GB2579083A

GB2579083A - Phase difference measurement

Info

Publication number: GB2579083A
Application number: GB1818865.6A
Authority: GB
Inventors: Halsall Brian
Original assignee: Oxford Instruments Nanotechnology Tools Ltd
Current assignee: Oxford Instruments Nanotechnology Tools Ltd
Priority date: 2018-11-20
Filing date: 2018-11-20
Publication date: 2020-06-10
Anticipated expiration: 2038-11-20
Also published as: GB201818865D0; GB2579083B

Abstract

A method of measuring a phase difference between the current and voltage of a cyclic signal output by a signal generator to a load, is provided. The method, suitable for a plasma processing device, comprises monitoring the current through, and voltage across, a load at a load input S110, and outputting the monitored current and voltage. First and second signals having the same period are respectively derived from the monitored current and voltage, the phase information being preserved in each signal. For each zero-crossing point of the first and second signals within a selected period, a pair of phase intervals comprising the intervals between the zero-crossing point and the last, and last but one, zero-crossing point of the other signal are measured S150. The measured phase intervals are converted to angular phase difference samples S160 in the range ±180 degrees based on the zero-crossing point used and the period of the first and second signals, where a positive value indicates lead and a negative value indicates lag. An average of the phase difference samples is computed S180. The method may further include automatically adjusting the phase difference towards a target value. An apparatus and a method of tracking a phase difference in a plasma processing device are also provided. The phase difference measuring method may be used for impedance matching in a plasma treatment system.

Description

PHASE DIFFERENCE MEASUREMENT

FIELD OF THE INVENTION

The present invention relates to a method for measuring a phase difference between cyclic signals. In particular, the method is suitable for measuring the phase difference between cyclic current and voltage signals for the purposes of impedance matching in a plasma treatment system.

BACKGROUND TO THE INVENTION

Plasma processing devices can facilitate plasma-based processes such as etching and deposition of material at the surface of a target substrate. Typically in such systems a power source is configured to deliver a cyclic electrical signal, via an impedance matching unit, to a gas contained in a plasma chamber, which ionises the gas to form a plasma. The substrate can then be exposed to the plasma inside the chamber for treatment.

WO-A-2010/073006 describes an example signal generating system for a plasma treatment system. A signal generator supplies power to a plasma chamber via a radio frequency (RF) impedance matching circuit. To effectively power the plasma load, it is desirable that the combined impedance of the matching circuit and plasma chamber is kept purely resistive -i.e. with no reactive component -and at a fixed value. Wien this is achieved, the current and voltage at the input of the matching unit are in phase and the power reflected by the load is minimised.

Conditions in the plasma fluctuate over time and consequently its impedance varies. To compensate for these changes, variable capacitors or other devices are controlled to vary the resistive and reactive components of the impedance of the matching circuit so that the combined impedance of the plasma and the matching circuit is kept at the desired value. These adjustments can be determined based on measurements of the phase difference between the current and the voltage through the plasma chamber since this phase difference depends on the reactive component of the impedance. When the reactive component of the impedance is zero, the current and voltage are in phase.

If the system fails to maintain the correct impedance, the power that is delivered 5 to the plasma chamber may vary and may even be insufficient to sustain the plasma, in which case the plasma may consequently be extinguished. This can cause the substrate being processed to be spoiled. It is therefore essential that the variable capacitors can be controlled in a timely and accurate manner so as to reliably sustain the plasma, but this can be limited by the quality of 10 measurements of the phase difference between the current and the voltage and the speed with which these measurements can be obtained. Improvements to the quality of phase difference measurements obtained in plasma treatment systems and the speed with which they are acquired are therefore desirable.

SUMMARY OF THE INVENTION

According to a first aspect, a method for measuring in a plasma processing device a phase difference between the current and voltage of a cyclic electrical signal of a first frequency output by a signal generator to a load comprises (I) monitoring, at an input to the load, the current through the load and the voltage across the load and outputting the monitored current and the monitored voltage; (II) deriving a first signal from the monitored current and a second signal from the monitored voltage, the phase information between the monitored current and the monitored voltage in the cyclic electrical signal being preserved in the first and second signals, and the periods of the first signal and the second signal being the same; (Ill) for each zero-crossing point of the first and second signals within a selected sampling period, measuring a pair of phase intervals comprising (i) the phase interval between the zero-crossing point and the last zero-crossing point of the other signal, and (ii) the phase interval between the zero-crossing point and the last but one zero-crossing point of the other signal; (IV) converting the measured phase intervals to corresponding phase difference samples in the range of -180 degrees to +180 degrees, the conversion of each measured phase interval being based on the zero-crossing points used to measure the phase interval and the period of the first and second signals, where a positive phase difference sample represents the first signal leading the second signal and a negative phase difference sample representing the second signal leading the first signal, or vice versa; and (V) computing an average of the phase difference samples.

This method allows two phase difference samples to be recorded each time either the current or the voltage goes through zero. A large number of samples can therefore be obtained within a given sampling period relative to previous techniques, so more reliable measurements of the instantaneous phase difference can be obtained using a set of measurements collected from within a narrow, recent interval. Conditions in the plasma, and consequently the phase difference, are more likely to have evolved between the time at which a less recent zero-crossing point was recorded and the present, so this method provides measurements that are more accurate as regards the current state of the system. This allows a matching circuit in a plasma treatment system to be controlled more accurately than is permitted by previous techniques and consequently leads to improved impedance matching. This in turn improves the reliability and effectiveness of the plasma treatment system.

Different kinds of interval, each defined by a zero-crossing point of the first signal and a zero-crossing point of the second signal, are used to obtain samples of the same phase difference, and it is necessary to adjust the set of measured intervals to account for this. This is the purpose of step (IV). For example, a pair of intervals measured between a zero-crossing point of one signal and the last and last-but-one zero crossing points of the other signal should differ by approximately 180 degrees, and converting the measured intervals might involve subtracting 180 degrees from the measurement corresponding to the second of these intervals.

In general, every interval defined by zero-crossing points of the first and second signals contains information relating to the phase difference. If variations of the phase difference within the interval are neglected -this assumption will typically be more valid for smaller intervals -the phase difference can be extracted by adding to the interval, or subtracting the interval from, an appropriate number of half-cycles.

The concept of a phase difference between two cyclic signals is well known, and those skilled in the art would recognise an appropriate set of adjustments to be applied to the measured intervals in accordance with a chosen definition of the phase difference.

In preferred embodiments, step (I) further comprises the introduction of a phase offset between the monitored current and the monitored voltage, the phase offset having a known magnitude, such that the output monitored current and the output monitored voltage have a phase difference which includes the phase offset; and step (IV) further comprises removing the known phase offset from the measured phase intervals.

When measuring the interval between, for example, a zero-crossing point of the first signal and a previous zero-crossing point of the second signal, when the first signal slightly leads the second, the measured interval will be small; but when the first signal slightly lags the second, the measured interval will be large since the closest previous zero-crossing point is now a different, earlier one. A result of this is that the measured value of the interval is discontinuous at the point at which the phase difference is zero -the so-called "two-pi ambiguity".

When a known offset exists between the monitored current and voltage and the physical current and voltage are matched, the monitored current and voltage appear to be out of phase by an amount corresponding to this offset. The measured interval between zero-crossing points of the two signals is continuous through this point, so the measured values vary smoothly as the phase difference changes sign. Once phase difference samples have been obtained, the known offset can be subtracted from each sample in order to return values representative of the physical phase difference between the current and voltage.

In particularly preferred embodiments, the phase offset is introduced by an apparatus used to monitor the current through the load and the voltage across the load. Sensing circuits of the kind that may be used to monitor the current and voltage can give rise, as a result of their electrical properties, to such a phase offset between the monitored current and voltage signals. This phase offset can be known and may be exploited to overcome the two-pi ambiguity as described above. Alternatively, a phase offset could be introduced after the monitored signals have been obtained. This could be done by, for example, adding a constant offset to each of the actual data points recorded for one of the signals.

Advantageously, the phase offset is between 10 degrees and 170 degrees, preferably about 90 degrees. This ensures that the two-pi ambiguity that arises when the first signal and the second signal are in phase occurs substantially away from the point at which the current and voltage are matched; though the offset could alternatively take any other value.

