Research Article Cite This: ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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Pulse Dynamics of Electric Double Layer Formation on All-SolidState Graphene Field-Effect Transistors Ke Xu,† Md Mahbubul Islam,‡ David Guzman,‡ Alan C. Seabaugh,§ Alejandro Strachan,‡ and Susan K. Fullerton-Shirey*,†,∥ Department of Chemical and Petroleum Engineering and ∥Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States ‡ School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, United States § Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556, United States Downloaded via UNIV OF WINNIPEG on November 29, 2018 at 17:59:59 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
†
S Supporting Information *
ABSTRACT: Electric double layer (EDL) dynamics in graphene field-effect transistors (FETs) gated with polyethylene oxide (PEO)-based electrolytes are studied by molecular dynamics (MD) simulations from picoseconds to nanoseconds and experimentally from microseconds to milliseconds. Under an applied field of approximately mV/nm, EDL formation on graphene FETs gated with PEO:CsClO4 occurs on the timescale of microseconds at room temperature and strengthens within 1 ms to a sheet carrier density of nS ≈ 1013 cm−2. Stronger EDLs (i.e., larger nS) are induced experimentally by pulsing with applied voltages exceeding the electrochemical window of the electrolyte; electrochemistry is avoided using short pulses of a few milliseconds. Dynamics on picosecond to nanosecond timescales are accessed using MD simulations of PEO:LiClO4 between graphene electrodes with field strengths of hundreds of mV/nm which is 100× larger than experiment. At 100 mV/nm, EDL formation initiates in sub-nanoseconds achieving charge densities up to 6 × 1013 cm−2 within 3 nanoseconds. The modeling shows that under sufficiently high electric fields, EDLs with densities ∼1013 cm−2 can form within a nanosecond, which is a timescale relevant for high-performance electronics such as EDL transistors (EDLTs). Moreover, the combination of experiment and modeling shows that the timescale for EDL formation (nS = 1013 to 1014 cm−2) can be tuned by 9 orders of magnitude by adjusting the field strength by only 3 orders of magnitude. KEYWORDS: electric double layer, field-effect transistor, EDLT, molecular dynamics, graphene, solid polymer electrolyte, ion transport, iontronics superconductivity,6,7 spintronics,8 and insulator-to-metal transitions.9 EDLs have been formed on insulators,6,7,9 metals,10 and semiconductors including two-dimensional (2D) crystal semiconductors.8,11−13 Because of the versatility and large carrier densities achievable by EDL gating, the technique has been explored for use in next-generation electronics, such as 2D crystal EDL transistors (EDLTs).2,11,13,14 Furthermore, because the electrical response of EDL formation and dissipation resembles synaptic dynamic plasticity in neurons,15,16 EDLTs show
1. INTRODUCTION Electric double layer (EDL) gating is a commonly used technique to access regimes of transport in semiconductors that cannot be achieved with conventional gate dielectrics. In response to an applied electric field, ions accumulate at the interface between an ion-conducting electrolyte and a semiconducting channel. The ions induce counter charges in the channel leading to high capacitance density (∼10 μF/cm2) and large field strength (>1 V/nm) at the interface.1,2 For example, while the maximum sheet carrier density for transistor dielectrics (e.g., HfO2, Al2O3, and SiO2) is on the order of 1013 cm−2,3 EDLs can induce charge carrier densities exceeding 1014 cm−2.4,5 These high charge densities have enabled studies of exciting new physics and material properties including © XXXX American Chemical Society
Received: August 9, 2018 Accepted: November 13, 2018 Published: November 13, 2018 A
DOI: 10.1021/acsami.8b13649 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Research Article
