Thickness Dependence of Carrier Mobility and the Interface Trap Free

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Thickness Dependence of Carrier Mobility and the Interface Trap Free Energy Investigated by Impedance Spectroscopy in Organic Semiconductors Hui Xu,† Wen-Juan Zhai,† Chao Tang,*,† Shao-Ya Qiu,† Rui-Lan Liu,†,‡ Zhou Rong,†,‡ Zong-Qiang Pang,†,‡ Bing Jiang,†,‡ Jing Xiao,∥ Chao Zhong,† Bao-Xiu Mi,*,† Qu-Li Fan,*,† and Wei Huang*,†,§ †

Key Laboratory for Organic Electronics and Information Displays & Institute of Advanced Materials (IAM), Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), Nanjing University of Posts & Telecommunications, 9 Wenyuan Road, Nanjing 210023, China ‡ College of Automation, Nanjing University of Posts and Telecommunications (NUPT), Nanjing 210023, China § Key Laboratory of Flexible Electronics (KLOFE) & Institute of Advanced Materials (IAM), Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), Nanjing Tech University (NanjingTech), 30 South Puzhu Road, Nanjing 211816, China ∥ College of Physics and Electronic Engineering, Taishan University, Taian, Shandong 271021, China ABSTRACT: The authors report the hole mobilities of organic semiconductors (OSCs): N,N′-di-[(1-naphthalenyl)-N,N′-diphenyl]-1,1′-biphenyl)-4,4′-diamine and N,N′-bis (3-methyl- phenyl)-N,N′-diphenylbenzidine in various thick films (50−800 nm) by impedance spectroscopy. The experimental results show that the mobility increases with the increase of thickness. After extrapolating the area of electric field by fitting the P−F equation, we find that the thickness ratio is the primary cause for the change of the carrier mobility. Based on this, after excluding the crystallization and morphology influence factors through XRD and AFM, the conception of interface trap free energy was proposed, and at last such phenomenon was ascribed to the interface trap free energy λTrap between electrode and the material, namely dG = λTrap·dA.

1. INTRODUCTION The discovery of highly efficient organic light-emitting-diodes (OLEDs) in the 1980s has attracted extensive attention on organic semiconductors and devices.1 Besides OLEDs, organicfield-effect transistors (OFETs) and organic photovoltaic cells (OPVs) are also showing very promising application.2−5 With respect to such devices, charge carrier dynamics always play the key function for the device performance,6 which leads to great devotion of scientists to carrier dynamics research in such organic semiconductors (OSCs).7,8 Up to now, the widely used method for carrier dynamics is time-of-flight (TOF).9 It needs film thickness over at least 1000 nm in order to provide a flight distance to meet the photon penetration length of laser, which results in large material consumption. However, the film thickness in real organic devices such as OLEDs, OFETs, and OPVs is always thinner than 100 nm. Therefore, considering the film thickness, the mobility value measured from TOF method could obviously not be directly applied to the device design. As a powerful electric testing technique based on space charge limited current (SCLC) theory, impedance spectroscopy (IS) (or admittance spectroscopy (AS)) has been proposed to evaluate the mobility of OSCs.10−17 Under a small signal © XXXX American Chemical Society

disturbance, the theoretical IS or AS model can be established.18−21 Most of the OSCs in fact show low admittance value, and in contrast, as the reciprocal of admittance, the impedance shows greatly larger values. Under the situation of the finite instrument precision, the larger value will lead to the smaller testing error, and finally, the subsequent data fitting will be much easier and more correct. This is why the impedance spectroscopy has an advantage over admittance spectroscopy on the OSCs. As to the very important data fitting process, the leastsquares algorithm is widely used in the built-in programs of the common mathematical software such as MATLAB, MATHEMATICA, and MAPLE. However, the fitting results are greatly sensitive to initial values, and unsuitable initial values will give rise to no convergence, which means that the fitting has failed. In order to overcome such difficulty, the Particle swarm optimization (PSO) algorithm was used, which was a multipoint iterative algorithm. Recently we have proved that Received: April 19, 2016 Revised: June 1, 2016