In step (II) the first signal and the second signal are preferably derived so as to each be of a second frequency that is lower than the first frequency. The cyclic current and voltage typically have a frequency (the first frequency) on the order of MHz, and it can be difficult to contemporaneously measure, manipulate and react to such quickly-evolving signals. It can therefore be useful to derive the first and second signals, which are representative of the monitored current and voltage respectively, so as to have a frequency (the second frequency) that is lower and therefore more easily managed. Alternatively, and particularly in applications in which the current and voltage through the load are in a lower frequency range, the first and second signals could have a frequency that is equal to or greater than the first frequency.

In order to provide first and second signals of a lower frequency than the first frequency, step (II) preferably comprises mixing each of the monitored current and the monitored voltage with a reference signal output by a second signal generator so as to produce a lower-frequency heterodyne signal. Each of the monitored current and voltage can be combined with a signal of a similar frequency in a heterodyne circuit to produce low-frequency output signals which preserve the phase information between the monitored current and voltage. A heterodyne circuit can be implemented simply, though other means of deriving the first and second signals from the monitored current and voltage could also be chosen. In preferred embodiments the frequency of the reference signal is chosen such that the heterodyne signal has a frequency of between 100 hertz (Hz) and 10 kilohertz (kHz).

Alternatively, it may be that the first signal is the monitored current and the second signal is the monitored voltage. In such embodiments, step (II) simply involves outputting the same signals as were input directly from the monitoring step. If the monitored current and voltage are of a frequency that is sufficiently low that it is easily managed, the phase difference could be measured directly from these signals. This would simplify the apparatus required to perform the method.

The sampling period preferably includes at least one zero-crossing point of each of the first signal and the second signal. In order to obtain a phase difference measurement it is only necessary that one zero-crossing point falls within the sampling period, since the method defined above does not preclude the use of previous (i.e. last and last-but-one) zero-crossing points that fall outside the sampling period. However, it is preferable that at least one zero-crossing point of each signal falls inside the sampling period (and hence there are at least two zero-crossing points in the sampling period) to prevent the measurement of the phase difference being spoiled by a single outlier.

In preferred embodiments the sampling period includes no more than 10 zero-crossing points of each of the first signal and the second signal. Keeping the size of the sampling period reasonably narrow, such as this, reduces the likelihood of the phase difference between the current and the voltage having evolved significantly within the period of time corresponding to the sampling period.

In particularly preferred embodiments the sampling period includes exactly two zero-crossing points of each of the first signal and the second signal. In this case eight phase intervals are measured using zero-crossing points distributed over a range of about one and a half times the period of the first and second signals. This is a reasonable compromise between the number of phase difference samples used to compute the average, which for the purposes of reliability is preferably high, and the width of the sampling period, which is preferably low since the measured phase difference should be representative of the current state of the system.

In step (IV) the conversion of each measured phase interval is preferably further based on the crossing directions of the zero-crossing points used to measure the phase interval. Each zero-crossing point may be either positive-going (i.e. the signal changes from a negative value to a positive value as it passes through the zero-crossing point) or negative-going (i.e. the signal changes from a positive value to a negative value). A signal with a steady frequency may in principle be translated by 180 degrees without changing the positions at which its zero-crossing points appear, so phase intervals having a particular magnitude could correspond to two different values of the phase difference. Which of these is correct is reflected by the relative crossing directions of the zero-crossing points defining the interval, and the conversion of the phase intervals to phase difference samples can be performed giving consideration to this.

A further advantage of this is that knowing the crossing directions of the zero-crossing points can allow the correct adjustment to be identified without needing to correctly identify the last and last but one zero-crossing points of either signal. If a zero-crossing point of one signal is erroneously identified as the "last" or "last but one" (when it is in fact an earlier one) with respect to a zero-crossing point of the other, knowing the crossing directions allows the interval to nevertheless be converted into a correct phase difference sample by adjusting the sample by an integral number of periods of the first and second signals.

Where the conversion of each measured phase interval is further based on the crossing directions of the zero-crossing points, step (IV) preferably further comprises: for a phase interval measured between a zero-crossing point of the first signal and a previous zero-crossing point of the second signal, subtracting the phase interval from (a) one period, where the crossing directions of the zero-crossing points used to compute the interval are the same, or (b) half of one period, where the crossing directions of the zero-crossing points used to compute the interval are different; and for a phase interval measured between a zero-crossing point of the second signal and a previous zero-crossing point of the first signal, subtracting from the phase interval (c) half of one period, where the crossing directions of the zero-crossing points used to compute the interval are different, or (d) nothing, where the crossing directions of the zero-crossing points used to compute the interval are the same. For phase intervals defined using a zero-crossing point of one signal and the last or last-but-one zero-crossing point of the other, this leads to each interval being converted to a phase difference sample that increases the more the first signal leads the second signal and is in the range -P/2 to P, where P is the period of the first and second signals.

Step (IV) preferably further comprises: identifying any phase difference samples that lie outside of the range of -180 degrees to +180 degrees, and adding or subtracting one or more integral periods to or from each of the phase difference samples outside of the selected range so as to bring each of the identified phase difference samples within the selected range. For example, a sample initially corresponding to a phase value of 230 degrees would have one period subtracted to return a sample of -130 degrees. A sample corresponding to a phase value of 110 degrees would be unchanged. In the example described above, in which phase difference samples initially between -P/2 and P are produced, this step would involve subtracting a period from each value corresponding to a phase difference greater than 180 degrees. The result of this step is that each phase difference sample will be positive if the first signal leads the second signal (i.e. if the current leads the voltage) and negative if the second leads the first (and the voltage leads the current). It is alternatively possible that the calculations (a) to (d) as above are reversed, resulting in positive phase difference samples representing the voltage leading the current and negative phase difference samples representing the current leading the voltage.

In particularly preferred implementations, further steps may be performed in order to remove outlying phase difference samples, which may be the result of erroneous measurements. Thus, preferably, before step (V), each phase difference sample is placed into one of a plurality of bins in the phase angle domain based on the value of each phase difference sample, each bin defining a range in the phase angle domain; and step (V) comprises computing an average of the phase difference samples in one of the plurality of bins.

It is generally expected that the phase difference samples will form a narrow distribution around the value corresponding to the actual phase difference between the current and voltage. There may, however, be outliers, and these may be dealt with by defining a plurality of bins in the phase angle domain and discounting phase difference samples that fall outside of a chosen bin.

Furthermore, when the phase difference is close to a point at which a discontinuity such as the two-pi ambiguity occurs, samples that correspond to similar values of the actual phase difference can in fact be far apart. When this occurs, averaging of all of the phase difference samples may produce a result that is meaningless. This issue can be mitigated by selecting values in a single bin that is appropriately defined.

For example, in instances where a known phase offset is introduced between the monitored current and the monitored voltage, the two-pi ambiguity may occur at a point that is substantially away from zero phase difference. When the plasma is first generated, the current and voltage may be significantly mismatched and in such instances phase difference measurements might be therefore be influenced by this ambiguity. It would therefore be advantageous to select values from only one side of the discontinuity, and placing the phase difference samples into bins and computing an average of the values in a single bin as set out above can mitigate this issue.

In implementations where a known phase offset of the kind described above is applied, this step can be performed before or after the phase offset is removed. The range of each of the plurality of bins may be chosen accordingly.

The single bin is preferably chosen as the bin containing the greatest number of phase difference samples. It is expected that the majority of phase difference samples are at least approximately correct, so it may be preferable to base the average on the bin that contains the greatest number.

In particularly preferred implementations, the plurality of bins comprises a first bin spanning a range that includes zero phase difference. This is particularly advantageous where a known phase offset is introduced between the monitored current and voltage and is removed before the phase difference samples are placed into bins (or if no phase offset is introduced at all). Equivalently, if the phase offset is removed at a later stage, the plurality of bins may comprise a bin spanning a range that includes (and is preferably centred on) a value corresponding to that of the phase offset.

