Fast electrochemical doping due to front instability in organic semiconductors
V. Bychkov, P. Matyba, V. Akkerman, M. Modestov, D. Valiev, G. Brodin, C. K. Law, M. Marklund, L. Edman
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J a n Fast electrochemical doping due to front instability in organic semiconductors
V. Bychkov , P. Matyba , V. Akkerman , M. Modestov ,D.Valiev , G. Brodin , C. K. Law , M. Marklund , and L. Edman Department of Physics, Ume˚a University, SE-90187 Ume˚a, Sweden and Department of Mechanical and Aerospace Engineering, Princeton University,D323-A, Engineering Quad., Princeton NJ 08544-5263 USA
The electrochemical doping transformation in organic semiconductor devices is studied in applica-tion to light-emitting cells. It is shown that the device performance can be significantly improved byutilizing new fundamental properties of the doping process. We obtain an instability, which distortsthe doping fronts and increases the doping rate considerably. We explain the physical mechanism ofthe instability, develop theory, provide experimental evidence, and perform numerical simulations.We further show how improved device design can amplify the instability thus leading to a muchfaster doping process and device kinetics.
Organic semiconductors (OSCs) are expected to revo-lutionize everyday electronics by offering interesting andattractive properties which distinguish them from con-ventional inorganic semiconductors [1–3]. In addition tosimple processing, low cost, soft and conformable char-acter, OSCs provide the intriguing possibility of in-situ chemical and electrochemical doping. This doping trans-formation leads to significant changes in important ma-terial properties, such as conductivity, color, volume, andsurface energy [2, 3]. The opportunity for a controllabletuning of the properties of OSCs via doping has stim-ulated the emergence ”organic electronics” with a largenumber of novel and flexible applications [1–4]. Opera-tionally, electrochemical doping is performed by apply-ing a potential to a metal electrode coated with an OSCin contact with an electrolyte. During n-type (p-type)doping, electrons (holes) are injected into the OSC fromthe cathode (anode) and subsequently compensated byredistribution of cations (anions) in the electrolyte [5–9].When OSC is populated by light charges, its conductivityincreases by two-three orders of magnitude in comparisonwith the original conductivity due to bulky ions. A com-plex manifestation of the electrochemical doping is the in-situ formation of a dynamic p-n junction when p- andn-doping fronts meet in a light-emitting electrochemicalcell (LEC) [10–18]. However, the electrochemical dop-ing involves redistribution of heavy and slow ions, whichmakes such organic electronics devices slow to turn-on.The speed-up of the doping process is thus vitally im-portant for technical applications. Here we obtain, the-oretically and experimentally, instability of the dopingtransformation front, which leads to much faster kineticsof the process. We suggest an improved device design onthe basis of the attained fundamental insight. We showthat a corrugated pattern in the electrode surface am-plifies the instability and increases the doping rate; thussubstantially reducing the device turn-on time.The configuration of two doping fronts counter-propagating towards each other in an LEC device isschematically illustrated in Fig. 1(a). Fig. 1(b) shows the internal structure of two such planar fronts, as cal-culated using the method of [19]. The doping fronts,however, can never be ideally planar because the unavoid-able small perturbations grow with time and distort theirshape. The physics behind this new instability is relatedto the phenomenon of St. Elmo’s fire, caused by the in-creased electric field at a convex conducting surface. Inthe present configuration, any leading perturbation humpat a doping front causes local increase of the electric fieldin the undoped region. Since the front velocity is pro-portional to the electric field, see Eq. (1) below, thisstronger electric field will force the front to propagatefaster locally, thus producing a positive feedback and anunstable growth of the hump.To study the instability growth, we employ the p/n-doping front velocity [19] U p,n = ± n n h,e ( µ + + µ − ) E , (1)where E = −∇ φ is the electric field intensity just aheadof the front, φ the electric field potential, n the ini-tial ion concentration in the pristine active material, n h,e the final concentration of the holes/electrons behind thefront (determined by the thermodynamic properties of aparticular OSC), µ + and µ − the mobilities of the posi-tive/negative ions. The ” ± ” sign in Eq. (1) indicates thatthe p-type (+) and n-type ( − ) doping fronts propagate inopposite directions. We consider a perturbation Fouriermode ˜ X ( t ) exp( iky ) of a p-doping front x = X p ( y, t ) inFig. 