- Overview
- Oscillator
- Resonance
- Noise Induced Switching
-
A micromechanical torsional oscillator is used to perform all of my experiments.
The oscillator, an example is shown on the right, is
fabricated using a surface micromachining process offered by MEMSCAP. This technique
involves depositing layers of polysilicon and oxide onto a silicon substrate with a nitrate
layer. The polysilicon acts as the structural layer of the device and the oxide is used as a
sacrificial layer. The oxide can be removed post fabrication using concentrated hydrofluoric
acid. This method allows the production of suspended structures. Our particular device
consists of three main parts: a movable top plate, two electrodes positioned directly beneath
the top plate which can be used for applying and detecting a signal, and two torsional springs
which are used to suspend the top plate 2um above the electrodes.
The frequnecy response of the oscillator is well fitted by a Lorentzian, as shown in the figure to the left (mouse over to magnify). As the driving
torque is increased the nonlinear terms begin to affect the oscillator response. The
shape becomes asymmetric and the peak begins to shift to lower frequencies When the peak of the response reaches a frequency of w = w0 - \sqrt{3 gamma} a
discontinuity appears in the response. For stronger driving torques the response is well modeled as a duffing oscillator. The response exhibits hysteresis and the oscillator posseses three dynamic states; two stable and one unstable. The transition
from a linear response to a hysteretic response is shown in the figure to the left.
The two oscillation amplitudes, which exist between the the lower bifurcation frequency f1 and the upper bifurcation frequency f2, are stable in the absence of fluctuations. The history of the oscillator determines which state the system resides. For a constant driving torque, increasing the driving frequency past f1 places the oscillator in the lower oscillation amplitude of the system. The system will stay in this state until the driving frequency surpasses f2, where it abruptly switches to the upper amplitude state. When the driving frequency is swept back down the oscillator resides in the larger oscillation amplitude state until the driving frequency passes f1. At this frequency the system switches back to the lower amplitude state. When noise is injected into the driving voltage the system can be induced to switch from one of the stable oscillation amplitudes to the other, assuming the driving frequency lies within the hysteresis loop. Figure 3(a) shows an example of the system switching from one oscillation amplitude to the other and back for a particular driving frequency and amplitude. By taking a longer time trace of the oscillation response and making a histogram of the data, as shown in Fig. 3(b), the relative occupation between the two states can be inferred. In this case the system favors the larger oscillation amplitude. This indicates that the activation barrier needed to be overcome by the noise intensity when going from the lower state to the upper state is smaller than the barrier separating transitions from the upper state to the lower state.
