2686 | Phys. Chem. Chem. Phys., 2014, 16, 2686--2692 This journal is© the Owner Societies 2014

Cite this:Phys.Chem.Chem.Phys.,

2014, 16, 2686

Carrier motion in as-spun and annealedP3HT:PCBM blends revealed by ultrafast opticalelectric field probing and Monte Carlo simulations

Vytautas Abramavicius,*ab Dimali Amarasinghe Vithanage,c Andrius Devizis,a

Yingyot Infahsaeng,c Annalisa Bruno,d Samuel Foster,d Panagiotis E. Keivanidis,e

Darius Abramavicius,b Jenny Nelson,d Arkady Yartsev,c Villy Sundstromc andVidmantas Gulbinasa

Charge transport dynamics in solar cell devices based on as-spun and annealed P3HT:PCBM films are

compared using ultrafast time-resolved optical probing of the electric field by means of field-induced

second harmonic generation. The results show that charge carriers drift about twice as far during the first

3 ns after photogeneration in a device where the active layer has been thermally annealed. The carrier

dynamics were modelled using Monte-Carlo simulations and good agreement between experimental and

simulated drift dynamics was obtained using identical model parameters for both cells, but with different

average PCBM and polymer domain sizes. The calculations suggest that small domain sizes in as-spun

samples limit the carrier separation distance disabling their escape from geminate recombination.

1. Introduction

Diminishing sources of fossil fuels and the need to meet risingglobal demands for carbon-free energy have led to renewablesources being explored as replacements. Conjugated polymershave been investigated as alternatives to solar cells based oninorganic semiconductors1 due to their light weight, flexibility,abundance of material, low material usage and manufacturingcosts. The invention of the bulk heterojunction structure (BHJ)using a donor and acceptor homogeneously mixed to produce theactive material2 has aided the increase in solar cell efficiency,which is presently 9.2% for the best reported cells.3 To improvedevice efficiency, the charge dynamics have also been investigatedand three key stages in the charge separation pathway have beenidentified – charge generation,4 transport5 and recombination.6

Excitons are generated when light within the absorptionspectrum of the material impinges on the devices. These excitonsvery rapidly6 separate into positive and negative charges formingCoulombically bound electron–hole pairs (or charge transferstates (CT)). In order to separate further, the charges have to

overcome the Columbic attraction and form mobile chargeswhich can move towards the electrodes through a combinationof diffusion and drift.7 The collection of the separated chargesresults in completion of the circuit and current produced bythe solar cell.

Here we study the polymer:fullerene combination poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl-C61butyric acidmethyl ester (PCBM). The method of processing P3HT:PCBMdevices is known to impact the active layer morphology and, as aresult, the efficiency of devices, and has therefore been extensivelystudied. Several factors have been investigated with the aimof improving device efficiency, such as the effect of solvent,morphology, film thickness and processing conditions.8–17

Annealing was shown to have a great impact on the conversionefficiency of P3HT:PCBM solar cells, quite different from mostother polymer:fullerene blends. The carrier dynamics ofannealed and as-spun P3HT:PCBM films have been studiedusing several techniques aiming at investigating differences inmobility,5,15 morphology,14–17 EQE14 and I–V characteristics.5

Annealing to a high temperature changes the morphologyand enhances the hole mobility,5,9 resulting in it being only an orderof magnitude below the electron mobility.5 A similar effect wasachieved with slow solvent evaporation.18 Using microsecond timescale techniques, a large spread in mobilities and their differencesin as-spun and annealed samples have been reported.5,15,19 Themeasurements show that the two different processing methodsdrastically affect the mobility and charge separation time scales.Morphological studies have shown that high temperature

a Center for Physical Sciences and Technology, Savanoriu 231, LT-02300 Vilnius,

Lithuaniab Department of Theoretical Physics, Vilnius University, Sauletekio 9-III,

LT-10222 Vilnius, Lithuania. E-mail: Vytautas.Abramavicius@ff.vu.ltc Chemical Physics, Lund University, Box 124, 221 00 Lund, Swedend Imperial College London, South Kensington Campus, London SW7 2AZ, UKe Center for Nano Science and Technology@PoliMi, Istituto Italiano di Tecnologia,

