High-mobility, trap-free charge transport in conjugated polymer diodes

Charge transport in conjugated polymer semiconductors has traditionally been thought to be limited to a low-mobility regime by pronounced energetic disorder. Much progress has recently been made in advancing carrier mobilities in field-effect transistors through developing low-disorder conjugated polymers. However, in diodes these polymers have to date not shown much improved mobilities, presumably reflecting the fact that in diodes lower carrier concentrations are available to fill up residual tail states in the density of states. Here, we show that the bulk charge transport in low-disorder polymers is limited by water-induced trap states and that their concentration can be dramatically reduced through incorporating small molecular additives into the polymer film. Upon incorporation of the additives we achieve space-charge limited current characteristics that resemble molecular single crystals such as rubrene with high, trap-free SCLC mobilities up to 0.2 cm2/Vs and a width of the residual tail state distribution comparable to kBT.


Supplementary Note 1 -SCLC characteristics in devices without traps or discrete trap levels
The concept of space-charge limited currents arises in device geometries where charge carriers are injected from an electrode and, at sufficiently high charge density, the associated space charge modifies the electrostatic potential in the device from that induced by the external, applied electric field. This cloud arises from the incapacity of a material to carry away the emitted charges fast enough. Therefore, space charge generally only occurs in a dielectric media since only here charges cannot be screened or neutralized fast enough. The current density at which a space charge is formed is hence a direct measure of a material's charge carrier mobility. In a planar diode geometry and in the absence of trap states in the material, the mobility is related to the current density via Mott-Gurney's or Child's law: where J is the current density, ε is the material's dielectric constant (~3.5 for most organic semiconductors), ε0 is the permittivity of free space, V is the applied voltage and L is the thickness of the dielectric material.
In the presence of trap states confined in a single or multiple discrete energy levels, the J-V characteristics will only follow Child's law for high applied voltages. When plotted on a ln-ln (or log-log) plot the J-V characteristics will ideally exhibit 4 characteristic regimes: (i) an Ohmic regime in which the material is behaving like a resistor showing J  V m with a slope of m = 1; (ii) an SCLC regime in which Child's law is obeyed, i.e. m = 2, but the extracted mobility is low and limited by the presence of trap states; (iii) a trap filling regime in which m >> 2; (iv) The trap-free SCLC regime with m = 2, in which all the trap states are filled and in which the extracted mobility is no longer affected by traps and is much higher than in regime 2. There may be modifications of the extracted voltage dependence, for example if the mobility is dependent on the magnitude of the applied electric field.

Supplementary Note 2 -Degradation, reproducibility and effects of heating
For the investigation of temperature dependent SCLC measurements, it is crucial that device stability is sufficient to draw reliable conclusions. We find that our DPP-BTz diodes show very good stability over the course of the measurement (5h). Within the voltage range applied the J-V characteristics is also not affected by hysteresis or polymer degradation effects at the high current densities present. Although the on-current slightly reduces (we attribute this to a slow evaporation of solvent), the overall shape of the device characteristics remains highly stable even after 46 repetitive measurements. We have also investigated the effect of heating on our SCLC diodes to exclude any measurement artefact. As precaution, we measured the J-V characteristics 3 times to monitor if degradation is taking place between consecutive sweeps. We find that even at temperatures as low as 180K, measurements are highly reproducible as evident by the identical m = dLn(J)/dLn(V) plots in Supplementary Figure 3. Nevertheless, once applied voltages are increased beyond 5V, we do see that the plots of m exhibit an inflation point followed by a gradual reduction of the slope. We attribute this behavior to significant heating caused by an increase of the power dissipation from 140 W/cm 2 at 200 K to 830 W/cm 2 at 180 K after the measurement range is extended from 5 V to 7 V. The resulting degradation is permanent and any consecutive measurement will follow the degraded characteristics; only a further extension of the measurement range will lead to an additional loss of current. For all data presented in this work, we have made sure that the measurement range was chosen in such a way that characteristics did not get close to the inflection point and therefore, we avoided the onset of this heat induced degradation. All the SCLC diodes we present in this work were fabricated on glass substrates. We have also prepared devices on silicon substrates to exclude that the lower thermal conductivity of glass did not lead to an excessive heating and thus to measurement artefacts. However, we find that the choice of substrate did not have a major impact on the SCLC characteristics of our diodes (Supplementary Figure 4).