The range of the first bin is preferably from -X degrees to +X degrees, where X is in the range of 90 to 120. This is again particularly suitable where the known phase offset (if such an offset has been applied) is removed before the phase difference samples are placed into bins. Since the two-pi ambiguity has been dealt with in these implementations, phase difference samples are not expected to fall outside of this range when the current and voltage are close to being matched. Any values that do fall outside of this range might be the result of, for example, mismeasurement due to the incorrect identification of the relevant zero-crossing points and may therefore be disregarded as outliers.

The phase intervals are preferably measured in the time domain, for example in units of seconds or as a number of pulses of a periodic clock signal. Alternatively, the first and second signals could be converted to the phase angle domain before the phase intervals are recorded.

The phase intervals may be measured using a cyclic clock signal having a period less than, preferably significantly less than, the period of the first signal and the second signal. This is achieved by counting the number of cycles of the clock signal that fall within the interval. Alternatively, each phase interval may be measured by computing a time difference between the zero-crossing points by which it is defined if the time at which each zero-crossing occurred has been recorded. This could be achieved by, for example, referring to an external clock to record the point in time at which each zero-crossing point takes places or to measure the time intervals between zero-crossing points as they occur.

In preferred implementations, before step (V) either each phase interval or each phase difference sample is converted from the time domain to the phase angle domain. Since the period of the first and second signals is known, intervals measured in the time domain can be converted to the phase angle domain by computing the ratio of the magnitude of the interval to the period of the first and second signals and multiplying this ratio by a phase angle corresponding to one cycle, such as 360 degrees or 2 pi radians.

The cyclic electrical signal preferably has a frequency in the range of 50 kHz to 100 megahertz (MHz), preferably in the range of 10 MHz to 20 MHz, and most preferably approximately 13.56 MHz.

In preferred embodiments, the load comprises a matching network with a variable impedance and a plasma load, and the current and the voltage are measured at the input to the matching network. In such embodiments the impedance of the matching network can be varied in such a way that maintains a ratio between the magnitudes of the current and the voltage at the input to the load at a value that minimises the power reflected by the load. An example of a suitable matching network is disclosed in WO-A-2010/073006.

A second aspect of the invention provides a method for controlling a phase difference between a cyclic current and a cyclic voltage through a load, wherein the current and voltage are generated by a cyclic electrical signal output from a signal generator to the load, the method comprising: measuring the phase difference by a method in accordance with the first aspect of the invention; and based on the measured phase difference, automatically adjusting the phase difference between the current and the voltage towards a target value. The load could include, for example, a matching network with a variable impedance, and by varying the impedance of the matching network in response to the measured phase difference, the phase difference could be adjusted (since the phase difference will depend on the total impedance of the load).

A third aspect of the invention provides an apparatus comprising: a signal generator adapted to output a cyclic electrical signal to a load; a monitoring module adapted to monitor, at an input to the load, a current through the load and a voltage across the load; and a processor adapted to measure a phase difference between the current and the voltage by a method in accordance with the first aspect of the invention.

In preferred embodiments the apparatus preferably further comprises a phase control module configured to automatically adjust the phase difference between the current and the voltage, based on the measured phase difference, towards a target value. This could be achieved by the implementation of a matching network (of the kind discussed above with reference to the second aspect of the invention) and a control unit configured to vary the impedance of the matching network based on the measured phase difference.

A fourth aspect of the invention provides a method of tracking in a plasma processing device a phase difference between the current and voltage of a cyclic electrical signal of a first frequency output by a signal generator to a load, the method comprising: (I) measuring the phase difference between the current and voltage by a method in accordance with the first aspect of the invention at a first instant of time; (II) outputting the measured phase difference; (Ill) at a second instant of time later than the first instant, redefining the sampling period so as to include at least one zero-crossing point of the first signal or the second signal that lies between the first instant and the second instant; and (IV) repeating steps I-Ill at least once.

In one example, the period of the first signal and the second signal is 1 millisecond (ms). In this instance, if the sampling period contains exactly two zero-crossing points of each of the first signal and the second signal, the width of the sampling period is in the region of 1 ms also. The phase difference is measured by a method in accordance with the first aspect of the invention at a time T1 with a sampling period encompassing the two most recent zero-crossing points of each of the first signal and the second signal. At a later time 12 = Ti + 0.5 ms, each of the first signal and the second signal will have passed through a new zero-crossing point. The method can then be repeated with a sampling period redefined so as to encompass the two new zero-crossing points in addition to the immediately preceding zero-crossing point of each of the first signal and the second signal. In this way, the measured phase difference can be updated every 0.5 ms.

BRIEF DESCRIPTION OF THE DRAWINGS

Examples of methods and systems in accordance with the present invention will now be described in detail with reference to the following figures: Figure 1 schematically shows an exemplary plasma processing device suitable for use with embodiments of the invention; Figure 2 schematically shows an exemplary matching circuit suitable for use with embodiments of the invention; Figure 3 is a flow diagram illustrating an exemplary method in accordance with embodiments of the invention; Figure 4 shows current and voltage signals measured at the input to the matching circuit in accordance with a first embodiment; Figure 5 shows a first signal and a second signal derived from the measured current and voltage signals shown in Figure 4; Figure 6 schematically shows an exemplary measurement circuit used to measure the current and voltage at the input to the matching circuit in a second embodiment of the invention; Figure 7 shows current and voltage signals measured at the input to the matching circuit using the circuit of Figure 6 in accordance with the second 30 embodiment; Figure 8 shows a first signal and a second signal derived from the measured current and voltage signals shown in Figure 7 in accordance with the second embodiment; Figure 9 schematically shows an exemplary heterodyne frequency mixing unit suitable for use in preferred embodiments of the invention; Figure 10a shows an exemplary distribution of phase intervals measured in accordance with the second embodiment in an idealised scenario; Figure 10b shows the distribution of phase difference samples obtained from the intervals of Figure 10a; and Figure 10c shows the distribution of the phase difference samples of Figure 10b after the removal of a known phase offset.

Figure 11 shows a further example of a first signal and a second signal obtained in accordance with embodiments of the invention; Figures 12a to 12c show examples of the distributions expected to be formed by a set of phase intervals and phase difference samples of the kinds shown in Figures 10a to 10c respectively in a real world scenario; Figure 13 is a flow diagram illustrating steps for converting measured phase intervals to phase difference samples in accordance with the second embodiment of the invention; Figure 14 shows an example of first and second signals obtained in accordance with embodiments of the invention between which a negative phase difference exists; Figure 15 is a flow diagram illustrating optional additional steps for removing outliers in accordance with a third embodiment of the invention; Figure 16 is a graph showing measurements of the reflected power over time for a series of test loads in a system controlled using conventional methods; and Figure 17 is a graph showing measurements of the reflected power over time for a series of test loads in a system controlled in accordance with aspects of the invention.

DETAILED DESCRIPTION

Figure 1 shows an example plasma processing device 101 in which methods according to the present invention could be implemented. The plasma processing device 101 comprises a process chamber 102 within which a substrate 130 is placed during use. To perform etching or deposition, one or more input gases are introduced to the process chamber 102 and the conditions controlled in order to effect the desired deposition or etching mechanism. The term "input gases" includes precursor gases as well as inert, carrier gases if required. The process parameters within the chamber are controlled and can be adjusted by a set of at least one (but more typically a plurality of) devices, of which examples are shown schematically in Figure 1. In this example, the tool 101 is equipped with two input gas supplies 104(a) and 104(b) for supplying first and second input gases, 01 and 02 respectively, to the process chamber 102.

The ingress of each gas to the chamber 102 is controlled by respective mass flow controllers 106(a) and 106(b). These essentially comprise valves which can be opened to a greater or lesser extent depending on the desired flow rate of each gas. The exhaust gas, including unreacted input gases and any reaction products, is removed from process chamber 102 via a duct 107 and associated pump 108, the pump 108 typically being capable of reducing the pressure within the chamber to near-vacuum conditions. The chamber pressure will be determined in the main part by the exhaust pump system and particularly the pumping speed and the "conductance" of the pumping line from the chamber to the pump (this is a factor related to the geometry of the pumping line). However during processing, when a plasma is created and/or when etching or deposition takes place, gaseous species may be lost or created inside the chamber thereby having an effect on the pressure. In order to regulate for such variation, an automatic pressure control valve 108a is preferably provided as known in the art.

