Dynamic Slingshot Operation for Low-Operation- Voltage Nanoelectromechanical (NEM) Memory Switches

A dynamic slingshot pull-in operation is presented by using the influence of inertia and damping on the nanoelectromechanical (NEM) memory switch operation. To confirm the validity of the proposed idea, a finite element analysis (FEA) simulation, that reflects the actual cantilever beam structure, is performed, and an analytical one-dimensional (1D), the parallel plate model is tested. According to the analytical and FEA data, the dynamic slingshot pull-in voltage can be achieved ~0.78 times and ~0.73 times lower than conventional pull-in voltage under near-vacuum conditions, respectively. It is also shown that the proposed dynamic slingshot operation is more effective for lowering operation voltage ( $V_{\mathrm {DD}}$ ) and boosting the chip density of complementary-metal-oxide-semiconductor (CMOS)- NEM hybrid reconfigurable logic (RL) circuits than the static slingshot operation.


I. INTRODUCTION
Conventional complementary-metal-oxide-semiconductoronly (CMOS-only) reconfigurable logic (RL) circuits, a well-known example of which is a field-programmable gate array (FPGA), suffer from some fundamental limitations including, low chip density, high energy consumption, and low speed [1], [2]. These limitations mainly stem from the fact that routing blocks (RBs) that determine data signal paths consist of CMOS devices horizontally integrated on a silicon substrate suffering from high leakage current and high resistance. To address these issues, researchers have tried to replace CMOS devices with novel routing devices such as nanoelectromechanical (NEM) memory switches [3]- [6]. Fig. 1 shows the conceptual view of our previously proposed monolithic-three-dimensional (M3D) CMOS-NEM hybrid RL circuit and NEM memory switch [7], [8]. As NEM memory switches can be integrated with metal The associate editor coordinating the review of this manuscript and approving it for publication was Chaitanya U. Kshirsagar. interconnection layers using the CMOS backend process, CMOS-NEM hybrid RL circuits achieve higher chip density, higher performance, and lower power consumption than CMOS-only circuits [7]- [12]. These merits make the NEM memory switch as attractive as the routing switch. Fig. 1(b) shows the conceptual view of a NEM memory switch whose movable cantilever beam length, width, and thickness are expressed as L beam , W beam , and t beam , respectively. Conventionally, as shown in Figs. 1(b) and 2(a), the movable beam is separated from the two metal electrodes, called selection lines (L1 and L2), by air gaps (t gap ) in the pristine state. Pull-in occurs if the voltage applied between the beam and selection line is greater than the pull-in voltage (V p ): the movable beam becomes stuck to either L1 (State 1) or L2 (State 2) due to electrostatic force. The voltages applied to L1 and L2 are called V L1 and V L2 , respectively. Subsequently, to toggle between states 1 and 2, the applied voltage should exceed the switching voltage (V s ). More details on the conventional operation of NEM memory switches have been presented in prior studies [7]. One of the most critical problems of M3D CMOS-NEM hybrid RL circuits is the high operation voltage (V DD ) of the NEM memory switches [8], [13]. This is challenging because if the V DD of the NEM memory switch is higher than that of the CMOS logic circuits, the overall V DD of M3D CMOS-NEM hybrid RL circuits will increase. According to prior studies, the V DD of the NEM memory switches is determined by V p when the L beam is optimized to achieve minimum V DD [13]. The V p reduction of NEM memory switches is thus the key to lowering the overall V DD of M3D CMOS-NEM hybrid RL circuits. Conventionally, V p is reduced by introducing new structures and materials [15]- [17]. However, they have limitations in terms of CMOS-process compatibility and chip density.
Slingshot operation has recently been proposed as a novel pull-in method for lowering V p while maintaining structures and materials [18]. The feature of the slingshot is to perform a pull-back operation before the pull-in operation to store elastic potential energy (E pot ), which reduces the electrical energy (E elec ) required for the pull-in operation following the energy conservation law. It is noteworthy that the slingshot pull-in operation is only a small fraction of the whole operation of NEM memory switches. Thus, the latency and FIGURE 2. NEM memory switch operations using three kinds of pull-in operation methods: (a) conventional pull-in operation, (b) the static and (c) the proposed dynamic slingshot pull-in operation. Note that the switching operation between State 1 and 2 is the same in the three cases. NEM memory switches store higher potential energy in the case of the dynamic slingshot operation than in the case of the static slingshot operation during their pull-back operation. energy consumption originated from the pull-back step of the slingshot pull-in operation due is not critical. It has been proven, in a prior study, that V p using static slingshot operation (V p,sling,st ) is theoretically ∼0.84 times lower than conventional V p without slingshot operation (V p,conv ), assuming an analytical parallel plate model [18]. V p,conv is written as where k is the beam spring constant, and ε 0 is the vacuum permittivity.
