Abstract:
Samples representing signals and noise from a plasma system across a frequency range are collected. A first complex frequency-domain signal component is identified from a sample corresponding to a frequency value F at which a local maximum signal is found. This first component is phase-adjusted by a variable angle θ to a predetermined phase angle φ, and stored. A further complex component is identified corresponding to a frequency F(N) representing an Nth order harmonic of F. This further component is phase-adjusted by an angle N×θ, and stored. The procedure is repeated to build up sets of phase-adjusted first and further components, with θ chosen in each iteration for the first component to give a constant phase angle φ, and within any iteration the value of θ used for the first component is employed in the adjustment of the further component. The aggregated, phase-adjusted components exhibit increased signal-to-noise.

Description:
TECHNICAL FIELD 
       [0001]    The present invention generally relates to the analysis of RF signals from plasma systems, including analysing optical signals of a plasma load modulated at RF frequencies. 
       BACKGROUND ART 
       [0002]    Plasma processes are used in a wide range of industries such as the semiconductor, flat panel and solar fields. These plasma processes are required to perform complex processes such as deposition, etching or modification of a surface in real time. 
         [0003]    The plasmas are formed by passing an RF current through a low pressure gas. The density of the plasma depends on the frequency of the RF waveform through the relationship between collision frequency and RF frequency. Relatively high frequencies are used to maximise the plasma density. Often a second frequency RF wave is used to bias the substrate being processed so that ions strike the surface with the correct energy to maximise etch rate. In recent years the structures to be etched are being reduced in dimension and more complex plasma excitation regimes are being used. Often the plasmas are generated from multiple frequencies in order to control the plasma density and energy of ions arriving at the wafer surface separately. Pulsed plasmas are also being used to better control the electron energy and quality of the etch. 
         [0004]    The yield and overall efficiency of a plasma process is often determined by the physical geometry of the substrate holder and its environs and the plasma power source and matching. The RF impedance of the plasma and the quality of the power delivered are important factors that now need to be monitored to ensure the process is running correctly. The plasma impedance and power are complex values containing both a real and imaginary components, the measured impedance includes both the chamber and plasma impedances and because the chamber impedance often dominates over the plasma impedance very accurate measurements are required. 
         [0005]    Directly monitoring the plasma parameters is difficult because of the problems associated with plasma disturbance and contamination arising from introducing sensors into the plasma reactors. Therefore external probes on the RF delivery path or optical probes mounted on a window are becoming more important in ensuring that the plasma is performing correctly and in supporting closed loop control of the plasma process. 
         [0006]    Difficulties arise in the current art in that multiple frequencies are used. Typical frequencies are 400 kHz, 800 kHz, 2 MHz, 13.56 MHz, 27 MHz and 40 MHz. Because the plasma is a non-linear load the plasma produces harmonics which are present in the signals and confuse the sensors. Also when two frequencies are present the non-linear plasma load produces an inter-modulation between the two frequencies. These inter-modulation components also add to the complexity of the RF waveforms. In some systems the two frequencies are not fixed but can move in order to facilitate matching of the power to the load. The challenge for a diagnostic system is to isolate and measure the fundamental parameters of the plasma process such as power delivered, plasma impedance, or optical intensity in such a complex signal. 
         [0007]    U.S. Pat. No. 6,522,121 B2 describes a method of down-converting each RF signal to a base band and analysing the signal using a quality audio digitizer. This approach creates a plurality of signals and digitizers. Such a system can become quite complex and only a limited number of signals can be monitored at any one time. The system is limited in pulsed application if the pulse frequency is of the order of, or higher than the local oscillator used to down convert the signal. Frequency tuning means that the fundamental will move and so the local oscillator must track this movement, which is not an easy solution to implement and is a drawback. 
         [0008]    To overcome these issues an improvement has been proposed in WO2006/135515 based on sampling-based frequency converters that bring the RF voltage and current signals to a fixed intermediate frequency. However, such down converters are limited in application where there are multiple frequencies or where there is a high repetition pulse rate. Direct sampling of the RF requires that the sampler operates at twice the maximum frequency measured (referred to as the Nyquist frequency). Existing high-resolution analogue to digital converters have limited bandwidths and this creates a need for a sampling system that does not require extremely high sampling rates but avoids down conversion to an IF frequency. 