The valve 108a changes the conductance of the pumping line to thereby enable the chamber pressure to be maintained substantially constant at the desired level as the plasma is struck and the material etched.

In this example, the plasma processing device 101 is equipped with a plasma source for generating a plasma within the process chamber by means of an electrical discharge. Here, the plasma source is depicted as an inductively-coupled plasma source comprising a coil 109 surrounding chamber 102, which is supplied with RF power from power supply 110 via a RF matching unit 200. The RF matching unit 200 is configured to match the plasma impedance to that of the RF supply 110 in order to maximise efficiency of power transfer from the supply to the plasma. A schematic example of a suitable matching unit is described below with reference to Figure 2. Other types of plasma source such as a capacitively-coupled plasma (CCP) or microwave plasma source could be used instead.

The substrate 130 is mounted in use on a table 114. As described below, in certain process steps it is advantageous to apply a bias voltage to the substrate 130 and this is achieved by connecting a voltage source 112 to the table 114. If an RF power supply 112 is used then an Automatic impedance Matching Unit (AMU) may preferably be provided to ensure good coupling of power from the power supply 112 to the table 114. The plasma processing device 101 may further comprise a temperature control unit 16 such as a heater and/or cooling system for adjusting the processing temperature of the substrate (additional devices for heating and/or cooling of the process chamber and plasma source may be provided to assist with process control and/or to maintain hardware stability). For instance, where etching is primarily to be carried out, the substrate is preferably cooled using a circulating coolant to prevent the significant amount of energy transferred to the substrate during ion bombardment and/or during exothermic chemical reactions causing an undesirable increase in the substrate temperature.

The various devices in the plasma processing device operate upon instruction from a controller 120, such as a programmable logic controller (PLC) or similar.

In some cases, more than one controller can be provided, with each controller controlling one or a subset of the devices. The controller is also connected to a user interface device such as a computer workstation 125 for receiving input from the user and/or returning outputs In Figure 1, the data connections between the various devices and the controller are indicated by dashed lines. In practice, this may be implemented as a network. An example of a network protocol which could be used for the issuing of commands for the control of the devices is given in WO-A-2010/100425. Of course, many other network implementations are possible as will be appreciated by the skilled person.

Figure 2 is a block diagram representing an exemplary matching unit 200 suitable for use with embodiments of the invention. Also shown are the RF signal generator 110 and the plasma chamber 102 of the plasma processing device 101 shown in Figure 1.

The RF signal generator 110 delivers an RF signal to a load comprising the matching unit 200 and the plasma chamber 102 via a cable 215. The matching unit comprises a detection circuit 236, a control unit 230 and a matching network 216. The detection circuit 236 is configured to output via a port 237 an RF signal having an amplitude directly proportional to the instantaneous voltage at the input 217 to the detection circuit 236. In addition to this signal, a signal having an amplitude directly proportional to the current at the input 217 to the detection circuit 236 via a port 238.

The signals output via the ports 237, 238 are received by the control unit 230. The matching network 216 is configured such that it has an impedance with variable reactive components. The components of the impedance of the matching network 216 are controlled by the control unit 230 so as to minimise the power reflected towards the RF signal generator 110. To achieve this, the control unit can generate phase difference measurements from the signals received at ports 237, 238 using methods in accordance with the present invention and be configured to control the matching network 216 in order to reduce the magnitude of the phase difference between the current and the voltage at the input to the detection unit 236 (and hence reduce the reflected power). The reduction in the phase difference is achieved by controlling the variable reactive components of the matching network 216 so as to adjust the phase difference between the voltage and the current at the input to the matching unit 200 towards a value at which the phases of the current and the voltage are matched. The matching network 216 may also be configured to control other parameters. For example, it may vary the magnitude of the ratio of the amplitudes of the current and the voltage signals in order to match the input impedance of the load (comprising the matching unit 200 and the plasma chamber 102) to the output impedance of the RF signal generator 110. A detailed example of a matching network in accordance with the schematic example shown in Figure 2 is given in WO-A-2010/073006.

It should be noted that, as an alternative, the phase difference measurements could be calculated by another controller (not shown) and then supplied to control unit 230 for use in controlling the matching network 216.

Figure 3 is a flow diagram depicting an exemplary method for measuring phase differences in accordance with embodiments of the invention. In Figure 3 and in the other flow diagrams discussed herein, optional steps that may be performed in preferred embodiments are indicated by boxes with dashed outlines. Reference will be made to Figures 4 and 5 to illustrate some of the steps further.

The method begins at step S110. The current, I, at the input to the matching unit 200 is monitored. The voltage, V, with respect to ground at the input to the matching unit 200 is also monitored. The current and the voltage may be monitored by the use of any suitable apparatus such as ammeters and voltmeters appropriately implemented in the plasma processing device 101. The values of the current and voltage are recorded as functions of time.

In preferred embodiments, a known phase offset may be introduced between the monitored current and the monitored voltage at step S120. As discussed above, the introduction of a known phase offset is advantageous since it can resolve the so-called two-pi ambiguity. The known offset could be the result of the electrical properties of the plasma processing device 101, or could alternatively be introduced by, for example, applying a constant temporal offset to one of the monitored current and voltage as these signals are recorded. An exemplary measurement circuit that naturally introduces an offset with a magnitude of approximately 90 degrees between the monitored current and the monitored voltage is described later with reference to Figure 6.

Figure 4 shows examples of a monitored current signal 410 and a monitored voltage signal 420 obtained in accordance with a first embodiment of the invention. The period of the current signal 411 and the period of the voltage signal 421 are indicated on the drawing. The amplitudes of the signals have been normalised along the vertical axis for convenience.

In the example shown in Figure 4, the current and voltage are cyclic signals with a frequency of approximately 13.56 MHz, and accordingly each have a period of approximately 74 nanoseconds (ns). The phase difference 430 is approximately 9 ns in magnitude, which corresponds to a phase angle of approximately 45 degrees, and the current I leads the voltage V. In this example and in those described hereafter, the phase difference will be defined as positive when the current leads the voltage and negative when the current lags the voltage. The phase difference 430 between the current signal 410 and the voltage signal 420 is therefore approximately +45 degrees in this example. The phase difference could alternatively be defined as positive when the current lags the voltage and negative when it leads the voltage; it is only important that a consistent definition is used throughout any particular application of the method.

Returning to Figure 3, the current and voltage signals may be converted to lower-frequency first and second signals respectively at step S130. This is preferred because in typical applications the current and voltage signals can have frequencies on the order of tens of MHz, which are in practice difficult to process. This can be overcome by converting the current and voltage signals to lower-frequency signals, which are more easily manipulated. In embodiments in which step S130 is omitted, the first signal is simply equal to the monitored current and likewise the second signal is equal to the monitored voltage. In particularly preferred embodiments, step S130 involves heterodyne frequency conversion of the monitored current and voltage signals, and this is described in detail later with reference to Figure 9. Heterodyne frequency conversion can be implemented easily and can produce first and second signals with frequencies on the order of approximately one kilohertz (kHz), for example.

Figure 5 shows an example of a first signal and a second signal derived from the current and voltage signals shown in Figure 4. The first signal 540 is derived from the monitored current 410 and the second signal 550 is derived from the monitored voltage 420. If the optional step S130 was performed, the first signal 540 and the second signal 550 would be of a lower frequency than the monitored current and the monitored voltage; or if step S130 was been omitted, then the first signal 540 and the second signal 550 are simply equivalent to the monitored current 410 and the monitored voltage 420 respectively (and would therefore be of the same frequency of approximately 13.56 MHz).

In preferred embodiments, a sampling period is defined at S140. The sampling period is a range in time that determines which zero-crossing points of the first signal 540 and the second signal 550 are used to measure the phase difference between the current and the voltage. In some applications it will be required that a phase difference measurement is continually updated by repeatedly performing the method of Figure 3, and redefining the sampling period upon each iteration of the method allows the measured phase difference to be computed using the most recently-obtained data that is available, which will be most accurately representative of the instantaneous state of the system. The sampling period could, for example, be defined so as to encompass a most recent given number of zero-crossing points of the first signal 540 and the second signal 550. The sampling period could then be redefined each time one of the first signal and the second signal passes through a new zero-crossing point. In a particularly preferred embodiment, the sampling period is chosen to include exactly two zero-crossing points of each of the first signal and the second signal. These could advantageously be the most recent two zero-crossing points of each of the first signal 540 and the second signal 550.