Via Giovanni Pascoli, 70/3, 20133 Milano, Italy

Received 31st October 2013,Accepted 5th December 2013

DOI: 10.1039/c3cp54605e

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results in phase separation due to crystallization of thepolymer5,15,16,20 and formation of large PCBM clusters.12,14–17

There is a consensus that thermal annealing results in improveddevice efficiency due to enhanced phase segregation, whichconsequently leads to increased charge separation efficiency,21,22

improved hole conductivity and formation of optimized chargetransport pathways9,15 and consequently reduced bimolecularrecombination.23

The mechanism through which the thermal annealingprocess enables higher charge carrier mobilities is now fairlywell understood. Annealing induced crystallisation of the polymerresults in larger domains (thicker lamellae) of the pure polymerand at the same time expels fullerene molecules out of thecrystallising polymer, thereby making more fullerene availableto build a robust electron transport network.20,24–26 It is clear fromsuch studies that the improvement in charge collection (reflectedthrough photocurrent quantum efficiency) is associated with thegrowth in pure polymer and fullerene domains and resultingimprovement in charge carrier mobility relative to the recombina-tion coefficient.5,9

In this paper, we aim at unveiling how morphology affectscharge transport by investigating charge mobility and chargeseparation at earlier timescales using electric field-inducedsecond harmonic generation (TREFISH)7,27,28 and MC simula-tions. We find the morphology to influence the mobility andcarrier separation on the ps to ns time scale. MC simulationsshow that the different carrier drift kinetics in as-spun andannealed blends may be explained by more extensive materialsegregation, leading to larger P3HT and PCBM domains inannealed material, enabling fast separation of carriers at largerdistances and preventing their geminate recombination.

2. Experiment

The experimental setup and theory have been previouslydescribed,7,27,28 so only a brief account is given here. TREF ISHis a pump–probe technique, employing a femtosecond laser pulseto excite the sample devices and generate charges, and a probepulse that generates the SHG signal probing the dynamics ofthe charges. An applied electric field breaks the symmetry of thematerial, allowing to generate the second harmonic signal ofthe probe pulse. The intensity and time dependence of thesecond harmonic signal monitors the electric field dynamics inthe sample. The excitation pulse (400 nm, 36 nJ per pulse) wasobtained by frequency doubling the fundamental of the Ti:Salaser at 800 nm; a photon density of B1012 photons per cm2 perpulse for the sample was used, which is below the onset of strongsecond order (non-geminate) recombination. The probing wave-length was obtained using an optical parametric amplifier(TOPAS) at 1200 nm, the second harmonic of which was withinthe sensitivity of the photomultiplier detector. The sample devicewas made using a PEDOT:PSS/ITO anode and an aluminium (Al)cathode. The PEDOT:PSS was spun to form a 40–60 nm film andthe total device had an overall thickness of B115 nm. The samplecells were all prepared in a clean room environment.

3. Monte-Carlo simulation model

The simulation model has been described in ref. 7. Briefly, chargecarrier motion in the P3HT:PCBM blend was modelled by assuminga cubic lattice, characterized by a lattice constant a in all threedimensions. The lattice is divided into the donor part, where onlythe hole is allowed to reside and the acceptor part for the electron.The acceptor sites are defined by filling the lattice volume withellipsoids of acceptor material (see Fig. 2) with typical averagevolume, which is later on used as a fitting parameter. The ellipsoidshave arbitrary proportions and they are placed in arbitrary positionsin the lattice and they overlap each other, thus mimicking thedistribution of PCBM in the actual blend. Next, the remaining spacein the lattice is filled with donor sites, which are used to createarbitrarily oriented and folded chains representing the polymer. Thelength of a chain is chosen randomly from the interval [L� 3, L + 3],where L is the average length of chains. It should be noted, thatsuch a blend model apparently cannot reproduce the real blendmorphology, particularly of the annealed blend where a lamellarstructure is suggested to be formed. The results of the calculationshould rather be seen as a qualitative representation of morphologyto rationalize the observed carrier dynamics.

