Patent Publication Number: US-2021175050-A1

Title: Frequency Tuning for Modulated Plasma Systems

Description:
CLAIM OF PRIORITY UNDER 35 U.S.C. § 120 
     The present application for Patent is a Continuation in Part of patent application Ser. No. 16/934,257 entitled “Apparatus and System for Modulated Plasma Systems,” filed 21 Jul. 2021, which is a Continuation in Part of patent application Ser. No. 16/230,923 entitled “Plasma Delivery System for Modulated Plasma Systems” filed 21 Dec. 2018, and issued as U.S. Pat. No. 10,720,305 on Jul. 21, 2020, and all of the above-identified applications are assigned to the assignee hereof and hereby expressly incorporated by reference herein. 
    
    
     BACKGROUND 
     Field 
     The present disclosed embodiments relate generally to plasma processing systems, and more specifically to plasma processing systems with modulated plasma. 
     Background 
     Plasma processing systems for etching and deposition have been utilized for decades, but advancements in processing techniques and equipment technologies continue to create increasingly more complex systems. These increasingly complex systems lead to more problematic interactions between multiple generators driving the same plasma system. 
     SUMMARY 
     An aspect may be characterized as a power generation system comprising a high-frequency generator configured to apply power to a plasma chamber at a primary frequency and a filter configured to suppress mixing products to limit variation of a time-varying load reflection coefficient presented to the high-frequency generator. The power generation system also includes a frequency-tuning subsystem configured to apply, while the high-frequency generator is applying power at the primary frequency, a probe signal comprising one or more probe frequencies and adjust the primary frequency of the high-frequency generator in response to the one or more probe frequencies indicating an improved measure of performance. 
     Another aspect may be characterized as a method for automated frequency tuning of a power generation system comprising applying a primary power signal at a primary frequency to a plasma load with a high-frequency generator and applying a probe signal at one or more probe frequencies to the plasma load. Mixing products are suppressed with a filter to reduce variation of a time-varying load reflection coefficient presented to the high-frequency generator, and the primary frequency is adjusted based upon a measure of performance in response to probe signal. 
     Yet another aspect may be characterized as a plasma processing system comprising a plasma chamber, a high-frequency generator configured to apply power to a plasma chamber at a primary frequency, and a low-frequency generator to apply power to the plasma chamber at a low frequency. A filter in the system is configured to suppress mixing products of the primary frequency and the low frequency to limit variation of a time-varying load reflection coefficient presented to the high-frequency generator. And the system comprises means for frequency tuning the high-frequency generator using a probe signal that is concurrently applied with the power applied to the plasma chamber at the primary frequency. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram depicting a power supply system and a plasma processing system; 
         FIG. 2  is a graph depicting how power may be perceived by measuring power using different measurement-system-filter bandwidths; 
         FIGS. 3A and 3B  are graphs depicting modulation of load reflection coefficient, and  FIG. 3C  is a graph depicting the resulting reflected power that may be seen by the high-frequency generator when the filter depicted in  FIG. 1  is not utilized; 
         FIG. 4A  comprises two graphs depicting performance aspects for an exemplary design of the filter depicted in  FIG. 1 , and  FIG. 4B  is a graph depicting the net power that may be delivered to the plasma load by the high-frequency generator at the fundamental and mixing product frequencies when the filter depicted in  FIG. 1  is not utilized; 
         FIGS. 5A and 5B  are graphs depicting modulation of load reflection coefficient, and  FIG. 5C  is a graph depicting resulting reflected power that may be seen by the high-frequency generator when the filter depicted in  FIG. 1  is utilized; 
         FIGS. 6A and 6B  are graphs depicting modulation of load reflection coefficient, and  FIG. 6C  is a graph depicting resulting reflected power that may be seen by the filter depicted in  FIG. 1 ; 
         FIG. 7  is a flowchart depicting a method that may be traversed in connection with embodiments disclosed herein; 
         FIGS. 8A and 8B  are diagrams depicting equivalent circuits of embodiments of the filter described with reference to  FIG. 1 ; 
         FIG. 9  is a perspective view of an exemplary water-cooled filter design with two parallel helical resonators; 
         FIG. 10  is a view of the interior of a water-cooled filter design with two parallel helical resonators; 
         FIG. 11  is a cutaway view of a water-cooled filter design with two parallel helical resonators; 
         FIG. 12  is a detail view of the capacitor block of a water-cooled filter design with two parallel helical resonators; 
         FIG. 13  is an exploded view of a water-cooled filter design with two parallel helical resonators; 
         FIG. 14  is a view of a filter comprising provision to tune the filter; 
         FIG. 15  is a block diagram depicting an exemplary high-frequency generator; 
         FIG. 16  is a flowchart depicting a method that may be traversed in connection with embodiments disclosed herein; 
         FIG. 17  is a graph depicting a multi-state waveform that may be applied by the high-frequency generators of  FIGS. 1 and 15 ; 
         FIG. 18  is a graph depicting exemplary aspects of a frequency tuning method; 
         FIG. 19  is a graph depicting additional aspects of the frequency tuning method described with reference to  FIG. 18 ; 
         FIG. 20  is a graph depicting operational aspects of yet another frequency tuning method; 
         FIG. 21  illustrates a power generation system configured for automated frequency tuning of power delivered to a plasma load; 
         FIG. 22  illustrates one embodiment of a power generation system where the sensor resides within a power generation system along with a power source and one or more circuits; 
         FIG. 23  illustrates one embodiment of a power generation system where a sensor resides outside the power generation system; 
         FIG. 24  illustrates a further embodiment of a power generation system; 
         FIG. 25  illustrates an embodiment of a power generation system where the primary power signal and the secondary power signal are combined before amplification by a power amplifier; 
         FIG. 26  illustrates an embodiment of a power generation system where the power source generates the primary power signal and a noise source generates the secondary power signal in the form of noise; 
         FIG. 27  illustrates an embodiment of a power generation system where the secondary signal is noise and the primary power signal and the secondary power signal are combined before amplification by a power amplifier; 
         FIG. 28  shows a plot of a measure of performance as a function of frequency; 
         FIG. 29A  is a graph depicting a measure of performance (e.g., reflection coefficient) as a function of frequency; 
         FIG. 29B  is a graphical representation depicting how a primary power signal frequency may be adjusted to minimize the measure of performance depicted in  FIG. 29A ; 
         FIG. 29C  depicts a spectrum (power per bandwidth, e.g., Watts per 3 kHz bandwidth) of the power generation system output at time t 2  in  FIG. 29B ; 
         FIG. 30A  is a graph depicting a measure of performance versus frequency; 
         FIG. 30B  is a plot depicting how a global search using the primary power signal can lead to an extinguished plasma; 
         FIG. 30C  is a graph showing a spectrum of the power generation system output at time t 2  in  FIG. 10B ; 
         FIG. 31A  is graph depicting an estimate of optimum frequency using a secondary power signal; 
         FIG. 31B  is a graph depicting adjustment of a primary frequency after a determination of the desired frequency using a secondary power signals; 
         FIG. 31C  is a graph showing spectral components of the power at the primary signal and the secondary signal of  FIG. 31B ; 
         FIG. 32A  is a graph depicting an estimate of optimum frequency using a secondary power signal; 
         FIG. 32B  is a graph depicting adjustment of a primary frequency after a determination of the desired frequency using secondary power signals; 
         FIG. 32C  is a graph depicting spectral components of the power at the primary signal and the secondary signals of  FIG. 32B ; 
         FIG. 33A  is a graph depicting an estimate of optimum frequency using a secondary power signal; 
         FIG. 33B  is a graph depicting noise power as a function of time where noise is added to the power generation system output; 
         FIG. 33C  is a graph depicting shows the spectrum of the power generation system output at time t 2  in  FIG. 33B ; 
         FIG. 34A  is a graph depicting aspects of a method for frequency tuning; 
         FIG. 34B  is a graph depicting additional aspects of the method for frequency tuning shown in  FIG. 34A ; 
         FIG. 34C  is a graph depicting further aspects of the method for frequency tuning depicted in  FIGS. 34A and 34B ; 
         FIG. 34D  is a graph depicting yet additional aspects of the method for frequency tuning depicted in  FIGS. 34A, 34B, and 34C ; 
         FIG. 35A  is a graph depicting aspects of a method for frequency tuning; 
         FIG. 35B  is a graph depicting additional aspects of the method for frequency tuning depicted in  FIG. 35A ; 
         FIG. 35C  is a graph depicting further aspects of the method for frequency tuning depicted in  FIGS. 35A and 35B ; 
         FIG. 36  illustrates a method for frequency tuning a power generation system that may be traversed in connection with embodiments described herein. 
         FIG. 37A  is a diagram depicting an exemplary sensor. 
         FIG. 37B  is a diagram depicting another embodiment of a sensor. 
         FIG. 37C  is a diagram depicting yet another embodiment of a sensor. 
         FIG. 38  is a diagram depicting aspects of an exemplary identification module. 
         FIG. 39  is a block diagram depicting components that may be utilized to realize embodiments disclosed herein. 
     
    
    
