Extremely Wide Tuning Range of Mechanical Oscillation of a Silicon Waveguide Driven by Optical Gradient Force

MEMS oscillators are well-suited for filter and timing applications owing to high resonator quality factors. Active compensation of frequency variation in conventional commercial MEMS oscillators is limited by their tuning range, which is typically <1,000ppm. This paper demonstrates an extremely wide tuning range for oscillations of a silicon clamped-clamped beam via the optical spring effect. Frequency tuning from 3.1MHz to 19.4MHz is achieved by varying the intra-cavity power, corresponding to an optical-tuning coefficient of 1312.5ppm/μW. To the best of our knowledge, this is the largest reported tuning range in literature for MEMS oscillators. INTRODUCTION MEMS resonators are attractive for oscillator design on account of their extraordinary small size, high level of integration, low cost and high volume manufacturing capability. MEMS oscillators can be integrated either on the CMOS die or as two-chip solution using a separate CMOS die for interface electronics in a single package [1]. Typically high quality factors of MEMS resonators also enable superior noise performance and frequency stability compared to electrical oscillators. MEMS oscillators thus fill the gap between high-performance, non-CMOS compatible technologies on the one hand, and low-performance CMOS compatible technologies on the other. Frequency stability is one of the most important parameters of an oscillator. Since the output of an oscillator is the frequency of oscillation, it is possible to use the frequency measurement in an active feedback loop to counter the mechanism that causes the shift in frequency. The frequency variation of MEMS oscillators is typically dominated by temperature fluctuations in the device. Compared to quartz, silicon resonators have much larger temperature coefficient of frequency (TCF) [2]. To overcome the linear TCF of MEMS resonators, recent advances [3, 4] have relied upon using oxide plugs to reduce the TCF magnitude to sub25ppm and a quadratic temperature dependence of frequency. Achieving even lower TCF requires ovenization [5]. For commercial oscillators, tuning ranges on orders of few hundred ppm have been demonstrated [2, 4]. For voltage controlled crystal oscillators (VCXO), typical tuning coefficients are on the order of ~100ppm/V. To counter frequency variation due to manufacturing imperfections and package stresses, and long term frequency drift due to aging, having a method to achieve larger tuning range without significant added power consumption and die-space is desirable. Contrary to the small tuning range achieved by electrostatic spring softening, the optical spring effect has been leveraged to achieve significantly larger tuning ranges in opto-mechanical resonators [6, 7]. In this paper, we demonstrate an all-optically transduced silicon opto-mechanical oscillator, and leverage the optical spring effect to show large frequency tuning range of 525% for an n=1 in-plane bending mode of a clamped-clamped silicon beam from 3.1MHz to 19.4MHz. The following section describes the theory of operation for the oscillator and the optical spring effect. The subsequent sections detail the device design, fabrication and experimental results. THEORY OF OPERATION Optical gradient force driven mechanical oscillations Our group has previously demonstrated and explained the phenomenon of optical radiation pressure driven oscillations in an opto-mechanical resonator [8]. Alternatively, optical intensity gradients found in the near-field of guided wave nanostructures can be harnessed to create large gradient-like optical forces [9]. In contrast to the radiation pressure force, the gradient force depends upon the transverse evanescent-field coupling between adjacent cavity elements. One example of such a system that will be employed in this paper is a suspended optical waveguide coupled to an opto-mechanical cavity resonator. When the light wavelength is chosen such that it is detuned to an optical resonance of the resonator, the light intensity inside the cavity is enhanced due to its large optical quality factor. Thus if Pin represents the input laser power, and Qopt is the optical quality factor, the intra-cavity power is denoted by Pcavity = QoptPin. This results in a large field gradient between the light field in the cavity and light field in the waveguide (Pin) over a small gap. The optical gradient force acting on the resonator results in an optical anti-damping force acting on the waveguide and the resonator. The anti-damping rate Γopt is proportional to the circulating optical power and the detuning of the laser light from the cavity resonance [10]. By adjusting both the power and the detuning, the anti-damping rate can be increased to overcome the intrinsic mechanical damping rate (b= Ωm/2Qmech, where Ωm and Qmech denote the mechanical resonance frequency and quality factor respectively) in the resonator or the waveguide. This results in self-sustained mechanical oscillations of the device. Optical spring effect According to the derivation in [9], the mechanical spring constant of the cavity (k’) depends on the input laser power (Pin) as follows: k’ = k0(1+ηosPin) (1) where k0 is the intrinsic mechanical spring constant and ηos is the optical spring coefficient. The optical spring coefficient varies with the detuning as follows: ηos ∝ d(Qopt)2/[ Ω0(d2+0.25)]2, d = (λ0-λin)/ΔλLW (2) In the equation above, d denotes a normalized representation of the detuning that is in turn dependent on the input laser wavelength (λin), the optical cavity resonant wavelength (λ0) and the