Silicon p–n diode actuators with depletion layer embedded in a beam of cantilever

Abstract

In this paper, we describe the p-n diode actuators that are driven by the force induced in a depletion layer. It was previously reported that the position of the p-n junction generates the actuation of p-n diode actuators. However, the spread of the depletion layer should also play an important role in p-n diode actuators. We develop a new theory, in which p-n diode actuators are driven by the forces induced by the spread of the depletion layer as well as the position of the p-n junction. For the silicon cantilever-type p-n diode actuator fabricated using an epitaxial substrate, the force generated by the spread of the depletion layer is shown to become dominant. The amplitude of actuators with the depletion layer embedded in a beam is also shown to be proportional to DC bias. These features are very different from those of previously reported actuators. We also present the first actuator that is driven by the depletion layer formed under a root in a beam. Although the amplitude induced under the root of the beam is small, the displacement of the tip of the cantilever is enlarged by resonance. Good agreement of experimental results with the theory is confirmed by evaluating fabricated p-n diode actuators. In addition, the temperature dependence of p-n diode actuators is presented. The measured data show that the temperature coefficient of frequency (TCF) is strongly suppressed by the depletion layer embedded in a beam.

Various vibration modes in a silicon ring resonator driven by p–n diode actuators formed in the lateral direction

“…The theory on p-n diode actuators has been investigated using an analytical model. 8,10,11) Although the calculated values agree well with the measured ones, the theory is limited to simple vibration modes. Today, computer simulation is widely used for calculating mechanical responses; Laterally vibrating resonators that have a piezoelectric thin film deposited on a silicon layer have been reported.…”

“…Note that the p-n diode actuators formed in the lateral direction, as will be described later, do not use Poisson's ratio, which plays a key role in the p-n diode actuators formed in the vertical direction. 11) The application of a reverse voltage between the n-and p-type layers yields a depletion layer. When the frequency of the excitation voltage applied to one of the half-circular plates (actuator) is close to the resonant frequency of the ring plate, the small displacement generated in the p-n diode is markedly amplified, resulting in a large mechanical vibration in the half-circular plate.…”

“…Therefore, the amplitude on the outer edge of the p-type silicon is the same as that of the vibration of the electrode formed in the p-type silicon, as given by Eq. (11).…”

“…In the case of p-n diodes formed in the perpendicular direction, the position of the p-n junction has a strong influence on the amplitude. 11) Figure 5 shows the model used for the simulation. The resonant modes are obtained from a suitable combination of normal modes.…”

“…8) The actuators using the electrostatic force induced in the p-n diode are activated by two different principles: actuation using a force perpendicular to the depletion layer 8) and actuation using a force parallel to the p-n diode through Poisson's ratio. 9,11) The theory for actuation perpendicular to p-n diode is simpler than that for actuation parallel to the p-n diode because the consideration of Poisson's ratio is not necessary. However, the earlier works using actuation perpendicular to the p-n diode were performed in the out-of-plane direction.…”