JOURNAL OF APPLIED PHYSICS 108, 084511 共2010兲
Determination of free polaron lifetime in organic bulk heterojunction solar cells by transient time analysis Kejia Li,a兲 Yang Shen, Nabanita Majumdar, Chong Hu, Mool C. Gupta, and Joe C. Campbell Department of Electrical and Computer Engineering, University of Virginia, 351 McCormick Road, Charlottesville, Virginia 22904, USA
共Received 7 August 2010; accepted 21 August 2010; published online 26 October 2010兲 A transient response technique that is widely used to measure the minority carrier lifetime in inorganic semiconductors is proposed to measure the lifetime of free polarons in a polymer:fullerene bulk heterojunction 共BHJ兲 solar cell. A numerical model that can be used to describe the transient behavior of BHJ devices has been developed. Using the proposed method, the lifetime of free polarons in poly 共3-hexylthiophene兲 and 关6, 6兴-phenyl C61-butyric acid methyl ester blend film is estimated to be in the range of 300–400 ns. © 2010 American Institute of Physics. 关doi:10.1063/1.3493114兴 I. INTRODUCTION
Organic bulk heterojunction 共BHJ兲 materials have been the subject of numerous studies in recent years as they could potentially be used for the fabrication of very thin, flexible, and low-cost solar cells.1–3 They are formed by mixing two materials in solution that have donor and acceptor properties. Compared to the bilayer structure, charge transfer at the donor-acceptor interface is facilitated because the length scales of both polymer:fullerene phases are on the order of the exciton diffusion length, the excitons can be quickly dissociated at the donor/acceptor interface. Charge transfer is accomplished by the formation of polaron pairs proximate to the interface, which is an intermediate step from an exciton to free polarons. Current flow occurs when the polaron pairs dissociate into negative and positive polarons, which are transported to their respective electrodes by a hopping mechanism.4–6 The promise of BHJ solar cells is mitigated to some extent by the low efficiencies that have been reported. To date, the maximum demonstrated efficiency of a BHJ solar cell is ⬃7.9%.7,8 Several loss mechanisms may lead to this low efficiency in BHJ structures. One of the primary loss mechanisms is the low percentage of excitons that dissociate to free polarons at short-circuit conditions. Mihailetchi et al.9 have demonstrated that only 60% of the optically generated excitons in poly 关2-methoxy-5-共3⬘ , 7⬘-dimethyloctyloxy兲-p-phenylene vinylene兴-共OC1C10-PPV-兲:关6, 6兴-phenyl C61-butyric acid methyl ester 共PCBM兲 blends dissociate and contribute to the short-circuit current. Another important loss mechanism in BHJ solar cells is charge recombination. Typically, BHJ devices have an active layer thickness of ⬃100 nm in which only 60% of the incident light is absorbed. Thicker active layers improve absorption but also result in increased charge recombination, which will reduce the efficiency.10 In order to better understand charge recombination in BHJ devices, it is beneficial to study the lifetime of free polarons. In an inorganic semiconductor solar cell, the cura兲
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rent is formed by the transportation of minority carriers. Therefore, minority carrier lifetimes are key parameters for charge transport. Several methods have been utilized to measure minority carrier lifetime, such as photoconductance decay,11,12 short-circuit current/open-circuit voltage decay,12–15 free carrier absorption,12,15 and reverse recovery.12,16 However, since the mechanism for current generation is different in organic BHJ devices, those methods either can not be implemented or need to be justified. To date, the techniques that have been developed to determine lifetimes or recombination in BHJ devices are very limited. One method that has been employed is impedance spectroscopy. Using this method, Garcia-Belmonte et al.17,18 found that the effective charge lifetime lies within the milliseconds timescale in poly 共3-hexylthiophene兲 共P3HT兲:PCBM blends and that the charge lifetime is a function of Voc. In their model, the effective lifetime is defined as a product of recombination resistance and distributed chemical capacitance. Time-resolved vibrational spectroscopy is another method that can be used to study recombination dynamics of BHJ solar cells. Pensack et al.19 reported bimolecular charge recombination lifetime of 73 s in CN-MEH-PPV:PCBM. Montanari et al.20 reported that the recombination dynamics of localized polarons in MDMO-PPV:PCBM result in lifetimes in the 100 ns–10 ms range. The carrier dynamics in an organic solar cell can be divided into three categories: the lifetime of excitons, the lifetime of the bound polaron pairs, and the lifetime of the free polarons. Since the current is formed by the transportation of free polarons, the lifetime of free polarons assumes a critical role in the characterization of charge recombination. In this paper, a transient response technique21,22 that is widely used to measure the minority carrier lifetime in semiconductor devices is proposed to measure the lifetime of free polarons in a polymer:fullerene BHJ solar cell; the measured lifetimes are in the range 300–400 ns. In this paper, a brief description of the model is presented with an overview of the relevant equations. This is followed by a description of BHJ solar cell fabrication and the experiment setup. Finally, the
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unoccupied molecular orbital level of the acceptor and the highest occupied molecular orbital level of the donor, respectively. C. Transient response theory for an organic solar cell
The transient response can be determined by solving the continuity equations, FIG. 1. 共a兲 Basic switching circuit for inorganic solar cell devices; and 共b兲 a typical current and voltage switching characteristics of an inorganic solar cell.
experiment values of the lifetime of free polarons and the associated diffusion length for P3HT:PCBM blends are presented.