     DETAILED DESCRIPTION 
     Interaction between generators driving the same plasma where one of the generators modulates the load seen by another generator is becoming increasingly problematic as power levels are increased; thus, there is a need for new and improved methods and systems for dealing with this problem. 
     The word “exemplary” is used herein to mean “serving as an example, instance, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments. 
     Referring to  FIG. 1 , shown is a block diagram depicting an exemplary environment in which embodiments may be implemented. As shown, a plasma load of a plasma chamber  100  is coupled to a high-frequency generator  102  via a filter  104  and a matching network  106  (also referred to as a match  106 ). In addition, a low-frequency generator  108  is also coupled to the plasma load via match  110 . In many applications the match  106  may be combined with the match  110 . Also shown are optional wideband measurement components  114 ,  116 ,  118 , and  120  and an optional delay element  112 . The optional delay element  112  can be realized using a length of coaxial cable or a fixed or variable RLCM (i.e., a circuit containing resistors, inductors, capacitors and coupled inductors) circuit or a circuit containing distributed circuit elements (i.e. transmission line circuits). Also shown are optional connections  122  and  124  that allow one of the optional wideband measurement systems  116 ,  120  to take over functionality of the other if the optional delay element  112  is properly characterized. 
     Although the high-frequency generator  102  and the low frequency generator  108  may each operate over a range of frequencies, in general, the high-frequency generator  102  operates at a frequency that is higher than the low-frequency generator  108 . In many embodiments, the high-frequency generator  102  may be a generator that delivers RF power to the plasma load in the plasma chamber  100  in the 10 MHz to 200 MHz frequency range, and the low frequency generator  108  may be, for example, in the 100 kHz to 2 MHz range. So, exemplary frequency ratios of the frequency of the low-frequency generator  108  to that of the high-frequency generator  102  are between 0.0005 and 0.2. In many embodiments for example, the frequency ratio of the frequency of the low-frequency generator  108  to that of the high-frequency generator  102  is less than 0.05, and in some embodiments the frequency ratio of the low-frequency generator  108  to the high-frequency generator  102  is less than 0.01. For example, the ratio may be 1:150 or about 0.0067. 
     In terms of applications, the high-frequency generator  102  may be used to ignite and sustain the plasma load in the plasma chamber  100 , and the low-frequency generator  108  may be utilized to apply a periodic voltage function to a substrate support of the plasma chamber  100  to effectuate a desired distribution of ion energies at a surface of a substrate in the plasma chamber  100 . 
     With respect to power levels, the low-frequency generator  108  may apply a relatively large amount of power (e.g., in the 10 kW to 30 kW range) to the plasma load of the plasma chamber  100 . The large amount of power applied to the plasma at low frequency modulates the plasma impedance presented to a high-frequency generator  102 . 
     Applicant has found that, in prior systems with a generator (e.g., the low-frequency generator  108 ) that modulates the plasma load, power is not measured at a sufficient number of mixing products generated by the system. And failure to do so is a problem that leads to errors on the order of 100% or more in power measurement. Typical approaches taken in the past (when there is low-frequency power perturbing the plasma) is to simply filter out the mixing frequency components that result from applying high-frequency power to a load that is modulated at a low frequency (e.g., filtering out 59.6 MHz and 60.4 MHz components when the low and high generator frequencies are 400 kHz and 60 MHz, respectively). But when a low pass filter is utilized, the apparent complex impedance trajectory collapses to a point, and misleadingly, it appears as though the high-frequency generator  102  is delivering power into 50 ohms. 
     Referring to  FIG. 2 , shown is a graph depicting how power may be perceived by measuring power using different measurement-system-filter bandwidths. The measurement system filtering is applied after down conversion or demodulation of the measured signal; thus, the measurement system filters frequency components centered on the generator output frequency. For example, a measurement system bandwidth of 100 kHz applied to a generator producing a 60 MHz output will suppress frequency components below 59.9 MHz and above 60.1 MHz. As shown, when the filter bandwidth of a measuring system is selected to be less than the modulation frequency of the plasma, then it appears as though there is much less reflected power than there actually is (so, it appears as though only forward power is going to the plasma load), but in reality, that is not what is happening. 
     In contrast, when power is measured with sufficient bandwidth (e.g., by one or both of the wideband measurement systems  116 ,  120 ), it is clear that only a fraction of the power (e.g., only half the power) is going to the plasma load. So, an aspect of the present disclosure comprises adjusting a measurement system so that its filter bandwidth exceeds the modulation frequency to capture mixing products at higher frequencies. U.S. Pat. No. 7,970,562 entitled System, Method, and Apparatus for Monitoring Power (which is incorporated herein by reference) discloses types of sensors (e.g., directional coupler or voltage/current (VI) sensor) that may be used to realize the sensors  114 ,  118  in addition to the sampling and processing techniques that may be utilized by the wideband measurement systems  116 ,  120  to achieve a filter bandwidth that is capable of capturing information about the mixing products at higher frequencies. It should be noted that the filter bandwidth if the measurement systems  116 ,  120  should not be confused with the filter  104 . 
     Another problem is that the high-frequency generator  102  needs to deliver power to a time varying load (the modulated plasma load) where the time-averaged load reflection coefficient magnitude is high. Referring to  FIGS. 3A and 3B  for example, shown are graphs depicting the load reflection coefficient that is seen by the high-frequency generator  102  over the time period of one cycle of the low frequency generator  108 , and  FIG. 3C  is a graph depicting resulting reflected power that may be seen by the high-frequency generator  102  when the filter  104  depicted in  FIG. 1  is not utilized. As shown, the peak load reflection coefficient magnitude seen by the high-frequency generator  102  may be close to 1 (and may even exceed 1 meaning net power is flowing from the plasma load to the high-frequency generator  102 ) while an average load reflection coefficient magnitude seen by the high-frequency generator  102  may be 0.76. The relatively high load reflection coefficient magnitude means that, in general, the high-frequency generator  102  may struggle to apply a desired level of power and be more susceptible to failure. Thus, the high-frequency generator  102  may require many more power devices (bipolar transistors, MOSFETS, etc.) than would normally be required to deliver the required amount of power to the plasma chamber  100 . 
     Aspects of the disclosure herein are directed to solutions to remove or mitigate against the effects of plasma modulation. An aspect depicted in  FIG. 1  is the depicted filter  104 . As discussed above, absent the depicted filter  104 , the modulated plasma load presents a time varying nonlinear load to the high-frequency generator  102 , which presents challenging problems. 
     In many embodiments, the filter  104  depicted in  FIG. 1  may be implemented as an extremely-narrow bandwidth, high-power filter that is disposed between the high-frequency generator  102  and the plasma chamber  100 . The filter  104  may have reasonably low losses at the frequency of the high-frequency generator  102  and suppress the mixing products sufficiently to limit the variation in load reflection coefficient presented to the high-frequency generator  102  at the input to the filter  104  while being stable under application of high power. When implemented, the filter  104  may have a narrow bandwidth to filter the side-band frequencies. As used herein, bandwidth is defined as a frequency range that exists between a lower-cutoff frequency and a higher-cutoff frequency, wherein each of the cutoff frequencies is 3 dB below the maximum center or resonant peak while attenuating or weakening other frequencies outside of these two points by more than 3 dB. 
     In some embodiments for example, the low-frequency-generator  108  is realized by a 400 kHz generator and the high-frequency generator  102  is realized by a 60 MHz RF generator; thus, presenting a frequency ratio of 1 to 150. As a consequence, in these embodiments the filter  104  may suppress power at a frequency that is less than a percent away from a center frequency. As a specific example, the low-frequency generator  108  may be a bias supply that applies a voltage function to a substrate support and the high-frequency generator  102  is a source generator that ignites and sustains a plasma. 
     And in many embodiments, the suppression of power at the frequency of the high-frequency generator  102  is, at most, 2 dB, and the suppression of power at frequencies more than the frequency of the low-frequency generator  108  from the frequency of the high-frequency generator  102  is at least 2 dB higher than the suppression of power at the frequency of the high-frequency generator  102 . In some implementations, the bandwidth of the filter  104  is 2% (or less) of the frequency of the high-frequency generator  102 . If the high-frequency generator  102  is realized by a 60 MHz RF generator, for example, the bandwidth of the filter may be 1.2 MHz or less. 
     Referring briefly to  FIG. 4A , shown are graphs depicting performance aspects for exemplary designs of the filter  104 . In  FIG. 4A , a bandwidth of the filter  104  has a center frequency of about 60 MHz, and at a fraction of a megahertz away from the center frequency, power is suppressed by 8 dB.  FIG. 4B  shows the net power that may be delivered to the plasma load by the high-frequency generator when the filter depicted in  FIG. 1  is not utilized.  FIG. 4B  shows that the filter with a response such as shown in  FIG. 4A  will allow power delivered to the plasma load at the fundamental frequency of 60 MHz to pass from the high-frequency generator  102  to the plasma load with relatively high efficiency and suppress the power reflected from the plasma load back to the high-frequency generator  102 . 
     But those of ordinary skill in the art have not been led to implement the filter  104  with characteristics that are similar to the filter characteristics in  FIG. 4A . A lack of awareness of the underlying problem of plasma modulation is one reason. But in addition, designing a filter with the characteristics depicted in  FIG. 4A  is challenging (even at low power levels). But in many embodiments the filter  104  handles high amounts of power (e.g., several kW of power), and the high-power and narrow-band combination is not a combination that those of skill in the art are likely to try. 
     As discussed above,  FIGS. 3A and 3B  depict a load reflection coefficient as seen by the high-frequency generator when the filter  104  is not utilized. And  FIGS. 5A and 5B  depict a load reflection coefficient as seen by the high-frequency generator  102  when an exemplary filter  104  is implemented. As shown in  FIG. 5A , when the filter  104  is deployed, the reflection coefficient is compressed to stay much closer to the center of the graph (as compared to the load reflection coefficient in  FIG. 3A ) over the cycle of the plasma&#39;s modulation. 
       FIG. 3B  depicts reflection coefficient magnitude in the time domain without the filter  104  being utilized. The corresponding level of forward power (close to 100 watts) depicted in  FIG. 3C  is much lower than the power utilized during plasma processing, but the reflection coefficient depicted in  FIG. 3B , and relative magnitudes of forward and reflected power in  FIG. 3C , is instructional. As shown, forward power is 99.8 watts and reflected power is 63.4 watts. In contrast, as shown in  FIG. 5C , with the filter  104  in place, there are 99.9 watts of forward power and 3.4 watts of reflected power; thus, the high-frequency generator  102  is placed under much less stress. And on the load side of the filter  104 , as shown in  FIG. 6C , the filter  104  may increase the average forward power. 
