Physicists from the Technological Institute for Superhard and Novel Carbon Materials, the Moscow Institute of Physics and Technology, and the Siberian Federal University have mathematically modelled diamond-based microstructures for producing compact high sensitivity sensors.

The researchers' study investigates the problem of selecting a useful acoustic signal taking into account the excitation of Lamb waves in promising microwave microresonators with substrates of synthetic diamonds. The scientists proposed a mathematical model and experimentally studied acoustic waves in the piezoelectric layered structure, described their dispersion and proposed a number of ways of decreasing the effects of spurious peaks.

In the future, diamond crystal based structures may be able to be used as high sensitivity sensors to detect pressure, acceleration, temperature, the thickness of ultrathin films etc. The paper has been published in Applied Physics Letters.

"I think that the results we have obtained from a piezoelectric layered structure based on synthetic diamonds are ahead of world-class research in this field. Our microresonators were used to obtain resonances at record high microwave frequencies in a range of up to 20 GHz, with the quality factor remaining at several thousand. The behaviour of diamond as a substrate for the acoustic microresonator was very significant and I hope that using diamonds in acoustics and electronics will lead to more exciting discoveries," said the corresponding author of the study, Boris Sorokin, in an interview with MIPT's Communications Office.

The quality factor is a feature of an oscillating system. It describes how quickly oscillations die down in a system; the higher the quality factor, the smaller the energy loss.

A piezoelectric layered structure is a "sandwich" of various different materials with a piezoelectric effect. This term means that under compression or tension an electric field occurs around the material - and when an electrical voltage is applied, the material itself changes shape. Non-scientists will have seen the piezoelectric effect in lighters (pressing the button compresses the piezoelectric, which provides enough voltage for a spark).

However, aside from lighters, the effect is used in microphones, precise micromanipulators, and many kinds of sensors for pressure, humidity, temperature etc. Another very important application of piezoelectrics is in highly stable piezoelectric resonators, which enable quartz clocks to display time accurately, for example, or computers to run programs smoothly.

The effect of an electric field on a piezoelectric, in this case a thin film of aluminium nitride AlN, leads to deformation and causes elastic waves which pass to the substrate in the same way that an elastic wave falling on the piezoelectric film causes an electric field. When it reaches the edge of the substrate, the wave is reflected and within the layers of several materials a number of oscillations occur at the same time - this effect resembles an echo that can be heard when you shout in a tunnel or into a wide tube.

Diamonds and waves
Diamond substrates were not chosen by chance. Piezocrystals are ideal for such devices, as they have a combination of properties such as low acoustic absorption, a high electromechanical coupling coefficient, and a high speed of sound. Diamonds satisfy all these requirements except for one - there is no piezoelectric effect.

This is why the devices needed the aluminium nitride film. Engineers are, of course, slightly apprehensive regarding the price, but synthetic diamonds are now becoming more affordable. The properties of synthetic diamonds are superior to those observed in natural diamonds, particularly in terms of their impurity profile and reproducibility, however large natural gem-quality diamonds are much more expensive. The authors of the study believe that synthetic single crystal diamonds are most promising for developing new acoustoelectric devices.

Voluminous waves excited in the layered structure are able to resonate, creating both the basic type (mode) of oscillations, and also generating additional modes. In the substrate and piezoelectric film, in addition to the useful longitudinal-type oscillations, Lamb waves also occur under certain conditions. The spectrum of these waves is in separate branches with the phase velocity dependent on the frequency.

Lamb waves are a complex combination of elastic oscillations occurring in thin layers of elastic media and were first described by the British physicist Horace Lamb. Interestingly, the particles in these waves follow an elliptical path. There are symmetric and antisymmetric (bending) Lamb waves. Phase velocity is the velocity at which a point moves from a predetermined phase - e.g. the crest of a wave; the phase velocity of waves in a particular medium often depends on their frequency and this effect is called dispersion.

In this case it is geometric dispersion of waves in two-dimensional acoustic waveguides. On the one hand, excitation of Lamb waves is not useful in terms of the quality factor of the acoustic resonator in the main (longitudinal) mode, however these types of waves themselves may be of special interest.

Using mathematical modelling, researchers studied in detail the spectrum of various acoustic modes occurring within the diamond structure, using a visualization of the areas of acoustic displacement. They paid particular attention to resonances that occur as a result of there being a whole spectrum of natural oscillation frequencies in the layered "sandwich". In the simplest case, this frequency corresponds to the frequency at which an elastic system would oscillate in the absence of external influences. If, for example, you touch and release an ordinary pendulum, it will swing with a natural frequency and applying force with this frequency is most effective for its swing. Resonance is when the natural frequency and the excitation frequency coincide - the oscillation amplitude increases sharply.

Natural frequencies depend on the properties of the materials, as well as the geometry of the structure. This means that detectors can be made that are able to detect even individual bacteria that have become attached to their surface - the bacteria slightly increase the mass of the entire system and shift the resonant frequency.

One of the main results was that the researchers succeeded in selecting and identifying different types of waves and forming dispersion laws for them. The results obtained will be useful in the development of microwave acoustoelectronic devices.

Acoustoelectronics is a science combining solid-state physics, semiconductors, and radioelectronics that studies the principles of building devices to detect, convert, and process signals. Acoustic resonators are widely used in science and technology as sensing elements in various physical and chemical sensors and in medical devices. Cavity resonators are popular because of their miniature size and high quality factor, while resonating at high and ultra-high frequencies. The higher the operating frequencies, the smaller the cross-sectional dimensions of resonators are required (~100 microns for a frequency of ~10 GHz).

The acoustic properties of these sensitive elements are developed and studied at MIPT's Department of Physics and Chemistry of Nanostructures, which is based at the Technological Institute for Superhard and Novel Carbon Materials. It was at this institute where scientists from a number of Russian organisations worked together to develop a method of creating a material harder than diamond; it was also the place where the secret of the abnormal stiffness of polycrystalline diamonds was uncovered - it was found that they are more rigid than single crystals.