The electron and hole dynamics are controlled by site energyproperties. In the presence of an external electric field the energy ofan electron (hole) in the lattice consists of three parts: (1) the internalsite self-energy Er, which is assumed to be a random Gaussian value;(2) the energy due to the constant external electric field F, and(3) the energy due to the Coulomb interaction between chargesof opposite sign EC. The electron (hole) energy thus equals to:

Ef(r) = Er 8 (F�r) + EC. (1)

The site self-energy is distributed according to a modifiedGaussian distribution, which is defined as a weighted sum of anormal Gaussian distribution with addition of longer exponentialtails. The energy of the external electric field was accountedfor by projecting the site position to the electric field direction.The electrostatic interaction energy is given by the shiftedCoulomb potential

EC ¼ �q

4pee0� 1

reh þ ba(2)

Here q is the electron charge, reh is the distance between theelectron and the hole, e is the mean permittivity of the material, ais the lattice constant and b is a positive dimensionless parameter,which accounts for deviation of the Coulomb potential from thepoint charge approximation at short distances and sets theappropriate initial electron–hole interaction energy.

Both types of charges perform hopping in their respectivedomains of the lattice. The hopping is simulated using theMonte-Carlo algorithm as follows. As the initial configurationthe hole and electron are placed on neighbouring sites in theinterfacial region of the donor and acceptor domains. Only thenearest neighbour sites are taken into account for the hoppingevent. A charge can hop into one of six surrounding sites whenit is far from the interface while hopping possibilities are fewerin the interfacial region. The hopping rates nmn for both the

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electron and the hole are calculated using the Miller–Abrahamsformula:29

nmn ¼ n0 exp �2grmnð Þ � exp �En � Em

kT

� �;En 4Em

1;En � Em

8<: ; (3)

where g is a parameter which characterizes the inverse localiza-tion length of a charge density, rmn is the distance between theorigin site m and the target site n, Em and En are their energiesrespectively. In the acceptor domain the hopping rate n0 � nA isconstant, while in the donor part we assume the value n0 � nD1

for hopping to a target site located in a straight part of the samepolymer chain as the origin site, n0 � nD2 for hopping to a targetsite located on a folding point (the point where the orientationof the polymer chain changes) of the same polymer as theorigin site and n0 � nD3 for hopping to a target site located on adifferent polymer chain.

It is assumed that a hole is less likely to hop to a site locatedon another polymer chain, thus the corresponding hoppingrate prefactor nD3 is smaller than both nD1 and nD2. We alsoassume that a hole avoids folding points where holes moveslower than in straight sections of the polymer chain, thusnD2 o nD1. It should be noted that a simple isotropic mediummodel was unable to reproduce the carrier drift kinetics duringinitial tens of ps therefore this more complex model, previouslysuggested to simulate carrier motion in the pure polymer,28

was used.When all rates of possible hopping events (including holes

and electrons) have been evaluated, the rates are being translatedinto hopping probabilities according to:

pmn ¼nmnPk

nk; (4)

where the summation is performed over all calculated rates ofboth the hole and the electron. These probabilities are thenused to determine the destination site n for either the hole orthe electron, chosen by a linearly distributed random number.The charge configuration is then switched to the one that hasbeen determined and the rates of the next hopping eventsare recalculated.

For the simulation a 100 � 400 � 400 lattice was used. Thislattice simulates the actual structure of the blend, motivatingthat no cyclic boundary conditions are introduced. Initially,charges were created at a random location at the interfacebetween the donor and the acceptor regions and due to theexternal electric field they drifted apart in opposite directions.While charges moved through the lattice, the distance betweenthem projected in the direction of the external electric field F,dk(t) was recorded and the result was averaged over 5000realizations.

Only one electron–hole pair was present in the lattice at atime, thus the model did not account for the nongeminatecharge carrier recombination. The geminate recombinationwas also not accounted for assuming it to be much slower thanthe examined time domain.

