Advanced RF Metrology for Plasma Process Control

Semiconductor radio-frequency (RF) process chambers typically exhibit a wide and varying range of plasma impedances. Often, this variation extends from tool to tool, and the degree of difference in performance is uncertain. This presents the challenge of repeatable run-to-run, wafer-to-wafer, and lot-to-lot control.
 
RF diagnostic systems provide essential parameters for both statistical process control (SPC) and automated process control (APC). To achieve process repeatability and process control of RF plasma processes such as plasma-enhanced chemical vapor deposition (PECVD) and plasma etching, it is necessary to accurately monitor and control the actual plasma impedance and RF power delivered to the plasma.

The metrology of the RF system can determine the accuracy of SPC control limits and will dictate the accuracy and repeatability of the APC RF control points.

The components comprising an RF metrology system are the RF sensor and its associated signal-processing unit. Field configurations vary; one example is shown in Figure 1 . The RF sensor is located on the RF transmission line, generally near the input to the plasma chamber. The sensor contributes minimal insertion loss and provides two voltage outputs that represent the time-varying electric field and the time-varying magnetic field present in the RF sensor assembly.

1. RF metrology systems consist of the RF sensor and its associated signal-processing unit. One of various configurations is shown.

A variety of methods can be used to couple the electric and magnetic fields present on the transmission line. The coupling methods can be in the form of capacitive for the electric field and a current transformer (i.e., Pearson) or strip line for the magnetic field. The most important factor for any sensor is the sensor's directivity. The MKS proprietary RF sensor is one of the most accurate sensor available to measure impedance and power in highly reactive loads. The directivity of the sensor affords this capability. The uncertainty of an RF sensor's power measurement can be predicted for a specified directivity. Figure 2 compares the absolute forward power measurement uncertainty for the directivity of an industry-accepted wattmeter sensor and the MKS sensor over a VSWR (voltage standing-wave ratio) range of 1.0:1 to nearly 6.0:1. The MKS sensor exhibits measurement uncertainty of less than ±0.2% over the VSWR range. In contrast, the typical commercial RF wattmeter sensor exhibits a measurement uncertainty of more than ±2.0% at 2.0:1 VSWR.

2. The absolute forward power measurement uncertainty for the directivity of an industry-accepted wattmeter sensor is compared to the MKS sensor over a VSWR (voltage standing-wave ratio) range of 1.0:1 to ~6.0:1. The MKS sensor exhibits measurement uncertainty of less than ±0.2% over the VSWR range.

The signal-processing unit measures the voltage and current, and the phase difference between these signals, and scales these measurements to the corresponding RF voltage, current and phase. The signal-processing unit can also derive other RF parameters such as impedance and power. Various methods of signal processing are employed for the analysis of the RF sensor signals. The signal-processing domain can be analog, digital or a combination of these. Digital signal processing uses frequency or spatial (time) analysis methods. The method chosen for the signal-processing unit balances cost and performance in meeting the demands of today's plasma processes.

Classical requirements for RF metrology are repeatable and accurate measurements. The demands of plasma processing require simultaneous monitoring of multiple RF sources, autonomous frequency tracking, harmonic content analysis, and RF pulse monitoring. Plasma processing can often use multiple RF sources.

Autonomous frequency tracking decouples the dependency between the RF source(s) and metrology for RF delivery systems that employ frequency-tuning sources. Because of the nonlinear properties of the plasma load, the spectral content of the RF will contain a plurality of harmonic tones and intermodulation products. A number of papers have been published referencing applications using these harmonic tones for endpoint detection and uniformity.¹

One of several design challenges is to design the signal-processing unit to account for the differences in dynamic ranges of the fundamental and the harmonics. Not considering the difference in the dynamic ranges could compromise the system's signal-to-noise ratio (SNR) for accurate and repeatable harmonic measurement. Reference 2 discusses the relationship between the RF fundamental and associated harmonics for a particular plasma process. Pulsing the RF can provide a variety of process benefits. The measurement of the impedance of pulsed plasmas has been described.³

Principal RF metrology design challenges to meet these application objectives are:

• The dynamic range must be optimized for the harmonic frequencies as well as the fundamental.
   