     Referring to  FIG. 7 , shown is a flowchart  700  depicting a method for plasma processing in a modulated plasma system. As shown, power is supplied to the plasma chamber  100  with the high-frequency generator  102  to ignite and sustain a plasma (Block  710 ). In addition, power is supplied to the plasma chamber  100  with the low-frequency generator  108  (Block  720 ). Power transfer between the high-frequency generator  102  and the plasma chamber  100  is suppressed at frequencies corresponding to mixing products of the high and low frequencies with the filter  104  disposed between the plasma chamber  100  and the high-frequency generator (Block  730 ). The tuning of the matching network  106  may be adjusted (e.g., optimized) to balance the requirements of providing a well-matched impedance to the high-frequency generator  102  and the efficiency of power transfer to the plasma chamber  100  (Block  740 ). 
     Referring briefly back to  FIG. 6A , note that the trajectory of the load reflection coefficient is not symmetrical around the origin as is the case in  FIG. 3A . This is a characteristic of the impedance required on the load side of the filter  104  in order to match the input of the filter  104  to a load reflection coefficient that is close to zero and get efficient power transfer from the high-frequency generator  102  to the plasma load. The average load reflection coefficient on the load side of the filter  104  is indicated with a “+” in  FIG. 6A . The average value of the load reflection coefficient on the load side of the filter  104  as indicated in  FIG. 6A  is approximately −0.23−j0.00. The average value of the load reflection coefficient on the high-frequency generator  102  side of the filter  104  as indicated in  FIG. 5A  is approximately 0.04−j0.02. This illustrates an aspect of using this filter  104 , namely that the load reflection coefficient on the load side of the filter  104  is not tuned to a matched load (50 ohm in most systems), but is typically set to achieve a low, time-averaged load reflection coefficient magnitude as measured by a wideband measurement system. As a consequence, in many implementations, the wideband measurement component  116  or  120  is utilized to capture at least the first order mixing products. The wideband measurement systems  116  or  120  may be implemented as an integral component of the matching network  106 , the high-frequency generator  102 , or may be implemented as a separate component. Thus, the step of adjusting the matching network at Block  740  is different from what is normally required of a matching network  106 . 
     In many implementations, the impedance presented to the filter  104  by the plasma chamber  100  is adjusted to optimize efficiency of power transfer from the high-frequency generator  102  to the plasma chamber  100 . For example, the time-average of an absolute value of the load reflection coefficient presented to the filter may be minimized, and the load reflection coefficient may be measured (e.g., by the wideband measurement system  116  or  120 ) using a bandwidth at least equal to the frequency of the low-frequency generator  108 . It is also contemplated that a time-average of a load reflection coefficient is optimized away from 0+j0. 
     Referring again to  FIG. 7 , a length of cables between the matching network  106  and the filter  104  may be adjusted (e.g., optimized) to control the impedance with which the power mixing products are terminated (Block  750 ). Although cable lengths (between a match network and a plasma processing chamber) are adjusted in other plasma processing systems (e.g., for stability), when the filter  104  is used, there are additional considerations when choosing this cable length, namely: the termination impedance provided to the plasma system at the frequencies of the mixing products by the filter  104 ; cables connecting the filter  104  to the matching network  106 ; and the matching network  106 . Changing the cable length changes the nature of the modulation on the load side of the filter  104 . This cable length also affects frequency tuning in multi-state applications; thus, the choice of this cable length may be more complicated than in prior plasma processing systems. 
       FIGS. 8A and 8B  are equivalent circuits of embodiments of the filter  104  described with reference to  FIG. 1 .  FIG. 8A  shows the equivalent circuit of a lossless prototype, and  FIG. 8B  shows the equivalent circuit of the filter  104  when reduced to practice using realizable lossy components. There are other ways of realizing such a narrowband, high power filter (for example using a large ring resonator or cavity), but in all cases careful attention must be paid to high voltages, high currents, and high-power dissipation present in such filters. 
     Referring next to  FIG. 9 , shown is a perspective view of the exterior of a water-cooled filter  904  designed with two parallel helical resonators. The filter contains two water connections  910  and  920  for passing water through the filter for cooling, an input connector  930 , and an output connector (not visible in this view). 
       FIG. 10  is a view of the interior of the filter  904  design with two parallel helical resonators. As shown, each of the helical resonators comprises a hollow helical coil  1020 , and each hollow helical coil  1020  is coupled to a copper block  1024 . Extending from the copper block  1024  are copper straps  1026  and insulating the copper straps  1026  from the copper block  1024  are ceramic insulators  1028 . In this implementation, metallization  1030  is disposed on the ceramic  1028  to form input and output capacitors  810  and  820 . In addition, each hollow helical coil  1020  comprises a grounded end  1022 . The filter  904  also comprises a potted cylindrical enclosure  1032  (represented transparently for purposes of viewing internal components of the filter  104 ) that surrounds the hollow helical coils  1020  and the copper block  1024 . 
       FIG. 11  shows a cutaway view of the filter  904 . This view shows how the copper straps  1026  connect to the input and output connectors,  1110  and  1140 , to the capacitors formed on the ceramic insulators  1120  and  1150 . This view also shows how the hollow helical coils  1130  and  1160  connect to the copper block  1024 . 
       FIG. 12  shows more detail of the copper block  1240  ( 1024  in  FIG. 10 ). This assembly provides the required capacitive coupling from the input and output to the helical resonators. Due to the small value of the capacitors required, the high voltage the capacitors must withstand, and the power the capacitors must dissipate, implementing the capacitors on a ceramic substrate is used in the design of the filter. The copper block contains a water channel  1210  into which the hollow helical coils are attached (by e.g. soldering). The capacitors formed on the ceramic insulators  1220  and  1260  are thus water cooled. The ceramic insulators have front and back metallization  1280  and  1250 , respectively. The size of the front metallization  1280  controls the capacitance realized by the assembly. The ceramic insulators can be attached to the copper block  1240  using electrically conductive epoxy. The straps  1270  and  1230  can be soldered to the front metallization and to the connectors  1110  and  1140 . 
       FIG. 13  shows an exploded view of the filter  904 . An insulating bracket  1310  holds the hollow helical coils in place and provides mechanical stability to the assembly. The bracket is made from a suitable low loss dielectric material, e.g. PTFE plastic or ceramic and contains holes to allow the potting material to flow through. Due to the high voltages that may be encountered in this design, the high voltage area of the filter is potted (e.g. using silicone dielectric gels) to reduce the risk of failure due to the breakdown of air. Alternatively, the entire assembly can be evacuated to a high vacuum, filled with a high-quality dielectric liquid, or filled with an insulating pressurized gas such as, but not limited to, sulfur hexafluoride (SF6). 
     It should be recognized that those of ordinary skill in the art, in view of the present disclosure, are able to design aspects of the helical coils  1020  (e.g., a number of turns, radius, length, pitch, inner and outer coil diameter, and outside diameter of coil) to achieve the desired bandwidth and heat dissipation. It should also be recognized that variations of the design of the filter  904  depicted in  FIGS. 9-13  are certainly contemplated. 
     Using helical resonators close to resonance on the low frequency or inductive side of resonance rather than an inductor achieves a similar bandwidth as compared to a design using an inductor, but in contrast to a design with an inductor, the helical resonators provide a smaller effective inductance. In addition, using two resonators in parallel allows ground-connected water cooling of the entire assembly where the water system can remain grounded. More specifically, water provided from the ground-connected water system is fed through the hollow helical coils  1020  enabling a large amount of heat to be dissipated. For example, the filter  904  (and variations of the filter  904 ) may operate at relatively high-power levels (e.g., in the 1 kW to 30 kW power range). By virtue of its design, the filter  904  (and its variations) may operate at relatively high-power levels while operating at efficiencies of at least 75%. 
       FIG. 14  shows a filter  1404  with tuning slugs. Tuning may be required for setting the passband frequency of the filter due to component manufacturing tolerance but may also be actively adjusted to compensate for changes in component values due to, for example, self-heating of the filter  1404 . The tuning slugs  1420  and  1440  may be, for example, ferrite rods that may be moved along the depicted Y axis within the hollow helical coils  1020 , but more typically, the tuning slugs may be made of copper. Cups  1410  and  1430  made of suitable insulators (e.g. PTFE plastic) provide an area free of potting compound in which the tuning slugs can be moved. 
     The use of the filter  104 ,  804 B,  904 ,  1404  compresses the frequency range over which frequency tuning (for impedance matching) can be done to a very small frequency range. This requires a different approach to deal with multi-state operation of the generator. An example of multi-state operation may be switching between multiple power levels in which each power level represents a state and in which the high-frequency generator  102  sees a different load impedance in each state due to the nonlinear nature of the plasma load and where the high-frequency generator  102  may operate at a different frequency in each state in order to improve impedance matching or stability for that state. To facilitate multi-state operation in a system using the filter  104 , one may need to ensure that the impedances presented to the load side of the filter  104  for the different states lie along or close to the line of impedances that can be matched by frequency tuning the high-frequency generator  102  frequency. This can be done by adding a fixed or variable time-delay, such as delay element  112 , on the load side of the filter. 
     An aspect of the present disclosure is frequency tuning of the high-frequency generator  102  to adjust an impedance presented to the high-frequency generator  102 . Referring to  FIG. 15  for example, shown is a block diagram of a high-frequency generator  1502  that may be used to realize the high-frequency generator  102  described with reference to  FIG. 1 . As shown, the high-frequency generator  1502  comprises an exciter  1505 , power amplifier  1510 , filter  1515 , sensor  1520 , and frequency-tuning subsystem  1525 . The exciter  1505  (which may include an oscillator) generates an oscillating signal at RF frequencies, typically in the form of a sinusoidal or square wave. Power amplifier  1510  amplifies the signal produced by exciter  1505  to produce an amplified oscillating signal. For example, the power amplifier  1510  may amplify an exciter output signal of 1 mW to 3 kW. Filter  1515  is optional (and distinct from filter  104 ) and may filter the amplified oscillating signal to produce a signal composed of a single RF frequency (a sinusoid). 
     The sensor  1520  measures one or more parameters indicative of the plasma load in plasma chamber  100 . In one embodiment, sensor  1520  measures power parameters indicative of the impedance, Z, of the plasma load. Depending on the particular embodiment, sensor  1520  can be, for example and without limitation, a VI sensor or a directional coupler. 
     A measure of how close the load impedance is to the desired impedance can take many forms, but typically it is expressed as a reflection coefficient 
     
