Suppression of electromagnetic crosstalk by differential excitation for SAW generation

Surface acoustic waves (SAWs) hold a vast potential in various fields such as spintronics, quantum acoustics, and electron-quantum optics, but an electromagnetic wave emanating from SAW generation circuits has often been a major hurdle. Here, we investigate a differential excitation method of interdigital transducers to generate SAWs while reducing the electromagnetic wave. The results show that electromagnetic waves are suppressed by more than 90 % in all directions. This suppression overcomes the operating limits and improves the scalability of SAW systems. Our results promise to facilitate the development of SAW-based applications in a wide range of research fields.

Meanwhile, such developments of SAWs often face the persistent problem of electromagnetic wave crosstalk.High frequency components in experimental circuits to generate SAWs emit electromagnetic waves while generating SAWs.This electromagnetic wave is picked up by the metal gates of the target structure, which are used to conduct the intended experiments (e.g., the metal gates that define the quantum dots), and generates fluctuation of the electric potential in the target.This undesired fluctuation not only hides the desired effect by the SAW, but also interferes with the SAW to produce a negative effect Kataoka et al. [2006], ota [2023].Indeed, this crosstalk is pronounced and should be one of the reasons why quantum current sources using SAWs were eventually largely abandoned, despite great efforts over the years Shilton et al. [1996], Talyanskii et al. [1997], Cunningham et al. [1999Cunningham et al. [ , 2000]], Ebbecke et al. [2002], P. Utko andLindelof [2003], Ford [2017].In the field of electron-quantum optics, the crosstalk problem has been avoided by shifting the arrival timing of the electromagnetic wave and the SAW at the target structure where electrons are transported.This could be done by making the length of the SAW generation signal sufficiently shorter than the propagation time of the SAW from the generated position to the target structure.Since the electromagnetic wave propagates with the speed of light (3 × 10 8 m/s), which is 5 orders of magnitude faster than the speed of SAWs (∼3000 m/s), it disappears immediately after we stop applying the SAW generation signal and before the SAW arrives at the target structure.Although this method allows for avoiding critical influence of the crosstalk, it severely limits the timing of SAW generation and continuous generation of SAW is prohibited.This inflexibility is a clear disadvantage for various applications.For example, in electron-quantum optics, it makes it difficult to scale up the system, where many single electrons are transferred by SAWs at different timings.In this study, we investigate the way not to avoid the crosstalk but to suppress it by devising the SAW generation method.With the developed method we have succeeded in radically reducing the electromagnetic crosstalk.
SAWs are generated by using comb-shaped electrodes called an interdigital transducer (IDT) on a piezoelectric substrate.Top part of Fig. 1a shows a typical scheme to generate SAWs, where one pad of the IDT is grounded while the other is excited by an ac voltage.In this study, this scheme is called a single excitation.Here, IDTs with a double-finger pattern are employed.This type of IDT is often employed because it suppresses reflections of SAWs inside the IDT and improves conduction efficiency.When we apply an ac voltage whose frequency corresponds to the resonance frequency, f SAW , determined by the period of the IDT fingers, λ, and the SAW velocity of the substrate, V SAW , as f SAW = v SAW /λ on the IDT, SAWs generated from each finger constructively interfere and strong SAWs propagate along the substrate towards the both directions.In this process, electromagnetic waves with the same frequency, f SAW , are emitted from the metal pad where the excitation voltage is applied.In this study, we perform a differential excitation of the IDT as shown in the bottom part of Fig. 1a to suppress the radiation of the electromagnetic waves.In the differential excitation, the resonant ac voltage is applied to the both metal pads with a same amplitude but a phase shift of π between one to the other.Since the shape of the applied ac field is same for the differential excitation and the single excitation as depicted in Fig. 1a, SAWs are generated as in the case of the single excitation.Different from the single excitation, electromagnetic waves are emitted from the both pads.These electromagnetic waves have a phase difference of π and the amplitude is expected to be equal if the shapes of the metal pads are symmetrical.Since the wavelength of the electromagnetic waves, which is about 100 mm for f SAW = 3 GHz, are about 100 times longer than the scale of the IDT, which is typically less than 1 mm for the IDT with a resonant frequency in the GHz range, the two electromagnetic waves are expected to destructively interfere.As a result, the electromagnetic wave radiated from the IDT should be strongly suppressed.
A simple simulation is performed to estimate the expected cancellation effect of electromagnetic waves due to the differential excitation.In this simulation, waves of the same frequency emitted from two different center points are modeled as electromagnetic waves and their interference with each other is calculated.Each center point is assumed to be the center of the metal pads to which the resonant ac voltage is applied.In our sample design, spacing of the two metal pads are 110 µm.The waves emitted from both center points have a frequency of 1 GHz, an equal amplitude of 1, and a velocity of 3 × 10 8 m/s.The phase of the wave from center point A is set to 0 and the one from center point B is set to π.This produces waves in perfectly opposite phases.These waves are calculated on a 1 m square two-dimensional plane so that the interference pattern could be easily checked.The circular waves are calculated taking into account the phase difference that depends on the distance from the center, and the amplitude is set to a constant value independent of distance.Fig. 2 shows the respective electromagnetic waves (Wave A and Wave B) in the top panels and the interference pattern resulting from the synthesis of both waves (Combined Wave) in the lower panels.In the lower left panel, the amplitude range of Combined Wave is set from -1 to 1, and the cancellation effect of the combined electromagnetic wave can be clearly observed.In the lower right panel, the amplitude range is set from -0.01 to 0.01 in order to confirm the detailed interference pattern.From this result, the cancellation effect of the electromagnetic waves is estimated to be over 99 %.The reason why a considerable suppression is estimated after taking into account the phase shift due to the difference in emission position of the two electromagnetic waves is that the difference in emission position (110 µm) is small enough for the wavelength of the 1 GHz electromagnetic wave (300 mm).Similar results are also obtained at other frequencies commonly used for SAW generation signals (3 GHz -4 GHz).