A

DOI: 10.1021/acs.jpcc.6b03964 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C it can always find a better solution to the data fitting and does not require much information about the initial data.15 Moreover, because the establishment of the mathematical physical model does not have the limitation of the film thickness, the IS method could easily be used in the research of carrier dynamics with different film thickness. So in this report, the thickness dependence of the carrier mobility has been investigated by impedance spectroscopy and the particle swarm optimization (PSO) fitting method. Based on such data, the carrier influencing factors, such as molecular structure, film morphology, carrier trap, and interfacial trap states, have been systematically researched. At last, from the point of thermodynamics, we propose the interface Gibbs free energy to explain the thickness dependence of hole mobility.

generally introduced according to Scher and Montrol theory (SM).22 The normalized mobility is written as μ ̃(Ω) =

μ(Ω) = 1 + M(iωτdc)1 − α = 1 + M(i 2πfτdc)1 − α μdc (3)

For no dispersive materials, M = 0, α = 1, and μdc is the carrier mobility under dc bias, and f is the working frequency of the impedance analyzer. According to the formulas 2 and 3, impedance Z = Z(ε, d, A, f, M, α, τdc). A, d, ε are constant, f is the working frequency, the three unknown parameters M, α, τdc are performance parameters to characterize the OCSs. μdc can be obtained from the formula μdc = d 2/(τdcVdc)

2. THEORETICAL MODELING The device consists of an organic semiconductor with a dielectric constant ε and a thickness d, which is sandwiched between two electrodes, as shown in Figure 1. The anode

3. EXPERIMENT The devices were fabricated with the thickness from 50 to 800 nm, which are shown in Table 1. Table 1. Layer Structure of Devices device layer structure A B

The samples were obtained from Shanghai Weizhu Chemical Science and Technology and were used without further purification. Organic films thicknesses were measured by a quartz oscillator. The indium tin oxide (ITO) prepatterned anode on glass was cleaned by a sequence of alcohol, acetone, plasma water ultrasonic bath, and oxygen treatment after being stoved. A thinner layer of organic materials was coated on the anode, and Al was then evaporated on the organic to form the cathode. Since there is a significant energy difference between the lowest unoccupied molecular orbital (LUMO) of the organic and the work function of Al (4.3 eV), few electrons can be injected from the cathode. Thus, Al cathode also acts as an electron-blocking contact. On the other hand, the ITO/organic interface is approximately Ohmic as there is relatively small energy difference between the work function of ITO and highest occupied molecular orbital (HOMO) of the organic materials.22 Therefore, the overall current is dominated by the hole current. The impedance, as a function of the device frequency, was measured by an impedance analyzer Wayne Kerr 6500 B. To achieve the impedance values, an ac modulation of amplitude 50 mV ( f = 20 − 106 HZ) was superimposed on the dc-biased voltage which was typically varied. During all measurements, the devices were placed in the shielding box under room temperature.

Figure 1. Structure diagram and measurement schematic of the device.

electrode is assumed to form Ohmic contact with the organic material, and the cathode contact is an electron block. Under a forward dc bias voltage Vdc, holes are injected from the anode and then drifted toward the cathode. Superposing a small ac signal (modulation) vac = Vm sin (ωt)( f = ω/2π) on the device, a small ac alternating current signal iac = Im sin(ωt + θ) will be produced. The impedance of frequency dependence follows the relationship of Z(ω) = vac/iac = 1/(G + iB) = 1/(G + iωC)

(1)

where i = −1, and G, C, and θ are the conductance, capacitance, and phase difference between current and voltage signal of the device, respectively. The space charge limited current (SCLC) is based on the drift current equation and Poisson equation. Considering the linear superposition between dc and ac signal, the ac current density can be obtained according to the above two assumptions. Then, through the Fourier transform, the impedance formula can be written in the form 2