II. MODEL, EQUATIONS, AND TRANSIENT BEHAVIOR A. Transient behavior of inorganic and organic solar cell
The transient response technique is a widely used method to measure minority carrier lifetime in inorganic devices. A typical switching circuit for measuring the minority carrier lifetime in inorganic solar cells is shown in Fig. 1共a兲. For t ⬍ 0, a forward current, IF, flows in the inorganic solar cell. At t = 0, the switch is thrown to the right 共i.e., connected to the reverse bias circuit兲 with initial reverse current, IR. Figure 1共b兲 illustrates the current and voltage switching characteristics of an inorganic diode. By varying IF and IR, the minority carrier lifetime can be derived by using the expression
冉 冊
t1 = ln 1 +
IF . IR
共1兲
For organic the BHJ solar cell, we have used the same circuit.
B. Model for BHJ device
A BHJ device can be described in terms of the metalinsulator-metal model3,4 shown in Fig. 2. The metals are represented by their Fermi levels, whereas the conduction and valence bands of the semiconductor correspond to the lowest
1 p共x,t兲 = Gp − Up − ⵜ Jp , t q
共2a兲
1 n共x,t兲 = Gn − Un + ⵜ Jn , t q
共2b兲
where p and n are the positive and negative polaron densities, respectively; G p and Gn are the positive and negative polaron generation rates that originate from external sources such as optical excitation; and Un = 䉭 n / n and U p = 䉭 p / p are the recombination rates for positive and negative polarons. In order to solve the above equations, we use the following current density equations:4 共3兲
J = J p + Jn , J p = − q p pE − qD p
dp , dx
共4a兲
Jn = − qnnE + qDn
dn , dx
共4b兲
冉 冉
冊 冊
ⵜJ p = − q p p
E p 2 p + q pE − qD p 2 , x x x
共5a兲
ⵜJn = − qnn
E n 2n + q nE + qDn 2 . x x x
共5b兲
It is also necessary to define the recombination rates. Different from inorganic solar cells, the current of organic solar cells is attributed to the majority carrier, i.e., free polarons. This is equivalent to the high-level injection case in an inorganic solar cell. It follows that the lifetimes of the positive and negative polarons are the same. Therefore, the recombination rate can be expressed as: U p = 共p − p0兲/ p = 䉭 p/ ,
FIG. 2. 共Color online兲 共a兲 Schematic of the energy levels; and 共b兲 device model in flat band condition.
共6a兲
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FIG. 3. 共Color online兲 Test circuit to characterize transient behavior of BHJ solar cell.
Un = 共n − n0兲/n = 䉭 n/ .
共6b兲
冋
冉 冊册
Q共t兲 = − IR + 共IF + IR兲exp
−t
.
D. Transient behavior analyses for organic solar cell
By setting Q = 0, t1 can be obtained as
An explicit expression for t1 共the time interval from t = 0 to the time when the voltage on the BHJ device drops to zero兲 can be obtained using a charge-control model. In the dark, G p and Gn are zero. The total charge carrier in the device at time t is given by the integral
t1 = ln 1 +
Q共t兲 = qA
冕
关⌬p共x,t兲 − ⌬n共x,t兲兴dx,
共7兲
which is obtained by subtracting Eq. 共2b兲 from Eq. 共2a兲, multiplying by qA, and integrating x over the thickness of the active region. After the current is switched to the reversed mode, Eq. 共2b兲 becomes qA兰 p共x,t兲dx qA兰 n共x,t兲dx − t t =−
qA兰关⌬p共x,t兲 − ⌬n共x,t兲兴dx qA − q
=−
qA兰关⌬p共x,t兲 − ⌬n共x,t兲兴dx
− + =−
qA q
冕冋 冉
再冋 冉
− q p p
− q nn
冕
共ⵜJ p + ⵜJn兲dx
冊
E p 2 p + q pE − qD p 2 x x x
冊
E n 2n + q nE + qDn 2 x x x
册冎
册
dx
qA兰关⌬p共x,t兲 − ⌬n共x,t兲兴dx
−A
冋冉
− q p pE − qD p
冊冉
dp dn + − qnnE + qD p dx dx
冊册
冉 冊
IF . IR
III. DEVICE FABRICATION AND MEASUREMENT PROCEDURE
P3HT:fullerene 共PCBM兲 solar cells were prepared using the following procedure: P3HT and PCBM were dissolved in chlorobenzene 24 h before fabrication. The blend solution was 1 wt % total, composed of 0.45 wt % P3HT 共SigmaAldrich supplier兲 plus 0.55 wt % of PCBM 共Nano-C supplier兲. ITO-coated glass substrates were first cleaned with acetone and isopropyl alcohol and subsequently air dried. A 40-nm-thick, highly-conduction poly共3,4ethylenedioxythiophene兲:poly共styrenesulfonate兲 共PEDOT:PSS兲 共H.C. Starck supplier兲 layer was then spin-coated on the ITO-coated glass substrate. After first baking at 110° for 15 min, the blend solution was spin-cast on the PEDOT:PSS layer. Then the sample was baked in vacuum at 60 ° C for 30 min. An 80 nm Al layer was deposited as the top electrode using electron beam physical vapor deposition. Finally, the sample was annealed at 130 ° C for 2 min in air.