  
• The selection of sample rate is based on acquisition of the RF signals for analysis, frequency tracking, and RF pulsing. The sample rate is the rate of conversion of the analog signal to a digital signal. A byproduct of sample rate is spectral folding. Without judicious consideration of the sample rate, spectral folding can cause one particular frequency (i.e. harmonic tone) to be aliased in the digital domain and simultaneously represent another frequency of interest (i.e. RF source frequency). This problem makes it difficult to distinguish the two sampled frequencies. This is further escalated in frequency tuning systems, where similarly in the analogy described for a single-frequency source, one bandwidth may coincide with another bandwidth.
   
  
• Achieving the appropriate processing gain to process the bandwidth of the RF fundamental source or sources and their respective harmonic tones. Processing gain is the rejection of out-of-band noise. This occurs when the frequency of interest occupies less bandwidth than the input signal bandwidth. The bandwidth of the processing unit must accommodate both the RF fundamental (or fundamentals) and the respective harmonics. The design challenge is to apply the appropriate filter that eliminates distortion in the RF measurement. Distortion in the measurement of the fundamental RF frequency cannot be introduced by the appearance of the harmonic tones. In addition, the measurement of the harmonics cannot be affected by the fundamental signal. Intermodulation products should also be given consideration in the filter design. Intermodulation products typically occur in plasma processes that utilize multiple RF sources. The plasma discharge can act as an RF source mixer. The resulting RF will contain the RF sources, their corresponding harmonics, plus frequencies embedded about the higher of the two frequencies. For illustration, suppose that F1 and F2 are the two primary RF sources. The frequency of F2 is greater than F1, and F1 exhibits n significant harmonic tones. Intermodulation products are then defined by F2 ± F1 ... ± nF1, which will surround the spectrum of F2.

The design for an advanced digital signal-processing (DSP) unit is depicted in Figure 3 . The RF voltage and current inputs are coupled with the voltage and current outputs of the RF sensor. These inputs are applied to low- and high-pass filters.

3. In this digital signal processing unit, the RF voltage and current inputs are coupled with the voltage and current outputs of the RF sensor.

The selection of the frequency response of these filters and associated attenuation is based on optimizing the data channel path for the fundamental RF source (or sources) and associated harmonics. The low-pass filter frequency response is the data channel typically assigned to the fundamental of the RF source. The high-pass filter frequency response is the data channel assigned to the harmonic tones.

Each filter is coupled to a high-speed analog-to-digital (A/D) converter. The converters operate as a pair by simultaneously sampling the respective output signals of the filter. The sampling rate of the A/D converters is chosen to eliminate coincidence of harmonic frequencies in the digital domain.

The advent of high-speed, high-resolution, high-bandwidth A/D converters permits the realization of the proposed scheme. These converters have sampling rates as high as 100 MHz with analog bandwidths in the range of 250 MHz. The outputs of the A/D pair are connected to a programmable device via large-scale integration (LSI). In this case, a field-programmable gate array (FPGA) is used.

The FPGA implements high-speed signal processing by reducing the sample rate of the A/D converter pair to a data rate manageable by the DSP. For applications that use the feedback from post-match RF metrology, it is critical that the DSP does not introduce significant group delay in the control loop of the plasma RF source.

The process of converting a signal from a given sample rate to a different sample rate is called sample rate conversion. Multirate conversion is the process of converting multiple sampling rates. References 4 and 5 are excellent sources of information on these digital signal processing methods.

The core of the DSP functionality is illustrated in Figure 4 , showing a typical data channel. The dashed line is the interface boundary between the FPGA and the DSP. This scheme is repeated for the number of RF sources and harmonic tones to be measured (1...n). For silicon preservation, the harmonic tones can be spatially multiplexed through a common data channel.