4. Experimental results

Fig. 1 shows the carrier drift dynamics in as-spun and annealedsamples for various applied voltages, calculated by the proce-dure described in ref. 19 from the experimentally measuredTREFISH kinetics (not shown). Briefly, the electric field kineticswas reconstructed from the EFISH kinetics by using steady stateEFISH dependence on the electric field strength. Next weassume that the electric field drop is proportional to the carrierdrift distance and obtain the drift distance kinetics by normal-izing the time-resolved field drop to the total field drop at longdelay time when all carriers are extracted and, thus, theiraverage drift distance equals to the half of the film thickness.The drift distances presented in Fig. 1 are averaged overelectrons and holes and rapidly increase on the tens of ps timescale in both samples. At long times (>200 ps) the increaserate gradually slows down to reach a separation distance of15–30 nm (depending on film treatment) at 2.5 ns. The driftdistances are approximately proportional to the internalelectric field, suggesting that the initial carrier mobility isindependent of the electric field strength. Qualitatively, similardrift dynamics has been observed for neat polymers28 and

Fig. 1 (a) Experimental (symbols) and simulated (lines) charge driftdynamics in the as-spun (a) and annealed (b) samples at various electricfields strengths.

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attributed to carrier relaxation within a distributed density ofstates. The drift distances in the as-spun sample are about halfof those in the annealed sample at the same applied voltages.

The electron and the hole drift in opposite directions byabout 2.5 nm during the initial 10 ps at 6.7 � 105 V cm�1

electric field in the annealed sample. Thus, the electron–holeseparation distance along the electric field is about 5 nm. Thisseparation distance is around half as large in the as spunsample as in the annealed sample and is approximately propor-tional to the applied field.

5. MC calculation results

Monte Carlo simulations by the procedure described abovehave been performed to model the carrier drift dynamics andto gain insight into the microscopic properties responsible forthe observed differences in drift dynamics of annealed andas-spun material. The modelling of the hole motion dynamicsaccounts for the hole relaxation within the density of states(DOS), different hole hopping rates within a conjugated segment(nD1), between segments (nD2) and between polymer chains (nD3).The electron motion is simpler – the model accounts for theelectron relaxation within the DOS and electron motion insidePCBM domains is characterised by a single electron hopping rateprefactor, nA. Both electron and hole motions are also affectedby the domain structure of the blend; reaching the domainboundaries carriers are forced to search for alternative pathwaysto continue their motions – this process results in a domain-sizedependence of carrier mobility. The drift kinetics at differentvoltages were simulated with the same model parameters, onlyvarying the internal field strength.

Carrier drift kinetics in as-spun and annealed samples havebeen modelled by using exactly the same motion parametersexcept for polymer and PCBM domain sizes. The best agree-ment was obtained with an average acceptor domain diameterof 7.5 nm for the as-spun sample and 33 nm for the annealedsample. As a result of fullerene aggregation the polymer domaindimensions were accordingly larger for annealed samples aswell, but because of nonregular shapes their quantitative char-acterization, is more difficult. Fig. 2 illustrates the correspondingmaterial morphologies and Fig. 1 shows the simulated carrierdrift dynamics. The quite good agreement with experimental

results obtained for all curves with only one free variable, thedomain size, validates the simulation results. The obtaineddomain dimensions of the annealed samples are somewhatlarger than the B10 nm domains estimated in similar samplesfrom experimental results.30 On the other hand, quite similardomain sizes of 10 to 30 nm were estimated by MC modelling ofcarrier recombination in a P3HT:PCBM blend.23 The MC simula-tions do not perfectly reproduce the carrier drift kinetics in annealedsamples at high applied electric fields (6.7 � 105 V cm�1) at timeslonger than 1 ns. This is not very surprising taking into account therelatively simple blend structure used in calculations.

We proceed to infer effective charge carrier mobilities fromthe data for separation as a function of time. Note that these arenot mobilities as usually defined, describing drift of relaxedpopulations of charges in the steady state, but instantaneousmobilities describing the instantaneous separation velocity ofunrelaxed charge carrier populations. Since the experimentaldata gives us information on the sum of electron and hole driftdistances, the actual electron and hole mobilities remainundisclosed, the ratio between electron and hole hopping ratesbeing a free parameter. We have chosen the electron hoppingrate on the basis of additional available information on theultrafast time-resolved electron mobility and on the basis of thebest agreement between experimental and calculated carrierdrift kinetics. By means of time-resolved microwave conductivity,Savenije et al.31 obtained the electron mobility inside PCBMnanocrystals of 8 � 10�2 cm2 V�1 s�1 and a similar mobility ofabout 0.1 cm2 V�1 s�1 was also obtained on a subpicosecond-several ps time-scale in PCBM film by dynamic Stark effectmeasurements.32 Thus, we have chosen an electron hoppingrate prefactor nA to give an electron mobility of 0.1 cm2 V�1 s�1