1(a), which induces also perturbations of the elec-trical field in the undoped region. The doped region maybe treated as equipotential due to high conductivity. Thefront thickness may be characterized by a length scale L p ,of about 10 − − − mm, determined by ionic diffusion[19]. Since the characteristic size of the experimentallyobserved front perturbations (approximately 0 . L p , then we may treat the front as in-finitesimally thin. Most of the time the doping fronts aresufficiently far away from each other, k ( X n − X p ) ≫ FIG. 1. Schematic of the p- and n-doping fronts in an organicsemiconductor film (a), and internal structure of the planarfronts at 90 s (b). the other. The linearized form of Eq. (1) ∂ t ˜ X = − n n h ( µ + + µ − ) ∂ x ˜ φ, ikU p ˜ X = n n h ( µ + + µ − ) ∂ y ˜ φ. (2)together with the solution to the Laplace equation for theelectric potential in the udoped region, ˜ φ ∝ exp( iky −| k | x ), yields the equation ∂ t ˜ X = U p | k | ˜ X describing theperturbation growth with time. Thus, we obtain an in-stability for the p-type doping front, where the initiallysmall perturbations grow exponentially as ˜ X ∝ exp( σt ),with the growth rate σ = U p | k | . The same result holds forthe n-type doping front by replacing U p with U n . Thisnew instability shows interesting mathematical similar-ities to the Darrieus-Landau instability encountered incombustion [20, 21] and inertial confined fusion [22].To observe the instability experimentally, we utilize anopen planar LEC device, comprising an { MEH-PPV +PEO + KCF SO } active material positioned betweentwo Au electrodes as described in [19]. Two counter-propagating doping fronts can be distinguished in Fig.2 (a, b); the dark regions with quenched fluorescencecorrespond to the doped MEH-PPV; the electrodes areindicated with white dashed lines. When the fronts meetand form a p-n junction, recombination of subsequentlyinjected holes and electrons can lead to light emission(see Fig. 2(c), taken in darkness). Figures 2 (a,b) clearlydemonstrate that both doping fronts are unstable with FIG. 2. Experimental photos of the doping fronts demon-strate development of the instability at the initial stage (a), t = 46 s, at the developed stage (b), t = 80 s, and the dy-namic p-n junction (c), t >
170 s. Plot (d) compares thep-front shapes obtained in the simulations (white curve) andexperiments (shading) at 70 s. Plots (e), (f) show relativeincrease of the electric field in the undoped region obtainednumerically for the whole front squeezed along Y-axis, (e),and for the selected part with equal scales, (f). respect to small perturbations, though with different out-comes at the nonlinear stage. The instability of thep-front produces smooth humps with a relatively largescale, about (0 . − . U − p ∂ t ˜ X = ˆ J ˜ X + ( ∂ y ˜ X ) + U − p ˆ H h ∂ t ˜ X ∂ y ˜ X i + λ p π ∂ yy ˜ X, (3)where the Darrieus-Landau operator ˆ J and the Hilbertoperator ˆ H imply products by | k | and | k | /ik in Fourierspace, respectively, and λ p ∝ L p is the cut-off wavelengthrelated to the small front thickness (detailed derivationwill be presented elsewhere). Equation (3) has beensolved numerically with initial conditions extracted fromthe experimental data at t = 10 s. The numerical model-ing reproduces well the characteristic shape of the p-front FIG. 3. Mean front position for p- and n-fronts versus timeobtained experimentally; predicted theoretically for the pla-nar fronts; and calculated numerically for the wrinkled fronts(see the legend). The error bars of the experimental dataindicate difference in the positions of the fastest and slowestparts of the corrugated front brush. at later instants, e.g. at t = 70 s, see Fig. 2(d). Figs.2(e) and (f) show the computed electric field ahead of thecorrugated p-type front. The observed increase in theelectric field at the humps of the front demonstrates theinstability mechanism, as explained earlier. The analyt-ical, experimental, and numerical results for the dopingfront positions are presented in Fig. 3. The analyticalresult (solid lines) shows two planar fronts acceleratingtowards each other. The acceleration takes place becausea constant potential difference is effectively