Thermal analysis of organic solar cells using an enhanced opto-thermal model

Organic Electronics 25 (2015) 184–192

Contents lists available at ScienceDirect

Organic Electronics journal homepage: www.elsevier.com/locate/orgel

Thermal analysis of organic solar cells using an enhanced opto-thermal model R. Zohourian Aboutorabi, M. Joodaki ⇑ Department of Electrical Engineering, Ferdowsi University of Mashhad, 9177948974 Mashhad, Iran Sun-Air Research Institute, Ferdowsi University of Mashhad, 9177948974 Mashhad, Iran

a r t i c l e

i n f o

Article history: Received 28 April 2015 Accepted 22 June 2015 Available online 2 July 2015 Keywords: Opto-thermal analysis Photovoltaic device Organic solar cells

a b s t r a c t In this paper, an opto-thermal model is presented in order to specify the dominant thermal phenomena in organic solar cells (OSCs), as rather low efficiency photovoltaic devices. This model is capable of predicting the amount of optical heat generation (Qth_opt), also the transient and steady state thermal behavior of an organic photovoltaic cell combining both the optical and thermal models. In a typical organic solar cell, Qth_opt plays a significant role in heating up the device while the electric heat generation (Qth_elec) does not effectively have such a role. Developing an optical model for a solar cell, Qth_opt can be determined in every position of the device; also, the contribution of each layer in heat generation is precisely specified. The device thermal behavior is predicted by feeding the thermal model with Qth_opt. This is done for an organic solar cell with a typical architecture and it is shown that thermal convection and radiation are two determinative thermal phenomena while conduction plays a minor role; furthermore, the electrodes, Aluminum (Al) cathode and Indium Tin Oxide (ITO) anode, are two strong light absorbers which contribute to more than 80% of optical heat generation. Assuming Stefan–Boltzman radiation loss, the temperature rise for a typical single junction OSC is estimated under different conditions. The device temperature rise might be even larger for other architectures consisting of several layers depending on their thicknesses and absorption coefficients. This temperature increase enhances the OSCs’ efficiency while degrading the lifetime. The model can be applied to thermal analysis of other types of photovoltaic cells and optoelectronic devices with minor modification. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction During the past few years, extensive researches have been conducted towards improving the applicability of novel photovoltaic technologies. The key advantage of these technologies is that they are fed by solar energy as a clean and abundant source of energy [1,2]. The main challenge which prevents widespread commercial applications of these technologies all around the world is their relatively high total electricity price; therefore, great efforts have be made to develop low cost thin film solar cells, one of the most promising types of which is organic based cell. Organic photovoltaic cells also offer several interesting advantages over other types of photovoltaic devices, such as full mechanical flexibility, semi-transparency, light weight, compatibility with other organic electronic devices and simple production methods in large scale (screen printing, inkjet printing, etc) [1,3–12]. ⇑ Corresponding author at: Department of Electrical Engineering, Ferdowsi University of Mashhad, 9177948974 Mashhad, Iran. E-mail address: [email protected] (M. Joodaki). http://dx.doi.org/10.1016/j.orgel.2015.06.034 1566-1199/Ó 2015 Elsevier B.V. All rights reserved.

So far, there have been numerous works on electric and optical modeling of organic solar cells (OSCs) using numerical and analytical methods [13–24]. Some works also tried to clarify how temperature variation correlates with OSC performance in terms of short circuit current, open circuit voltage, fill factor, efficiency and lifetime [25–27]. In this paper, we aim to answer the question that how OSC temperature changes when it works continuously under sunlight illumination and in different ambient conditions, also what factors may influence the device temperature. We first propose two thermal models that are both useful in predicting the device temperature, depending on what is looked for. The first model is the steady state (SS) thermal model, which is more straightforward and calculates the device temperature in steady state. It also provides more intuition about the device internal condition in comparison with the other model. The second model is the transfer matrix based (TM) thermal model which specifies the transient and steady state device temperature at the expense of more complexity and algebraic labor. Coupling the appropriate thermal model with 1-D TM optical model, a comprehensive opto-thermal model is

R. Zohourian Aboutorabi, M. Joodaki / Organic Electronics 25 (2015) 184–192

developed, which can specify the amount of optical heat generation and heat flow mechanism in photovoltaic devices. So far, there have not been a thorough research on thermal analysis of organic solar cells; therefore, we have applied this model to understand the thermal mechanism of these devices in detail; however, the model can be extended to be used in other opto-electronic devices, as well. The paper is organized in four sections: firstly, the thermal models (TM and SS) and the mathematical concepts behind them are presented; also, they are verified using experimental data of an organic light emitting diode (OLED); then, these two models are compared to each other. Secondly, the 1-D optical model is briefly presented and verified for a typical OSC. Thirdly, the thermal and optical models are combined to specify the thermal phenomena in an organic photovoltaic device under different sunlight illuminations. Finally, the whole idea and results are summed up and other potential applications of the model are discussed.

185

Fig. 1. Thermal resistor network for a slab of material with no internal heat generation.

