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\author{Dnyanesh D. Sarawate}

\author{Priscilla M. Prem}




\affiliation[UPitt]
{Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA}



\author{Eric J. Beckman}

\affiliation[UPitt]
{Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA}

\author{Ke Xu}

\affiliation[RIT1]
{Department of Physics and Astronomy, Rochester Institute of Technology, Rochester, NY}
\alsoaffiliation[Second University]
{Microsystems Engineering, Rochester Institute of Technology, Rochester, NY}
\email{ke.xu@rit.edu}

\author{Susan K. Fullerton-Shirey}
\affiliation[UPit Chem]
{Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA}
\alsoaffiliation[Second University]
{Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, PA}

\email{fullerton@pitt.edu}

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\title[An \textsf{achemso} demo]
  {Supplementary Information: Electric-Field-Triggered Ion Trapping for Non-Volatile Doping of Graphene Transistors}

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\pagebreak
\section{Part 1: Ion mobility and EDL dynamics of poly(DEAEMA-co-PEGMA) electrolytes
}

The temperature-dependent ionic conductivity of poly(DEAEMA-co-PEGMA) and LiClO$_4$ is reported in the main manuscript, Figure 1c, with a molar ether oxygen to Li$^+$ ratio of 20:1 . Here, the raw impedance and phase angle data, along with the calculated frequency-dependent conductivity are show in Figure \ref{Fig1_BDS}. The DC conductivity in Figure 1c corresponds to the frequency-independent conductivity in Figure \ref{Fig1_BDS}(c) and (f).

\begin{figure}[!ht]
    \centering
    \includegraphics[width=1.0\textwidth]{Images/SFigure1.png}
    \caption{\textbf{Impedance data} Frequency-dependent (a, d) impedance, (b, e) phase angle and (c, f) conductivity of poly(pDEA-co-PEGMA) and LiClO$_4$ with EO:Li$^+$ = 20:1 before (top row) and after (bottom row) thermal crosslinking at 70 $^{\circ}$C for 24 hours.}
    \label{Fig1_BDS}
\end{figure}

Impedance measurements quantify bulk ion mobility, and time-dependent current-voltage (IV) measurements capture EDL dynamics. Lateral Ti/Au (5/145 nm) capacitors were defined on 90 nm SiO$_2$/Si using a maskless aligner (Heidelberg MLA100 Direct Write Lithographer). Figure \ref{Fig2_Cap}(a) is an optical image of a lateral capacitor with an electrode separation distance of 5 $\mu$m. Lateral capacitors were chosen because of the easy fabrication process and straightforward measurement (i.e., the signature of ion mobility is a time-dependent current response to a voltage on the timescale of milliseconds to seconds. 

Poly(DEAEMA-co-PEGMA) with and without salt and crosslinker were deposited on the capacitors by drop-casting 25 $\mu$L of 1 wt\% electrolyte in acetonitrile. Figure \ref{Fig2_Cap} (b) are the time-dependent IV (IV-t) measurements comparing the neat co-polymer, co-polymer with salt (EO:Li$^+$ molar ratio of 350:1), co-polymer with DBH crosslinker (DEAEMA:DBH molar ratio of 2:1), and co-polymer with salt and crosslinker.

\begin{figure}[!ht]
    \centering
    \includegraphics[width=1.0\textwidth]{Images/SFigure2.png}
    \caption{\textbf{Electrical conductivity} \textbf{(a)} Optical image of a lateral capacitor with 5 $\mu$m distance between the plates. \textbf{(b)} IV-t of poly(DEAEMA-co-PEGMA) neat polymer, with salt (EO:Li$^+$ = 350:1), with crosslinker (CL) added (no salt), and with salt and crosslinker. \textbf{(c)} IV-t from (b) of poly(DEAEMA-co-PEGMA) neat polymer and with crosslinker only zoomed in on y-axis at low current. \textbf{(d)} IV-t of poly(DEAEMA-co-PEGMA)(EO:Li$^+$ = 350:1 and 20:1) and polyethylene oxide (PEO) (EO:Li$^+$ = 20:1).  For all measurements V$_1$ = 3 V, V$_1$ = 0 V and T = 296 K.}
    \label{Fig2_Cap}
\end{figure}

In the polymer without salt and crosslinker, only a dissipation current of $< 10 \ pA$ is observed (see Figure \ref{Fig2_Cap} (c)).  In samples containing ions, EDL formation is detected as a larger initial current ($> 60 \ pA$) followed by current saturation as the EDL approaches its fully formed state and ion mobility decreases. The initial charging current is the largest ($\sim$110 pA) when both the crosslinker and salt are included, suggesting that the crosslinker favors EDL formation.