applied overthe continuously decreasing distance between the dop-ing fronts [24, 25], and because the front velocities arecontrolled by the potential gradient, Eq. (1). The ana-lytical result relies on our experimental data [19], withthe average hole concentration n h = 8 . · m − .The experiments reveal a noticeably faster propagationof the non-planar doping fronts compared to the analyt-ical result for planar fronts. In Fig. 3, open diamondsshow the mean positions of the experimental non-planardoping fronts, where the ”uncertainty” bars indicate thedifference between the fastest and the slowest parts ofthe front brush. The difference can be attributed to thedeveloping instability and the associated wrinkled front,which is not accounted for in the analytical descriptionof the planar fronts. The analytical prediction for posi-tions of the planar fronts correlates well with the slowestpoints of the experimentally observed fronts, while theleading points in experiments move approximately 1.4times faster. In contrast, the numerical modeling does ac-count for the instability and shows good agreement withthe experiments.The present results therefore verify that front insta-bility increases the doping rate. However, the instability FIG. 4. Experimental photographs showing the time evolu-tion of the p-type doping front in an LEC device with theinitial corrugations of the anode. The corresponding time in-stances are indicated on the photographs. The insert showscharacteristic shape of a strongly curved hump obtained inthe theory. theory also indicates that the time and space available forthe perturbation growth in the employed LEC devices arenot sufficient to achieve a strongly curved front. Specifi-cally, the theory suggests that the instability may doublethe velocity of a curved front in comparison to a planarone, which is not observed in the experimental results ofFig. 3 discussed above. Such strong increase of the frontvelocity happens due to strongly curved humps, whichmay develop at the front (see the insert of Fig. 4). There-fore, to achieve a strongly curved front and a faster turn-on, we have triggered the instability growth by modifyingthe initial conditions so that the slowest initial stage ofhump growth from natural ”white-noise” perturbations iseliminated. Figure 4 presents results from an experimentwith a corrugated pattern introduced as the surface ofthe anode (see the dotted line); the corrugation size wascomparable to the humps observed in Fig. 2. The corru-gations, though negligible in comparison with the total(1 mm) width of the active material, were anticipated togive rise to the desired initial perturbations of the p-typefront. Confirming our anticipation, we observed stronglycurved and rapidly growing humps at the p-type front,see Fig. 4. The position of the humps in this experi-ment is also included in Fig. 3, which shows that, indevices with a corrugated electrode surface, the dopingrate may increase significantly; by a factor of two in thepresent case. We have also performed experiments withcorrugations included into both the cathode and anode,and, as expected, we observed intensified front dynamicsand much faster turn on. By introducing corrugationson the cathode we also find that the initial delay in thedevelopment of the n-type front was reduced.To summarize, we have demonstrated theoretically andexperimentally that electrochemical doping fronts are un-stable. The obtained instability distorts the fronts andincreases the doping rate considerably. This understand-ing of new fundamental properties of organic semicon-ductors was utilized in the design of light-emitting elec-trochemical cells with distinctly improved turn-on times.We further propose that similar design principles can beemployed in other kinetically limited electrochemical de-vices, such as actuators [26] and transistors [27–30].The authors are grateful to Kempestiftelserna, CarlTryggers Stiftelse, and the Swedish Research Council(VR) for financial support. L.E. is a “Royal SwedishAcademy of Sciences Research Fellow” supported by agrant from the Knut and Alice Wallenberg Foundation.The work at Princeton University was supported by theCombustion Energy Frontier Research Center funded bythe Office of Basic Energy Sciences of the U.S. Depart-ment of Energy. [1] Pei Q. B., Yu G., Zhang C., Yang Y., Heeger A. J., Sci-ence , 5227, 1086 (1995).[2] Forrest, S. R., Nature , 911 (2004).[3] Leger M. J., Adv. Mater. , 837841 (2008).[4] Arkhipov V. I., Emalianova E. 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