At step S150, a number of phase intervals that exist between the first signal 540 and the second 550 signal are measured. In the example of Figure 5, the horizontal axis is time, and each phase interval is the difference in time between a zero-crossing point of one of the first signal and the second signal and an earlier zero-crossing point of the other of the first and second signals.

The zero-crossing points of each signal, i.e. the points in time at which the signal goes from a negative value to a positive value or vice versa, are identified and recorded during step 5150. In some embodiments the crossing direction, i.e. whether the signal is positive-going or negative-going at the zero-crossing point, of each zero-crossing point is also recorded. Zero-crossing points could be identified in a variety of ways. These include, for example, identifying adjacent positive and negative values and interpolating to estimate the location of a zero-crossing point, or fitting a function such as a waveform to the first and second signals and identifying zero-crossing points of the fitted function. The crossing direction of a zero-crossing point could be determined by; for example, measuring the gradient of the signal in the vicinity of the zero-crossing point (a positive gradient would indicate that the zero-crossing point is positive-going; a negative gradient would indicate that it is negative-going).

Returning to the example shown in Figure 5, the sampling period 560 encompasses two zero-crossing points 543, 544 of the first signal 540 and two zero-crossing points 552, 553 of the second signal 550. For each zero-crossing point that falls within the sampling period 560, a phase interval is measured as the time difference between the zero-crossing point and the two preceding zero-crossing points of the other signal. For example, the phase interval 501 is defined by a zero-crossing point 544, which occurs at time t7, of the first signal and the last zero-crossing point 553, which occurs at time t6, of the second signal. The interval 501 is therefore measured as t7 -te. Similarly, the interval 502 is measured as t7 -t4, since the last but one zero-crossing point 552 of the second signal occurs at time L. Table 1 lists each of the intervals marked in Figure 5 together with the time values defining the interval and the phase angle to which the interval corresponds. The phase angle that corresponds to any particular interval is the fraction of one full cycle (360 degrees) equivalent to the fraction of the period of the first and second signals to which the magnitude in time of the interval corresponds.

Phase interval Definition Magnitude (degrees) 501 t7-t5 135 502 t7-t4 315 511 t6 -t5 45 512 t5-t3 225 521 t5 -t4 135 522 t5 -t2 315 531 LI. -t3 45 532 LI -t1 225

Table 1

Once the phase intervals shown in Figure 5 and listed in Table 1 have been obtained, the method proceeds to step S160, in which the measured phase intervals are converted to phase difference samples.

Each measured phase interval contains information relating to the phase difference between the first signal and the second signal. However, not every phase interval is directly equivalent to the phase difference and some phase intervals must be converted in order to extract a corresponding phase difference sample. In essence, this conversion involves removing any portion of each measured phase interval which represent something other than the phase difference between the two signals, such as will be the case when the interval between two different points on each respective signal's cycle is measured.

For example, here the phase interval 511 has a magnitude equal to what would be regarded as the magnitude of the phase difference between the first signal and the second signal. This interval can therefore be taken to be a phase difference sample without any modification. Like the phase interval 511, the phase interval 512 is defined by a later end-point at time t6, but its earlier end-point is at time t3, which lies half a cycle earlier than time t5, which is the later end-point of the interval 511. The phase interval 512 can therefore be converted to a phase difference sample by subtracting from it half a period.

The phase interval 521 is effectively half a period (as defined by the zero-crossing points 542, 543) minus the phase difference 570 between the first signal and the second signal. The phase interval 521 can therefore be converted to a phase difference sample by subtracting it from half a period of the first and second signals. The phase interval 522 has the same later end-point at t5 as the phase interval 521, but contains an additional half period since its earlier end-point is at time t2 rather than time t4. The phase interval 522 can therefore be converted to a phase difference sample by subtracting it from half a period of the first and second signals.

In view of this discussion the skilled person would recognise a variety of ways to convert phase intervals of the kind described herein to phase difference samples. A particular procedure for doing so is described later with reference to Figure 13.

Once the set of phase difference samples has been obtained, outliers may be identified and removed at step S170. This optional step is omitted in this example, but is discussed in detail later with reference to Figure 15.

At step S180 an average of the phase difference samples is computed. The average can then be output as a phase difference measurement for the sampling period in question. If outliers have been removed at step S170, an average of the remaining phase difference samples is computed. In preferred embodiments the average can be a mean value.

In this example, each of the phase intervals listed in Table 1 was converted to a phase difference sample of 45 degrees during step S160. The mean average of the phase difference samples is therefore 45 degrees. Idealised values have been used in this example, and in practice there is likely to be some variation between the individual samples This will be discussed later with reference Figures 10 to 12.

Figure 6 shows an exemplary measurement circuit 600 that could be used to monitor the current and voltage at the input to a matching unit in a plasma processing device, for example matching unit 200 of the plasma processing device 101 shown in Figure 1, in embodiments of the invention.

The RF generator 110 is on one side connected in series with a first coil 631 of a transformer 630, which is in turn connected to a first output terminal 651. The other side of the RF generator 110 is grounded, and is connected to a second output terminal 652. A second coil 632 of the transformer 630 is in series with a first resistor 613 in a grounded loop 601. A capacitor 621 and a second resistor 614 are connected in parallel across the RF generator 110 and the coil 631.

At a current sense point 641, the current through the grounded loop comprising the second coil 632 and the first resistor 613 is monitored. The RF generator 110 gives rise to an AC current through the first coil 631, which consequently induces a current through the second coil 632. The polarity of the coils 631, 632 is such that the current through the loop 601 is in phase with the current generated by the RF generator 110. Consequently, the current monitored at the current sense point 641 is in phase with the current generated by the RF generator 110.

At a voltage sense point 642, the voltage with respect to ground is monitored.

The current through the capacitor 621 and the second resistor 614 is in phase with the current output by the RF generator 110. However, the capacitor 621 causes the voltage with respect to ground at the voltage sense point 642 to lag the voltage at the output of the RF generator 110 by approximately 90 degrees.

This results in a phase offset of approximately 90 degrees being introduced between the monitored current and the monitored voltage. In a real-world scenario this offset may not be exactly 90 degrees, though it is usually between 70 and 110 degrees. In more general examples, it has been found that a phase offset between 10 degrees and 170 is preferable.

To implement the measurement circuit 600 in the plasma processing device 101, the first output terminal 651 would be connected at the input to the matching unit 200 while the second output terminal 652 would be grounded as shown in Figure 6. In preferred embodiments, the measurement circuit 600 is used to monitor the current and the voltage at the input to the matching unit 200 and serves to introduce a known phase offset (of approximately 90 degrees) at step S120 of the method illustrated in Figure 3. The current and voltage signals monitored from the circuit therefore correspond to the signals after step S120 and before S130 in Figure 3.

Figure 7 shows examples of a current signal 710 and a voltage signal 720 monitored using the measurement circuit 600 shown in Figure 6. This example shows the same current and voltage signals illustrated in Figure 4 but with an additional known phase offset introduced by the measurement circuit 600. The period of the current 711 and the period of the voltage 721 are the same as in the example of Figure 4, i.e. approximately 74 ns, though the phase difference is approximately 18.5 ns, or equivalently 90 degrees (as a phase angle), greater in magnitude.

Figure 8 shows a first signal 840 and a second signal 850 derived from the monitored current 710 and the monitored voltage 720 of Figure 7. The monitored current and voltage signals 710, 720 have been converted to lower frequency first and second signals 840, 850 in a way that preserves that phase information between the monitored current and voltage 710, 720, so an additional 90 degree phase offset exists between the first signal 840 and the second signal 850 with respect to the first signal 540 and the second signal 550 shown in Figure 5. The phase difference 870 between the first signal 840 and the second signal 850 is therefore 135 degrees. In order to obtain phase difference samples from the first and second signals 840, 850 shown in Figure 8, the same steps that are described above with reference to Figure 5 are performed. However, an additional known phase offset has been introduced and this must be subtracted once the phase intervals have been measured and converted so that the phase difference samples are representative of the phase difference between the current and the voltage at the input to the matching unit 200.