Next, we perform measurement of the device with a semi-automatic probe station at room temperature.The device is fabricated on a GaAs substrate and consists of IDTs and metal pads connected to the IDTs.The electrodes of the IDTs are fabricated using a standard electron-beam lithography with successive thin-film evaporation (metalization Ti 3 nm, Al 27 nm).The metal pads are fabricated using a standard photolithography with successive thin-film evaporation (metalization Ti 20 nm, Au 100 nm).Two IDTs of the same design are placed facing each other in the direction of SAW propagation, at a distance of 1000 µm, as shown in Fig. 1b.One IDT acts as a SAW generator and the other as a SAW detector.The both IDTs are designed to generate and detect SAWs at a resonant frequency of 1 GHz (λ =2.86 µm) and have 40 pairs of electrodes , an aperture of 30 µm.The SAW propagation direction is set to [110] direction.Contact metal pads (330 µm length and 60 µm width) are connected to the upper-and the lower-electrode sets of each IDT.High-frequency probes make contact with these pads, thus establishing a connection to the IDTs.These pads also act as a detector of electromagnetic waves.The resonant ac voltage to excite SAWs is provided by an arbitrary waveform generator (AWG, Keysight M8195A) and fed through different coaxial cables to the upper and lower electrodes of the IDT, respectively, in the case of differential excitation.A phase shifter (WAKA 02X0442-00) is connected to one of the input lines for fine phase difference adjustment before the signal is input to the IDT.The phase shifter is adjusted and fixed so that there is minimal phase displacement at the probe when the same ac voltage is output from two channels of AWG.On the detector side, the set of lower electrodes is grounded (embedded in the surrounding ground pad).The set of upper electrodes is connected to a high-speed sampling oscilloscope (Keysight N1094B DCA-M) to observe the generated SAW and the electromagnetic wave.The detected signal is amplified by a series of broadband amplifiers (SHF S126A, ZHL-4W-422+).
SAWs and electromagnetic waves are generated and observed with the single and differential excitation.To generate SAWs, we apply a sinusoidal signal at the resonance frequency, 1 GHz, with a time span of 60 ns and a peak-to-peak amplitude of 350 mV in a repetition period of 1520 ns.Here the time span of the signal, 60 ns, is chosen to be longer than 40 ns which is the minimum length to fully excite the IDT and to be shorter than the propagation time of SAWs between the IDTs, ∼ 350 ns which is calculated from the distance between the IDTs (1000 µm) and the SAW speed in GaAs (∼ 2860 m/s).Since the electromagnetic waves emitted from the IDT propagate with the speed of light (∼ 3 × 10 8 m/s), they reach the other detector IDT almost instantaneously in less than 10 ps.Therefore, when we perform a real-time detection of the signal at the detector IDT, we first observe the electromagnetic waves and later observe the SAW signal with a well-defined separation between within the repetition period of 1520 ns.Here we apply the signal with the same amplitude for both the single and the differential excitation and hence the detected SAW signal is expected to be double for the differential excitation compared to the single.To compare the ratio between the amplitude of the SAW signal and the electromagnetic waves for both excitation methods we double the detected signal for the single excitation.
Fig. 3 shows the signal measured with the sampling oscilloscope.The blue line is the data obtained when we perform the single excitation.The signal observed in the earlier time comes from electromagnetic waves and the one observed in approximately 350 ns later comes from SAWs.For the single excitation, the signal coming from electromagnetic waves is as large as the one coming from SAWs.The red line shows the data obtained when we perform the differential excitation.The signal coming from SAWs is as large as the one from the single excitation.On the other hand, the signal coming from electromagnetic waves is strongly suppressed as expected from our simple simulation.Comparing the average values of the signal amplitude coming from electromagnetic waves from the single and the differential excitation, it is calculated that 92.4 % of the signal is suppressed for the case of the differential excitation.In our simple simulation, the electromagnetic-wave suppression of about 99 % is expected.The residual amount of the electromagnetic waves can be attributed to minute discrepancies between the two emitted electromagnetic waves due to the difference of response functions of the metal pads.These discrepancies manifested as time-dependence components that exhibited different phases and intensities and could not be addressed by simple adjustments of the phase or the amplitude of the SAW generation signal.Such fluctuations are considered to be intricately related to high-frequency circuit components like a shape or a thickness of the metal pads.It suggests that optimization of these components is essential for even better suppression of the electromagnetic waves.
Finally, we experimentally confirm the spatial dependence of the electromagnetic-wave suppression.For that purpose, we prepared the other device illustrated in the schematic in the middle of Fig. 4. On the left side, an IDT and metal pads having the same design as the device measured in Fig. 3 are placed.On the right side, multiple metal pads (220 µm in length and 60 µm in width) are arranged to pick up and detect electromagnetic waves.They are symmetrically arranged about the horizontal line passing through the middle of the IDT.The signal used to generate SAWs is the same as in Fig. 3.Each plot in Fig. 4 shows the signal coming from electromagnetic waves detected by the individual metal pads for the case of the single and the differential excitation.From these results, it is confirmed that the electromagnetic-wave suppression occurs similarly at all positions of the metal pads.
In conclusion, our study demonstrates the effectiveness of the differential excitation in mitigating electromagnetic crosstalk in SAW-based devices.The experimental results have shown that this approach is capable of nullifying over 90 % of the undesirable electromagnetic components, achieving a substantial reduction.This suppression of the electromagnetic crosstalk will certainly contribute to the improvement of the accuracy to control single flying electrons using SAW potentials Kataoka et al. [2006].Furthermore, the spatial dependence of the electromagnetic wave cancellation effect has also been investigated.Consistent reduction in electromagnetic waves has been evident at all measured positions.This consistency is important for the scalability of SAW-based devices.In addition, although our experiments have been conducted at room temperature, we anticipate that the principles of the electromagnetic-wave suppression with the differential excitation are equally applicable in low-temperature environments.The electromagneticwave suppression has been investigated with a double-finger IDT in this study.However, it will be equally applicable to various types of IDTs Morgan [2007], Lima et al.

