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A Versatile Memristor Model With Non-linear Dopant Kinetics Themistoklis Prodromakis, Member, IEEE, Boon Pin Peh, Christos Papavassiliou, Senior Member, IEEE and Chris Toumazou, Fellow, IEEE.
Abstract—The need of reliable models that take into account the non-linear kinetics of dopants is nowadays of paramount importance, especially with the physical dimensions of electron devices shrinking to the deep nanoscale range and the development of emerging nano-ionic systems such as the memristor. In this paper we present a novel non-linear dopant drift model that resolves the boundary issues existing in previously reported models that can easily be adjusted to match the dynamics of distinct memristive elements. With the aid of this model, we examine switching mechanisms, current voltage characteristics and the collective ion transport in two terminal memristive devices, providing new insights on memristive behaviour. Index Terms—Memristor, memristive devices, memristor model, non-linear dopant kinetics.
I. I NTRODUCTION
T
HE 20th century has witnessed an exceptional technological progress that has mainly been driven by the invention of the transistor and integrated circuits. Chemistry and materials science have played a pivotal role in this evolution by enabling the development of active devices with distinct and reliable properties that over the past 60 years have been following Moore’s scaling trend [1]. CMOS technology is however approaching the nano-scale floor, with devices attaining comparable dimensions to their constituting atoms. This imposes significant challenges on the performance, reliability and eventually the manufacturability of analogue and digital circuits. Yet, in 1959 R. Feynman [2] proposed that there is plenty of room at the bottom and he correctly predicted that the operation of emerging devices would rely on the manipulation of just a few atoms; the memristor is nowadays considered as an exemplar device. Memristive behaviour has in fact existed for many years [3-5], but the phenomenon was not properly deciphered until 2008 when a team from HP Labs successfully correlated the characteristics of nanoscale switches in crossbar architectures [6-7] with the theory presented originally by Chua [8] and later on by Chua and Kang [9]. Since then, the various attributes of memristors such as their infinitesimal dimensions, their ability to be operated with low power and their dynamic response Manuscript received XXX, XXX; revised XXX, XXX. This work was partially supported by Mr. Wilfred J. Corrigan and the Lindemann Trust Fellowship Programme. T. Prodromakis and C. Toumazou are with the Centre for Bio-inspired Technology, Department of Electrical and Electronics Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK (e-mail:
[email protected]). B.P. Peh and C. Papavassiliou are with the Department of Electrical and Electronics Engineering, Imperial College London.
have been proclaimed to be fitting in diverse applications, from non-volatile memory [10] to programmable logic [11] and beyond [12]. Particular emphasis is however given to the non-linear nature of the device that resembles the behaviour of chemical synapses [13-14]. Whilst memristors have already been used to demonstrate primitive artificial intelligence [15], this marks a new era for neuromorphic engineering. To date, memristive dynamics are described through a number of analytical models that approximate the kinetics of intrinsic dopants in linear [16] as well as non-linear manners [17-19]. On the other hand, memristors come in many flavours; with active cores that are based on oxygen-rich T iO2 films (T iO2 /T iO2+x ) [20-21], Ag loaded Si films [14] and T iO2 sol-gel solutions [22], with the switching mechanisms of such nanoionic systems troubling engineers even up to date [23]. In this paper we present a novel memristor model that takes into account the non-linear nature of the dopant kinetics as well as boundary limiting effects. Section II reviews existing models with distinct attributes being briefly compared. In section III, we present our modeling approach, which comprises of two control parameters for appropriately refining the model to match the distinct dynamics of diverse systems. Finally, a thorough comparison between our model and the pre-existing models is performed, while the paper is concluded by evaluating our model against measured data of in-house fabricated memristors. II. M EMRISTIVE DYNAMICS W ITH L INEAR A ND N ON - LINEAR K INETICS Memristance was initially postulated [8] as the functional property of memristors that correlates charge and flux: M=
dφ dq
(1)
Later on Kang [9] generalised the concept to memristive systems: v = R(x)i (2) dx = f (x, i) (3) dt where v is the voltage, i is the current and R(x) is the instantaneous resistance that is dependent on the internal state variable x of the device. This state variable x is bounded within the interval [0,1] and it is simply the normalised width of the doped region x = w/D, with D being the total thickness of the switching bi-layer. At time t, the width of the doped region w depends on the amount of charge that has passed
