Direct measurement of exciton dissociation energy in polymers

Exciton dissociation energy was obtained based on the comparison of thickness of the space charge region estimated from the measurement of capacitance of prepared Schottky diode and from the measurement of photovoltage spectra. While the capacitance measurements provide information about the total width of the space charge region (SCR) the surface photovoltaic effect brings information only about the part of the SCR where electric field is sufficiently high to cause dissociation. For determination of the dissociation energy it is sufficient to find the electric potential in the SCR where the process starts.


INTRODUCTION
The exciton dissociation energy is an important parameter which affects operation of many optoelectronic organic devices.For example, a low value of this variable is advantageous for the function of solar cells because production of free electrons and holes prevails above their recombination.Poly (3-hexylthiophene) (P3HT) is one of the most-studied conductive polymers in the last decade.Although P3HT based solar cells have reached power conversion efficiency of only 6.5 % 1 P3HT is still a widely used model material to demonstrate the functionality of polymer bulk heterojunction solar cells.One of the important parameters influencing the efficiency of solar cells based on semiconducting polymers and other organic materials is the energy E b needed for dissociation of photogenerated excitons.Value of E b (0.70) eV has been estimated for P3HT in the experimental paper 2 using UV photoelectron (UPS) and inverse photoelectron spectroscopy (IPES) measurements.4][5] Our method based on capacitance and surface photovoltage spectra demonstrated here on Al/P3HT diode is straightforward, inexpensive and it consumes little time.Different thickness of the space charge region obtained from the two spectra is the basis for the exciton dissociation energy determination assuming constant concentration of dissociated states in the space charge region.

EXPERIMENT
Poly(3-hexylthiophene), P3HT, M w = 44000, regioregularity 96 %, obtained from LISICON, and chloroform CHROMASOLV HPLC 99.9% purity grade obtained from Sigma Aldrich, were used as received.Glass substrates with 100 nm thick ITO layer (Ossila Ltd.) etched to a single 5 mm wide electrode strip were used as a sample substrate.Thin polymer films with thickness 75 and 120 nm were deposited onto the substrate using a spin-casting method (5000 rpm and 1000 rpm respectively, rotation for 30s) from a chloroform solution (P3HT concentration 1 wt.%).After the deposition the samples were annealed at 150 Schottky diode rectifying contact a strip of Al electrode was deposited by physical vapor deposition (PVD, pressure 2•10 5 torr, deposition rate 0.5 nm/s) through a shadow mask on the top surface of the P3HT layer perpendicular to the ITO bottom electrode, which served as an Ohmic contact.The thickness of the deposited Al electrode (50 nm), as well as the deposition rate were determined using a crystal balance monitor.The sample active area was encapsulated under N 2 atmosphere in a glovebox (60 ppm O 2 , 2 ppm moisture) with a microscopic cover slip separated from the substrate with a 50 µm gap (using a pair of optical fibers), and sealed at the edges with an epoxy resin.Electrical and photoelectrical properties were studied by measuring the surface photovoltage and capacitance.All measurements were performed at room temperature.

Measurements of capacitance
Precision LCR Meter E4980A was used to acquire the capacitance of the samples.An automated program enabled us to measure at different modulation frequencies up to 1 MHz.AC modulation voltage 10 mV was applied.DC bias voltage was performed to 1.2 V in the reverse regime and to + 0.6V in the forward regime.Very weak frequency dependence of capacitance was found in the range from 200 Hz to 1 kHz in our diodes.

Surface photovoltage measurement
Evaluating photovoltage spectra of thin films is a technique which was introduced in our previous papers. 6,7The photovoltage was measured in the arrangement shown in Fig. 1.The samples were irradiated by low-intensity monochromatic light chopped with a low frequency of 11 Hz generating an alternating voltage, which was measured by lock-in amplifier.The measured photovoltage spectra were recalculated for constant impinging photon flux density and corrected for the transparency of the glass/ITO.

SURFACE PHOTOVOLTAGE METHOD
The photovoltaic effect requires the presence of an electric field to facilitate the dissociation of photogenerated excitons, which can lead to the generation of a photocurrent in an external circuit.In our case, such field is formed in the space charge region (SCR) at the Al/polymer interface.Our model 6 assumes a layer with an electrically neutral bulk extending between x = 0 and x = d and a space charge region of thickness w (Fig. 1).After illumination, excitons are created both in the bulk and in the SCR.The model considers that there is a place in the SCR where the charge separation of excitons diffusing from the bulk occurs.Bulk contribution to the total current is formed in this way.Drift current results from the excitons photogenerated in the SCR and dissociated by the electric field within this region.The total photocurrent is a sum of the diffusion current from the bulk and the drift current from the SCR.The advantage of our SPV model is the possibility to apply it to samples with arbitrary thickness of the SCR and of the bulk.We are only limited by the value of the measured signal which could be very low for thick polymer samples with quite high α and low diffusion length.
The samples were illuminated from the side of the bulk.
The transport of diffusing excitons is controlled by the diffusion equation Here ∆n(x) is the concentration of photogenerated excitons at depth x, L is the exciton diffusion length, and D is the exciton diffusion coefficient.In the case of multiple reflections, neglecting interference effects, the photogeneration rate g(x) can be expressed as where α is the absorption coefficient, I 0 is the photon flux density impinging on the polymer layer, h represents the total thickness of the layer, and R 1 , R 2 are the reflectance from the illuminated and the top surfaces, respectively.To find the photogenerated current, two boundary conditions are required: at the ITO/polymer interface in the SCR where s is the surface recombination velocity and w 1 is the coordinate in the SCR where the dissociation starts.The internal electric field sweeps the dissociated charges towards the electrodes.On solving equation ( 1) with the boundary conditions ( 3), ( 4) ∆n(x) is obtained and the diffusion current density is where d is the thickness of the bulk.The current density, J drift from the SCR is given by integration of the exciton photogeneration rate over distance (w-w 1 ) where dissociation of excitons takes place.The origin of coordinates was shifted to the bulk-SCR interface: a 1 and a 2 represent relations for the case of multiple reflections. 6he factor G ∈ <0,1> characterizes recombination losses in the SCR., a 1 and a 2 are connected with the SPV signal generated by photons spreading in the direction of the impinging light and with that from the reflected photons, respectively.Total photocurrent density is the sum of ( 5) and (6).
The experimentally verified linear relation between the photovoltage and the light intensity leads to the proportionality between the photovoltage V and the photogenerated current density J.