2. Thermal model The mathematical duality of heat flow and electric current propagation is of significant help in understanding the thermal analysis problems. Several mathematical techniques, which have been already developed to solve electric circuits, are also applicable in the case of thermal analysis. In order to solve the heat flow in a one-dimensional (1-D) slab of material, one needs to consider two basic equations: Fourier’s law and continuity equation [28]. Fourier’s law states how temperature (T) changes spatially with heat flux (Q),



@Tðx; tÞ 1 ¼ Q ðx; tÞ @x K

ð1Þ

where K is the material thermal conductivity (W/km). This is electrically analogous to Ohm’s law and can be used to predict the SS temperature in a system. The continuity equation implies how T changes temporally with spatial variation of Q and it is shown below:



@Tðx; tÞ 1 @Q ðx; tÞ ¼ @t C @x

ð2Þ

where C is the volumetric heat capacity (J/m3 K). The full (transient and steady state) thermal response of the slab is determined by combining (1) and (2) which yields:

@ 2 Tðx; tÞ @Tðx; tÞ ¼ RC @x2 @t

ð3Þ

where R is 1/K [28,29]. In order to get rid of solving complex differential equations, also incorporating the effect of internal heat generation, the SS and TM thermal models are presented, verified and discussed in the following sections. 2.1. Steady state thermal equivalent circuit A 3-D steady state model is a resistor network that specifies the device temperature in steady state. Considering heat flow in three dimensions makes the result much reliable since it takes the heat flow in parallel paths into account. Each slab of material with no internal heat generation can be thermally modeled as in Fig. 1 in steady state. Since Rth ¼ t=K (where Rth is the thermal resistance (K m2/W) and t is the thickness in heat flow direction), the thermal model would be realized knowing device materials and dimensions (L and W stand for thickness and width, respectively). The architecture of an encapsulated OLED is shown in Fig. 2(a). In case of optoelectronic devices such as OLEDs and OSCs, the internal heat generation should also be taken into account. To

Fig. 2. (a) General OLED architecture consisting of series of layers surrounded by glass encapsulation and air with an effective thickness. (b) Schematic showing how thermal mechanisms (conduction, convection and radiation) occur in an OLED [28].

minimize the mathematical complexity, it is assumed that the internal heat source injects heat at a single point of device (ITO–organic interface) (Fig. 2(b)). In the following sections, it will be shown why such an assumption is valid. The heat conduction occurs in three dimensions and heat convection is described by considering an air layer with an effective thickness (tair-z and tair_xy). To consider the radiation losses, Stefan–Boltzman law may be employed:

Q rad ¼ erðT 4src  T 40 Þ ffi hrad ðT src  T 0 Þ

ð4Þ

where r is Stefan–Boltzman constant and e represents the OLED emissivity (in this case 0.5) [28]. Using the above approximation, the three dimensional radiation losses can be modeled as an effective resistive path. This is interesting to note that some works claim that heat radiation does not follow Stefan–Boltzman law in very small scales (less than thermal wavelength) [30]. In fact, it has been

186

R. Zohourian Aboutorabi, M. Joodaki / Organic Electronics 25 (2015) 184–192

found that in very small scales, the radiation is proportional to material volume rather than its surface area; however, we did our simulations considering the conventional Stefan–Boltzman law and we achieved reasonable fittings. Generally, this could be an open question for scientists. Table 1 summarizes the OLED dimensions. Finally, Fig. 3 shows the whole circuit, which models the steady state thermal behavior of an optoelectronic device such as an OLED. Using commercial softwares that are optimized for solving the electrical equations, this model can be simply solved. It also provides scientists with information on internal condition of the device such as temperature gradient along each layer and amount of heat flux through parallel conduction and radiation paths. This model cannot calculate the transient thermal response of the device, which is of great importance in specific circumstances and in some devices as OLEDs. This is the main idea behind developing the TM model. 2.2. Transfer matrix based thermal model: mathematics As we have already shown that the thermal behavior of the system described by (3) is dual to electric behavior of the electric quadripole of Fig. 4 [29]. Through using this concept, it would be possible to solve more complicated systems consisting of multiple layers with internal heat sources. One approach to thermally solve a system is to solve its dual electric system in Laplace space. Taking Laplace transforms of (1) and (2), the quadripole can be specified in Laplace space as following [29]:

T s1

!

 ¼

Q s1

coshðhÞ

Z 0 sinhðhÞ



T s2

!

Q s2

sinhðhÞ=Z 0

coshðhÞ !  !  s A=B 1=B T s1 Q1 ¼ 1=B A=B T s2 Q s2

 ¼

A

B

C

D



T s2 Q s2

! ;

Fig. 3. Thermal resistive network for a multi-layer structure such as an OLED (nodes with the same names are connected to one another).

