Surface Acoustic Wave Resonator

Yadav P. Kandel

University of Rochester, Department of Physics

1. Introduction

Surface acoustic wave (SAW) is mechanical wave, like ripple on water surface, which propagates mostly through material surface. Amplitude of the wave decreases exponentially with depth of substrate. The penetration depth of SAW is just couple of wavelength. Thanks to this property, SAW can propagate relatively longer distance with very low power loss compared to other bulk modes.

Speed of SAW is order of magnitude 5 smaller than typical electromagnetic wave. For example wavelength of typical electromagnetic microwave is few centimeter while that of SAW is few micron. This means electromagnetic wave resonators and delay lines in microwave frequencies are bulky and this is where SAW based smaller devices replace them. SAW based debices are being used in MEMS for long time, such as high frequency filters, delay lines, stress sensor and resonators so on. Heart of all of these devices is interdigited transducer (IDT), as shown in figure-1, which could be used as SAW transducer to convert external voltage to SAW on piezoelectric substrate and detect back piezoelectric voltage induced by SAW. Recently, it has also shown that SAW based devices could also be useful in quantum information storage and transmission.

Figure 1: Schematic diagram of surface acoustic wave resonator (SAWR). Input voltage in left IDT produces surface acoustic waves (SAW). Array of shorted electrodes on left and right act like SAW mirror and hence forms SAW resonator. Right IDT could be then used to detect SAW in cavity.

Analogous to the reflection of optical waves because of index difference, metal electrodes or grooves on substrate could reflect SAW. An array of them act like SAW mirror. Two such arrays facing each other and separated by distance equal to integer multiple of the half SAW wavelength forms acoustic Fabry Perot resonator. Such surface acoustic wave resonator (SAWR) could be coupled to external circuits using IDTs.

GaAs is being used as prominent host material for spin qubits with long coherent time. At the same time, it is pizoeletric which is essential for coupling of SAW based devies to other circuit elements. This makes GaAs very interesting substrate for making qubit and manipulating them using SAW. In this project, SAW based megahertz and gigahertz resonators were made on gallium arsenide (GaAs) substrate with possible application in spin qubit manipulation and quantum information storage in mind. At first, a resonator with fundamental mode at megahertz frequeicies was fabricated using standard photolithography and tested as proof of concept. After that, gegahertz resonator was fabricated using e-beam lithography.


2. Sample Preparation

Sample preparation was done in two stages: design and fabrication.

I. Design:

Size and shape of device was designed to operate at 142 MHz amd 2.86 GHz using substrate and electrode material parameters. The distance between two reflector was chosen to be odd integer multiple of half the wavelength. Separation between IDT - reflector and IDT-IDT was chosen to support constructive superposition of wave. Figure-2 shows actual gigahertz SAWR pattern design:

Figure 2: Artistic rendering of gigahertz resonator. Each reflector shown in green color contain 1000 shorted electrodes of linewidth 250 nm separated by 250 nm. Each IDT shown in red color contains 51 electrodes, linewidth and electrode spacing is the same as that in reflector. Bond pads were connected to IDT to connect SAWR to circuit board.

II. Photolithography:

To test the design, a resonator working at ~142 MHz was fabricated using photolithography. Mask was designed here and sent out for fabrication. Once mask on hand, patterns were exposed using Mask Aligner , and palladium was deposited using e-beam deposition.

III. E-beam Lithography:

Standard photolithography has few micron resolution. For gigahertz resonator the device features were of sub micron resolution, it was impossible to make this device using photolithography method. Thanks to e-beam lithography which allows generating patterns with nanometer resolution. The standard steps in ebeam lithography are: device design in appropriate format, resist coating, e-beam exposure, development, deposition, and lift-off. As always, dose test was done at first to figure out suitable resist (PMMA) thickness, exposure dose, depositon and liftoff. Once best recipe was figured out, full device was made. The substrate for this device was GaAs and the electrodes were made up of silver.

After successfully creating sample using e-beam lithography, it was imaged to figure out how well the pattern developed. As the sample was very small and made of of metal on top of semiconductor, no additional steps like coating or drying were necessary. The images obtained from different microscopic methods are presented in next section.