ACS Applied Materials & Interfaces promise in the emerging field of synaptic devices for neuromorphic computing.16−18 However, in the aforementioned applications for which the EDL is an active device component, the EDL-gated device must operate at a sufficiently fast speed to be competitive with Si metal oxide semiconductor technology (e.g., milliseconds or faster for flash memory, nanoseconds or faster for transistors, and dynamic random access memory).19,20 When EDL gating is used as a tool to explore transport, a common approach is to hold the applied bias constant until the EDL is fully formed, which requires seconds or more in a solid-state polymer electrolytes at room temperature.5,21,22 While this is too slow for the applications mentioned above, there are several approaches to overcome this limitation. First, the formation time can be reduced by increasing the ionic mobility and/or applied electric field strength. While the maximum voltage that can be applied is limited by the electrochemical window of the electrolyte (i.e., the voltage at which the electrolyte will undergo oxidation and reduction reactions), it could be possible to avoid these reactions if the field is applied only for a short time (e.g., milliseconds or less). Second, although full EDL formation (i.e., up to 1014 cm−2) will require longer times to complete, the onset of EDL formation is predicted to happen at much shorter timescales (e.g., nanoseconds under electric field of ∼1 V/nm).23,24 If a sufficient number of charge carriers are induced during the initial stages of EDL formation to achieve a distinguishable modulation in the channel resistance, the device could potentially operate at faster speed with partial EDL formation. For these reasons, it is critical to understand (1) the fundamental limit to EDL formation/dissipation times and its relationship to the applied electric field strength and ion mobility within the dielectric and (2) the percentage of the EDL that forms as a function of timeespecially at picosecond to nanosecond timescales which have not been reported previously. In addition to speed, a solid-state electrolyte is more desirable than an ionic liquid or ion-conducting gel for straightforward device integration and design flexibility. Solidstate polymer electrolytes can serve as a negative resist for direct patterning by electron beam lithography25 and can be made compatible with optical lithography.26 Despite significant achievements in the use of EDL gating, a comprehensive understanding of EDL dynamicsespecially over timescales relevant to digital applications (i.e., 0) in the n-type graphene channel. The timing of the pulse measurements is summarized in Figure 1b, where each pulse at a particular voltage is repeated three times. Between each pulse, all contacts are set to zero volts for 30 s to reset the ions to equilibrium. Previously, we showed that EDL relaxation occurs on the timescale of hundreds of milliseconds for Li+ and ClO4− in PEO at room B
DOI: 10.1021/acsami.8b13649 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
Figure 2. (a) Schematic of an exfoliated graphene FET with 90 nm SiO2 on Si (control sample) and backgate pulse response. (b) Schematic of an ion-gated graphene EDL FET on SiC for which the voltage is applied to a sidegate through a polymer electrolyte (SiC substrate is floated). The current response for each Epulse is repeated three times, and only the third measurement is shown for clarity. The channel length (width) for (a,b) is 5 (2) μm and 8 (3) μm, respectively. The contact metal in both devices is Ti/Au (5/100 nm).
before ion diffusion occurs. Therefore, ΔID will include a combination of both electronic and ionic responses. While the electronic response cannot be time-resolved by the instrument, the electronic signal (i.e., ΔID as a result of dielectric gating) can be detected. To distinguish the electronic and ionic contributions, control experiments were first conducted on bare, back-gated graphene FETs (i.e., no electrolyte gate, Figure 2a) to monitor the electronic response. Multiple pulses with different pulse voltages were applied to the backgate while monitoring ΔID. As shown in Figure 2a, ΔID increased during the pulse, but returned to zero as soon as the pulse voltage was removed because the response of electrons is faster than the millisecond sampling rate. In Figure 2b, the polymer electrolyte is applied and the measurement is repeated. In contrast to the bare FET, ΔID increases during the pulse but does not return to zero immediately after VG is set to zero. Instead, ΔID gradually decays over a few hundreds of milliseconds, corresponding to the ions in the EDL relaxing back to their equilibrium positions in the bulk electrolyte over timescales consistent with our previous report.21 The current decay indicates that the ions responded to the electric field and formed an EDL on times shorter than the pulse width (7 ms). 