Electronic oscillators are the most fundamental building block in almost any electronic system for a variety of applications such as frequency control (Achenbach et al., 2000) and environmental sensing (Bianchi et al., 2000; Walls and Gagnepain, 2002). In addition to traditional quartz resonator-based reference oscillators (Vittoz et al., 1988) and quartz crystal microbalance (QCM) sensors (Ferrari et al., 2006), miniaturized oscillators using microelectromechanical systems (MEMS) technology have been intensively studied in both academia and industry over the past two decades (Lavasani et al., 2011; Chance et al., 2014; Zaliasl et al., 2015; Naing et al., 2020; Kalia et al., 2021; Chang et al., 2022) to be used in demanding applications with size constraints. Among the existing MEMS oscillator fabrication approaches, the CMOS-MEMS technology is one of the most promising approaches to achieving the monolithic integration of mechanical resonators and electronic circuits (Xie et al., 2002; Dai et al., 2005; Chen et al., 2011; Li C.-S. et al., 2012; Chen et al., 2019; Valle et al., 2021). In this approach, MEMS mechanical structures can be formed from the back-end of line (BEOL) metal/dielectric (Verd et al., 2006; Li et al., 2012c; Li et al., 2015b; Liu et al., 2018) or the front-end of line (FEOL) polysilicon layers (Verd et al., 2005; Lopez et al., 2009) by removing predefined sacrificial layers, thereby eliminating the thermal budget constraints that are often encountered in other custom IC-MEMS integration processes (Fedder et al., 2008). Although the constituent materials of the CMOS-MEMS resonators are limited to the composite metals, dielectrics, and polysilicon, it still features great mechanical properties such as high-quality factor (Q) (Chen et al., 2012; Li et al., 2015a) and low-temperature coefficient of frequency (TCF) (Liu and Li, 2019), providing potential for being used in practical oscillator applications.

To make up an oscillator, the CMOS-MEMS resonator is connected in a positive feedback loop with a CMOS amplifier on the same chip (Verd et al., 2008). Such a monolithic integration scheme helps reduce the parasitic capacitance between the MEMS resonator and the amplifier, hence extending the available bandwidth of the amplifier and reducing the input-referred noise. According to the feedback oscillator theories, the Barkhausen stability criterion should be met: 1) the loop gain at the oscillation frequency equals unity, and 2) the phase delay in the oscillation loop should be equal to a multiple of 2π (Rhea, 2010). Despite the simplicity of the concept, implementing a high-performance CMOS-MEMS oscillator is not an easy task. There are several parameters to evaluate the overall performance of an oscillator, including the oscillation frequency, temperature stability, power dissipation, and phase noise. Since phase noise represents random fluctuations in the phase of the output signal (Rubiola, 2008), it should be kept as low as possible to enhance oscillator stability, which is critical for precision applications such as timing references and high-resolution sensors. However, the most challenging issue to achieve low-noise CMOS-MEMS oscillator is the high motional resistance (R _m ) of the on-chip MEMS resonator. Although several energy transduction mechanisms including electrostatic (Li et al., 2015c), thermal-piezoresistive (Zope and Li, 2021), and capacitive-piezoresistive (Li C.-S. et al., 2013) have been explored in CMOS-MEMS technology, the electrostatic transduction is the most widely adopted scheme in resonator due to its simplicity. Since the typical transduction gap size from 400 to 1,000 nm is limited by lithographic limitations in 0.35 and 0.18 μm CMOS platforms (Li C.-S. et al., 2012; Chen et al., 2019), typical CMOS-MEMS resonator impedance lies in the MΩ range in previous reports even under high bias voltages (Liu et al., 2013). As will be shown in the next section, such a high impedance not only raises the design complexity and difficulty of the sustaining circuit but also contributes a significant portion to the phase noise. In addition to R _m , recent studies also confirm that the inherent nonlinearity in CMOS-MEMS resonators also plays a key role in the phase noise spectrum (Li et al., 2018). In order to make a breakthrough in the performance of existing CMOS-MEMS oscillators, it is crucial to understand the characteristics of the prior arts.

To capture the important parameters that contributed phase noise in both MEMS resonator and CMOS circuit, an equivalent circuit model is depicted in Figure 1A. The circuit is divided into two stages where the first stage is a transimpedance amplifier (TIA) to convert the motional current i m from the resonator to the corresponding voltage v T I A and the second stage is a gain-boosting amplifier to provide an additional gain A to satisfy the Barkhausen criterion. Note that the transimpedance gain should be in ohms rather than V/V. At the oscillation frequency f o , the overall gain R A = R T I A ⋅ A should be greater than the equivalent resonator impedance Z m and the overall feedback phase is φ T I A + φ A + φ M E M S = 2 n π . Considering a practical resonator with a certain nonlinear effect, Z m is greater than R m in a general case (Pardo et al., 2012). Based on this circuit, the phase noise of the oscillator can be expressed as ℒ ( f m ) = 10 ⁡ log { ( 4 k T Z m + i n 2 ¯ Δ f Z m 2 ) 2 V O U T 2 ¯ ( 1 + ( f o 2 Q eff f m ) 2 ) + | ∂ f n ∂ V O U T | 2 S A n ( f m ) f m 2 } (1) where k is the Boltzmann constant, T is the temperature in Kelvin, f m is the offset frequency from carrier, i n 2 ¯ / Δ f is the input-referred current noise density of the TIA stage, Q eff is the equivalent quality factor of a nonlinear resonator, | ∂ f / ∂ V O U T | 2 is a coefficient to describe the A-f effect of an nonlinear MEMS resonator (Li et al., 2018), and S A n ( f m ) is the amplitude noise spectrum of the oscillator. According to Eq. 1, the first component of phase noise is obviously from the Leeson effect and the second component is from the nonlinear amplitude-to-phase modulation (AM-PM) effect (Ward and Duwel, 2011).

