**4. Charge transport in thin polymer films**

Electronic conductivity of organic molecular compounds differs from that of metal and inorganic semiconductors such as silicon and germanium. The well-known band theory of crystal lattice is a good base to understand the conduction mechanism of crystalline molecular solids and conjugated and unconjugated polymers. At the same time, the applicability of the ideal elongated chain model to materials with a complicated morphology is naturally limited. Even within the frames of the idealized model, the inorganic conductors and semiconductors differ considerably from polymers. Besides, in polymers, the screening of interactions between charge carriers is less; electron– electron and electron–hole interactions play an important role causing considerable localization of electron states as compared with inorganic materials [27]. Absence of macroscopic ordering means inadequacy of band conduction model to describe electron conductivity of bulk polymer materials, though it can be used to a limited extent when studying the conduction process.

In amorphous layers of thin organic films the terms "conduction band" and "valence band" are usually replaced by the terms of the LUMO and the HOMO, respectively. The states' density is mainly described quite satisfactorily by Gaussian distribution of localized molecular orbitals of individual molecules [28].

Depending on the size of barrier on the interface of electrode with polymer film, electric current flowing through the sample can be of injection type, that is, limited by space charge. In this case, one of the electrodes should be an ohmic one, that is, it should provide more charge carriers in time unit than the sample is able to transport, not breaking Poisson's law. Otherwise, charge carrier transport across the interface will be limited by the barrier. The tunneling model of Fowler-Nordheim (FN) and Richardson-Schottky's (RSch) thermionic emission model are usually used to study injection in polymers in a rather strong electric field [29–31].

A thermal electron emission from hot metal is called thermionic emission. Electronic emission from metal contact into vacuum or dielectric conduction band by their thermal transportation through the potential barrier in electric field is called Schottky emission. Taking into account image forces in parabolic approximation, it is possible to get the Richardson-Schottky equation for current density [32]:

However current uncertainty \(\omega\):

$$J = A \cdot T^2 \exp\left[\frac{-\varepsilon(\eta\_b - \varepsilon F/4\pi\varepsilon\varepsilon\_0)}{kT}\right] \tag{1}$$

In Biglova et al.'s works [35], the temperature dependences of the electrical conductance were measured for films of different polyaniline forms. The measurements were carried out for soluble forms of the modified polyaniline homopolymer, that is, **12**, and its copolymers with o-toluidine in different molar ratios. The temperature measurements of the electrical conductance *G* of the polymer films in the range from 300 to 450 K demonstrated that the dependence

(o-toluidine with 2-(1-methyl-2-buten-1-yl)aniline) in different molar ratios: (2) 1:3, (3) 1:1, and (4) 3:1.

In the *lnG – 1000/T* coordinates, the experimental points, within the limits of error, fall on a straight line (**Figure 5**). The quantity *ΔE* (**Table 1**) can be interpreted as the interval between

From the data presented in **Table 1**, it follows that the band gap varies from sample to sample and lies in the energy range from 1.39 to 1.66 eV. The dependence of the band gap on the molar ratio of the copolymers used for the preparation of thin films is an extremely important characteristic for their practical application in various electronic devices. The polymer compounds studied in this chapter can be used for the subsequent development of electronic

In order to understand how charge transfer occurs through the metal-polymer interface, we measured the temperature dependences of the current I flowing through the film structure. In

are well approximated by straight lines (**Figure 5**) in accordance with Eq. (1). The current density is defined as *J = I/S*, where *S* is the cross-sectional area of the film, which remains unchanged during the measurement. Therefore, the graphical dependences can be constructed using the values of the current flowing through the sample, rather than the values of current density. According to Eq. (1), the slopes of the straight-line sections are proportional to the Schottky barrier height *ϕ*B. The results of the calculations are presented in **Table 1**.

*–1000/T* coordinates, the graphical dependences, within the error of measurement,

HOMO and LUMO (an analog of the band gap) in semiconductor polymer films.

