Precision measurement underpins scientific research [1], with frequency measurement exhibiting the highest precision among physical quantities. This makes frequency measurement essential to the definitions of several base units in the International System of Units, including time, length, current, mass, and temperature [2,3]. These quantities can be converted into frequency, creating demand for portable, high-precision time-frequency standards. Atomic clocks, the most advanced instruments for such standards, are widely applied in navigation, radar, precision measurement, and communications, requiring high frequency stability while minimizing size and power consumption.

An atomic clock stabilizes its frequency to a quantum reference spectral line, producing a highly precise frequency standard [4–6]. Central to this process is the atomic vapor cell, the source of the reference transition. Traditional vapor cells, produced through glass-blowing, result in centimeter-scale glass bulbs that limit miniaturization, chip integration, and cost-effective mass production. Here, we utilize micro-electro-mechanical systems (MEMS) technology to design and fabricate a silicon-based wafer-level MEMS vapor cell. This millimeter-scale cell supports batch production, significantly reducing costs. The design incorporates an innovative silicon–glass–silicon transverse optical path structure, facilitating future device integration and chip-level implementation.

As the next generation of atomic clocks, optical frequency standards achieve up to 102-fold higher precision than microwave standards. The accuracy and stability of optical frequency standards have reached the 10−18 level [7–10]. However, most current optical frequency standards are large, costly, and complex to operate, limiting their applications. Efforts to miniaturize these systems have led to thermal atomic optical frequency standards, which are compact, low-power, and offer approximately 102 times better frequency stability than microwave compact standards without requiring laser cooling or ultra-stable cavities. Key stabilization techniques for thermal atomic optical standards include saturated absorption spectroscopy (SAS) [11–13], polarization spectroscopy (PS) [14–17], modulation transfer spectroscopy (MTS) [18–25], two-photon spectroscopy (TPS) [11,26–28], and dual-frequency sub-Doppler spectroscopy (DFSDS) [29–31]. Recent miniaturization efforts have led to notable advancements in compact optical frequency standards, including the U.S. National Institute of Standards and Technology (NIST) achieving a stability of 2.9×10−12 at 1 s with TPS [26] in 2020, Humboldt University reaching 1.7×10−12 at 1 s with SAS [32] in 2022, Peking University achieving 2.1×10−13 at 1 s using MTS [19] in 2022, FEMTO-ST in France reporting 3×10−13 at 1 s with DFSDS [30], and the U.S. Air Force Research Laboratory attaining 9×10−14 at 1 s with TPS in 2024 [4]. Although MEMS vapor cells have been validated in schemes such as in Refs. [11,13,28,30], they have not yet been demonstrated in MTS-based systems. Furthermore, despite efforts toward miniaturization, these standards do not yet incorporate wafer-level MEMS vapor cells. In this study, we fabricate wafer-level MEMS rubidium (Rb) vapor cells using MEMS technology, enabling scalable production. Notably, we introduce a silicon–glass–silicon transverse optical path design that overcomes the 2 mm depth limit of silicon deep reactive-ion etching (DRIE) and allows customizable optical path lengths, set at 10 mm. Additionally, a single wafer is used to fabricate 24 identical atomic vapor cells, each with precise dimensions of 14mm×14mm×4.3mm, ensuring scalability. Using MTS and a high-speed feedback system, we lock the laser frequency to the Rb8752S1/2F=2 to 52P3/2F′=3 cycling transition within the vapor cell. The compact frequency standard achieves a volume of 11.37 L and demonstrates high frequency stability, with a short-term stability of 2.6×10−13 at 1 s and reaching 5.1×10−14 at 200 s. The single laser linewidth is reduced to 3.9 kHz, marking a substantial improvement over existing thermal standards. By combining MEMS vapor cells with MTS, we establish an optical frequency standard of its kind and demonstrate the application of wafer-level MEMS vapor cells in optical frequency standards. This compact optical frequency standard, with its narrow linewidth and high stability, serves as a transportable frequency standard, potentially applicable to precision spectroscopy, quantum information and sensing, and coherent optical communications.

