INTRODUCTION
For centuries, mechanical computers have dominated the history of human calculation. As early as circa 1000 AD (Song Dynasty), Su Song had invented the Cosmic Engine as one of the earliest mechanical computing instruments. In 1642, Pascal invented the Pascaline, a mechanical calculator that achieved addition and subtraction operations. Then in 1673, Leibniz followed up and invented the Stepped Reckoner, a mechanical calculation engine which could automatically perform multiplication and division operations1. Later in 1822, Charles Babbage designed a mechanical calculating engine called Difference Engine, which contained both computing units and memory units, and is more than a century before von Neumann developed his theory for modern electronic computers2. In the 20th century, a number of hand-cranked calculating machines including handheld ones such as the Curta Calculator have been invented, which could perform calculations with 11 to 15 digits of precision. During WWII, mechanical computers reached their high point, and were broadly used for calculation tasks such as bomb path estimation (e.g. the Norden bombsight3), encryption (e.g. the Enigma), and code deciphering (e.g. the Bombe4).
With the rise of vacuum tubes and subsequent transistors, great inventions have led to the great era of electronic computing and then digital revolution5. By just moving electrons rather than mechanical parts, electronic computing devices exhibit high speed and good reliability. For decades, driven by Moore's Law, huge advances in integrated circuits have been achieved, leading to relentless reduction in the cost and form factor of electronic devices. These advantages, among many others, have helped electronic computers to prevail over their mechanical predecessors and revolutionized our lives.
With the continuous improvement of integration density, however, metal-oxide-semiconductor field-effect transistors (MOSFETs) have started to face a series of challenges, such as short-channel effect, hot-carrier injection, off-state leakage, gate oxide leakage, limited temperature range, and lack of reconfigurability, etc. To overcome these challenges, the semiconductor industry continues to develop a number of advanced fabrication technologies or device configurations, such as strained silicon, HfOx high-κ dielectric layer, FinFETs, nanosheets, and gate-all-around transistors, etc. In spite of the fact that these optimization methods have sustained the scaling of the device, they could only mitigate the problems, and it is still challenging to fundamentally overcome these limitations6. Hence, explorations of alternative computing devices become an imperative issue.
Thanks to the advancements in modern semiconductor manufacturing, microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) can now be reliably fabricated and integrated in on-chip circuits and systems. These devices are capable of using the mechanical motion or vibration for sensing, actuation, radio-frequency (RF) signal processing, as well as for representation of information, i.e., functions of computing and memory7. MEMS/NEMS-based computing/memory devices are endowed with a number of advantages, such as near-infinite subthreshold slope (i.e., a high ON/OFF current ratio can be achieved with a tiny gate voltage change), near-zero leakage current, ultra-low power consumption, harsh environment compatibility, high tunability, and high reconfigurability8. Besides, delicate MEMS/NEMS structures could enable multi-bit memory and computing, offering the potential to increase the density of stored information, as well as make the extraction of information more efficient9. Therefore, such on-chip mechanical computing systems have attracted increasing attentions from researchers around the world as a promising route towards future high-performance computing solutions under the “More than Moore” scheme, revitalizing the idea of mechanical computing from more than a century ago, this time with these highly-integrated solid-state devices as exquisite minuscule computing machines.
In the review, we focused on the working principles, current progresses, as well as challenges and perspectives of nanomechanical computing. Based on the scheme of device motion, MEMS/NEMS-based mechanical computing/memory devices can be classified into two categories: contact mode ones with quasi-static motion (i.e., switches or relays), and non-contact mode ones with mechanical vibration (i.e., resonators or oscillators), as illustrated in Fig. 1. In Section II, contact-mode mechanical memory and computing was summarized. Then in Section III, memory and computing devices based on non-contact mechanical resonators were introduced. In Section IV, important considerations and promising directions for modern nanomechanical computing were discussed. Finally, Section V provided the summary and conclusion.
Fig. 1. Characteristics of MEMS/NEMS-based mechanical computing devices. The left illustration shows a single-pole-double-throw mechanical switch, and the right illustration shows a cantilever-shaped mechanical resonator. |
CONTACT-MODE MEMS/NEMS-BASED COMPUTING/MEMORY
Basic device structures and operation principles
Since silicon-based mechanical switches came into being in 197810, a wide variety of MEMS/NEMS-based contact-mode mechanical computing/memory devices have been explored11. Typically, MEMS/NEMS switches/relays possess movable structures which could conduct either out-of-plane (Fig. 2a-b) or in-plane (Fig. 2c) motion12-14. When the moveable component and the fixed electrode are separated by an air/vacuum gap, there is nearly no current flowing through, thus leading to an ideal OFF state. When the moveable component is actuated to become in contact with the fixed electrode, the current can flow through, leading to an ON state.
Fig. 2. Illustrations of several typical MEMS/NEMS switch/relay structures. a, A cantilever-shaped switch with out-of-plane beam motion. b, An out-of-plane four-terminal switch structure with a body gate. c, An in-plane single-pole-double-throw switch. The fixed electrodes are colored in gold and the moving parts are colored in light gray. |
Electrostatic driving is the most widely used driving scheme among MEMS/NEMS switches15-17. When applying a DC gate voltage (VGS) to the gate (G) electrode and grounding the source (S) electrode, the electrostatic actuating force Fes can overcome the elastic restoring force Fm and deflect the beam. Assuming that a high aspect-ratio gap (so the parallel-plate approximation holds throughout device motion) exists in most device designs, the net force Fnet on the movable part is given by the following formula18,19:
where ε is the permittivity of the air/vacuum gap between the two electrodes, A is the overlapping area of the electrodes, g is the as-fabricated gap between the electrodes, x is the deflection of the moveable component, and keff is the effective spring constant. With the increase of VGS, the electrostatic actuating force increases faster than the elastic restoring one (quadratic vs. linear), and beyond certain deflection, the system can no longer find an equilibrium position (an x value for which Fnet = 0) and the electromechanical pull-in effect would appear. Here the pull-in voltage is dependent on the boundary condition, and can be generally described as: 20. It leads to an abrupt switching with a near-zero subthreshold swing in MEMS/NEMS switches, which is desirable for low-power logic operations17.