2.2. Millisecond Pulse Dynamics (Epulse ∼ 0.1−10 mV/ nm). Whereas Figure 2b shows the ion response to an Epulse varying from 0 to 0.8 mV/nm, Figure 3a shows the ID response when the Epulse is increased up to 6.7 mV/nm. To achieve these field strengths, the voltage applied to the gate must exceed the electrochemical window of the electrolyte (i.e., Vpulse > ±3 V;34 Epulse > 0.2 mV/nm); however, the ID response is consistent and repeatable at each applied bias, suggesting no irreversible change to the channel material or electrolyte. The data contain no features suggesting that electrochemical reactions are occurring, such as electrical shorts or increased leakage current from gate to source that could indicate the formation of conductive cesium filaments (for more discussion of gate leakage current, see the Supporting Information, Part II). The data suggest that when applying Vpulse on the timescale of milliseconds, it is possible to exceed the electrochemical
temperature,21 and a similar time constant is observed in this study, indicating that a 30 s reset time is sufficient for ions to return to equilibrium. Our objective is to characterize the dynamics of both the EDL formation and relaxation in response to a voltage pulse; however, depending on the pulse width and amplitude, the timescale of these two processes can differ by orders of magnitude,21 and therefore two different measurements with two different pulse widths were used. The resolution of the first approach (Section 2.2) is on the timescale of milliseconds (data taken every 5 ms, pulse width 7 ms), so that EDL dissipation can be captured in the window of the measurement. The resolution of the second approach, which will be discussed in Section 2.3, is on the timescale of microseconds (data taken every 0.3 μs, pulse width 1 ms), to focus on EDL formation. For both experimental approaches, the pulse parameters were optimized to apply the minimal pulse width that can achieve a reasonable signal-to-noise ratio (e.g., >5) so that the ion response can be clearly distinguished. Because initial formation of the EDL occurs on the timescale of picoseconds to nanoseconds (faster than the sampling rates of commercial semiconductor parameter analyzers used here), we study dynamics in this time regime using MD simulations (Section 2.4). Herein, we refer to the gate voltage applied during the pulse as the pulse voltage (Vpulse). Dividing Vpulse by the gateto-channel distance in the experiments and the distance between graphene electrodes in the MD simulations gives the pulsed electric field (Epulse). 2.1. Distinguishing Electronic and Ionic Responses to Epulse. The results of the millisecond resolution pulse measurements are shown in Figure 2. The change of current, ΔID = ID(t) − ID (t = 0), where ID (t = 0) is the drain current before the pulse is applied (i.e., before an EDL is formed). ΔID will arise from two contributions: (1) an electronic response from electronic and atomic polarization similar to conventional oxide dielectrics and (2) an ionic response, which includes the diffusion of mobile ions that result in the formation of the EDL. Because PEO has a dielectric constant of about 5 at room temperature,33 the ion gate will function as a conventional gate dielectric on sub-nanoseconds timescales C
DOI: 10.1021/acsami.8b13649 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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Figure 3. (a) Pulse voltage measurement on EDL FET with Epulse varying from 0 to 6.7 mV/nm. The green, horizontal bar highlights the current before EDL formation, while the red bar represents the change of current corresponding to the max EDL at Epulse = 6.7 mV/nm. Each pulse voltage was repeated three times, and all terminals were set to 0 V for 30 s between pulses. (b) Constant VG measurement to obtain the steady-state ID, corresponding to the strongest EDL that can be formed at VG = 3 V.
