A model for studying the performance of P3HT:PCBM organic bulk heterojunction solar cells

Optik 126 (2015) 1429–1432

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Optik journal homepage: www.elsevier.de/ijleo

A model for studying the performance of P3HT:PCBM organic bulk heterojunction solar cells Hossein Movla a,∗ , Amin Mohammadalizad Rafi b , Nima Mohammadalizad Rafi c a b c

Azar Aytash Co., Technology Incubator, University of Tabriz, Tabriz, Iran Department of Engineering, Kharazmi University, Tehran, Iran Department of Engineering, Islamic Azad University, Malard Branch, Malard, Iran

a r t i c l e

i n f o

Article history: Received 27 February 2014 Accepted 9 April 2015 Keywords: Plastic solar cells Organic photovoltaics P3HT:PCBM blend Drift–diffusion Electrical modeling

a b s t r a c t In the study of bulk heterojunction (BHJ) solar cells based on poly(3-hexylthiophene) (P3HT) and a methanofullerene derivative (PCBM), P3HT/PCBM device performance is strongly depending on the thickness of active region, materials in use and fabrication methods. In such devices, optoelectronic behaviors such as charge carrier generation and recombination, photocurrent generation and charge transport mechanism are different in devices of different fabrication methods. An electrical model accounting for study of the performance of P3HT:PCBM organic bulk heterojunction solar cells is developed to achieve the device parameter for high performance of the polymer-fullerene bulk heterojunction solar cells. In this model, by solving the drift–diffusion equations by considering the boundary condition and uniform potential energy, the effects of the active region thickness, potential energy and photocurrent generation on the performance of P3HT:PCBM bulk heterojunction solar cell have been studied. Simulated current–voltage characteristics as a function of active layer thickness reveal relatively good agreement between the model’s predictions and published modeling and experimental reports. © 2015 Elsevier GmbH. All rights reserved.

1. Introduction Organic photovoltaic (OPV) research has developed during the past 30 years due to its flexibility and extremely high optical absorption coefficients which offer the possibility for the production of very thin solar cells [1–3], but it has the main disadvantages of low efficiency, low stability and low strength [4,5]. Semiconducting polymers and molecules have received considerable attention in the last few years for use in the active region of organic bulk heterojunction (BHJ) solar cells where they combine the optoelectronic properties of conventional inorganic semiconductors with the flexible properties of plastic materials [6–8]. Therefore, in the last decade it has attracted scientific and economic interest triggered by a rapid increase in power conversion efficiencies by the introduction of new materials, improved materials engineering, and more sophisticated device structures [9,10]. The currently most efficient class of OPV has an absorber consisting of a blend of donor and acceptor molecules together, which creates a heterojunction throughout the bulk of the device. In addition to experimental studies, numerical device model, for the electronic and optical processes, allows researchers to have a good

∗ Corresponding author. Tel.: +98 9146352945. E-mail address: [email protected] (H. Movla). http://dx.doi.org/10.1016/j.ijleo.2015.04.020 0030-4026/© 2015 Elsevier GmbH. All rights reserved.

understanding and also, efficient optimization of organic optoelectronics devices [11–14]. In the study of bulk heterojunction solar cells based on poly(3-hexylthiophene) (P3HT) and a methanofullerene derivative (PCBM), P3HT:PCBM device performance is strongly dependent on the thickness of active region, fabrication methods, materials in use, encapsulation, etc. in which optoelectronic behaviors such as charge carrier generation and recombination, efficient exciton dissociation, photocurrent generation, charge collection and charge transport mechanism are different in different devices [2,13,15]. Schematic diagrams of the organic solar cell based on Glass/ITO/PEDOT:PSS/P3HT:PCBM/Al heterojunctions has been shown in Fig. 1. Drift–diffusion modeling of organic solar cells has been demonstrated to be a powerful tool to explain the influence of various effects on the device performance and current–voltage characteristics (J − V curve) and besides the experimental results, these simulations can be employed predictively to define requirements of desired material properties [16]. In this manuscript, an electrical model accounting for the study of the device performance is developed to optimize the device parameter for high performance of the polymer-fullerene BHJ solar cells. In this model, by solving the drift–diffusion equations and by considering the boundary condition, solar cell characteristics at optimum device thickness which is 100 nm, in dark and different illuminated condition, has been calculated. Simulated current–voltage characteristics as a function of