       
         
           
             Γ 
             = 
             
               
                 Z 
                 - 
                 
                   Z 
                   0 
                 
               
               
                 Z 
                 + 
                 
                   Z 
                   0 
                   * 
                 
               
             
           
         
       
     
     where Γ (gamma) is the reflection coefficient of the impedance Z with respect to the desired impedance Z 0 . The magnitude of the reflection coefficient (|Γ|) is a very convenient way to express how close the impedance Z is to the desired impedance Z 0 . Both Z and Z 0  are in general complex numbers. 
     In general, the frequency-tuning subsystem  1525  receives the measurements indicative of the impedance, Z, of the plasma load from sensor  1520  and processes those measurements to produce frequency adjustments that are fed to exciter  1505  via a frequency control line  1530  to adjust the frequency generated by exciter  1505 . 
     As an alternative to sensor  1520  (as discussed below), the sensor  114  may be used to measure power parameters on a load side of the filter  104 , and the wideband measurement system  116  may provide a signal to the frequency-tuning subsystem  1525  that is indicative of an impedance, Z, of the plasma load. 
     The frequency-tuning subsystem  1525  performs computations (based upon frequency tuning methodologies) to generate frequency adjustments (e.g., frequency steps) that are fed to exciter  1505  via frequency control line  1530 . In some use cases, the objective is to adjust the frequency of exciter  1505 , thereby changing the impedance of the plasma load, in a manner that minimizes |Γ| (i.e., that achieves a Γ as close to zero as possible). The frequency that achieves this minimum |Γ| may be termed the target frequency. As those skilled in the art understand, an ideal complex reflection coefficient of zero corresponds to a matched condition in which the plasma-load impedance is perfectly matched to the desired impedance Z 0 . In other embodiments, the objective is not minimum |Γ|. Instead, frequency-tuning subsystem  1525  intentionally tunes exciter  1505  to generate a frequency other than the frequency that produces minimum |Γ|. Such an embodiment may be termed a “detuned” implementation and the target frequency may not minimize F. 
     Referring next to  FIG. 16 , shown is a flowchart  1600  depicting a method that may be carried out in connection with embodiments disclosed herein. As shown, power with a multi-state waveform is applied to the plasma chamber  100  with the high-frequency generator  102 ,  1502  (Block  1610 ), and power is also applied to the plasma chamber  100  with a low frequency generator  108  (Block  1620 ). Mixing products of the high and low frequencies are suppressed with the filter  104  (Block  1630 ). And as shown, a power signal between the filter  104  and the plasma chamber  100  is delayed (Block  1640 ), and a frequency of the high-frequency generator  102  is adjusted during each of the states to adjust an impedance presented to the high-frequency generator (Block  1650 ). 
     Accurate power measurement may require measuring power on the load side of the filter  104  with a bandwidth sufficient to capture a sufficient number of mixing products. This is so because the efficiency of the filter  104  is dependent on the trajectory of the load impedance presented to the filter  104 . Measuring on the high-frequency generator  102  side of the filter  104  may not provide an accurate measure of power delivered to the plasma load because it is difficult if not impossible to take into account the efficiency of the filter  104 . 
     A variety of different frequency tuning methods may be used to adjust the frequency of the high-frequency generator  102  at Block  1650 . In general, the frequency tuning methods determine which direction to adjust the frequency (whether to increase or decrease the frequency) and determine a magnitude of the frequency step used when a change is made to the frequency. 
     Assuming that a desirable frequency of operation is a frequency at which the magnitude of the load reflection coefficient is at or substantially close to its minimum, it is noted that the relationship between the controlled variable (frequency) and the error is not necessarily monotonic. Furthermore, the optimum point of operation is at a point where the gain (defined as change in error divided by change in frequency) is zero. 
     To add to the challenges, it is also possible that local minima may exist in an area which a control method can get trapped. In some special cases, where a priori information about the load is known, it is possible to arrange for an error function to be a monotonic function of frequency, so that a simple linear controller may be used. For example, such a system is disclosed in U.S. Pat. No. 6,472,822, entitled “Pulsed RF Power Delivery for Plasma Processing,” issued to Chen et al., on Oct. 29, 2002. Such linear control is rarely applicable due to the non-monotonic relationship between frequency and error, except in those special cases where a priori information about the load is available. 
     It has been found that two common problems with plasma loads are: (1) the nonlinear nature of the load because the plasma load impedance is a function of power level; and (2) the load impedance changes over time because of changing chemistry, pressure, temperature and other physical characteristics of the non-linear plasma load. Another problem that is unique to plasma (or plasma-like) loads is that the plasma can extinguish if the delivered power to the plasma falls below a minimum value for a long enough time. Thus, a frequency where insufficient power is delivered to the plasma load cannot be applied for very long, or the plasma will extinguish. 
     Moreover, when the power (e.g., RF power) to the load is pulsed, frequency tuning becomes even more problematic. Due to the nonlinear nature of the load and the relatively high quality factor (ratio of stored energy to energy delivered per cycle (e.g., RF cycle), often denoted by “Q”) that impedance matching networks employ, the load impedance changes very rapidly during the first few microseconds of the applied pulse (e.g., RF pulse). 
     U.S. Pat. No. 7,839,223 entitled “Method and Apparatus for Advanced Frequency Tuning,” issued 23 Nov. 2010 to van Zyl, et al. (the &#39;223 patent), which is incorporated by reference, discloses a variety of frequency tuning approaches that may be utilized in connection with embodiments disclosed herein. In one approach described in the &#39;223 patent, the frequency step size is permitted to increase if the error (e.g., a difference between a desired value of gamma and an actual value of gamma) is decreasing step-over-step, and the frequency step may decrease (or stay constant) if the error is increasing step-over-step. This approach may be utilized in connection with embodiments disclosed herein to help keep up with a time-varying load (e.g., to limit or reduce variation of a time-varying load reflection coefficient). 
     One method for simultaneous application of a multi-state waveform (e.g., pulsing) and frequency tuning discards information at the start of the pulse while the impedance is still rapidly changing and effectively controls frequency using only information once the load impedance is stable. This approach avoids the need for tuning within the pulse but manages to obtain a good average frequency of operation. 
     To avoid aliasing affects, the measurement and control may be synchronized with the rising edge of the pulse. By delaying the start of the measurement and control cycle from the start of the pulse, reasonable operation on plasma-type loads is possible. Typically discarding the first 10 microseconds after the start of the pulse is sufficient to achieve reasonable results. 
     In some cases it is not possible to totally discard information at the start of a pulse, but it is undesirable to use intra-pulse information due to the danger of aliasing effects, or due to insufficient control bandwidth, or due to the risk of unstable operation due to the high bandwidth requirements placed on the frequency control system. By using memory, it is possible to design a system with similar performance to a true intra-pulse control system, but which is implemented using a lower speed stable controller controlling on inter-pulse information. 
     Since the measurement and control cycle may be synchronized with the pulse, it is possible to use identical time slots in sequential pulses and a slower (than an intra-pulse controller) control system to control the frequency on an inter-pulse basis. In addition, measurements of identical timeslots of sequential pulses may be combined with measurements of time slots adjacent to those time slots. Not only the frequency, but also other control parameters may be stored and used by the control system to, for example, control delivered power to the load. Such other control parameters may comprise DC voltage supplied to the power devices, gate bias voltage in the case of MOSFETs (base emitter in case of bipolar devices) and RF drive level. Graphs depicting operation of an inter-pulse-controlled system for a high pulse repetition frequency are shown in  FIGS. 17, 18, and 19 . If the pulse on time becomes very long, it may be more advantageous to simply ignore information from the first few time slots, or switch to intra-pulse control at some time later in the pulse. 
       FIGS. 17, 18 and 19 , viewed together, illustrate the disclosed inter-pulse frequency tuning. In this scheme, f a2  is a function of only (or predominantly if adjacent time slots are also considered with some weighting) e a0 , e a1  and f a1 . Similarly, f b2  is a function of only (or predominantly) e b0 , e b1  and f b1 , and so forth. 
     Another problem is getting trapped in local non-optimal minima Using the fact that there is a fixed time in which the plasma can operate with substantially reduced power without extinguishing, it is possible to sample and store information about operation at frequencies completely different from the current operating point. Assuming that the plasma will not extinguish if power is substantially reduced for a short enough time, T, the method works by operating, for example, 99% of the time at the optimum frequency (as determined by the frequency tuning method) and using the remaining 1% of the time in time slots not exceeding T in duration to explore operation at other frequencies. In some implementations, power may be delivered at a selected frequency for at least 90% of a total time and power may be delivered at a test frequency during test periods that are no longer than 10% of the total time. 
     In some implementations, a value of the test frequency may change from test period to test period. In other implementations, the same test frequency is visited multiple times, each time adjusting the power delivered to the plasma load towards a desired power level. 
     Although many variations are possible, the following method is exemplary and illustrative. Consider operating for a time equal to 99T at the optimum frequency and then switching to a different test frequency for a time of T. The entire frequency range from f min  to f max  can be divided into, for example, 16 equally spaced frequencies f 0  through f 15 . The number of frequencies in which to divide the entire frequency range is a function of the known quality factor of the matching circuits employed. Sixteen is a typical number to make sure the true optimal point will not be missed in subsequent searches for the optimal frequency. 
     The method may start by sequentially searching f 0  through f 15  in the time slots of duration T to find a coarse optimum. The space may need to be searched a few times because the power control system may not be able to adjust the power correctly within the time T. Due to the nonlinear nature of the typical loads encountered, it is beneficial to measure the load reflection coefficient (or other error metric used by the method) at or close to a desired power level. By storing the control value and power level every time that a frequency is visited, the correct power level can be attained after a few visits to the same frequency. 
     Once the coarse optimum has been found, for example at f k , where k is an integer from 0 to 15, then the method may start using the time slots of length T to find an optimum. One option is to go to f 16 =0.5(f k−1 +f k ) provided k&gt;0 and f 17 =0.5(f k +f k+1 ) provided k&lt;15. The frequency at which the error is at a minimum between f 16 , f k  and f 17  then becomes the new desired frequency. The interval to the left and right of the new optimum is again split in two, and the minimum among the previous minimum and the two newly tested frequencies is selected. And when the minimum frequency happens to be f min  or f max , only one new frequency is generated. Due to the fact that the interval is split in half every time, the optimum frequency is found with sufficient accuracy within just a few iterations. And because the load is generally time-variant, once the optimum frequency has been found, the method generally has to start over to make sure conditions have not changed and a new global optimum has not been created. 
     While this method to find the global optimum is being executed, the previously described local tuning method can be run during the 99T time slot to maintain operation at the current local minimum. And staying at the current optimum frequency 99% of the time ensures that the average delivered power to the load remains virtually unchanged.  FIG. 20  graphically illustrates exemplary operating characteristics that may be associated with a method which uses a small percentage of the time with a maximum time slot T to search for a global optimum frequency. 