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through the device, thus the time derivative of w is a function of current, which can be described as: dw µRon i(t) = UD = µE = (4) dt D where UD is the speed at which the boundary drifts between the doped and undoped regions, µ is the average dopant mobility, E is the electric field across the doped region in the presence of current i(t) and Ron is the net resistance of the device when the active region is completely doped1. When assuming that the generated electric field is small enough, the linear dopant drift model can approximate the dynamics of a memristor. However, this model is invalidated at the boundaries wD. This is due to the influence of a non-uniform electric field that significantly suppresses the drift of the dopants. The limitations of this model are revealed when for example driving a T iO2 /T iO2−x memristor (Ron =100Ω, Rof f =16kΩ, w0 =5nm, D=10nm and µ=10−14 m2 /V s) into its extreme states, i.e. saturation (w = D) and depletion (w = 0). These two extremes can be achieved when the device is biased with a ±1V sinusoidal stimulus of ω=1rad/s, as demonstrated in Fig. 1. In the case of saturation, w exceeds the limit value of D (10nm) while the device’s memristance falls below the 100Ω cut-off value (Ron ). Likewise, in depletion, w can take negative values with the memristance exceeding the upper limit of 16kΩ (Rof f ), which is clearly erroneous. Saturation region
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0
coordinate of the device’s width w. Any effective window function should therefore fulfil the following: • Take into account the boundary conditions at the top and bottom electrodes of the device. • Be capable of imposing non-linear drift over the entire active core of the device. • Provide linkage between the linear and non-linear dopant drift models. • Be scalable, meaning a range of fmax (x) can be obtained such that 0≤ fmax (x) ≤1. • Utilize an in-built control parameter for adjusting the model. Joglekar et al. [18] proposed the following window function: f (x) = 1 − (2x − 1)2p
(6)
with p as a positive exponent parameter [18]. This window function ensures zero drift at the boundaries, i.e. f (0) = f (1) = 0. For p = 1, the non-linear drift is imposed over the entire active-region D, where for p → ∞ the model resembles the linear dopant drift, thus aims 1, 2, 3 and 5 are achieved. However, a significant liability of this model lies in the fact that if w hits any of the boundaries (w = 0 or w = D) the state of the device cannot be further adjusted. This will be from now on termed as the “terminal state problem”. Biolek [17] addressed this issue by suggesting an alternative window function that included memristive current i as an additional parameter:
10
25
5
2
5 20
Fig. 1. Modelling of memristance M and doped region width w modulation at saturation (w → D) and depletion (w → 0) for a ±1V sinusoidal stimulus at 1rad/s, under a linear dopant drift approximation. When the model memristor is operated in the saturation (depletion) mode, the doped region width w becomes greater than D (wRof f ) values.
Non-linear dopant drift can be taken into account by introducing an appropriate window function f (x) equation (4): dx µRon i(t) f (x) (5) = dt D2 This window function models the non-linear dopant kinetics in the active bi-layer and returns a scalar value based on the 1 We should note here that in practise an impeding drift term also exists, as described by Strukov et al. [24], which is however omitted here for simplicity as well for enhancing the versatility of our model.
f (x) = 1 − (x − sgn(−i))2p
(7)
where sgn(i) = 1 for i ≥ 0 and sgn(i) = 0 for i < 0. A positive (negative) current is associated with increasing (decreasing) width of the doped region. The depleted or saturated device can be brought out of the terminal states when the current reverses direction. This is achieved via the steep throughs at x = 0 and x = 1. The features of this particular window function fulfil aims 2, 3 and 5 with limited success however in 1 and 4. Strukov et al. [16] proposed the following window function: f (w) = w(D − w)/D2
(8)
which can be rewritten in terms of the state variable giving f (x) = x − x2 . This window-function was also excersized by Benderli and Wey [19] to form a SPICE macromodel of T iO2 memristors. The boundary condition at the OFF state when w = 0 is resolved since f (x) = 0, while it also imposes a nonlinear drift over the bulk of the device. However, this particular window function lacks of flexibility, while the terminal state problem remains prevalent. It is interesting to note that this window function is in fact a scaled version of Joglekar’s model (by a factor of four) when p is set to 1. Table 1 summarises the attributes of the aforementioned window functions. At this point, we also like to acknowledge the possibility of the dopants drift exceeding the values that are calculated through the pre-existing linear and non-linear models, especially in the bulk of the memristor giving f (x) > 1. An example where such a case is valid is shown in [25] where programmable nanowires exhibit a hysteretic behaviour along with gain.