In addition to electrostatic driving, other driving schemes have also been investigated, including electrothermal21, electromagnetic22, piezoelectric23, etc. The thermal driving scheme utilizes the thermal expansion in the device structure, but its actuation speed is usually limited by the thermal constants. The magnetic driving scheme applies an external magnetic field to actuate a movable part made of magnetic material or with current flowing through. Generally, the inverse piezoelectric effect was utilized by the piezoelectric driving scheme to induce mechanical motion with an applied voltage. These driving schemes have all been used for actuating MEMS/NEMS switches.
Adhesion between contacting surfaces
When the mechanical contact occurred between the movable and the fixed electrodes, the physical spacing at the contact interface could approach the atomic scale. Therefore, electrodynamic force, which is also known as van der Waals force for shorter range and Casimir force for longer range, become dominant over the elastic restoring force and cause adhesion24-27. Such electrodynamic force is derived from the modification of quantum and thermal fluctuations of the electromagnetic field due to material boundaries, which is intrinsic to these devices.The zero-point energy in vacuum contributes to higher electromagnetic mode density in free space compared with that between the two surfaces, thus making such electrodynamic force attractive for two surfaces in air or vacuum. The adhesion force will lead to hysteresis in their drain current (ID) vs. VGS characteristics, as shown in Fig. 3a-b. When VGS sweeps up and reaches the turn-on threshold voltage, the moveable beam is pulled down to make contact with the fixed electrode, and the device enters the ON state (Fig. 3d), allowing a considerable drain current to flow. Then as VGS sweeps down, for a voltage range below the turn-on voltage, the beam is still stuck to the fixed electrode due to the adhesion force, allowing current to continue to flow. When VGS eventually drops below the turn-off threshold voltage, the electrodes are separated as the elastic restoring force finally exceeds the sum of the adhesion force and electrostatic actuating force, and the device returns to the OFF state with negligible leakage (Fig. 3e). Such hysteresis can be leveraged to realize memory devices, but is undesirable when used as logic devices, as it can lead to device degradation or even failure.
Fig. 3. Hysteretic ID-VGS characteristics of electrostatically driven MEMS/NEMS switches. a, The expected I-V characteristic, with the hysteresis window shown between the turn-on voltage VON and the turn-off voltage VOFF. b-c, Electrical measurement results for two typical silicon carbide (SiC) NEMS switches, showing b normal operation and c stiction. d-e, SEM images of SiC nanocantilever switches when the cantilever is d in contact with the drain electrode (ON state), and e separated from the drain (OFF state). Note that the false-colored SEM image in e is taken from an angle instead of top-down, b-e are adapted from ref.24. © 2020 Wiley-VCH. |
By exploiting this hysteresis window, it is possible to realize a contact-mode mechanical memory unit that stores one bit of information, because the currents of a given VGS in the hysteresis region could be different, which can be controlled by using upward and downward VGS sweeps. Furthermore, in some device designs, the contact may still exist when VGS is fully removed, resulting in non-volatile memory operation, with the retention time exceeding 106 s28. Moreover, such non-volatile memory can work robustly at 200 °C, as measured on a moment-driven serpentine hinge-based NEMS switch29. For silicon nanowire NEMS switches, resistive switching behavior has also been observed after the mechanical contact due to oxidization of the contact surfaces, forming a hybrid NEMS switch and resistive switching memory device20. Such MEMS/NEMS memories are nonvolatile and high-temperature compatible, which opens new avenues for novel memory devices.
In contrast, when used as logic devices, a larger adhesion force may induce metal welding and lead to device failure (Fig. 3c). In order to avoid such effects, some studies have used special contact surface geometries and rougher surfaces to help significantly reduce the adhesion force24,30,31. For example, the adhesion resulting from electrodynamic force can be reduced by up to 25 times compared with smooth surfaces via creating sinusoidal grooves at the contact surface24. The relationship between adhesion force and restoring force in MEMS/NEMS switches can be estimated32, allowing rational design of contact-mode devices with specified “relay mode” (volatile) or “memory mode” (non-volatile). Anti-stiction coating such as self-assembled molecules have also been explored for reducing the chance of stiction33. However, many stiction reduction measures have also reduced the ON current, and active researches are still underway to overcome this important tradeoff.
Low-voltage operation
The air gap between electrodes makes MEMS/NEMS switches exhibit extremely low leakage current and thus high ON/OFF current ratio, and therefore approximately zero subthreshold swing (SS) was caused due to the mechanical pull-in effect, which allows low voltage for switching while maintaining small leakage in these devices34. In comparison, MOSFETs have a minimum SS of ∼60 mV dec−1 at room temperature and a non-negligible subthreshold leakage current, this leads to a relatively high OFF-state leakage power consumption when the threshold voltage is decreased. Furthermore, the short-channel effect will lead to more severe leakage current issue when MOSFETs scale down. In contrast, the near-zero leakage can still be ensured by the air/vacuum gap when the NEMS switches scale down.
By using an anti-stiction molecular coating layer to reduce the contact adhesion force, a NEMS relay Fig. 4 achieves sub-50 mV operation with the help of a body bias33. A silicon-based cantilever NEMS switch with a long beam also reports sub-50 mV switching without body biasing35, showing an SS of 2 mV dec−1 and an ON/OFF ratio of 109. One of the lowest SS values reported for NEMS switches is less than 0.3 mV dec−1, far below that of MOSFETs at room temperature36.
