Supplementary Information

Exploration and Characterization of the Memcapacitor and Memristor Properties of Ni-DNA Nanowire Devices

Hsueh-Liang Chu1,2‡, Jian-Jhong Lai3‡, Li-Ying Wu3, Shen-Lin Chang3, Chia-Ming

Liu3, Wen-Bin Jian3*, Yu-Chang Chen3*, Chiun-Jye Yuan1, Tai-Sing Wu4, Yun-Liang

Soo4, Massimiliano Di Ventra5, Chia-Ching Chang1, 6*

1. Department of Biological Science and Technology, National Chiao Tung

University, Hsinchu, Taiwan, 30068, R.O.C.

2. Ph.D. program for Translational Medicine, College of Medicine

and Technology, Taipei Medical University, Taipei city, Taiwan,

10031, R.O.C.

3. Department of Electrophysics, National Chiao Tung University, Hsinchu,

Taiwan, 30010, R.O.C

4. Department of Physics, National Tsing Hua University, Hsinchu, 30050,

R.O.C.

5. Department of Physics, University of California, San Diego, 92093, U.S.A

6. Institute of Physics, Academia Sinica, Taipei, Taiwan, 11529, R.O.C.

‡ These authors contributed equally.

*Corresponding authors:

1. Chia-Ching Chang, Affiliation: Department of Biological Science and Technology, National

Chiao Tung University, Hsinchu, 30068, Taiwan Postal: R203, Bio-Lab II, National Chiao Tung University, 75,

Bo-Ai Street, Hsinchu, 30068 Taiwan. Tel: +886-35731633E-mail: ccchang01@faculty.nctu.edu.tw

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2. Wen-Bin JianAffiliation: Department of Electrophysics, National Chiao Tung University,

Hsinchu, 30010, TaiwanPostal: R512, Science Building III, National Chiao Tung University, No

1001, Ta Hsueh Rd, Hsinchu 300, Taiwan.Tel: Phone number: +886-3-5712121 ext. 56159 E-mail: wbjian@mail.nctu.edu.tw

3. Yu-Chang Chen, Affiliation: Department of Electrophysics, National Chiao Tung University, Hsinchu, 30010, TaiwanPostal: R403, Science Building III, National Chiao Tung University, No 1001, Ta Hsueh Rd, Hsinchu 300, Taiwan.Tel: +886-3-5712121 ext. 31203 E-mail: yuchangchen@mail.nctu.edu.tw

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I. THEORETICAL MODEL AND SIMULATIONS FOR Ni-DNA

The insulating DNA nanowire conducts the current through Ni ions chelating on

it, as shown in Figure S4. When the current driven by AC source traversing the Ni-

DNA system, it triggers redox reactions:

¿2+¿

oxidation→

reduction← ¿3+¿+e−¿ ,¿¿ ¿ (1)

where the ¿2+¿¿ (¿3+¿¿) ions release (absorb) electrons due to the oxidation (reduction)

reactions via the positive (negative) biased voltage.

The Ni-DNA system records information through the nickel ion states. The

voltage-driven dynamic state of the nickel ions offers the key to an understanding the

functionality of the multifunction memcomputing device. The number of ¿3+¿¿ ions as

a function of time, denoted by N (t ), serve as the state variables for memristor and

memcapacitor subcomponents. N (t ) can be estimated by the modified Arrehenius rate

equations:

dN (t )dt

=kox [T ,V (t)] ∙[N 0−N (t)]k red [T ,V (t)] ∙ N ( t) , (2)

where kox[T,V(t)] (kred[T,V(t)]) is the oxidation (reduction) rate constant which depends

on temperature and the AC source. The rate constants are estimated by,

k ox [T , V (t ) ]=kox0 exp {−β [ Eox−eV (t ) ]

α k BT } (3)

and

k red [T ,V ( t ) ]=kred0 exp {(1−β )[ Ered−eV (t ) ]

α kB T } (4)

respectively, where k ox0 (k red

0 ) is the rate constant of the redox reaction; Eox (Ered) is the

activation energy required to trigger significant oxidation (reduction) reactions; we

choose symmetry factor =1/2; k Bis the Boltzmann constants; α ≈30 is a parameter to

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tune the rate constants suitable for the particular Ni-DNA system. This nanowire

length dependent conducting current enhance effect indicate that the nickel ion redox

reaction effect acts as negative resistance element.

Memristor defined here is a nonlinear resistive device, where the resistance is a

function of dynamic states, which keeps track of the system’s past dynamics. The

concept of memristor can be generalized to capacitive system. Let us first introduce

the definition of voltage-controlled memristor and memcapacitor.

Definition of a voltage-controlled memristor

We define a voltage-controlled memristive system is described by

V ( t )=R ( x , V ,t ) I (t ) ,

x=f (x , V ,t ) ,

where x is a dynamic state variables; V(t) and I(t) denote the voltage and current

across the memristor device; R is the memrisitance which depend on the state.

Definition of a voltage-controlled memcapacitor

We define a voltage-controlled memcapacitive system is described by

qMC ( t )=C ( x ,V , t )V (t ) ,

x=f (x , V ,t ) ,

where C is the memcapacitance which is a function of the state variables.

Our experiments provide convincing evidence in support of the Ni-DNA system

as a multifunction memcomputing device. More specifically, the Ni-DNA

memprocessor device incorporates the functionality of memristor and memcapacitor

simultaneously.