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TABLE I E VALUATION OF E XISTING N ON - LINEAR D OPANT D RIFT M ODELS .
W indow f unction f (x)/f (w)
Joglekar [18]
Biolek [17]
Strukov [16]
1 − (2x − 1)2p 1 − (x − sgn(−i))2p
x − x2
Resolve boundary conditions
Discontinuities
Impose non-linear drift over entire D
Linkage with linear dopant drift model
N/A
Scalable 0≤ fmax (x) ≤ 1
N/A
Limited
N/A
Flexibility (control parameter)
N/A
1
III. A N OVEL M EMRISTOR M ODEL
0.9
f (x) = −Ax2 + Bx + C
(9)
where the three constants A, B and C are determined through: df =0 (10) dx x=0.5
f (0.5) = 1
(11)
f (0) = f (1) = 0
(12)
A simple calculation shows that f (x) = −4x2 + 4x, which coincides with Joglekar and Wolf’s window function when p = 1, but still considerably different from f (x) = 1 − (2x − 1)2 . Expanding the terms in the bracket gives f (x) = 1 − (4x2 − 4x + 1). It is immediately obvious that all terms containing the state variable x can be grouped under the influence of an exponent control parameter, yielding a family of curves. In addition, by introducing +1 outside the brackets ensures fmax (x) = 1. The purpose of having a control parameter as an exponent is to incorporate scalability as well as flexibility in the window function f (x) that describes the dopant kinetics. Although Joglekar and Wolf’s p parameter is successful in creating a family of distinct curves, it lacks the necessary scalability, i.e. scaling f (x) either upwards or downwards. Motivated by this observation, we proceed to modify Strukov’s window function, since it is based on a smooth parabolic function. Completing the square and ensuring fmax (x) = 1 yields: f (x) = x − x2
= =
−[(x − 0.5)2 − 0.25] 2
1 − [(x − 0.5) + 0.75]
Finally, a control parameter p is introduced: h ip 2 f (x) = 1 − (x − 0.5) + 0.75
(13) (14)
(15)
where p ∈ R+ . This new window function is demonstrated in Fig. 2 for various values of p, where it can be observed that for p=1 it becomes identical to Strukov’s model. The introduced control parameter p acts in three dis-
0.8 0.7 0.6
f(x)
The non-linear nature of the dopants is typically dominating at the two extremes (w → 0 and w → D). This can be modelled through a parabola that is symmetric at x = 0.5 and is of the form:
0.5 0.4 0.3 0.2 0.1 0
p=1
0
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p=2
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p=4
p=8
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p=10
0.5
p=20
0.6
p=40
0.7
p=60
0.8
p=80
0.9
1
x Fig. 2. Plot of our proposed window function f (x) = 1−[(x−0.5)2 +0.75]p versus normalised width of the doped region x with p as a variable.
tinct roles. It allows the window function to scale upwards, which implies that fmax (x) can take any value within 0 ≤ fmax (x) ≤ 1. In addition, p can take any positive real number unlike the constraint of the control parameter being an integer in the models proposed by Joglekar [18] and Biolek [17], allowing a greater extent of flexibility. Values of p=1, 2, 4, 8 and 10 can be chosen to impose a distinct non-linear drift over the entire bi-layer (Fig. 2), while a very large value of p can provide linkage with the linear dopant drift model. The boundary issues are now resolved with the window function returning a zero-value at the active bi-layer edges, while the drift of the dopants is strongly suppressed near the metal contact interfaces. On the other hand, the terminal state problem is eradicated by adopting a feedback implementation. Therefore, the proposed window function as represented by equation (15) satisfies all prerequisites and improves on the shortcomings of existing models. In the peculiar case where the dopant’s drift is such that fmax R 1, the proposed window function can be adjusted: h ip f (x) = j 1 − (x − 0.5)2 + 0.75 (16) where p and x are defined as previously and j is a scalar acting as a second control parameter. For any particular p, f (x) can be scaled upwards or downwards with a suitable value of j. The alternative window function with p fixed at 10 is illustrated in Fig. 3. As j varies, a family of curves is formed allowing easy modification of the model.