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H. Movla et al. / Optik 126 (2015) 1429–1432

Electrical field (MV/cm)

0

−5

−10

−15

−20

Fig. 1. Schematic diagrams of the organic solar cell based on Glass/ITO/ PEDOT:PSS/P3HT:PCBM/Al heterojunctions.

active layer thickness reveal relatively good agreement between the model’s predictions and published modeling and experimental reports [19,20]. 2. The electrical model In the typical BHJ solar cells, organic materials have been inserted in the two metal contact as a anode and cathode. Schematic energy level diagrams of the PEDOT:PSS/P3HT:PCBM/Al BHJ solar cell with the electrode materials are shown in Fig. 2. In this figure, highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels, active region and energy diagram in applied voltage (V) have been plotted. Detailed calculation of the energy level diagram is shown in Figs. 4 and 5. Anode and cathode contacts have produced Schottky contacts. If the Schottky barriers are large at both the contacts, mathematical calculations show that the electric field is constant in the cell structure but if the Schottky contact is Ohmic the field is large near the contact and becomes nonuniform [15,17]. In organic solar cell based on blend, P3HT acts as hole-conducting polymer and electrons through the PCBM channels in which the cell total current is obtained by the combination of electrons and holes currents. In this model we used a simple model and we assumed that hole current and electron current follow in different organic polymer. The mobility of charge carriers are kept constant at 10−4 cm/V s

0

20

40 60 thickness (nm)

80

100

Fig. 3. Electrical field distribution versus thickness of the active region.

in accordance to literature values for P3HT and PCBM [12,14]. The Poisson equation is: d q E(x) = (p(x) − n(x)), εε0 dx

(1)

where E, p, n, ε0 , ε and q are applied electric field, hole concentration, electron concentration, vacuum permeability, relative permeability and absolute charge, respectively. This equation correlates the electrons and holes mobilities to spatial variations of the electric field. By simultaneous solving of coupled self-consistent charge continuity rate equations, electrical field distribution in active region of polymer-fullerene BHJ solar cells has been calculated and is shown in Fig. 2. As is seen in Fig. 3, in our case a good approximation of the electric field may be assumed to be constant in the active region of the P3HT/PCBM. Solving the Poisson’s equation for the case of a semiconductor with donor like (n-type) doping concentration, it was observed that the conduction band edge is dependent on distance x and active region thickness d as [17], q 1 x2 Nd − εε0 2 d

−qU(x) =



1 − 2 − qV +

q d2 Nd εε0 2



x + 1 ,

(2)

where U(x) is the potential distribution in the semiconductor, Nd is the doping concentration of the active region, and 1 and 2 are the electron injection barriers from the anode and cathode, respectively. Variation in the band edge of the semiconductor in terms of the distance from anode for different donor like (n-type) doping is shown in Fig. 4. In this figure, left side is 1 = 0.9 eV and right side is 1.2 15

N =10 d

1 φ1

16

Nd=10

17

0.8

N =10

−qV(x) (eV)

d

0.6

φ2

0.4 0.2 0 −0.2

Fig. 2. Schematic energy level diagrams of the organic solar cell based on PEDOT:PSS/P3HT:PCBM/Al heterojunctions.

0

20

40 60 thickness (nm)

80

100

Fig. 4. Variation in the band edge of the semiconductor in terms of the distance from anode for different n-type doping in thermal equilibrium.

H. Movla et al. / Optik 126 (2015) 1429–1432 −10

0.95

x 10

0.9

V=0.5 V, d=100 nm

Current Density (mA/cm2)

−qV(x) (eV)

0.85 0.8 0.75 0.7 0.65 0.6 0.55

1431

0

20

40 60 thickness (nm)

80

Drift Diffusion 1.5

1

0.5

100

0

Fig. 5. Variation in the band edge of the semiconductor in terms of distance from anode. Left side is 1 = 0.9 eV and right side is 2 = 0.6 eV.