Supplementary Note 3 -TD-SCLC measurements
We have used the TD-SCLC method to extract the density of trap states from our diode characteristics. The theoretical details and derivation of TD-SCLC can be found elsewhere 1,2,3 and here, we only give a summary of the key formulas to facilitate readability of the paper as well as a key amendment we have added to the deconvolution mechanism used in this method.
The shape of the J-V characteristics is directly related to the increment of space charge with respect to the shift of the Fermi energy dn/dE and related by = 0 2 (2 −1) 2 (1 + ) , with C = and Where m=m(V,T) is the slope of the J-V characteristics on a ln-ln (or alternatively log-log) scale (m = dln J/dln V), kB is the Boltzmann constant, L is the thickness of the diode, e is the elementary charge and ε the dielectric constant of the semiconductor (assumed to be 3.5). In agreement with what has been observed elsewhere [Ref. 17], we found that running the above analysis from the raw J-V data introduces a substantial amount of noiseespecially due to the [ (1 + )]/ term, which involves a third derivative of ln J with respect to ln V and is thus extremely sensitive to small amounts of measurement noise in the raw data. This resulted in an unphysical scatter of the dn/dE values. Therefore, we instead, fitted smoothing Bayesiansplines (henceforth referred to as B-splines) with a fixed error of 1% to all our raw data (Supplementary Figure 5). Even though by naked eye these fits were indistinguishable from the raw data, they enabled a clean differentiation of the data down to the 3 rd order and resulted in reliable extraction of dn/dE values. 6 The activation energy was extracted from the J-V characteristics for 50 evenly spread data points. A smoothing B-spline was subsequently applied to the extracted data using the same conditions as used for the J-V raw data. The activation energy was then used to translate the voltage scale of the extracted dn/dE(V) values into an energy scale (i.e. the position of the Fermi level). In order to do so, it has to be corrected by the dominant energy ED : with n' being the experimentally determined derivative of the activation energy with respect to applied voltage [n'

Supplementary Figure 6: Activation Energy extracted for DPP-BTz SCLC diodes. Extracted activation energy as well as computed ED for a pristine DPP-BTz SCLC diode. The reduction of EA for voltages V<0.5 V is an artefact of noise affecting the measurements at low temperatures and low voltages. Since data for V < 0.5 V was not used for our analysis, this artefact did not have an impact on the extracted dn/dE(E) values.
From the dn/dE(E) values, the density of states can be extracted. The two quantities are related by the Fermi-Dirac distribution according to: where h(E) is the density of states and f(E-EF) is the Fermi-Dirac function. In the literature h(E) and f(E) have previously been deconvoluted using cubic splines. However, we found that in our case this method introduces a significant scatter in the coefficients. We have therefore decided to compare only the more reliable dn/dE values in the main text.
We have however applied a deconvolution method based on 3 rd order ridge regressions giving more reliable fits and continuous coefficients 4 . The data set was regularized to a 1000-point grid and for each point the regression's coefficients Ak, Bk, Ck and Dk (Supplementary Figure  7) were determined according to: From the data the statistical shift can also be extracted, which gives useful information on the pinning of the Fermi level and the reliability of the reconstruction of trap densities extracted with TD-SCLC spectroscopy. The statistical shift arises from the temperature dependence of the Fermi level in the case of space-charge-free conductivity. It can be written by using the linear term of a Taylor expansion around the temperature independent value EF0 at T = 0 K: EF (T) = EF0 − γF kBT with γF being the statistical shift of the Fermi level. The so-called Meyer-Neldel parameter G can be used to relate the statistical shift to the slopes m and n of the J-V characteristics and the activation energy, respectively, according to:

Supplementary Figure 7: Extraction of the DOS of DPP-BTz using ridge regression. Coefficients Ak, Bk, Ck and Dk extracted from a 3 rd order ridge regression to the dn/dE data for a DPP-BTz device with additive at 180K.
For the polymer DPP-BTz, we show the statistical shift/Meyer-Neldel parameter explicitly (Supplementary Figure 9). In all our polymer devices we observe a negative Meyer-Neldel parameter for high energies which correlates to a Fermi-level pinning at trap states. For a Meyer-Neldel parameter below approx. 30 eV -1 , the reconstruction of the density of trap states yields reliable results. A strong shift of the Meyer-Neldel parameter towards high negative values at lower energies, on the other hand, suggests that the Fermi level jumps significantly between two sets of states (e.g. one delocalized and one localized). In this region, the reconstruction of the dn/dE values cannot be trusted and hence, such data points have been removed for all materials shown in this work. For the determination of SCLC mobilities, a precise knowledge of film thickness is essential. For all devices for which we report SCLC mobilities in this work, we have measured the film thickness using atomic force microscopy (AFM). The film thickness was measured by removing the polymer film with a scalpel and measuring the resulting trench both on gold (bottom electrode) as well as on the glass substrate.

DPPBTz (Device2) t = 220nm
Supplementary Note 4 -Low temperature measurements for other low disorder polymers DPP-BTz without additive: After the solvent additive is removed, the current density is much reduced, but it is still possible to measure the temperature dependence of the J-V characteristics. There is no more maximum in the slope m between 0 and 1 V which is indicative of the fast filling of traps followed by an extended plateau with constant slope at higher voltages. Instead, the slope m is increasing monotonically until a plateau is reached at much higher values of m DPP-DTT without additive: We subsequently annealed our devices at 90 °C in an N2 glove box to remove the solvent additive completely (Fig. S14). As anticipated these devices exhibit significantly lower current levels. A complete trap filling and subsequent trap-free SCLC behavior can no longer be observed.

Since the slope m did not exhibit a clear plateau region, EB was extracted for several voltages. At high temperatures the extracted EB values depend on voltage but at low temperatures they converge towards a value that is significantly higher than in the presence of an additive.
IDT-BT with additive: IDT-BT SCLC-diodes used for low temperature measurements were slightly thinner (110 nm) and did not show the same ideal SCLC-characteristics as DPP-BTz or DPP-DTT or the thicker IDT-BT device shown in the paper (Figure 3). Due to its amorphous microstructure the solvent additive evaporates faster in these devices, making it harder to fabricate a device of sufficient quality for TD-SCLC analysis. Furthermore, there remains a small injection barrier in all our IDT-BT devices. Especially at lower voltages we did not observe an Ohmic behavior (m = 1) and the measured currents were very small. These devices also exhibited an SCLC slope of m < 2 which is furthermore suggestive of injection limitations. Nevertheless, we did observe a similar plateau in the slope (m) as seen for DPP-BTz and DPP-DTT. Additionally, we did not find major differences in the crucial trap filling domain, making this device as suited for the TD-SCLC analysis as the device shown in Figure 3.

Supplementary Figure 18: Low-T measurements on IDT-BT diodes without additive. a) Loglog J-V characteristics of a IDT-BT diode after the solvent additive has been removed measured at temperatures between 300K and 160K; each characteristic was recorded 3 times to exclude degradation; b) Corresponding plot of m; the width of the trap distribution cannot be extracted as the previous extended plateau has vanished. Due to lower current densities, recorded data exhibits increased scattering at lower temperatures.
MEH-PPV without/with additive:

Supplementary Figure 19: Low-T measurements on MEH-PPV diodes with additive. a) Log-log J-V characteristics of a MEH-PPV diode measured at temperatures between 300K and 160K; each characteristic was recorded 3 times to exclude degradation; b) Corresponding plot of m; the width of the trap distribution cannot be easily extracted as there is an additional field dependence.
It is important to note that MEH-PPV devices did not perform significantly differently in the presence or absence of the solvent additive. In contrast to the low disorder polymers we have investigated, our MEH-PPV devices furthermore do not exhibit a plateau at lower voltages where the slope m is constant with voltage and hence field independent. We attribute this to the field dependence of the charge carrier mobility which we do not account for in our analysis. Nevertheless, despite the uncertainty induced by this, we cannot extract values lower than 55 meV for the width of the trap distribution, which is at least twice as high as for the low disorder polymers in the presence of an additive.
Our data on MEH-PPV are qualitatively very similar to data reported in the literature 6,7 .
Clearly, for polymers such as MEH-PPV an Extended Gaussian disorder model (EGDM) as used in the literature provides a more accurate model of the data; our simple analysis based on r values on the other hand can only identify an approximated lower bound on the energetic disorder. However, it is applied here to provide a comparison with the low disorder polymers whose SCLC characteristics are limited by water-induced traps and not by inherent energetic disorder like MEH-PPV.