Fig. 4. Representative electrostatically driven MEMS/NEMS switches with low-voltage switching characteristics. a, SEM image of a carbon nanotube NEMS switch, and the measured I-V characteristics of the device, adapted from ref.39. © 2006 American Chemical Society. b, False-colored SEM image of a low-voltage NEMS switch based on a SiC nanowire, including a zoom-in image for the contact region (top), and the measured I-V characteristics showing the switching events from several similar devices, with insets showing the data in semi-logarithmic scales (bottom), adapted from ref.37. © 2010 American Chemical Society. |
Low voltage operation is further ensured by the possibility of scaling in device sizes for NEMS switches. SiC nanowire NEMS switches have been demonstrated (Fig. 4b), with widths as small as ∼20 nm and lateral switching gaps as narrow as ∼10 nm, showing ∼1 V switching37. Air gap down to 4 nm has been demonstrated in a NEMS switch with a pipe clip structure, which results in an operating voltage below 1 V38. NEMS switches based on single-walled carbon nanotubes (SWNTs) have also been demonstrated, showing switching speed down to a few nanoseconds39.
Low-power NEMS logic circuits
One experimental study compares the power consumption of 32-bit adders composed of complementary metal-oxide-semiconductor (CMOS) and MEMS switches40. Despite the relatively larger delay in MEMS switches, their energy-delay products are almost 10 times better than those of the CMOS-based devices. When NEMS switches scale down to the size of a transistor at an advanced technology node, the energy consumption can be further reduced28,41. Moreover, a NEMS switch-based look-up table (LUT) circuit is reported to consume much lower readout energy (1 pJ for 4 output pins) compared with CMOS-based LUTs42. These encouraging results suggest that, with further advancement of nanofabrication technology, it is reasonable to expect that the power consumption (or energy-delay product) of MEMS/NEMS switch-based devices will greatly outperform their CMOS-based counterparts, thus making MEMS/NEMS switch-based logic and memory devices promising candidates for future energy-efficient integrated circuits and systems.
High-temperature compatibility
MEMS/NEMS switches can withstand harsh environments, such as radiation, corrosive gas, or high temperatures far beyond the temperature limit of CMOS devices. For example, high-temperature environments can be found in certain power systems or jet engines, where the temperature may exceed 500 °C43. Si MOSFETs usually fail to operate at such temperatures, due to the fact that the thermally-generated carriers will quickly increase and start to dominate over dopant-induced carriers, and the device cannot be properly turned ON and OFF by the gate voltage. While FETs based on wide-bandgap semiconductors such as SiC44 can mitigate such effect, they could withstand issues such as low switching speed45. In contrast, Instead of operating by controlling the electron concentration as in FETs, MEMS/NEMS switches operate by controlling the nanomechanical contact or separation, which can prevent OFF-state leakage even at elevated temperatures46. As a result, it has been demonstrated that NEMS switches and inverters could operate at temperatures as high as 500 °C (nitrogen environment is used to avoid oxidation), with a leakage current four orders of magnitude lower than that of SiC junction FETs47. SiC NEMS switches have also been reported to operate at 500 °C in ambient air, showing a low switch-on voltage of ∼3 V and no measurable leakage current48,49. High-temperature compatibility of mechanical computing devices is an attractive and unique advantage compared with electronic switching devices50.
Versatile device and integrated circuit design
MEMS/NEMS switches offer a great degree of flexibility in the design of logic devices, which can be leveraged to optimize device performance. For example, the simplest three-terminal switch design (Fig. 2a) faces the issue of trade-off between low actuation voltage and fast switching speed, since the fast switching speed usually requires a beam with large effective spring constant, which then requires a large actuation voltage51. Such challenges can be addressed by the single-pole-double-throw switch design (Fig. 2c)52, apart from providing an opposite electrostatic force to detach the cantilever from the gate to avoid adhesion, the second gate electrode can also decouple the two parameters: when the beam is in contact with one gate, the beam stores elastic energy due to deflection, which can help reduce the required actuation voltage when using the other gate to switch. Furthermore, the switch can have both normally-open (NO) and normally-closed (NC) output pins by placing the drain electrode next to the second gate electrode. Such structure also allows for tri-state switching, in which the cantilever beam does not contact any of the drain electrodes in the third high-impedance state53. NEMS switches can also be integrated with embedded piezoresistive transducers to monitor the contact process, as shown in Fig. 5a-5b25. By exploiting the strong piezoresistive effect in the two silicon nanowires attached to the switch, one can monitor cold switching events, especially when the contacts are not highly conductive or are degrading over time. Moreover, four-terminal switches with gate, drain, source, and body electrodes can mimic both n-type and p-type MOSFETs by simply changing the body electrode to connect with VDD or GND (Fig. 2b)14.
Fig. 5. Various MEMS/NEMS switch structures showing distinct features for computing. a, SEM image with measurement scheme for a cantilever with two gates (G1 and G2) and two integrated piezoresistive transducers (P1 and P2). b, Measured switching characteristics of a similar device as in a, with blue solid lines showing the gate current and red dashed lines showing the piezoresistive transducer current, adapted from ref.25. © 2021 IOP Publishing Ltd. c, SEM image of a NEMS memory switch with state "1" (conducting), and d, measured I-V characteristics; adapted from ref.53. © 2020 IEEE. e-f, A MEMS relay-based full adder circuit, with e the SEM image showing the terminal arrangements for the sum bit of the adder, and f measurement results of this mechanical adder, adapted from ref.57. © 2021 IEEE. |
As MEMS/NEMS switches are similar to MOSFETs in terms of their ON/OFF switching function, it is possible to realize circuits based on conventional semiconductor devices using mechanical switches. A variety of circuits have been proposed and demonstrated using MEMS relays, such as adders, accumulators, static random-access memories (SRAMs), dynamic random-access memories (DRAMs), flip-flops, digital-to-analog converters (DACs), and oscillators40. For example, it has been demonstrated that a MEMS switch-based oscillatorcould be applied for the implementation of an Ising machine54. MEMS/NEMS switch-based memory units55 and even memory array-based field-programmable gate arrays (FPGA)56 have also been explored. Although the current switching speed of MEMS switches is not as high as that of CMOS circuits, it can be further optimized by reducing the number of devices in the critical path or further scaling down the device sizes. For example, it has been experimentally demonstrated that a MEMS switch-based full adder requires only 16 devices, which is less than 28 devices required for a traditional CMOS adder57.