Figure 1 :
Figure 1: (a) Schematic diagram of the excitation method.Top: single excitation, bottom: differential excitation.The SAW generation signal V (ϕ) is input into the pads connecting to the comb-like electrodes of the IDT, and the SAWs and electromagnetic waves (EM) are generated.In the case of the single excitation, the electromagnetic wave originated from V (ϕ) is emitted from the high-frequency circuit such as metal pads.In the case of the differential excitation, the two types of electromagnetic waves originated from V (ϕ) and V (ϕ + π) destructively interfere with each other and cancel out.(b) Schematic diagram of the experimental setup and the device for the differential excitation.

Figure 2 :
Figure 2: Two-dimensional simulation results of the cancellation effect due to the interference between two circular waves with opposite phases: Wave A and Wave B. The wave centers correspond to metal pads 110 µm apart on our device, where a resonant ac voltage is applied to excite SAWs.Top left: Wave A -a frequency 1 GHz, a phase 0, a velocity 3 × 10 8 m/s, from point A (0 µm,55 µm).Top right: Wave B -a frequency 1 GHz, a phase π, a velocity 3 × 10 8 m/s, from point B (0 µm,−55 µm).Lower left: Combined Wave -interference pattern resulting from the combination of Wave A and Wave B, showing the cancelation effect.Lower right: Combined Wave (Detailed View) -Detailed interference pattern with a narrowed amplitude range.

Figure 3 :
Figure 3: Time-resolved measurements on the IDT with the single excitation and the differential excitation.Trace of the detector response for the resonant ac voltage(1 GHz, a time span 60 ns, a peak-to-peak amplitude 350 mV).The blue line represents the SAW and the electromagnetic wave signals obtained from the single excitation, with the SAW on the right and the previously detected electromagnetic wave on the left.The red line represents the obtained signal from the differential excitation, where the SAW amplitude is similar to the single excitation while the electromagnetic component is significantly suppressed .
[2003],Schülein et al. [2015],Ekström et al. [2017],Dumur et al. [2019].Our research focuses on fundamentally suppressing the electromagnetic crosstalk that has long hindered advancements of SAW-based single-electron control devices.The differential excitation of IDTs provides a new perspective for addressing the problem of electromagnetic crosstalk in SAW-based systems and opens up the possibility of application of SAWs in various fields of research such as spintronics and quantum acoustics.For example, in electron-quantum optics, the methodologies and insights obtained in this study are expected to significantly improve the scalability of SAW-based single-electron manipulation devices and make important contributions to the evolution of sophisticated SAW quantum information processing devices.

Figure 4 :
Figure 4: Spatial dependence of electromagnetic-wave suppression.A schematic of the sample is shown in the middle.Surrounding plots are electromagnetic waves detected on each metal pad with the single and the differential excitation.The numbers of the metal pads in the schematic correspond to the numbers of the plots.The suppression effect is almost same for all positions.The change in the amplitude of the electromagnetic waves from the results in Fig. 3 can be attributed to the different design of the metal pads for detection.