         [0009]    A further limitation of the existing art is the handling of noise and obtaining good signal-to-noise (S/N) ratios, especially for higher harmonics and in the presence of multiple frequency signals. The state of the current art consists of either synchronised averaging where the S/N increases with the square root of the number of measurements that are averaged. Synchronisation is possible but requires hardware isolation of the signals and a circuit to lock on the required signal. Such systems are complex to build and are not suitable for pulsed operation because of the time needed to lock to the sync signal, there are also not suitable for variable multi-frequency systems. 
         [0010]    In the case of non-synchronous RF signals the current art provides that the signals be captured in time in samples of fixed length. A periodogram is computed from a finite-length digital sequence using the fast Fourier transform (FFT). The raw periodogram is not a good spectral estimate because of spectral bias and the fact that the variance at a given frequency does not decrease as the number of samples used in the computation increases. The spectral bias problem arises from a sharp truncation of the sequence, and can be reduced by first multiplying the finite sequence by a window function which truncates the sequence gradually rather than abruptly. Averaging periodograms does not improve S/N and leaves the interference from inter-modulation and overlapping harmonics in place. Techniques to reduce S/N such as Bartlett&#39;s method cannot be used because the complex spectral data requires that the data retain the maximum spectral frequency resolution possible. 
         [0011]    If the sample frequency is below the highest frequency required to be measured then high frequency components will be aliased and appear in the time sequence at lower frequencies further complicating the spectrum and adding often unwanted spectral features. The state of the art normally removes this problem by adding a hardware based anti-aliasing filter on the input to the analog-to-digital converter (ADC). This reduces to the bandwidth of the system. 
         [0012]    Thus it can be seen that the current state of the art either down converts the raw signals to an intermediate frequency and captures the data using high resolution ADC&#39;s or uses direct conversion and measures the periodogram. Both approaches are limited by the spectral complexities of the signals of interest and do not allow the reduction of variance and subsequent increase in S/N that is desired to produce reliable signals for process control in multi-frequency, variable frequency and pulsed frequency applications. 
       SUMMARY OF THE INVENTION 
       [0013]    There is provided a method of analysing RF signals from a plasma system, comprising the steps of:
       (a) receiving from the plasma system one or more signal channels, wherein the or each signal channel comprises a data source representing signals and noise from the plasma system across a frequency range;   (b) identifying, in a first RF signal sample from one of said signal channel(s), a first frequency value, F, at which a local maximum is found in the frequency domain;   (c) determining a first complex frequency-domain signal component at said first frequency value, F in said first signal sample;   (d) identifying, in said first RF signal sample or in a further RF signal sample from one of said signal channel(s), a further frequency value F(N), where N is an integer representing an Nth order harmonic of said first frequency F, and wherein N=1 for the 1st order harmonic at the first frequency F;   (e) determining a further complex frequency-domain component at said further frequency value in the RF signal sample in which said further frequency value is identified;   (f) transforming the first complex frequency-domain component by adjusting its phase by an angle θ to a predetermined phase angle φ, to provide a phase-adjusted first complex signal component;   (g) transforming the further complex frequency-domain component by adjusting its phase by an angle equal to N×θ, to provide a phase-adjusted further complex signal component;   (h) iteratively repeating steps (b) to (g) in respect of a plurality of signal samples from the same plasma system, wherein in each iteration the value of θ is chosen to give a constant phase angle φ for the phase-adjusted first complex signal component across different iterations, and wherein within any iteration the value of θ chosen in step (f) is employed in the adjustment of step (g);   (i) aggregating or averaging the phase adjusted first complex signal components obtained in each iteration;   (j) aggregating or averaging the phase-adjusted further complex signal components obtained in each iteration.       
 
         [0024]    The phase shift operation essentially allows multiple periodograms to be averaged without the desired fundamental and its harmonics being reduced. Other signals which are not in phase with the fundamental voltage will add vectorally in such as way as they tend to cancel. This also includes noise, so that the variance of the signal will reduce by the square root of the number of periodograms averaged. This leads to a dramatic increase in the S/N of the averaged signal. 