The DNA guided Ni ions chain is a multifunction device, which incorporates

the functionality of memristorm, memcapacitor, and negative resistance element. The

circuit model of the Ni-DNA system is shown in Figure S6, where the Ni-DNA

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system consists of a voltage-controlled memristor, a voltage-controlled memcapacitor,

and a cyclic voltammetry connected in parallel. The voltage-controlled current is the

sum of contribution from three subcomponents independently, i.e.,

I (t )=I MR ( t )+ I MC (t )+ I red ( t ) . (5)

I MR (t )=V (t)R(t ) is the current flowing through the voltage-controlled memristor with a

memristance, R(t ), described as follows:

R ( t )=[1− N ( t )N0 ] R

2+¿+[N (t )N0

] R3+¿¿ ¿, (6)

where N0 is the total number of the ¿2+¿¿ and ¿3+¿¿ions; R2+ ¿=1.26 ×109 Ω¿ [R3+¿=1.05 ×109 Ω¿ is

chosen for the resistance when all nickle ions base pair are completely in the ¿2+¿¿ (

¿3+¿¿) states. The variable resistance is a function of N (t ), which serves as a state

variables of the memristive system.

The charge accumulation due to electron emission and absorption introduces

forms a source of memcacipctor with a memcapacitance C (t).

I MC ( t )≡ ddt

[qMC (t )]= ddt [C ( t )V ( t )] is the current flowing through the voltage-

controlled memcapacitor described as follows:

1C(t )

= 1

C2+¿+N (t )N0

¿¿ (7)

where C2+¿=1.08 × 10−9 F ¿ ¿¿] is chosen for the capacitance when all nickel ions are

completely in the ¿2+¿¿ (¿3+¿¿) states. N (t ) is the state variable of the memcapacitive

system.

The current flowing through the redox reaction is I red ( t )=fe dN (t)dt

, which is due

to the redox couple and N (t ) describes the dynamic redox states of ¿3+¿¿ ions, where

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f =106.

The current flowing through (charge accumulated on) the Ni-DNA system

depends on the history of the voltage. The current (charge) and the voltage form

hysteresis I-V (q-V) loops, as shown in Figure 2. Response of the current (charge)

depends on the history of V(t) is one of the most important characteristics of the

memristor (memcapacitor) functionality.

The time evolution of ¿3+¿¿ ion states,N (t ), can be solved from the modified

Arrehenius rate equations when the initial condition of N (t ) is given. However, when

the system reach steady state, the secular solution is independent of the initial value of

N (t ). ¿2+¿¿ and ¿3+¿¿ states finally reach chemical equilibrium via redox reaction

under ambient environment and zero bias, limt → ∞

N (t)/ N0 ≈ 0.42412, as shown in Figure

S7. In this study, all the time-dependent calculations use a single set of parameters

with an initial value of N (t=0)/ N0=0.42412.

Generally, about 60% fabricated Ni-DNA devices showed correct

redox I-V loops. About 20 of these successfully fabricated Ni-DNA

devices were tested and all of them exhibited similar electric

properties. The data from all 20 devices were presented in Figure S8.

Three different Ni-DNA devices of the twenty were further analyzed their

memrestor/memcapacitor characteristics in this study. Additionally, the I-V loops of

Ni-DNA and native DNA nanowires were shown in Figure S9 as control.

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II. FIGURES (a)

(b)

FIG. S1. Ni K-edge X-ray absorption near-edge structure (XANES) spectra. (a)

XANES spectra of NiO (red line), Ni2+-histidine complex (green line), and Ni-

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DNA (blue line). (b) XANES spectra of NiCl2 (black line) and Ni-DNA (red

line).

(a)

(b)

FIG. S2. (a) The LUMO molecular orbital of Ni-G-C base pair. The cyan sphere

denoted the Ni ion. (b) The excited state molecular orbital of Ni-G-C base pair. The

red circle denoted the position of water molecule.

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FIG. S3. Circuit diagram and SEM image of patterned electrodes for trapping

Ni-DNA nanowires in the gap by DC electrophoresis. The blue area marks the

area covered by a drop of Ni-DNA solution. The scale bar on the SEM image is

20 μm.

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FIG. S4. Schematic diagram of Ni-DNA device and its circuit configuration.

The blue and the red spheres denote Ni2+ and Ni3+ ions, respectively, whereas

the ions are aligned by the DNA template.

FIG. S5. The comparison of experimental (red open squares) and calculated (red solid

line) I-V loops showing the hysteresis feature. The experiment was carried out by step

voltages with a scan rate of 0.33 V/sec. The black dotted line shows the background

current signals of the patterned electrodes without any Ni-DNA nanowires attached in

the gap.

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FIG. S6. The effective circuit model for the Ni-DNA system connected to a

programable AC source. Symbols 1, 2, and 3 denote the devices of memristor,

memcapacitor, and Ni ion redox-induced hysteresis (NDR) device, respectively.

FIG. S7. The evolutions of N (t )/N 0 as a function of time under the ambient

environment at zero bias calculated by the modified Arrehenius rate equation for

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various initial conditions: (i) N (0)/ N0=¿0.5 (black solid line), (ii) N (0)/ N0=¿1 (red

dot-dotdashed line), and (iii) N (0)/ N0=¿0 (blue dotted line). Dashed line is the

asymptotic value of 0.42412 when the chemical equilibrium is reached.

FIG. S8. Typical I-V loops of Ni-DNA nanowires for twenty different devices.

FIG. S9. Typical I-V loops of Ni-DNA (black open circles) and native DNA (red open squares) nanowires. It is noted that the current of native DNA nanowires is much

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smaller than that of Ni-DNA nanowires.

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