Universal Trap Effect in Carrier Transport of Disordered Organic

Apr 28, 2014 - ABSTRACT: In order to unravel the effect of trap energy on carrier transport in disordered organic semiconductors, a comprehensive stud...
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Universal Trap Effect in Carrier Transport of Disordered Organic Semiconductors: Transition from Shallow Trapping to Deep Trapping Chen Li, Lian Duan,* Haoyuan Li, and Yong Qiu Key Lab of Organic Optoelectronics & Molecular Engineering of Ministry of Education, Department of Chemistry, Tsinghua University, 100084 Beijing, China S Supporting Information *

ABSTRACT: In order to unravel the effect of trap energy on carrier transport in disordered organic semiconductors, a comprehensive study was conducted on hole transport in a series of organic molecular hosts with explicit traps at different trap energies. The mobility measured by time-of-flight experiments was found to decrease significantly at shallow trapping, but hardly decreased at deep trapping, where a sharp decrease of carrier density was observed. By analyzing temperature dependence of the mobility, the decreased mobility at shallow trapping were found to originate from increased energetic disorder and activation energy, whereas both energetic disorder and activation energy are changeless at deep trapping. We find it reasonable to cover the different effects of deep trapping and shallow trapping in a universal mechanism based on the Miller−Abrahams hopping model, and carry out multiple-carrier Monte Carlo simulations to elaborate how, within a universal mechanism, that deep and shallow traps affect energetic disorder, transporting trajectories and carrier density in different ways. The results suggest transporting at shallow trapping always is involved in a multiple-trapping-release process owing to frequent thermal reactivation, thus leading to winding transporting trajectory, increased effective energetic disorder, and increased activation energy; while deep traps tend to immobilize the carriers and act as ionized scattering centers, thus mainly decreasing the carrier density and just elongating the trajectory slightly. Investigating the change of mobility with continuous trap energy suggests a transition region, rather than a strict borderline existing between deep traps and shallow traps, where carrier transport is controlled by both deep traps and thermal reactivation from shallow traps. of a carrier in a trap, τtr, is proportional to exp(ET/kBT), thus larger trap energies make the drift transport slower.14−16 In studies based on the GDM, increasing trap energy was found to result in increasing energetic disorder (which was extrapolated from the temperature varying mobility), and eventually, decreasing mobility.17−19 It was not until very recently, however, that researchers began to notice deep traps may not act the same way as the shallow ones, owing to their insensitivity to thermal activation. Podzorov et al, has found that in tetracene and rubrene crystal field-effect transistors (FETs) shallow traps greatly decease the carrier mobility, while deep traps increase the field-effect threshold without affecting carrier mobility.5,20,21 Our recent time-of-flight (TOF) study of the 4,4′-bis(carbazol-9-yl)biphenyl (CBP) hosted system also indicates shallow traps may be more harmful to carrier mobility than the deep ones in amorphous molecular semiconductors.22 In fact, the two very contradictory results may be unified if we assume the ET investigated in the former was not large enough to reach the deep trapping region, but unfortunately, studies have suggested decreased mobility even until ET was as large as

1. INTRODUCTION Carrier traps, which refer to the states whose energy levels are located in the forbidden band of a semiconductor,1 have for a long time been undesirable in organic semiconductors owing to the negative influence on carrier transport.2 Therefore, great efforts have been made in the past decades to suppress the effects of traps.3−5 However, the inspiring progress in host− guest organic light emitting diodes (OLEDs) 6−9 and heterojunction organic photovoltaics (OPVs)10−12 indicates that carrier traps via doping may be unavoidable, or even indispensable, in the approach to high performance organic electronic devices. Thus, the importance of understanding the trap effect on carrier transport never vanishes. The most crucial parameter of a trap that affects carrier transport is the trap energy (ET), which refers to the potential well depth of a trap.13 On the basis of ET, researchers have distinguished between shallow traps (when ET is on the order of kBT, where kB is the Boltzmann constant and T is the temperature) and deep traps (when ET is much larger than kBT).2 Considerable works have indicated that a larger ET may result in a more serious decrease of the mobility.14−19 Both the multiple trapping release (MTR) model14−16 and the Gaussian disorder model (GDM)17−19 have been used to interpret this result. In the framework of the MTR model, the relaxation time © 2014 American Chemical Society

Received: March 6, 2014 Revised: April 25, 2014 Published: April 28, 2014 10651

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Figure 1. Chemical structures of the materials investigated.