RESULTS AND DISCUSSION
The surface photovoltage measurements were evaluated to obtain the exciton diffusion length and the thickness of the space charge region.Fig. 2 displays the experimental and theoretical photovoltage spectra.The spectral dependence of the absorption coefficients is in the inset.The theoretical curve fitted to the experimental points provides diffusion length and thickness of the "active space charge region" (w -w 1 ).The exciton diffusion length in our samples was 12-14 nm.
The capacitance measured at the frequency of 200 Hz was evaluated in Fig. 3. Concentration of the charge carriers in the samples under study was obtained from the bias voltage dependence of capacitance in the form of C 2 versus V.The built-in voltage was found from the intersection of the linear graph with the horizontal axis.Fig. 3 represents the plot of 1/C 2 versus V from which the carrier density 2.5x10 17 cm 3 equal to concentration of ionized states N A was obtained.The built-in voltage V D = 0.45 V was found from the intersection of this linear plot with the horizontal axis.
The usual relation for the width of the space charge region calculated from the capacitance measurement is Using ε r = 3 we obtain w = 24 nm The value (w-w 1 ) = 15 nm obtained from the SPV measurements determines the coordinate w 1 where dissociation of excitons starts.This point is located inside the space charge region of the diode and, consequently, (w-w 1 ) is shorter than w.This situation is demonstrated in Fig. 4 where E max is the maximum value of the linearly increasing electric field in the space charge region of the diode.Dissociation of excitons occurs starting from the field E 1 = E (w 1 ).
The potential ϕ which influences dissociation of excitons in the space charge region was derived using Poisson equation Where N A is the concentration of ionized (it is negatively charged) localized states in the p-type P3HT, ε r , ε 0 is the relative permittivity and the permittivity of vacuum.The electrostatic potential in the bulk is constant and for simplicity we put ϕ = 0 for x = 0. We integrated equation (10) with the boundary conditions: ϕ = 0 for x = 0, ϕ = V D for x = w and we obtained the potential in SCR as a function of x Derivative ϕ(x) with respect to x leads to the electric field Because V D = eN A w 2 /2ε 0 ε r and E(w) = E max = eN A w/ε 0 ε r it holds The energy of a particle with charge e is eϕ (w 1 ) at x = w 1 .While the hole in the exciton entering into the SCR overcomes the repulsive force and its energy consequently increases with coordinate x, energy of the electron decreases.resulting change in energy of the exciton is 2 eϕ (w 1 ).Inserting values N A = 2x 10 23 m 3 , V D = 0.45 V, ε r = 3, w = 24 nm, w 1 = 9 nm into Eq.(11) and multiplying by elementary charge e yields dissociation energy of exciton 0.14 e V.As shown in Ref. 1 and 8 the exciton binding energy changes in a wide range depending on the length of molecules and on the torsional disorder across the chain.Low exciton dissociation energy comparable with our result is reached at long molecule lengths.In the case that the exciton binding energy is comparable with kT, both space charge thicknesses, namely from capacitance and surface photovoltage measurements, are equal.The dissociation occurs close to the bulk-SCR interface which is determined with the accuracy 2kT, limiting in this way the accuracy of the exciton dissociation energy.The relation (13) can also be used for determination of exciton dissociation energy if the maximum field E m in the junction is found.Then Eq.(13) after multiplying by the charge e and integrating across the thickness of the SCR gives the dissociation energy.

CONCLUSION
Exciton dissociation energy was obtained based on the comparison of thicknesses of the space charge region (SCR) estimated from the measurement of capacitance and of the photovoltage of Al/P3HT Schottky diode.While the capacitance provides a total SCR of the diode, the SPV method indicates the part of SCR ("active SCR") where the dissociation occurs.The energy was calculated using the results of capacitance measurement, namely constant ionized states concentration and a linear increase of electric field and an "active SCR" thickness found from the photovoltage spectra.The dissociation energy 0.14 eV hereby obtained falls into the range published in the literature and shows that this simple experimental method can provide reliable information on the dissociation energy of excitons in semiconducting polymers.

FIG. 2 .
FIG.2.Normalized photovoltage spectrum of Al/P3HT diode.Full line -theory fitted to the experimental points with L = 12 nm and (w -w 1 ) = 15 nm.The spectrum of absorption coefficient of P3HT is shown in the inset.

3 .FIG. 4 .
FIG.4.Electric field in the polymer layer under Al electrode as a function of coordinate.The excitons are entering from the neutral bulk into the space charge region at the point x = 0 and they are dissociated at x = w 1 .The thickness of the space charge region is w.