From Eq. 1, it can be seen that the overall phase noise is dominated by the amplified circuit noise, ( i n 2 ¯ / Δ f ) ⋅ Z m 2 . Since the typical values of Z m lies in MΩ range for CMOS-MEMS resonators, the input-referred current noise of the TIA stage should be designed as low as possible to minimize this term. The resonator current noise 4 k T Z m is not significant for CMOS-MEMS devices. Therefore, some amplifier architecture, such as regulated-cascode TIA (Nabki et al., 2009), is not suitable for CMOS-MEMS oscillator design due to its high input-referred current noise. In addition to the impedance issue, when the resonator is driven at a large vibrating magnitude, the phase noise-folding caused by the AM-PM conversion can be described as an additive term, which dominates the close-to-carrier phase noise (Lee et al., 2011). To solve this issue, several design techniques such as high-stiffness driving (Su et al., 2015) and phase-feedback (Li et al., 2014) schemes were explored and implemented in CMOS-MEMS.

Through the articles that have been discussed in the Complementary Metal-Oxide-Semiconductor-Microelectromechanical Systems Oscillator Architecture section, we observe large discrepancies in phase noise between distinct CMOS-MEMS oscillators, which can be attributed to differences in the dc-bias voltage, resonator volume, vibrating mode shape, and transduction gap size. To understand the reason behind this, the state-of-the-art CMOS-MEMS oscillators are tabulated in Table 1 with their phase noise at different offsets. Apparently, the oscillators based on tiny resonators with small transduction gaps (Verd et al., 2008; Verd et al., 2013) feature worse close-to-carrier phase noise compared to the other samples. This is because the tiny resonator elements usually have strong mechanical and bias-dependent nonlinearities (Chen et al., 2022), so the phase noise caused by the AM-PM effect is more pronounced. To overcome this issue, despite the conventional approach which operates the oscillator at lower carrier power to guarantee a linear MEMS operation, it has recently been demonstrated that the close-to-carrier phase noise can be effectively suppressed by increasing the excitation power as operating the MEMS resonator in the nonlinear regime (Yurke et al., 1995; Kenig et al., 2012). For a typical nonlinear Duffing resonator, there are two bifurcation points that present a steep phase-frequency slope to potentially minimize the AM-PM conversion coefficient. It has been shown theoretically and experimentally in a nanoelectromechanical oscillator system (Villanueva et al., 2013), that the phase noise of the nonlinear oscillator is greatly improved by operating the feedback phase closed to the lower bifurcation point.

For CMOS-MEMS oscillators, nonlinear AM-PM noise cancellation is firstly explored by (Li et al., 2014) based on a double-ended tuning fork resonator. By operating the oscillator at the lower bifurcation point through a variable-gain R-TIA, it can be observed that the phase noise changes drastically (close to 30 dB at 10 Hz offset) when the applied bias voltage is perturbed by only 0.1 V. The nonlinear phase noise cancellation leads to a great performance improvement, which is only 7 dB above the theoretical limit predicted by Leeson’s model. In addition, this method is not restricted to a specific oscillator topology. The phase noise optimization is also achieved through an off-chip phase shifter circuit and supply voltage (V_DD) adjustment in other nonlinear CMOS-MEMS oscillator studies (Sobreviela et al., 2017; Uranga et al., 2017). In a recent study (Li et al., 2018), a 1.2 MHz 180 μW DETF oscillator combined with ultra-low-noise ID-TIA and nonlinear phase noise optimization technique achieves phase noise of -80 dB and -127 dB at 10-Hz and 1-MHz offsets, respectively, yielding a very competitive FOM of 189.3 dB.

CMOS-MEMS oscillator is an important technology to produce on-chip frequency references and oscillating sensors. In this review, we focused on the recent advances in CMOS-MEMS oscillators in terms of oscillator circuit topologies and phase noise performances. For high impedance resonators, it is reasonable to use voltage buffers and charge integrators as MEMS-circuit interfaces to take the advantage of their low input-referred noise. On the other hand, for low impedance resonators, resistive feedback TIA with moderate gain becomes a more suitable topology to avoid saturation and Q-loading effect. On the phase noise, it has been pointed out that the resonator impedance is the fundamental limit of the phase noise spectrum since the noise at the circuit input will be amplified by a factor of R _m to satisfy the oscillation criteria. Finally, the phase noise optimization based on phase feedback technique and nonlinear MEMS resonator operation is reviewed, which is a useful technique for oscillator stability improvements. So far, the CMOS-MEMS oscillators have been designed based on flexural mode resonators. The low stiffness characteristic becomes a fundamental limitation of frequency scaling. Thus, for future CMOS-MEMS oscillator designs, high-Q and high-frequency bulk-mode resonators (Chen et al., 2012) will be a potential solution to overcome current performance limitations.