Design of a novel MEMS resonator based neuromorphic oscillator

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Design of a novel MEMS resonator based neuromorphic oscillator

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Masoud Baghelani a,b , Afshin Ebrahimi c,∗ , Habib Badri Ghavifekr c a

Islamic Azad University (IAU) – Ilam Branch, Ilam, Iran Department of Engineering, Ilam University, Ilam, Iran c Electrical Engineering Department, Sahand University of Technology, Tabriz, Iran b

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a r t i c l e

i n f o

a b s t r a c t

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Article history: Received 3 November 2012 Accepted 27 May 2014

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Keywords: Neuromorphic oscillator MEMS resonator Resonator coupling Trans-impedance amplifier Automatic amplitude controller

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1. Introduction

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A novel MEMS based neuromorphic oscillator is presented. Due to compatibility with CMOS process, on-chip integration of electro-statically actuated microresonators is possible with very small size. Also, taking advantage of sacrificial sidewall spacer technique for fabrication of 100 nm vertical gap, as low actuation voltages as 0.5 V is enough for such resonators. Oscillatory neuron dynamics are also studied and design of the resonator and its characteristics are described as a neuromorphic oscillator. There are several practical barriers associated with MEMS implementation of neuromorphic oscillators such as existence of near-to-main mode spurious modes, requiring of UHF high gain trans-impedance amplifier because of very high motional resistance of such resonators, and automatic amplitude control circuit which all investigated in the paper and surmounted as well. A coupling technique for weak connection of such resonators is also described in the paper which allows mechanical low velocity connection of UHF contour mode disk resonators for the first time. © 2014 Published by Elsevier GmbH.

Although artificial neural networks experience tremendous progresses during last several decades, their hardware implementation does not go so far. Lots of papers related to hardware implementation of artificial neural networks, are based on digital FPGAs [1,2]. Due to their digital nature, implementation of requiring nonlinear functions, e.g. Sigmoid, is very difficult on FPGAs and always containing quantization error. Another candidate, analog CMOS current mode circuits [3–5], has successful results. However, most of them operate in the same time scale as neuronal cells and it is difficult to drastically increase its speed without sacrificing power consumption. A novel method introduced by Izhikevich and Hoppensteadt [6] is implementation of spiking neural networks by MEMS resonators as associative memories. They mathematically proved that these resonators are capable of memorizing phase patterns when placed at a suitable circuit and connected appropriately. MEMS resonators achieved great deals of interest in recent years due to their high Q, extremely low power consumption, compatibility with the state of the art CMOS technology, etc. Hence MEMS implementation of neural networks has several potential

advantages over its counterparts. First of all, due to their high Q and small size, implementing of ultra low noise fully integrated oscillators is feasible [7]. Oscillating nature of the neurons is thought to be playing important rules in the learning and the memory in the brain. Rhythmic firing of the neurons is essential for information processing in olfactory bulb, hippocampus and thalamo-cortical [8]. Nevertheless, most of the researches in the field of artificial neural networks focus on non-oscillating sigmoid neurons [9]. Other advantage of MEMS implementation of neural networks for application to neuromorphic computing, high-speed operation and long mean-time-between-failure are most effective. Also their shock and vibration resistance are several decades greater than their quartz counterparts. This paper deals with the designing of a MEMS based neuromorphic oscillator and extracting its characteristics. The paper is organized as follows: after an introduction in Section 1, Section 2 describes the dynamical required properties of a system to be qualified as a neuron. In Section 3, an ultra high frequency MEMS resonator is designed and its configurations are modified so to satisfy the conditions in Section 2. Also, the required CMOS circuits are introduced. In Section 4, connection possibility of such a neuron is described followed by a conclusion in Section 5. 2. Oscillatory neurons characteristics

∗ Corresponding author. Tel.: +98 412 345 9374; fax: +98 412 345 9352. E-mail addresses: [email protected] (M. Baghelani), [email protected], [email protected] (A. Ebrahimi), [email protected] (H.B. Ghavifekr).

There are several models in mathematical biology such as ordinary language, comprehensive, empirical and canonical models

http://dx.doi.org/10.1016/j.aeue.2014.05.015 1434-8411/© 2014 Published by Elsevier GmbH.

