The Trade‐Off between Transconductance and Speed for Vertical Organic Electrochemical Transistors

The high transconductance gm of organic electrochemical transistors (OECTs) has received widespread attention and made OECTs a valid candidate for wearable sensor systems. However, the large transconductance is often accompanied by large switching time constants, τ, making the transconductance an imperfect benchmark. For a fair assessment, the ratio of transconductance to switching time constant gmτ$\frac{g_m}{\tau }$ has to be considered instead of any single parameter in isolation. One approach put forward to optimize OECTs is a vertical design, in which the channel length can be scaled into the sub‐micrometer regime. Here, a new vertical device geometry is proposed, in which the active volume of the mixed conductor is confined to a small cavity between source and drain, yielding excellent performance and reproducibility. It is shown that this approach yields optimized gmτ$\frac{g_m}{\tau }$ ratios instead of maximized transconductance only. However, this scaling is effective only in a small range of device dimensions and requires careful optimization of the device to not be limited by parasitic effects such as excess volume of the mixed conductor or parasitic series resistances. Overall, the design considerations discussed here provide new guidelines to optimize OECTs, not only for high transconductance but for operation at high frequencies as well.


Introduction
Organic electrochemical transistors (OECTs) [1,2] are unique as they are not operating based on the field-effect.Instead, OECTs use organic mixed ion-electron semiconductors as channel material, which enables control of the effective doping state and hence resistance of the channel by the injection of ions. [3]This efficient ion-to-electron transduction, in combination with their biocompatibility, low operation voltage, and ease of fabrication, make for DOI: 10.1002/aelm.202300673[11] For this application, the extremely high transconductance of OECTs [12] was shown to be essential to increase the signal-to-noise ratio by amplifying the signal close to its source.
The high transconductance and high signal amplification of OECTs are caused by the mixed conduction of the semiconductor used for OECTs and in particular, by the nature of their gate capacitance C, which was defined as the density of ions injected into the transistor channel per applied voltage. [13]Although it was initially proposed that the capacitance C scaled with device area, Rivnay et al. [14] found that the gate capacitance actually scales with the total volume of the semiconductor channel.Defining a volumetric capacitance C*, the transconductance g m in the saturation regime can be written as where W is the channel width, T is the channel thickness, L is the channel length, V T is the threshold voltage, and V g is the gate voltage.Hence, due to the volumetric scaling, the absolute transconductance can be increased, which yields a strong coupling between ion fluxes and changes in electric currents and hence a high transconductance.However, the volumetric capacitance comes at a cost.It was shown that on and off switching of OECTs can be considered to be limited by charging the gate capacitance C through the ionic resistance of the electrolyte R. [13,15] Hence, the time constant of switching the OECT  scales with the thickness of the mixed conductor as well Therefore, the increase in transconductance due to the large capacitance seen in Equation ( 1) is accompanied by a slow down of the transistor, as seen in Equation (2).One finds for the ratio of transconductance and switching time Assuming the ionic resistance R does not depend on the channel dimensions, which is a good approximation for transistor geometries where the distance between gate electrode and channel is larger than the channel length, the ratio of transconductance and switching speed is expected to increase proportionally to the square of the channel length L. Traditional OECTs have planar source and drain electrodes, and, in particular, as OECTs are usually seen as a low-cost technology, it is challenging to scale the channel length to the sub-micrometer regime, which limits the g m  ratio.Still, however, extremely large transconductance levels were reached, albeit at the cost of a slow response (or vice-versa).