at 0.3 ps, while its subsequent evolution was obtained from thebest fitting with experimental data. Similar information on theinitial hole mobility in P3HT is not available and therefore itwas obtained from the modelling of the carrier drift kinetics.The best agreement was obtained with about ten times lowerhole mobility than that of electrons. The simulation parametersused to obtain the best agreement between calculated andmeasured drift kinetics (see Fig. 1) are presented in Table 1.

A lower initial hole mobility in comparison with the electronmobility was also concluded for a polyfluorene/fullerene blend.33

On the other hand, mobilities obtained from time resolved THzmeasurements on another polyfluorene low-bandgap polymer/fullerene blend (APFO3/PCBM) show that picosecond time scalehole mobility is higher than the electron mobility by approxi-mately a factor of five.34 The reason for this difference in therelative mobility of holes and electrons is probably a result ofdifferent sensitivity to intra- and inter-chain hole transport ofthe experimental methods. Fitting of the simulation andexperimental results allows significant freedom of correlatedvariation of hopping rates of electrons and holes in differentdirections, thus the distinction of electron and hole mobilitiesis not reliable. Therefore we present, in Fig. 3, the carriermobility averaged over electrons and holes, obtained directlyfrom the experimental data. The short time carrier mobility isalmost two times larger for the annealed sample. Carrier mobilities

Fig. 2 Cross section of typical simulated structures of as-spun (left) andannealed (right) samples. Dark areas denote acceptor regions (PCBM) andwhite areas denote donor regions (P3HT). The red line represents thelength of 50 nm.

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in both samples drop down several tens of times during 1 ns.The TREFISH mobilities at t > 1 ns approach literature data forsteady state mobility,5,18,19 indicating that carrier populations havealmost relaxed into trap states during this time. Qualitativelysimilar mobility dynamics was observed in pure polymer films,27,28

showing that both inherent polymer and PCBM properties,as well as nanostructured blend morphology, are responsiblefor the mobility dynamics.

Our experimental data give information on the carrier driftdistance, while the absolute carrier separation distance is deter-mined by carrier diffusion as well as drift. These two processes areinterrelated through the Einstein relation D = mkBT/q, where D is thediffusion coefficient, m is the carrier mobility, kB is the Boltzmanncoefficient, T is the temperature and q is the electron charge. In ourprevious paper we have shown that the diffusion distance on a pstime scale significantly exceeds the drift distance at low fields and isresponsible for the weakly field dependent carrier separation yield.7

MC simulation is a convenient approach to obtain averageabsolute carrier separation distances caused by both carrier

drift and diffusion from the carrier drift kinetics. Fig. 4 shows acomparison of the absolute carrier separation distances inas-spun and annealed samples at different electric field strengths.At zero electric field, only the diffusion drives the carriermotion, thus curves at zero field represent diffusion drivencharge separation dynamics. At 0 and 1.7 � 105 V cm�1 electricfields the separation distances on a tens of ps time scale arealmost independent of the sample annealing. The differenceappears on a ns time scale, when electrons approach theboundaries of small PCBM domains in the as-spun sample,while in the annealed sample with larger PCBM domains, theycontinue an unrestricted motion. At higher electric field, whenthe carrier drift contributes more to their motion, charge

Fig. 3 Carrier mobility averaged over electrons and holes for as spun(closed circles) and annealed (open circles) samples at 4.7 � 105 V cm�1

field strength.