The phase intervals 801, 821 have magnitudes of 45 degrees; intervals 802, 822 have magnitudes of 225 degrees; intervals 811, 831 have magnitudes of 135 degrees; and intervals 812, 832 have magnitudes of 315 degrees. Like in the example described with reference to Figure 5, once these intervals have been obtained, they must be converted to phase difference samples. In this case, the values of the intervals 811, 831 are equal to the phase difference 870 between the first signal 840 and the second signal 850, so these do not need to be changed. Intervals 801, 821 are equal to 180 degrees minus the phase difference 870, so each of the intervals 801, 821 is converted by subtracting the interval from 180 degrees. The intervals 802, 822 are equal to 360 degrees minus the phase difference 870, so each of the intervals 802, 822 is converted by subtracting the interval from 360 degrees. The intervals 812, 832 are equal to the phase difference 870 plus 180 degrees, so are converted by subtracting 180 degrees from each interval. These steps for conversion lead to each interval being converted to a phase difference sample with a value of 135 degrees.

Once the phase intervals 801, 802, 811, 812, 821, 822, 831 have been converted to phase difference samples, the known phase offset must be removed in order to make the phase difference samples representative of the phase difference between the current and the voltage at the input to the matching unit 200. In this example the known phase offset is 90 degrees, and subtracting this offset from each phase difference sample results in the phase difference samples each having a value of 45 degrees. This set of results can then be averaged to obtain a phase difference measurement.

Figure 9 shows schematically a heterodyne unit 900 that could be used to convert the monitored current and voltage signals to lower frequency first and second signals in preferred embodiments if step S130 is to be implemented. An input signal 910, which, in the example of Figures 7 and 8, could be either the monitored current 710 or the monitored voltage 720, and a reference signal 920 having a known frequency are input to a mixer 930. The reference signal 920 could be provided by any device capable of producing an AC output signal of a constant frequency, such as a phase-locked-loop circuit. The mixer 930 is a conventional frequency mixer and combines the two input signals so as to produce two output signals: one having a high frequency 941 that is the sum of the frequencies of the input signal 910 and the reference signal 920, and the other having low frequency 942 that is the difference between the frequencies of the input signal 910 and the reference signal 920. The two output signals are output to a low pass filter 950, which eliminates the high frequency output signal 941. The result is a single low-frequency output signal 960, which is the first signal 840 if the input signal 910 was the monitored current or the second signal 850 if the input signal 910 was the monitored voltage 720.

The purpose of the heterodyne unit 900 is to convert an input signal 910 to a lower-frequency output signal 960. The frequency of the output signal 960 is the difference between the frequencies of the input signal 910 and the reference signal 920, so it is preferable that the frequency of the reference signal 920 is close to the expected frequency of the input signal 910. For example, WO-A2010/073006 describes in one example mixing a signal with a frequency in the region of 13.56 MHz with a reference frequency of 13.5599 MHz so as to give an output frequency of about 100 hertz (Hz). In preferred embodiments the input signal 910 has a frequency of approximately 13.56 MHz, and in such embodiments a low-frequency output signal 960 with a frequency of 1 kHz could be produced by the use of a reference signal 920 with a frequency of 13.561 MHz.

Figures 10a to 10c show, in an idealised scenario, the distribution of the measured phase intervals of Figure 8 as these intervals are converted to phase difference samples.

Figure 10a shows the distribution of the measured phase intervals shown in Figure 8. These intervals have the values listed above with reference to Figure 8. Figure 10b shows the distribution of the phase difference samples obtained by converting the phase intervals 801, 802, 811, 812, 821, 822, 831, 832 by the arithmetic steps described above with reference to Figure 8. At this point, all eight phase difference samples have a value of 135 degrees. Figure 10c shows the distribution of the phase difference samples once the known phase offset of 90 degrees has been subtracted from each one. There are now eight phase difference samples each with a value of 45 degrees, which can then be averaged to produce a phase difference measurement (which would in this example be exactly 45 degrees).

The scenario shown in Figure 10a to 10c is idealised. In practice, the positions of the zero-crossing points that define the phase intervals are subject to errors and this results in there being some variation between measured phase intervals that in principle represent precisely the same phase value. For example, the phase intervals 801, 821 represent the same interval in principle but may in reality have slightly different values when measured.

The effect of errors becomes particularly pertinent when one of the zero-crossing points of the first and second signals that define an interval is close in time to another zero-crossing point. Figure 11 shows a first signal 1140 and a second signal 1150 between which exists a phase difference 1170 that is close to zero. The phase intervals 1101, 1102 are defined by the zero-crossing point 1153 of the second signal 1150 and the last and last-but-one zero crossing points 1143, 1142 of the first signal, and their magnitudes are close to 0 degrees and 180 degrees respectively.

In an example scenario, an error could lead to the zero-crossing point 1143 of the first signal being recorded as having occurred slightly later than the zero-crossing point 1153 of the second signal. In this case, at step S150 the two intervals defined using the zero-crossing point 1153 as a later end point would now have the zero-crossing points 1142, 1141 as their earlier end points because these are now the two nearest preceding zero-crossing points of the first signal 1140 with respect to the zero-crossing point 1143. As a result, phase difference intervals with magnitudes of approximately 180 degrees and 360 degrees would be measured. If this is not accounted for, the phase difference samples derived from these measured phase intervals will each be approximately 180 degrees too large. This is an example of the two-pi ambiguity discussed above. This effect can lead to the appearance of outliers with extreme values in the set of phase difference samples, and an exemplary method for removing these is described later with reference to Figure 13.

The method of Figure 3 can be implemented in a plasma processing device (such as the plasma processing device 101 of Figure 1) in order to measure a phase difference between the current and voltage at the input to a matching unit with the objective of reducing this phase difference to zero. An advantage of introducing a known phase offset between the monitored current and the monitored voltage, for example by the implementation of the measurement circuit of Figure 6, is that errors of this kind are unlikely to be experienced when the phase difference between the current and voltage are close to zero. This is because the phase difference between the first and second signals (between which phase intervals are measured at step S150) will have a value close to that of the known phase offset, rather than zero, when the phase difference between the current and the voltage at the input to the matching unit is zero.

Figures 12a to 12c show an example illustrating the distributions that a set of measured phase intervals might be expected to form in a realistic scenario and show the same steps illustrated by Figures 10a to 10c. Figure 12a shows the measured phase intervals, which are close to but not precisely equal to the corresponding values in the example of Figure 10a. When the measured phase intervals are converted to phase difference samples, which are shown in Figure 12b, the samples are all distributed around the expected value of 135 degrees.

Similarly, when the known phase offset is subtracted from the samples shown in Figure 12b, the resulting phase difference samples, which are shown in Figure 12c, are distributed around the value of 45 degrees. The phase difference samples shown in Figure 12c can be averaged to output a phase difference measurement with a value of approximately 45 degrees.

Figure 13 is a flow chart showing a method that may be used in preferred embodiments for converting measured phase intervals such as those in the example of Figure 8 to phase difference samples at step S160. The phase interval 802 shown in Figure 8 will be used as an example to illustrate this process.