ð5Þ Q si

T si

where and (i = 1, 2) are Laplace transforms of Ti and Qi, respecpffiffiffiffiffiffiffiffiffiffiffi tively. h is operational propagation coefficient and equals L Cs=K (s pffiffiffiffiffiffiffiffiffiffiffiffiffi is the Laplace variable); Z 0 ¼ 1=KCs is also the characteristic thermal impedance. The total equivalent matrix of a multilayer structure consisting of layers in series (assuming neither internal heat source nor parallel heat loss) can be found by multiplying all matrices corresponding to layers in series. The SS model confirms that in thin film optoelectronic devices such as OLEDs or OSCs, heat conduction is so effective that there is no temperature difference along different layers; this is why the schematic shown in Fig. 5 works for such a device. In fact, the heat source can be integrated in a single point of device; also, heat flux may flow through radiation path, right or left paths and resistive parallel paths (xy planes) which are all in parallel. Right and left paths consist of layers in series. Heat convection is described by considering an air layer with an effective thickness; thus, for right path we have:

T ssrc Q ssrc;R

!

!

¼ ðM R Þ

T s0 ; Q s0R

T ssrc Q ssrc;R

!

 ¼

AR

BR

CR

DR



T s0 Q s0R

! ð6Þ

Fig. 4. Electric quadripole [29].

Fig. 5. Schematic illustration of different thermal heat flow channels in the OLED (radiation path, right path, left path, parallel resistive paths); Qsrc,pl, Qsrc,R, Qsrc,L and Qrad are input heat flux in parallel, right, left and radiation paths, respectively and Q0,pl, Q0,R and Q0,L are output heat flux in parallel, right and left paths, respectively.

where MR is obtained multiplying all matrices corresponding to different layers in right path. Manipulating (6) one can write:

Table 1 OLED dimensions. Layer

Lz

Wx  Wy

Glass ITO anode Organic layer Al cathode Airgap

700 lm 120 nm 120 nm 100 nm 30 lm

5 cm  5 cm 5 cm  (5 cm–700 lm) (5 cm–700 lm)  (5 cm–700 lm) (5 cm–700 lm)  5 cm (5 cm–700 lm)  (5 cm–700 lm)

Q ssrc;R Q s0R

! ¼

DR BR

R BR  AR DRBC R

1 BR

 ABRR

!

T ssrc T s0

! ð7Þ

where (AR – DR). This method is also applicable to the left path. For parallel resistive paths in +x direction, we have (w is the width):

R. Zohourian Aboutorabi, M. Joodaki / Organic Electronics 25 (2015) 184–192

Q ssrc;pl

!

Q sm

0 Pn

K i¼1 i



B W=2 ¼ @ Pn

K i¼1 i

Q ssrc;pl

!

 ¼

Q sm



W=2

M 11

M 12

M 21

M 22

Pn

K i¼1 i

1

s C T src Pn A K T sm i¼1 i W=2

W=2



T ssrc

187

! ; ð8Þ

!

T sm

where n is the number of layers (6 in our case) and Ki is thermal conductivity of ith layer. Including the effect of air convection (air layer with thickness of tair-xy) in +x direction yields:

!

T ssrc Q ssrc;pl T ssrc

¼

i¼1

Ki



0 1

!

 ¼

Q ssrc;pl

!

1 PW=2 n Apl

Bpl

C pl

Dpl



Q s0;pl

1

t airxy K air

0 1 !

!

Q s0;pl T s0

! ; ð9Þ

T s0

Considering linearity, superposition is valid and we can solve for Tsrc when T0 = 0 and finally add the result with ambient temperature (T0 = 25 °C). Using this technique, very simple mathematical expressions are obtained since all T0 coefficients would be elimi(right path), nated; so, we have Q ssrc;R ¼ T ssrc ðDR =BR Þ

Fig. 6. TM model fitting results for red OLED in different bias conditions (turn on response).

Q ssrc;L ¼ T ssrc ðDL =BL Þ (left path), 4Q ssrc;pl ¼ 4T ssrc ðDpl =Bpl Þ (parallel heat losses in four directions) and Q srad ¼ hrad T ssrc (radiation losses). KCL states that Q th ¼ Q src;R þ Q src;L þ 4Q src;pl þ Q rad ; thus, the device temperature is:

T src ¼ D

Q th R

BR

þ

DL BL

D

þ 4 B pl þ hrad

þ T0

ð10Þ

pl

In both thermal models, all parameters are known except exact values for fitting parameters (hrad, tair-z and tair-xy), which should be specified fitting simulation results with experiments. 2.3. Thermal model: verification and discussion In order to guarantee the precision of the proposed models, the simulation results are compared with experimental data of red OLED presented in literature [28] (data are extracted using the online software, Webplotdigitizer). As in the reference work, we assumed that hrad = 2.5 W/m2 K and tair-z = 1.2 cm. Fitting the simulation results with experiments also yields tair-xy = 2.3 mm. All other parameters are the same as the reference work. The SS OLED temperature in different bias voltages (9 V, 10 V, 11 V and 12 V) can be specified using SS model. The results are in great agreement with experiments. The SS model confirms that there is negligible temperature difference along different layers and the device temperature increase is mainly due to heat convection and radiation. It also shows that parallel heat losses are very large due to this fact that we assumed more heat convection in xy than z direction (tair-xy < tair-z). The TM model is capable of calculating the transient and steady state thermal response of the red OLED. The simulation results are shown in Figs. 6 and 7. Fig. 6 shows the turn-on thermal response of the red OLED while Fig. 7 illustrates the turn-off thermal response of the device, in different bias voltages. The conductivity of air (Kair) depends on several parameters such as pressure, temperature, presence of wind, etc. Fig. 8 shows how Kair may influence the temperature rise of red OLED in different bias conditions. Clearly, as Kair decreases, the temperature would go up and this increase would accelerate as Kair reduces more and more. The temperature variation versus Kair is more severe in case of larger input heat flux; therefore, it can be concluded that the condition where device is working also the device architecture significantly change its thermal behavior.