         [0025]    The first frequency F is preferably, but need not be, a fundamental frequency from the plasma system, e.g. F may be the 13.56 MHz signal often found in a plasma system. However, the first frequency could itself be a harmonic, such as the second harmonic at 27.12 MHz, in which case the value N=1 (in the phase shifting method disclosed herein) represents the 27.12 MHz signal and N=2 represents the harmonic at 54.24 MHz (which is in reality the 4th harmonic of the 13.56 fundamental). 
         [0026]    What is important is that the first frequency is phase-adjusted by an angle θ to a predetermined phase angle φ, and then the or each further frequency is adjusted by an angle N×θ where N represents the frequency multiplier between the first and further frequencies. 
         [0027]    In some embodiments, the signal channel in which the first frequency value is identified is not the same as the signal channel in which the further frequency value is identified. 
         [0028]    Thus, one may identify a signal maximum in (say) a voltage signal channel, and use the phase shift operation on a corresponding or harmonic frequency in (say) a current or optical signal channel, with the phase shift operation allowing the current or optical periodograms to be cleaned up by reduction of noise and reinforcement of the signal component which has the correct phase relationship with the first frequency in the voltage channel. 
         [0029]    Preferably, therefore, the signal channel in which the first frequency value is selected is one of a voltage signal channel, a current signal channel, and an optical signal channel, and the signal channel in which the further frequency value is identified is a different one of a voltage signal channel, a current signal channel, and an optical signal channel. 
         [0030]    Preferably, on each iteration, steps (d), (e) and (g) are carried out more than once such that a plurality of further frequency values are identified in step (d) each representing a harmonic of said first frequency F found within a signal channel from the plasma system, and for each such harmonic a respective further complex frequency-domain component is determined in step (e) which is transformed in step (g) to provide a respective phase-adjusted further complex signal component, and wherein step (i) is repeated separately for each such phase adjusted further complex signal component. 
         [0031]    In this way, identifying and isolating a signal maximum in a single signal channel allows the method to be repeated on multiple harmonic signals across different channels. 
         [0032]    More preferably, steps (d), (e) and (g) are carried out at least once for a further frequency value identified in said first RF signal sample, and at least once for a further frequency value identified in a further RF signal sample from a different signal channel. 
         [0033]    Preferably, the first frequency value is identified as a fundamental frequency in a voltage signal channel and at least one further frequency value is a harmonic of said fundamental frequency in said voltage signal channel of order N&gt;1, and further wherein another of said further frequency values is identified as a harmonic (N&gt;=1) of the same fundamental frequency within a signal sample from a current signal channel or an optical signal channel. 
         [0034]    Alternatively, the first frequency value may be identified as a fundamental frequency in a current signal channel and at least one further frequency value is a harmonic of said fundamental frequency in said current signal channel of order N&gt;1, and further another of said further frequency values is identified as a harmonic (N&gt;=1) of the same fundamental frequency within a signal sample from a voltage signal channel or an optical signal channel. 
         [0035]    Preferably, the first frequency value and plurality of further frequency values include at least the first and second order harmonics from a current signal channel and the first and second order harmonics from a voltage signal channel. 
         [0036]    In preferred embodiments:
       the step (b) of identifying a first frequency value comprises identifying a bin number b1 of a discrete Fourier transform in which a local maximum of signal magnitude is located or expected, and   the step (d) of identifying a further frequency value comprises determining the identity of a bin number b2=N×b1, subject to modulo arithmetic where the modulus is the total number of bins, and selecting a bin which lies within N bins adjacent to bin b2.       
 
         [0039]    Typically, one will choose a bin number b2 which is a simple multiple, subject to modulo arithmetic. For example, if there are 512 bins, and a first frequency (N=1) is identified in bin b1=204, then the second harmonic (N=2) may be identified simply as the complex signal component in b2=408. Or the third harmonic (N=3) may be identified simply as the complex signal component in b2=100 (i.e. 612 becomes 100 under modulo 512 arithmetic). 