line-width of the cavity resonance (ΔλLW). The spring coefficient is directly proportional to the optical quality factor (Qopt) and inversely proportional to the intrinsic mechanical resonance frequency, suggesting that the largest tunability is noticed for low frequency mechanical modes excited with a high quality factor resonance. Oscillations occur only when the laser is blue detuned with respect to the cavity (d>0). The optical spring coefficient is thus always positive (spring stiffening), and has the highest magnitude at d ≈ 0.3. Operating at this detuning results in the largest deviation from the natural mechanical resonance 978-1-940470-02-3/HH2016/$25©2016TRF 5 Solid-State Sensors, Actuators and Microsystems Workshop Hilton Head Island, South Carolina, June 5-9, 2016 frequency for the oscillator. As the laser wavelength is increased and swept into resonance, the normalized detuning transitions from 1 to 0, and the resulting mechanical resonance shifts from a rising trend to a falling trend, crossing a local maximum at d ≈ 0.3. DESIGN AND FABRICATION As noted in equation (2), the largest tuning range is observed for low frequency mechanical modes. This demonstration uses a silicon opto-mechanical resonator coupled to a suspended silicon waveguide. Since the micro-ring resonator is designed for higher frequency modes (radial breathing mode at 175MHz and compound radial mode at 1.1GHz) [11], for this experiment we focus on the waveguide modes, which are at much lower frequencies (fundamental in-plane bending mode at 3.4MHz). The device comprises of a silicon waveguide of length 30μm and width 400nm. The waveguide is coupled to a silicon opto-mechanical resonator. Each individual ring in the coupled resonator has a width of 3.8μm. The device thickness is 220nm. The waveguideresonator gap is <100nm. The fabrication process flow was described in detail in earlier work on multi-GHz opto-mechanical oscillations of the coupled ring resonator [11]. Fabricating the device involves a five mask process flow on a custom silicon-on-insulator (SOI) wafer (undoped 250nm device layer for low optical loss and 3μm thick buried oxide for optical isolation from the silicon substrate). The top silicon is thermally oxidized to obtain a thin oxide hard mask layer of thickness 60nm atop a 220nm thick silicon device layer. The devices are defined in the oxide mask using electron beam lithography and a CHF3/O2 based reactive ion etcher. The pattern is then transferred into the silicon device layer using a chlorine based reactive ion etch. The mechanical resonator, the electrical routing beams and the bondpads are doped via boron ion implantation using a second photolithography mask to protect the optical section of the device. A third mask is then used to deposit metal over the bond pads for electrical contact using lift-off lithography. The metal stack used for the bond pads comprises of 25nm Nickel, 25nm Titanium and 50nm Platinum, respectively in the order of deposition. For the experiment described in this paper, the second and third masks are not necessary. A fourth mask is used to define release window for the waveguide and opto-mechanical resonator via photolithography, followed by a timed release etch in buffered oxide etchant to undercut the devices. The samples are then dried using a critical point dryer to prevent stiction. Fig. 1 shows a scanning electron micrograph (SEM) of the fabricated device. Figure 1: Scanning electron micrograph (SEM) of the device used for the experiments described in this manuscript. EXPERIMENTAL RESULTS Optical characterization To characterize the optical transmission spectrum of the resonator, light from a continuous wave (CW) Santec TSL-510 tunable diode laser is coupled into the on-chip waveguide through grating couplers and the transmitted power is measured using an optical power meter. The wavelength of the laser is swept to identify optical resonances of the device. Fig. 2 shows an optical transmission spectrum of such a device. At low laser power (0Bm), the optical resonances are clearly seen as dips in the optical transmission spectrum. At higher laser power (15dBm), the thermal nonlinearity of the optical resonator combined with the mechanical oscillations of the waveguide distort the optical transmission spectrum. Figure 2: Comparison of optical output transmission spectra at 0dBm and 15dBm input laser power. Oscillations set in as the laser is swept beyond 1563nm when operating with 15dBm power, manifesting as a distorted optical transmission spectrum. Mechanical oscillation To probe the mechanical mode of the waveguide, the transmitted light is passed to a Newfocus 1647 Avalanche Photodiode with gain setting of 6,000V/W. The motion of the waveguide and the opto-mechanical ring resonator leads to phase modulation of the intra-cavity light, which is converted into amplitude modulation via shaping by the optical resonator transfer function [11]. The ring resonator is designed such that it does not have mechanical modes in the vicinity of the resonance frequency of the fundamental in-plane and out-of-plane bending modes of the waveguide. The RF signal is analyzed on an Agilent 5052B signal analyzer. Fig. 3 shows a sketch of the experimental setup. Figure 3. Experimental setup used to study opto-mechanical oscillation of the silicon waveguide. As the laser wavelength is swept into an optical resonance of the cavity, the intra-cavity optical power in the resonator builds up. When the built up power is sufficiently high such that the antidamping introduced by the optical gradient force overcomes the intrinsic mechanical damping in the silicon waveguide, mechanical