Figure \ref{Fig2_Cap} (d) shows the impact of salt concentration and polymer identity on EDL formation dynamics. PEO:LiClO$_4$ with a molar ratio of 20:1 is included because it is frequently used to gate 2D FETs \cite{Kim2013Electrolyte-gatedElectronics, Li2017ElectricTransistors} and this particular concentration is known to give the largest ion mobility in PEO:LiClO$_4$.\cite{Fullerton-Shirey2009EffectElectrolytes} To quantify the formation time, the data are fit to a stretched exponential: \cite{Lukichev2019PhysicalFunction} 

\begin{equation}
    \frac{I_1}{I_0} = (1-E)\exp{\left(-\left(\frac{t}{\tau}\right)^\beta\right)}+E \label{eq1_KWW}
\end{equation} 

where $I_1$ is the measured current, $I_0$ is the current at the first time point, E is a fraction of current that decays outside the time window of the measurement, $\tau$ is the time constant, and $\beta$ is a stretching factor ranging from 0.2 to 0.5, indicating the distribution of time constants. All time constants are on the order of seconds, confirming that the charging current is due to ion mobility and not electron/hole transport. 

\pagebreak
\section{Part 2: AFM Cleaning}

AFM contact-mode cleaning is use to remove lithography residue from the channel surface to maximize the ionic gate control.\cite{Liang2019ImpactTransistors} Topographical AFM scans of the channel of device D2 before and after cleaning are provided in Figure \ref{Fig3_AFM} (a) and (b), respectively. Each scan is 256 lines. Figure \ref{Fig3_AFM} (c) show step height scans corresponding to the locations at the edge of the flake shown by the white rectangle in (a) and (b). The flake is $\approx$1.1 nm thick and the polymer residue is approximately 0.8 nm thick. Transfer measurements before and after cleaning are shown in Figure \ref{Fig3_AFM} (d). The Dirac point shifts from +2 to -1 V after cleaning, indicating that the lithographic polymer residue induced some p-type doping. 

\begin{figure}[!h]
    \centering
    \includegraphics[width=0.80\textwidth]{Images/SFigure3.png}
    \caption{\textbf{AFM cleaning of lithographically patterned FET.} Topography AFM scan of the channel of device D2 \textbf{(a)} before and \textbf{(b)} after cleaning. \textbf{(c)} Step height scans corresponding to the locations indicated by the white rectangles in (a) and (b). \textbf{(d)} Transfer characteristics before and after cleaning of device D2 with $V_{DS}=10\ mV$, T = 296 K, Sweep rate $\approx$ 6.3 V/s}
    \label{Fig3_AFM}
\end{figure}


%Ideally, the Dirac point of graphene is positioned at 0 V. However, there is a very small initial shift in the Dirac point ($\sim$2 V). This doping shift depends on various factors, including the interaction of graphene with the p-doped SiO$_2$ substrate\cite{FanInteractionSurface}, polymer residue remaining after the EBL procedure\cite{Gammelgaard2014GrapheneTreatments}, and contact resistance of the graphene-Ti-Au electrode system\cite{FreedyTitaniumTransport}. Although we cannot control the graphene-SiO$_2$ interaction, we can minimize the effect of residue using an AFM cleaning method developed by former lab member Jierui (Jerry) Liang. \cite{Liang2019ImpactTransistors} In this method, AFM is used in contact mode instead of tapping mode, which is used for obtaining height topography. Initially, the graphene channel is scanned horizontally, scraping off the polymer residue towards the electrodes. This is followed by a vertical scan to remove any remaining residue beyond the edges of the flake.
\pagebreak
\section{Part 3: Side-gated measurements}

Double-sweep transfer characteristics in Figure \ref{Fig4_Side}(a) show both sweeps for device D1 (the data in Figure 2c of the main text includes only the initial, single sweep). The hysteresis between the forward and reverse sweeps highlights the sluggish ionic dynamics.