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10
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x Fig. 3. Proposed window function f (x) = j(1 − [(x − 0.5)2 + 0.75]p ) vs normalised width of the doped region x with p = 10 and j varying.
IV. R ESULTS A ND D ISCUSSION A. Solving the “state-terminal” problem. The presented model has been evaluated by simulating the response of a single memristor with identical parameters to the one presented in Section II of this paper. Particular emphasis is given when the device is driven into depletion and saturation, since these extremes have been identified to be problematic in existing models. Our window function was first implemented with p = 10 to impose a non-linear drift across the whole bi-layer. The resulting I-V curve is depicted in Fig. 4. When compared with previously reported data [16-19], this pinched hysteresis loop is shown to be asymmetrical while the OFF state of the device is highly non-linear. The first observation arises due to the different switching rates of the ON and OFF states while the second can be explained as a non-ohmic characteristic of the OFF state. These results are in good agreement with measured data provided in [7] and [24]. 3
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Fig. 5. Modelling of memristance M and doped region width w modulation at saturation (w → D) and depletion (w → 0) for a sine wave of ±1V at 1rad/s. Our proposed model was implemented with p = 10 and j = 1, demonstrating that no hard-switching occurs.
B. Accounting for non-linear and linear dopant kinetics. In the case of the linear dopant drift model, it takes 650msec to drive the memristor into saturation as denoted in Fig. 1. However, for the same applied bias, the proposed non-linear dopant drift model requires a significantly larger timeframe of 3.15sec to reach saturation at w=9.892nm with a corresponding memristance of 271.6Ω. Likewise, this divergence is investigated for a non-saturation condition, for a 1µC of charge. If a linear dopant drift is assumed, the change in ˚ where a non-linear w is calculated to be ∆w = 1.2A, ˚ Moreover, it dopant drift model results into ∆w = 0.14A. is observed that for the same stimulus, the net displacement of w is 4.892nm and 4.673nm for the positive and negative bias polarity respectively. This is in agreement with the notion that the ON and OFF switching rates are not identical, due to the asymmetric nature of the device.
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When the device is driven into its OFF state, the corresponding memristance remains high, which is illustrated in Fig. 5 for 6sec≤t≤7sec. It is also evident that the width w of the doped region does not exceed D, while the memristance is correctly limited by Ron =100. When the bias polarity is reversed, the depletion extreme is modelled and is demonstrated in the same figure that the device does not take any erroneous states, i.e. w ≤0 or M >Rof f . This demonstrates that our model is essentially free of the terminal state problem.
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Memristance (kΩ)
Fig. 4. I-V characteristic of a 1V sinusoidal input at 1rad/s for non-linear drift model with p = 10. The inset illustrates the non-linear single-valued function between charge and flux.
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j = 0.2 j = 0.4 j = 0.8 j = 1.2 j = 1.6
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Fig. 6. Modelling of memristance M and doped region width w modulation at saturation (w → D) and depletion (w → 0) for a sine wave of ±10V at 1rad/s. Our proposed model was implemented for p = 40 and j = 1, demonstrating an effective solution to the “terminal-state problem”.
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Next, we set p = 40 to approximate the linear dopant drift model and test the robustness of our window function by applying a large voltage bias, as shown in Fig. 6. Under a 10V sinusoidal biasing scheme, the device is driven harder but caution is exercised to ensure the current flow does not exceed the maximum allowable current given by Vmax /Ron = 100mA. It is illustrated that the device remains in saturation most of the time. In addition, the memristor is capable of memorizing the exact amount of charge that has passed through it, even when the device is saturated, which was also validated by Biolek [17], in contradiction to the original HP memristor model [16]. The same argument also holds when the bias polarity is reversed and the device is driven to its OFF state. −2
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j=0.5 & p=1 j=0.5 & p=10 j=0.5 & p=100 j=1 & p=1 j=1 & p=10 j=1 & p=100 j=1.5 & p=1 j=1.5 & p=10 j=1.5 & p=100
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As a figure of merit, Fig. 8 depicts the I-V characteristics of our standard memristor as calculated by the proposed model as well as the models presented over Section II of this paper. Wherever applies, p was set to 1, for obtaining a more fair comparison. For a 2V peak to peak sine wave of ω=1 rad/s, our proposed model coincides with Strukov’s model, which can not be however scaled in its original description. Joglekar’s and Biolek’s models however, diverge significantly and particularly the latter demonstrates some discontinuities, which are evident in the negative voltage domain. To further illustrate the versatility of our model, we have matched the corresponding I-V responses of Joglekar’s as well as Biolek’s models by setting j=4/p=1 and j=0.5/p=200 respectively. −2
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D. Evaluation against pre-existing models.