4. The core of the DSP functionality is illustrated, showing a typical data channel. The dashed line is the interface boundary between the FPGA and the DSP.

The front end of the data channel has a pair of digital complex multipliers that mix the complex (cosine and sine) digital output from a digital frequency synthesizer with the digitally sampled current and voltage samples. The digital current and voltage samples are the outputs from the corresponding A/D converter pair. The digital frequency synthesizer is programmed to an offset of the frequency of interest (RF source or harmonic).

The trigonometric operation of multiplying two frequencies produces a spectral output that includes both the sum and difference of the two multiplied frequencies. The difference frequency equates to the programmed frequency offset and represents the RF frequency of interest (the RF source or harmonic tone). The spectral output of the digital complex multipliers is modified by a decimation process with a cascaded integrator comb filter (CIC).⁶ Decimation converts the A/D sample rate to a data rate manageable by the DSP. The CIC filter is an efficient implementation of a narrow low-pass filter that extracts or attenuates the sum frequency and any other undesirable frequencies that may be contained in the spectrum while retaining the difference or offset frequency.

The CIC filter is followed by a complementary low-pass filter that shapes the frequency response of the CIC filter. A DSP acquires the data from the data channel via a parallel interface, converts the complex data from Cartesian to polar coordinates, and applies a scaling algorithm to convert the measured values to equivalent RF values.

This feature-rich scheme has demonstrated high signal fidelity on the order of 96 dB and a high data rate of 125 kHz. The 96 dB is a significant improvement over similar analog implementations of 60 dB. Because of the digital implementation, the signal-processing unit is resilient to thermal drift and long-term drift associated with component aging. The digital filters are exactly matched, reducing the effective compensation of the scaling algorithm. The FPGA programmability permits field upgrades to meet the ever-increasing demands of RF metrology for plasma processes.

The data channel block diagram can be exploited for autonomous frequency tracking (Fig. 5). As with the data channel block diagram shown in Figure 4, the modified channel of Figure 5 can be repeated for each RF frequency source. The similarities differentiate for the output of the CIC filter, the input to the digital frequency synthesizer, and the data rate of the CIC filter. The CIC filter in Figure 5 operates at a data rate several times faster than the CIC filter in Figure 4 .

5. The data channel block diagram can be exploited for autonomous frequency tracking.

Effectively, the block diagram in Figure 5 is analogous to a phase lock loop (PLL). The complex output of each CIC is connected to a coordinate rotation digital computer (CORDIC), which resembles a phase detector in a classical PLL implementation. The CORDIC performs the inverse tangent function to derive phase. The voltage and current phase outputs are acquired by the DSP at a fixed interrupt interval to calculate the derivative of each phase with respect to time. This derivative equates to frequency.

A three-tap median filter is used as a smoothing function. The output of the median filter is connected to the frequency discriminator. The functionality of the frequency discriminator provides the closed-loop control of the frequency tracker and the state machine data that determines if the operational mode is to track a changing frequency, search in a predefined bandwidth, or to remain locked to a steady-state frequency. This scheme is robust to amplitude and phase modulation that can perturb the frequency tracking state machine to detect erroneous frequency transients. The efficacy has been demonstrated with a plasma discharge under severe arc transient conditions. In the event that the data rate of a data channel is not sufficient for RF pulsing applications, the voltage and current data from the CIC in Figure 5 can be used for RF measurement.

Repeatable and accurate calibration is critical for RF metrology. This can be accomplished using NIST-traceable power, frequency and impedance standards. The equations that govern the relationship between the RF sensor signals and the RF parameters are included in Figure 6 . The most effective calibration method is to use the NIST-traceable standards of open, short and 50 V loads in conjunction with a calorimetric standard for power output.

6. The most effective calibration method uses the NIST-traceable standards of open, short and 50 Ω loads in conjunction with a calorimetric standard for power output. The equations that govern the relationship between the RF sensor signals and the RF parameters are included here.