L Hamidouche

Non-Member S Hol'

E G' Eron

An Overview on the Sensitivity of Electro-Acoustic-Reflectometry (EAR) Method

Keywords: Space charge, spatial resolution, microwave system, reflection coefficient, sensitivity

Non-

INTRODUCTION

High Voltage Direct Current (HVDC) technology allows to reduce power losses when transporting electrical energy over a long distance. Another advantage is that there are no synchronization problems from one country power grid to another, which usually occur with the alternative power regime. Before this power is used in households and factories, HVDC must first be converted down to usable levels and to an alternating regime using DC/AC converters. The electronic devices including insulating films within these converters are subjected to high levels of applied voltage in such operating conditions. Charge injection from electrodes into the insulating films is very likely in this situation. The injected charges migrate through the material and get trapped in sites in the bulk of the film. The accumulation of space charge over time gives rise to an internal electric field which leads mainly to the acceleration of the film aging and eventually to dielectric breakdown (1) and hence damaging the electronic device and leading to failure of the whole electric system.

The study of space charge buildup in the bulk of the dielectric film may help preventing such a scenario. Although several methods have been developed to study space charge in dielectric materials (2) , still there is a need for developing new methods (3) (4) (5) . Actually, the nondestructive methods namely, the thermal method (6) , the pressure wave propagation (PWP) method (7) and the pulsed electro-acoustic (PEA) method (8) are unable to provide a spatial resolution (9) (10) in the submicrometer range which is necessary to the study of space charge in thin films. In this context, the Electro-Acoustic Reflectometry (EAR) method has been proposed (11) .

EAR Method

The difficulty to enhance the spatial resolution of the elastic methods (PWP and PEA) stems from the insufficient bandwidth of the excitation and measurement systems used by these methods. This is a limitation imposed mainly by the available technology. In IEEJ Trans. XX, Vol.138, No.1, 2018 fact to achieve, for example a 100 nm spatial resolution in a polymer material (with speed of sound around 2000 m/s), the excitation duration must be 50 ps. This order of magnitude implies a bandwidth as large as 10 GHz. To overcome this problem, both excitation and measurement are made in frequency domain with the EAR method. In fact, working in frequency domain allows to reach a broad bandwidth by carrying out measurements on successive narrow frequency ranges.

The main idea with the EAR method is to generate an equivalent time domain pulse with a sufficient narrow width using frequency sweeping (12) . This allows to have control over the excitation bandwidth. For the sake of clarity, we can draw a parallel between the excitation used in the PEA method and the one used in the EAR method. In the case of PEA method, a given number N of short duration voltage pulses are generated at a given rate f p , all these pulses producing as many signals which are averaged for improving signal-to-noise ratio. That series of pulses is shown in time and frequency domains in Fig. 1a. However pulses are not perfect and have a given amplitude A and a given duration at mid amplitude δt. This leads to a bandwidth limitation of the order of 1/δt as illustrated in time and frequency domains in Fig. 1b. If a series of pulses (left side of the figure) implies a given spectrum (right side of the figure), the reciprocal is also true. Therefore the generation of that equivalent pulse series in time domain from frequency domain requires to generate a series of frequencies with 2f p /N bandwidth and evenly distributed each f p up to 1/δt. In the case of the EAR method, all these frequencies are generated one by one by applying to the sample a sine waveform during N/f p (see Fig. 1c). With the involved frequency range, a microwave approach should be used for the excitation and measurement. In fact due to the propagating nature of electrical quantities such as voltage and current the usual low frequency approach common with conventional methods no longer holds. In microwave theory, the sample under test is considered as a black box fully characterized by its measured scattering parameters matrix.

If a purely dielectric material is considered, the excitation is an electric wave incident on the sample. Part of the energy given to the sample by this electric excitation wave is transformed into elastic energy through electro-elastic coupling if any charge is present within the sample (12) as in the case of PEA method. The reflected wave is measured and since part of the incident energy is used at least by the electro-elastic coupling, the reflected wave has an amplitude smaller than that of the incident wave. Therefore, the reflected signal contains features corresponding to the amount of the generated elastic energy which in turn gives information about space charge. As illustrated in Fig. 2, in microwave theory the electrical quantities are considered as electric waves because the wavelength is small compared to circuit dimensions. When line and load impedances are different ( Z L = Z 0 ), part of the incident energy is reflected which creates a standing wave in the line. Measuring the reflection allows to determine the electrical impedance Z L . The sample of interest can be considered as a load impedance hence reflection measurement is performed in a similar way.