Although this trade-off between transconductance and switching speed was recognized earlier, [16] its precise origins and potential limits of a linear scaling between transconductance and switching time constants have not been studied thus far.Only a handful of reports specifically aim to address this trade off and improve the ratio g m  instead of optimizing one parameter in isolation.Cea et al. [16] report on an OECT design in which hydrated ion reservoirs are embedded into the mixed conductor, which shorten the ion transit time.They reached a g m  = 640 S s −1 , which still represents the highest performance of lateral OECTs reported so far.
Recently, an alternative approach to overcome the intrinsic limit imposed by Equation ( 3) has moved into the focus of research.By stacking the source and drain electrodes with a passivation layer between them, that is, by using a vertical architecture, submicron channel lengths become possible.This vertical architecture, although widely used for field-effect transistors, [17] is still relatively new for OECTs.The first vertical OECTs, from Kawahara et al. [18] in 2013, used screenprinted PEDOT:PSS on two sides of a paper or PET substrate, with the channel defined by a hole through the substrate.Despite the vertical structure, the channel length was still large (around 50 μm).In 2017, Donahue et al. [19] first achieved submicron channel lengths in their vertical OECT design.Using a step-shaped PEDOT:PSS channel defined by a 450 nm thick parylene-C passivation layer, a maximum transconductance of 24 mS (814 S m −1 ) was reached.They also calculated an intrinsic transconductance of 57 mS accounting for the series resistance of the contact lines to the OECT.The record-high transconductance for PEDOT:PSS OECTs of 275 mS (intrinsic 498 mS) was accomplished by Koutsouras et al. [20] in 2023.In their structure, a 60 nm thick SU-8 layer defined the channel dimensions, which were filled by electopolymerized PE-DOT:PSS grown on the bottom gold electrode.A top gold electrode was then sputtered directly on the PEDOT:PSS channel.The exceptionally large transconductance is due to the 1mm × 1mm (W × T) device footprint (or channel "area") and submicron channel length.The overall highest transconductance in OECTs of 384mS was recently achieved by Huang et al. [21] in 2023.The key to their process is the mixing of a p-type (gDPP-g2T) semiconductor with a photocurable polymer (cinnamate-cellulose) in an ideal ratio to optimize performance and prevent delamination of their top contact electrode.Along with this record-high transconductance, these devices had exceptional switching speeds, with shortest off-switching time constants as low as  off = 45 μs ( on = 366 μs for the same device).As the on-and off-switching time constants were different in this design, one has to adjust the figure of merit to g m  on + off = 203.5 mS 425 μs+85 μs = 399 S s −1 for p-type and g m  on + off = 101.2mS 366 μs+45 μs = 246 S s −1 for n-type transistors. [21,22]Aside from this increase in g m  ratio due to the vertical structure compared to the lateral ones, vertical OECTs are expected to be beneficial for sensors as well, as the high transconductance will result in an inherent amplification of the sensor signal.
However, despite the success of vertical OECTs, it has not been established that the scaling law Equation (3) applies to the vertical structure as well, for example, if the vertical structure can indeed help to overcome the trade-off between g m and .In deriving Equation (3), it is assumed that the volume of the mixed conductor that is charged with ions (V = WTL, cf.Equation ( 2)) is identical to the volume V that conducts electric current from source to drain (e.g., the geometric dimensions used to derive Equation ( 1)).Although this assumption is safely justified for lateral OECTs, [23,24] the complex structure of vertical OECTs complicates this analysis, and hence the improvement in performance due to the vertical structure might be smaller than expected.
Here, we propose a novel vertical OECT design based on electropolymerized PEDOT:PSS layers, in which the electrically active volume of the mixed conductor is well defined by a small cavity formed between the source and drain electrode.This structure and the high stability of the vOECTs proposed here allow us to systematically study the precise origin and scaling of the g m  limit.We can identify different regimes of device operation.Only in a small regime, g m and  are directly proportional, whereas in other regimes, either the transconductance or the switching speed is limited by external effects.Understanding the origins of these limits allows us to design transistors with high performance in terms of a max g m  on + off , high ON/OFF ratios and, most importantly, high switching stability as well.Overall, the results shown here allow us to propose strategies for optimizing the performance of vertical OECTs further.