Current (A)
j=1 & p=10 j=1 & p=100
j=1 & p=1 j=0.5 & p=100
for vertically scaling the window function while p supports a rather lateral scaling and both essentially modulate the effective mobility of the device. This model demonstrates indeed a higher flexibility from the pre-existing ones that can be beneficial in describing devices of distinct dynamics.
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Fig. 8. Calculated I-V characteristic response of our standard memristor for a 1V sinusoidal input at ω=1rad/s according to Biolek’s [17], Strukov’s [16] and Joglekar’s [18] models. These responses have been successfully emulated with our model for j=0.2/p=200, j=p=1 and j=4/p=1 respectively.
(b) Fig. 7. Our model memristor was biased with a 1V sine wave of ω=1rad/s for three distinct cases in which our model was set with j=0.5, 1 and 1.5 and p=1, 10 and 100. Shown are the calculated: (a) log(I)-V curves and (b) time-evolution of the memristance and total charge (inset) for all nine cases.
C. Adjusting the window-function. The versatility of our model is illustrated in Fig. 7a where the I-V characteristic curves of our memristor model are plotted for nine representative cases. These cases combine three distinct j values (j=0.5, 1 and 1.5) while p is set to 100, to resemble a linear drift model, as well as p=1 and p=10, for establishing a non-linear drift window function. The benefits of having two calibration parameters are further revealed in Fig. 7b where the corresponding time-evolution of our device’s memristance is calculated for all nine cases. The inset of the same figure depicts the total calculated charge when our model device is simulated with the same p and j values as utilized previously. The j parameter is responsible
E. Reproducing the response of a T iO2 /T iO2+x memristor. As a final test, the proposed model was employed to emulate the response of an in-house fabricated memristor. The device was developed based on the process-flowchart described in [20], with a 20nm thick T iO2 /T iO2+x bi-layer. A microphotograph of the device and the interfacing pads is presented in inset A of Fig. 9. The device was characterised with a symmetric triangular wave of ±4V at ω=0.82rad/s and it was simulated with the following parameters: D=20nm, w0 =10nm, ROF F =250Ω, RON =25Ω. At the same time, the control parameters of the proposed model were set to j=1.3 and p=3. Fig. 9 illustrates the measured along with the simulated I-V characteristic response of the device with the arrows indicating the biasing sequence. Clearly, the experimental and simulated results are in very good agreement. Some discrepancies appear above 2V and below -3.5V, which are however associated with the bipolar switching of the device between its high and
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low resistive states, and are only signified when observing the device’s current in a logarithmic scale. A better matching is observed in inset B of the same figure, where the I-V relation is plotted linearly. A small disagreement between measured and simulated data is shown to exist on the peaks of both hysteretic loops, which are due to the 100mA compliance current of our instrumentation and is thus insignificant. 0
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−2
10μm 2
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Fig. 9. Simulated and measured I-V characteristic response of a memristor with an oxygen-rich active core (T iO2 /T iO2+x ). Inset A is a microphotograph of the as fabricated device while inset B is a linear demonstration of the measured and simulated data.
V. C ONCLUSION A versatile memristor model is presented that renders the non-linear kinetics of the mobile dopants within the active bilayer of the device. The drift of dopants is described through a novel parabolic window function that resolves issues that typically appear when the device is driven at its extremes, i.e. depletion and saturation. In addition, two control parameters j and p are introduced that enable a diverse scaling of the window function, which is shown to support both linear as well as non-linear dopant kinetics. This flexibility is particularly important as it allows our model to be utilized in memristive systems of dissimilar mechanics. Finally, the proposed model was validated with measured results from key publications as well as an in-house fabricated T iO2 /T iO2+x memristor, with measured and simulated data matching rigorously. VI. ACKNOWLEDGEMENTS The authors wish to acknowledge the support of Dr. W.J. Corrigan as well as the English-Speaking Union and the Lindemann Trust. R EFERENCES [1] G. Moore, Progress in digital integrated electronics, Proc. IEEE Int. Electron Devices Meeting, pp. 1113, Washington, DC, USA, 1975. [2] R.F. Feynman, There’s Plenty of Room at the Bottom, Engineering and Science magazine, vol. XXIII, no. 5, Feb 1960. [3] B. Widrow, W.H. Pierce and J.B. Angell, Birth, Life, And Death In Microelectronic Systems, Office of Naval Research Technical Report 1552-2/1851-1, May 1961.