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Fig. 1. Cross sectional view of the RSACMDR and its electrical connections; key dimensions for the air gap and the thickness of the resonator are also provided.

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[10]. Most of the conventional models such as McCulloch-Pits neurons are empirical models, but critical regimes of brain dynamics could be best described by canonical models. Canonical models study neurons in specific local conditions such as bifurcations [11]. The neurons must be excitable to perform signal processing. There are several types of excitability dynamics in biological systems, but we focus on class-2 excitability in this manuscript [12]. The class2 excitability in a neuron can be produced by a scenario that the resting state of the neuron’s model loses its stability via super- or sub-critical Andronov–Hopf bifurcation as the result of increasing the external stimulus current [13]. It’s been numerically studied that class-2 excitability could leads to easy neuronal synchronization [14]. An interesting phenomenon in class-2 excitable systems is their sensitivity to frequency of applied signal rather than its amplitude. As this sensitivity increases purer oscillations are resulted. In electrical engineering terminology, the above sentence could be translated to decreasing the phase noise by increasing the tank’s quality factor. Mathematical model of a MEMS based oscillator is derived in [6]. Although it’s been mathematically proven that arbitrary oscillators could work as neurons [15,16], there are sort of practical issues which addressed in the next section where a MEMS based oscillator is designed and its performances are improved to be qualified as a very reliable neuromorphic oscillator.

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3. MEMS resonator neuromorphic oscillator

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As mentioned in Section 2, oscillators are required to work at a same frequency. Recently demonstrated MEMS resonators provide very stable and miniaturized stabilizers for high Q and low noise oscillators. Considering a constant number of requiring periods for convergence of an oscillatory network, as the oscillation frequency is increased the overall time of those requiring periods and so the convergence time of the network might be reduced. Therefore, recently introduced Ring Shape Anchored Contour Mode Disk Resonator (RSACMDR) is studied here as the neuron core due its reliability, and the ability to work in UHF frequencies without power handling problems [17]. Shown in Fig. 1, resonance equations of RSACMDR have been extracted in [17] and we skip repeating them for the sake of abbreviation. The resonance amplitude of the resonator operating in 940 MHz frequency is chosen quite small for small amplitude activity leading to a weakly connected neural network. Weakly connected oscillatory networks exhibit associative properties and have been studied as the most important mechanisms in central pattern generators, visual and olfactory systems, and bio-inspired architectures for information and image processing [10]. Also, strong coupling of oscillators could results in several monotones which

Fig. 2. Frequency response of the resonator of Fig. 1 [19].

maybe far from each other in the frequency domain and therefore jeopardize the synchronization [18]. Like any other resonators, the lumped model of the system is: mr r¨ + cr r˙ + kr r + εr r 3 = 0

(1)

where mr , cr , kr and εr are equivalent mass, damping, spring constant and Duffing nonlinearity of the oscillator, respectively, and r is the radial component in the cylindrical coordination. The electrostatic force applied to the resonator at the resonance frequency is:



Fi = −VP vi

∂Cin,i ∂r

+

∂Cin,o



(2)

∂r

Cin,o are the input electrodes to resonator overlap capacitances at inside and outside of the resonator, respectively, and VP and vi are bias and excitation voltages, respectively. The time varying excitation capacitance could be considered as: Cex (t) =

ε0 ϕh d0

 

rin 1 +

ur (t)|r=rin

−1

 + rout 1 −

d0

ur (t)|r=rout d0

−1

where ϕ is the overlap angle of excitation electrodes to the resonator and ε0 is the air permeability. Therefore, for the symmetric design of excitation and sensing electrodes, the output current is: io = VP

∂Cex ∂r



∂u(r, t)|r=rin + ∂u(r, t)|r=rout



(4)

∂t

Considering an elastic structure: ur =

(5)

At the resonance frequency: QFi kr

(6)

(7)

Considering Eq. (2) we will have: ∂Cout,i ∂r

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∂ur (r, t) ω0 QFi = kr ∂t

io = VP

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And therefore:



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132

Fi kr

ur (r, t) =

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(3)



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+

∂Cout,o ∂r



ω0

Q kr



 −VP vi

∂Cin,i ∂r

+

∂Cin,o



137

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∂r (8)

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Hence, assuming symmetric excitation and sensing for the resonator, below expression for output current is achieved:

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io = −VP2 vi

∂Cex ∂r

2

ω0 Q kr

(9)

Also, the lumped model could be achieved by below equations:

0 0 ⎪ kr = ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪  ⎪ ⎪ ⎪ ⎩ c = kr mr r

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Fd =

2 r˙

(11)

Hence, the dynamics of the circuit including both the resonator and the amplifier is: mr r¨ + cr r˙ + kr r + εr r 3 = Fd

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And then:



mr r¨ +



cr − Ramp VP2

∂Cex ∂r

(12)

2  r˙ + kr r + εr r 3 = 0

(13)

Since, the resonance amplitude of the resonator is very small and is in the range of 1 nm, the term r3 could be simply neglected. 157 When the system starts to oscillate, as the result of super-critical 158 Andronov–Hopf bifurcation, the damping term becomes negative 159 and after saturation of the system, when the oscillation amplitude 160 is fixed, the damping becomes zero and the system achieves to its 161 stable limit cycle. Eq. (13) implies that besides the damping of the 162 resonator, the overall circuit damping factor is depends on bias volt163 age, circuit gain and the variation of the electrodes to resonator 164 capacitance versus radius where each one (or a mixture of them) 165 could be considered as the bifurcation parameter. Capacitance vari166 Q2 ation is given by: 167 156

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∂Cex ∂r

2 =

(ε0 ϕh(rin + rout ))



d0 + (C1 JP (kr) + C2 YP

×

 



2

(kr))r b

− kC1 −JP+1 (kr) +

4 





where Jx (.) and Yx (.) are Bessel functions in the order of x and in types of 1 and 2, respectively, and other constants are obtained for 940 MHz resonator and 1 nm of resonance amplitude as below:

a = 8 × 10

m = 0.5(1 + );

;

 ⎪ ⎪ 2 ⎪ ⎪ ⎩ k = ω0 (1 −  ) ; E

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(17)

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(10)

the possibility of the above equation to be considered as a neuron has been proved. One of the most important barriers of MEMS resonators to be neurons practically is spurious modes. Spurious modes are non-harmonic vibration modes of resonators excited by the same mechanisms as desired mode [20]. Harmonic analysis of the resonator of Fig. 1 is provided in Fig. 2. It can be seen that there are several spurious modes in addition to fundamental mode where the circuit may be trapped in them and therefore the oscillator could not oscillate at the desired frequency [19]. This phenomenon can disorganize the network of oscillators and make synchronization impossible. By a special electrode and anchor configurations according to phase discriminating lines of nearby spurious modes to fundamental mode, the spectrum of Fig. 3 is achieved. The crossed ring anchored resonator (Fig. 3), may also causes the selfanchor alignment process feasible without any extra fabrication processes. More analytical investigations about spurious modes of RSACMDR could be found in [19]. Although they have excellent properties, RSACMDRs have very high motional resistances as well as the other electrostatic disk resonators. According to near GHz frequency of operation, ordinary techniques could not be utilized for the sustaining amplifier and a specific technique should be employed for feasibility of oscillator implementation. Also, due to inherent 180◦ phase shift of the resonator, the amplifier should provides extra 180◦ phase shift satisfying Barkhausen criteria for oscillation. The proposed technique is to providing the required phase shift and gain just at the resonance frequency of RSACMDR. The frequency response of the proposed trans-impedance amplifier (TIA) is shown in Fig. 4. Circuit schematic is illustrated in Fig. 5. By controlling of RF2, one can tune the operating frequency of the amplifier. Also, for minimizing Q loading effect, input and output impedances of the TIA must be as low as possible. Transistors M1–6 construct a modified current mirror based current amplifier providing a low noise middle gain stage and low input impedance at the front-end of the TIA. The second stage is a high gain regulated cascode with an internal feedback

P P JP (kr) + kC2 YP+1 (kr) + YP (kr) kr kr

⎧  ⎪ P = 0.5 52 − 2 + 1; q = 12k × 10−6 ; ⎪ ⎪ ⎪ ⎨ −6 173

174

ranchor

(∂u(r)/∂r)dr

153

155



rin

∂Cex ∂r

(16)

mr r¨ + kr r = 0

((∂2 u(r)/∂r 2 ) + ( ∂u(r)/r∂r) − (u(r)/r 2 ))r dr dϕ dz

Now, consider the resonator in a closed loop with the transimpedance gain of Ramp . It is obvious that for oscillation build up, Ramp should be greater than io /vi of the resonator. The applied force to the resonator by the amplifier is: Ramp VP2

u(r) = (C1 JP (kr) + C2 YP (kr))r b

The subsequent mathematical equations to achieve the canonical model of the proposed oscillator are the same with [6], where