(2) the changes may be permanent or semipermanent and only reversed by applying a voltage of opposite polarity to create a counter reaction. The results above suggest that larger electric fields can be applied and irreversible changes to the device can be avoided as long as the Vpulse width is sufficiently small. It is important to note that the high estimated charge density (1014 cm−2) is not unrealistic. The charge density is proportional to the applied voltage which, as mentioned above, is limited by the electrochemical window of the electrolyte. Previously, Efetov and Kim used a low-temperature approach to increase the applied voltage beyond the electrochemical window, and they report charge densities up to 3 × 1014 cm−2 in EDL-gated graphene FETs.4 However, the timescale of their approach is much longer (i.e., minutes) than the timescales demonstrated here. The millisecond pulse measurements capture the current decayand therefore the EDL dissipation dynamicsafter Vpulse for 500 ms. The EDL relaxation time was quantified by fitting the current decay to a stretched exponential (Figure S2a) described by the Kohlrausch−Williams−Watts equation, which is used to describe polymer dynamics.35 The extracted relaxation time constants (τ) are on the order of hundreds of milliseconds (Figure S2b), in agreement with our previous study of dissipation dynamics after applying a constant dc gate voltage.21 This result suggests that the dissipation timescale is similar in the pulsed and dc voltage measurements, and that the 30 s reset time is sufficient for ions to return to equilibrium. The fact that EDL forms (partially) within 7 ms and dissipates over of hundreds of milliseconds confirms that the timescales of formation and dissipation can differ by orders of magnitude, which is potentially useful for applications such as in neuromorphic computing.16−18 2.3. Microsecond Pulse Dynamics (E p u l s e ∼ 0.1−10 mV/nm). Although detailed information regarding EDL dissipation dynamics can be learned by making measurements on millisecond timescales, limited information can be extracted regarding the initial formation and strengthening of the EDL. Therefore, a second set of pulse measurements were conducted on another device with microsecond time resolutionthe highest resolution of our instrumentation. The data are shown in Figure 4 with a sampling interval of 0.3 μs, pulse width of 1 ms, and rise/fall time of 3.9 μs. Although the pulse width itself is 1 ms, the sampling interval is 0.3 μs, thus enabling EDL dynamics to be
window of the electrolyte without inducing electrochemistry because the pulse time is sufficiently short. Note that the while the polymer electrolyte is in contact with source−drain, graphene channel, and gate, the electric field between the source and drain (∼7 × 10−3 mV/nm) is 2−3 orders of magnitude smaller than the gate electric field; therefore, ion transport is controlled by the gate. While the pulse measurement results show that cationic EDL formation occurs on milliseconds timescales under an electric field of ∼mV/nm, it is also clear that the strength of the EDL (i.e., the amount of charge induced in the channel and the resulting ΔID) depends on the pulse amplitude. To quantify the EDL strength, a control measurement was performed on the same device by applying constant VG = 3 V and monitoring ΔID after the device reached steady state (Figure 3b). This steady-state current reflects the maximum charge that can be induced by the EDL under a dc gate voltage of 3 V. Comparing the ΔID in Figure 3b from a dc bias to ΔID in Figure 3a from pulsing, the ΔID increases by about 3× by pulsing at Epulse = 6.7 mV/nm. Thus, by pulsing the voltage, larger field strengths can be achieved and therefore a stronger EDL can be created. Note that the larger maximum current obtained via pulsing cannot be attributed to the electronic contribution to the signal because the current does not decay back to its original value immediately after the pulse. In addition, to show that the pulse voltage source itself does not contribute to the current increase, the waveform of the pulse is reported in Figure S1a,b with a resolution of 20 ns; no spikes in the waveform are observed. We previously measured steady-state sheet carrier densities (ns) on the order of 5 × 1013 cm−2 under a constant gate voltage of 2 V by the Hall-effect.21 Because ns is directly proportional to ΔID, our result in Figure 3a,b in combination with our previous Hall measurement indicate that the achievable sheet carrier density in response to the Vpulse is in the order of 1014 cm−2. Creating a stronger EDL using a millisecond voltage pulse instead of a continuously applied dc voltage shows that a wider range of carrier density modulation can be achieved by pulsing, which could be important for applications such as EDLTs. The range of modulation is usually limited by the electrochemical window of the electrolyte because once a reaction happens, (1) intrinsic material properties of the channel, such as mobility and surface topology, can be affected and often degraded, and D
DOI: 10.1021/acsami.8b13649 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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Figure 4. (a) Schematic of bare graphene FET (control sample). Epulse (1 ms, 0.11 V/nm) is applied to the backgate through 90 nm of SiO2 while monitoring the ΔID. (b) Schematic of ion-gated graphene EDL FET. Epulse (1 ms, 2.3 mV/nm) is applied to the sidegate through the polymer electrolyte. A zoomed view of 100 μs before and after applying Epulse (indicated by pink square) is shown in (c). (d) Increasingly large Vpulse is applied for 1 ms, corresponding to an Epulse range of 0.3−2.3 mV/nm. The current response for each Epulse is repeated three times, and only the third measurement is shown for clarity.