Fig. 7. TM model fitting result for red OLEDs under different bias conditions (turn off response).

The advantage of utilizing these two models over finite element based softwares (like COMSOL Muliphysics) is that they are computationally much less demanding, hence, suitable for solving optimization problems. Using TM model is not sufficient to specify the system internal condition such as temperature distribution along each layer, the amount of heat flow in each direction, etc; determining these parameters needs more algebraic labor. On the other hand, taking the inverse Laplace transform of the final solution is somehow troublesome and the convergence of results must be guaranteed. As a result, if the transient thermal behavior of the device is not of interest, using the SS model is much easier, more straightforward, fast and informative, hence, is suggested; however, fitting the TM simulation results with temperature–time curve of the device ensures that the fitting parameters are estimated with more precision.

3. Optical model Numerous works have been done on optical modeling and simulation of optoelectronic devices such as organic solar cells. There

188

R. Zohourian Aboutorabi, M. Joodaki / Organic Electronics 25 (2015) 184–192

Eþ0

!

E0

¼ ðSÞ

Eþmþ1

! ð12Þ

Emþ1

where m is the number of layers. This correlation would specify the total reflection and absorption of device. In order to specify the contribution of each layer in optical field absorption, we need to determine the optical field all along the device. This could be easily performed following mathematical procedure in the previous works [34,35]. After determining the optical field along the device (Ej ðxÞ), the time average of the power dissipation per unit volume of the jth layer (Qj) is given by:

Q j ðxÞ ¼

1 ce0 aj gj jEj ðxÞj2 2

ð13Þ

where c is the speed of light, e0 is permittivity of free space, aj ¼ 4pjj =k (jj is the imaginary part of complex refractive index of the ith layer) and gj is the real part of the complex refractive index of the jth layer. Qj is related to the exciton generation rate in the active layer and the heat generation rate in the other layers. Fig. 8. Red OLED temperature variations versus air conductivity (Kair) in different input heat flux.

are several reasons why an optical model can be advantageous in case of OSCs. Coupling the optical model with an electric one, one could find the optimum thickness for active layer of an OSC, leading to the maximum efficiency [31–33]. Also, employing the optical model, we can find the exciton generation rate and internal quantum efficiency (IQE) in solar cells and therefore, optical engineering can be performed to further improve these parameters [24,34,35]. When metal nanoparticles in OSC (Plasmonic effects) are considered, 2D models are needed [36]. In case of optimization problems, mostly a mathematically simplified model, which is computationally efficient, is preferred over a software which fully solves the differential equations. In our case, we aim to analyze the heat generation in a simple structure of an OSC with no two-dimensional (2-D) structures incorporated; hence, a 1-D optical model is sufficient. The simple Beer–Lambert relationship states that the intensity of light in a slab of material exponentially decreases as,

I ¼ I0 expðaxÞ

ð11Þ

where I0 and a are intensity of light and absorption coefficient of material, respectively. In case of OSCs, the presence of Aluminum electrode with high reflection, also thin-layer structure of the device, make the effect of interference more significant; therefore, a more accurate model is required to take the effect of multiple reflections and interference into account. The 1-D transfer matrix based model performs this task; also, it is mathematically simple and fast. The model is capable of precisely specifying the absorbed optical field in any desired depth of device. The full details are discussed in other papers [34,35]; therefore, just a brief review would be presented here. 3.1. Optical model: a review on mathematics Based on the mathematical concepts presented in previous works [34,35], the optical model was developed. In fact, two sets of matrices were defined to describe how field changes when it travels along the slab of material and when it meets the interface. In terms of multiple layers, multiplying the corresponding matrices of the path in which optical field moves would give us an equivalent matrix, S; this matrix correlates the forward-moving and backward-moving fields at two sides of device:

3.2. Optical model: verification and discussion of results The model verification is performed by fitting the calculated results with the literature [34]. The OSC structure consists of glass: ITO: PEDOT: PEOPT: C60:Al (Fig. 9). The device reflection is illustrated in Fig. 10. In order to avoid Fabry–Perot oscillation caused by thick glass substrate (1 mm) in TM method, averaging over an oscillation cycle is used [35]. This is because the TM method assumes complete coherence, which does not stand in case of thick glass substrate. The results are in good agreement with literature. The slight deviation may refer to difference between refractive indices used in this work and the reference work [34] and also the different methods implemented to eliminate the oscillations. The normalized modulus optical field versus position is depicted in Fig. 11. The simulation results are in great agreement with that of the main reference [34]; this confirms the precision of the developed model. It is interesting to note that the optical field goes zero in metal (Al cathode) as we predicted; also, changing the thickness of active layer, the optical field peaks at different positions. This emphasizes the importance of accurate engineering of device architecture. The main advantage of optical model is that one can take advantage of the model to determine the exciton generation rate (G) in the active layer. This parameter strongly correlates with OSC short circuit current; thus, significantly influences the device performance. It has been shown that increasing the thickness of active layer would not necessarily increase the number of absorbed photons (GLactive), hence, the device current. In fact, there are certain thicknesses where this parameter peaks due to strong constructive interference [31,32]; this would give us the optimum thickness of active layer in terms of optical properties. Fig. 12 illustrates the maximum possible reversed bias current (Jsat) which could be derived from an OSC versus active layer thickness (Lactive). The OSC architecture is: glass (1 mm):SiO2 (10 nm):ITO (150 nm):PEDOTPSS (50 nm): P3HT/PCBM (Lactive):LiF (1 nm):Al (100 nm). Electrically, the optimum thickness was proved to be 100 nm for P3HT:PCBM bulk heterojunction (BHJ)

Fig. 9. OSC general architecture.

R. Zohourian Aboutorabi, M. Joodaki / Organic Electronics 25 (2015) 184–192

189

4. Organic solar cells thermal behavior The proposed opto-thermal model is now employed to specify the heat flow mechanism and contribution of different layers in thermal energy generation of organic photovoltaic cells. First, the optical model is employed to specify the optical heat generation in different layers of a typical single junction OSC (Fig. 14); secondly, using the results obtained, the thermal model is solved to find the device temperature rise. This approach is also useful to determine the amount of device temperature rise under different ambient conditions (stagnant, forced-air cooling, sunlight illumination, etc.), as well as to understand how OSC architecture may influence its thermal behavior. 4.1. Heat generation in organic solar cells

Fig. 10. Total reflection of OSC versus wavelength.

OSC [37]. Optically, the optimum thickness which satisfies the electric limitations is the peak around 80–90 nm. Coupling the optical model with the electric one would give the electro-optical optimum thickness. In case of low leakage currents (large shunt resistance), Jsat can be a good approximation for OSC short circuit current (JSC). Needless to say that the active layer morphology also plays a critical role in determining the device optical and electric properties. The morphology depends on several parameters such as duration and temperature of annealing, blend ratio, solvent, etc [38–44]. The variation of G with respect to Lactive is shown in Fig. 13; however, the number of absorbed photon is much more informative than G since it also considers the effect of active layer thickness.

As stated before, the optical model is capable of predicting the optical power per unit volume (W/m3) along the OSC. This correlates with exciton generation rate (#/m3 s) in active layer and the thermal heat (W/m2) in other layers. In case of thermal analysis, wide range of optical wavelengths must be taken into account. This is because the sunlight effective range of illumination is about 280 nm–4 lm; also, some materials such as Aluminum have strong absorption in long wavelengths which would lead to large amount of heat generation. Considering these issues, the simulation was performed for the typical OSC of Fig. 14 and the result is shown in Fig. 15. Glass and SiO2 have no effective absorption in sunlight spectrum (>280 nm), therefore, no contribution in device heat generation; furthermore, the electrodes (ITO anode and Al cathode) and PEDOT:PSS buffer layer are the significant heat generators in the device. These effects may be more important in case of tandem solar cells where several layers are stacked over each other. In order to find the heat flux (W/m2) along the device, the averaged heat generation per volume (W/m3) is multiplied by layer thickness. The results are summarized in Table 2. The electrodes (ITO anode and Al cathode) play the most significant role in heat generation, while other layers do not effectively generate heat. The electric current flow may also heat the device up. In order to find electric heat generation, we have:

Q th

Fig. 11. Normalized modulus optical field versus position at wavelength 460 nm, (a) when C60 thickness is 35 nm and (b) when C60 thickness is 80 nm.

elec

¼ J 2 ðVÞRs ðVÞ

ð14Þ

Fig. 12. Variation of maximum reversed current versus active layer thickness. In case of large enough shunt resistance, this would be a good approximation for short circuit current.