Challenges and prospects for optimizing the actuation voltage, speed, and lifetime
Despite the existing advantages of MEMS/NEMS switches, there still remain several challenges, specifically, the operation voltage needs to be lower, the device size smaller, the operating speed higher, and the lifetime longer. To minimize the switching voltage, a large capacitance is desirable, thus a larger area or a smaller air gap is needed58,59. However, smaller air gap may degrade the reliability60. On the other hand, the switching time during the pull-in process is , where VPI is the pull-in voltage and ω0 is the fundamental flexural mode angular frequency of the movable component37. This indicates a trade-off between minimizing the actuation voltage VGS and switching time.
Continuous efforts have been made to address these challenges. By using carbon nanotubes39,61 or silicon nanowires62 for NEMS switches, a high resonance frequency ω0 could be potentially achieved, which leads to fast operation with small voltage. A numerical analysis suggests that the actuation voltage and switching speed of cantilever-shaped inverters could be lower than 0.7 V and 1 µs, on condition that the nanoscale devices can be reliably fabricated63. In another attempt, a contact region gap was designed to be much smaller than the actuation gap, allowing the MEMS/NEMS switches to operate in non-pull-in mode, which achieved a switching voltage of down to 50 mV36. Reducing the actuation voltage can significantly improve the device's lifetime64. When these NEMS switches are actuated in dynamic mode of operation with intermittent mechanical contact, the actuation voltage is usually reduced, and “hot” switching (with current flowing through) of 106 cycles has been demonstrated at an actuation speed of 1 kHz65. When the cantilever beams are operating in the resonant mode and with the tips tapping on the contact electrodes, over 10 billion cycles in “cold” switching mode (with contact but no current flowing through) have been demonstrated with milli-Volt actuation voltage66. Furthermore, by engineering the contact material, the lifetime can also be improved, and over 1010 cycles of switching have been achieved by using ruthenium dioxide (RuO2)-Au contacts67.
Static bistability and multistability
Static bistability and multistability can be achieved by engineering the device structure, which can form two or more stable states which require no static power for maintaining the state, and are promising for developing new types of computing and memory devices. Bistable behavior has been observed in a curved double-beam structure with the mid-points clamped together, where the buckled beam can be reconfigured to two stable shapes68. Simulation of the bistable MEMS devices with electrostatic actuation were also conducted by adopting the latching mechanism in a curved and prestressed beam69. Electrothermal tuning has also been experimentally demonstrated for bistable MEMS devices by using the self-latching mechanism70. The footprint of the bistable device can be reduced by using a single electrode for bidirectional switching, with the compressive stress controlled by the Joule heating71. Mechanical static logic devices can be modelled and designed using bistable buckled beams72. In addition, both the pull-in voltage and the snap-through voltage can be decreased significantly by redesigning the shape of gate electrodes73.
Beyond bistable MEMS devices, multistability has also been demonstrated. Tristability has been achieved by exploring the floating, arc-shaped and S-shaped states in cantilevers, induced by electrostatic and surface forces74,75. A tristable MEMS switch has also been achieved by designing a single-pole-double-throw structure, in which the three stable states include the beam contacting each of the two ports, and an OFF state where the beam is in the middle76. Furthermore, curved coupled beams have also been used to demonstrate tristable devices77. Further researches, such as decreasing the voltage required to switch between different states, increasing the reliability for changing the state, and developing structures with even more stable states, will be promising to drive these static bistable or multistable MEMS/NEMS devices towards future applications.
In summary, MEMS/NEMS switches exhibit a series of obvious advantages, such as near-zero subthreshold leakage current, ultra-low subthreshold swing, ultra-low power operation, and harsh environment compatibility. These devices can be fabricated with processes compatible with CMOS processes30 and are highly scalable. Meanwhile, there still remain open challenges that require further investigation, which can potentially lead to practical applications of these devices.
RESONANT-MODE MEMS/NEMS-BASED COMPUTING/MEMORY
In addition to MEMS switches that flip only when the input signal changes, there are also MEMS computing devices which operate in resonant mode, i.e., constantly vibrating. Some resonant MEMS/NEMS devices operate in contact mode, or more precisely, tapping mode (as in atomic force microscope, or AFM), and are less susceptible to issues such as stiction78. However, most resonant MEMS/NEMS computing devices operate in non-contact mode, which will be discussed in greater detail in part below.
Operation principles and typical device structures
The contact-mode switches discern the ON and OFF states for logic operations based on the change of conductance, which are similar to MOSFETs, however, the non-contact resonant MEMS/NEMS computing devices are different. They use the vibrational amplitude at a certain frequency, or the resonance frequency, to represent different logic states79. These devices are suitable for computing, moreover, they can also be used as memory units by exploring various physical phenomena intrinsic to these devices.
The ultralow power operation, which is resulted from the absence of static current flowing through the device, is an important potential advantage of non-contact devices. The minimum operating power level required to operate a NEMS resonator is to drive the amplitude just above thermal fluctuation, which can be estimated using 80. For a NEMS resonator operating at such minimal amplitude, the power level can be down to 10 attowatts (10−17 W) level. This suggests that, one can achieve 105 signal-to-noise ratio in NEMS resonators in theory just with picowatt (10⁻12 W) level of input.This input is sufficient for most computation applications, while at least six orders of magnitude smaller power is consumed compared with MOSFETs, which is typically microwatt (10−6 W) level (estimated using 1 fJ per switch81 with 1 GHz switching rate).