The study, however, is limited to static analysis and a onedimensional parallel plate model. In the case of the static analysis, the time-dependent terms, such as inertia and damping, affecting the actual beam operation are ignored. This means that V p,sling , derived by static analysis, can be different from that derived by dynamic analysis [19]. Additionally, the one-dimensional (1D) parallel plate model may lead to error, as it does not reflect the actual beam structure [20]. This study thus proposes a dynamic slingshot operation for further reduction of V p , which eventually lowers the overall V DD of M3D CMOS-NEM hybrid RL circuits. Furthermore, the study accurately evaluates the value of V p using dynamic slingshot operation (V p,sling,dy ) using the dynamic analytical model and 3D finite element analysis (FEA) simulation, and compares it with the previously proposed static slingshot operation case.

II. RESULTS AND DISCUSSION
Figs. 2(b) and 2(c) compare the proposed dynamic slingshot operation with the previous static one of a NEM memory switch. Following the pristine state, it is assumed that pull-back occurs toward L2, and pull-in occurs onto L1. The absolute values of x r,st and x r,dy , which have negative values in the coordinate system, are defined as the static and dynamic pull-back distances, respectively. In the case of the static slingshot operation, the optimized static pull-back position (x r,st,opt ) that minimizes V p is −t gap /7 and the optimized V p,sling,st (V p,sling,st,opt ) becomes ∼0.84 times lower than V p,conv , as shown in previous research [18]. On the contrary, in the case of the proposed dynamic slingshot operation, the optimized x r,dy (x r,dy,opt ) can be made larger than x r,st,opt , indicating that more E pot can be stored in the movable beam owing to the inertia effect. Assuming a vacuum environment in which the quality factor (Q) is infinite, using the dynamicmode d'Alembert's equation, the V L2 required to pull the movable beam back to x is derived as [21], Then, by replacing x with x r,dy , the pull-back voltage (V p,back ) in the dynamic slingshot operation (V p,back,dy ) is determined by, When V p,back,dy is applied to L2, the beam is pulled back to x r,dy , which means that the movable beam stores E pot (x = x r,dy ). Once the pull-back operation is completed, 0 V is applied to L2, and V L1 is applied to L1 to add E elec to E pot (x = x r,dy ). Subsequently, the beam moves towards L1, making x = x f,dy. x f,dy is defined as the pull-in distance under the dynamic slingshot operation. When the movable beam reaches x = x f,dy , following the energy conservation law, it stores E pot (x = x f,dy ) as follows: E elec is derived as, Each term in (4) is expressed as follows: Combining (4)- (7), the V L1 required to move the beam from x r,dy to x f,dy (V L1 (x r,dy -> x f,dy )) is calculated as, The maximum value of x f,dy (x f,dy,max ) is calculated by applying the following condition: Then, x f ,dy,max = (t gap − x r,dy )/2.
which represents the pull-in location. By combining (8) and (10), V p,sling,dy is calculated as For the minimization of the total voltage required to pull in the movable beam, V p,sling,dy should be equal to V p,back,dy .
To meet this condition, x r,dy becomes −0.236t gap , which is called the optimized x r,dy (x r,dy,opt ). It has been proved that the movable beam can store more E pot under the dynamic pull-back operation than under the static one as x r,dy,opt is larger than x r,st,opt . The optimized V p,sling,dy (V p,sling,dy,opt ) becomes, The three V p 's including V p,conv , V p,sling,st,opt , and V p,sling,dy,opt are compared as follows: This confirms that the proposed dynamic slingshot operation makes V p 0.78 times and 0.92 times lower than conventional pull-in and static slingshot operations, respectively. However, it should be noted that the above-shown results are derived assuming the ideal vacuum condition and 1D parallel plate model. The proposed dynamic slingshot operation is reevaluated, reflecting a finite Q and the actual cantilever beam shape. FEA simulation was performed in comparison with the 1D parallel plate model, referring to the simulation parameters summarized in Table 1. Fig. 3 compares the proposed dynamic slingshot operation with the previously proposed static operation in terms of V p,sling,dy,opt /V p,conv ,  V p,sling,st,opt /V p,conv , x r,dy,opt , and x r,st,opt , with the variation of Q. Q is known to be inversely proportional to damping [22]. A high Q case is discussed as NEM memory switches are generally operated under near-vacuum environments in CMOS metal interconnection layers [23]. According to the analytical model, when Q is ∼10 4 V p,sling,dy,opt /V p,conv is ∼0.78 as predicted in (13), V p,sling,st,opt /V p,conv is ∼0.84, as shown in our previous work [18]. In contrast, the FEA model shows that the slingshot operation is more effective than the analytical model because the movable beam stores more E pot during pull-back operation in the case of the FEA model than in the case of the analytical model considering different x r,dy,opt values. According to the FEA simulation, V p,sling,dy,opt /V p,conv is ∼0.73, and V p,sling,st,opt /V p,conv is ∼0.80 when Q is ∼10 4 . This highlights that the proposed dynamic slingshot operation is more advantageous in actual cases than predicted in (13) and (14) as the FEA model is generally more accurate than the analytical model [20]. Subsequently, as Q decreases, both V p,sling,dy,opt /V p,conv and V p,sling,st,opt /V p,conv increase. This is because the movable beam loses more energy during both pull-back and pull-in operation due to higher damping. This can be explained by observing that both x r,dy,opt , and x r,st,opt increase as Q decreases. Thus, as the damping increases, it lowers the advantages of the slingshot operation over conventional pull-in operation. However, even when Q is ∼10, V p,sling,dy,opt /V p,conv is ∼0.77, which is better than V p,sling,st,opt /V p,conv under infinite Q.