Measurement instrumentation

A microwave measurement system dedicated to the EAR method could be designed and implemented. However, the EAR method is still in the early stage of development and validation so a vector network analyzer (VNA) is used instead since it can provide the functionality required by this method. Figure 3 shows the block diagram of a two-port VNA. An internal source generates the excitation signal for the selected frequency range. A number of attenuators allows to adjust the power level. A microprocessor controlled switch selects the port to be used. For each port a splitter divides the power into two signals, one serves as a reference signal (R 1 , R 2 ) and the second part is used for excitation of the device under test (DUT). A coupler allows to separate the reflected signal from the DUT which undergoes a frequency analysis in the detection block before it is displayed. The circuit responsible for frequency analysis is shown on the right side. It is a mixer with the reference signal as a local oscillator and the reflected signal as the RF signal. The output of the mixer passes through a band-pass filter called IF filter. Reducing the bandwidth of the IF filter (making it more selective) results in a reduced noise level in the measured signal, in other words, it increases the equivalent averaging number commonly known with the PEA method. The IF filter selects the frequency accuracy, which corresponds to 2f p /N in Fig. 1. For the EAR method, only one port is needed.

Figure 4 shows the measurement setup that was used to test the EAR method. A PVDF material is chosen because it provides an electric impedance well matched with 50 Ω internal impedance imposed by the network analyzer and thanks to its permanent polarization, no DC polarization is necessary.

Signal reconstruction

The measured reflected signal S 11 for a 9 µm thick sample with approximately 1 mm in diameter with an excitation of -10 dBm is shown in amplitude in Fig. 5a as delivered by the network analyzer. Two kinds of behavior can be seen in this measured signal, the overall behavior having a slow variation with frequency and corresponding to the dielectric response of the PVDF sample, the second one is the notches that one can see around frequencies 130 MHz, 390 MHz, 650 MHz and 910 MHz. These correspond to the elastic resonances produced by the excitation through electro-elastic coupling. It follows that this is the signal holding information about the charges in the PVDF sample. The lower frequency is the fundamental resonance which occurs at the velocity of sound divided by twice the sample thickness when the interfaces of the sample are free. The higher frequencies are the odd harmonics of the fundamental frequency, even harmonics being canceled by the symmetry of the sample. The elastic signal is extracted from the measured one by polynomial fitting. Indeed, the dielectric response of the sample varies very slowly with frequency compared to elastic resonances. Hence a polynomial is easily adjusted on S 11 background, both in amplitude and phase, and then subtracted. Figure 5b shows the magnitude of this operation which contains only the elastic response of the sample since this part of the reflection coefficient corresponds directly to the amplitude of the generated elastic waves within the sample. The time domain signal is computed using this elastic spectrum by a simple inverse Fourier transform. Since the excitation corresponds to an equivalent pulse in time domain, the elastic response to that excitation corresponds to the space charge distribution in time domain as in the case of a PEA measurement. More details can be found in (11) (12) . The obtained time domain signal is shown in Fig. 6. One can see that the permanent dipole in the PVDF sample is well detected. The two peaks correspond to the electrodes on the side faces of the sample. The time distance between the observed peaks is the time that is necessary for the sound waves to travel from one side of the sample to the other. Its value along with the sample thickness give a speed of sound in PVDF around 2400 m/s which is in good agreement with usual values.

The value of the spatial resolution in the obtained time domain signal is computed using the rise time ∆t = 0.54 ns and the speed of sound in PVDF (2400 m/s). It is found to be around 1.2 µm as already reported in (11) (12) (13) . The signal-to-noise ratio (SNR) which is a figure of merit for any measurement (9) can be computed using SN R = A/2B where the quantities A and B are the amplitudes of the useful signal and noise respectively as shown in Fig. 6. The SNR for this signal is better than 20.

Sensitivity investigation

The signal-to-noise ratio of the resulting time domain signal depends on the excitation level as well as on the IF filter bandwidth of the measurement instrument as explained above. To experimentally investigate the sensitivity (lowest level of excitation power below which no signal could be detected) of the EAR method, the excitation and measurement are conducted for different levels of excitation power starting from the highest one then it is gradually decreased by 10 dB until the signal of interest is completely sunk in noise. To give a clear idea about the meaning of employed excitation power levels, examples of the equivalent voltage excitation are given in Table 1. As discussed earlier, the bandwidth of the IF filter is adjusted to increase the equivalent averaging number, thus enhancing the detection when working with a low power excitation. In Fig. 7 One can see that even with a low level of excitation power, narrowing the IF filter bandwidth results in a better detection of the elastic response. The enhancement between 10 Hz and 30 Hz is not very noticeable though. The computed time signals with these two measurements are shown in Fig. 8a and Fig. 8b.

One can see that the same spatial resolution is obtained. The computed SNRs are 4 and 6, respectively. As explained earlier, narrowing the IF filter bandwidth is equivalent to increasing the number of measurements averaged when using a time domain method such as PEA. The equivalent number of time domain measurements for the three values of the IF filter bandwidth are summarized in Table 2. It is worth noting that taking these numbers of measurements in time domain would have taken huge amounts of time whereas in frequency domain, the time it takes to make a sweep and an acquisition is in the range of few minutes.