         [0040]    However, in some scenarios one will need to consider that the bin b1 spans a finite frequency range and the actual signal peak may lie at the frequency equivalent to bin location 204.8 (which is within the frequency range covered by bin 204, but close to bin 205). In such cases, the third harmonic would be at a frequency which is equivalent to bin location 614.4 or by modulo arithmetic, within the frequency range covered by bin 102. Hence the selection of the complex frequency component for the third harmonic in this case may involve determining the identity of a bin number b2=100 as above described, but then selecting a bin (e.g. bin 102) which lies within 3 bins adjacent to bin b2. 
         [0041]    The selection of a bin which lies within N bins adjacent to bin b2 may involve identifying a bin within said range where a local maximum of signal magnitude is found. 
         [0042]    Alternatively, and more preferably where possible, the selection of a bin which lies within N bins adjacent to bin b2 may comprise selecting a bin in which a frequency multiple F(N) will be found where the frequency F is known with a precision greater than the bin size. 
         [0043]    The value of the fundamental or first frequency F may drift between successive iterations and preferably, on each iteration the first frequency value F is identified as a local maximum signal within an expected frequency range. 
         [0044]    Preferably, the method comprises the initial steps of receiving at least one RF signal sample from a signal channel and performing a transform of said at least one RF signal sample to the frequency domain. 
         [0045]    Preferably, said transform is a discrete Fourier transform, and preferably a fast Fourier transform. 
         [0046]    In preferred embodiments, steps (b) to (j) are repeated based on a different first frequency F′, at which a local maximum is found in the frequency domain, where F′ and F are not harmonics of one another. 
         [0047]    For example, a signal analysis may be carried out in each iteration on the fundamental voltage frequency component at F=27.12 MHz, its second and third harmonics (i.e. F(2) and F(3) within the same signal channel, and the first, second and third harmonics of the current signal for 27.12 MHz, 54.24 MHz and 81.36 MHz (i.e. F(1), F(2) and F(3) within a different signal channel). Then the entire procedure can be repeated in terms of repeating steps (b) to (j) based on (say) a 800 kHz fundamental and one or more of its harmonics within voltage and/or current. 
         [0048]    There is also provided a computer program product comprising machine-readable instructions which, when executed in a processor provided with data representative of one or more RF signals of a plasma system, are effective to carry out any of the methods herein. 
         [0049]    The computer program product may be provided on a data carrier, or as instructions in a computer memory, or may be implemented as a hardwired circuit, or may be implemented as logical rules in a programmable circuit such as a field programmable gate array. 
         [0050]    When implemented as programmable instructions the processor can be a processor of a general purpose computer system, or a dedicated processor such as a digital signal processor chip. 
         [0051]    There is further provided a system for analysing RF signals from a plasma system, comprising one or more processing circuits programmed to execute any of the methods herein. 
         [0052]    Preferably, the one or more processing circuits are implemented as a field programmable gate array and said programming of said circuits comprises configuring said field programmable gate array with a logic function implementing said method. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0053]      FIG. 1  is a schematic diagram of a system for analysing RF signals from a plasma system; 
           [0054]      FIG. 2  shows simulated voltage and current signals on the RF line due to a 800 kHz RF power supply and a 27.12 MHz power supply; 
           [0055]      FIG. 3  shows the results of a fast Fourier transform on the current signal of  FIG. 2 ; 
           [0056]      FIG. 4  shows a close-up of the 800 kHz peak and associated harmonics; 
           [0057]      FIG. 5  shows the data from a range of frequency bins around first to fifth harmonic peaks of a 800 kHz signal for voltage and current signals, both before and after application of the method of the invention; 
           [0058]      FIG. 6  shows datasets arranged as in  FIG. 5  but with the addition of noise; and 
           [0059]      FIG. 7  shows equivalent datasets to  FIG. 5 , arranged as in  FIG. 5 , but for the first to fifth peaks of a 27.12 MHz signal, with noise. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0060]    As seen in  FIG. 1 , the RF sensor indicated at  10  consists of a broadband capacitive voltage pick-up  12  to capture the voltage on an RF line  14  connected to the plasma electrode. The broadband capacitive voltage pick-up  12  is designed to have a flat frequency response over the frequency range of interest. The sensor  10  also has a current loop  18  to capture the RF current in the RF line connected to the plasma. The RF loop is designed to operate in a transformer mode so that it essentially has a flat frequency response over the frequency range of interest. The voltage  12  and current  18  pick-ups are embedded in a power transmission line  16  surrounding the RF line  14 . 