3. Result of Microscopy and Discussion

Different microscopic methods yield information about different aspects of the sample. In this project three distinct modes of microscopic methods were used to probe the sample. Which are: (i) Optical microscopy, (ii) Electron microscopy ,and (iii) atomic force microscopy (AFM). In section A, the optical image and two port measurement of megahertz resonator are presented. The gegahertz resonator is very challenging to make, for its smaller feature size. Detail analysis of device patter was carried out using different imaging techniques and the results are presented in section B.

A. Megahertz Resonator:

Image of megahertz resonator recorded using light microscope is shown in figure-3. The substrate is GaAs and the electrodes are made up of palladium.

   
     

Figure 3: Megahertz SAWR and two port measurement plots.

The electrodes look smooth and edges are straight. In second row of figure-3, two port measurement parameters: absolute value of reflection coefficient (|S11|) and transmission coefficient (|S12|) are plotted as function of frequency. It is clearly seen that |S11| has sharp dip at expected frequency 142 MHz and |S12| has peak at corresponding frequency. This is the signature of resonance. The cavity actually supports two modes separated by ~200 kHz.

B. Gigahertz Resonator:

The gegahertz resonator obtained using e-beam lithography was interogated using different imaging techniques and the resulting images are presented in this section.

I. Optical Microscopy:

Optical microscopy probes sample in the way our eyes see objects but with higher resolution and magnification. Optical images are good source of information about a overall structural properties. Figure-4 shows the images of the device recorded using optical microscope.

Figure 4: Optical imge of device taken at different magnification. It shows that intended device was successfully patterned using e-beam lithography. Image on the left was taken at 20x. Image on the right, taken at 100x, shows section boxed on left images. Individual electrodes of width 250 nm could be seen clearly. Silver deposition, as expected, does not look smooth.

As seen from optical image, overall result of e-beam lithography was pretty good. It is apparent from the figure-3 that electrodes for megahertz resonator are more smooth. Rough electrode surface is due to silver deposition and the smoothness of the structures could be improved in future by using aluminium or palladium instead of silver.

II. Electron Microscopy:

In electron microscopy, instead of visible spectrum of light, electrons of different origin are used as signal. Electron microscopy could be done in many different modes, but two ubiquitous modes are: scanning electron microscopy and transmission electron microscopy. In principle, transmission mode could give micrograph of higher resolution than scanning but sample for former has to be just about 100 nm thick. As the chip was much thicker and main concern was with topography of the electrodes on chip, it was imaged using scanning electron microscope.

In scanning electron microscope (SEM) high energy and highly focused beam of electron is shot on the sample. Electrons on beam interact with sample in different way and produce different singnals. The effective region over which electrons from beam interact in sample is called the interaction volume. Electron on outer shell of elements in sample are released in inelastic collision with beam electron. Those relatively low energy electrones are termed secondary electrons (SE). They carry precious information about topography of the sample. Many of the beam electron get elastically scattered back, which are called back scattered electron (BSE). Since scattering process depends on scattering cross-section of nucleus, BSE carry information about elemental composition of the sample. The SEM micrograph of the sample recorded using SE and BSE are presented below:

     
     

Figure 5: SEM images of sample recorded using secondary electrons at different magnification. Image on top left shows whole device, top right image shows part of IDT, image on the bottom left shows section of electrodes on left reflector and the image on right side of second row shows section of electrode on IDT in red box on top right image. The firt three images where take using SE2 detector while fourth was taken using In-Lens detector. Under suitable working condition, In-Lens detector gives better topological information and resolution because it is mounted on the column, i.e. it is normal to the sample and hence could gather more sample compared to other secondary electron detector mounted on side.

As seen from the secondary images, the electrodes look nicely developed. In general silver deposites in bigger chunks compared to other elements like aluminum. This is the reason for ruggedness on the edge of the electrodes. In future, aluminum will be deposited which should eliminate the problem. If looked carefully thin layer chromium, used to stick silver on substrate, could be seen on the bottom of the silver electrode. The chromium layer looks nice and uniform. This also confirms that the ruggedness on the electrode edge is not dose related problem but has to do with nature of silver depositon.