Structure of Vertical OECTs
[27] The crosssection and top view of the vOECT are sketched in Figure 1a,b.A circular channel was chosen to reach a larger transistor density, which improves the spatial resolution of sensor arrays.The channel is formed by a circular gold source electrode and ring-shaped drain electrode, with a 300 nm polyimide passivation layer defining the channel length L between them.By varying the number of rings in the drain structure, the inner circumference of the channel and therefore, the effective channel width W increases.Finally, an additional polyimide layer is added to form an insulation layer that avoids direct exposure of contact pads and connecting metal lines to the electrolyte during electrical characterization.The top polyimide layer is structured to selectively open the channel region of the device.Other passivation materials are possible, for example, parylene-C, which is a common choice for lateral OECTs as well.
After electrode and polyimide structuring, PEDOT:PSS is electropolymerized on the surface of both electrodes simultaneously to build the channel.The thickness of the PEDOT:PSS layer is precisely controlled by how long the electrodes are electropolymerized-a growth rate of ≈100 nm min −1 is observed on flat surfaces (see Figure S2, Supporting Information).Figure 2 shows transistors with a channel width of 1.73mm with varying deposition times ranging from t = 5 to 300s.Clearly, thicker films, appearing darker in the optical image, are grown for longer times.
Although the entire gold surface of the source and drain is homogeneously covered by PEDOT:PSS, the detailed film geometry is more complicated.It can be seen in the cross-section SEM image of the transistor taken before PEDOT:PSS deposition (Figure 3a) that the PI layer is underetched during structuring of the thin polyimide layer, forming a cavity between the source and drain electrode.During PEDOT:PSS deposition (Figure 3b), the cavity is filled, although not in a continuous fashion.For shorter polymerization, thin filaments of PEDOT:PSS grow between the source and drain (cf. Figure 4a, taken after t = 30s) forming a webbing-like structure.For longer times (e.g., t = 60s shown in Figure 4b) a closed film is grown, completely filling the cavity between source and drain.
The origin of this formation of this fiber-structure is currently not entirely understood.However, it can be explained by the formation of PEDOT:PSS globules [28] on the surface of each electrode.As these cauliflower-shaped aggregates form and stack, they will eventually connect with aggregates on the opposite electrode, forming connections with some probability.This is similar to the intentional dentritic electropolymerization used for neuromorphic OECTs, [29] but here the electrodes are held at the same potential and there is no directional growth.

Steady State Characterization
Figure 5 shows the steady-state characteristics of transistors grown by electropolymerization for 300 s (Figure 5a) and 5s (Figure 5b) and with channel widths ranging from W = 95 … 1730 μm.The thicker devices (Figure 5a) show on-currents in the range of I D = 10 mA, whereas the on-current drops slightly  to I D = 1…10 mA for thinner transistors (Figure 5b).Off-currents are only limited by gate currents in the range of 10…100 nA.The off-currents scale with the channel width, indicating a direct but small leakage current from gate to drain electrode.
The excellent gate control obtained in the devices leads to large ON/OFF ratios in the range of 10 5 , a subthreshold swing in the range of 80 mV per decade, and a good saturation in the output characteristic (cf. Figure S3, Supporting Information).The devices show a hysteresis of ≈0.1 − 0.2 V between the forward in backward sweeps, which is shown in Figure S1, Supporting Information.In the following, only the forward sweep is used for the discussion.Otherwise, a high reproducibility and stability of the vOECTs is reached, which is shown in Figure S4, Supporting Information.
The high on-currents correspond to high transconductances g m , as plotted in Figure 5c,d for thicker and thinner devices, respectively.The transconductance follows the characteristic peaking behavior, known from lateral OECTs. [30]The peak in transconductance g max increases for larger channel width, which for the thicker devices is accompanied by a shift of the position of the maximum toward larger voltages for larger channel width.
Although the maximum transconductance increases with channel width W, the increase is sublinear, that is, smaller than expected from Equation (1).In Figure 6, the dependence of maximum transconductance on channel width is plotted.Although the maximum transconductance of 89.64 mS is found for the largest width (channel width 1730 μm, electropolymerization time 300s), a saturation of the transconductance is clearly seen beyond W = 1mm.This saturation resembles a saturation caused by parasitic series resistance of the metallic contact lines, [3] and methods to overcome this limit will be discussed later.
However, there is a second saturation mechanism visible in Figure 6.The transconductance not only saturates with the channel width, but with the thickness of the electropolymerized PE-DOT:PSS film as well.Overall, the maximum in transconductance for a given channel width is reached at 60 s of electropolymerization time, that is, there is no more transconductance to be gained by increasing the channel thickness beyond that point.
The change in behavior at about 60 s of electropolymerization and the saturation in transconductance for longer electroploymerization correlate with changes in the growth of the electropolymerized PEDOT:PSS seen in Figure 4a,b.For very short electropolymerization times, nanoscale wire-like connections forming the channel.Eventually, at ≈60 s, the cavity will be entirely filled with a bulk layer (see Figure 4b).
Once the cavity is completely filled, any additional PEDOT:PSS deposited does not reduce the resistivity of the channel any further.This effect is shown in Figure 7, where the channel resistance without adding electrolyte and without applying a gate potential is plotted versus the electropolymerization time.As can be clearly seen, the resistance drops sharply until ≈60 s, but saturates afterward.Overall, the effective channel thickness of these vOECTs seems to be determined by the height of the cavity formed between the source and drain electrode, and is not determined by the electropolymerization time, that is, the thickness of the PEDOT:PSS layer deposited onto the electrodes.Hence, any additional PE-DOT:PSS deposited beyond 60 s does not significantly improve the transistor performance, that is, the transconductance saturates (cf. Figure 6).Although the resistance drops for short times, it reaches a plateau for longer times, that is, beyond t > 60s.This behavior can be explained by the particular design of the transistor.At longer times, the cavity formed between source and drain is completely filled with PEDOT:PSSincreasing the amount of deposited PEDOT:PSS does therefore not decrease the resistance any further.