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[4] F. Argall, Switching Phenomena in Titanium Oxide Thin Films, SolidState Electronics, Pergamon Press, vol. 11, pp. 535-541, Jul 1967. [5] A. Beck, J. G. Bednorz, Ch. Gerber, C. Rossel and D. Widmer, Reproducible switching effect in thin oxide films for memory applications, Applied Physics Letters, vol. 77, no. 1, Jul 2000. [6] R. Williams, How we found the missing memristor, IEEE spectrum, vol. 45, no. 12, pp. 2835, 2008. [7] J.J. Yang, M.D. Pickett, X. Li, D.A.A. Ohlberg, D.R. Stewart and R.S. Williams, Memristive switching mechanism for metal/oxide/metal nanodevices, Nature Nanotechnology, vol. 3, pp. 429433, Jul 2008. [8] L.O. Chua, Memristor-The missing circuit element, IEEE Trans. on Circuits Theory, vol. CT-18, no. 5, pp. 507 519, Sep 1971. [9] L.O. Chua and S. Kang, Memristive devices and systems, Proc. of the IEEE, vol. 64, no. 2, pp. 209223, 1976. [10] M.J. Rozenberg, I.H. Inoue, and M.J. Sanchez, Nonvolatile Memory with Multilevel Switching: A Basic Model, Physical Review Letters, vol. 92, no. 17, Apr 2004. [11] J. Borghetti, G.S. Snider, P.J. Kuekes, J.J. Yang, D.R. Stewart and R.S. Williams, Memristive switches enable stateful logic operations via material implication, Nature Letters, vol. 464, 2010. [12] S. Shin, K.Kim, S.M. Kang, Memristor Applications for Programmable Analog ICs, IEEE Trans. on Nanotechnology, vol. 8, Issue 6, 2009. [13] B. Linares-Barranco and T. Serrano-Gotarredona, Memristance can explain Spike-Time-Dependent-Plasticity in Neural Synapses, Nature Precedings, Mar 2009. [14] S.H. Jo, T. Chang, I. Ebong, B.B. Bhadviya, P. Mazumder and W. Lu, Nanoscale Memristor Device as Synapse in Neuromorphic Systems, Nano Letters, American Chemical Society, vol. 10, no. 4, pp. 12971301, 2010. [15] Y. Pershin, S. La Fontaine and M. Di Ventra, Memristive model of amoeba learning, Phys. Rev. E, vol. 80, pp. 021926, Aug 2009. [16] D.B. Strukov, G.S. Snider, D.R. Stewart and R.S. Williams, The Missing Memristor Found, Nature, vol. 453, pp. 83-86, May 2008. [17] Z. Biolek, D. Biolek and V. Biolkova, SPICE Model of Memristor with Non-linear Dopant Drift, Radioengineering, vol. 18, pp. 210-214, Jun 2009. [18] Y.N. Joglekar and S.J. Wolf, The Elusive Memristor: Properties of Basic Electrical Circuits, European Journal Of Physics, vol. 30, pp. 661-675, 2009. [19] S. Benderli and T.A. Wey, On SPICE macromodelling of TiO2 memristors, IET Electronics Lett., vol. 45, pp. 377-379, 2009. [20] T. Prodromakis, K. Michelakis and C. Toumazou, Fabrication and Electrical Characteristics of Memristors with TiO2/TiO2+x active layers, IEEE ISCAS, May 2010. [21] T. Prodromakis, K. Michelakis and C. Toumazou, Switching mechanisms in microscale Memristors, IET Electronic Letters, vol. 46, no. 1, pp. 63-65, 2010. [22] N. Gergel-Hackett, B. Hamadani, B. Dunlap, J. Suehle, C. Richter, C. Hacker, and D. Gundlach, A flexible solution-processed memristor, IEEE Electron Device Letters, vol. 30, no. 7, pp. 706-708, 2009. [23] R. Waser, R. Dittmann, G. Staikov and K. Szot, ”Redox-Based Resistive Switching Memories - Nanoionic Mechanisms, Prospects, and Challenges”, Adv. Mater., vol. 21, pp. 2632-2663, 2009. [24] D.B. Strukov, J.L. Borghetti and R.S. Williams, Coupled Ionic and Electronic Transport Model of Thin-Film Semiconductor Memristive Behavior, vol. 5, no. 9, Small, Wiley-VCH Verlag, 2009. [25] H. Yan, S.W. Nam, Y. Hu, S. Das, J.F. Klemic, J.C. Ellenbogen and C.M. Lieber, Programmable nanowire circuits for nanoprocessors, Nature Letters, vol. 470, 2011.