     Another approach to frequency tuning of the high-frequency generator  102  to adjust an impedance presented to the high-frequency generator  102  is described with reference to  FIGS. 21-38 . For example, in some implementations, the power source  2110 , circuits  2114 , sensor  2112 , power generation system  2200 ,  2300 ,  2400 ,  2500 ,  2600 ,  2700  described further herein may be integrated with the high-frequency generator  102 . In other implementations, the power source  2110 , circuits  2114 , sensor  2112 , and one or more components of the power generation system  2200 ,  2300 ,  2400 ,  2500 ,  2600 ,  2700  may be distributed. For example, circuits (e.g., circuits  2114 ,  2214 ,  2314 ,  2414 ) and/or sensors (e.g., sensors  2112 ,  2312 ,  2412 ) may be implemented in a centralized controller that is housed separately from the high-frequency generator  102 . As an additional example, circuits (e.g., circuits  2114 ,  2214 ,  2314 ,  2414 ) may be implemented as a part of the frequency-tuning subsystem  1525 . 
     As described with reference to  FIGS. 21-38  a plasma-sustaining power may be applied at a primary frequency while a secondary power signal (e.g., comprising one or more frequencies) that is much lower in power than the plasma-sustaining power is used to probe for an alternative primary frequency. Beneficially, the application of the secondary power signal enables one or more aspects of the plasma load to be monitored without adversely affecting the plasma load itself. In addition, when the plasma-sustaining power is applied to a plasma load via a match network, the application of the low level signal may be applied with one or more particular frequencies that result in detectable frequencies (e.g., mixing and intermodulation frequencies) that are passed by the narrow filtering band of the match network. Moreover, information obtained about the plasma load may be used to control one or more aspects of the generator. 
     In terms of generator control for example, automated frequency tuning may be performed using the information about the plasma load. For example, a global optimum of some measure of performance may be obtained, and the high-frequency generator  102  may be adjusted towards this global optimum frequency—without extinguishing the plasma. Exemplary approaches comprise processing noise generated by the primary operating frequency of a generator in order to effectively perform a low-power sampling sweep of an interested frequency range or generating a low power signal in addition to the primary power signal, where the low power signal is used to scout or probe for the global optimum. 
     In both cases, the low power nature of the noise or the probe signal enables exploration of a frequency range of one or more probe frequencies while the primary power signal of the generator remains at a frequency (e.g., at a local optimum of the measure of performance) where sufficient power can be delivered to the plasma load to sustain the plasma. For instance, the primary power signal can remain at or near a local optimum while the scouting signal or noise (both will be hereafter referred to as a “secondary power signal” or “probe signal”) finds the global optimum thereby continuing to allow substantial power to reach the plasma load while the probing occurs. 
     In the case where the secondary power signal is noise, the noise can either be inherent noise generated as a result of the primary power signal, or the noise can be added to the primary power signal. The noise can occur at a plurality of secondary probe frequencies sometimes limited to a bandwidth governed by a filter applied to the primary power signal. Where the secondary power signal is a low-level signal, such a probe signal can be orders of magnitude lower than an amplitude of the primary power signal (e.g., −3 dB, −5 dB, −10 dB, −20 dB, −50 dB, −100 dB). The low-level signal can be sinusoidal or any other type of periodic signal and can be generated at RF or other frequencies. Signals that start at a finite time and eventually become sinusoidal or periodic are considered to be sinusoidal or periodic, respectively. The low-level probe signal can be swept across a fixed range of secondary probe frequencies. Alternatively, the low-level probe signal can ‘hop’ between secondary probe frequencies according to a tuning algorithm that searches for a global optimum. 
     A global optimum may be found by comparing the optimality of different frequencies and choosing the most optimal frequency. For example, if the measure of optimality is the smallest load reflection coefficient magnitude, then the estimated load reflection coefficient magnitude at the different frequencies scouted by secondary power signal source are compared and the frequency at which the load reflection coefficient is the smallest is chosen as the global optimum frequency. The measuring and comparing to find the optimum can occur sequentially or, e.g., in the case where noise is used as the secondary power signal, the optimality of different frequencies can be computed simultaneously and the most optimal frequency chosen after the computation at the different frequencies. 
     Once the global optimum has been found, the primary power signal can be shifted to a frequency of the global optimum. Such shifting can involve a sudden switch from one frequency to another or can involve a power to the secondary power signal being ramped up while power to the primary power signal is ramped down such that the secondary power signal becomes the primary power signal. 
     Once the primary power signal is operating at a frequency of the global optimum, further fine tuning can occur. For instance, the secondary power signal can again go out in search of the global optimum, either because the global optimum at the power level of the primary power signal is different than a global optimum for the lower power of the secondary power signal, or because the global optimum varies and has changed since the first iteration of tuning occurred. 
     For the purposes of this disclosure, a “low level signal” is one that is substantially lower than a primary signal being delivered to a plasma chamber, for instance at least an order of magnitude smaller. 
     For the purposes of this disclosure, a “circuit” can comprise any combination of electrical components that generate an output signal based on an input signal. A circuit can be digital, analog, or part of or comprising a processor or central processing unit (CPU). A circuit can comprise, or can read from, a non-transitory, tangible computer readable storage medium with processor readable instructions for performing the methods described below. 
     For the purposes of this disclosure, components can be in communication, which in some cases comprises electrical communication (e.g., able to send signals therebetween) However, one of skill in the art will recognize that communication can also comprise optical and wireless radio communications, to name two non-limiting examples. 
     For the purposes of this disclosure, a “global optimum” can comprise a minimum or maximum value for a characteristic as sampled across a range of frequencies. For instance, where reflected power is the characteristic, the global optimum can be a global minimum, while where delivered power is the characteristic, the global optimum can be a global maximum. 
       FIG. 21  illustrates a power supply system configured for automated frequency tuning of power delivered to a plasma load. The power generation system  2100  is configured to provide radio frequency (RF) power to the plasma  2106  or plasma load via RF impedance matching circuits which can be an optional filter  2122  internal to the power source  2110  and/or a matching network  2104  external to the power source  2110 . Filtering and impedance matching are frequently done by the same physical network. Thus, a filter such as optional filter  2122  can perform the function of both filtering and impedance matching. 
     The power generation system  2100  can comprise a power source  2110  that converts external power  2140  to RF power and the power source  2110  may be a 13.56 MHz generator, but this is certainly not required. Other frequencies and other power sources are contemplated. The power generation system  2100  is configured to provide RF power (e.g., an RF voltage) at a sufficient level to ignite and sustain a plasma  2106  that is contained in the plasma chamber  2108 . The plasma  2106  is generally used to process a work piece or substrate (not shown) but is well known to those skilled in the art. 
     The power source  2110  can apply a primary power signal primarily at a primary frequency to an output  2111 . The output  2111  can be configured for coupling to an optional matching network  2104  and to a plasma chamber  2108 . In particular, the primary power signal can be delivered to a plasma  2106  or to a load of the plasma  2106  (also known as the plasma load). The connection(s)  2130  from the power source  2110  to the optional matching network  2104  are frequently coaxial cables, although other cable types and connection types are also possible. The connections(s)  2131  from the matching network  2104  to the plasma chamber  2108  are frequently made via custom coaxial connectors, although other cable types and connection types are also possible. In some applications there is no matching network  2104  and the output  2111  of the power source  2110  is connected directly to the plasma chamber  2108 . In this case RF impedance matching is done internal to the power source  2110  with the optional filter  2122 . 
     In some applications, other optional RF or DC generators  2150  can be connected to the plasma chamber  2108  via the optional matching network  2104 . And in some applications, other optional RF or DC generators  2151  (e.g., the low-frequency generator  108 ) can connect to the plasma chamber  2108  via other means, e.g., other optional matching networks  2105 . The connection of other generators to the plasma load either via the matching network(s)  2104  or through other means (e.g. connected to a different electrode to deliver power to the same plasma) generally makes the frequency tuning problem more complicated. In the following descriptions the possibility of other optional generator(s)  2150  and  2151  and other means of connecting to the plasma (e.g. matching network(s)  2105 ) are not excluded, but for simplicity will not be illustrated or discussed further. 
     The sensor  2112  may monitor a characteristic indicative of generator-delivered power or delivered power capability, such as reflected power, delivered power or impedance mismatch, to name just three non-limiting examples. Further non-limiting examples of a characteristic indicative of delivered power or delivered power capability comprise power delivered to the matching network  2104 , the power reflected from the matching network  2104 , the power delivered to the plasma chamber  2108 , the load impedance seen by the power generation system  2100 , and a characteristic of the plasma chamber  2108  such as plasma density. The sensor  2112  can also monitor a characteristic indicative of stability of the plasma system such as fluctuations in load impedance. The sensor  2112  can also monitor a characteristic indicative of the nonlinear nature of the plasma load such as the generation of mixing and intermodulation products. 
     The use of a secondary signal source to implement frequency tuning of the generator has the additional benefit that measurements of the plasma properties can be made from the generator. The optional matching network(s)  2104  typically act as band pass filters. This property of the matching network(s)  2104  makes it difficult to make reliable measurements of the plasma at the harmonics of the generator output frequency although such information could be useful. However, the modulation of the plasma impedance can be characterized by observing the mixing and intermodulation products that are generated by the secondary signal source. For example, if the primary signal source is at 13.56 MHz and the secondary signal source is at 13.57 MHz, one expects a mixing product at 13.55 MHz and intermodulation products at 13.56 plus multiples of 10 kHz, e.g. at 13.53, 13.54, 13.58, etc. Measuring the amplitude and phase relationship of the mixing and intermodulation products and deducing e.g. the amount of amplitude and phase modulation present can provide information about the plasma properties. The processing of the information can be done in a number of ways, from simply analyzing the time series of measurements from the sensor and performing higher order statistics on the time series to using dedicated receivers tuned to the mixing and intermodulation product frequencies to extract the amplitude and phase relationships to using any number of mathematical transformations comprising but not limited to the discrete Fourier transform. Monitoring the mixing and intermodulation products and detecting changes in the characteristics of the plasma indicated by e.g. the amount of phase modulation to name but one property can be useful in e.g. end-point detection in e.g. etch operations in the manufacture of semiconductors. 
     The sensor  2112  can be a directional coupler, current-voltage sensor or other multi-port network and can monitor current and voltage or combinations of voltage and current (e.g. incident and reflected signals) between the power source  2110  and matching network  2104  or between the matching network  2104  and the plasma chamber  2108 . In another non-limiting example, the sensor  2112  can be an optical detector directed into the plasma chamber  2108  to optically measure a density of the plasma  2106 . These examples in no way describe the scope or limits of the sensor  2112  or the positions where the sensor  2112  can be arranged, but instead demonstrate that the sensor  2112  can take a variety of forms and can be coupled to the system in a variety of ways (see  FIGS. 22-27  for various non-limiting examples). In addition, the sensor  2112  may be a sensor or sensors that already reside in the optional matching network(s)  2104  or plasma chamber  2108 . 
     Signals from the sensor  2112  or sensors already residing in the matching network(s)  2104  and plasma chamber  2108  can be provided to the one or more circuits  2114  that are also in communication with, and control, the power source  2110 . The one or more circuit(s)  2114  can use the information from the sensor  2112  and/or sensors already residing in the matching network(s)  2104  and plasma chamber  2108  to tune the primary and/or secondary probe frequencies that the power source  2110  operates at to optimize delivered power to the plasma  2106  or to optimize another measure of optimality such as plasma stability. 