distance is 3 orders of magnitude larger than the backgated control sample, so the charging current would be orders of magnitude smaller than the total drain current (see Supporting Information Part III). The formation and strengthening of the EDL is indicated by the continuous increase of ΔID during the pulse and the constant and non-zero ΔID after removing the pulse voltage, as shown in Figure 4b. Note that the current does not saturate within 1 ms, and the pulse width was not extended to observe saturation to minimize the possibility of electrochemical reaction. To learn more about the initial ion response, we first focus on the initial 100 μs after applying Vpulse, where ID continuously increases (Figure 4c). Because the increase reflects the strengthening of the EDL, this result shows that the ions are responding to the applied field and starting to form an EDL on the timescale of tens of microseconds. To determine the relationship between Epulse and the ion response speed, multiple measurements are made with pulse widths of 1 ms, and with Epulse varying from 0.3 to 2.3 mV/nm (Figure 4d). ΔID shows a similar trend for all field strengths, where ID continuously increases during the pulse and remains constant for 100 μs after removing the pulse and grounding the electrodes. The data at each applied field are repeatable over multiple measurements, and the initial ID for each pulse measurement remains constant. The gate leakage current is at least 3 orders of magnitude smaller than the channel conduction current (Figure S3). These observations suggest
monitored in sub-microseconds timescale. The waveform of the pulse was measured with a resolution of 0.8 ns (Supporting Information Figure S1) to confirm that there are no instrumental spikes in the pulse source. Similar to the millisecond pulse measurements presented in Section 2.2, the electronic and ionic contributions are decoupled with microsecond resolution using control measurements on a bare, back-gated graphene FET. As shown in Figure 4a, the ID increases instantly after applying the pulse voltage, remains constant during the pulse, and returns to the initial value immediately after removing pulse voltage, just as expected for an electronic response without an ion gate. A current spike is detected during the initial rise/fall of the pulse (e.g., ΔID decreased to −7.5 μA at t = 0 before increasing to 35 μA at t = 5 μs), which is caused by the displacement current similar to a parallel plate capacitor. In contrast, for the iongated sample shown in Figure 4b, ID increases abruptly by a small amount (e.g., ∼1.5 μA for Epulse = 2.3 mV/nm) during the rise of the pulse and continues increasing during the pulse (e.g., up to ∼50 μA for Epulse = 2.3 mV/nm). During the fall of the pulse voltage, ΔID decreases abruptly by a small amount (e.g., ∼1.5 μA for Epulse = 2.3 mV/nm) and remains nearly constant for the next 100 μs. The responses during the rise/fall of the pulse are expected because of (1) dielectric gating and (2) the initialization of the EDL, which will be discussed in detail in Section 2.4. The displacement current spike is not observed in ion-gated sample because the gate-to-channel E
DOI: 10.1021/acsami.8b13649 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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Figure 5. MD simulation of EDL formation for an applied electric field of 50 mV/nm. (a) Simulation snapshots of ion dynamics. (b) Temporal evolution of induced charges (Δqρ) on both electrodes. The center two curves labeled “Ionic” are the charges induced by ionic motion only (i.e., the electronic contribution has been subtracted). A break in the X axis is placed at t = 1.0 ps to highlight the evolution of charges and ion motion within 1 ps. (c) Time evolution of the center of mass position of both positive and negative ions scaled by the thickness of the electrolyte.