As MEMS/NEMS resonator can assume a number of geometries/clamping conditions (Fig. 6), such as singly-clamped82, doubly-clamped83, fully-clamped84, or more complicated geometries such as free-free beam85 or comb-drive structure86. The driving mechanisms can include electrostatic83, photo-thermal87, magnetomotive88,89, photo-acoustic90 and piezoelectric79, etc., and the choice of driving mechanism is often related to the geometry. For example, magnetomotive actuation requires that a current pass through the resonant body, and is therefore used more in doubly-clamped structures and does not work for singly-clamped ones.
Fig. 6. Illustrations of representative MEMS/NEMS resonator structures. Schematic illustrations of a, a cantilever resonator; b, a doubly-clamped beam resonator; c, a fully-clamped circular membrane resonator; and d, a free-free beam resonator. Anchors are colored in light gray, initial positions are colored in yellow, and motion in fundamental-mode resonances are shown (translucent). |
Resonance frequency tuning
The computing functionality of MEMS/NEMS resonators can be achieved by frequency tuning91,92, which results in different resonance amplitudes at a given frequency and thus can be used to represent logic “1” or “0” states. Using a lumped model, the resonant frequency can be written as , where keff is the effective spring constant, and meff is the effective mass. The resonance frequency can be tuned by different mechanisms such as strain or temperature. In some NEMS resonators with high aspect ratios, the frequency can be efficiently tuned by strain because these resonators are in the string or membrane limit93-98. For example, one-dimensional (1D) carbon nanotube resonators show up to 2000% frequency tuning by using a piezoelectric substrate to generate strain99, and two-dimensional (2D) graphene resonators show up to 1300% frequency tuning by using Joule heating to induce additional strain100. The static deflection induced by gate voltage can also efficiently induce tensile strain in the suspended resonant structure. For a tungsten diselenide (WSe2) resonator, a frequency tuning range Δf/f0 of 231% can be achieved with just 10 V of gate voltage101. These values are much higher than those in larger Si-based MEMS resonators, which typically have a frequency tuning range of about 10% or less102,103, and can be potentially beneficial for low-power operation of frequency-shift-based MEMS/NEMS computing.
Resonator-based computing with high reconfigurability
High reconfigurability is another attractive feature for MEMS/NEMS resonator-based computing. For example, by tuning resonance frequency, MEMS/NEMS resonators are capable of implementing several basic logic gates using a single device.Some devices use two DC voltage (which, when applied, can shift the resonance frequency) as 2-bit inputs105. When the input logic is (0, 0), the resonance frequency is at f0; as for (0, 1) or (1, 0), the frequency is shifted to f1; when the input is (1,1), it further shifts to f2 (Fig. 7b). By using f2 as the reference frequency, an AND gate can be realized, as the S21 is sufficiently high (> −80 dB) only when the input logic is (1, 1). The resonator can also implement NOR, NOT, XNOR, and XOR gates by selecting different reference frequencies without changing the connections. By extending such a design, n-bit logic can be realized by simply adding n parallel DC biases106. Fig. 7a-c hereby show another example107.
Fig. 7. Resonators as reconfigurable logic devices. a, SEM image of a doubly-clamped beam resonator performing two-input logic operations. b-c, Frequency response when implementing the b XOR and c OR logic operations using the resonator in a. a-c are adapted from ref.107. © 2018 AIP Publishing LLC. d, Illustration of a cantilever resonator-based reconfigurable logic device. e, Simulated resonances when the device in d functions as XOR or AND gates. d-e are adapted from ref.92. © 2021 IOP Publishing Ltd. |
Compared with electrothermal frequency modulation, electrostatic tuning can exhibit faster response and lower power consumption, and reconfigurable logic functionalities can also be achieved. Such devices are of highly varied designs, and can exhibit four108, six92, or any other number of logic inputs. In the six-input device, for example, when AC signals are used as inputs, the resonance amplitude is directly modulated by the input signal. When DC voltages are used as inputs, the resonance frequency is tuned, and by using the connection shown in Fig. 7d-e, the logic function can be reconfigured to XOR or AND gates depending on whether X1 is fixed to logic “1” (1 V in this case) or “0”. Therefore, MEMS/NEMS resonators have the potential to reduce the overall complexity of digital circuits due to their reconfigurability. Furthermore, these logic devices can be cascaded into more complex circuits and systems107,109. With scaled nanofabrication technology, such reconfigurable resonator logic devices can exhibit energy consumption per operation on the order of 1 aJ (10−18 J) with resonance frequency above 1 GHz110, and thus are promising to be used in ultralow power logic circuits.
MEMS/NEMS resonators also provide the ability to perform multiple logic functions in parallel within a single device by using multiple output ports with different configurations, thus offering additional flexibility in applications. In one example, OR/NOR logics and XOR/AND/NOR logics are demonstrated using different parts within the same MEMS resonator111. In another example, multiple channels of binary information are encoded in the same MEMS resonator using mechanical oscillations at different frequencies, which allows logic operations to be executed simultaneously112.
Resonators for memory
The resonant response can be driven into the nonlinear regime by increasing the driving force in these MEMS/NEMS resonators. Analytical solution of the nonlinear response shows a bistable state in a certain frequency range, which can be used to represent two logic states. Such logic states can be set by choosing the frequency sweeping direction (Fig. 8a)113,114. For a 2D molybdenum disulfide (MoS2) NEMS resonator shown in Fig. 8b, two such states can be obtained this way (Fig. 8c-d)115. Typically, a stronger driving can lead to a larger hysteresis region and thus a greater operation window (in terms of frequency) for such NEMS memory device. The hysteresis window can also be tuned by DC gate voltage116, however, DC tuning can also lead to frequency shift which might be undesirable in certain applications.