     

Figure 6: SEM micrograph of far end section of right reflector. Left image was recorded using SE electrons and the right image was recorded using the BSE electrons. TV frame integration of 16 frame was used to reduce noise and beam shift artifacts.

In figure-6 SE and BSD image of same section of right reflector are shown. Resolution on the SE image is compromised because of large working distance condition imposed by insersion of BSE detector. The SE micrograph shows topographical features. But the BSE micrograph almost look flat. They are better suited to probe information about elemental composition of the sample. The atomic number of the substrate elements (GaAs) and the electrode material (Ag) arenot much different. So the BSE contrast is moderate. Still, it could be concluded from the right image that BSE give information about elemental composition. The electrodes look more zig-zag than those on figure-5. Images on the figure-5 corrospond to center of the wright field of e-beam lithography. So the beam was properly focused. Images on figure-6 are from the far end of reflectors, that means from the wright field far from center. In e-beam lithography, stage or the sample is fixed while beam is rastered over the wright field by deflecting it. The focus changes as the beam is diflected from center of wright field. The beam shift on off-center writing is responsible for more rugged lines.

Althought, electron microscopes give subnanometer resolution on lateral directions, which means individaul atoms could be imaged under suitable conditions, resolution along z-axis is not so high. There are methods to get around this issue and do some kind of hight measurement. It is not always an easy job and depending on sample imposible also. There comes the atomic force microscopy with subnanometer resolution of height. Together with subnanometer resolution of electron microscopy along lateral direction and subnanometer resolution on height measurement on atomic force microscopy, almost all structural information of sample could be acquired.

III. Atomic Force Microscopy:

Scaning probe microscope gathers information either by semi physical contact to the sample (electrostatic force sensing or commonly known as atomic force microscope AFM) or by scanning the tunneling current profile. Sample under investigation was interogated using atomic force microscope (AFM). AFM has fine tip hanging on small cantilever. The tip taps on the surface and hight profile is determined based on the damping on vibration of cantilever-tip system. The AFM micrographs of gigahertz resonator are shown in figure-7.

Figure 7: AFM micrograph of gigahertz resonator. Left image on first row shows height profile of electrodes on far end of the reflector. Top right image and bottom left images show 2D and 3D images of IDT electrodes while height profile of same region is shown in bottom right image.

Electrodes on different part of the device look like differently dosed. Also the height profile is very nonuniform.Some region of electrodes look taller than other. Actual height deposited according to PVD was ~55 nm, but from height profile some section look as tall as ~80 nm.

4. Colorization:

False color image of section of IDT recorded using In-Lens detector, shown in figure-5, presented below:

Figure 8:False color image of IDT.

Three different regions are shown in image. The green backround, light green region highlighting chromium layer of about 5 nm used to stick silver on substrate and red silver electrodes.

5. Conclusions

Megahertz resonator testing revealed that the concept of device is valid and the design works. Fabrication and imaging of gegahertz resonator helped to figure out right recipe to fabricate such device. Further, it is very interesting on its own to be able to pattern thousands of 250 nm features together using e-beam lithography. Working gigahertz resonator will be fabricated in near future using improved recipe and aluminium as electrode material.

Acknowledgments

I would like to acknowledge Prof. John Nichol for providing all logistics and work space at Quantum Nanostructures for this project. I sincerely thank Brian McIntyre for help from begning to the end of this project. Last but not the least, thank you Elliot Conners and Haifeng Qiao at Quantum Nanostructures , lab partner Tinghong Zhou, James Mitchell at URnano clean room, and and TA Hatice Kokbudak (Nursah).

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References

1. Datta, Supriyo. Surface Acoustic Wave Devices. Englewood Cliffs, N.J: Prentice-Hall, 1986.

2. R. Manenti et al., “Circuit quantum acoustodynamics with surface acoustic waves,” Nat. Commun., vol. 8, no -1, pp. 1–5, 2017.

3. T. Aref et al., “Quantum Acoustics with Surface Acoustic Waves,” Springer, pp. 217–244, 2016.

4. Y. Chu, P. Kharel, W. H. Renninger, L. D. Burkhart, L. Frunzio, P. T. Rakich, and R. J. Schoelkopf, “Quantum acoustics with superconducting qubits,” Science, 1511:1–10, 2017.