0.3 eV,17 which is much larger than the usually mentioned ET (few kBT) for shallow traps.2,20,21 To sum up, the effects of traps on carrier transport in organic semiconductors remains vague. And in order to understand the effects of traps properly, two crucial issues are worth studying: (1) whether and how the deep traps and shallow traps act in different ways; (2) how to understand the borderline between deep traps and shallow traps. Here, we made a comprehensive study on the effects of traps upon hole transport in disordered organic semiconductors. Explicit traps with ET from 0.1 to 0.6 eV were introduced by doping various guest materials, which acting as traps, into three model hole transporting materials. Hole mobility were studied by TOF method, which is the benchmark method dealing with the carrier transport in disordered organic semiconductors. It is found that shallow traps (ET from 0.1 to 0.25 eV) decrease the mobility for one or two orders magnitudes, while deep traps (ET larger than 0.4 eV) mainly decrease the photocurrent without significantly affecting the mobility. For possible origins, the energetic disorder and activation energy is established by fitting temperature dependence of mobility to the GDM and the MTR model. Multiple-carrier Monte Carlo (MC) simulations based on Miller−Abrahams model were implemented to elaborate how deep and shallow traps affect energetic disorder, transporting trajectories and carrier density in different ways. The results suggest shallow traps always involved in a multiple trapping release process owing to easy thermal reactivation thus leading to winding transporting trajectory, increased effective energetic disorder and increased activation energy; while deep traps tend to immobilize the carriers and act as scattering centers, thus mainly decreasing the carrier density collected and just elongate the trajectory slightly. In addition, the borderline between deep trap and shallow trap were studied experimentally by investigating the change of mobility with continuous effective trap energy. We conclude that the borderline can be material specific and a transition region, rather than a strict borderline exists between deep traps and shallow traps.

between an occupied site i and an unoccupied site j has always been described using the Miller−Abrahams model:24 ⎧ ⎛ εj − εi ⎞ ⎪ ⎟ εj > εi ⎪ exp⎜ − vij = v0e−2rij / a⎨ ⎝ kBT ⎠ ⎪ ⎪ 1 εj ≤ εi ⎩

(1)

where v0 is the attempt hopping frequency, rij is the distance between site i and site j, a is the average localization radius, and εi and εj is the respective localized energy levels of the sites. In situations where electron−phonon coupling is strong, the semiclassical Marcus model25 for electron-transfer rates is valid, which takes into account reorganization energy and charge transfer integral. Unlike the band transport in the inorganic crystal semiconductors, electron−phonon coupling in moderate to low mobility molecular materials is always strong.26 Therefore, Marcus model may serve as a more accurate description of the intrinsic transfer rate at the molecular level. However, approach to the charge transfer integral request for the knowledge of the microscopic morphology of the material,27 which greatly limits its use at the material level. On the other hand, the classical Miller−Abrahams based models, including the MTR model and the GDM, has been successfully used to explain the effects of extrinsic factors, like trapping, electric field and temperature, on transporting properties in both the crystal and the disordered organic materials during the past decades.14−16 The GDM is a semiempirical model that developed from the MC studies by Bässler and co-workers.28 In the framework of the GDM, the general behavior of the mobility as a function of temperature and electric field (E) is given by ⎧ ⎡ ⎛⎛ ⎤ ⎞ ⎞2 ⎪ ⎢C ⎜⎜ σ ⎟ − Σ2⎟E1/2 ⎥ Σ ≥ 1.5 exp ⎟ ⎪ ⎢ ⎜⎝ kB T ⎠ ⎥ 2⎤ ⎡ ⎛ ⎠ ⎣ ⎝ ⎦ 2σ ⎞ ⎥⎪ ⎢ μ = μ0 exp −⎜ ⎟ ⎨ ⎢⎣ ⎝ 3kBT ⎠ ⎥⎦⎪ ⎡ ⎛ 2 ⎤ ⎞ ⎛ ⎞ ⎪ exp⎢C ⎜⎜ σ ⎟ − 2.25⎟E1/2 ⎥ Σ < 1.5 ⎜ ⎟ ⎥ ⎪ ⎢ ⎝⎝ kB T ⎠ ⎠ ⎦ ⎩ ⎣

(2)

2. THEORETICAL BASIS Carrier transport in disordered organic semiconductors has for long been viewed as a successive hopping process between the localized states.23 The most crucial parameter is the hopping rate between the states. Two main models for the hopping rate are always considered in the literatures. In case of weak electron−phonon coupling, the thermal assisted hopping rate

where μ0 is the mobility at zero electric field and the high temperature limit, which refers to the intrinsic localized hopping mobility at no disorder and is determined by reorganization energy and charge transfer integral, σ is the energetic disorder which represents the standard deviation of the density of states, C is a constant, and Σ is the positional disorder referring to the relative positions and orientations 10652