Fig. 8. Nonlinear responses and memory characteristics in MEMS/NEMS resonators. a, Duffing nonlinear frequency response showing a bistable state (formula in ref.114 is used), with the unstable solution defining a bi-stable window between f1 and f2. The colored arrows indicate that the two states can be accessed via different frequency sweeping directions. © 2021 Nature Publishing Group. b, Optical image showing a circular drumhead MoS2 NEMS resonator. c, Nonlinear resonance spectra showing that the hysteresis window is tunable by the RF driving voltage vg. d, Memory operation by applying voltage pulses. b-d are adapted from ref.115. © 2022 IEEE. |
Nonlinear resonators can be used not only for memory, but also for computing. By utilizing the nonlinear bistability in a doubly-clamped beam resonator, several basic logic gates are demonstrated117. Specifically, the two stable states within the bistability can be viewed as two local energy minima separated by a potential barrier. When a perturbation signal exceeds the threshold, the device can be switched between the two steady states (different resonance amplitudes), with which the AND/NAND logic gates are achieved, and NOT logic is realized by just inverting the amplitude-logic representation. In another example, both logic and memory functions are achieved in the same comb drive resonator118,119.
Besides vibrational amplitude, memory function can also be realized by exploiting other degrees of freedom in NEMS resonators, such as frequency. In one such example, a 2D resonator showing thermal hysteresis in its resonance frequency can make a thermally modulated memory120. After each switching, no additional energy is required by the resonator requires to maintain its resonant frequency, making it a promising candidate for ultra-low power non-volatile memories.
Resonators for neuromorphic computing
Human brains are inherently less power-consuming and more intelligent in many ways than digital computers, therefore neuromorphic computing beyond the von Neumann architecture has emerged since the 1980s121, and has attracted increasing interest due to the advances in device technology and algorithms. Due to the complex behaviors of the human brain and neurons, mainstream analog and digital components are generally not efficient in terms of area and energy when implementing neuromorphic systems. Conversely, other devices with rich dynamic behaviors, such as MEMS/NEMS, may be more efficient in simulating the spiking dynamics and other behavior of biological neurons, and may truly enable the ultra-low power computing in biological systems122. Neurocomputers based on oscillators have been proposed, which can shrink the n2 connections using conventional neurocomputers to n dynamic connections using oscillatory neurocomputers (for n neurons), by coupling through a common medium123. Numerical simulation of such oscillatory neurocomputers has been achieved using coupled nonlinear MEMS self-sustained oscillators with feedback loops, which can robustly operate even with noise sources and manufacturing process variations124. Based on the firing rate theory, simulation of the MEMS-based continuous-time recurrent neural network (CTRNN) exhibits high energy efficiency and high accuracy in classification for human activity recognition125. Another neuron firing rate model, the dynamic field theory, has also been experimentally implemented using double cantilever MEMS capacitive accelerometers by leveraging their bistability and hysteresis122. In addition, colocalized sensing and computing has been experimentally demonstrated with finger arrays of parallel plate actuators adopting the usually undesirable pull-in/pull-out hysteresis, which expands the CTRNN concept using MEMS devices126. Furthermore, genetic algorithm has been adopted to train MEMS networks for solving the categorical perception problems127.
Recently, emerging MEMS-based neuromorphic computing schemes such as reservoir computing (RC) have attracted increasing attention. A typical RC system consists of an input layer, a reservoir which is not trained, and an output layer which will be trained. MEMS/NEMS resonators and oscillators can function as the reservoir. Delay-based RC using time-multiplexed scheme has been demonstrated using a single Duffing nonlinear MEMS oscillator, with high accuracy in time series classification tasks128. Colocalized sensing and delay-based RC has been experimentally achieved by using a MEMS accelerometer as the reservoir129. A similar MEMS neuroaccelerometer that uses RC with delayed feedback to process the acceleration data locally can accurately simulate the nonlinear autoregressive moving average model and process random bit streams130. Non-delay-based RC with a single MEMS resonator has also been achieved by leveraging the hybrid nonlinear dynamics, including transient nonlinear response and Duffing nonlinearity, which can remove the time-delayed feedback and improve efficiency for RC131. To improve the prediction accuracy in nonlinear transformation tasks, a pre-training method is used to tune the parameters of MEMS-based reservoir132. Despite the development of these RC systems achieved using MEMS/NEMS devices, further improvements remian to be made in a number of aspects such as the tuning of nonlinearity and dynamics, device scaling, and external circuit optimization, which are being actively researched.
Emerging NEMS computing devices
NEMS-based computing devices have been explored in quantum computing studies, for example as nanomechanical quantum bits (qubits)133,134. When using NEMS resonators for qubits, an anharmonic potential is necessary. Carbon nanotube NEMS qubit has been proposed by inducing strong anharmonicity through coupling the flexural resonance mode to the charge states of a double quantum dot135. In addition, the design with an array of doubly-clamped resonators such as carbon nanotubes, which is coupled to a common resonance mode of a high finesse optical cavity such as the evanescent field of a whispering gallery mode cavity, have also been proposed136. Atomically thin graphene resonant NEMS systems have also been proposed to exhibit anharmonicity in the quantum regime by leveraging its strong Duffing nonlinearity. With a lateral size of ∼10 to 30 nm, sufficient anharmonicity in potential can be realized to form 2D NEMS qubits137.
By exploring parametric oscillation in NEMS/MEMS resonators138, Ising Hamiltonian can be realized by building networks of parametric oscillators (“parametrons”)139. Furthermore, an Ising machine is proposed by exploring the strong bilinear coupling and detuning between two parametrons140. Compared with conventional CMOS circuits, such Ising machines could be used to solve hard combinatorial optimization problems with a potentially higher speed and better energy efficiency. Variations of the Ising model could simulate neural networks such as the Hopfield network or Boltzmann machine.
Moreover, MEMS/NEMS resonators also show promises for emerging computing paradigms such as reversible computing. For example, a MEMS Fredkin gate (one type of reversible logic gate) has been experimentally demonstrated by interconnecting four doubly-clamped beam resonators141. Due to the fact that not a single bit of information is deleted during the calculation, such reversible logic devices have the potential to overcome the von Neumann-Landauer (VNL) limit.