2kT). (3)

on the inverse temperature for films of copolymers

New Organic Polymers for Solar Cells http://dx.doi.org/10.5772/intechopen.74164 93

As heterostructures.

of *G* on the temperature *T* has an exponential character:

**Figure 5.** Dependences of (a) the electrical conductance and (b) I/T<sup>2</sup>

<sup>G</sup> <sup>=</sup> <sup>G</sup><sup>0</sup> exp(−\_\_\_\_ ∆E

devices similar to those based on inorganic Ga1–x Alx

the *lnI/T2*

where *J* is a current density, *А* is the Richardson constant, *е* is an electron charge, φ<sup>B</sup> is a barrier height, *F* is a field density, *ε* is a dielectric permeability of a sample, *ε*<sup>0</sup> is the electric constant, *k* is the Boltzmann constant and *Т* is temperature. An important assumption in RSch model is that electron can be taken out from the metal once it gets enough heat energy to cross the potential barrier which is formed by a superimposition of the external field and images forces.

According to the quantum theory, electron wave function within dielectric area located between two electrodes is different from zero. Wave function exponentially decreases with a distance into the barrier. If the barrier is very narrow, the probability to pass through the barrier for an electron has a finite value depending on the height and form of the potential barrier. Tunneling (auto-emission) can be observed in the case of a wide barrier if its effective thickness decreases under the influence of a strong electric field.

In the FN model image forces are disregarded and the tunneling of electrons from metal through a triangle barrier to free states of conduction area is considered. When the field intensity increases, the height and width of the potential barrier decreases to such an extent that a new physical effect appears and prevails: quantum mechanic tunneling of electron across the potential barrier. Current caused by the tunnel emission facilitated by a field is described by Fowler-Nordheim equation. In this case the current density can be described by the expression [33]:

$$J(F) = B\,F^2 \exp\left(-\frac{4\sqrt{2\,m\_{gt}(e\,\eta\_b)^3}}{3\hbar eF}\right) \tag{2}$$

which is independent of temperature. Here, *meff* is the effective mass of a charge carrier in polymer and *ħ* is Planck's constant.

In spite of disadvantages of both FN and RSch concepts, they have been applied successfully to describe injections of a charge carrier in organic light-emitting diodes. For example, the FN model was applied to give reasonable values for the barrier height and to take into account independence of the temperature characteristic *J(F)* in strong fields [34]. Thermionic emission prevails at the high temperatures and relatively low electric fields. Current caused by tunnel emission takes place at low temperatures and high values of electric fields.

carriers in time unit than the sample is able to transport, not breaking Poisson's law. Otherwise, charge carrier transport across the interface will be limited by the barrier. The tunneling model of Fowler-Nordheim (FN) and Richardson-Schottky's (RSch) thermionic emission model are

A thermal electron emission from hot metal is called thermionic emission. Electronic emission from metal contact into vacuum or dielectric conduction band by their thermal transportation through the potential barrier in electric field is called Schottky emission. Taking into account image forces in parabolic approximation, it is possible to get the Richardson-Schottky equa-

*k* is the Boltzmann constant and *Т* is temperature. An important assumption in RSch model is that electron can be taken out from the metal once it gets enough heat energy to cross the potential barrier which is formed by a superimposition of the external field and images forces. According to the quantum theory, electron wave function within dielectric area located between two electrodes is different from zero. Wave function exponentially decreases with a distance into the barrier. If the barrier is very narrow, the probability to pass through the barrier for an electron has a finite value depending on the height and form of the potential barrier. Tunneling (auto-emission) can be observed in the case of a wide barrier if its effective

In the FN model image forces are disregarded and the tunneling of electrons from metal through a triangle barrier to free states of conduction area is considered. When the field intensity increases, the height and width of the potential barrier decreases to such an extent that a new physical effect appears and prevails: quantum mechanic tunneling of electron across the potential barrier. Current caused by the tunnel emission facilitated by a field is described by Fowler-Nordheim equation. In this case the current density can be described by the expres-

4 √

which is independent of temperature. Here, *meff* is the effective mass of a charge carrier in

In spite of disadvantages of both FN and RSch concepts, they have been applied successfully to describe injections of a charge carrier in organic light-emitting diodes. For example, the FN model was applied to give reasonable values for the barrier height and to take into account independence of the temperature characteristic *J(F)* in strong fields [34]. Thermionic emission prevails at the high temperatures and relatively low electric fields. Current caused by tunnel

emission takes place at low temperatures and high values of electric fields.