chemical dynamics with implicit degrees of freedom (EChemDID)24,38 method is used to apply an external electrochemical potential to the electrodes. Note that during EDL formation, the field strength experienced by each ion is a function of its position with respect to the electrodes, both in the experiments and the simulations. For example, the field within a few nanometers of the electrolyte/electrode (channel) interface will increase up to V/nm when the EDL is formed.2,14 The field strength near the channel cannot be measured experimentally in this study; therefore, to compare the MD simulations to the experiments, the field strength is reported the same way for both: Epulse = Vpulse/d where d is the distance between the electrodes in the simulation and the gate to source distance in the experiments (see Supporting Information, Part V). Figure 5a shows atomistic snapshots of the simulation at time = 0, 0.1, 1, 2, and 4 ns with an applied field of 50 mV/nm. Interestingly, the snapshots show that while ClO4− ions (green) have higher mobility than Li+, in agreement with experiments as will be discussed below, the Li+ accumulates closer to the electrode than the ClO4− ions. We attribute this difference to the size of the ions and the strength of the applied field. Note that when the field strength is doubled from that in Figure 5a, the ClO4− ions migrate closer to the electrode surface (Figure S6). While Li+ accumulates closer to the graphene electrode than ClO4− under 50 mV/nm, the saturation charge density is similar at both electrodes. The time evolution of the induced charge density in the graphene electrodes is provided in Figure 5b, and the time evolution of the center of mass of the Li+ and ClO4− ions along the direction of the field and scaled to the dimension of the electrolyte is shown in Figure 5c. The scaled center of mass equals 0 (1) when all ions are at the interface of anode (cathode), respectively. As soon as the electric field is applied, QEq reassigns the atomic charges instantaneously, corresponding to the electronic response of the system as
the device was completely reset after each measurement (i.e., the ions relaxed back to their equilibrium positions between measurements), and that there is no irreversible change to the channel material or the electrolyte. The results in Figure 4d show that the EDL formation speed is proportional to the magnitude of the applied electric field. For example, it takes 670 μs to increase the drain current by 5 μA at 0.3 mV/nm, and the time can be reduced 7× by increasing the field to 2.3 mV/nm (horizontal cutline in Figure 4d). On the other hand, at t = 1000 μs, the ΔID increases by a factor of 10 (from 5 to 50 μA) when the field increased from 0.3 to 2.3 mV/nm (vertical cutline in Figure 4d). A linear dependence of ΔID on electric field (Figure S4) in the range of 0.3−2.3 mV/nm implies that the ion response speed also depends linearly on applied field. Thus, with further device scaling (i.e., higher electric fields), it could be possible for the ion response time to be orders of magnitude faster. Experimentally, the microsecond resolution is approaching the limit of our instrument, and the field strength is limited by the geometry of the devices. To validate and explore the limits of ion response time, we performed MD simulations at 100× larger electric fields than the experiments, which are discussed in the next section. 2.4. Nanosecond Pulse Dynamics (Epulse ∼ 10−100 mV/nm). To explore the limits of switching speed and miniaturization, we performed MD simulations with short voltage pulses at fields up to 100 mV/nm. While the electronic and ionic responses from the EDL can be distinguished but not resolved in the experiments, MD simulation can resolve both contributions with sub-nanosecond resolution. A parallel plate geometry is used for the model, with 15 nm of PEO:LiClO4 separating graphene electrodes with a surface area of 19.55 nm2 (Figure 5a). Atomic interactions are described using the Dreiding force field36 with charges computed self-consistently at each step of the simulation using extended charge equilibration (QEq).37 The electroF