In addition, by modulating either the amplitude or the frequency of the excitation signal applied to the resonator, generation of chaotic signal has been experimentally and numerically demonstrated using a nonlinear MEMS resonator142. Also, bistable states have been achieved using curved doubly-clamped beams with dynamic trapping, and the transition between the two stable states can be achieved by stepwise control of the voltage143.
PROSPECTS OF MEMS/NEMS-BASED COMPUTING/MEMORY
Challenges towards future applications
While MEMS/NEMS-based computing devices have exhibited unique advantages and promises to be alternatives to traditional semiconductor electronic devices, there still remain some challenges. Firstly, due to the fact that modern integrated circuits often include millions or more logic gates, large-scale integration of MEMS/NEMS devices is still essential. However, at such a scale, it would be difficult to control the uniformity and yield of MEMS/NEMS devices. Secondly, further optimization for the device properties of MEMS/NEMS devices is required. For contact-mode MEMS/NEMS switches, the contact degradation and stiction issue need to be better resolved, and the switching voltage and delay remian to be further reduced. For noncontact-mode MEMS/NEMS resonators, there is still room for further optimization in the aspects of the resonance frequency, quality factor Q, and frequency tuning properties. Furthermore, when cascading these MEMS/NEMS-based logic devices, additional electronic components such as buffers and amplifiers are often required, which poses considerable challenges for scaling up mechanical circuits. To address such issues, MEMS/NEMS resonators and oscillators with intrinsic gain would be particularly useful, and certain neuromorphic computing that does not require cascading can offer practical alternatives to conventional logic circuits. Finally, before electronic design automation (EDA) techniques can be applied to MEMS/NEMS-based large-scale circuits and their heterogeneous integration with CMOS circuits, circuit design for driving and readout device arrays and device equivalent-circuit models are still required.
Comparison with other devices
In Table 1, several aspects of NEMS-based computing devices were qualitatively compared with mainstream MOSFETs and resistive random-access memories (RRAMs)144-146. Currently, transistors driven by Moore's law are still dominant, so mechanical computing is expected to be used in niche applications, such as internet of things (IoT) devices with strict power constraints, devices operating in harsh environments, or when reconfigurability is more important than scale and speed. In addition, hybrid computing devices (such as CMOS-MEMS) provide unique possibilities by combining the advantages of different device techniques102,147. For example, a resonator-based memory can be integrated with heterojunction FETs to directly transduce resonance into electrical signals90. Such hybrid devices can possess both the advantages of CMOS devices such as high operation speeds, and the unique characteristics of mechanical devices such as low power and high reconfigurability.
Table 1. Comparison of individual NEMS-based computing device with other computing devices. |
| Device characteristics | MOSFET | RRAM | NEMS-based computing |
|---|---|---|---|
| Static power consumption | ∼10⁻9 W | Zero when not writing/reading | ∼10⁻12 W96 |
| Reconfigurability | Poor | Poor | Good |
| High temperature (≥ 500 °C) compatibility | No | Fair144 | Yes47 |
| Reversibility | Not yet reported | Not yet reported | Yes141 |
| Switching speed | GHz | 10-100 MHz145 | GHz146 |
| ON/OFF ratio | > 105 | > 102 145 | > 109 35 |
| Subthreshold swing (300 K) | ≥ 60 mV dec−1 | N.A. | Near zero36 |
Unique advantages offered by nanomaterials
NEMS based on 1D & 2D nanomaterials have emerged rapidly, and the clear advantage of which is that the resonance frequencies can be highly tunable by strain84,148. Owing to the fact that the functions can be easily reconfigured by altering the resonance frequency, tunability provides a useful degree of freedom when the resonators serve as computing devices. Another appealing aspect is that the power consumption of 1D & 2D NEMS can be orders of magnitude lower than that of the mainstream MEMS devices, which is mainly ascribed to the small mass of atomically thin resonant material.
Estimation of device performance
To offer an overview and comparison of the performance matrixes of various 1D & 2D NEMS devices, a number of device parameters were summarized in Table 2, including two key parameters: the energy consumption per logic operation, and the switching time which is directly related to operating speed. Here, how these two parameters are estimated is described.
