Nanofluidic memristor based on the elastic deformation of nanopores with nanoparticle adsorption

ABSTRACT The memristor is the building block of neuromorphic computing. We report a new type of nanofluidic memristor based on the principle of elastic strain on polymer nanopores. With nanoparticles absorbed at the wall of a single conical polymer nanopore, we find a pinched hysteresis of the current within a scanning frequency range of 0.01–0.1 Hz, switching to a diode below 0.01 Hz and a resistor above 0.1 Hz. We attribute the current hysteresis to the elastic strain at the tip side of the nanopore, caused by electrical force on the particles adsorbed at the inner wall surface. Our simulation and analytical equations match well with experimental results, with a phase diagram for predicting the system transitions. We demonstrate the plasticity of our nanofluidic memristor to be similar to a biological synapse. Our findings pave a new way for ionic neuromorphic computing using nanofluidic memristors.

1 Methods and Materials Figure S1: (a) the schematic picture of a single energetic heavy ion bombard the polymer foil, forming a single 1D latent track on the polymer foil.The chemical etching rate of latent track along the trajectory of heavy ion irradiation is over two orders magnitude of the bulk materials, which enables to fabricate 1D nanotube in the PET foil.(b) shows the etching-stopping etching procedure of a conical nanochannel [1,2].The 9M KOH solution etched the single single side of the latent track, forming a base side of the nanochannel.We applied a DC bias voltage on the conical nanochannel, and stop the etching process by replacing the KOH stead of HCOOH acid, once we observed an current in the pico-ammeter.The etching process was immersed in a water bath with a constant temperature of 50 degrees.The tip side typically can be controlled within a few nanometers.(c) shows the resistance characterization by 1M KCl electrolyte solution, after the whole etching process.The diameter of base side can be estimated by the etching rate of the PET foil, and calculated the diameter of tip side by resistance of the conical pore as G = κπdD/L where d, D, L, κ are the diameter at tip side, base side, length of channel and conductivity of solution respectively.(d) The SEM image of the base side of nanochannel, which were etched after 70 minutes in the water bath.-5 .

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C u r r e n t ( µA ) T i m e ( s ) -5 .

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T i m e ( s ) -5 .

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T i m e ( s ) Figure S7: (a), (b), (c), (d) and (e) are the current recording in the experiments with scanning frequencies of 0.01Hz, 0.05Hz, 0.1Hz, 0.25Hz and 0.5Hz with amplitude of 5V.The devices can excellent repeat the I-V curves for over 30 cycles and up to 60 cycles at frequencies of 0.05Hz, 0.1Hz, 0.25Hz and 0.5Hz.shown in the manuscript, although we can found various type of current hysteresis in different specimens possibly due to the thin film properties at tip side.Our results in amplitude of 1V didn't represents clear current hysteresis, illustrating that the amplitude of voltage or electrical field is critical for inducing the resistance switches in our nanofluidic memristor.The results shows that the limit of current in positive and negative bias voltage, possibly indicates the saturated strain of the tip.The represented results here is measured from the same specimens in the main text.As can be seen, the deformation is limited at the negative applied pressure, since the roughness at the circumstance of tip may resist a perfect close of the channel.Thus, as we found in the experiments, we have a smallest value of the conductance at negative voltage (∼ 0.1).To mimic this process, we set a stress of σ/σ 0 ∼ e −d/d 0 , where d 0 = 7.93nm is a critical diameter that resists further deformation.Finally, we could account the position and calculate the strain of polymer tip as a function of applied voltage shown in (c) as the solution in equilibrium states (or saying in ∆t/τ ≫ 1), which matched well with the experimental results with frequency of 0.005Hz and amplitude of 5V.

1. 1
Fabrication of a single conical track etched nanochannel

Figure S2 :
Figure S2: The nanofluidic memristor with addition of SiO 2 nanoparticles (green dots) in the base side, in 1M KCl solution at pH=8.5.Two Ag/AgCl electrodes were placed in two reservoirs, connected with pico-ammeter or electrochemical station for the scanning of voltage and current measurements.The sedimentary of NPs will not affected the performance of devices, once NPs adsorbed at the inner surface of nanochannel.The experimental measurements in pure KCl after NPs adsorbed channel proved our hypothesis as shown in Fig.S3.