Z(Ω) =

ITO/NPB (50−800 nm) /Al (100 nm) ITO/TPD (50−-800 nm) /Al (100 nm)

τdcd ⎛ 2i[0.75μ ̃(Ω)]2 {1 − exp[ − i 4Ω/3μ ̃(Ω)]} + 1.5μ (̃ Ω)Ω − i Ω2 ⎞ ⎟ ⎜ εA ⎝ Ω3 ⎠

4. RESULTS AND DISCUSSION Figure 2 shows the electric field dependence of hole mobility at various film thicknesses of NPB and TPD. Taking the NPB for instance, as the thickness increases, the mobility increases and it approaches the stable value at 600 nm. With the decrement of thickness from 600 to 50 nm, the mobility values decrease. Such a trend is consistent with TPD. Another method, TOF technique, requires quite thicker films of several microns. Hence, our results can be helpful to estimate the carrier mobility of OSCs in the typical device of OLEDs.

(2)

where Ω = ωτdc is the normalized frequency, μ̃(Ω) is the normalized mobility, τdc is the average mobility of carrier which is in steady-state, A is the effective area of the device, d is the thickness of organic layer, and ε is the dielectric constant. The active area of the devices was about 0.09 cm2. In order to describe the charge-carrier transporting properties of disorder materials, dispersive parameters M, α are B

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Figure 2. Thickness dependence for hole mobility of NPB and TPD estimated by IS for (a) ITO/NPB(x)/Al and (b) ITO/TPD(x)/Al. The inset shows the structure of NPB and TPD.

In Figure 3, all the curves can fit the P−F equation μ = μ0 exp(β E ), which can describe the relationship between mobility and electric field of disordered organic materials. It is also easy to find that the slopes of all curves are not the same, which means that they might intersect under the higher electric field. But due to the use limitation of the instrument itself, the impedance at larger electric field scope is very difficult to be obtained. Because the relationship between the mobility and electric field is always linear, we could get longer curves under large scope of electric field by extrapolating the area of electric field according to the P−F equation, as seen in Figure 5. It is certain that the mobility of both of the two materials reaches the intersection point at the electric field value about 500 (V/ cm)1/2 when the thicknesses are over 200 nm. The intersection point means that when the film thickness is more than 200 nm, the hole mobility of every film in different thickness reaches the same value under this electric field. The interface thickness ratios are the interface thickness proportions of the whole functional film. Although the thickness of interface is unknown, we can assume that the interface thickness is from 1 to 10 nm and divide the interface thickness by the total film thickness. The achieved value is just the interface thickness ratios. In this way, the interface thickness ratios at the device thickness from 50 to 800 nm could be obtained. Then under the fixed electric field at 500 (V/cm)1/2, the mobility under different interface thickness ratios can be evaluated according to Figure 5, which could be seen in Figure 6. TPD and NPB have different molecular structures. From Figure 6, we can see that their carrier mobility values under different thickness are a little different, but their curves of mobility− interface thickness ratio are similar to each other. Figure 6 shows that the carrier mobility increases as the ratio of the interface thickness decreases, and it reaches the saturated value at the range of 200 nm, which is in agreement with the results in Figure 5. In other words, the film mobility measurement of more than 200 nm is meaningless. TOF, which needs the micron level thickness to evaluate the mobility, will lead to a large material consumption. But the real film thickness in organic optoelectronic device is always smaller than 100 nm. Thus, the results in our work can be useful for a device design and performance analysis. So, it is the interface thickness ratio in the whole thickness, not the thickness itself, nor the molecular structure and film morphology, that plays the key role in the process. The

The experimental results in Figure 2 have proved the thickness dependence of hole mobility. However, the underlying reasons were worth being carefully investigated. Generally, the carrier mobility of one organic material will be influenced by molecular structure, film morphology, carrier trap, and interfacial trap states. Single crystal, of course, is helpful to carrier mobility, but there is always no single crystal in organic optoelectronic device. Considering that some organic materials still might form polycrystal in the film, the crystallization of NPB and TPD might be a possible parameter which is responsible for the lower mobility under thinner NPB or TPD film. It has been reported that NPB or TPD could grow in islandlike modes on bare ITO and have inhomogeneous morphology.23 So, the XRD was used to ensure whether the polycrystal of NPB or TPD is formed in the experimental conditions. As shown in Figure 3, the tendency of intensity to 2θ is the same as to the

Figure 3. X-RD of the NPB and TPD with different thickness.