Transient Characterization of Vertical OECTs
To determine the transient response time of the vOECTs, a square potential wave of magnitude 1.2 V is applied to the devices while keeping the drain potential at −0.1 V.The resulting response in the drain and gate current for OECTs with a thin (polymerization time of t = 5 s) and thick (polymerization time of t = 300 s) PE-DOT:PSS layer is shown in Figure 8.A strong influence of the PEDOT:PSS layer thickness is apparent -whereas the thin and not-continuous film (cf. the webbing-like structures in Figure 4a) switches extremely fast ( on = 31 μs,  off = 25 μs), the thick layer needs significantly more time to switch between the two states ( on = 1.3ms,  off = 4.0ms).
The off-switching time constant  off for a wider range of electropolymerization times is shown in Figure 9a, alongside its dependency on the channel width (Figure 9b).A linear dependency is observed for both electropolymerization time and channel width, in line with Equation ( 2), again assuming the ionic resistance R does not depend on the channel dimensions.
Most interestingly, the switching time constant does not saturate with the electropolymerization time as the transconductance g m .To explain this difference, the charge injected into the vOECT, calculated by integrating the gate current over time, is plotted versus the electopolymerization time and channel width in Figure 10a,b.The total injected charge increases linearly with channel width and electropolymerization times, even beyond t = 60 s.Therefore, the whole PEDOT:PSS film is charged during switching, not only the PEODT:PSS volume that fills the cavity between the source and drain electrode.Overall, switching vOECTs is limited by the total capacitance of the whole PE-DOT:PSS film, which scales with the deposited volume.