         [0061]    The current and voltage signals are passed from the capacitive pick up and current loop respectively to an analog-to-digital converter  20 , and the digitised signals are processed in a field programmable gate array  22  as described below with reference to  FIG. 2 . 
         [0062]    For this example we will refer to the RF sensor, but we also envisage an optical sensor monitoring optical data at the RF frequencies or other sensors that record useful information in the RF spectral region. 
         [0063]    In  FIG. 2 , we show the simulated voltage and current signal on the RF line due to a 800 kHz RF power supply and a 27.12 MHz power supply. The voltage and current signals from the sensor are fed to a voltage and current ADC ( FIG. 1 ) where the V and I signals are converted to a high resolution digital word (16 bit) at a fixed sample rate greater than the highest fundamental frequency (27.12 MHz) such as approximately 50 MSPS (million samples per second) this can be achieved using a low cost digitiser. It is preferred not to use an anti-aliasing filter and that the signal bandwidth of the digitizer should be at least 5 times the Nyquist frequency (&gt;150 MHz). 
         [0064]    We then obtain a standard N=512 FFT of both the of the voltage and current signals. This is achieved using a Field Programmable Gate Array chip. The 512 samples require 17.4 us to acquire and about 50 us to complete the FFT. Because the plasma load in non-linear there is significant harmonic distortion of the current, in particular. The non-linear load also leads to an inter-modulation of the two frequencies and a significant inter-modulation component which is again more pronounced in the current signal. 
         [0065]      FIG. 3 , shows the FFT of the simulated current signal. Here we see the fundamental 800 kHz signal with magnitude 1 and the 27.12 MHz with magnitude 1. In the simulated data the harmonics of the 27.12 MHz signal are set to 10% of the magnitude of the fundamental and will appear at 54.24 MHz, 81.36 MHz, 108.48 MHz and 135.6 MHz. Because of the aliasing of the digitizer running at 49.5 MSPS the harmonics of 27.12 appear within the range 0-25 MHz. The non-linear load will produce an inter-modulation signal at +/−800 kHz distance from the 27.12 MHz and its aliases. These are clearly seen in  FIG. 3 . 
         [0066]    The 800 kHz fundamental will also be distorted by the non-linear load and harmonics will appear at 1.6 MHz, 2.4 MHz, 3.2 MHz and 4 MHz. The amplitudes of the 800 kHz harmonics were set in the simulation at 30%, 20%, 10%, and 5% of the fundamental magnitude respectfully.  FIG. 4  shows a close-up of the 800 kHz peak and associated harmonics. The 2 nd  harmonic of the 27.12 MHz signal is aliased and appears at 4.8 MHz and its inter-modulation peaks appear at 4 MHz and at 5.6 MHz. It is clear that the 13.56 MHz harmonics and inter-modulation products corrupt the 5 th  harmonic and make its measurement impossible with the standard state of the art. Noise will also contribute to the uncertainty in the measurement of the peak values and will limit the ability of this approach to accurately establish the phase of any of the signals. 
         [0067]    To overcome these limitations the present invention allows the user to select a frequency range in which the first signal is expected, say F1=27.56+/−0.5 MHz and a second range in which a second frequency may be found, say F2=800 kHz+/−100 kHz. Further frequency ranges may be selected if required for multi-frequency applications. The FFT bin size in the current example is 97 kHz. If the range is greater than the bin size then the signal may be found in one of several bins. The range of frequencies is needed in applications where the frequency is variable to aid matching the power to the plasma load. 