0

20

40 60 thickness (nm)

80

100

Fig. 6. Diffusion and drift currents for d = 100 nm at 0.5 V.

2 = 0.6 eV. It is seen that for large n-type doping, the band edge and therefore the electric field depends on the impurity concentration. From Fig. 4 it is clear that in the typical solar cells with low doping concentrations, electrical field is constant in the active region of the cell but in higher doping concentrations, electrical field strongly depends on the doping concentration. The results of Eq. (2) which plotted Fig. 3 were calculated for inorganic semiconductors materials but with some approximations, also it can be used for organic semiconductors as well. Fig. 5 shows the band edge of the active region semiconductor in 100 nm thicknesses of the active region in thermal equilibrium (T = 300 K). To model the J − V characteristics of P3HT/PCBM solar cells we assume the P3HT/PCBM blend to be a single virtual semiconductor having electron and hole mobilities equal to electron mobility of PCBM and hole mobility of P3HT, respectively. The HOMO and LUMO levels of the virtual semiconductor correspond to the HOMO of P3HT and LUMO of PCBM, respectively. In the thermal equilibrium condition, the electric field in the active region of the sample is equal to Vbi /d, which reduces to (Vbi − V)/d when a forward bias voltage V is applied to it.

where J is the integration of the j over the sample thickness 0 to d

2.1. Dark current



Drift and diffusion equation for electrons in a typical semiconductor is given by

∂n(x) j = qn n(x)E(x) + qDn , ∂x

(3)

where n is the electron mobility and Dn is the electron diffusion coefficient. By using above-mentioned equation, the diffusion and drift components of the current can now be calculated independently. As is shown in Fig. 3, electrical field in a BHJ solar cell structure is uniform and in this respect, related potential energy is: U(x) = U(0) − qE(x).

(4)

In this case, E(x) = − ∂U(x)/∂x, and Eq. (3) can be written as



j = qDn



∂U(x) ∂n(x) q − n(x) , + kT ∂x ∂x

(5)

where k is Boltzmann’s constant and T is the absolute temperature. In the above equation, integrating with respect to x over the whole thickness of the active region, we get

 J=



d

qDn 0

q ∂U(x) ∂n(x) − n(x) + kT ∂x ∂x



dx,

(6)

d

(J = 0 j dx). In the above equation, multiplying by the integrating factor exp [− qU(x)/kT] on both sides of Eq. (6) and integrating with respect to x over the whole thickness of the active region we get qDn n(x) exp

d

J=

0

 −qU(x) kT

 −qU(x)

exp

kT

(7)

. dx

Using the boundary conditions at x = 0 and x = d [14,17], we find that



qDn Nc exp

d

J=

0

exp

 qV kT

 −qU(x) kT

−1

(8)

.

dx

In BHJ solar cells doping concentration is very low and by assuming (1 − 2 ) = qVbi , furthermore Eq. (4) can be written as qU(x) = q

V − V  bi d

x − 1 .

(9)

Using the value of qU(x) from Eq. (9), the denominator of Eq. (8) gives d

exp 0

×



 −qU(x)  kT

1 − exp

dx =

dkT exp q(Vbi − V )

 −q(V − V )  bi kT

  1

kT

.

(10)

Now substituting this value in Eq. (8) we get

J=

q2 Dn Nc (Vbi − V ) exp



dkT



1 − exp

−1 kT





exp

−q(Vbi −V ) kT

 qV kT



−1

.

(11)

The above-mentioned equation takes correctly into account the influence of spread of the carriers and increment in their concentration and also, their mobility due to applied voltage. By using Eq. (11) the diffusion and drift components of the current can be calculated independently. Fig. 6 shows diffusion and drift components of the electron current as a function of x. The currents have been calculated for 0.5 V and two currents flow in the opposite directions. From Fig. 6 it was found that at dark condition, diffusion current is larger than the drift current. In a semiconductor material the change carriers have the tendency to move from the region of higher concentration to that of lower concentration of the same type of charge carriers. Thus the movement of charge carriers takes place resulting in diffusion current but drift current is defined as

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H. Movla et al. / Optik 126 (2015) 1429–1432

