At a Glance
	Accurate energy demands on rf generating equipment for semiconductor processing continue to grow. As IC geometries shrink, so do process parameter tolerances. The actual amount, frequency spectrum and time duration of rf energy applied to a process has become increasingly critical to process performance. Power tolerances of 3-5% are no longer acceptable to many modern semiconductor processes.

Paul Rummel,
Comdel, Gloucester, Mass.

Repeatable rf power delivery requires that an rf generator's internal power sensor be repeatable and accurate in the plasma system environment. A generator's energy delivery performance driving its intended plasma application may be quite different from that of driving a broadband, resistive dummy load. To be of any diagnostic value, attempts to monitor or verify energy delivery performance through the use of externally applied in-line wattmeters requires an understanding of the measurement type and also requires probable accuracy of the meter being used.

This article describes two commonly used methods of detecting rf power and the implications of using those methods in a plasma system environment. The descriptions for these two detection methods apply to both an rf generator's internal power detector and an externally applied wattmeter. Next, a discussion of rf system harmonic energy sources exposes potential added errors to the power measurement methods.

Power measurements in rf delivery systems

1. A typical rf delivery system with some common points for rf power measurement.

Figure 1 shows a typical rf delivery system with some common points for rf power measurement (1-4). In the rf generator block (rf gen), a power amplifier produces a waveform that can be very high in harmonic content. This is typical because high amplifier efficiencies can be realized if the waveform is not constrained to the fundamental only. Because of the high amplifier harmonic content, a low-pass filter (LPF) or band-pass filter (BPF) is typically used to attenuate energies at the harmonic frequencies. Most commercial rf generators contain a power detector of some sort (circle 1) between the filter and the generator's output to monitor and control the forward or delivered output power to a desired set point.

An rf plasma system may or may not utilize a transmission line (Xmission line) between the rf generator and an impedance transformation (Z xfrm), or matching network circuit. When a transmission line is used, two convenient power-monitoring points are at the line termination points as shown as circles 2 and 3. These are common locations to insert a commercial in-line power meter for diagnostic purposes.

A power measurement point between the impedance transformation circuit and the plasma (circle 4) is shown as more of a side note. This location is often not a convenient in-line power monitoring point because the voltages and currents can be quite high and only specialty devices are used here.

These devices are typically built into the system, because connectors and added components at this location introduce unwanted losses and reactances that can drastically affect a process. Because of these added complications, in-line power monitoring at the plasma load is beyond the scope of this article.

Diode peak-detectors

2. The operation of forward and reflected diode peak-detector circuits is shown.

The most widely used power detection circuit is the diode peak-detector. This circuit is commonly used for the internal power sensor in many rf generator designs and in many commercially available in-line power meters. The basic diode peak-detector circuit is comprised of components that provide an rf voltage sample summed with an rf current sample, and then turned into a dc signal or "peak-detected" with a diode. Figure 2 illustrates the operation of forward and reflected diode peak-detector circuits.

For the forward case, voltage and current samples are summed to produce a signal that is detected with a diode to give a dc signal that is proportional to the square root of forward power. Because voltage and current are both proportional to the square root of power, so is the sum of voltage and current.

For the reflected case, the current sample is 180° out of phase with the actual current being detected. This is easily accomplished by reversing the leads of a current sampling transformer. If the power detector is designed for 50 W load impedance, the voltage and current samples are designed to present equal amplitudes at the summation point. If the detector is placed in a circuit that has a 50 W load, then these two samples will be of the same amplitude and exactly out of phase with each other, giving a very small or zero summation signal. This is also peak-detected to give a dc signal proportional to the square root of reflected power.

Errors in the diode peak-detection method are due to several factors. First, diodes used for detection have a nonlinear characteristic at low levels, which, for more accurate detection circuits, must be accounted for. Second, the output signal must be squared through either a squaring circuit or a mathematical algorithm, which can introduce more errors. Third, the accuracy is highly dependent upon the peak value giving a true representation of the fundamental power. Any small amount of harmonic energy present in the rf being detected can misshape the waveform, introducing a large "fundamental" detected power error.

Multiplier detectors

3. Four-quadrant analog multipliers produce the waveforms shown at the bottom of this figure by squaring the summed signals.

As in the diode peak-detector described above, multiplier detectors use multiplication circuits in place of the diode to produce dc signals directly proportional to power. Figure 3 illustrates multiplier detector operation.

As in the diode peak-detector, voltage and current samples are summed. Where the multiplier circuit differs is how the proportional dc signals are produced. Four-quadrant analog multipliers are used to square the summed signals to produce the waveforms shown at the bottom of the figure. Since the squared signals are no longer bipolar, a simple RC integrating circuit is used to "average" the signals, providing dc levels directly proportional to forward and reflected power. The relationship of the detectors' outputs are directly proportional to power because the summed (square root proportional) signals get squared in the process by the multipliers.