\_\_\_\_\_\_\_\_\_\_ 2 *meff* (*e* φ*B*)<sup>3</sup> \_\_\_\_\_\_\_\_\_\_

−*e*(φ*<sup>B</sup>* − *eF*/4 *ε*0) \_\_\_\_\_\_\_\_\_\_\_\_\_

*kT* ], (1)

<sup>3</sup>ℏ*eF* ) (2)

is a barrier

is the electric constant,

usually used to study injection in polymers in a rather strong electric field [29–31].

where *J* is a current density, *А* is the Richardson constant, *е* is an electron charge, φ<sup>B</sup>

height, *F* is a field density, *ε* is a dielectric permeability of a sample, *ε*<sup>0</sup>

thickness decreases under the influence of a strong electric field.

*J*(*F*) = *B F*<sup>2</sup> *exp*(−

polymer and *ħ* is Planck's constant.

tion for current density [32]:

92 Emerging Solar Energy Materials

sion [33]:

*J* = *A* ∙ *T*<sup>2</sup> *exp*[

**Figure 5.** Dependences of (a) the electrical conductance and (b) I/T<sup>2</sup> on the inverse temperature for films of copolymers (o-toluidine with 2-(1-methyl-2-buten-1-yl)aniline) in different molar ratios: (2) 1:3, (3) 1:1, and (4) 3:1.

In Biglova et al.'s works [35], the temperature dependences of the electrical conductance were measured for films of different polyaniline forms. The measurements were carried out for soluble forms of the modified polyaniline homopolymer, that is, **12**, and its copolymers with o-toluidine in different molar ratios. The temperature measurements of the electrical conductance *G* of the polymer films in the range from 300 to 450 K demonstrated that the dependence of *G* on the temperature *T* has an exponential character:

$$\mathbf{G} = \mathbf{G}\_0 \exp\left(-\frac{\Delta \mathbf{E}}{2\mathbf{k} \mathbf{T}}\right). \tag{3}$$

In the *lnG – 1000/T* coordinates, the experimental points, within the limits of error, fall on a straight line (**Figure 5**). The quantity *ΔE* (**Table 1**) can be interpreted as the interval between HOMO and LUMO (an analog of the band gap) in semiconductor polymer films.

From the data presented in **Table 1**, it follows that the band gap varies from sample to sample and lies in the energy range from 1.39 to 1.66 eV. The dependence of the band gap on the molar ratio of the copolymers used for the preparation of thin films is an extremely important characteristic for their practical application in various electronic devices. The polymer compounds studied in this chapter can be used for the subsequent development of electronic devices similar to those based on inorganic Ga1–x Alx As heterostructures.

In order to understand how charge transfer occurs through the metal-polymer interface, we measured the temperature dependences of the current I flowing through the film structure. In the *lnI/T2 –1000/T* coordinates, the graphical dependences, within the error of measurement, are well approximated by straight lines (**Figure 5**) in accordance with Eq. (1). The current density is defined as *J = I/S*, where *S* is the cross-sectional area of the film, which remains unchanged during the measurement. Therefore, the graphical dependences can be constructed using the values of the current flowing through the sample, rather than the values of current density. According to Eq. (1), the slopes of the straight-line sections are proportional to the Schottky barrier height *ϕ*B. The results of the calculations are presented in **Table 1**.