DOI: 10.1021/acsami.8b13649 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces indicated by two arrows in Figure 5b and labeled “Electronic”. On this short timescale, the ions have not yet moved, as shown in Figure 5c, and this response is associated with the highfrequency dielectric constant. Because the focus of this study is ion response speed, we subtracted the electronic contribution, and focused on the charges induced by ionic motion (labeled “(Ionic)” in Figure 5b). Two distinct ionic responses are observed in Figure 5b. The first occurs on sub-picoseconds timescalescorresponding to a few molecular vibrationswhere ions polarize in response to the applied field and increase the induced charge by approximately 1013 cm−2. The second regime involves longer timescales and is associated with the diffusion of mobile ions, leading to the full formation of the EDL. Ionic motion and its effect on the carrier density is monitored for the 4 ns duration of the simulation for both ClO4− and Li+. The complete accumulation of ClO4− at the electrode interface (i.e., complete anionic EDL formation) is indicated by saturation in the time-dependent charge density which occurs within ∼100 ps. After 100 ps, the net displacement of ClO4− is nearly zero, and only Li+ remains mobile, eventually saturating after 2 ns (i.e., complete cationic EDL formation). The shorter time required for the anion EDL to form is consistent with previous reports showing that ClO4− mobility in PEO is three times larger than Li+,39,40 and experiments where the formation time of ClO4− EDL is ∼20 times shorter than Li+ EDL.21 The difference in mobility arises because ClO4− interacts weakly with the polymer backbone compared to Li+, which interacts more strongly with ether oxygens of the PEO chain.41 A larger cation, Cs+, was used in the experiments compared to Li+ used in the modeling. There are two reasons for this. From an experimental perspective, Cs + decreases the possibility for ion intercalation because of its larger ionic radius. While it is possible to drive Cs+ into the van der Waals gap of the 2D crystal, we see no evidence of electrochemistry in our measurements. From a computational perspective, Li+ is selected because Li+-based polymer electrolytes have been well-studied by the battery community providing wellestablished force fields that can be implemented in simulations to enhance the accuracy of the results. The transport mechanism and mobility through the polymer is expected to be similar for both ions, with only a slight enhancement in Cs+ mobility due to the smaller charge density compared to Li+.42 The simulations suggest that EDL formation can be achieved on ns timescales, which is at least 3 orders of magnitude shorter than those in experiments (microseconds to milliseconds). The faster response speed is attributed to the applied electric field, which is 3 orders of magnitude larger in the simulations because the device geometry is 3 orders of magnitude smaller. A similar report of picosecond response times is predicted for ion-gated SrTiO3 transistors with an extremely miniaturized geometry.43 Because the EDL response is strongly coupled to the magnitude of the applied field, additional EDL formation dynamics are simulated for field strengths ranging from 33 to 100 mV/nm (Figure 6a). As before, the electronic response is subtracted (details in Figure S7), leaving only the charges induced by ions. Increasing the electric field from 50 to 100 mV/nm increases the saturation Δqρ by 3× (from ∼2 × 1013 to ∼5.6 × 1013 e/cm2), while the time required to achieve a Δqρ of 2 × 1013 e/cm−2 is reduced by 200× (from about ∼1600 to ∼8 ps, Figure S7).
Figure 6. (a) Time evolution of the charge density at the anode under electric fields varying from 33 to 100 mV/nm (ionic contribution only). (b) Charge density as a function of electric field at different stage of EDL formation (time = 0.05, 20, 100, 500, and 3000 ps).