1. 3
Figure S3: To avoid the effects of sedimentary of NPs in solution, we first work with KCl solutions to make nanoparticles adsorbed at surface by directional electrophoretic (left figure).The solution can be less than 1M KCl, to ensure the adsorption of NPs.Then, we refreshed with the pure KCl solutions (without NPs) and operated the electrical measurements.The results shown in this response letter were operated in the pure KCl solutions, which well repeated the memrisistive behavior in manuscript.The memrisistive characteristics in pure KCl solution indicates the results of memristor can be well repeated in pure KCl solution, avoiding the impacts of NPs sedimentation.The blue and red dots are ions in solution, and yellow dots are nanoparticles.

Figure S4 :
Figure S4: The I-V curves measured at 2022.December (a) and measurements recently at 2023.April (b).Our nanofluidic devices can repeated well after four months storage.The results in (b) followed the two-step measurement procedures in Fig.S3 in pure 1M KCl solutions, where no SiO 2 nanoparticles dissolved in the 1M KCl aqueous solution.We could still excellent repeated the current hysteresis in long-term storage.

2. 2
FigureS5: (a).Measured I-V curve after adsorption of PS NPs.We first operated with DC voltage to drive the PS nanoparticles in the channel.Then we measured with a pure KCl solution (1M) at pH over 8.5 in various range of voltage amplitude.We still found a clear current hysteresis in the system, as similar to the results of SiO 2 NPs.(b).We repeated the electrical measurement process by dissolving CrSe quantum dots instead (pH over 8.5), where we found similar results in the devices.Since the conductance transition was caused by the stress on the tip side of nanochannel, the geometry deformation thus conductance transitions was dominated by the surface charge properties of dielectric NPs.Thus, it matters with the weak surface charge density on NPs, instead of material properties of NPs.The SiO 2 , CrSe and PS NPs showed similar current hysteresis in 1M KCl solution.

Figure S6 :
FigureS6: The typical I-V curves followed the two-step measurement procedure, using SiO 2 NPs with various KCl electrolyte solutions at pH=8.5.(a).The results in 1M KCl solutions showed clear current hysteresis which well repeated the previous results again in manuscript.(b).The shape of current hysteresis is even enlarged in 0.1 M KCl solutions, possibly due to the increase of surface charge density of NPs and contribution of surface conduction.However, as (c), (d) and (e) show the ohmic relationship between current and voltage in 0.01 M, 0.001 M, 0.0001 M KCl solution respectively, the current hysteresis gradually vanished as decreases of concentration , which indicates the surface conduction dominated so that the geometry change of pore tips will not affect the system conduction (comparable to the conduction plateau when double layer overlaps, as Ref.[3]. r e n t ( µA ) Figure S8: (a) the I-V curves with amplitude of scanning voltage of 10V, in various scanning frequencies.(b) the I-V curves with amplitude of scanning voltage of 20V, in various scanning frequencies.(c) The typical I-V curves with voltage amplitude of 1V in various scanning frequencies.Our results in amplitude of 1V didn't represents clear current hysteresis, illustrating that the amplitude of voltage or electrical field is critical for inducing the resistance switches in our nanofluidic memristor.The results shows that the limit of current in positive and negative bias voltage, possibly indicates the saturated strain of the tip.The represented results here is measured from the same specimens in the main text.

Figure S9 :
Figure S9: As we suspect the strain of nanopore tip side was activated by electrical force on the NPs.Hereby we measured the current responses under scanning frequencies of 0.025Hz in different solutions.(a) The current represents a current hysteresis at pH 8.5 solution, however not in pH3.5 solution(b) in the same frequencies.The measurements were measured in specimen 2.

2. 7 Figure
Figure S10: To find the impact of particle size, we use the NPs with diameter of 100nm instead of the 15nm NPs in specimen 3. The figure (a) shows the typical I-V curves before adding NPs while figure (b) shows the typical I-V curves after NPs addictive.The resistance significantly increases with NPs, however still behave with a current hysteresis, again approving the key role of NPs in current hysteresis.