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between the molecules. Energetic disorder can be extrapolated from the temperature dependent mobility at zero electric field according to the GDM model. The MTR model has been introduced to describe carrier transport in situations where traps coexist with the intrinsic states. In the framework of the MTR model, the trap limited carrier mobility can be described as29 ⎛ E ⎞ μ = μi α exp⎜ − a ⎟ ⎝ kBT ⎠

Table 2. Structures of Transporting Layers of the Devices

(3)

where μi is the intrinsic mobility at the perfect crystal (delocalized) hypothesis, α represents the ratio between the density of intrinsic states available for trap free transport and the density of traps, and Ea (the activation energy) reflects the temperature related potential barrier which combines the effects of the reorganization energy30 and the average trap energy.31 Both μi and Ea can be extrapolated by fitting μ(T) to eq 3.

CBP DPYPA TCTA TPD NPB DCJTB m-TDATA

−6.0 −5.9 −5.65 −5.5 −5.4 −5.3 −5.1

μh/cm2 V−1 s−1 2 8 2 1.1 5.1 − 3

× × × × ×

−3

10 10−4 10−5 10−3 10−4

× 10−5

ϕ

ET/eV

L/μm

0 0.1 0.1 0 0.02 0.02 0.02 0 0.02 0.02 0.02

0 0.1 0.6 0 0.15 0.25 0.55 0 0.1 0.2 0.4

2.0 2.0 2.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

g(ε) =

⎛ ε2 ⎞ 1 exp⎜ − 2 ⎟ 2π σ ⎝ 2σ ⎠

(4)

σ is set to be 70 meV for both the host states and trap states according to the typical experimental energetic disorder of the molecular semiconductors.17−19,40 Only hops between adjacent sites are considered and the hopping rate, vij, is calculated from the Miller−Abrahams equation. The average site radius, a, is set to 1 nm in accordance with the typical crystal constant of molecular semiconductors,23 and v0 is set to 6 × 1011 s−1.41 The carrier dwelling time (τi) on site i and the hopping direction (k) are determined by the following equations:28

Table 1. Hole Transporting Parameters of the Materials HOMO/eV

dopant − DPYPA NPB − TPD NPB m-TDATA − NPB DCJTB m-TDATA

and the thickness L, the mobility was calculated as L2/tTV. Temperature varying experiments were done from 193 to 293 K. 3.2. Monte Carlo Simulations. The MC method here is a modification of the method by Bässleret al.,28 which allows simulations involving traps. The grid size is nx(1001) × ny(1001) × nz(1001) and mx(101) × mz(101), respectively in the 3-D and 2-D situations. The trap sites are introduced randomly to the grids using a random 0−1 distribution. Both the site energies of the host states and the doped trap states obey Gaussian distribution:

3. METHODS 3.1. Experiments. The materials studied (see Figure 1 for the chemical structures) are all typical organic small molecular semiconducting materials. CBP, 4,4′,4″-tris(carbazol-9-yl)triphenylamine (TCTA), and N,N′-bis(3-methylphenyl)-N,N′bis(phenyl)benzidine (TPD) were used as host materials. 9,10Bis(3-(pyridin-3-yl)phenyl)-anthracene (DPYPA), TPD, N,N′bis(1-naphthalenyl)-N,N′-bis(phenyl-(1,1′-biphenyl))-4,4′-diamine (NPB), 4-(dicyanomethylene)-2-tertbutyl-6-(1,1,7,7-tetramethyljulolidin-4-yl-vinyl)-4H-pyran (DCJTB), and 4,4′,4″tris-(N-3-methylphenyl-N-phenylamino)triphenylamine (mTDATA) were doped to the host materials as explicit traps. The purity of the materials is higher than 99.9%. Their hole mobilities (μh) and HOMO energies from literatures are shown in Table 1. The TOF devices were prepared by coevaporating

material

host CBP CBP CBP TCTA TCTA TCTA TCTA TPD TPD TPD TPD

references 22, 33 34 35 36 37 38 39

τi = −

ln(λ1) ∑j vij

k−1

∑ j = 1 vij ∑j vij

(5) k

< λ2 ≤

∑ j = 1 vij ∑j vij

(6)