To further examine the relationship between applied field and EDL formation speed, the change in charge density is plotted in Figure 6b as a function of electric field at five different times, corresponding to five vertical cut lines in Figure 6a. Three dependences on applied field are observed: (1) linear at short times (0.05 ps), (2) nonlinear at intermediate times (20−500 ps), and (3) linear at longer times where the EDL is fully formed (3000 ps). The first, sub-picoseconds, stage corresponds to the polarization of the polymer electrolyte, where the image charge induced is directly proportional to the applied field. Depending on the electric field strength, the polarization contributes only 12−30% of the total EDL; that is, the majority of the EDL is formed by mobile ions inducing image charge in the electrode, which is the second stage (20−500 ps). During the second stage, the charge density increases nonlinearly with field strength (Figure 6b t = 20, 100, and 500 ps), suggesting the carrier density during EDL formation may be tuned considerably by comparatively small variations in the applied field. For example, in the first 500 ps, Δqρ increases by 160% (from 2 to 5.2 × 1013 e/cm2) by increasing the field strength 50% (from 67 to 100 mV/nm). A recent report by Asano et al. suggests a nonlinear relationship between ion response time and electric field,10 which is similar to our observations by MD simulation. While such a nonlinear response was not observed experimentally in this study (Figure S4), this can likely be attributed to the 1000× smaller experimental field strength. Additional evidence exists for nonlinear transport within solid electrolytes, where it is only observed at large (V/nm) applied electric fields.44,45 The third stage (up to 3 ns) becomes linear again because when the EDL is fully formed at steady state, the electrolyte will behave similar to a conventional gate dielectric with charge directly proportional to applied electric field. G
DOI: 10.1021/acsami.8b13649 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
Figure 7. (a) Change in current (ΔID) as a function of time under electric field of 0.2 mV/nm (red, top X axis) and 2.3 mV/nm (blue, bottom X axis). Right Y axis is the estimated charge density. (b) Charge density vs time during EDL formation from both simulation (left panel, light blue to dark blue indicate 50−100 mV/nm) and experiment (right panel, yellow to green indicate Epulse from 0.3 to 2.3 mV/nm). The lower dashed line corresponds to no EDL formation, and the top dashed line corresponds to a formed EDL with a charge density of 6 × 1013 cm−2. (c) ΔID as a function of time at 300 K (1 and 10 ms pulse widths) and 325 K (1 and 5 ms pulse widths).
ΔID can be achieved in this device by applying Epulse = 2.3 mV/ nm for ∼10 ms (Figure 7a, blue data). Thus, charge density in the order of 1013 cm−2 can be induced within 1 ms under electric field of 2.3 mV/nm, which is about 17% of the max EDL achievable under steady state with a constant VG of 3 V. EDL formation dynamics are quantified and summarized for both modeling and experiment in Figure 7b. Experimentally, we show that by applying pulsed voltages with 10× higher electric field than a dc voltage, the EDL formation time is reduced by 103. These pulses are long enough to drive EDL formation, but short enough to avoid electrochemistry. In MD simulations, we learned that EDL formation can occur on ns timescales if the field strength is sufficiently high, which could be achieved by further scaling the device geometry. Although it is unclear from the current data whether the relationship between electric field strength and EDL formation time is linear, exponential, or a combination, the data suggest that the timescale for EDL formation can be tuned by up to 109 by adjusting the field strength by 103. These findings indicate that EDL dynamics can occur over timescales relevant to electronics (GHz). In addition, the tunability of EDL strength over a wide range of pulse width suggest the potential to achieve spike-timing-dependent plasticity (STDP).18 Other reports show that the electrical response corresponding to EDL formation and dissipation resembles synaptic dynamic plasticity in neurons,15,16 and the measured timescale of EDL dissipation in this study (10 to a few 100 ms) is similar as the timescale for a post-synaptic current to last in a post-synaptic neuron (1−104 ms).17,46 These results underscore the potential of EDLs for applications in neuromorphic computing.16−18 In addition to scaling the device geometry to increasing the electric field strength, another method to increase the EDL response speed is to increase ion mobility.43 Ion mobility can be increased by lowering the polymer molecular weight,47 adding a plasticizer,48 or increasing the temperature.47
Note that while in simulations we use admittedly larger fields than in experiments to explore the limits of switching speed and miniaturization, the dynamics of mobile ions are still controlled by the polymer dynamics. The fields applied are insufficient to push ions through the polymer ballistically (Figure S8); thus, the ion transport in simulations can be considered similar to the experiments. The large electric fields in the simulations are achievable without dielectric breakdown because the applied voltage (
