system according to claim 19.   26. The laser control system of claim 25, wherein the repetition rate bin is initialized to a value of a trained bin having a similar repetition rate.   The laser control system according to claim 19, wherein the control circuit further includes the linear secondary regulator that feeds back a state of a filter that approximates the dose operator.

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