     In some cases, such tuning results in operation at a local optimum (e.g., a local minimum of reflected power or a local maximum of delivered power, to name just two examples), so some tuning algorithms are able to further adjust the primary frequency in order to seek out the global optimum (e.g., via a series of fast frequency ‘hops’). However, such searching can take the power through regions of the frequency spectrum that are poorly impedance matched (e.g., around fa in  FIG. 28 ), and thus can cause delivered power to drop significantly, and in some cases can cause the plasma  2106  to be extinguished (e.g., at fa in  FIG. 28 ). 
     To avoid this, such searching for the global optimum can be performed by one or more secondary signals, thus enabling the high powered primary power signal to remain at a frequency (e.g., at a local optimum) where sufficient power can be delivered to the plasma  2106  while the search for the global optimum proceeds.  FIGS. 31-33  show plots of the monitored characteristic as a function of frequency and how a secondary power signal having substantially lower amplitude than a primary power signal can be used to search out the global optimum. These plots will be discussed in depth later once related systems and apparatuses have been described. 
       FIG. 21  illustrates a power generation system for automated frequency tuning of power delivered to a plasma load. A power source  2110  can provide a primary power signal to a plasma load of a plasma  2106  in a plasma chamber  2108  where the impedance seen by the power source  2110  is impedance matched by a matching network  2104  arranged between the power source  2110  and the plasma chamber  2108  and by frequency tuning of the power source  2110 . The power source  2110  can be frequency tuned in order to find optimum frequencies, typically where delivered power is optimized, but other measures of optimality may be used. Such tuning can sometimes result in the primary power signal from the power source  2110  being tuned to a local optimum rather than a global optimum. In such cases, a probe signal comprising one or more probe frequencies can be generated by the power source  2110  and processed to identify a global optimum without having to use the primary power signal to scout out the global optimum. 
     In other cases, a secondary power source can provide the secondary power signal (also referred to as the probe signal)(for example, see  FIGS. 24 and 26 ). The one or more secondary power signals can be provided at an amplitude or power level below that of the primary power signal (or substantially below the primary power signal, a fraction of the primary power signal, or at such a substantially lower power level as to have a negligible effect on the plasma  2106  as compared to the primary power signal). The probe signal can comprise a plurality of secondary probe frequencies all generated at the same time (e.g.,  FIGS. 31-33 ). In an alternative, the one or more secondary power signals can be tuned to two or more different frequencies at different times (e.g., as depicted in  FIGS. 31-33 ). 
     The one or more secondary power signals can be used to sample power delivery at frequencies other than that of the primary power signal without applying so much power at these secondary frequencies as to influence the plasma. In other words, the primary power signal can remain at a frequency where the plasma can be sustained (e.g. at or near a local optimum) while the one or more secondary power signals are used to search for the global optimum. 
     In particular, the sensor  2112 , or two or more sensors, and/or sensors already present in other components of the power generation system  2100  can monitor a measure of performance at the frequency of the primary power signal as well as at the secondary frequencies. The one or more sensors (e.g., sensor  2112 ) can also measure at the frequencies of expected mixing and intermodulation products to extract information about the nonlinear characteristics of the plasma  2106 . For instance, changes in the mixing and intermodulation products can be used to sense plasma ignition or end-point detection for plasma processes. The injection of a secondary frequency component or components and measurement of the properties of the mixing and intermodulation products can sense nonlinear characteristics of the plasma  2106  at harmonics of the primary power signal even though the match network(s)  2104  and the filter  2122  may not allow direct measurement of the harmonics. 
     For instance, the sensor  2112  can be a reflected power sensor or a delivered power sensor, and the characteristic can be reflected power or delivered power, respectively. Other characteristics can also be monitored and used to identify local and global optimums (e.g., load impedance seen by the power source  2110 , voltage and current of power on a supply cable  2130  to the matching network(s)  2104 , and plasma  2106  density, to name a few non-limiting examples). The sensor  2112 , and/or other sensors can provide information describing the characteristic(s) to one or more circuits  2114  (e.g., logic circuits, digital circuits, analog circuits, non-transitory computer readable media, and combinations of the above). The one or more circuits  2114  can be in communication (e.g., electrical communication) with the sensor  2112  and the power source  2110 . The one or more circuits  2114  can adjust the primary frequency of the power source  2110  in order to tune the power source  2110  to optimize delivered power to the plasma load. 
     In some embodiments, optimizing a measure of performance comprises controlling a feedback loop that uses a secondary power signal in order to scout out or search for a global optimum. In such a case, the one or more circuits  2114  can control the secondary power signal and its one or more secondary frequencies, based on feedback from the sensor  2112  (or two or more sensors, and/or sensors already present in other components of the power generation system  2100 ) regarding a measure of performance. For instance, a frequency of the secondary power signal can be swept across a fixed range of frequencies encompassing the primary frequency of the primary power signal, and the one or more circuits  2114  can monitor a measure of performance as a function of frequencies of the secondary power signal. Based on this sweep, the one or more circuits  2114  can identify a global optimum and then instruct the power source  2110  to adjust its primary frequency so as to move the primary power signal to the identified global optimum. Frequency hops or other tuning schemes can be used to find the global optimum via the one or more secondary power signals. 
     The secondary power signal can take a number of different forms. In one case, the one or more circuits  2114  can instruct the power source  2110  to apply a secondary power signal in the form of a low level signal at the one (e.g., as depicted in  FIG. 11 ) or more (e.g., as shown in  FIG. 32 ) secondary frequencies, either applying a low level signal at those secondary frequencies in a particular order (e.g.,  FIG. 31 ), or according to an algorithm to optimize the measure of performance (e.g.,  FIG. 32 ). In another case, the one or more circuits  2114  can instruct the power source  2110  to apply a secondary power signal in the form of noise. This noise can be inherent to the primary power signal, in which case, the one or more circuits  2114  do not necessarily have to supply an instruction to the power source  2110 , or can be non-inherent noise that is added to an output of the power source  2110  (e.g., as shown in  FIGS. 26 and 27 ). 
     Whatever form the secondary power signal appears in, in many embodiments, its amplitude is one or more orders of magnitude lower than that of the primary power signal. For instance, the secondary power signal can be between 1 and 100 dB lower than the primary power signal. In other embodiments, the secondary power signal can be 1 dB, 5 dB, 10 dB, 20 dB, 50 dB, or 100 dB lower than the primary power signal. 
     As shown the one or more circuits  2114  may comprise a global optimum identification module  2116  and a frequency control module  2118 . The global optimum identification module  2116  can analyze the information from the sensor  2112  at each of the one or more secondary frequencies and identify a frequency corresponding to a global optimum. This frequency can be referred to as an identified-global-optimum frequency and it corresponds to a global optimum of the characteristic of the generator-delivered power. The frequency control module  2118  can adjust the primary frequency of the primary power signal both during initial tuning of the primary power signal, which may result in identification of a local optimum, as well as adjustment of the primary frequency towards an identified global optimum frequency once a global optimum is identified by the global optimum identification module  2116 . 
     In particular, once an identified-global-optimum frequency is identified, the frequency control module  2118  can instruct the power source  2110  to adjust the primary frequency to jump to the identified-global-optimum frequency, or to lower the amplitude of the primary frequency while increasing the amplitude of the secondary frequency at the identified-global-optimum frequency, so that the primary and secondary frequencies reverse roles. In this way, the primary frequency can be transitioned to a frequency corresponding to a global optimum of the power characteristic (e.g., low reflected power or low level of oscillations) without applying power in a region of the frequency spectrum that could inhibit or extinguish the plasma (e.g., around fa in  FIGS. 28-33 ). 
     The operation of the global optimum identification module  2116  and the frequency control module  2118  can be cyclical to repeatedly improve an accuracy of adjusting the primary frequency toward a global optimum. For instance, where the characteristic (e.g., plasma impedance) being monitored is nonlinear, a global minimum for the characteristic may be found when the low level secondary power signal is applied, but when the much larger primary power signal is applied at the same frequency, a different global optimum frequency may exist for the higher powered signal. So, the secondary power signal can again be used to further hone in on a global optimum for the primary power signal and this can continue in a looping fashion for multiple iterations. Adjusting a frequency toward a global optimum can comprise changing the frequency to a frequency associated with the global optimum or merely changing the frequency to a frequency closer to the global optimum than to an original frequency. 
     In some embodiments, the primary frequency can be switched to one of the one or more secondary frequencies as soon as the one or more secondary frequencies begin to descend/ascend a steep enough portion of the frequency curves (e.g., between fa and f0 in  FIGS. 28-34 ). When such a steep portion of the curve is identified, the global optimum identification module  2116  may determine that it is approaching a global optimum and thereby instruct the power source  2110  to switch the primary frequency to a frequency near that of the secondary power signal, thereby enabling the primary power signal to jump over and avoid regions of the frequency curve that could inhibit the plasma (e.g., around fa). Once the primary power signal switches frequency, the one or more secondary power signals can continue to hone in on the global optimum, or the primary power signal can be used to further hone in on the global optimum. 
     In many embodiments supply connection(s)  2130  can be realized by a pair of conductors, or a collection of two-conductor coaxial cables that connect the power source  2110  with the matching network  2104 . In other embodiments, the cable  2130  is implemented with one or more twisted-pair cables. In yet other embodiments, the cable  2130  may be realized by any network of cable, comprising, but not limited to, a simple conductor hookup and quadrapole connections. The connection(s)  2131  is frequently implemented with a connector, but can also take a variety of forms comprising simple conductor hookup. 
     The matching network  2104  may be realized by a variety of match network architectures. As one of ordinary skill in the art will appreciate, the matching network  2104  can be used to match the load of the plasma  2106  to the power source  2110 . By correct design of the matching network(s)  2104  or  2105 , it is possible to transform the impedance of the load of the plasma  2106  to a value close to the desired load impedance of the power source  2110 . Correct design of the matching network(s)  2104  or  2105  can comprise a matching network internal to the power source  2110  (e.g., via filter  2122 ) or a matching network external to the power source  2110  as seen in  FIGS. 21-27 . 
     The one or more circuits  2114  can be original equipment of the power generation system  2100 , while in other embodiments, the one or more circuits  2114  can be retrofit components that can be added to a power generation system that was not originally capable of the herein described frequency tuning. 
     In an embodiment, the power generation system  2100  can comprise an optional filter  2122 . The filter  2122  can be configured to attenuate portions of the primary power signal outside of a selected bandwidth and do additional impedance matching. For example, because 50 ohm is the dominant impedance for cables and connectors  2130 , the desired impedance seen at the output of the power source  2110  is typically 50 ohm or some other convenient impedance. The impedance at the input (at the opposite side from the output of the power source  2110 ) of the filter  2122  provides the impedance desired by the active elements of the power source (e.g. MOSFETs) and is typically very different from 50 ohm, e.g. 5+j6 ohm is typical for a single MOSFET amplifier. For such a system the filter  2122  will then be designed to match 50 ohm at the output to 5+j6 ohm at the input. In addition to impedance matching the filter is also typically designed to limit harmonics generated by the active elements. E.g. the filter can be designed to match 50 ohm at the output to a value close to 5+j6 over the range of frequencies over which the generator is expected to operate, e.g. from 12.882 to 14.238 MHz and suppress signals at frequencies higher than 25 MHz by a certain amount, typically at least 20 dB at the second or third harmonic of the output. 