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Themistoklis Prodromakis (AM04-M08) holds a Corrigan research fellowship in nanoscale science and technology, funded by LSI Logic Inc. and the Corrigan-Walla Foundation, within the Centre for Bio-inspired Technology at Imperial College London. He received his PhD from the Department of Electrical and Electronic Engineering at Imperial College in 2008, during which he successfully pioneered the use of interfacial polarisations for demonstrating miniature passive devices. During his research career he has contributed in several projects in the areas of RF and Microwave Design and particularly Electron Devices, including: miniaturisation techniques MEMS-based phase-shifting topologies, slow-wave filters on laminar architectures, high-k dielectrics and processing techniques for engineering polarisation mechanisms. In 2006 he contributed in setting up the Cleanroom facilities and the Microelectronics Laboratory at the Institute of Biomedical Engineering. He recently applied his expertise in the biomedical arena with some examples involving: the development of integrated CMOS chemical sensors, encapsulation techniques and materials and biologically inspired systems. His hands on experience on fabricating and testing electronic devices by utilising intentionally planted deficiencies lead him to his latest exploitation of memristive elements.
Boon Pin Peh
Christos Papavassiliou (M’96-SM’05) was born in Athens, Greece, in 1960. He received the B.Sc. degree in physics from the Massachusetts Institute of Technology, Cambridge, and the Ph.D. degree in applied physics from Yale University, New Haven, CT. He has worked on monolithic microwave integrated circuit (MMIC) design and measurements at Foundation for Research and Technology - Hellas and has been involved in several European and regional projects on GaAs MMIC technology. In 1996, he joined Imperial College London, London, U.K., where he is a Senior Lecturer. He currently works on SiGe technology development as well as instrumentation and substrate noise coupling in mixed mode integrated circuit design. He has contributed to 40 publications.
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Christofer Toumazou (M’87-SM’99-F’01) holds a BSc degree in Engineering and a PhD from Oxford Brookes University, the latter in collaboration with UMIST (now University of Manchester). He is a Professor of Circuit Design, Founder and Executive Director of the Institute of Biomedical Engineering at Imperial College London, UK. Professor Toumazou has made outstanding contributions to the fields of low power analogue circuit design and current mode circuits and systems for biomedical and wireless applications. Through his extensive record of research, he has invented innovative electronic devices ranging from dual mode cellular phones to ultra-low power devices for both medical diagnosis and therapy. He has published over 320 research papers in the field of RF and low power electronics and is a member of many professional committees.. He holds 23 patents in the field, many of which are now fully granted Patent Cooperation Treaty (PCT). He is the founder of four technology based companies with applications spanning ultra low-power mobile technology and wireless vital sign monitors (Toumaz Technology Ltd, UK), biomedical devices (Applied Bionics PTE, Singapore), digital audio broadcasting (FutureWaves Pte Taiwan) and DNA detection (DNA Electronics Ltd, UK). These companies employ over 50 RF/low power engineers worldwide many of whom are Professor Toumazou’s ex-graduate students. Professor Toumazou was invited to deliver the 2003 Royal Society Clifford Patterson Prize Lecture, entitled ”The Bionic Man”, for which he was awarded The Royal Society Clifford Patterson bronze medal. He was recently awarded the IEEE CAS Society Education Award for pioneering contributions to telecommunications and biomedical circuits and systems, and the Silver Medal from the Royal Academy of Engineering for his outstanding personal contributions to British engineering. In 2008, he was elected to the grade of Fellow of both the Royal Society and Royal Academy of Engineering.