At step S161 a particular phase interval that has not yet been converted to a phase difference sample is selected. At step S162, the signal that corresponds to the later of the two zero-crossing points that define the interval is identified. If the first signal has the later zero-crossing point, the process proceeds to the decision S163a; and if the second signal has the later zero-crossing point, the process proceeds to the decision S163b. The interval 802 is defined by the zero-crossing point 844 of the first signal and the earlier zero-crossing point 852 of the second signal, so in this example the first signal has the later zero-crossing point. Step S163 asks if the crossing directions of the two zero-crossing points defining the interval in question are the same, and leads on to the appropriate operation at S164, which provides the appropriate arithmetic operation to convert the phase interval to a phase difference sample. Operation 5164a is to subtract the interval from the period, P, of the first and second signals; operation S164b is to subtract the interval from half of the period; operation S164c is to subtract nothing from the interval (thereby leaving the interval unchanged); and operation S164d is to subtract half the period from the interval. The zero-crossing points 844, 852 are both positive-going so in the example of the phase interval 802, the process proceeds to step S164 along the "yes" path. This leads to the operation S164a being applied to the interval 802. As described above, the interval 802 corresponds to the period of the first and second signals minus the phase difference between the first and second signals, so the process of Figure 13 has led to the correct operation (subtract the interval 802 from P) being applied to this interval. Applying steps S162, S163, S164 to each of the phase intervals shown in Figure 8 leads to each interval being converted to a phase difference sample with a value of 135 degrees.

In the examples described above with reference to Figures 5 and 8, the first signal led the second signal, so the phase difference between the first signal and the second signal was positive. The appropriate arithmetic operations to be applied to each interval were identified based on a reasoned interpretation of how each interval related to the actual phase difference between the signals.

The method of Figure 13 leads to the appropriate conversion being identified automatically.

When the first signal leads the second signal, a zero-crossing point of the first signal and the last (i.e. immediately preceding) zero-crossing point of the second signal will always have different crossing directions. The appropriate operation to apply to an interval defined by these zero-crossing points in this scenario would be to subtract the interval from P/2, and the process of Figure 13 would indeed lead to this outcome at operation S164b. In Figure 8, this would apply to the intervals 801, 821. Furthermore, the last-but-one zero-crossing point of the second signal would have the same crossing direction as the zero-crossing point of the first signal in question, and the process of Figure 13 would lead to an interval defined by these zero-crossing points being subtracted from one period at operation S164a. Similar reasoning confirms that the process of Figure 13 leads to the correct operations being applied at S164c, S164d to intervals defined by a zero-crossing point of the second signal and a last or last-but-one zero-crossing point of the first signal. In addition to identifying the correct operation to convert a phase interval to a phase difference sample, the combination of steps S162, 5163 and 5164 distinguishes positive and negative phase differences. This will be discussed in more detail later with reference to Figure 14.

After performing the appropriate arithmetic operation at step 5164, the method proceeds to the optional step S165. This step is to subtract the known phase offset, such as that introduced by the measurement circuit 600 of Figure 6, and is performed if such an offset has been applied.

The next step is an optional step S166. Under some circumstances, the phase difference samples produced at step S164 are not all in the range -180 degrees to +180 degrees. This occurs in the example shown in Figure 14, in which the phase difference 1470 between a first signal 1440 and a second signal 1450 is negative, with a value of -45 degrees. For each phase interval 1401, 1402, 1411, 1412, 1421, 1422, 1431, 1432 shown in Figure 14, Table 2 lists the magnitude of the interval, the operation that is performed on the interval at step 5164 of the method of Figure 13, and the value of the resulting phase difference sample. In this example the zero-crossing points 1441, 1443, 1452, 1454 are positive-going, and the zero-crossing points 1442, 1451, 1453 are negative-going.

Phase interval Magnitude (degrees) Operation Phase difference sample (degrees) 1401 135 Subtract P/2 from -45 interval 1402 315 Subtract nothing from interval 315 1411 45 Subtract interval from P 315 1412 225 Subtract interval from P/2 -45 1421 135 Subtract P/2 from -45 interval 1422 315 Subtract nothing from interval 315 1431 45 Subtract interval from P 315 1432 315 Subtract interval from P/2 -45

Table 2

The phase difference samples in Table 2 are not all equal to the value of the phase difference of -45 degrees that exists between the first signal 1440 and the second signal 1450. The phase difference samples derived from the phase intervals 1402, 1411, 1422, 1431 in fact each have a value of 315 degrees. This is not incorrect: a phase difference of +315 degrees is equivalent to a phase difference of -45 degrees (as the difference between these values is exactly 360 degrees), but the samples with values of 315 degrees must be brought into conformance with the definition of a phase difference as being in the range of -180 degrees to +180 degrees. This can be achieved by subtracting 360 degrees from each of the phase difference samples with a value of 315 degrees. In general, it is possible to obtain phase difference samples at step S164 that are either above or below the range of -180 degrees to +180 degrees. The purpose of the optional step S167 is to ensure that an appropriate correction is made to each phase difference sample that is outside the range of -180 degrees to +180 degrees. This step, in combination with the preceding steps of the method of Figure 13, allows the appropriate conversion for a particular phase interval to be identified knowing only which signal has the later zero-crossing point of the two zero-crossing points that define the interval and the crossing directions of these zero-crossing points. It is not necessary to explicitly identify the last and last-but-one zero-crossing points of one signal with respect to a zero-crossing point of the other.

Step S167 is to check whether all of the phase intervals defined with respect to the chosen sampling period, for example the sampling period 860, have been converted to phase difference samples. If all phase intervals have been converted, the method proceeds to the optional step S170; otherwise, it returns to step 5161 and a new, unconverted phase interval is selected. As explained above, two phase difference samples separated by some multiple of ±360 degrees are physically equivalent; step 5167 merely brings these values into conformance with the definition of the phase difference as being in the range of -180 degrees to +180 degrees.

Figure 15 shows an exemplary method for removing outliers from a set of phase difference samples that may be performed in preferred embodiments. The method involves placing the phase difference samples into bins based on their values, and in this example a first bin contains all of the phase difference samples that are greater than 120 degrees; a second bin contains all phase difference samples that are less than or equal to 120 degrees and are greater than or equal to -120 degrees; and a third bin contains all phase difference samples that are less than -120 degrees.

At step S171, a phase difference sample that has not yet been placed into one of the three bins is selected. At step S172, the phase difference sample is placed into the first bin if its value is greater than 120 degrees and the method proceeds to step S175; otherwise the method proceeds to step S173. At step S173, the phase difference sample is placed into the third bin if its value is less than -120 degrees and the method proceeds to step S175; otherwise the method proceeds to step 5174, in which the phase difference sample is placed into the second bin.

Step S175 checks if all of the phase difference samples have been placed into bins. If so, then the method proceeds to step S176; otherwise, the method returns to step S171 and a next, un-binned phase difference sample is selected.

At step S176, the bin containing the greatest number of phase difference samples is identified and the phase difference samples in the other two bins are discarded. The values in the remaining bin are retained and at step S180, an average of these values is computed in order to return a phase difference measurement.

In this example the bins are demarcated at ±120 degrees. The purpose of this is to ensure that any extreme outliers that appear when the system is close to being matched (i.e. when the phase difference between the current and the voltage at the input to the matching unit 200 is close to zero) are removed. Other values could be used to define the positions of the bins, however, and the first bin does not necessarily need to be symmetric about zero.

The exemplary methods described above can be implemented to track the phase difference between the current and voltage at the input to a matching unit in a plasma processing device such as the matching unit 200 of the plasma processing device 101 shown in Figure 1. As explained above, the impedance of the matching unit 200 can be continually adjusted in accordance with the phase difference between the current and voltage at the input to the matching unit 200 in order to minimise the phase difference between the current and the voltage. So that the matching unit 200 can be updated frequently and accurately, it is preferable that the phase difference measurement is updated regularly. The exemplary methods described above could be performed at regular intervals to achieve this. For example, each time the first signal and the second signal have each passed through a new zero-crossing point, the sampling period could be redefined (at step 3140) so as to encompass the two new zero-crossing points. This would allow the phase difference measurement to be updated every half period of the first and second signals. If the first signal and the second signal each has a frequency of 1 kHz, for example, then the phase difference measurement could be updated every 0.5 ms. The impedance of the matching unit 200 could correspondingly be updated every 0.5 ms.