. 共8兲
共9兲
Equation 共9兲 is essentially the same as that used to calculate the minority carrier lifetime for inorganic semiconductor devices.22 The solution can be obtained by two approaches. For inorganic semiconductor p-n junction devices, since the current is almost constant in the time interval t1 关Fig. 2共b兲兴, Eq. 共9兲 can be solved using the initial condition Q共0兲 = IF and the solution is
共11兲
Equation 共11兲 is the same equation as Eq. 共1兲, which means Eq. 共1兲 can be applied to BHJ devices, if the assumption of constant current I in the time interval t1 is valid.
Substituting Eq. 共7兲 into Eq. 共8兲, yields dQ Q = − − IR共t兲. dt
共10兲
FIG. 4. 共Color online兲 Current flows through a BHJ solar cell.
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FIG. 5. 共Color online兲 Current and voltage on solar cell for different IF to IR ratios.
The transient behavior was measured with an Agilent Infiniium DSO81004B Oscilloscope and an Agilent 81110A pulse generator. The bandwidth of the oscilloscope is 10 GHz with sample rate up to 40 GSa/s. The input impedance of each channel of the oscilloscope is 50 ⍀. With an Agilent E2697A 1 M⍀ adapter, the input impedance of the oscilloscope can be adjusted to 1 M⍀. A 1:10 10073C probe is attached to the adapter. The testing circuit is shown in Fig. 3. A 100 Hz square wave was generated by the pulse generator and applied to the parallel circuit. The rise and the fall times of the square wave are both 2 ns. The current flow through the BHJ solar cell was detected by one channel of the oscilloscope with 50 ⍀ input impedance. The voltage on the BHJ solar cell was the voltage difference between V1 and V2. IV. EXPERIMENTAL RESULTS AND DISCUSSION
The power conversion efficiency was first measured for 80-nm-thickness devices. Under AM1.5 illumination, the efficiency was 1.7%. A typical transient current curve of a BHJ solar cell is shown in Fig. 4. In this figure, t1 is the time interval when the current is almost constant. When the applied voltage switches from positive to negative, the BHJ current 共VF / 50 ⍀兲 quickly drops to a peak reverse value 共VR / 50 ⍀兲 and then after t1 it decays to a steady reverse current. By
changing the amplitude of the applied voltage, we obtained a set of data for IF, IR, and t1 that were used to calculate the free carrier lifetime using Eq. 共11兲. The current and the voltage of the BHJ device for different IF / IR ratios are shown in Fig. 5. When IF / IR was very small, we did not observe a constant current phase. The reverse current quickly reached a peak at the beginning and then decayed to a steady current. This phenomenon is the same as the “over-driven” condition in inorganic devices.21 In this case, Eq. 共11兲 cannot be used because the current is not constant. For inorganic devices, the lifetime is typically measured at the condition IF / IR ⬃1. We followed the same procedure for the organic device. The lifetime of free polarons of the BHJ solar cell is shown in Fig. 6. In the experiment, first the reverse voltage was fixed and then lifetimes at different IF to IR ratios were derived by changing applied forward voltage. The measured lifetime of free polarons is in the range 300–400 ns. Since the electron 共negative polaron兲 and hole 共positive polaron兲 mobility for the 55:45 PCBM:P3HT blends are 2.58⫻ 10−3 cm2 / V s and 7.17⫻ 10−4 cm2 / V s, respectively,23 the electron 共negative polaron兲 and hole 共positive polaron兲 diffusion lengths are in the range of 44 nm to 52 nm, and ⬃25 nm, respectively. V. CONCLUSION
In this paper, a transient response technique for measuring the lifetime of free polarons in polymer:fullerene BHJ solar cells has been presented. The transient behavior of a BHJ solar cell was proposed and analyzed. Using this method, we estimate the lifetime of free polarons in P3HT:PCBM blends to be in the range 300–400 ns. Electron 共negative polaron兲 and hole 共positive polaron兲 diffusion lengths are in the range of 44 nm to 52 nm, and ⬃25 nm respectively. ACKNOWLEDGMENTS
FIG. 6. 共Color online兲 Lifetime of free polarons of P3HT 共45 wt %兲:PCBM 共55 wt %兲 BHJ solar cell.
This work is supported as part of the Center for Energy Nanoscience, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences under Award No. DE-SC0001013. We thank Professors Stephen Bradford, P. Daniel Dapkus,
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