energy-reversible complementary nem logic gates
TRANSCRIPT
Energy-Reversible Complementary NEM Logic Gates Kerem Akarvardar, David Elata, Roger T. Howe, H.-S. Philip Wong
Center for Integrated Systems, Stanford University, Stanford CA 94305, [email protected]
Energy-reversible complementary nanoelectromechanical (ER CNEM) logic gates are introduced. For the
same delay, ER CNEM gates can operate at much lower supply voltages relative to conventional (CMOS-like) CNEM
gates and their reliability is significantly higher. NEM relays are attractive candidates for ultra-low power computation since their leakage is practically zero.
Indeed, there is a growing interest on realizing logic and memory functions by using NEMS-based devices [1-3]. The
characteristics of conventional (MOSFET-like) NEM relays (Fig. 1) and CMOS-based CNEM gates were analyzed in
[4]. The main drawbacks of conventional NEM relays were found to be: 1. long settling time after turn-off due to high
quality factor (Q >> 1), and 2. cantilever tip bouncing during turn-on due to high impact velocity. The ER logic gates
proposed in this work solve these problems while enabling smaller supply voltages at the same delay.
The layouts of the ER CNEM inverter and NAND gate (following the bi-stable RF switch design [5]) are
shown in Fig. 2. The structures feature, for each input, a NEM cantilever beam, which may deform laterally. In the ER
CNEM inverter, the cantilever shorts the output to VDD for Vin = 0 and to GND for Vin = VDD (Fig. 3). In the ER CNEM
NAND gate (Fig. 2b), for A or B = 0, the output is connected to VDD by one or both beams. However the connection of
the output to GND is only possible when A = B = 1. An ER CNEM NOR gate is obtained by swapping the GND and
VDD electrodes of the NAND gate.
The main advantage of the circuits in Fig. 2 is that, once the mechanism is initialized (i.e., once the beam is
pulled in towards one of the electrodes by applying a sufficiently high DC voltage or, preferably, an AC voltage at the
resonance frequency [5]) the beam can travel from one electrode to the other using the potential elastic energy that was
stored due to bending (Fig. 3). This energy (that would be dissipated by damping in a conventional relay after the beam
is released [4]) is reversible, since the beam is bent at both stable states. Electrostatic force is not required for the beam
displacement as in the conventional relay. As a result, VDD can be substantially reduced, since its role is not to actuate
(pull-in) the beam but merely to hold the beam bent (in contact) by inducing an electrostatic force that adds to attractive
surface forces (van der Waals). Also, in the ER configuration, the settling problem of the conventional relay is solved,
since at steady-state the cantilever tip is necessarily in contact with the GND or VDD electrode.
By assuming a 1D structure (Fig. 4) and realistic dimensions (achievable by the current NEMS technology
[6]), we compared the characteristics of the conventional NEM relay with those of the ER NEM inverter. As shown in
Fig. 5, in the ER NEM inverter, VDD can be as small as the pull-out (hold-down) voltage, Vpo, while the conventional
relay requires a VDD larger than the pull-in voltage, Vpi (in our example Vpo = 0.5 V, Vpi = 2.24 V).
When the damping is taken into account, VDD needs to be larger than Vpo in the ER inverter in order to
compensate the related energy loss [5]. For the dimensions we consider, the quality factor is 18.2 and VDD should be
increased by 90 mV above Vpo in order to compensate the damping loss. The ER inverter with VDD = 0.59 V and the
conventional relay with VDD = Vpi = 2.24 V achieve the same delay (10.8 ns, Fig. 6a). However, in the ER inverter the
beam velocity decreases gradually towards the end of travel leading to a much lower impact velocity (Fig. 6b) and
minimizing the tip bouncing.
The fundamental difference in the principle of operation between the two types of relays is apparent in Fig. 7
where the variation of the energy components during the switching is shown. In the conventional relay, the switching
work is done by the power supply and the energy drawn from the voltage source dominates all other components (Fig.
7a). In contrast, in the ER CNEM inverter, the largest component is the stored elastic energy (Fig. 7b). When the beam
is released from one of the electrodes, the potential elastic energy is first transformed to kinetic energy and then back to
elastic energy when the beam arrives at the opposite electrode. The substantial difference between the stored elastic
energy and the source energy (Fig. 7b) shows that the switching work is done by the elastic potential energy rather than
the voltage source. The performance of the conventional and ER relays is compared in Table 1. For the same delay, the
ER NEM inverter outperforms the conventional relay in terms of voltage, energy, and reliability.
In the ER CNEM gates, the VDD (@ Vpo in vacuum operation) can, in principle, be reduced below 100 mV as
illustrated in Fig. 8. However this would only be possible at the expense of a very high sensitivity to dimensions, which
would reduce the process margin.