190

R. Zohourian Aboutorabi, M. Joodaki / Organic Electronics 25 (2015) 184–192

Fig. 13. Exciton generation rate versus active layer thickness.

where Qth_elec is electric heat generation, J(V) is OSC current density at operating voltage and Rs is the OSC voltage dependent series resistance. As a rule of thumb, if we assume Rs = 10 O cm2 and J = 20 Am2, Qth_elec would be 0.4 Wm2 which is negligible in comparison with optical heat generation; thus, the optical heat is dominant in typical low efficiency organic solar cells; however, in case of III–V compound solar cells, where the efficiency is up to 40%, the electric heat generation would also be considerable. 4.2. Heat flow in organic solar cells The steady state thermal model for each OSC layer is as in Fig. 16. The heat flux generated by each layer is modeled as a current source that injects thermal energy in the middle of the layer. We also assume that the fitting parameters are the same as the case of discussed red OLED, i.e. tair-z = 1.2 cm and tair-xy = 2.3 mm and hrad = 2.5 W/m2 K. Although the real values for fitting parameters should be specified fitting simulation results with experiments, still the calculations can be advantageous to estimate the device thermal behavior. The other input parameters used in the thermal model are also indicated in Table 3. The device area is assumed to be 5 cm  5 cm. It was found that the device temperature highly depends on convection (Kair and tair) and radiation (Rrad) by using the SS model. The conduction plays minor role since the device is too thin to prevent heat conduction. We also found out that modeling all the heat sources as a single heat source in the middle of device (as in Figs. 3 and 5) would not change the result in comparison with normal modeling (error is less than 103) °C. Using the TM thermal model, the transient thermal behavior of the OSC is as in Fig. 17. In fact, the device temperature would reach its final value in few minutes. The OSC temperature versus air conductivity for AM0 sunlight illumination is shown in Fig. 18 (T0 = 25 °C). The air conductivity values on the earth have been reported to be 0.01–0.2 W/km

Fig. 14. A typical architecture of an organic solar cell (glass: 1 mm, SiO2: 10 nm, ITO: 150 nm, PEDOTPSS: 50 nm, P3HT/PCBM: 100 nm, LiF: 1 nm, Al: 100 nm).

Fig. 15. Absrobed optical power in unit volume of different layers of a typical organic OSC (under AM0 sunlight illumination) specified by different colors. From left to right: SiO2, ITO, PEDOT:PSS, active layer, LiF and Al. The LiF buffer layer is only 1 nm and hence, cannot be shown in the picture. The optical power would convert to heat power in all layers expect active layer.

Table 2 Optical Heat Generation in OSC under different Illuminations: 1) AM1.5: Global tilt (GT), 2) AM0, 3) AM1.5: Direct circumsolar (DC). Layer

1

2

3

Glass SiO2 ITO PEDOT:PSS P3HT:PCBM LiF Al

0 0 77 W/m2 16 W/m2 0 0 40 W/m2

0 0 110 W/m2 21 W/m2 0 0 50 W/m2

0 0 69 W/m2 14 W/m2 0 0 36 W/m2

depending on the temperature and pressure. At air conductivity of 0.01 W/km the OSC would heat up to about 8 °C; however, in specific applications in outside the earth’s atmosphere where the air convection starts to disappear (Kair approaches zero), the temperature would considerably increase and thermal radiation would be dominant. Changing the thickness of PEDOT:PSS layer in range of 50– 200 nm, the total optical heat generation increases from 181 Wm2 to 217 Wm2; also, it was found that in lower air conductivities, the temperature dependence on internal heat

Fig. 16. The thermal resistive model for a slab of material with heat generation.

191

R. Zohourian Aboutorabi, M. Joodaki / Organic Electronics 25 (2015) 184–192 Table 3 Thermal parameters used in modeling. Layer Glass and SiO2 ITO PEDOT:PSS P3HT:PCBM LiF Al Air

K (W/km) 3 8 0.2 0.2 1.74 200 2.5  102

cv (J/kg K) 2

8.2  10 3.4  102 1.7  103 1.7  103 1.6  103 9  102 1  103

q (kg/m3) 3

2.6  10 7.2  103 1.2  103 1.2  103 2.6  103 3.9  103 1.2

L (lm) 1000 0.15 0.05 0.1 0.001 0.1 –

5. Conclusion

Fig. 17. Transient thermal behavior of organic solar cell in AM0 sunlight illumination when Kair = 2.5  102 W/km (free convection).

In conclusion, two thermal models were presented to study the thermal behavior of optoelectronic devices, specifically photovoltaic devices. The steady state model is fast, straightforward and can be easily employed to predict the device temperature in steady state. The TM model is capable of predicting the transient and steady state device temperature at the expense of more complexity and algebraic labor. Coupling the appropriate thermal model with optical model would determine the optical heat generation as well as heat flow mechanism in the photovoltaic device. The proposed opto-thermal model was employed to study the thermal behavior of organic solar cells. It was found out that the electrodes contribute to more than 80% of heat generation and air thermal conductivity significantly influences the device temperature. The model is also applicable to inorganic photovoltaic devices. Specifically, this will be more important when concentrator photovoltaic devices are used and a large amount of heat is generated. Acknowledgements The authors would like to thank Prof. Li of South China University of Technology for his helps and supports. He kindly handed over his experimental data to be used in this project. The Ministry of Energy of Iran supported this work (project M/145/93). References

Fig. 18. OSC temperature dependence on air conductivity under AM0 illumination (0.001 < Kair < 0.2 W/km).

generation is much more stronger than in normal air conductivities (this is also previously shown in Fig. 8). Increasing the Al cathode thickness more than its skin depth would not have a considerable effect on the internal heat generation. 4.3. Effect of temperature on organic solar cells performance It has been found that increasing the temperature in organic photovoltaic devices improves the device short circuit current [25]. This is because increasing the temperature facilitates the hopping process in polymer, hence, enhances the charge transport efficiency. We can explain this as mobility increase that would also result in series resistance reduction, thus, fill factor improvement. The open circuit voltage gradually decreases upon temperature increase. Generally, the temperature dependence of short circuit current and fill factor is dominant and the device efficiency strongly increases by temperature [25]. On the other hand, organic solar cells operational lifetime greatly decreases when working at higher temperatures [26,45]. Therefore, optimization is needed to meet efficiency-lifetime requirement for a specific OSC.