Here λ1 and λ2 are uniformly distributed random numbers between 0 and 1. As the carrier density in TOF experiment is limited to 0.01−0.1 CV (where C is the capacity of the device and V is the applied bias voltage), the effect of coulomb interaction is not so significant.42 Here, short-range coulomb interactions are taken into account in an approximation that two carriers cannot occupy the same site, and this is implemented by set the hopping rate to an occupied site to zero. The multiparticle carrier simulation is implemented by performing one hop of one carrier every step.43 Each carrier has its local time. The carrier to hop in each step is chosen when its movements cause the smallest increase of the global time. After each hop, dwelling time of all carriers and the site energies are updated. Electric field is applied in the z direction. At the beginning of the simulation, the carriers is generated randomly at z = 1. The process is repeated until all carriers have

the host materials and the dopants onto ITO anode, with evaporated Mg: Ag alloy as the cathode. Within the transporting layer (see Table 2 for details of the 11 devices), various ET with different trap fractions (ϕ) were introduced into TPD, TCTA, and CBP host materials. Thicknesses (L) of the organic layers were monitored in situ with a quartz crystal sensor. The TOF transients are measured by Sumitomo Electric’s TOF 401. A nitrogen pulsed laser (pulse width 10 ns, wavelength 337 nm, generated by Uhso KEC-160) was used as the excitation light source, which is directed from the ITO side to generate a thin sheet of excess carriers near the ITO/ organic interface. The transient photocurrent signals were recorded by a digital storage oscilloscope (Tektronix TDS3052C) with the background current being deducted. The transit time (tT) was estimated from the double-logarithmic plot of the transient photocurrent.32 With the applied bias V 10653

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Figure 2. Transients of the CBP (a), TCTA (b), and TPD (c) hosted TOF devices measured at 3.5 MV/cm at 293 K plotted in log−log graphs.

reached the electrode (z = 1001). The time and position of each carrier at each step are collected, so the transit time (tT) is calculated by the sum of the time of each step, and the transporting trajectory of each carrier is achieved by connecting the position of each step.

4. RESULTS AND DISCUSSION 4.1. Dependence of Hole Mobility on Trap Energy. Transients of the 11 TOF devices were measured under various bias voltages. As an example, the TOF transients measured at the electric field of 3.5MV/cm are shown in Figure 2. Most of the transients exhibit two regions separated by a sharp kink: the plateau region described by I(t) ∼ t‑a (a ∼ 0) before the kink and the decay region described by I(t) ∼ t‑b (b > 0) after the kink. The transit times, tT, are well-defined by the sharp kinks.32 In dispersive situations where the kinks are not sharp (CBP with ET of 0.1 eV, TCTA with ET of 0.25 eV, and TPD with ET of 0.2 eV), tT are determined by the intersections of the tangents of the two regions. The dispersive behavior of the TOF transient is signature of the fact that the spatial distribution of the carriers is widen by large energetic disorder or traps.44 In both the three hosts, tT increases monotonically with ET by 1−2 orders of magnitude at the relatively shallow trapping situations (at ET from 0.1 to 0.25 eV), but just slightly increased at the deep trapping situations (at ET from 0.4 to 0.6 eV). Meanwhile, the photocurrent decreases monotonically (from 10−4A to 10−6A) as ET increases. The transients under other electric fields (see Figure S1−S3 in the Supporting Information) give similar results. These results indicate that the relatively shallow traps may slow down the drift velocity of the collected carriers more seriously than the relatively deep traps, and the deeper traps may result in smaller carrier density collected by the electrode. Electric field dependences of hole mobility at 293 K in CBP, TCTA and TPD hosted systems are shown in Figure 3a. The hole mobilities of undoped CBP, TCTA and TPD at 3.5 MV/ cm is 3 × 10−3 cm2 V−1 s−1, 5 × 10−5 cm2 V−1 s−1 and 1 × 10−3 cm2 V−1 s−1, respectively, which are similar to that in the literature (Table 1). For all the three systems, hole mobility in

Figure 3. (a) Electric field dependence of hole mobility and (b) ET dependence of zero-field mobility for the CBP, TPD, and TCTA hosted materials. The inset in part b shows the normalized zero-field mobility as a function of ET.

the shallow trapping situations (with ET from 0.1 to 0.25 eV) decreases as ET increases. Whereas hole mobilities in the deep trapping situations (with ET from 0.4 to 0.6 eV) only slightly decease. A linear dependence of the logarithmic hole mobility on the square root of electric field suggests the feasibility of the Poole−Frenkel law45,46 10654