Our work offers three key advantages: (1) the wafer-level MEMS vapor cell enables low-cost mass production and features an innovative silicon–glass–silicon transverse optical path design that overcomes DRIE limitations, facilitating chip integration; (2) using MTS, we obtain a high signal-to-noise ratio (SNR) atomic spectral line, achieving the compact thermal atomic optical frequency standard based on a wafer-level MEMS vapor cell with high stability across 1–400 s averaging time; (3) a high-speed servo feedback mechanism narrows the laser linewidth to the kHz range, providing a low-noise, narrow-linewidth laser source.

The vapor cell, containing an alkali metal vapor and permitting light transmission, is a transparent chamber that serves as the core component of an atomic clock. It must meet strict requirements for hermetic sealing, high-temperature resistance, and non-reactivity with alkali metals. Traditional methods, such as glass-blowing, make miniaturization challenging and often leave a glass extension known as a cold finger. Advances in microfabrication, such as glass–silicon anodic bonding [33] and glass reflow, have enabled the fabrication of MEMS-based vapor cells [34]. In recent years, atomic clocks integrated with MEMS vapor cells have achieved smaller volumes and lower power consumption [35,36]. Wafer-level MEMS technology allows for the construction of microstructures across an entire wafer, offering advantages such as scalability, improved uniformity, and easier integration with microelectronic devices. We utilize this approach to fabricate wafer-level vapor cells.

The traditional MEMS vapor cells are usually fabricated with a glass–silicon–glass three-layer structure, whose optical path length is generally less than 2 mm, which is limited by the DRIE technology of silicon wafers. In order to solve this problem, there are some vapor cell structures that increase the optical path length, such as the addition of diffraction gratings [37], the use of glass reflow technology [38], and the use of water jet processed deep silicon chambers [39], but these processes are relatively complex and difficult to fabricate. We propose an innovative design for vapor cell structure, achieving a horizontal optical path length of up to 10 mm, as shown in Fig. 1(i). The cell has two chambers [40] connected by a micro-channel: a high-power laser activates the Rb dispenser in the reactive chamber [41,42], releasing vapor that diffuses into the optical chamber through the micro-channel, while residuals remain confined, preventing interference with the interaction between light and Rb atoms in the optical chamber. The polished side-walls in both chambers ensure efficient laser transmission.

Figure 1 illustrates the wafer-level fabrication process. First, chambers were mechanically drilled by a computer numerical control machine tool and polished by a precision mechanical polisher into a BF33 borosilicate glass wafer [Fig. 1(a)]. Anodic bonding is then performed to join the glass wafer with a 150-μm-thick silicon wafer, forming a two-layer structure, as shown schematically and photographically in Figs. 1(b) and 1(c). Next, Rb dispensers (SAES Getters RB/AMAX/PILL/1-0.6) were filled into the reactive chambers [Fig. 2(d)], followed by a second anodic bonding step to attach another silicon wafer under a pressure of 1×10−3Pa, creating a three-layer structure, as shown schematically and photographically in Figs. 1(e) and 1(f). The wafer was subsequently diced into slices and polished on the outside [Fig. 1(g)]. To activate the Rb dispenser, a 980 nm laser beam of 15 W was focused on the surface of a Rb dispenser for 20 s. Figures 1(h) and 1(i) show the final vapor cell structure and a photograph, with external dimension of 14mm×14mm×4.3mm and an inner optical chamber of 10mm×6mm×4mm. This process successfully produced a batch of miniature MEMS vapor cells.

As illustrated in Fig. 2, we assembled two identical MTS-based optical frequency standards using the fabricated MEMS vapor cells [Figs. 2(a) and 2(b)]. The systems were assembled approximately one week after the vapor cells were fabricated. MTS leverages four-wave mixing to transfer modulation signals, offering a high signal-to-noise ratio, high sensitivity, and Doppler-free detection.