[1] N. Grossiord, J.M. Kroon, R. Andriessen, P.W.M. Blom, Degradation mechanisms in organic photovoltaic devices, Org. Electron. 13 (2012) 432–456. [2] B. Parida, S. Iniyan, R. Goic, A review of solar photovoltaic technologies, Renewable Sustainable Energy Rev. 15 (2011) 1625–1636. [3] P.W.M. Blom, V.D. Mihailetchi, L.J.A. Koster, D.E. Markov, Device physics of polymer: fullerene bulk heterojunction solar cells, Adv. Mater. 19 (2007) 1551–1566. [4] J. Nelson, Polymer:fullerene bulk heterojunction solar cells, Mater. Today 14 (2011) 462–470. [5] A. Facchetti, Polymer donor–polymer acceptor (all-polymer) solar cells, Mater. Today 16 (2013) 123–132. [6] J. You, L. Dou, Z. Hong, G. Li, Y. Yang, Recent trends in polymer tandem solar cells research, Prog. Polym. Sci. 38 (2013) 1909–1928. [7] G. Li, R. Zhu, Y. Yang, Polymer solar cells, Nat. Photonics 6 (2012) 153–161. [8] H. Hoppe, N.S. Sariciftci, Organic solar cells: an overview, J. Mater. Res. 19 (2011) 1924–1945. [9] G. Dennler, M.C. Scharber, C.J. Brabec, Polymer-fullerene bulk-heterojunction solar cells, Adv. Mater. 21 (2009) 1323–1338. [10] C. Deibel, V. Dyakonov, C.J. Brabec, Organic bulk heterojunction solar cells, IEEE J. Sel. Top. Quantum Electron. 16 (2010) 1517–1527. [11] C.J. Brabec, N.S. Sariciftci, J.C. Hummelen, Plastic solar cells, Adv. Funct. Mater. 11 (2001) 15–26. [12] W. Bruttings, Introduction to the physics of organic semiconductors, in: Physics of Organic Semiconductors, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2006. [13] J. Cuiffi, T. Benanti, W.J. Nam, S. Fonash, Modeling of bulk and bilayer organic heterojunction solar cells, Appl. Phys. Lett. 96 (2010) 143307. [14] A. Cheknane, H.S. Hilal, F. Djeffal, B. Benyoucef, J.P. Charles, An equivalent circuit approach to organic solar cell modelling, Microelectron. J. 39 (2008) 1173–1180. [15] F. Ghani, M. Duke, Numerical determination of parasitic resistances of a solar cell using the Lambert W-function, Sol. Energy 85 (2011) 2386–2394.

192

R. Zohourian Aboutorabi, M. Joodaki / Organic Electronics 25 (2015) 184–192

[16] P. Granero, V.S. Balderrama, J. Ferré-Borrull, J. Pallarès, L.F. Marsal, Twodimensional finite-element modeling of periodical interdigitated full organic solar cells, J. Appl. Phys. 113 (2013) 043107. [17] L. Koster, E. Smits, V. Mihailetchi, P. Blom, Device model for the operation of polymer/fullerene bulk heterojunction solar cells, Phys. Rev. 72 (2005) 085205. [18] B. Mazhari, An improved solar cell circuit model for organic solar cells, Sol. Energy Mater. Sol. Cells 90 (2006) 1021–1033. [19] J.D. Servaites, S. Yeganeh, T.J. Marks, M.A. Ratner, Efficiency enhancement in organic photovoltaic cells: consequences of optimizing series resistance, Adv. Funct. Mater. 20 (2010) 97–104. [20] L.H. Slooff, S.C. Veenstra, J.M. Kroon, W. Verhees, L.J.A. Koster, Y. Galagan, Describing the light intensity dependence of polymer:fullerene solar cells using an adapted Shockley diode model, Phys. Chem. Chem. Phys. 16 (2014) 5732–57328. [21] J. Szmytkowski, Modeling the electrical characteristics of P3HT:PCBM bulk heterojunction solar cells: implementing the interface recombination, Semicond. Sci. Technol. 25 (2010) 015009. [22] V. Mihailetchi, J. Wildeman, P. Blom, Space-charge limited photocurrent, Phys. Rev. Lett. 94 (2005) 126602. [23] J.D. Servaites, M.A. Ratner, T.J. Marks, Organic solar cells: a new look at traditional models, Energy Environ. Sci. 4 (2011) 4410. [24] J. Williams, A.B. Walker, Two-dimensional simulations of bulk heterojunction solar cell characteristics, Nanotechnology 19 (2008) 424011. [25] I. Riedel, J. Parisi, V. Dyakonov, L. Lutsen, D. Vanderzande, J.C. Hummelen, Effect of temperature and illumination on the electrical characteristics of polymer–fullerene bulk-heterojunction solar cells, Adv. Funct. Mater. 14 (2004) 38–44. [26] M. Jørgensen, K. Norrman, F.C. Krebs, Stability/degradation of polymer solar cells, Sol. Energy Mater. Sol. Cells 92 (2008) 686–714. [27] P. Yongju, N. Seunguk, L. Donggu, Y.K. Jun, L. Changhee, Temperature and light intensity dependence of polymer solar cells with MoO3 and PEDOT:PSS as a buffer layer, J. Korean Phys. Soc. 59 (2011) 362. [28] X. Qi, S.R. Forrest, Thermal analysis of high intensity organic light-emitting diodes based on a transmission matrix approach, J. Appl. Phys. 110 (2011) 124516. [29] L.A. Pipes, Matrix analysis of heat transfer problems, J. Franklin Inst. 263 (1957) 195–206. [30] M. Krüger, T. Emig, M. Kardar, Nonequilibrium electromagnetic fluctuations: heat transfer and interactions, Phys. Rev. Lett. 106 (2011) 210404. [31] A.J. Moulé, J.B. Bonekamp, K. Meerholz, The effect of active layer thickness and composition on the performance of bulk-heterojunction solar cells, J. Appl. Phys. 100 (2006) 094503.