Transconductance and Switching Speed Relation
As seen in Figure 6 and observed by Khodagholy et al. already, [16] the transconductance scales with channel width and thickness, indicating that a larger device volume increases the amplification.However, this increase in steady state performance is accompanied by an increase in the switching time constant , an effect similar to the gain-bandwidth limit of conventional electronics. [16]Indeed, as discussed in the introduction and as seen in Equation (3), the transconductance g m and switching time  are expected to be directly proportional.
As the on-and off-switching time constants can be significantly different, [24] the maximum transconductance is plotted versus the sum of the on-and off-switching time constants  on +  off in Figure 11.From this plot, a direct proportionality of g m and  is indeed seen for low polymerization times and small channel widths, that is, in the lower left of the diagram (red dashed line in Figure 11).The slope in this regime is in the range of g m  on + off ≈ 125 S s −1 , which is still lower, but in the same order of magnitude as the record devices reported by Huang et al. [21] Although a direct proportionality is observed for small channel widths, that is, small switching time constants, it can be seen that the slope of the g m () plot drops for longer electropolymerization times (cf. the dotted line for 300 s electropolymerization   time in Figure 11).This effect is in line with the observation that the transconductance saturates for higher electropolymerization times (cf. Figure 6), but that the time constants  on and  off continue to increase (cf. Figure 9a).The saturation in transconductance was explained by the observation that only the PEDOT:PSS inside the cavity formed between source and drain carries the drain current; any layer deposited after the cavity is filled does not increase the channel conductance further (cf.Figure 7).However, adding additional PEDOT:PSS, that is, beyond filling the cavity, continues to increase the capacitance of the film (cf. Figure 10a), which slows down the transistor.Overall, adding PEDOT:PSS beyond the amount needed to fill the cavity is counterproductive-it does not increase steady-state performance but slows the transistors, leading to a smaller slope and smaller g m  ratio in Figure 11 ( g m  on + off ≈ 24.2 S s −1 for 300 s electropolymerization).Furthermore, it can be seen in Figure 11, that the regime of direct proportionality is limited and that the transconductance saturates at about 90 mS, in line with the results shown in Figure 6.The maximum transconductance of 90 mS is in the range of the conductance of the contact lines of the vOECT design; that is, the saturation is most likely caused by parasitic series resistances. [19]o approach the intrinsic limit of our vOECT, a four-point probe measurement is performed, which minimizes the effect of series resistance due to the connections between the OECT and the measurement equipment.The design of a vertical OECTs with four connections is shown in Figure 12a.The OECT features two thick connections, which connect the OECT to the sourcemeasurement unit, and two thin lines, that are used to measure the effective voltage dropping across the OECT.Using this setup, the output voltage of the source measurement unit can be controlled to force the desired voltage drop across the OECT (i.e., between the two thin sense contacts), thereby eliminating the losses in the lead connections.This results in a significantly higher transconductance (Figure 12b), which is nearly double that of a typical, two-point vOECT measurement.The transconductance reaches 160 mS for small channel widths already.
However, the transconductance is still saturating at larger channel widths W, although at a higher value.This is likely due to another source of resistance that is intrinsic to the transistor.Here, contact resistances between the organic semiconductor and gold electrodes have to be considered, as well as the resistance of the gold electrode ring structures.

Discussion
Organic electrochemical transistors are often praised for their very high transconductance, which sometimes even exceeds the performance of inorganic semiconductors.Although this is certainly correct, the high transconductance is accompanied by a long switching time constant, that is, the g m  ratio is constant, and one parameter is traded against the other.As the g m  is expected to inversely scale with the square of the channel length, vertical OECTs are highly promising.In these vertical architectures, the channel length can be reduced to the sub-micrometer regime without sophisticated and expensive structuring techniques.
Indeed, vertical OECTs were shown to reach a record performance in terms of g m  . [21]Here, we propose a new vertical setup that yields devices with excellent gate control, for example, high on-off ratios, and large g m  .In this setup, a small cavity formed between the source and drain electrode is filled by electropolymerization of the organic semiconductor PE-DOT:PSS, which leads to a defined device volume.The high reproducibility of the setup allows us to study the limits of channel length scaling in vertical OECTs.We are able to show that indeed, reducing the channel length leads to fast devices with high transconductance, but that this regime is narrowly limited.
The most severe limit is imposed by the ionic component of the vOECT.Although electric currents are concentrated within a small cavity formed between source and drain electrode, the whole film deposited on the total area of the device is charged with ions, which increases the switching time constants and hence reduces the g m  ratio.Overall, it has to be ensured that not only the channel length of the devices is reduced (i.e., the distance between the source and drain electrode), but that the total volume of the mixed conductor is scaled as well.In this respect, the setup proposed here, which relies on filling a small cavity between the source and drain electrode, is beneficial, as it allows to confine the channel within the cavity (by controlling the electropolymerization time) and not add unnecessary volume of the semiconductor that only slows the device down.
The second limit is caused by parasitic lead resistance, that is, series resistance of connecting metal lines on the substrate.As soon as the transconductance reaches the conductance of the connecting lines, the apparent transconductance saturates.Here, it is shown that by a four-wire measurement, this effect can be reduced, but that the transconductance still saturates.The origin of this limitation is still not understood-it could be caused by the remaining series resistances of the ring structures of our drain electrode, or the contact resistances of the OECTs.
Overall, the results shown here provide guidelines to increase the performance, in particular the gain-bandwith limit g m  of OECTs further, and to facilitate their use as high-speed amplifiers in, for example, flexible sensing applications.An additional field of application is the addition of vertical OECTs on neural probes that are used to measure small electrical signals in intracortical structures. [9,11]As the PEDOT:PSS is selectively deposited on the source and drain electrode during the last processing step only, device performance is not affected by harsh processing steps of the needle, for example, by deep reactive ion etching or lithography.