\begin{figure}[!ht]
    \centering
    \includegraphics[width=0.8\textwidth]{Images/SFigure4.png}
    \caption{\textbf{Side-gated transfer measurements} \textbf{(a)} Three consecutive double-sweep measurements of device D1 before programming. \textbf{(b)} Initial sweep (+V$_{SGS}$ to --V$_{SGS}$) of device D1 programmed sequentially with increasingly negative programming bias after the positive programming sequence was completed in Figure 2 (d) of the main manuscript. $V_{DS}=20\ mV$, T = 310 K, Sweep rate = 1 mV/s, EO:Li$^+$ = 350:1. Transfer characteristics of Device D2 \textbf{(c)} when unprogrammed and then programmed sequentially at increasing negative gate bias, and \textbf{(d)} programmed sequentially at increasing positive gate bias after negative programming in (c). $V_{DS}=10\ mV$, T = 296 K, Sweep rate = 1 mV/s, EO:Li$^+$ = 350:1.}
    \label{Fig4_Side}
\end{figure}

Figure \ref{Fig4_Side}(b-d) show initial, single-sweep transfer data for devices D1 and D2 under varying programming sequences. Figure \ref{Fig4_Side}(b) corresponds to device D1, showing the complete set of transfer curves for negative programming steps, extending the data shown in the main manuscript in Figure 2(d). Figure \ref{Fig4_Side}(c) and S\ref{Fig4_Side}(d) correspond to device D2, where the programming sequence was reversed from that of D1 (i.e., negative programming followed by positive programming).

\section{Part 4: Dirac point shift due to temperature}

%The glass transition temperature ($T_g$) of the co-polymer electrolyte with and without salt (350:1) was measured using Differential Scanning Calorimetry (DSC) as shown in Figure 1(d) of the main document. For all samples (neat polymer, unreacted and reacted), the onset and end of the $T_g$ covered the range of –60 to –40 $^\circ$C (213–233 K).  This means ion mobility is expected at T $>$ –40 $^\circ$C and ion mobility is arrested at T $<$ –60 $^\circ$C.

Measurements of the glass transition temperature ($T_g$) in Figure 1c of the main manuscript do not provide a clear indication of the onset of polymer mobility. This is not unusual given the temperature range of most DSC instruments and the fact that $T_g$ is a broad, second-order phase transition. To confirm the onset of ion mobility in a FET, the device was cooled to 153 K, which is well below the midpoint $T_g$ detected by DSC, and heated in 10 K increments to nearly 400 K. Transfer characteristics ($I_D$–$V_{SGS}$) were measured at each temperature to monitor the onset of gate modulation.

As shown in Figure \ref{Fig5_Temp}(a) and (b), no gate modulation is observed until 233 K, at which point a clear modulation in $I_{DS}$ with $V_{SGS}$ was detected. At temperatures above the $T_g$ (273 K and 283 K), the modulation increases significantly. The degree of modulation was quantified by the ON/OFF ratio and hysteresis (difference in $V_{SGS}$ required to achieve the same $I_{DS}$ in forward and reverse sweeps). The highest ON/OFF ratio and minimum hysteresis were observed after heating to 303 K, which is expected, as it is about 60 $^\circ$C above the $T_g$.

\begin{figure}[!ht]
    \centering
    \includegraphics[width=1.0\textwidth]{Images/SFigure5.png}
    \caption{\textbf{Thermal response of poly(pDEA-co-PEGMA)} Drain current($I_{DS}$) modulation with increasing temperature from \textbf{(a)} 153 to 233 K and \textbf{(b)}  273 to 323 K with $V_{DS}$ = 10 mV, Sweep rate = 10 mV/s, EO:Li$^+$ = 350:1. \textbf{(c)} Initial thermal sequence to stabilize the Dirac point. \textbf{(d)} Transfer characteristics of device D5 before and after following the thermal protocol in (c) with $V_{DS}$ = 10 mV, T = 200 K, Sweep rate $\approx$ 3-7 V/s, EO:Li$^+$ = 20:1.}
    \label{Fig5_Temp}
\end{figure}

Another observation from the thermal experiments was the gradual shift in the graphene Dirac point after multiple heat–cool–heat cycles, even in the absence of an applied programming voltage. Notably, the repeatable transfer measurements of Figure \ref{Fig4_Side}(a) confirm that no significant polymer crosslinking occurs at room temperature, suggesting that the observed shift with temperature is not caused by chemical changes.