Supplementary Note 5 -TD-SCLC measurements on MEH-PPV
We measured SCLC diodes fabricated with and without a solvent additive for 70 nm thick films of the polymer MEH-PPV (Supplementary Figure 21a). We find that in the case of MEH-PPV, annealing does not have a major influence on the diode characteristics; the presence of a solvent additive hence does not have a beneficial impact on device performance in the case of MEH-PPV diodes. This result is in stark contrast to what we observe for all of the low-disorder donoracceptor polymers we have investigated in this paper, which show significant degradation once trap-passivating solvents are removed. We attribute this to the higher intrinsic disorder of MEH-PPV, which concomitantly exhibits similar FET and bulk mobilities; water induced traps in this material hence do not seem to be the dominant transport limiting factor. We furthermore observed that after processing, our MEH-PPV diodes exhibited a substantial injection barrier that manifests itself as a suppression of the current at low applied voltages (< 0.3V) (red/black dots in Supplementary Figure 21b). After exposure to air, the low voltage performance of our diodes improves, whereas the performance at higher voltages remains unchanged. We associate these differences to oxygen doping which leads to better injection from the contacts and seems necessary to obtain an MEH-PPV SCLC device with ideal performance that matches data published in the literature (Supplementary Figure 21b We used the temperature dependent SCLC diode data measured for MEH-PPV to perform TD-SCLC spectroscopy. For MEH-PPV we did not observe a difference in the characteristics in the presence or absence of solvent additives. Therefore, here we only show MEH-PPV devices that have been annealed in nitrogen, which resulted in slightly improved characteristics (See Supplementary Figure 21). We would like to stress that since the high field performance of our MEH-PPV diodes remains unchanged by oxygen exposure, the steeper slope seen after processing may be an artefact of contact resistance (with the current rising more steeply at higher voltages when overcoming contact resistance limitations). We nevertheless extracted the dn/dE values for a device before oxygen exposure and did not find a substantial impact on the overall trap density (Supplementary Figure 24). Yet, due to the non-ideal SCLC characteristics of these devices (as evident as well by the large scatter in the data), we consider this data less reliable at higher energies.

Supplementary Note 6 -TD-SCLC measurements on DPP-DTT
We measured DPP-DTT SCLC diodes fabricated with a solvent additive in the temperature range from 300K to 160K (Supplementary Note 4). The extracted activation energy as well as the computed ED values for a pristine DPP-DTT SCLC diode are shown in Supplementary  Figure 25

Supplementary Note 7 -TD-SCLC measurements on IDT-BT
We measured IDT-BT SCLC diodes (thickness 110 nm) fabricated with a solvent additive in the temperature range from 300K to 160K. The extracted activation energy as well as computed ED values for a pristine IDT-BT SCLC diode are shown in Supplementary Figure 28

Supplementary Note 8 -Microstructure of polymer films
We also performed ellipsometry measurements to determine the film thicknesses independently and to investigate the optical anisotropy due to chains being aligned in the plane of the film.
The film thicknesses extracted for polymer films spun on silicon and gold are shown in Table  S1. For DPP-BTz and IDT-BT this gave reliable results consistent with the AFM measurements. For DPP-DTT the film thickness determined by ellipsometry is slightly lower than what we obtained using Atomic Force Microscopy (AFM). This mismatch might also be the explanation why on gold the optical constants for DPP-DTT appear to be isotropic, which is not fully consistent with the GIWAXs data obtained for the polymer (Figure 4). To determine the uniaxial, anisotropic optical properties the following layered optical model was used: (i) substrate 1mm of Si; (ii) native SiO2-layer of 1.2nm thickness; (iii) gold of 50nm thickness; (iv) biaxial polymer layer (see Table S1 for thicknesses used).