         [0068]    The algorithm calculates the range of bins in which the fundamental component of the F1 component of signal can be found. It determines the bin where the maximum voltage signal resides and assumes this is the fundamental F1, the algorithm then rotates the voltage vector in this bin through a phase angle θ until the imaginary component of that bin goes to a predetermined phase angle φ. For convenience φ is preferably set to zero as this eliminates the imaginary component of the phase-adjusted first frequency component. The algorithm also rotates the current vector of the equivalent frequency bin of the current FFT through the same angle θ. The real component of the voltage vector is stored as V m11  and the new current vector I m11  (reakimaginary) for the equivalent frequency bin is stored. The algorithm calculates the range of bins where the second m12-n12, third m13-n13 and higher harmonics will lie. It looks for aliased signals at the appropriate part of the spectrum and rotates each voltage vector and current vector by the twice the angle (i.e. 2θ) for the second harmonic and three times the angle (3θ) for the third harmonic etc. and stores the complex vectors. The procedure is repeated for F2 and its harmonics. In reality, the bins selected may not be unique and harmonics from two frequencies may overlap and the selected bins may contain noise, other harmonics and inter-modulation components. Once all the relevant vector values are stored the remaining unused bins are discarded. 
         [0069]    A new data set is collected and the FFT is obtained and the procedure is repeated a number of times, say 1000 times. For each such data set, the rotation angle θ is varied such that the fundamental voltage component of F1 is rotated to the same phase angle φ as for the first data set, and then, for each further frequency component in that data set (e.g. 2 nd , 3 rd , etc. voltage harmonics and 1st, 2 nd , 3 rd  current harmonics) this new rotation angle θ or a multiple Nθ thereof is employed to rotate the vector in question. This requires about 67 ms in the current example. The voltage and current vectors are added to produce a time averaged periodogram. It will be appreciated that in this example, if a value of φ=zero was employed in the first iteration, then all of the vectors for the 1000 N=1 voltage components will have been rotated to a phase angle zero, with a different rotation angle θ being required for each data set. Each of the 1000 N=1 current components is individually rotated by the same angle θ as its counterpart voltage vector. Each of the 1000 3 rd  harmonic voltage vectors will have been rotated by three times the rotation angle used for the fundamental voltage vector, as will each of the 1000 3 rd  harmonic current vectors, again preserving a constant phase difference between the voltage and current. 
         [0070]      FIG. 5  shows an example of the algorithm applied to the simulated data of  FIG. 2 . The black line in each graph is the magnitude of the vector for voltage (top five graphs) or current (bottom five graphs) for a range of frequency bins around each harmonic from F1 to F5 (moving from left to right). The grey line in each graph is the result of applying the phase shift algorithm and averaging over 1000 periodograms. The grey line overlays the black line and conceals it where they coincide. 
         [0071]    In the case with the 5 th  harmonic of the current we see a blue signal that represents an inter-modulation component of the current signal at 54.24 MHz aliased to appear close to the 5 th  harmonic of the 800 kHz of the current. The red line is the 5 th  harmonic of the 800 kHz averaged over a 1000 periodograms with the voltage phase shift algorithm applied. The vector magnitude is now 0.05 which is the correct value with the inter-modulation components removed. 
         [0072]    The voltage phase shift operation applied to fundamental and harmonics essentially allows multiple periodograms to be averaged without the desired fundamental and its harmonics being reduced. The operation also preserves the phase difference between the voltage and current. A true representation of the RF waveform can also be obtained. Other signals which are not in phase with the fundamental voltage will add vectorally in such as way as they tend to cancel. This also includes noise, so that the variance of the signal will reduce by the square root of the number of periodograms averaged. This leads to a dramatic increase in the S/N of the averaged signal. 
         [0073]    In  FIG. 6  we see datasets for 800 kHz arranged in the same manner as in  FIG. 5  but with noise added. In  FIG. 6  each harmonic (N=2, 3, 4, etc.) is set to be 10% of the magnitude of the fundamental (N=1). The number of periodograms averaged is set  100  as simulation was much slower with noise added. One can see that the red line, showing the data after applying the phase adjustment algorithm and averaging is far cleaner than the blue line (pre-processing). 
