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October 24, 2020

Demonstration of a novel scheme to generate chaotic signals using a MEMS oscillator

- Basic device elements for signal processing technology such as machine learning -

NTT Basic Research Laboratories (NTT-BRL) and Tokyo Institute of Technology (Tokyo Tech) have demonstrated for the first time a simple and generic method to generate chaotic*1 signals using a microelectromechanical oscillator*2.
Recently, there has been wide interest in applying chaotic signals in the field of information technologies, such as machine learning and secure communications. With such applications, the efficient generation of chaotic signals using on-chip devices takes on an added importance. MEMS (microelectromechanical systems) oscillators are one of the promising candidates that could meet such requirements, as they have advantages of high integration capability and precise electrical control. We succeeded in generating chaotic signals using the libration*3 motion of a MEMS oscillator with one-order of magnitude lower voltage than previously reported in the scientific literature. This new method also enables the integration of chaos generators with standard MEMS devices, such as ultra-small microphones and sensors. The method allows machine learning*4 of the output data from these devices directly on a common semiconductor chip.

The results obtained represent the outcome of a successful collaboration between NTT-BRL and Tokyo Tech. NTT-BRL performed the device fabrication and measurements. Whereas Tokyo Tech. undertook the data analysis, performed based on the theoretical calculations. The results appeared in Physical Review Letters on October 23rd, 2020.

=> Nanomechanics Research Group

Background and summary of results

Chaos is a commonly observed phenomenon in various physical environments. From appearance, chaotic signals look random, but this apparent randomness is in fact underpinned by deterministic and simple laws of physics. There are recently various studies performed to use the complex behavior of chaos in information technologies, such as the machine learning, secure communications, and random number generation.
MEMS is a sort of fine structure devices that functionalize the physical “motion” of the composing elements. MEMS is used in many practical systems such as high-performance sensors, high frequency filters, and digital mirror devices. Producing chaotic signals using a MEMS oscillator was first proposed some years ago as a promising technology for processing the output data from MEMS sensors but have so far been only partial success. This is because chaos generation using standard MEMS technologies requires a large area of electrodes as well as high-applied voltages up to several tens of volts. We here propose a new scheme to untangle the problem by utilizing “libration” of MEMS oscillator. This scheme generates chaotic signal simply by applying two different frequencies of electric signals. The efficiency is so high that we do not need either high voltage or large electrode structures so that highly integrated devices with low operation voltage can be fabricated.


The device used in this demonstration consists of a suspended mechanical oscillator called a doubly clamped beam*5 (Fig. 1). The structure was fabricated by processing piezoelectric semiconductor, where applying an alternating voltage induces mechanical vibration. We confirmed that as a two-frequency excitation voltage is applied, a periodic libration oscillation is first generated, this later changes to an aperiodic oscillation when the motion becomes large (Fig. 2). Theoretical analysis proved that the observed signal has the features expected for chaos. The voltage required to generate chaos was only a few volts, which is one order of magnitude smaller than previous methods.

Key technologies

  1. It is well known that the nonlinearity*6 in beam motion plays an essential role to generate chaotic signal. The doubly clamped beam structure induces enough amount of nonlinearity for chaos generation because the tension increases the resonance frequency when the vibration becomes large. It was also important to use a piezoelectric*7 single-crystalline semiconductor heterostructure*8, which induces large amplitude of stable vibration when applying a few volts of actuation voltage.
  2. Moon and earth have a very slow oscillatory motion with a period from several years to tens of thousands of years in the neighborhood of its normal revolution orbit. The slow and small motion is called “libration”, which is caused by several origins, such like ebb and flow of the tide and/or the force from other planets. Similar motion is observed in nonlinear mechanical oscillators and can be enhanced by applying a two-frequency oscillating force. The libration amplitude is increased when the difference of two frequencies is close to the libration period so that by adjusting the two frequencies libration amplitude can be controlled. When the libration amplitude becomes large, the nonlinearity in the beam structure generates chaotic motion.


The frequency of mechanical vibration in this study is several megahertz, which is not high enough to utilize the present devices for practical applications. We aim to generate chaotic signals at higher frequencies. After the development of the high-frequency devices, we direct the study to move toward practical applications such as reservoir computation and secure communication.