Experimental Section
Device Fabrication: The transistors were fabricated in the IMSAS ISO-6 cleanroom on 4-in.silicon wafers coated with a 500 nm-thick silicon oxide layer.At first, a 5 μm-thick polyimide layer (U-Varnish S, UBE Corporation) was spin-coated and cured using a vacuum hotplate to create an insulation layer on the bottom.A 250 nm-thick gold layer was afterward deposited and structured using magnetron DC sputtering (Pro Line PVD 75, Kurt J. Lesker Company Ltd.), photolithography (AZ 1518, MicroChemicals GmbH) and wet chemical etching (Au etch 200, NB Technologies GmbH) to create the source electrodes.Then, a 300-nm thin layer of polyimide was spin-coated and cured to insulate the source electrodes and define the channel length of the transistor.Afterward, the second gold layer was created using the same processes as described before to fabricate the ringshaped drain electrodes.To insulate the conducting paths and define the area for electropolymerization of PEDOT:PSS, another 5 μm thick polyimide layer was spin-coated and cured.To increase adhesion between the polyimide layers significantly, a short (30 s) oxygen RIE plasma treatment (STS ICP) was performed directly before the coating of polyimide.The top insulation layer was then structured together with the thin polyimide layer using photolithography (AZ 10XT, MicroChemicals GmbH) and oxygen RIE plasma (STS ICP).After wafer dicing, the electropolymerization process was performed.For electrodeposition of PEDOT:PSS, a monomer solution of 10 mm EDOT (3,4-ethylenedioxythiophene, Sigma-Aldrich) and 2 wt% of NaPSS (poly(sodium 4-styrenesulfonate), M W 70 000, Sigma-Aldrich) dissolved in DI water was used.A constant current density of 5 μA mm −2 was applied between the samples and a platinum counter electrode.For better homogeneity of the coating, the monomer solution was stirred slowly.The source and drain electrodes were coated simultaneously with PEDOT:PSS.After coating, the samples were cleaned in DI water and dried with nitrogen.The coating thickness was controlled by the electropolymerization time.
Electrical Characterization: Steady-state measurements were performed with a Keithley 4200 SCS system.The transconductance was determined by a central difference derivative and a moving average to reduce noise.A relatively large area PEDOT:PSS-coated gold electrode (≈1cm 2 ) was used as an external gate electrode immersed in Ringer's solution as an electrolyte (B.Braun SE, Germany).
Transient measurements were performed with a Tektronix oscilloscope using a home-built amplifier to convert and amplify measured currents to voltage signals.On and off switching times were determined to be 63% of the time to switch fully between on and off drain currents.The ionic charge injection was then determined by the time integral of the gate currents during off-switching.
Four-point probe measurements were performed with a Keithley Series 2400 SourceMeter.Using the four-wire remote sensing configuration in one SMU to source the drain voltage.A voltage sweep was configured and supplied by the second SMU to a ≈1cm 2 PEDOT:PSS gold gate electrode to obtain the transfer characteristics using Ringer's solution (B.Braun) as an electrolyte.

Figure 1 .
Figure 1.Device setup: a) Cross-section of the vertical OECT.A circular gold electrode on the bottom and a ring-shaped one on the top form the source and drain electrodes.Source and drain are separated by a 300 nm thin polyimide (PI) passivation layer, defining the channel length L. PEDOT:PSS is grown by electropolymerization on top of the source and drain electrode.b) Top view of the vOECT design.To increase the integration density, the top-electrode has a ring-shaped form.The number of rings determines the channel width W.