         [0074]      FIG. 7  shows the equivalent datasets to  FIG. 5 , but (a) for the 27.12 MHz fundamental and its harmonics, and (b) with noise added. Again it can be seen that the effect of the algorithm is to reduce and remove spurious signals overlying the frequency components of interest, and to reduce noise dramatically. 
         [0075]    The current techniques does not require a lock-in period, the coherence length is determined by the time taken to capture the 512 data points and is reduced somewhat by the window function. However, if synchronisation is required to further improve performance it is possible by recording the phase shift required for each fundamental voltage. For a fixed frequency sampling frequency and fixed frequency fundamentals this phase will be constant from one sample to the next. So averaging the phase shift over a period on x seconds and using the average phase is equivalent to phase locking the measured voltage and current measurement with a bandwidth determined by the length of time used to average the phase. This approach would improve the quality of data but would be difficult to use where the frequency will shift quickly or in pulsed applications. 
         [0076]    Some examples of how the invention may operate as regards the first frequency (which sets the value of the phase adjustment angle θ) and the further frequencies (against which an adjustment of NO is applied) would include the following. In the following it is to be understood that “signal channel A” represents one channel containing an RF signal (such as a voltage, current or optical signal channel) and “signal channel B” represents a different channel but also containing an RF signal, and that both signal channels A and B include frequency components sharing a common fundamental frequency. (Alternatively, and less commonly, signal channels A and B might both be voltage signals but covering different parts of the spectrum in which different harmonic peaks are located). 
         [0077]    Most commonly, signal channels A and B will broadly cover the same range of frequencies and will contain each of the harmonic peaks of interest for a given signal (e.g. when studying an 800 kHz plasma RF modulation signal channel A might be a voltage signal having a bandwidth from 0 to 5 MHz and signal channel B a current signal with the same bandwidth, so that the fundamental and the 2 nd  to 6 th  harmonics of both current and voltage are captured. Less commonly, but also within the scope and ability of this method, signal channel A might be a voltage signal covering a narrow bandwidth around (say) an 800 kHz fundamental signal peak, while signal channel B might be a current signal channel containing frequencies from 1.5 to 1.7 MHz (and thus containing only the 2 nd  harmonic frequency component of the equivalent current signal). 
       Scenario 1: 
       [0078]    First frequency is a true fundamental component from signal channel A
       (i) further frequency is a higher harmonic (N=2, 3, etc. representing 2 nd  order, 3 rd  order harmonic etc.) from signal channel A   (ii) further frequency is equivalent fundamental (N=1) from signal channel B   (iii) further frequency is a higher harmonic (N=2, 3, etc. representing 2 nd  order, 3 rd  order harmonic etc.) from signal channel B       
 
       Scenario 2: 
       [0082]    First frequency is e.g. a second harmonic of a fundamental plasma frequency from signal channel A
       (i) further frequency is a harmonic multiple (N=2, 3, etc. representing 4 th  order, 6 th  order harmonic etc.) from signal channel A   (ii) further frequency is equivalent signal (N=1 representing the second harmonic) from signal channel B   (iii) further frequency is a higher harmonic (N=2, 3, etc. representing 4 th  order, 6 th  order harmonic etc.) from signal channel B       
 
         [0086]    It can be seen that the “first frequency” is always assigned the number N=1 and each further frequency is assigned a corresponding number N=1, 2, 3 etc. depending on whether it is the same frequency as the first frequency (i.e. a first order harmonic thereof with N=1), double the frequency (2 nd  order, N=2), triple the frequency (3 rd  order, N=3), etc. The first frequency at N=1 is usually but not necessarily an actual fundamental frequency found within the signal channel, as in Scenario 1. However, Scenario 2 indicates that in some cases the first frequency, assigned N=1, could be e.g. a 54.24 MHz peak, which in reality is a second order harmonic of a 27.12 MHz excitation frequency for the plasma system. In such a case, the 54.24 MHz signal will be rotated by an angle θ, as will any equivalent 54.24 MHz frequency components in other signal channels. N=2 will denote any frequency components at 108.48 MHz (which are 4 th  order harmonics of the base 27.12 MHz excitation) and these components will be rotated by 2θ, and so on.