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the TPD host and the TCTA host. At ET of 0.4 and 0.55 eV, μ0 stay almost the same as that of the pure material. For σ, an increase of about 15 meV is found at shallow trapping situations, and at deep trapping just a little change (2−3 meV) is observed. As μ0 is a prefactor and σ is on the exponent of eq 2, we may infer that, at a shallow trapping situation, the sharp decrease of mobility by 1−2 orders of magnitude can originated mainly from the increased σ rather than the slightly decreased μ0; and at deep trapping situation, the mobility hardly changes because both μ0 and σ do not change. Because μ0 is related to the intrinsic charge transfer integral and reorganization energy that determined by the chemical structure of the molecule,25 we may infer the decrease of μ0 at shallow trapping is caused by the hopping between the host sites and the trap sites, and at deep trapping, the changeless μ0 indicate that carriers collected in the TOF experiments may only hop between the host sites. The linear dependence of log(μE=0) on T−1 (Figure 4, parts b and d) also allow us to analysis the data in the framework of the Arrhenius-like MTR model (eq 3). The fitting results (listed in Table 3) give similar μi but different Ea in the pure, shallow trapping and deep trapping situations. As μi exclude the effects of reorganization energy to activation energy (Ea), the values are much larger than μ0, and the difference between them can be ascribed to the reorganization energy in the localized hopping process.47 The increase of Ea by 60−70 meV at shallow trapping can be mainly ascribed to the increased trap energy.29 The slight changed Ea at deep trapping also indicates deep traps may not participate in the transporting of the collected carriers, otherwise, Ea would increase more seriously owing to the larger ET. Combining the analysis with the GDM and the MTR model, it is reasonable to draw the points below: (1) shallow trapping can increase the energetic disorder and the activation energy, whereas deep trapping hardly affect the energetic disorder or the activation energy; (2) at trap fraction of 2%, hopping between the shallow traps and the host sites is probed by the increase of σ and Ea, whereas hopping between the deep traps and the host sites cannot be inferred as both σ and Ea are changeless. Although deep traps hardly affect the mobility, they are found to greatly reduce the carrier density in transporting. Figure 5 shows the collected charge quantities, Q, calculated by time integral of photocurrent, at various ET. It is seen that Q do not change much at ET 0.4 eV. A rational interpretation is that the large amount of carriers trapping in the deep traps may not release within the time scale (1 ns to 1 ms) of the TOF measurements. 4.2. Insight of the Effects of Traps. Up to now we have known from the experimental results that in CBP, TPD, and TCTA, shallow traps can significantly decrease the mobility mainly by increasing the energetic disorder; while deep traps mainly decrease the carrier density without affecting the mobility much. However, physical chemistry insight of how traps play its role in disordered organic semiconductors has yet to be investigated. In this part, we shall first give a concise description of the transporting mechanism, and then carry out Monte Carlo simulations to show how traps affect transit time, carrier density, and energetic disorder in different ways. The mechanism is based on the Miller−Abrahams model. A schematic of the localized hopping transports in the shallow trapping and deep trapping situations are depicted in Figure 6. In the shallow trapping situation, carriers are easy to hop to trap sites owing to lower potential energies. However, reactivation of the carrier is not difficult as ET is small. As a result, the carrier

(7)

where μE=0 is the zero field mobility and β is the Poole-Frenkel constant. Zero field mobilities extrapolated from the Poole-Frenkel law vs. ET are depicted in Figure 3b. To view the dependence more clearly, normalized zero field mobility (with the mobility of the undoped material set to 1) as a function of ET is seen in the inset. A super exponential decrease of the mobility is sighted at ET < 0.25 eV. The super exponential decrease is understandable, noting that the theoretical increase of the energetic disorder via doping can be described approximately as ϕ(1 − ϕ)ET2, when all the site energies are taken into account.22 The decrease of mobility at ϕ of 10% is more significant than that at ϕ of 2%, which may also result from a larger energetic disorder. However, when ET is larger than 0.4 eV, the zero field mobility is almost the same as the undoped material. And this is contradictory with our current understanding of the energetic disorder. For possible origins of the different mobility at shallow trapping and deep trapping, the energetic disorder, activation energy and the intrinsic mobility are established by investigating the temperature dependence of the mobility. The TOF mobilities of the TCTA and TPD hosted materials, with ϕ of 2%, at various temperatures from 193 to 293 K are measured. Poole-Frenkel like electric field dependence is valid for the mobilities at all temperature (see Figure S4 in the Supporting Information). And the extrapolated zero field mobilities as a function of reciprocal temperature and reciprocal square temperature are depicted in Figure 4. The zero field mobilities decrease monotonically with temperature, which is the typical feature of carrier transporting in disordered materials. The intrinsic localized hopping mobilities (μ0) and the energetic disorders (σ) are achieved by fitting log(μE=0) vs T−2 (Figure 4, parts a and c) to the GDM, and are listed in Table 3. μ0 at ET of 0.2 and 0.25 eV slightly decreases from 5.0 × 10−3 to 3.3 × 10−3, and from 9.0 × 10−5 to 4.8 × 10−5, respectively in