Q

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1 − 2

rin

C1 and C2 are constants from solving the resonance equation of the system:

Therefore, at the stable oscillation condition, (13) becomes:

rout ⎧ ⎪ 2h ru2r (r)dr ⎪ ⎪ ⎪ ⎪ r in ⎪ mr = ⎪ ⎪ ⎪ u2r (r)|r=rout ⎪ ⎪

2 h ranchor ⎪ ⎪ ⎨ E 145

3

b = 0.5(1 − );

(15)

r b − [C1 JP (kr) + C2 YP (kr)]br b−1

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2 (14)

for bandwidth extension. Last stages are two common source voltage amplifiers succeeded by a source follower for decreasing the output resistance. Circuit analysis could be found in [21] and is neglected here for the sake of abbreviation. Automatic Amplitude Control (AAC) circuit is an essential part of such oscillators. Since both the amplifier and the resonator have non-idealities, a compensation mechanism is required. Also, it is proved that AAC could remove 1/f3 phase noise component in MEMS oscillators [22]. Phase noise is very destructive in

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Fig. 3. (a) Crossed ring anchored contour mode disk resonator and its electrode configuration for spurious mode suppression and (b) frequency response of the resonator by finite element analysis; as it is obvious, all spurious modes addressed in Fig. 2 are suppressed.

Fig. 4. Frequency response of the proposed TIA; it can be seen that the circuit provides 180◦ phase shift with a sufficient gain around 940 MHz.

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synchronization of neuromorphic oscillators [15]. In addition, AAC could prevent non-uniform characteristic changing of oscillators occurred due to aging or environmental variations. Since the phase of proposed oscillator at the resonance frequency is very sensitive to the TIA parameters, conventional AAC implementations, which are based on changing a feedback resistor at the amplifier structure, could not be employed here [7,22]. The idea is to change the damping of the oscillator. According to (13) the damping of the oscillator has a square relation with bias voltage which could be produced by charge pump circuits. By changing the tail current of a charge pump, its output voltage could be controlled [23]. The whole circuit schematic is shown in Fig. 5. Proposed AAC includes a typical envelope detector [22] and a simple charge pump circuit just for justification of the method. Obviously more advanced charge pumps could achieve better functionalities [23]. The whole circuit including the resonator, TIA and AAC consumes less than 1150 ␮W and 4900 ␮m2 of die area.

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4. Connection possibility of micromechanical oscillators

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Coupled oscillators could memorize phase patterns when their connections are weak. In this case the amplitude of oscillations remains relatively constant during interactions [10]. As mentioned, coupled oscillators need to work at a same frequency for

maintaining the zero-phase. Here, rhythm adjustment of selfsustained oscillators is called synchronization which is essential for oscillatory neuro-computing. Unfortunately, ordinary contour mode disk resonators have no contour points for establishing weak connections. A novel method for weak coupling between RSACMDRs has been introduced in [18] which utilizes coupling from crossed anchors for neural interactions. Fig. 6 shows schematics of the design. Because there are 8 segments for the anchor, each resonator can interact with 8 other resonators in the network mechanically. Each neuron could be connected to 8 other neurons through the mechanical coupling. In addition, additional connections may be implemented electrically by resistors. Complete and precise analytical approach and design procedure of this specific method of coupling are given in [18] and are neglected here for the sake of brevity. Resonance characteristics of each resonator could be transmitted to other resonators through its anchor and coupling beam. Needless to say that, as the resonator contracts and expands its anchor segments are stretched and compressed with the same frequency but very much smaller amplitude. For preventing the mass loading effects of the coupling beam, the quarter waveform criteria should be satisfied [24]. This condition is fulfilled for several values and therefore, the couplers lengths could be chose to have different values which provide different

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Fig. 5. Schematic of the whole circuit including the resonator, TIA and AAC in details.