4. In the "direct multiplier" detector, a signal directly proportional to delivered power is obtained and then integrated to give the proportional dc signal.

Another variation of the multiplier detector is the "direct multiplier" detector. In this circuit, a signal directly proportional to delivered (forward-reflected) power is obtained by using a four-quadrant multiplier to directly multiply the voltage sample by the current sample. The resulting signal is then integrated to give the proportional dc signal. This method is illustrated in Figure 4.

This circuit has the advantage of providing a signal directly proportional to the amount of energy dissipated in all loads after the detector. Though it does not give any indication of the amount of reflected power from the load, this circuit can be used to accurately provide power information into highly mismatched loads.

For both of these multiplier power detectors, errors can be introduced by the nonlinearities of the four quadrant multipliers themselves. Also, the multipliers must have sufficient speed or bandwidth to follow the sampled voltage and current waveforms. Since the detected power signals are derived from the integration of the multiplied waveforms (area under the curve), these types of detectors provide power signals proportional to total forward or total delivered power. Total power means the power detected at the fundamental frequency plus power in the harmonic frequencies.

Harmonic energies in rf plasma systems

Harmonic energies found in rf-powered plasma-processing systems can be considered to have two sources: 1) the rf generator and 2) the nonlinearities of the plasma.

Harmonic energy from the rf generator is easily comprehended as any harmonic energy originating from a power amplifier that does not get completely rejected by the generator's internal harmonic filter. Typical harmonic energy levels from commercial rf power generators range from -20 dB to -50 dB (100 to 100,000 times less), from the amount of energy in the fundamental frequency. For example, if an rf generator is specified to have all harmonic energies -30 dB or more down from the fundamental, this means that, for 1 kW of power at the fundamental, no more than 1 W of output power is delivered at any of the harmonic frequencies. This may also mean that the energies in all of the harmonics combined do not sum to more than 1 W. In all cases, rf generator harmonic energies are specified into a broadband resistive dummy load. This means that not only is the fundamental loaded with 50 W, but so are each of the harmonic energies. In many plasma system applications, only the fundamental energy gets resistively loaded, while the harmonics see arbitrary reactive loads that can change with process and matching network positions. This can result in harmonic energies directly due to the rf generator far in excess of the generator's rated harmonic output .

The second source of plasma system harmonic energy can be much larger than the direct contribution of the rf generator. This is a contribution from the nonlinearities of the plasma itself. These nonlinearities convert fundamental energy into harmonic energy. Unless specifically trapped or filtered, harmonic energies, emanating from the plasma, can be supported and passed back through the matching network. These harmonic energies can then mix with the already present generator contributed harmonic energies. It would not be uncommon to find -20 dB of harmonic energy present along the transmission line of an rf delivery system using an rf generator specified for -40 dB harmonic content. This harmonic energy is either dissipated in the generator, transmission line, plasma, or simply remains as stored energy distributed throughout the components of the rf delivery system.

Harmonic energy consequences

5. The differences of diode peak-detected summation samples as a function of the third harmonic phase relationship 20 dB below the fundamental.

The end result of these two sources of harmonic energy is that any power detector sampling circuit with sufficient bandwidth will faithfully reproduce the actual rf voltage and current waveforms, inclusive of the distortions caused by the harmonics. Multiplying power detectors will detect the total energy (fundamental + harmonic). Diode peak-detector power sensors can exhibit large errors based on the phase relationships between harmonic voltages and currents, and the phase relationships between the harmonics and the fundamental. To illustrate the extent to which a diode peak-detecting power sensor can be affected, Figure 5 shows the differences of diode peak-detected summation samples as a function of the third harmonic phase relationship to the fundamental. It is assumed that the fundamental energy is perfectly terminated, (no reflected fundamental power).

In this example, the two V+I sampled sine curves having the same fundamental energy get distorted by the presence of third harmonic energy 20 dB below the fundamental. If the harmonic voltage is in phase with the harmonic current, then the distortions shown in the figure result. The flattened curve (0.9V peak) has the third harmonic energy in phase with the fundamental, while the second curve (1.1V peak) has the third harmonic out of phase with the fundamental. (If there were no harmonic distortion, the peak would be at 1V.) The peak-detected values are then squared to represent power, resulting in 0.81V and 1.21V signals. If the undistorted or fundamental power is represented by a 1V signal, then the -20 dB harmonic energy adds in a potential -19% to +21% power error depending upon the phase of the harmonic to fundamental energy. In reality, 20 dB down means that the energy in the third harmonic is only 1% of that in the fundamental. For diode peak-detecting power sensors, the added 1% of harmonic energy can create a potential ±20% power measurement error.