Figure 16 shows a graph displaying examples of real measurements of the input power and the reflected power measured at the input to a load in a plasma tool of the kind described above with reference to Figure 1 using a matching unit controlled by conventional methods (such as those described in WO-A-2010/073006). The horizontal axis is time, in seconds, and the vertical axis is measured power, in watts. Plotted on the graph are a series of reflected power profiles 1601, 1611, 1621, 1631, 1641, 1651, 1661, 1671, 1681, each of which represents the reflected power measured over time as an approximately constant input power was delivered to a test load by a signal generator. A different test load was in place as each of the reflected power profiles 1601, 1611, 1621, 1631, 1641, 1651, 1661, 1671, 1681 was obtained, and each test load had a different complex impedance in the range 0.67 + 13j ohms to 6.0 -164j ohms, where j is the unit imaginary number. The power delivered by the signal generator is shown by forward power profiles 1602, 1612, 1622, 1632, 1642, 1652, 1662, 1672, 1682. In each case, the reflected power diminished over time as the impedance of the matching unit was controlled so as to reduce the reflected power.

Figure 17 shows real measurements of the input power and the reflected power measured at the input to a load in a plasma tool of the kind described above with reference to Figure 1 using a matching unit controlled by methods in accordance with the present invention. This Figure includes a series of reflected power profiles 1701, 1711, 1721, 1731, 1741, 1751, 1761, 1771, 1781. As in Figure 16, the horizontal axis is time, in seconds, the vertical axis is measured power, in watts. The power delivered to each test load by the signal generator is shown by the forward power profiles 1702, 1712, 1722, 1732, 1742, 1752, 1762, 1772, 1782. The test loads with which each reflected power profile shown in Figure 17 was obtained was the same as the test load used in obtaining the corresponding reflected power profile shown in Figure 16. That is to say that the profile 1601 in Figure 16 shows measurements taken with the same test load as the profile 1701 in Figure 17; that likewise the same test load was in place when the measurements shown in profiles 1611 and 1711 were taken; and so on. In each of the profiles shown in Figure 17, the reflected power falls much more rapidly than in the corresponding profile in Figure 16. In some of the examples shown in Figure 17, matching of the impedance of the matching unit to that of the test load (so as to reduce the reflected power to a negligible value) was achieved within one second.

Claims

CLAIMS1. A method for measuring in a plasma processing device a phase difference between the current and voltage of a cyclic electrical signal of a first frequency output by a signal generator to a load, the method comprising: (I) monitoring, at an input to the load, the current through the load and the voltage across the load and outputting the monitored current and the monitored voltage; (II) deriving a first signal from the monitored current and a second signal from the monitored voltage, the phase information between the monitored current and the monitored voltage in the cyclic electrical signal being preserved in the first and second signals, and the periods of the first signal and the second signal being the same; (Ill) for each zero-crossing point of the first and second signals within a selected sampling period, measuring a pair of phase intervals comprising (i) the phase interval between the zero-crossing point and the last zero-crossing point of the other signal, and (ii) the phase interval between the zero-crossing point and the last but one zero-crossing point of the other signal; (IV) converting the measured phase intervals to corresponding phase difference samples in the range of -180 degrees to +180 degrees, the conversion of each measured phase interval being based on the zero-crossing points used to measure the phase interval and the period of the first and second signals, where a positive phase difference sample represents the first signal leading the second signal and a negative phase difference sample representing the second signal leading the first signal, or vice versa; and (V) computing an average of the phase difference samples.
2. The method of claim 1, wherein: step (I) further comprises the introduction of a phase offset between the monitored current and the monitored voltage, the phase offset having a known magnitude, such that the output monitored current and the output monitored voltage have a phase difference which includes the phase offset; and step (IV) further comprises removing the known phase offset from the measured phase intervals.
3. The method of claim 2, wherein the phase offset is introduced by an apparatus used to monitor the current through the load and the voltage across the load.
4. The method of claim 2 or claim 3, wherein the phase offset is between 10 degrees and 170 degrees, preferably about 90 degrees.
5. The method of any of the preceding claims, wherein the first signal and the second signal are derived so as to each be of a second frequency that is lower than the first frequency.
6. The method of claim 5, wherein step (II) comprises mixing each of the monitored current and the monitored voltage with a reference signal output by a second signal generator so as to produce a lower-frequency heterodyne signal.
7. The method of claim 6, wherein the frequency of the reference signal is chosen such that the heterodyne signal has a frequency of between 100 hertz and 10 kilohertz (kHz).
8. The method of any of claims 1 to 4, wherein the first signal is the monitored current and the second signal is the monitored voltage.
9. The method of any of the preceding claims, wherein the sampling period includes at least one zero-crossing point of each of the first signal and the second signal.
10. The method of any of the preceding claims, wherein the sampling period includes no more than 10 zero-crossing points of each of the first signal and the second signal.
11. The method of any of the preceding claims, wherein the sampling period includes exactly two zero-crossing points of each of the first signal and the second signal.
12. The method of any of the preceding claims, where in step (IV) the conversion of each measured phase interval is further based on the crossing directions of the zero-crossing points used to measure the phase interval.
13. The method of claim 12, wherein step (IV) comprises: for a phase interval measured between a zero-crossing point of the first signal and a previous zero-crossing point of the second signal, subtracting the phase interval from (a) one period, where the crossing directions of the zero-crossing points used to compute the interval are the same, or (b) half of one period, where the crossing directions of the zero-crossing points used to compute the interval are different; and for a phase interval measured between a zero-crossing point of the second signal and a previous zero-crossing point of the first signal, subtracting from the phase interval (c) half of one period, where the crossing directions of the zero-crossing points used to compute the interval are different, or (d) nothing, where the crossing directions of the zero-crossing points used to compute the interval are the same.
14. The method of claim 13, wherein step (IV) further comprises: identifying any phase difference samples that lie outside of the range of 180 degrees to +180 degrees, and adding or subtracting one or more integral periods to or from each of the phase difference samples outside of the selected range so as to bring each of the identified phase difference samples within the selected range.
15. The method of any of the preceding claims, wherein: before step (V), each phase difference sample is placed into one of a plurality of bins in the phase angle domain based on the value of each phase difference sample, each bin defining a range in the phase angle domain; and step (V) comprises computing an average of the phase difference samples in one of the plurality of bins.
16. The method of claim 15, wherein the single bin is chosen as the bin containing the greatest number of phase difference samples.
17. The method of claim 15 or claim 16, wherein the plurality of bins comprises a first bin spanning a range that includes zero phase difference.
18. The method of claim 17, wherein the range of the first bin is from -X degrees to +X degrees, where X is in the range of 90 to 120.
19. The method of any of the preceding claims, wherein the phase intervals are measured in the time domain.
20. The method of claim 19, wherein the phase intervals are measured using a cyclic clock signal having a period less than the period of the first signal and the second signal.
21. The method of claim 19 or claim 20, wherein before step (V) either each phase interval or each phase difference sample is converted from the time domain to the phase angle domain.
22. The method of any of the preceding claims, wherein the cyclic electrical signal has a frequency in the range of 50 (kHz) to 100 megahertz (MHz), preferably in the range of 10 MHz to 20 MHz, and most preferably approximately 13.56 MHz.
23. The method of any of the preceding claims, wherein the load comprises a matching network with a variable impedance and a plasma load, and the current and the voltage are measured at the input to the matching network.
24. A method for controlling a phase difference between a cyclic current and a cyclic voltage through a load, wherein the current and voltage are generated by a cyclic electrical signal output from a signal generator to the load, the method comprising: measuring the phase difference by the method of any of the preceding claims; and based on the measured phase difference, automatically adjusting the phase difference between the current and the voltage towards a target value.
25. An apparatus comprising: a signal generator adapted to output a cyclic electrical signal to a load; a monitoring module adapted to monitor, at an input to the load, a current through the load and a voltage across the load; and a processor adapted to measure a phase difference between the current and the voltage by the method of any of claims 1 to 23.
26. The apparatus of claim 25, further comprising a phase control module configured to automatically adjust the phase difference between the current and the voltage, based on the measured phase difference, towards a target value.
27. A method of tracking in a plasma processing device a phase difference between the current and voltage of a cyclic electrical signal of a first frequency output by a signal generator to a load, the method comprising: (I) measuring the phase difference between the current and voltage by the method of any of claims 1-23 at a first instant of time; (II) outputting the measured phase difference; (III) at a second instant of time later than the first instant, redefining the sampling period so as to include at least one zero-crossing point of the first signal or the second signal that lies between the first instant and the second instant; and (IV) repeating steps I-III at least once.