Table 1 Numerical values of the parameters of the model

Lattice dimensionin the x direction (nm)

Lattice dimensionin the y direction (nm)

Lattice dimensionin the z direction (nm)

Lattice constanta (nm)

Average size of theacceptor ellipsoid M (nm)

100 400 400 1 As-spun: 220 annealed: 19 800

Average length of thedonor chain (nm)

Hopping rate prefactorin the acceptor nA (s�1)

Hopping rate prefactorin the donor nD1 (s�1)

Hopping rate prefactorin the donor nD2 (s�1)

Hopping rate prefactorin the donor nD3 (s�1)

6 2.8 � 1016 2 � 1015 1 � 1015 5 � 1014

Parameter g (nm�1) Disorder in theacceptor sA (meV)

Disorder in thedonor sD (meV)

Temperature T (K) Mean dielectric permittivity e

5 70 80 293 3

Correction parameter b of the initial electron–hole interaction energy Fraction of exponential distribution exp(�E/s)in the modified Gaussian distribution

2 0.19

Fig. 4 Calculated absolute charge carrier separation distances in as spun(dotted lines) and annealed (solid lines) samples at different electric fieldstrengths obtained by Monte Carlo simulation using a model fitted to thedrift distance data in Fig. 1. The curves at higher electric field strengths arevertically shifted.

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carriers move faster and reach domain boundaries in the asspun sample already on a ps time scale, thus the difference inseparation distances appears already during tens of ps. Stronglyrestricted carrier motion in the as-spun sample with smallerPCBM and polymer domains prevents carrier escape from theCoulomb attraction. In devices such restricted carrier motionleads to enhanced charge carrier recombination, which isapparently one of the major factors limiting the carrier genera-tion yield and performance efficiency of non-annealed P3HT/PCBM solar cells.23

Our MC simulations have been performed assuming thatonly nearest neighbor e–h pairs are created by exciton splittingat the donor–acceptor interface as was suggested in ref. 7and 33. However, there are publications35–37 arguing that chargecarrier separation at much longer distances takes place on afemtosecond time scale and it helps for final separation of e–hpairs into free charges. Since this is still an open question,which could be also related to the blend annealing, we havealso performed additional calculations directed towards evalua-tion of the role of the initial carrier separation distance in thecharge separation process. Fig. 5 shows the calculated absolutecharge carrier separation distances at zero applied field withthe model parameters obtained from the above describedsimulations. Diffusion driven separation at long times is largewith larger initial separation, but the influence of the initialseparation gradually decreases with time and after several nsthe separation distance is almost independent of the initialultrafast separation if this separation is significantly smallerthan 8 nm. Thus, initial carrier separation only weakly influencesthe final carrier separation process (at several ns when chargeshave reached a distance where the electrostatic attraction energyis similar to kT), unless the initial separation is comparable withthe Coulomb capture radius. On the other hand, as we havediscussed in ref. 7, the large distance carrier separation is hardlycompatible with our experimental carrier drift data showing noquasi-instantaneous carrier drift component.

6. Conclusions

In conclusion, our experimental investigations of the initialcarrier motion in as-spun and annealed P3HT:PCBM blendstogether with Monte Carlo simulations of the carrier driftdynamics suggest a mechanism for the improved performanceof annealed solar cells. The initial carrier drift rates, on asubnanosecond–nanosecond time scale are about two times largerin annealed samples. Monte Carlo simulations of the motiondynamics suggest that the increase in the carrier separation ratecaused by blend annealing is related to the increased polymer andPCBM domain sizes enabling longer distance carrier separation ona ps time scale, which reduces the probability of their geminaterecombination and thus increases the free charge carrier genera-tion yield in annealed samples. On the other hand, the role ofother material properties such as the presence of energy traps, orformation of semicrystalline polymer domains, which change as aresult of annealing, cannot be completely ruled out.

Additional MC simulations directed towards evaluation ofthe role of the initial carrier separation distance showed that themore efficient carrier separation in annealed samples can behardly related to increased initial carrier separation distance.The initial separation distance only weakly influences the carrierseparation efficiency at times and distances where free chargesare formed if it is shorter than about 8 nm, while longer distanceseparation is non-compatible with our experimental data.

Acknowledgements

This research was funded by the European Social Fund underthe Global Grant measure, by the Swedish and EuropeanResearch Councils (ERC 226136-VISCHEM), by the SwedishEnergy Agency and the Knut & Alice Wallenberg Foundationand by Laser Lab Europe (project ID LLC001578, framework of theInitiative of Infrastructures Programme), by the UK Engineeringand Physical Sciences Research Council via the Supergenprogramme and by the Royal Society.

Notes and references

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Fig. 5 Calculated time dependence of the absolute carrier separationdistance at zero electric field and at various initial separation distances.

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