Figure 2 .
Figure 2. Controlling the thickness of the PEDOT:PSS layer.Images of vOECTs with a channel width of w = 1.73mm for increasing electrodeposition durations.The connection to the source electrode is on the left, and the ring-shaped drain electrode is contacted from the right.Increasing the electropolymerization time leads to thicker, for example, darker films.

Figure 3 .
Figure 3. Cross-section of the OECT channel.A focused ion beam (FIB) cross-section of the OECT channel a) before and b) after PEDOT:PSS deposition (180 s).The source (bottom) and drain (top) electrodes are separated by the polymide (PI) passivation layer.The rest of the space between and around the electrodes is covered by PEDOT:PSS.

Figure 4 .
Figure 4. Nature of the transistor channel.a) SEM image of the side-profile of a vertical OECT.Here, a short electropolymerization time was used (30 s).There are small nanoscale connections (webbing-like structures) between the top drain and bottom source electrode.b) SEM image of channel with a longer electropolymerization time (60 s).The channel is nearly entirely filled.

Figure 5 .
Figure 5. Steady-state characteristic of vOECTs.Transfer characteristics for five transistors at a drain voltage of V DS = −0.5 V that were electropolymerized for a) 300 s and b) 5 s.The scaling of the off currents (and the on/off ratio) with channel width can be seen.Transconductance characteristics with gate voltage for the c) 300 s and d) 5 s electropolymerized transistors.For the thicker device (c), the typical peak in transconductance is found to shift in voltage and increase in magnitude with channel width.

Figure 6 .
Figure 6.Scaling of transconductance with channel width and polymerization time.The dependence of maximum transconductance of each transistor by channel width (from 95 to 1730 μm).Here, the transistors with electropolymerization times of 60 s or higher have nearly the same maximum transconductance.There is a clear drop in transconductance for lower electropolymerization times.

Figure 7 .
Figure 7. Saturation of channel conductance with electropolymerization time.The resistance of the channel (for a 95 μm channel width) is plotted versus the electropolymerization time without the addition of an electrolyte.Although the resistance drops for short times, it reaches a plateau for longer times, that is, beyond t > 60s.This behavior can be explained by the particular design of the transistor.At longer times, the cavity formed between source and drain is completely filled with PEDOT:PSSincreasing the amount of deposited PEDOT:PSS does therefore not decrease the resistance any further.

Figure 8 .
Figure 8. Transient response of OECTs: a) The transient response of a transistor with a 300 s polymerization time and 1730 μm channel width.b) The transient response of a transistor with a 5 s polymerization time and 95 μm channel width.

Figure 9 .
Figure 9. Transient response of OECTs: a) The time constant for full switching from the on state to the off state  off is plotted over all electropolymerization times.A linear dependence is found for each channel width.b) The same time constant  off is plotted against channel width.A linear dependence (indicated by the fitted lines) is also found for each electropolymerization time.

Figure 10 .
Figure 10.Volumetric switching beyond saturation of transconductance.The injected charge calculated from the transient gate current is plotted versus the a) electropolymerization time and b) channel width.A linear dependence is also found for each electropolymerization time.Both results indicate volumetric gate capacitance.

Figure 11 .
Figure 11.The trade-off between transconductance and speed of OECTs: Plot of the maximum steady-state transconductance of each transistor versus its switching speed, where the fastest transistors are on the left.The saturation near 90 mS is seen just as in Figure 6.It is clear that additional thickness beyond the 60 s of electropolymerization slows down the device significantly.

Figure 12 .
Figure 12.Four-wire measurement of vOECTs to approach the intrinsic transconductance.a) To determine the intrinsic transconductance of the vOECT, the devices are characterized in a four-wire setup that forces the programmed drain potential V D = −0.5 V to drop between the thin sense contacts.b) The measured transconductance is increased by approximately a factor of 2.5.For some four-point measurements shown in (b) the channel length of the transistors is reduced from 300 to 100 nm by reducing the thickness of the polyimide layer.To account for this change, all transconductances are plotted versus the ratio W/L.