     The sensor  2112  can be arranged in a variety of locations, comprising those that are part of the power generation system  2100 , and those that are external thereto. Where the sensor  2112  monitors a characteristic can also vary from embodiment to embodiment, as will be seen in  FIGS. 22-27 . 
       FIG. 22  illustrates one embodiment of a power generation system  2200  where the sensor  2212  resides within a power generation system  2200  along with a power source  2210  and one or more circuits  2214 . The power generation system  2200  comprises an output  2220  configured for coupling to the optional matching network(s)  2204  or directly to the plasma chamber  2208  if the matching network(s)  2204  is not present. Thus, the primary power signal and the one or more secondary power signals can be provided to the output  2220  and hence configured for delivery to the matching network(s)  2204 . 
       FIG. 23  illustrates one embodiment of a power generation system  2300  where a sensor  2312  resides outside the power generation system  2300 . Here the power generation system  2300  comprises the power source  2310 , one or more circuits  2314 , an optional filter  2322 , and an output  2320  to the power generation system  2300 . The sensor  2312  is coupled to the one or more circuits  2314  and provides information describing a measure of performance (e.g. load reflection coefficient magnitude or plasma density). The sensor  2312  monitors the characteristic either between the power generation system  2300  and an optional matching network(s)  2304 , between the matching network(s)  2304  and the plasma chamber  2308 , or at the plasma chamber  2308 , or between the power generation system  2300  and plasma chamber  2308  if the match network(s)  2304  is not present. The sensor  2312  could also perform monitoring at or within the matching network(s)  2304 . 
     While  FIGS. 21-23  illustrate a single power source  2110 ,  2210 ,  2310 , one of skill in the art will recognize that this power source  2110 ,  2210 ,  2310  is capable of generating both the primary and secondary power signals concurrently. For instance, the power source  2110 ,  2210 ,  2310  can source both a high power primary power signal (e.g., using a primary oscillator) and a low level secondary power signal (e.g., using a secondary oscillator), or the power source  2110 ,  2210 ,  2310  can source a high power primary power signal (e.g., with a single oscillator-amplifier combination) and use the noise inherent to that primary power signal as the secondary power signal, to name two non-limiting examples. Alternatively, the power source  2110 ,  2210 ,  2310  can generate a primary power signal (e.g., with a single oscillator-amplifier combination) and combine this with generated or amplified noise. While each of these examples demonstrate how a single power source  2110 ,  2210 ,  2310  can produce both the primary power signal and the secondary power signal,  FIGS. 24-27  will illustrate embodiments where a power source generates the primary power signal and a low level signal source generates the secondary power signal. 
       FIG. 24  illustrates an embodiment of a power generation system  2400  having a power source  2410 , a low level signal source  2411 , one or more circuits  2414 , an optional sensor  2412  that can be arranged within the power generation system  2400  or an optional sensor  2413  that can be arranged outside the power generation system  2400 , and a combiner  2424  that combines the outputs from the power source  2410  and low level signal source  2411 . As one of ordinary skill in the art will appreciate, the combiner may be realized by a coupler known in the art. 
       FIG. 25  illustrates an embodiment of a power generation system  2500  where the primary and secondary signals are combined before being amplified by a power amplifier  2550 . 
       FIG. 26  illustrates an embodiment of a power generation system  2600  where the power source  2610  generates the primary power signal and a noise source  2613  generates the secondary power signal in the form of noise. The primary power signal and the secondary power signal, or noise, can be combined in the power generation system  2600  and the combined signal can be provided to an output  2620  of the power generation system  2600 . As one of ordinary skill in the art will appreciate the noise source  2613  may be realized by a variety of different types of devices comprise a noise diode. Beneficially, the noise source  2613  may generate a continuum of secondary frequencies, and the response of the secondary frequencies may be processed in parallel at a plurality of different frequencies (e.g., by a plurality of demodulating channels or fast Fourier transform module(s)). For example, a reflection coefficient at the plurality of frequencies may be arrived at in parallel to identify a frequency that provides a low reflection coefficient, a stable frequency, or a balance between stability and a low reflection coefficient. 
       FIG. 27  illustrates an embodiment of a power generation system  2700  where the primary and secondary signals are combined before being amplified by a power amplifier  2750 . In this embodiment, the secondary signal is generated by a noise source  2713 . 
     The systems illustrated in  FIGS. 21-27  can be more easily understood with reference to the plots seen in  FIGS. 28-35 . 
       FIG. 28  shows a plot of a measure of performance as a function of the frequency. The solid line  2801  shows the actual measure of performance (e.g., load reflection coefficient magnitude) as a function of frequency that would result if the primary power signal were adjusted to each frequency and the measurement made. The dotted line,  2802 , shows the estimated measure of performance obtained using a secondary power signal or signals while the primary power signal remains at a fixed frequency (e.g., f1). 
     As discussed, the power level of the primary frequency affects the measure of performance (e.g., load reflection coefficient); thus the measure of performance that is estimated using low-level power signals will differ from the measure of performance at the higher power of the primary signal. But as discussed further herein, the low level signals enable the desired primary frequency (e.g., that produces a low reflection coefficient and/or low instabilities) to be closely estimated. The frequency of the primary signal may then be fine-tuned at the higher power level without testing frequencies that may result in the plasma being extinguished. 
       FIG. 29  depicts an aspect where an initial primary frequency may be applied between f1 and fa, and how a frequency tuning algorithm (that relies on sweeping and testing the frequency of the primary power) can become trapped in a local optimum of a measure of performance without the information provided by low power secondary signals. More specifically, a tuning algorithm can tune the primary frequency toward what is believed to be an optimum frequency at f1. In particular,  FIG. 29A  shows a measure of performance (e.g., reflection coefficient) as a function of frequency; the solid line of  FIG. 29B  shows how an algorithm using only the primary power could adjust the primary power signal frequency to minimize the measure of performance; and  FIG. 29C  shows the spectrum (power per bandwidth, e.g., Watt per 3 kHz bandwidth) of the power generation system output  2220 ,  2320 ,  2420 ,  2520 ,  2620  or  2720  at time t 2  in  FIG. 29B . As shown by the dotted line in  FIG. 29B , a global optimum frequency could be identified using low level secondary signals. 
     But as shown by the solid line, upon reaching that local optimum at f1, if the primary frequency is used to search out the global optimum, such attempts might lead to application of power around the frequency fa, which may result in extinguishing the plasma as seen in  FIGS. 30A and 30B .  FIG. 30A  shows a measure of performance as a function of frequency. The solid line in  FIG. 30A  shows the measure of performance with a lit plasma, and the dotted line shows the measure of performance for an extinguished plasma.  FIG. 30B  shows how a global search using the primary power signal can lead to an extinguished plasma because not enough power can be delivered around fa to sustain the plasma.  FIG. 30C  shows the spectrum of the power generation system output at time t 2  in  FIG. 30B . 
     Instead, one or more secondary power signals can be used to search out the global optimum, as shown in  FIG. 31  (showing one secondary power signal) and  FIG. 32  (showing multiple secondary power signals), while the primary power signal remains at a fixed frequency (e.g., at or near a local optimum). In  FIG. 31 , shown is frequency tuning using a secondary power signal in the form of a low level signal at a single secondary frequency applied in a particular order.  FIG. 32  shows frequency tuning using a secondary power signal in the form of a low level signal with spectral components at multiple secondary frequencies adjusted according to an algorithm to optimize a measure of performance. 
     As shown, the one or more secondary power signals can be applied at power levels far below that of the primary power signal and can be applied at one or more secondary frequencies. The secondary frequencies can be fixed frequencies with equal or unequal spacing, or can be variable frequencies as shown in  FIG. 32 . Further, the primary and secondary power signal(s) can be applied concurrently. 
     As illustrated in  FIG. 31  the secondary signals (probe frequencies) can be applied continuously, or as illustrated in  FIG. 32 , only while searching for a global optimum. Further, while a single characteristic is shown in the plots of  FIGS. 28-33 , in other embodiments, multiple characteristics, e.g., load reflection coefficient magnitude together with plasma stability measured through (e.g., fluctuations in load impedance) can be simultaneously monitored and an analysis of all the monitored characteristics (or a plurality of the monitored characteristics) can be used to identify a global optimum. In this way, the global optimum is identified without applying the full power of the primary signal around fa or any frequencies that could extinguish the plasma. 
     In some modes of operation, the amplitude of the one or more secondary power signals applied at the one or more secondary probe frequencies is so small that it can be considered negligible in comparison to the primary power signal, and hence, does not have a significant influence on the plasma. In other applications, the amplitude of the secondary power signal or signals may be significant compared to the primary power signal if the goal is simply to not extinguish the plasma while searching for the global optimum. In such a case care must be taken not to exceed the voltage and current ratings of the plasma system because of high resulting amplitude at the beating frequencies. 
       FIG. 31  shows an embodiment where a single secondary probe frequency is continuously swept over a frequency range. The range over which the secondary probe frequency(s) is (are) swept would typically be the range of frequencies over which the power generation system is expected to operate (e.g. 12.882 to 14.238 MHz), but it does not have to be the case. Examples in which other frequency ranges can be considered comprise when information about the plasma condition is extracted using the secondary power signals by, for example, analyzing mixing and intermodulation products. In other cases as illustrated in  FIG. 32 , the secondary probe frequency or frequencies can be adjusted according to an algorithm to find the optimal frequency rather than sweep in a pre-determined pattern as shown in  FIG. 31 . Also as shown in  FIG. 32 , once a global optimum has been identified, the secondary power signals may be shut off rather than be applied continuously as shown in  FIG. 31 . 
     As illustrated in  FIG. 31A  and  FIG. 32A , the estimate of optimum frequency using the secondary power signal or signals may not correspond exactly to the true optimum. Typically such discrepancy would result from the nonlinear nature of the plasma load. As illustrated in  FIG. 31B  and  FIG. 32B , following a determination of the optimum frequency using the secondary power signals, the primary frequency may be adjusted to further optimize performance.  FIGS. 31C and 32C  depict spectral components of the primary and secondary probe frequencies of  FIGS. 31B and 31C , respectively. 
       FIGS. 33A-33C  show the case where the secondary power signal is noise.  FIG. 33C  shows the spectrum of the power generation system output at time t 2  in  FIG. 33B . The noise can either be inherent to the primary power signal or can be added to the power generation system output (e.g., see  FIGS. 26 and 27 ).  FIG. 33B  shows noise power as a function of time assuming the case where noise is added to the power generation system output. 
     Once a global optimum has been identified, the primary power signal can be adjusted or switched to (or toward) the frequency corresponding to the global optimum without the primary power signal passing through regions of the frequency spectrum that could inhibit the plasma (e.g., near fa). For instance, in  FIG. 14 , the primary power signal amplitude is ramped down while an amplitude of the secondary frequency at the global optimum is ramped up. In this way, the primary power signal and the secondary power signal switch places.  FIG. 35  shows another variation of switching the primary frequency toward the global optimum, in which the frequency of the primary power signal is changed abruptly to the identified global optimum frequency. 
     In some embodiments, the identified global optimum frequency can be selected from one of the secondary frequencies, but this is not necessary. For instance, the identified global optimum frequency may be between two of the two or more secondary frequencies. For instance, interpolation between ones of the secondary frequencies can be used to identify the identified global optimum frequency. 