It is still possible to further improve the SNR of the obtained signal without affecting the obtained spatial resolution by application of a numerical filter. The cutoff frequency must be chosen as not to be detrimental to the spatial resolution, i.e. without increasing the signal rise time. Since only elastic resonances below 1 GHz are detected in the measured signal and this is the useful signal, the frequency content above 1 GHz only adds noise to the final resulting time domain signal. Hence the application of a Gaussian filter as the one shown in Fig. 9 with a cutoff frequency at 1 GHz to the measured signal allows to reduce noise in the computed time domain signal. Choosing a lower cutoff frequency would have increased the rise time and thus it would have reduced spatial resolution, and choosing a higher cutoff The SNR in these resulting two signals is 13 and 55, respectively. This means that with EAR method approach it is possible to have a good SNR in the computed signal even with an excitation power as low as -50 dBm.

By applying a correction method similar to the first order method described in (14) but in a simpler manner we consider the relaxation function

h(t) = δ(t) + u(t) • • • • • • • • • • • • • • • • • • • • • • • • • • • (1)
where δ(t) is the impulse function and u(t) is the unit step function.

If the measured time signal is s m (t) then where s(t) is the generated signal that is due to an ideal impulse excitation and B the noise that adds to the measurement. Hence to obtain s(t), one has to perform deconvolution on s m (t) using h -1 (t). The obtained signal s p (t) is s p (t) = h -1 (t) * s m (t) = s(t) + h -1 (t) * B • • • (3)

s m (t) = h(t) * s(t) + B • • • • • • • • • • • • • • • • • • • • • • (2)
In our case, it is given by

h -1 (t) = ∂ ∂t (u(t) × exp(-t/τ )) • • • • • • • • • • • • • • (4)
with τ = 5.6 ns. The resulting signal is shown in Fig. 11. This is obtained when this method is applied to the signal shown in Fig. 10(b). It can be seen that both peaks are clearly detected.

Conclusion

The proof-of-concept of the recently proposed EAR method has shown a potential improvement of the spatial resolution of space charge measurement. Sensitivity of the EAR method was given attention in this article. It is shown that the high sensitivity of the EAR method stems from its frequency domain nature which allows to enhance the SNR without a cost on measurement time. Setting the bandwidth of the VNA to 10 Hz allows to reach an SNR of 55 with an excitation of -50 dBm which is equivalent to 1 mV in terms of peak voltage.

Fig. 1 .

 1 Fig. 1. Time domain equivalent for excitation with EAR method. (a) Theoretical excitation for N pulses in time (left) and frequency (right) domains. Frequencies are not precisely defined due to the finite number of pulses. (b) Real excitation for N pulses in time (left) and frequency (right) domains, a limited overall bandwidth appears. (c) Generation of an excitation frequency (right) from a sine of finite duration (left).

Fig. 2 .

 2 Fig. 2. Implementation of EAR method using a microwave system with line impedance Z0. (a) Classical measurement of reflection from a load impedance ZL. (b) Measurement of reflection from a dielectric sample put between two electrodes.

Fig. 3 .

 3 Fig. 3. Schematic showing the function of a twoport network analyzer with a DUT connected between its ports.

Fig. 4 .

 4 Fig. 4. Measurement setup used to test the EAR method. The sample is enclosed in a sample holder.

Fig. 5 .

 5 Fig. 5. (a) Amplitude of the measured reflection coefficient S11 (in dB scale) for a 9-µm-thick PVDF sample. The elastic response of the sample (encircled) is superimposed to the dielectric background response. (b) Amplitude of S11 (in linear scale) once the background subtracted.

  IEEJ Trans. XX, Vol.138, No.1, 2018

Fig. 6 .

 6 Fig. 6. Time domain signal obtained by inverse Fourier transform of the extracted elastic response of Fig.5b.

  only the measured signals with -50 dBm are shown since this is the lowest level for a proper detection. With an excitation power of -50 dBm and IF filter bandwidth of 3 kHz, no feature corresponding to the elastic response could be detected in the measured reflected signal S 11 shown in Fig.7a. The measured signals with the same level of excitation power and with an IF filter bandwidth of 30 Hz and 10 Hz are shown in Fig.7b and Fig.7c, respectively.

Fig. 7 .

 7 Fig. 7. Measured reflected signal S11 with -50 dBm excitation power level. (a) With an IF filter bandwidth of 3 kHz. (b) With an IF filter bandwidth of 30 Hz. (c) With an IF filter bandwidth of 10 Hz.

Fig. 8 .

 8 Fig. 8. Computed time domain signal with an excitation power level at -50 dBm. (a) With an IF filter bandwidth of 30 Hz. (b) With an IF filter bandwidth of 10 Hz.

Fig. 9 .

 9 Fig. 9. Applied Gauss filter with cutoff frequency at 1GHz.

Fig. 10 .

 10 Fig. 10. Computed time domain signal after application of a Gaussian filter. (a) With an IF filter bandwidth of 30 Hz. (b) With an IF filter bandwidth of 10 Hz.

Fig. 11 .

 11 Fig. 11. Computed time domain signal after application of a Gaussian filter and after correction using a first order method.

Table 1 .

 1 Examples of power levels and corresponding excitation peak voltage.

IEEJ Trans. XX, Vol.138, No.1, 2018

IEEJ Trans. XX, Vol.138, No.1, 2018