We presented a 780 nm laser system stabilized by MTS, as illustrated in Figs. 2(d) and 2(e). The system was anchored by a 780 nm external cavity diode laser (IF-ECDL) with an interference filter configuration, delivering up to 35 mW of output power and a linewidth below 100 kHz. Frequency tuning was achieved via modulation of the injection current and PZT voltage. After passing through an isolator, the laser output was split, with ∼1.5mW of power directed to the MTS-based frequency stabilization unit.

The beam was divided into a probe (0.2 mW) and a pump (1 mW) component. The probe beam passed through a wafer-level MEMS vapor cell containing rubidium (Rb) atoms and was detected by photodetector PD1 (Thorlabs PDA8A2). To maintain thermal isolation, a multilayer passive insulation structure was used, comprising nitrile foam and polyurethane. Magnetic shielding was provided by a permalloy enclosure, and temperature control was maintained using a Thorlabs TC300 controller.

The pump beam, driven at 9.6 MHz by an electro-optic modulator (EOM), counter-propagated with the probe beam. A half-wave plate (HWP) placed before the EOM ensured proper polarization alignment. The EOM generated first-order sidebands (±1), which transferred modulation to the probe beam via four-wave mixing. PD1 detected the beat signal between the carrier and sidebands. After demodulation using a mixer, a dispersion-like error signal was produced and fed into a PID controller to lock the laser to the Rb hyperfine transition.

The system employed a three-channel feedback loop: PZT control, fast current modulation to the laser head, and slow current feedback to the laser driver. The laser servo bandwidth was approximately 600 kHz.

As the core component of the optical frequency standard, the wafer-level MEMS vapor cell underwent detailed testing to evaluate its temperature effects. With increasing temperature, the atomic density increases, which in turn causes collisional shifts and broadens the spectral line. To minimize the influence of ambient temperature and geomagnetic fields, the vapor cell was enclosed using multilayer magnetic shielding and thermal insulation materials. Figure 3 illustrates spectra obtained using the MEMS cell, in which the red line is the saturated absorption spectroscopy (SAS), and the black line is the modulation transfer spectroscopy (MTS). The MTS D2 line cycling transition from Rb8752S1/2F=2 to 52P3/2F′=3 was the most prominent and was used for locking.

System optimization focused on the slope of the MTS signal at the zero-crossing point, where the laser is locked. A steeper slope indicates higher sensitivity and a better signal-to-noise ratio. Figure 4(a) shows the MTS slope as a function of vapor cell temperature. The slope increases with temperature, peaks at 0.45 V/MHz around 80°C, and then decreases. Therefore, 80°C is chosen as the operating temperature for the wafer-level MEMS vapor cell.

Previous studies [43] have conducted detailed calculations on the optimal temperature of atomic vapor cells. They found that as temperature increases, the relative intensity of Doppler-free hyperfine transitions initially rises and then falls, due to combined effects of atomic density, Doppler broadening, and magnetic susceptibility. While specific optimal temperatures vary depending on vapor cell dimensions and fabrication methods, the overall trend is consistent.

The system’s stability was evaluated using two methods: beat frequency testing and self-evaluation. In the first method, two identical MTS systems were tested, with the beat frequency detected by a photodetector (PD2, Hamamatsu C5658) and recorded using a frequency counter (Keysight 53230A). The resulting beat frequency stability was divided by 2 to estimate the stability of a single system. Note that throughout this paper, “stability” refers to a single system unless otherwise stated, such as in Fig. 4.

During optimization, one system was tuned first, and then the second, with several iterations. Figure 4 shows the temperature optimization process for the first system; the second system was not in its optimal state during this period. Self-evaluation was conducted by recording voltage fluctuations in the error signal and converting them to frequency stability using the MTS slope. The resulting trend aligns with the MTS slope–peaking at 80°C before degrading.

As shown in Fig. 5, two identical optical frequency standard systems based on wafer-level MEMS vapor cells were optimized through multiple iterations. Parameters such as vapor cell temperature, laser power, and EOM temperature were finely adjusted. As a result, the single-system stability reaches 2.6×10−13 at 1 s and 5.1×10−14 at 200 s.