Sophisticated timing control is required to take full advantage of the proposed dynamic slingshot operation. The pull-back operation should be converted into the pull-in operation when the movable beam reaches x r,dy,opt . This may be difficult to implement in the actual beam operation owing to the variation issues such as mechanical delay and signal propagation delay [24], [25]. Fig. 4 shows the influence of the timing error (τ er ) on V p,sling,dy,opt /V p,conv as a function of Q predicted by the analytical and FEA models. τ er is defined as the difference between the time when the pullback operation is converted into the pull-in operation and the time when the movable beam reaches x r,dy,opt . For example, zero τ er corresponds to the ideal case, while negative or positive τ er indicates that the conversion from the pull-back into pull-in operation before and after the beam reaches x r,dy,opt . A smaller τ er is desirable to store a higher E pot in the movable beam to maximize the merit of the proposed dynamic slingshot operation. As shown in Fig. 4, as Q becomes smaller, V p,sling,dy,opt /V p,conv becomes less sensitive to τ er . It is because that the difference between x r,dy,opt under the non-zero τ er case and x r,dy,opt under the zero τ er case is very small during τ er as Q decreases. However, even when Q reaches 10 4 , V p,sling,dy,opt /V p,conv is still insensitive to τ er . A ±30 ns deviation in τ er leads to only 1.4% and 1.3% variation in V p,sling,dy,opt , according to the analytical and FEA results, respectively. Notably, according to the FEA results, even if Q is reduced to 100 and τ er is ±30 ns, V p,sling,dy,opt /V p,conv continues to remain ∼0.74, indicating that the proposed dynamic slingshot operation is reliable and immune to process and timing variation issues.
Finally, the influence of the dynamic and static slingshot operation on the V DD of NEM memory switches is compared. As mentioned in an earlier study, the V DD of the NEM memory switch is determined as max(V p , V s ), which is equal to V p in the case of a small L beam [14]. Fig. 5 shows the analytical V p,conv , V p,sling,st,opt , V p,sling,dy,opt , V s , and FEA V p,sling,dy,opt as a function of L beam of NEM memory switch, whose W beam , t beam , and t gap are 900 nm, 65 nm, and 65 nm, respectively. According to [14], V s is derived in (15), as shown at the top of the next page, where p is the surface adhesion force per unit area, α is the length of the beam part that is not affected by p, β is the ratio of the capacitance calculated by the actual beam shape to that calculated by the parallel-plate model, and d vdw is the van der Waals distance. Values for these have  been calculated as p = 0.450 µN/µm 2 , β = 0.655 and d vdw = 1.5 nm [14]. In summary, among the three kinds of NEM memory switch operations, the proposed dynamic slingshot operation achieves the lowest V DD as well as the smallest L beam . The analytical model predicts that the minimal V DD and L beam are 1.56 V and 2.97 µm in the case of conventional operation, 1.31 V, and 2.95 µm in the case of the static slingshot operation, and 1.22 V and 2.94 µm in the case of the dynamic slingshot operation. Furthermore, the FEA model predicts that the minimum V DD and L beam using the proposed dynamic slingshot operation are 1 V and 2.93 µm, respectively. It should be noted that the V DD of the NEM memory switch reaches the sub-1 V region, which is lower than the V DD of the 65 nm CMOS node using the proposed dynamic slingshot operation.

III. CONCLUSION
A dynamic slingshot operation has been proposed. According to the FEA results, the proposed dynamic slingshot operation shows ∼0.73 times lower V p than conventional pull-in operation. Even when exposed to ±30 ns τ er , the V p,sling,dy,opt varies by < 2%. Therefore, it is confirmed that the proposed dynamic slingshot operation is superior to conventional pull-in and static slingshot operations in terms of V DD and size reduction. The proposed dynamic slingshot operation is also expected to be helpful for implementing low-operation voltage and high chip density of M3D CMOS-NEM hybrid RL circuits.