       FIG. 36  illustrates a method for frequency tuning a power generation system to hone in on a global optimum of a measure of performance using a secondary probe signal to find the global optimum. The method  3600  applies a primary power signal (e.g., with the high-frequency generator  102 ) primarily at a primary frequency to a plasma system (e.g., matching network(s)  2104  connected to a plasma chamber  2108 ) (Block  3602 ). Concurrently, the method  3600  applies a low-level signal to the plasma system at one or more or a continuum (e.g., as in the case of noise) of secondary probe frequencies (Block  3604 ). 
     The low-level signal can be periodic or the sum of periodic signals, can be noise inherent to the primary power signal, or can be noise added to the primary power signal. The one or more secondary frequencies can be equally spaced in frequency or can have a varying spacing. The one or more secondary frequencies can be applied all at once or at separate times and can be adjusted over time. The one or more secondary frequencies can be swept across a fixed range of frequencies. Alternatively, the one or more secondary frequencies can be adjusted via feedback to probe for and hone in on a global optimum. The one or more secondary or continuum of secondary frequencies can be applied all the time or only while needed. 
     The method  3600  monitors a characteristic that is a measure of performance (e.g., load reflection coefficient magnitude) as a function of frequency, particularly at the one or more or continuum of secondary frequencies and/or at the primary frequency and/or at expected mixing and intermodulation products of the primary and secondary frequencies (Block  3606 ). As shown, mixing products of the primary frequency and any low frequency from any low-frequency generator (e.g., low frequency generator  108 ) are suppressed (e.g., with the filter  104 )(Block  3607 ). The method  3600  then identifies an optimum frequency corresponding to a global optimum of the characteristic (Block  3608 ). This can be done via minimization and maximization algorithms familiar to those of skill in the art. Finally, the method  3600  adjusts the primary frequency of the primary power signal to the optimum frequency identified in the identifying operation (Block  3610 ). This adjustment can be made in a variety of ways. For instance, the adjustment may have to avoid applying primary power only in regions where reflected power approaches 100% (e.g., around fa in  FIG. 28 ) for extended periods of time since this may extinguish the plasma (unless e.g. the plasma is sustained by another power source  2150  or  2151 ). So, the primary power signal can be switched to the optimum frequency or the power levels of the primary and secondary power signals can be gradually reversed such that the power signals reverse places, to name two non-limiting examples. 
     In some embodiments, the method  3600  ends when the primary power signal has been moved to a frequency identified as the global optimum using the secondary power signal or signals. But in other instances, the method  3600  can loop to further refine the optimization or to account for changes to the global optimum due to e.g. the nonlinear nature of the plasma load or parameters that may change over time (e.g., plasma chamber gas pressure). 
     The identifying of an optimum frequency (Block  3608 ) can occur in real time as samples are obtained from the monitoring (Block  3606 ) or the analysis can occur after a range of frequencies has been sampled. The moving of the primary frequency (Block  3610 ) can occur only once the global optimum has been identified (Block  3608 ) or it can occur as soon as a more optimal frequency than the current primary frequency is identified. 
     The method of using a secondary power signal to monitor characteristics can also be used for the purpose of identifying plasma characteristics or changes in plasma characteristics. Instead of identifying an optimum frequency and adjusting the primary frequency towards the identified global optimum, the output or monitoring a characteristic (Block  3608 ) can be used to identify the plasma characteristics or changes in plasma characteristics. Monitoring mixing and intermodulation products can be used to monitor the nonlinear behavior of the plasma or simply to detect whether or not the plasma is lit. Rather than looking at particular mixing and intermodulation produces, higher order statistics (e.g., the bispectrum) can be used to identify plasma characteristics or changes in plasma characteristics. 
       FIG. 37  shows three exemplary implementations of the sensor e.g. sensor  2112  or  2412 . The sensor can, e.g., be a directional coupler  3710  as shown in  FIG. 37A  or a voltage and current (VI) sensor as shown  FIG. 37B , and either implementation can comprise a filter  3730  and analog to digital converter  3720  as shown  FIG. 37C . 
       FIG. 38  shows an exemplary implementation of the global optimum identification module (e.g.,  2116  or  2418 ). Part of the functionality shown in  FIG. 38  can also be part of the sensor.  FIG. 38  shows an implementation using multiple demodulators  3810  allowing the processing of multiple frequency components at the same time. The signals  3820  (labeled A) and  3830  (labeled B) can, for example, be forward and reflected power or voltage and current or some other measurement of interest. After multiplication  3850  by cosine and sine functions and filtering  3840 , complex vector representations of A and B at different frequencies labeled A 1 , B 1  through A N , B N  are used in the calculation of power and load reflection coefficients at multiple frequencies. Typically one channel will be reserved for the primary frequency. The other channels can be set to the secondary frequency or frequencies or to expected mixing and intermodulation products. As noted before this is just one implementation and many other implementations using, for example, e.g., the discrete Fourier transform rather than dedicated demodulation channels are possible. 
     The illustrated arrangements of the components shown in  FIGS. 21-27  are logical, the connections between the various components are exemplary only, and the depictions of these embodiments are not meant to be actual hardware diagrams; thus, the components can be combined or further separated in an actual implementation, and the components can be connected in a variety of ways without changing the basic operation of the systems. 
     Instead of a single secondary power source, as seen in  FIGS. 24-27 , two, three, four, or more secondary power sources could be used to generate two or more secondary power signals. 
     For the purposes of this disclosure, the secondary power signal can be periodic, for instance, an RF signal. However, in other embodiments, non-periodic power signals can be used (e.g., noise). 
     While this disclosure has repeatedly shown tuning for local and global minima, one of skill in the art will appreciate that tuning for local and global maxima is also envisioned and this disclosure can easily be applied to monitored characteristics where the primary frequency of the delivered power is optimized for a global maximum of a monitored characteristic. Moreover, the frequency tuning described herein need not be performed to arrive at local or global maxima/minima. Instead, applications where it is beneficial to arrive at a detuned frequency may be preferred in some instances, e.g., where a frequency of the high-frequency generator (e.g., high-frequency generator  102 ) that achieves a stable plasma is preferred over a minimum level of reflected power. 
     Those of skill in the art would understand that information and signals may be represented using any of a variety of different technologies and techniques. For example, data, instructions, commands, information, signals, bits, symbols, and chips that may be referenced throughout the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof. 
     Those of skill would further appreciate that the various illustrative logical blocks, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. The various illustrative logical blocks, modules, and circuits described in connection with the embodiments disclosed herein may be implemented or performed with a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. 
     The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in non-transitory memory comprising RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In the alternative, the processor and the storage medium may reside as discrete components in a user terminal. 
     Referring to  FIG. 39 , shown is an example of a computing system  3900  that may be utilized in connection with the embodiments disclosed herein. As shown, a display  3912  and nonvolatile memory  3920  are coupled to a bus  3922  that is also coupled to random access memory (“RAM”)  3924 , a processing portion (which comprises N processing components)  3926 , a field programmable gate array (FPGA)  3927 , and a transceiver component  3928  that comprises N transceivers. Although the components depicted in  FIG. 39  represent physical components,  FIG. 39  is not intended to be a detailed hardware diagram; thus, many of the components depicted in  FIG. 39  may be realized by common constructs or distributed among additional physical components. Moreover, it is contemplated that other existing and yet-to-be developed physical components and architectures may be utilized to implement the functional components described with reference to  FIG. 39 . 
     This display  3912  generally operates to provide a user interface for a user, and in several implementations, the display  3912  is realized by a touchscreen display. In general, the nonvolatile memory  3920  is non-transitory memory that functions to store (e.g., persistently store) data and machine readable (e.g., processor executable) code (comprising executable code that is associated with effectuating the methods described herein). In some embodiments for example, the nonvolatile memory  3920  comprises bootloader code, operating system code, file system code, and non-transitory processor-executable code to facilitate the execution of the methods described herein (including, but not limited to, the methods described with reference to flowcharts  FIGS. 7, 16-20, and 36 ). 
     In many implementations, the nonvolatile memory  3920  is realized by flash memory (e.g., NAND or ONENAND memory), but it is contemplated that other memory types may be utilized as well. Although it may be possible to execute the code from the nonvolatile memory  3920 , the executable code in the nonvolatile memory is typically loaded into RAM  3924  and executed by one or more of the N processing components in the processing portion  3926 . The non-volatile memory  3920  or RAM  3924  may be utilized for storage of a frequency of the global optimum as described in  FIGS. 28-34 . 
     In operation, the N processing components in connection with RAM  3924  may generally operate to execute the instructions stored in nonvolatile memory  3920  to realize aspects of the wideband measurement system  116 ,  120 , the frequency-tuning subsystem  1525 , global optimum identification module  2116 , the frequency control module  2118  the circuits  2114  and control aspects of the high-frequency generator  102 ,  1502  (e.g., frequency tuning aspects), the power source  2110  and match  106 . For example, non-transitory processor-executable instructions to effectuate aspects of the methods described with reference to  FIGS. 7, 16, and 16-20  may be persistently stored in nonvolatile memory  1620  and executed by the N processing components in connection with RAM  3924 . As one of ordinarily skill in the art will appreciate, the processing portion  3926  may comprise a video processor, digital signal processor (DSP), graphics processing unit (GPU), and other processing components. 
     In addition, or in the alternative, the field programmable gate array (FPGA)  3927  may be configured to effectuate one or more aspects of the methodologies described herein (e.g., the methods described with reference to  FIGS. 7, 16-20, and 36 ). For example, non-transitory FPGA-configuration-instructions may be persistently stored in nonvolatile memory  3920  and accessed by the FPGA  3927  (e.g., during boot up) to configure the FPGA  3927  to realize aspects of the wideband measurement system  116 ,  120  and control aspects of the high-frequency generator  102  (e.g., frequency tuning aspects) and match  106 . 
     The input component may operate to receive signals (e.g., from sensors  114 ,  118 ,  1520 ,  2112 ,  2312 ,  2412 ,  2413 ) that are indicative of one or more aspects of power. The signals received at the input component may comprise, for example, voltage, current, forward power, reflected power and plasma load impedance. The output component generally operates to provide one or more analog or digital signals (e.g. frequency control signal on the frequency control line  1530 ) to effectuate operational aspects of the generators  102 ,  108 , match  106 , and/or wideband measurements systems  116 ,  120 . For example, the output portion may provide control signals utilized by the oscillators and power amplifiers of generators  102 ,  108 , match  106 , and/or wideband measurements systems  116 ,  120 . 
     The depicted transceiver component  3928  comprises N transceiver chains, which may be used for communicating with external devices via wireless or wireline networks. Each of the N transceiver chains may represent a transceiver associated with a particular communication scheme (e.g., WiFi, Ethernet, Profibus, etc.). 
     The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. It should be recognized that the various depicted embodiments are not intended to be isolated embodiments. Instead, the several embodiments depicted herein should be viewed to convey several aspects that may be combined. For example, the probe signal and signal detection technologies described with reference to  FIGS. 21-38  may be utilized in connection with the frequency tuning algorithms described with reference to  FIGS. 1-20 . As another example, the filter  104 ,  904 ,  1404  and wideband measurement systems  116 ,  118  may be utilized in connection with the embodiments described with reference to  FIGS. 21-38 . Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.