**Table 1.** Electrochemical characteristics of the synthesized polyaniline derivatives.

The analysis of the dependences obtained in this study allows the assumption that the main mechanism of charge carrier transfer through the interface between the metal substrate and the polymer film is the Schottky thermionic emission, which determines carrier transport in the temperature range from 300 to 450 K. This confirms the conclusion that the transfer of charge carriers through the metal-polymer interface occurs as a result of the above-barrier transport. In this case, the barrier height is determined by the difference between the work function of the metal and the electron affinity of the polymer. For example, the calculation according to the results of the electrophysical measurements for film samples of copolymers **15** gives the barrier height of 0.77 eV (**Table 1**). Taking into account that the work function of aluminum is 4.26 eV and the electron affinity of the polymer lies in the range from 3.5 to 3.6 eV, we obtain the barrier height ranging from 0.76 to 0.66 eV, that is, we have the value comparable to that calculated within the framework of the Schottky model. Since the field addition in Eq. (1) does not exceed 0.1 eV, it is ignored. Thus, the above calculations are further evidence in favor of the model of above-barrier transport at the metal-polymer interface.

cell was 25 mm, the internal diameter was 4 mm and the working temperature varied within the range 500–650 K. Thermal heating of fullerene-containing monomers (FCMs) during deposition led to their polymerization. Some thin films were formed by the spin coating technique from a solution of fullerene-containing monomers. All the obtained films were uniform

**Figure 6.** (a) An energy level diagram of the PANI/FCM system; (b) process of photon absorption and charge separation

To increase the conductivity of polyaniline layers, the temperature conditions of deposition from the Knudsen cell were selected. The temperature range of 500–550 K proved to be the most optimal. In addition, protonation of the freshly prepared films in vapors of hydrochloric acid solution was carried out. For PANI films a conductivity value of 1.0 mS/cm was achieved as a result. The surface condition and thickness of the deposited films were monitored on the basis of analysis of AFM images obtained by a NanoScan 3D. The thickness of photoactive layers varied and took on values within the range 100–200 nm. It should be noted that a too large thickness of the films leads to exciton recombination and reduces the efficiency of charge separation. On the contrary, the incident photon absorption and quantity of formed excitons decrease in overly thin films.

The organic solar cell test samples based on the donor-acceptor polymer systems described earlier were formed on a glass substrate with conductive and transparent ITO layers. Resistance of ITO layers was about of 10 Ω/**□**. For experimental structures of the OSC in this research the following organic substances were used: PANI, conventional fullerene and a novel synthesized monomer—monosubstituted methanofullerene derivative [38] (**Figure 6a** and **b**). The aluminum films fabricated by thermo-diffusion deposition in vacuum were applied as the upper electrode. **Figure 6c** presents the structure of the OSC in which thin films of PANI and

The current–voltage characteristics (CV characteristics) of all the prepared OSC samples were measured and the numerical values of such parameters such as open-circuit voltage, short-circuit current, filling factor and PCE were calculated on their basis. Measuring the CV characteristics of a photovoltaic cell is usually done by exposing it to steady-state illumination and a known temperature. The sun or a sunlight simulator can act as a light source. Estimations of the coef-

The values of these parameters for the various OSC experimental structures studied in this

voltage) and FF = 0.6–0.8 (filling factor). The highest values of PCE for the investigated

(AM 1.5 G conditions).

New Organic Polymers for Solar Cells http://dx.doi.org/10.5772/intechopen.74164 95

(short-circuit current), Voc = 0.6–0.8 V (open-circuit

in thickness, and their conductivity was about 0.1–1.0 mS/cm.

in this structure; (c) multilayer film structure of OSC.

fullerene-containing polymers were used as photoactive layers.

ficient of efficiency were based on standard sun intensity *P*<sup>0</sup> = 1000 W/m<sup>2</sup>

work appeared to be Jsc = 0.6–1.8 mA/cm<sup>2</sup>

The obtained values of HOMO and LUMO indicate that the polyanilines studied in our work can be used for the development of new organic solar cells [36, 37]. The short-circuit current of the photo-converter is closely related to the difference in the energy between the HOMO of the PANI (donor) and the LUMO of the acceptor. The most appropriate acceptor can be represented by a methanofullerene [38]. This difference also determines the open-circuit voltage. Moreover, the band gap of the donor determines the minimum energy or the maximum wavelength of the absorbed photons. For the effective absorption in the visible part of the solar spectrum, the band gap should be in the range from 1.4 to 1.5 eV.

Thus, the poly-2-(1-methyl-2-buten-1-yl)aniline/methanofullerene heterojunction, which is composed of newly synthesized compounds, is optimal for manufacturing a laboratory sample of a solar energy photoconverter.