MEMS vapor cells attract significant attention for their compactness, low cost, and scalability, prompting growing efforts to integrate them into optical frequency standard systems. Figure 5 presents the single-system frequency stability of various thermal atomic optical frequency standards using miniature vapor cells; note that some of the vapor cells employed in these systems are not MEMS-based. The frequency standard developed in this work achieves near-optimal stability among systems using wafer-level MEMS vapor cells.

We next carry out a detailed analysis of the optical frequency standard. Figure 6(a) compares the frequency noise spectra of the beat notes from the free-running and locked lasers, while Fig. 6(b) presents the corresponding phase noise spectra. These measurements form the basis for evaluating the system’s noise characteristics.

There is a well-established mathematical relationship between phase noise and frequency noise. Specifically, the power spectral density (PSD) of frequency noise is Sν(f) related to the phase noise spectrum by Sφ(f) [13,41]: Sφ(f)=(v0f)2·Sν(f).(1)

Here, Sν(f) is the frequency noise PSD (in Hz2/Hz), representing the intensity of frequency fluctuations, and Sφ(f) is the phase noise PSD (in rad2/Hz). The commonly used single-sideband phase noise L(f) (in dBc/Hz) is related to the phase noise PSD via L(f)=12Sφ(f).(2)

Based on the frequency noise spectrum, we estimated the contribution of low-frequency phase noise to the fractional frequency stability using the following expression [44]: σy(τ)=2∫0fhSν(f)sin4(πf)(πf)2df≈b−2v02·τ,(3)where b−2 denotes the coefficient of the 1/f2 noise component, evaluated at 1 Hz (converted from 40dBc/Hz≈37dBrad2), v0=3.842×1014Hz, and the calculated short-term frequency stability at τ=1s was σy(1s)=1.57×10−13.(4)

This result represents the contribution of low-frequency phase noise (at 1 Hz) to the overall frequency stability of the system. Additionally, the theoretical frequency stability limit [45] imposed by photon shot noise is estimated to be approximately 1.7×10−14 at 1 s. A summary of the main noise sources and their estimated contributions to the short-term stability at τ=1s is provided in Table 1.Table 1.

Short-Term Stability Budget of the Optical Frequency Standard Using Wafer-Level MEMS Vapor Cell

We next analyze the key factors contributing to frequency stability in the optical frequency standard, including temperature variations of the EOM, fluctuations in the MEMS vapor cell temperature, changes in laser power, and electrical noise within the system. The results are shown in Fig. 7. Among these factors, EOM temperature variation has the greatest impact. As shown in Fig. 7(b), the EOM sensitivity coefficient varies with temperature and reaches approximately 50 kHz/K near 25.50°C, corresponding to 1.3×10−10/K.

Temperature fluctuations in the EOM influence laser frequency stability through several mechanisms.

(1) Phase modulation distortion: temperature-induced changes in the crystal’s refractive index affect the modulation depth and linearity, causing polarization shifts in the pump beam and altering four-wave mixing efficiency, which shifts the zero-crossing point of the MTS signal; (2) electro-optic coefficient drift: temperature dependence alters the modulation efficiency; (3) thermal expansion: crystal expansion changes the optical path length, affecting phase modulation; (4) residual amplitude modulation (RAM): temperature-induced etalon effects increase RAM, causing frequency offsets.

These effects are particularly pronounced in compact systems due to low thermal mass and constrained optical layouts. As a result, EOM temperature drift becomes a major factor limiting frequency stability. Improved temperature control of the EOM is recommended, along with RAM suppression strategies such as using passively angled crystals to minimize etalon effects or applying active RAM compensation through the EOM’s DC port feedback [46].

Temperature fluctuations in the MEMS vapor cell enhance collisional shifts and modify vapor pressure, altering the atomic population involved in the transition and degrading frequency stability. In our system, this effect causes a frequency shift of ∼20kHz/°C (5.2×10−11/K), making it a major source of long-term drift.

Laser power variations induce light shifts and power broadening, affecting both the spectral linewidth and the locking point. The corresponding frequency sensitivity is ∼80kHz/mW (2.1×10−11/mW), contributing significantly to short-term stability.