In the above example only the effect of the third harmonic is shown. It is entirely possible to have added errors from the combinations of other (second, fourth, fifth, etc.) harmonic energies that add to the peak values. The phase relationships of harmonic energies may be extremely difficult to predict or measure in any real rf delivery system. The worst-case power measurement error should always be assumed based upon the total harmonic energy content. This can be readily measured with a calibrated directional coupler and spectrum analyzer at the point of power measurement.

Table 1 shows the worst-case errors of diode peak-detecting power readings for different levels of harmonic distortion.

These potential errors should be added to the power meter's base accuracy. For example, if an in-line power meter's specified accuracy is ± 3% with a specified maximum harmonic content of -50 dB, then the accuracy tolerance due to harmonic content is ±0.6%. That means that the base accuracy (no harmonic content) is ±2.4%. Thus, if the system being measured has harmonic content -30 dB, then total expected accuracy is 2.4% + 6% = ±8.4%.

Conclusions

Without knowing the type of power detector used and the harmonic content present in an rf-driven plasma-processing system, power measurements must be highly suspect. It may be unrealistic to expect very low amounts of harmonic energy to be present in an rf delivery system. It is equally unrealistic to predict system harmonic content based solely upon the rf generator harmonic output specification from the manufacturer. Harmonic energy management requires careful design considerations in all components that make up an rf delivery system.

Harmonic energy by itself is not necessarily the direct cause of process non-repeatability. An rf delivery system may have a large amount of harmonic energy present that does not change amplitude or phase over process periods. This would result in a fixed, repeatable power control error. But even in this case, diagnosing the system with an in-line wattmeter can exhibit large power differences depending upon measurement position along the transmission line. Also, the fixed error may be highly dependent upon the actual rf system components used. Replacing a matching network could make a large difference to harmonic phase relationships due to very minor manufacturing differences. This could cause a large change to the previous fixed error.

Process non-repeatability can be the direct result of using the diode peak-detector to control process power in the presence of high harmonic content. Even if an rf generator uses a multiplier type or other power detection method that is immune to harmonic induced errors, attempts to diagnose an rf system with an externally placed diode peak-detecting wattmeter might only serve to cast doubt on the integrity of the system. Certainly, if this type of power meter must be used, a calibrated spectrum analyzer measurement should be included in the diagnosis to determine the error tolerance of the power reading.

Looking forward, there are two issues to achieving improved repeatability of rf power measurements: the accuracy and repeatability of rf power control , and the accuracy of added in-line diagnostic power meters. For this discussion, it is assumed that power control is performed by the system rf generator (Fig. 1, circle 1), and diagnostic power meters are inserted along the transmission line, (Fig. 1, circle 2 or 3). To achieve much lower rf power measurement tolerances for this scenario, there are at least three approaches that can be taken:

• Attenuate harmonic energies at the points in the system where power measurements are made.
• Decrease the sensitivity of diode type detectors to harmonic content.
• Use multiplier type power detectors.

Based on Table 1, it would require a diode peak-detecting power sensor to be exposed to less than -50 dB of harmonic energy to be affected less than ±0.6%. Approach number one would require that not only the rf generator's internal filter reject harmonics to this degree, but also require a similar filter on the other side of the power sensor to reject harmonics from the plasma side, (Fig. 1, circle 3). While this double filtering would be effective for power control and in-line diagnostic measurements, it could create further complications. The extra poles and zeroes of two -50 dB filters create the possibility of added resonances, which increases the potential for instabilities. Also, the filter on the plasma side would have loss, (in addition to matching network losses), which must now be accounted for in the process power requirements.

Approaches two and three are similar in that they involve using power detection circuits that are more immune to harmonic content error. High harmonic rejection in a diode type detector results in power measurements true to the fundamental power. Multiplier type power detectors give total, fundamental + harmonic power measurements. It is of the author's opinion that the fundamental power is the more appropriate parameter to control with the rf generator. Harmonic energy sourced from the generator does not typically do much work in the plasma because the matching network rejects much of this energy. It is the plasma-created harmonics that can do work in the process. Nonlinear plasma-created harmonics, which are sourced from the fundamental , are more likely to be reflected off the matching network, back into the plasma/process.

Paul Rummel is an rf engineer at Comdel Inc. He has been involved in rf design applications to the semiconductor industry for 18 years. He earned his B.S. in electrical engineering at California Polytechnic State University and his M.S. in electrical engineering at Michigan State University. Phone: 978-282-0620, ext. 133 e-mail: paul_rummel@comdel.com

Acknowledgments

The author would like to acknowledge Ken Smyth of Applied Materials, Steve Hilliker of Novellus and John Caughman of Oak Ridge National Laboratory for their help with this article.