*1 ... Chaos
Common physical phenomena observed in many systems, such as the growth of populations of living species, turbulence of water, electric circuits, and laser light. It is a complex behavior that seems to be random at first glance but it has a reproducibility that it shows the same behavior under the same initial conditions. This is not the case for noise, which shows completely random behavior. Chaos has features such as "aperiodicity" that does not repeat the same motion. It also shows "butterfly effect" that causes a big change by a slight difference in initial conditions. Nowadays, several applications, such as reservoir computation, pseudo-random number generation, and secure communication, are being considered as applications to chaos.
*2 ... Mechanical oscillator
An artificial structure in which mechanical vibration continues by periodically repeating elastic deformation. The musical instruments, such as bells and metallophones, is also a type of mechanical oscillator. Recently, it has become possible to integrate mechanical oscillators smaller than a human hair’s diameter on semiconductor chips, and they are being used to practical devices as MEMS (Microelectromechanical Systems) oscillators. One of the most typical shapes of mechanical oscillators is the doubly clamped beam, which is used in this research and has a shape similar to a bridge or a vibrating plate of metallophone.
*3 ... Libration
Astronomical objects such as the moon and the earth perform a fixed periodic motion such as rotation and revolution, but they also perform another slow periodic motion in the neighborhood of these major motion. Such movements are called "libration" and are much smaller than rotations and revolutions, and have a large cycle of several years to tens of thousands of years. It is caused by various factors, such as the ebb and flow of the tide and the attraction of other planets. A mechanical oscillator performs regular vibrational motion at a fixed frequency. However, the introduction of nonlinearity into the oscillator implies that it has no properly defined resonance frequency and would thus slowly change its frequency as its amplitude changes. Libration, in this context, is a slow periodic oscillation on top of the main oscillation. It is caused by the detuning between a drive and a nonlinear system and its amplitude is usually very small. When a weak periodic external force corresponding to the frequency of the libration is applied in addition to a main drive, the resonance causes a large libration amplitude. In this research, we succeeded in generating a chaos signal by electrically applying two frequencies whose difference is resonant with the libration period.
*4 ... Machine learning and reservoir computation
Machine learning is one of the technologies that make up artificial intelligence. It is a technology that enables various predictions of results by finding common patterns and rules from large number of past data. In reservoir computation, machines are trained only through the linear weighting of the output from a fixed non-linear network, in contrast to deep learning that trains the non-linear network itself. Reservoir computation provides simple methods and have recently attracted attention to use physical nonlinear network. It has been pointed out that the error rate can be improved by using the chaotic signal in the reservoir computation.
*5 ... A doubly clamped beam
One of the typical structures of mechanical oscillators manufactured by microfabrication technology. It consists of a bar structure with both sides fixed, and elastic vertical movement like that of a key of a metallophone. Since both sides are fixed, vibration increases the overall length and creates tension. This tension raises the resonance frequency and causes nonlinearity.
*6 ... Nonlinearity
Mechanical oscillators utilize the elastic deformation of structures. If the force exerted on the structure is small, it is proportional to the magnitude of its deformation, following so called Hooke's law. Such an oscillator is referred to as a linear oscillator. Depending on the structure, the force can have a component proportional to the square or cube of the deformation. Such an oscillator is called a non-linear oscillator. In the doubly clamped beam structure used in this result, tension is generated along the beam when the vibration amplitude becomes large because both sides of the beam are fixed. This tension creates a restoring force proportional to the cube of the deformation. In this experiment, we succeeded in generating chaos by using this non-linearity.
*7 ... Piezoelectric effect
The phenomenon of expansion and contraction when a voltage is applied to an object is called piezoelectric effect. Reversely, expansion and contraction can induce a force acting on an object.
*8 ... Single-crystalline heterostructure
It is the structure in which thin films made of different materials are bonded, while maintaining single crystallinity. The structure can be fabricated using high-quality crystal growth technologies such as molecular beam epitaxy and chemical vapor deposition. When used in a mechanical oscillator, stable vibration characteristics are obtained due to its high crystallinity. Another advantage is that a suspended structure such as a doubly clamped beam can be fabricated by utilizing the difference in the chemical-etching characteristics of the composing materials.