8

100 nm

6

J (mA/cm2)

4 2 0 −2 100 mW/cm2

−4

80 mW/cm2 40 mW/cm2 J

−6

dark

−8 −0.5

0

0.5

1

Voltage (V) Fig. 7. J–V characteristics in dark, 40, 80 and 100 mW/cm2 illumination intensity for 100 nm active region thicknesses. (For interpretation of the references to color in this sentence, the reader is referred to the web version of the article.)

the flow of electric current due to the motion of the charge carriers under the influence of an external electric field. 2.2. Illuminated current Detailed computer simulation shows that under illumination also the electric field remains constant and is given by (Vbi − V) [17]. The J − V characteristics under illumination can now be given as

J =

q2 Dn Nc (Vbi − V + JARs ) exp





dnkT +

1 − exp

−1 nkT



  ×

exp

−q(Vbi −V +JARs ) nkT

V − JARs − JL (V ), Rp A



q(V −JARs ) nkT







−1

(12)

where A is the active area of the device, n is the ideality factor, Rs and Rp are the series and parallel resistances and JL (V) is the photogenerated current, respectively. Series resistance is an important parameter and should always be considered; therefore we have taken into account its effect on the internal electrical field. In our simulation, we choose A = 0.1 cm2 , n = 4, Rs = 1  and Rp = 106  in accordance to literature values for typical BHJ solar cell. The number of the carriers which can be extracted from the devices equals the total number of photogenerated carriers multiplied by the ratio of the average drift length to the thickness of the sample. Now the overall photogenerated current (JL ) will be given as [11,14], JL (V ) = |Js c| if 

(−V + JARs + Vbi ) >d d

JL (V ) = −|Js c| if  JL (V ) = |Js c|

(−V − JARs − Vbi ) >d d

(−V − JARs − Vbi ) d

Voc of the OPV cells remains almost constant and is independent of the thickness of the polymer layer. This is not surprising as it has been reported previously that the Voc depends mostly on the energy levels of the electron donor and acceptor system, which in our study remains the same for all the devices. In different thicknesses of BHJ solar cells, Voc is almost constant and is about 0.5–0.6 V. FF of the cell is in optimized value which is about 0.50–0.60, and for two thicknesses in this paper we achieved FF as 0.50 and 0.54, respectively. Jsc has a different value for different published reports, which resulted in different cell fabrication methods. Power conversion efficiency (PCE) of 100 nm P3HT:PCBM blend thicknesses was calculated to be 1.6% which have a good agreement with reported data from Ref. [19,20]. In this model, we used a simple model which correctly demonstrates efficiency reduction by increasing the active layer thickness in which our simulation results are almost in good agreement with previous published works by several research groups about BHJ solar cell modeling and experimental data [11,18–21]. 3. Conclusion In this paper, by solving the drift–diffusion equations by considering the boundary condition and constant electrical field, the electrical characteristics of organic bulk heterojunction solar cells based on P3HT:PCBM were studied in the dark and under different illumination. As it was shown, in different thicknesses of BHJ solar cells, Voc is almost constant and is about 0.5–0.6 V while in our results Voc is 0.5 V. FF of the cell is in optimized value which is about 0.50 for 100 nm P3HT:PCBM blend thicknesses. Jsc has a different value for different published reports, which resulted in different cell fabrication methods. Power conversion efficiency of 100 nm active region thickness is calculated and it is 1.6% which relatively is a good agreement with reported data. Based upon the results of this model it will be possible to more intelligently design nanostructured photovoltaics and optimize them toward higher efficiencies. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

(13)

else.

Similar expressions can be obtained for the hole current as well. J − V characteristics of the device in dark, 40, 80 and 100 mW/cm2 illumination intensity for 100 nm is shown in Fig. 7. J − V characteristics of the cell in 100 mW/cm2 illumination intensity for 100 nm (dot dashed blue) are shown in Fig. 7. As seen from Fig. 7, the J − V characteristics under illumination change considerably on varying the thickness. For devices with active layer thickness of 100 nm, the short circuit current Jsc was 6.13 mA/cm.

[13] [14] [15] [16] [17] [18] [19] [20] [21]

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