Figure 4. Zero field mobility vs. reciprocal square temperature (a) and vs reciprocal temperature (b) for the TPD-hosted materials; zero field mobility vs. reciprocal square temperature (c) and vs reciprocal temperature (d) for the TCTA-hosted materials. 10655

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Table 3. Fit Parameters Obtained from the Temperature Dependence of the TOF Mobilities GDM material

ϕ (%)

ET (eV)

TPD TPD:DCJTB TPD:m-TDATA TCTA TCTA:NPB TCTA:m-TDATA

0 2 2 0 2 2

− 0.2 0.4 − 0.25 0.55

μ0 (cm2 V−1 s−1) 5.0 3.3 4.7 9.0 4.8 9.0

× × × × × ×

10−3 10−3 10−3 10−5 10−5 10−5

MTR model σ (meV)

μi (cm2 V−1 s−1)

Ea (meV)

60 75 62 63 78 66

0.17 0.17 0.16 0.01 0.011 0.01

146 211 150 169 224 172

Figure 5. Carrier quantity collected in the TOF experiments at the electric field of 3.5MV/cm as a function of the trap energy. Figure 7. Distributions of log(tT) under various ET from 3-D MC simulations at ϕ of 5% and electric field of 3.5MV/cm. The inset shows the distribution of log(tT) of the trapped carriers at ET of 0.5 eV.

dispersive distribution of tT is also observed at the shallow trapping situations. These results highly accord with our experimental results of tT and the transition of the TOF transients from nondispersive to dispersive when shallow traps are introduced (which has been discussed with Figure 2). Moreover, the number of the carriers collected (within the time range of 1 ns to 0.1 ms) at ET of 0.5 eV is by an order of 1−2 magnitudes fewer than in other situations, which is also in accordance with the experimental results shown in Figure 5. The simulations under trap fractions of 1% and 2% (see Figure S5) also give similar results. The results of the 3-D MC simulations suggest that the difference between the effects of deep traps and shallow traps is not just limited to the materials investigated in this article, but rather a generalized fact. In fact, we also collected the transit times of the carriers trapped in deep traps at ET of 0.5 eV. It is shown that tT of these carriers are distributed from the order of 0.1 ms to 10s (see inset of Figure 7), which means the reactivation of these carriers is quite slow and very sparse (noting that tT is in a log coordinate). Therefore, the current (dQ/dt) caused by the release of these carriers can be very small, and is inseparable with the noise in the TOF experiments. Not uniquely, deep traps have recently been assumed to contribute to the noise in the hall-effect measurement of the rubrene crystal.5 The multiple carrier results also help us to comprehend the possible misunderstanding of the effects of deep trapping in situations where the mobility is thought as the average of all the carriers.48 In these situations, the average operation can cover up the difference between the trapped carriers and the untrapped carriers, and result in monotonous decrease of mobility on ET. As carrier mobility is affected by traps mainly through the rate of each hop and the number of hopping a carrier

Figure 6. Schematic of the carrier transport process at shallow trapping and deep trapping. The blue solid and the red solid respectively represent the trajectory of the collected carriers and the deep trapping carrier.

tends to transport by a successive trapping-releasing process. Hence traps participate in transport to a large extend and result in increasing disorder of the site energies the carriers go through. In the deep trapping situation, thermal reactivation of a trapped carrier is very difficult as ET is much larger than kBT (which is 0.026 eV at 298 K). And when a carrier occupy the deep trap site for a long time, the like charges passed by will be scattered and change their directions. Hence, the trapped carriers may not contribute to the quantity of carriers collected by the electrode, whereas the untrapped carriers will experience a nearly trap-free hopping and the measured mobility just decreases slightly owing to the elongated transporting trajectory. In order to elaborate the insight of the trapping effects quantitatively, results of MC simulations is discussed below. Figure 7 shows the distributions of the logarithmic transit times, log (tT), in 3-D simulations at different ET (at ϕ of 5%, and electric field of 3.5 MV/cm). It shows clearly that tT for shallow trapping (ET of 0.1 and 0.2 eV) increase by up to an order of magnitude. However, for 0.5 eV trapping, tT stays almost the same as the pure situation (ET = 0 eV). A more 10656