Electrical noise–originating from components such as mixers, amplifiers, and PID controllers–has a minor influence on overall stability.

Overall, the system’s frequency stability is limited by several key factors. In the short term, the dominant limitations arise from laser phase noise, the error signal’s signal-to-noise ratio, and EOM temperature fluctuations. In the mid term, EOM thermal effects–including modulation distortion, thermal expansion, and residual amplitude modulation (RAM)–become the primary concern, with laser power fluctuations further degrading performance. In the long term, vapor cell temperature drift remains the main limiting factor due to its impact on vapor density and collisional broadening. Photon shot noise and electrical noise are secondary contributors across all time scales.

Although the Pound–Drever–Hall (PDH) technique [47,48] enables substantial linewidth narrowing by locking the laser to an ultra-stable optical cavity, it typically requires complex setups, including vacuum chambers, vibration isolation systems, and even cryogenic cooling. In contrast, thermal atomic spectroscopy provides a more compact and convenient alternative. While its linewidth reduction capability is relatively limited, it offers absolute frequency anchoring to atomic transitions and can be implemented without bulky infrastructure, making it well-suited for portable and integrated systems.

In our system, multi-path servo feedback–applied via the PZT, slow current, and fast laser head current ports–effectively suppresses frequency noise across a wide bandwidth, offering a practical solution for realizing narrow-linewidth lasers. To further reduce laser noise, we implement a high-speed MTS-based locking scheme using the same three feedback paths. This configuration enables efficient noise suppression over distinct frequency ranges, particularly in the hundreds-of-kHz domain, as evidenced by the pronounced servo bumps observed in the noise spectra shown in Figs. 6(a) and 6(b).

The laser linewidth was measured using the beat-note method and a spectrum analyzer (Keysight N9000B), as shown in Fig. 8. Before locking, the beat note exhibited a Lorentzian linewidth of 60.4 kHz, corresponding to a single-laser linewidth of 42.7 kHz after division by 2 (RBW=30kHz, sweep time=200ms). After locking, the linewidth narrowed to 5.5 kHz (RBW=1kHz, sweep=200ms), yielding a single-laser linewidth of 3.9 kHz–nearly a tenfold reduction.

The instantaneous linewidth is related to the frequency noise power spectral density Sv(f) [49,50]: Δv=Sv(f)2.(5)

Based on this relation, the estimated instantaneous linewidth was approximately 6 kHz, closely matching the measured linewidth of 5.5 kHz from Lorentzian fitting.

Compared to other thermal atomic spectroscopy techniques for laser linewidth narrowing, our approach achieves the narrowest linewidth to date, as summarized in Table 2. Notably, whereas previous studies employed conventional glass-blown vapor cells, our system utilizes wafer-level MEMS vapor cell technology, further underscoring the compactness and performance advantages of our design.Table 2.

Effectiveness of Laser Linewidth Narrowing in Thermal Atomic Spectroscopy Techniques

This work experimentally validates a compact MTS optical frequency standard based on a wafer-level MEMS vapor cell, enabling low-cost mass production and seamless silicon-based chip integration. The system demonstrates robust frequency stability over averaging times from 1 to 400 s, reaching 2.6×10−13 at 1 s and 5.1×10−14 at 200 s for a single system. Long-term stability is primarily limited by residual RAM effects in the EOM, underscoring the need for enhanced temperature control and active RAM suppression. Notably, the laser linewidth of this frequency standard is only 3.9 kHz–surpassing other thermal atomic frequency standards, particularly considering its use of a wafer-level MEMS vapor cell.

To further improve performance, we propose a high-signal-to-noise approach based on velocity-comb modulation transfer spectroscopy [54], which has the potential to enhance stability by up to three orders of magnitude [55]. This method has been preliminarily validated by other research groups.

Future work will focus on the miniaturization and integration of the laser and EOM, aiming to realize a low-cost, high-performance on-chip optical frequency standard. Such a portable device holds strong potential for applications in navigation, radar systems, and precision measurement.