Interestingly, the Dirac point shift stabilizes once the device undergoes a complete thermal conditioning cycle: heating to 300 K, cooling to 200 K, then reheating to 300 K followed by isothermal hold for approximately 12 hours. After this process, no further drift in the Dirac point is observed under ambient conditions. This behavior implies that the initial shifts are likely related to thermomechanical effects within the polymer rather than electrochemical programming. Although we cannot know for sure, the Dirac point shift could possibly arise from thermally induced changes in strain, which can impact graphene doping.\cite{Sharifzadeh2021Temperature-affectedTemperature} When the polymer is drop-cast on graphene, it changes in morphology during temperature cycling likely alter the local interfacial structure, and could shift the Fermi level of the graphene.\cite{Levesque2011ProbingTransistors,Wu2017DopingSolvents,Wang2020WillEffect} Once the polymer is stabilized with thermal cycling and annealing, the Dirac point is no longer temperature-sensitive. 

The stabilization procedure is illustrated in Figure \ref{Fig5_Temp}(c), where the programming sequence used to condition the device is shown. Transfer characteristics corresponding to Figure \ref{Fig5_Temp}(c) are presented in Figure \ref{Fig5_Temp}(d). This procedure is carried out before any programming sequences are preformed to ensure that any subsequent Dirac point shift is due to intentional programming rather than unintentional thermal–mechanical effects.

\pagebreak
\section{Part 4: Control measurements}

Control measurements in Figure \ref{Fig6_Control} confirm that the observed Dirac point shift originates from the programming of the crosslinked polymer electrolyte, and verify the proposed mechanism of ion trapping in the EDL.  The polymer electrolyte was prepared without crosslinker, leaving only the polymer matrix with dissolved ions in a concentration of EO:Li$^+$ = 350:1. This formulation lacks the ability to undergo crosslinking, and, therefore, cannot trap ions in the EDL upon e-field programming. The control electrolyte was drop-cast onto a fresh graphene FET, device D9, under identical conditions as the FETs with crosslinkers to ensure consistent interfacial behavior and comparable initial doping levels.

\begin{figure}[!ht]
    \centering
    \includegraphics[width=0.5\textwidth]{Images/SFigure6.png}
    \caption{\textbf{Transfer characteristics of control devices before and after programming.} Transfer characteristics of device D9: poly(DEAEMA-co-PEGMA) with EO:Li$^+$ = 350:1 and no crosslinker. $V_{DS} = 10\ mV$, T = 200 K, and Sweep rate $\approx$ 6.3 V/s.}
    \label{Fig6_Control}
\end{figure}

The same programming sequence that was applied in Figure 4(a) of the main manuscript was used for the control device. The resulting transfer characteristics in Figure \ref{Fig6_Control} show no significant Dirac point shift on programming. Thus, the non-volatile Dirac point shift shown in Figure 4 of the main manuscript occurs only when the crosslinker is included, supporting the proposed mechanism of ion immobilization within the crosslinked polymer. 

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\bibitem[Kim \latin{et~al.}(2013)Kim, Hong, Xie, Lee, Zhang, Lodge, and Frisbie]{Kim2013Electrolyte-gatedElectronics}
Kim,~S.~H.; Hong,~K.; Xie,~W.; Lee,~K.~H.; Zhang,~S.; Lodge,~T.~P.; Frisbie,~C.~D. {Electrolyte-gated transistors for organic and printed electronics}. 2013\relax
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Li,~H.~M.; Xu,~K.; Bourdon,~B.; Lu,~H.; Lin,~Y.~C.; Robinson,~J.~A.; Seabaugh,~A.~C.; Fullerton-Shirey,~S.~K. {Electric Double Layer Dynamics in Poly(ethylene oxide) LiClO4 on Graphene Transistors}. \emph{Journal of Physical Chemistry C} \textbf{2017}, \emph{121}, 16996--17004\relax
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\bibitem[Fullerton-Shirey and Maranas(2009)Fullerton-Shirey, and Maranas]{Fullerton-Shirey2009EffectElectrolytes}
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Wu,~G.; Tang,~X.; Meyyappan,~M.; Lai,~K. W.~C. {Doping effects of surface functionalization on graphene with aromatic molecule and organic solvents}. \emph{Applied Surface Science} \textbf{2017}, \emph{425}, 713--721\relax
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\bibitem[Wang \latin{et~al.}(2020)Wang, Sofer, and Pumera]{Wang2020WillEffect}
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