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Figure 8. (a) Simulated transporting trajectories of the carriers in 100 × 100 2-D grids under various trap fractions and various trap energies. The HOMO of the host is set to 0, and both the host site energies and the trap site energies follow a Gaussian distribution with σ of 70 meV. The red solids and the green solids respectively represent the trajectory of the collected carriers and the deep trapping carriers. (b) Distributions of the site energies in the trajectories of the carriers under various trap energies at ϕ of 5%.

experiences, we simulated the transporting trajectories of the carriers to demonstrate the effects of the two aspects intuitively. The transporting trajectories at ET = 0.1, 0.2, and 0.5 eV and ϕ = 0.01, 0.02, and 0.05 in 100 × 100 2-D simulations are depicted in Figure 8a (see Figure S6 for the result of the pure material (ϕ = 0)). It can be seen that the number of hops, N, increases significantly as ϕ increases at shallow traps (ET = 0.1, 0.2 eV), and result in more winding trajectories. However, at ET of 0.5 eV, N just increases from 268 to 286 as ϕ change from 1% to 5%. The distributions of the site energies in the trajectories at ϕ of 5% are shown in Figure 8b. It can be seen that at ET of 0.1 and 0.2 eV, the distributions shift toward ET and result in increasing effective energetic disorders characterized by the widths of the distributions. This result also suggests that the carrier collected often experiences hops between the trap sites and the host sites. At ET of 0.5 eV, the distribution is similar to that of the pure material, which means no deep traps are included in the trajectories of the collected carriers. In fact, the deep traps along the way were occupied by other carriers (of which the trajectories are depicted as green lines) before the collected carriers arrive, and the dwelling time can be as long as a few milliseconds according to the calculation by the Miller−Abrahams equation. By contrasting the distributions of the site energies, we conclude that the average hopping rate in the shallow trapping situation can be much smaller than in the deep trapping situation owing to larger energetic disorder. We can also find the distributions bias toward lower energy, which is because carriers tend to hop to sites with lower energies. 4.3. Borderline between Deep Traps and Shallow Traps. It is appropriate to summarize the insight gained so far. We have demonstrated in both TOF experiments and MC simulations that shallow traps and deep traps affect carrier transport in disordered organic materials in very different ways. Also, we have covered the different effects of deep trapping and shallow trapping in a universal mechanism based on the

Miller−Abrahams model. In shallow trapping situations, carriers tend to transport by a multiple trapping release process, which generate several results: increased energetic disorder, longer transporting trajectory, and consequently, sharply decreased mobility. In contrast, deep traps tend to immobilize the trapping carriers and act as scattering centers, thus decrease the photocurrent and just affect the mobility slightly. However, for practical purpose, the borderline between deep traps and shallow traps, i.e., the critical trap energy (Ec) needs to be discussed. In crystal organic semiconductors, ET of shallow traps is considered as few kBT.20,21 However, in disordered organic semiconductors, ET of shallow traps can be as large as 0.2−0.3 eV (which is pn the order of 10 kBT) according to the literatures.18,19 On the basis of the discussion in section 4.2, we may infer whether a trap is deep or shallow is related to the relative length of the trap dwelling time and the transit time of trap-free carrier. Therefore, the critical trap energy, Ec, may increase with the intrinsic disorder of the host, and thus be material specific. In fact, if the trap dwelling time is so long that the trapped carrier cannot catch up with the free hopping ones after reactivation; we can regard the trap as a deep trap. In our previous work,22 a rough model considering trapping and release once has given an expression of Ec, which is, Ec = kBT × ln(2(λ − 1)N), where λ is tT divided by the half-life (t1/2) of the photocurrent of the pure material, which weighs the dispersive degree of the transient and is determined by the intrinsic disorder of the material, and N is the hopping steps of the free hopping carriers in the material. This expression indicates Ec can be determined by temperature, the intrinsic disorder of the material, and the thickness of the device. It also helps us to understand why the critical trap energy in the disordered organic materials is often larger than that in the organic crystal materials. For typical organic molecular semiconductor in TOF configuration (of which λ is around 3, N is in the order of 103 as the site distance of these materials is around 1 nm, according 10657