Table 2. Comparison of performance parameters of some MEMS/NEMS resonators. |
| Metrics | Figure 4a in Ref.83 | Device F in Table S2 in Ref.96 | Ref.153 | Ref.90 | Ref.154 | Ref.104 | Ref.106 | Ref.109 | Ref.141 | Ref.155 | Ref.156 | Ref.157 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Structure | Doubly-clamped (2D) | Circular (2D) | Circular (2D) | Micro-cantilever | Nano-cantilever | Doubly-clamped | Doubly-clamped | Doubly-clamped | Doubly-clamped | Doubly-clamped | Doubly-clamped | Doubly-clamped |
| Material | Graphene | MoS2 | Graphene-MoS2 bimorph | GaN | Silicon | Silicon | Silicon | Silicon | Silicon | Silicon | Silicon | GaAs |
| Dimensions/µm | L = 2.7, W = 0.63, t = 5 nm | D = 1.5, t = 1.4 nm | D = 6, t = 1 nm | L = 250, W = 100, t = 1.3 | L = 10, W = 0.7, t = 0.75 | L = 15,W = 0.75, t = 1.85 | L = 500, W = 3, t = 30 | L = 600,W = 3, t = 30 | L = 20,W = 0.3, t = 0.5 | L = 500, W = 3, t = 30 | L = 500, W = 3, t = 30 | L = 260, W = 84, t = 1.35 |
| Aera/µm2 | 1.70 | 1.77 | 28.27 | 25000 | 7 | 11.25 | 1500 | 1800 | 6 | 1500 | 1500 | 21840 |
| Eigenfrequency f/MHz | 35.8 | 89.9 | 15.58 | 0.01569 | 7.47 | 23.36 | 0.1177 | 0.2 | 3 | 0.1215 | 0.1241 | 0.1379 |
| Energy per Operation/ Critical Energy Ec/J | 1.7 × 10−18 | 8.6 × 10−17 | 4.9 × 10−20 | 1.0 × 10−13 | 1.0 × 10−15 | 2.5 × 10−9 | 4.0 × 10−5 | 1.2 × 10−13 | 1.1 × 10−17 | 5.3 × 10−7 | 1.0 × 10−13 | 8.3 × 10−14 |
| Switching Speed ts/s | 1.6 × 10−6 | 4.0 × 10−7 | 4.2 × 10−5 | 6.0 × 10−1 | 6.0 × 10−5 | 2.3 × 10−5 | 4.2 × 10−3 | 6 × 10−3 | 6.7 × 10−5 | 5.3 × 10−2 | 6.1 × 10−2 | 8.3 × 10−1 |
| Quality Factor Q | 60 | 38 | 690 | 9450 | 450 | 820 | 490 | 1200 | 200 | 6103 | 7600 | 115000 (@2.5 K) |
| Resonant Body Mass M/kg | 1.9 × 10−17 | 1.2 × 10−17 | 1.1 × 10−16 | 2.0 × 10−10 | 1.2 × 10−14 | 4.8 × 10−14 | 1.0 × 10−10 | 1.2 × 10−10 | 1.2 × 10−14 | 1.0 × 10−10 | 1.0 × 10−10 | 1.6 × 10−10 |
| Effective Spring Constant keff/N·m−1 | 0.7 | 1.1 | 0.295 | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| Critical Amplitude ac/nm | 3 | 17 | 0.78 | 2810 | N/A | N/A | N/A | N/A | N/A | N/A | N/A | 8.15 |
For energy consumption, the energy Ec required to sustain the largest possible vibration amplitude which is still linear was calculated, so as to avoid underestimation. A common choice for such amplitude is the 1 dB compression point below critical amplitude ac, which is equal to 0.745ac, a value often considered as the onset of nonlinearity149. In this case, Ec can be calculated by the following formula96:
where keff is the effective spring constant, and the critical amplitude ac can be extracted from the backbone curve from a family of the resonator's Duffing nonlinear frequency responses with increasing driving amplitudes96. The term keff can be calculated using , where Meff denotes the effective mass of the resonant body, and ωdenotes the fundamental-mode resonance angular frequency.
The switching time was evaluated from the settling time ts to reach the new steady state upon actuation or perturbation. We model the settling process from the initial position to the new position as the damped motion of a resonator, which is released from a finite displacement x0 (initial position) and settles toward the new equilibrium position (x = 0). The time-dependent displacement x is150:
The device is considered to have reached the new steady state if x < 5% x0. The time it takes to achieve this is151:
Therefore, the settling time can be calculated by simply using Q and f. As a good approximation, is also used in the literature152.
Scaling of device performance
Further summary of the energy per logic operation and switching time for different devices was conducted and shown in Fig. 9. We observe a clear trend that both the energy consumption and the switching speed improve with the shrinking of the device size. In comparison, the first-generation 74HC00 CMOS logic IC consumes about 100 mW at the frequency of 50 MHz, roughly corresponding to 10−10 J per switch158. With 0.35 µm CMOS technology (a decade ago), a basic CMOS inverter gate consumes about 10−13 J per operation159. Using 7 nm technology node or beyond, the CMOS inverter consumes fJ (10−15 J) or sub fJ per operation160. Here, 2D NEMS resonators may consume theoretically as little as aJ (10−18 J) energy or even less (orange markers in Fig. 9) with large device footprint (achievable with older technology node), which opens up a promising pathway for ultralow-power computing.
Fig. 9. Summary of speed, energy, and size of some representative MEMS/NEMS resonators. The diameters of the markers represent the device lateral size, and the color represents the device type: blue for doubly-clamped beam, green for micro-cantilever, violet for nano-cantilever; and orange for 2D material-based resonators. All data used for this chart are presented in Table 2. |
CONCLUSIONS
In the review, an overview of MEMS/NEMS-based memory/computing devices was presented, including their operating mechanisms, state-of-the-art research progresses, outstanding challenges, and perspectives for their future applications. Compared with their MOSFET counterparts, these mechanical computing devices could potentially show better performanceand may enable different computing paradigms. Contact-mode MEMS/NEMS switches exhibit several advantageous characteristics, including near-zero leakage current, very low subthreshold swing and high-temperature operation, many of which are unavailable in the prevailing MOSFETs. Non-contact mode MEMS/NEMS resonators demonstrate a lot of superior performances, such as extremely high reconfigurability, nonlinearity for memory and computing, high tunability, and ultra-low power consumption, all of the above characteristics are highly desirable for devising new computing paradigms. With research continously conducted in this field, technological breakthroughs for these MEMS/NEMS devicescan be potentially achieved in several areas, such as ultralow-power computing, harsh environment computing, reversible computing, neuromorphic computing, in-memory computingand reconfigurable computing. Centuries after their inauguration, mechanical computing devices, now at a totally different scale, could once more play an important role in computing — enabling next-generation computing paradigms.
MISCELLANEA
Acknowledgements We gratefully acknowledge the support from National Natural Science Foundation of China (Grants 62250073, U21A20505, U21A20459, 62150052, 62104029, 12104086, 62004026, 62004032, 62104140), Sichuan Science and Technology Program (Grants 2021YJ0517, 2021JDTD0028), Fundamental Research Funds for the Central Universities (ZYGX2020ZB014 and ZYGX2020J029), Lingang Laboratory Open Research Fund (Grant LG-QS-202202-11), Biren Technology-Shanghai Jiao Tong University Joint Laboratory Open Research Fund, and Science and Technology Commission of Shanghai Municipality (STCSM) Natural Science Project General Program (Grant 21ZR1433800).
Declaration of Competing Interest The authors declare no competing interests.