[32] Y. Min Nam, J. Huh, W.H. Jo, Optimization of thickness and morphology of active layer for high performance of bulk-heterojunction organic solar cells, Sol. Energy Mater. Sol. Cells 94 (2010) 1118. [33] W.H. Lee, S.Y. Chuang, H.L. Chen, W.F. Su, C.H. Lin, Exploiting optical properties of P3HT:PCBM films for organic solar cells with semitransparent anode, Thin Solid Films 518 (2010) 7450. [34] L.A.A. Pettersson, L.S. Roman, O. Inganäs, Modeling photocurrent action spectra of photovoltaic devices based on organic thin films, J. Appl. Phys. 86 (1999) 487. [35] G. Dennler, K. Forberich, M.C. Scharber, C.J. Brabec, I. Tomiš, K. Hingerl, T. Fromherz, Angle dependence of external and internal quantum efficiencies in bulk-heterojunction organic solar cells, J. Appl. Phys. 102 (2007) 054516. [36] H. Shen, P. Bienstman, B. Maes, Plasmonic absorption enhancement in organic solar cells with thin active layers, J. Appl. Phys. 106 (2009) 073109. [37] S. Golmakaniyoon, (M.Sc. thesis), Ferdowsi University of Mashhad, Mashhad, Iran, 2012. [38] S. Rait, S. Kashyap, P.K. Bhatnagar, P.C. Mathur, S.K. Sengupta, J. Kumar, Improving power conversion efficiency in polythiophene/fullerene-based bulk heterojunction solar cells, Sol. Energy Mater. Sol. Cells 91 (2007) 757–763. [39] K. Tada, M. Onoda, Poor man’s green bulk heterojunction photocells: a chlorine-free solvent for poly(3-hexylthiophene)/C60 composites, Sol. Energy Mater. Sol. Cells 100 (2012) 246–250. [40] T. Umeda, H. Noda, T. Shibata, A. Fujii, K. Yoshino, M. Ozaki, Dependences of characteristics of polymer solar cells based on bulk heterojunction of poly(3hexylthiophene) and C 60 on composite ratio and annealing temperature, Jpn. J. Appl. Phys. 45 (2006) 5241–5243. [41] L. Li, H. Tang, H. Wu, G. Lu, X. Yang, Effects of fullerene solubility on the crystallization of poly(3-hexylthiophene) and performance of photovoltaic devices, Org. Electron. 10 (2009) 1334–1344. [42] Y. Yao, J. Hou, Z. Xu, G. Li, Y. Yang, Effects of solvent mixtures on the nanoscale phase separation in polymer solar cells, Adv. Funct. Mater. 18 (2008) 1783– 1789. [43] K. Kawano, J. Sakai, M. Yahiro, C. Adachi, Effect of solvent on fabrication of active layers in organic solar cells based on poly(3-hexylthiophene) and fullerene derivatives, Sol. Energy Mater. Sol. Cells 93 (2009) 514–518. [44] S. Rait, S. Kashyap, P.K. Bhatnagar, P.C. Mathur, S.K. Sengupta, J. Kumar, Effect of a buffer layer, composition and annealing on the performance of a bulk heterojunction polythiophene/fullerene composite photovoltaic device, Physica E 39 (2007) 191–197. [45] F.C. Krebs, Air stable polymer photovoltaics based on a process free from vacuum steps and fullerenes, Sol. Energy Mater. Sol. Cells 92 (2008) 715–726.