In summary, we introduced for the first time the ER CNEM logic gates and demonstrated their superiority
over the conventional relays in terms of voltage, energy, and reliability. The ER CNEM logic a promising candidate for
low standby and low operating power applications. References: [1] Q. Li et al., Nanotechnology 18, 315202, 2007. [2] W. Y. Choi et al., IEDM, pp. 603-606, 2007. [3] J. E. Jang et al., Nature
Nanotechnology, 3, pp. 26-30, 2008. [4] K. Akarvardar et al., IEDM, pp. 299-302, 2007. [5] H. Yang, L. Pakula, P. J. French, 14th European
MicroMechanics Workshop, pp. 33-36, 2003. [6] M.-S. Kim et al., ISDRS, pp. 1-2, 2007. Acknowledgments: DARPA and FCRP C2S2.
978-1-4244-1942-5/08/$25.00 ©2008 IEEE 69
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Fig. 1. Cross-section of the
conventional (MOSFET-like)
NEM relay.
out = in
in
VDD
GND
insulator cantilever
floating
electrode
out = AB
A
VDD
VDD
GND
B
Fig. 2. Top view of the ER CNEM logic gates: (a)
inverter, (b) NAND gate. Input current is zero, due to the
insulating region near the beam tip. The floating electrode
in (b) serves to obtain a conductive path between GND
and the output only when VA = VB = VDD.
out = VDD
in = GND
GND
VDD
out = GND
in = VDD
VDD
GND
Fig. 3. Cantilever profiles at steady-
state in the ER CNEM inverter.
S DG
air gap
cantilever beam
S
insulating substrate
Fig. 4. 1D structure used for the
analysis of the ER CNEM inverter. L
= beam length, W = beam width, h =
beam thickness, g0 = half-gap, g1 =
minimum (2-D equivalent) beam to
electrode distance determined by the
tip configuration of the cantilever (in
Figs. 2 and 3), k = equivalent spring
constant, b = damping coefficient.
(a) (b)
elastic energy storage due to bending
Table 1. Comparison between the ER
inverter and conventional relay for
the parameter set in Figs. 5 and 6.
Fig. 6. Step voltage response of the
normalized beam position (a), and the
beam velocity (b) for the ER NEM inverter
and the conventional relay, both using the
parameters in Fig. 5. The step voltage
amplitude is VDD = 0.59 V in ER inverter
and VDD = 2.24 V = Vpi in the conventional
relay. In (a), the distance is normalized to
2g0-2g1 for the ER inverter, and to g0-g1 for
the conventional relay. The delay is the
same for both structures (10.8 ns).
Characteristics take into account
electrostatic, elastic, van der Waals and the
damping forces (Q = 18.24, W = 100 nm).
Fig. 7. Step voltage response of the
energy components: (a) conventional
relay, (b) ER CNEM inverter.
Parameters as in Figs. 5 and 6.
Time (ns)
Energy (fJ)
source
elastic
kinetic
vdW
damping
Time (ns)
Norm
alized Beam Position
Conventional
Energy-
Reversible
Time (ns)
Velocity (m/s)
Conventional
Energy-reversible
impact velocity
Time (ns)
Energy (aJ)
source
elastic
kinetic
vdW damping
Fig. 5. Normalized beam position as a function
of VGS in a conventional relay. The behavior is
predicted by a 1-D model (consisting of half of
the structure in Fig. 4) and taking into account
electrostatic, elastic, and van der Waals (vdW)
forces. Silicon beam is assumed. g0 = 25 nm, h
= 25 nm, L = 650 nm, g1 = 4.5 nm, (k = 0.645
N/m). The addition of a second fixed electrode
to the conventional relay as in Fig. 4 enables to
reduce the minimum operating voltage, VDD,
from Vpi (2.24 V) to Vpo (0.5 V).
Fig. 8. Variation of the minimum supply voltage
(= Vpo) as a function of the minimum electrode
to beam distance, g1, in the ER CNEM inverter
whose parameters are given in Fig. 5 (damping
force is neglected). VDD can be reduced below
100 mV (leading the holding force be dominated
by the van der Waals forces) at the expense of a
very high sensitivity to dimensions.
(a)
(b)
(a)
(b)
g1 (nm)
Minim
um V
DD(V
)
2
GND
VDD
g0
cantilever
L
g1g1
g0 h
k
W
limit stops
b
VDD
VpiVpo
Gate to Source Voltage, VGS (V)
Norm
alized Position
g1/g0
2/3
VDD
VpiVpo
Gate to Source Voltage, VGS (V)
Norm
alized Position
g1/g0
2/3
640 aJ44.5 aJSource Energy
555 nA16.9 nAMaximumDisplacement
Current
8.72 m/s0.49 m/sImpact Velocity
2.24 V0.59 VSupply Voltage
10.8 ns10.8 nsDelay
ConventionalEnergy-
Reversible
640 aJ44.5 aJSource Energy
555 nA16.9 nAMaximumDisplacement
Current
8.72 m/s0.49 m/sImpact Velocity
2.24 V0.59 VSupply Voltage
10.8 ns10.8 nsDelay
ConventionalEnergy-
Reversible
978-1-4244-1942-5/08/$25.00 ©2008 IEEE 70
Authorized licensed use limited to: National University of Singapore. Downloaded on February 10, 2010 at 22:34 from IEEE Xplore. Restrictions apply.