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to their common crystal constants23), Ec can be estimated to around 0.25 eV at room temperature. Investigating Ec directly can be very difficult, as a series of materials with adjacent HOMOs or LUMOs separated by only few kBT is hard to achieve. Here, we demonstrate an alternative way to investigate this problem, which is by measuring the TOF mobility in a large range of bias voltage. The bias applied to the devices can lead to change of electric potential of the sites, and along the bias direction, the decrease of the potential caused by the bias (Vbi) for every step can be estimated as V/(L/a), where V is the bias, L is the thickness and a is the average site radius. For the 1 μm thick device, Vbi is V/1000 if we set a to 1 nm. Because of the decline of the potential, the effective barrier for a trap to move forward is decreased. In another word, the effective trap energy, ET,effective, for thermal reactivation is decreased by a value of eVbi. By measuring the mobility at various Vbi, one gets the dependence of the mobility on ET,effective, which equals ET − eVbi. The TOF transients of the TPD: m-TDATA (of which ET is 0.4 eV) device at bias from 70 to 250 V (ET,effective thus is from 0.33 to 0.15 eV) are seen in Figure 9a. It is clear that when bias

controlled region with no thermal reactivation. And when ET,effective is smaller than 0.20 eV, only mobilities from the later phase are detected, which means thermal reactivation of the carriers from the shallow traps is dominating. And for ET,effective between 0.21 and 0.27 eV, both the mobilities from the two phases are obtained, which means carrier transport in this region is controlled by the combined effects of deep traps and shallow traps. Thus, the results suggest that a transition region, rather than a critical point, exists between deep traps and shallow traps in TPD. Anyway, the result from a trapping and release once model is fit for indicating the transition region. We suggest understanding of the transition from deep trapping to shallow trapping is an important consideration in host−guest OLEDs and heterojunction OPVs. First, the awareness of the different effects of deep trapping and shallow trapping on mobility helps us to choose the energy levels properly in device design to guarantee good transport property. Second, the electric field induced transition from deep trapping to shallow trapping helps to explain some electric field-related phenomena, such as electric field induced spectrum drift.50 In addition, immobilization of the carriers in deep traps suggests that deep traps are reasonable to be treated as long-lived recombination centers in the devices, which are the main cause of the trap-assisted recombination.51,52

5. CONCLUSION In conclusion, we have studied the effects of traps on carrier transport in a series of model disordered organic semiconductors using TOF method. The experimental results show the shallow traps greatly decrease the mobility by orders of magnitude whereas deep traps mainly decrease the collected carrier quantity without significantly affecting the mobility. And this is consistent with the results of transit time from Monte Carlo simulations. Investigations based on the GDM model and the MTR model indicates that shallow traps increase the effective energetic disorder and the activation energy, while deep traps hardly change both. By carrying out MC simulations of the transporting trajectories, the different effects of shallow traps and deep traps on transport are interpreted with a universal Miller−Abrahams based mechanism: owing to small trap energy, carriers in the shallow trapping situation tends to transport by a multiple trapping and release process, which result in larger energetic disorder; on the contrary, carriers in the deep trapping situations are nearly immobilized once trapped and act as scattering centers, thus leading to decreased carrier density and slightly decreased mobility. In addition, our investigations on the critical trap energy suggest that a transition region (with a width of few kBT), rather than an exact borderline exists between deep traps and shallow traps. In the transition region, carrier transport is controlled by both deep traps and thermal reactivation from shallow traps.

Figure 9. (a) TOF transients of the TPD: m-TDATA device at bias from 70 to 250 V. The blue lines and red lines respectively mark the deep trap controlled transit times 2 μs. (b) Later transition phases at electric field from 130 to 190 V. (c) Hole mobilities obtained from the two phases vs the effective trap energy, ET,effective.

is from 70 to 90 V, there is only one transition phase (210 V), the later phases (on time scale >2 μs) become dominating. The mobilities, calculated from tT of the two phases, as a function of ET,effective are depicted in Figure 9c. It shows that when ET,effective is larger than 0.28 eV, the mobility calculated from the earlier phase is around 10−3 cm2 V−1 s−1, which corresponds to the deep trap

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ASSOCIATED CONTENT

S Supporting Information *

Figure S1−S3, TOF transients of the devices under various electric fields; Figure S4, electric field dependence of the hole mobility of the devices under various temperature; and Figure S5, distributions of the transit times under trap fraction of 1% and 2%. This material is available free of charge via the Internet at http://pubs.acs.org. 10658

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AUTHOR INFORMATION

Corresponding Author

*(L.D.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors express thanks for the financial support by the National Natural Science Foundation of China under Grant Nos. 50990060, 51173096, and 21161160447.

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