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delaying times. This effect could be very useful in implementation of neural network. Fig. 7 shows the simulation results of the output of the AAC and the oscillator together where the oscillation start-up is depicted. Fig. 8 displays the simulation result of the stabilized oscillations and the effects of suddenly manipulated changing of the oscillator’s output from 1.6 V to 1 V by temporarily connecting it to a dc voltage and its compensation by the operation of AAC. These results verify the operation of our circuit as intended. When the output of the TIA changed, the AAC changes the bias voltage of the resonator in an opposite way to act against the change occurred at the TIA. This operation of the AAC, compensates the output changes of the oscillator for achieving to stable oscillation. The startup time of TIA is 3.8 ns with −146 dBc/Hz phase noise at 100 kHz offset from the carrier. The output range of envelope detector is between 0.88 V and 1.1 V which can control the output voltage of the charge pump from 12.43 V to 13.2 V which itself could change the motional resistance of the resonator from 196.5 k to 174 k . In addition, the compensating time for the AAC loop to adjust as

Fig. 6. Two coupled resonators by the introduced novel low velocity coupling through anchors.

large variations of the oscillators’ output as 0.35 V is just about 90 ns. Lots of CMOS neuromorphic circuits have been designed for simulating of bio-inspired neurons which major parts of them was non-oscillating models (i.e. having stable oscillations with a certain frequency) with no requirements of phase synchronization and low bursting frequency and hence low speed [4]. Oscillatory associative memories require phase synchronization which needs for very low close-to-carrier phase noise which could be best achieved by MEMS based circuits. Also, the size of the utilized resonator is less than 35 ␮m × 35 ␮m which could be comparable with complex CMOS-only circuits. The disadvantage of the proposed structure is its circuit complexity which is as the result of ultra high frequency (speed) of the resonator and also utilizing not expensive

Fig. 7. The output of the oscillator from the start-up. The output of the AAC increases as the result of small output of the oscillator. This decreases the motional resistance of the resonator since the circuit achieves to its super-critical Andronov–Hopf bifurcation, where the overall damping of the system becomes negative and oscillation starts-up.

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mechanical computing systems including associative memory and pattern recognition. Acknowledgment This paper is a part of a project supported by Iran National Sci- Q3 ence Foundation (INSF). Q4 References

Fig. 8. This figure depicts the compensation effect of the AAC. When an intentional and strong change is occurred at the output of the oscillator, the AAC compensate it by changing the damping of the system through the bias voltage of the resonator.

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fabrication technologies. By employing more advanced techniques such as 20 nm side-wall-spacer technology, the gain of TIA circuit will becomes more than 600 times relaxed! That significantly reduces the complexity and power consumption of the circuit. When the 20 nm sidewall spacer technique is employed instead of 100 nm, the electrode to resonator gap (i.e. d) is reduced 5 times and therefore based on Eqs. (11) and (14), the motional resistance is reduced 54 times (i.e. 625 times). This reduction in the motional resistance of the resonator reduces the requiring gain of the TIA by the same value. It is obvious that, the mentioned technique is not related to the CMOS technology but it is a MEMS fabrication technology.

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5. Concluding remark

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A novel MEMS based neuromorphic oscillator has been presented and the possibility of constructing weakly connected neural oscillators has been studied. Neuro-scientific fundamentals of the subject have been discussed where the necessary properties for a neuromorphic oscillators have been described. Thereafter, the described characteristics have been realized by CMOS-MEMS components and the obstacles have been scrutinized and surmounted. Recently, demonstrated MEMS based filter has been introduced as a strong method for weakly connecting of the resonator oscillators. The presented work employed UHF oscillators which should result in very fast convergence of the prospective network. By a comparison between our work and the state of the art designs such as [5] one can see a significant improvement of the oscillation frequency as the price of power dissipation. Achieving of this high frequency is a very difficult and cumbersome work to do. Ultra high stable UHF oscillations results in much more speed of the neurons. Supposing a constant number of requiring cycles for convergence, the speed of a network constructed from the proposed neuron could be about 107 times faster than that of [5] but by consuming about 105 times of power and about twice in die area. We also have discussed a bidirectional connection between our neuromorphic oscillators. In the future works, unidirectional connection that mimics the chemical synapses will be developed for realizing low-power and low-noise neuromorphic

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