ITO glass. There are no peak values, and this indicates that there is no crystallization on the surface. And then such experiments exclude the impact of crystallization. Another possible parameter might be the surface topography of the organic films. Considering this, atomic force microscopy (AFM) with 3 × 3 μm2 images was then measured in Figure 4. It showed that the morphologies of ITO/NPB (from 50 and 600 nm) and ITO/TPD (50 and 600 nm) were almost the same with the ITO glass. Thus, the influencing factor of surface topography of different film in different thickness has been excluded. C

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Figure 4. AFM images for (a) ITO surface, (b) 50 nm of NPB on ITO, (c) 600 nm of NPB on ITO, (d) 50 nm of TPD on ITO, and (e) 600 nm of TPD on ITO in the area of 3 × 3 um2.

Figure 5. Fitting of the thickness-dependent hole mobility of NPB and TPD.

Figure 6. Hole mobility of NPB and TPD under different interface thickness ratios.

interface includes the combination of electrode and the material that always act as carrier traps in organic electronics. The trap mechanism has not yet been studied very well in the organic semiconductors. Chu et al.23−26 explained the interfacial trap phenomenon by the Gaussian disorder model,27 which is

wonderful. From the viewpoint of device application, the theory is very complex and not easy to be used in fact. And what people really want to know is how much the ratio of the interface acts as negative impact. After systematical invesD

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tigation, we obtain the influence of the interface ratio in whole thickness on the carrier mobility. In each device, the surface area of the interface is certain; thus, the difference of interface thickness represents the difference of the interface volume. The above experiment has proved that the interface layer acts as carrier trap and decreases the carrier mobility. It shows similarity to the concept of interface free energy. The relationship between interface free energy γ and the Gibbs free energy G could be clearly described as the following formulas dG = − S dT + V dP + γ dA +

Wen-Juan Zhai and Hui Xu contributed equally to this work. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the Project Funded by Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD, YX03001), Natural Science Foundation of Jiangsu Province (BM2012010), Program for Changjiang Scholars and Innovative Research Team in University (IRT1148), National Synergetic Innovation Center for Advanced Materials (SICAM), Synergetic Innovation Center for Organic Electronics and Information Displays, National Natural Science Foundation of China under Grant 61136003 and 61574098, Jiangsu Government Scholarship for Overseas Studies under Grant JS-2013-200, and Natural Science Foundation of Nanjing University of Posts and Telecommunications under Grant NY214090 and NY215160.

∑ μBdnB B

where A is the interface area, S is the entropy, T is temperature, V is volume, P is pressure, μB is the chemical potential, and nB is the amount of substance. When T and P are invariable, and for one substance, which are easily satisfied in organic electronic device, the formula could be as in the following. dG = γ dA , so γ =

⎛ ∂G ⎞ ⎜ ⎟ ⎝ ∂A ⎠ p , T , n

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B

Considering the similarity, when T and P are invariable, and for one substance, we can define the interface trap free energy as the following. After one device is accomplished, the interface thickness of the trap effect is certain. The larger the ratio of the interface thickness, the more obvious the capture effect, and the less the mobility.

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dG = λ Trap·dA

Here λTrap is defined as interface trap free energy and A is the effective area. Due to the same scale of the pixel (same area A), the interface trap free energy and Gibbs free energy are only related to the thickness ratio of the interface. This is the reason why we make the deep research of the thickness dependence of carrier mobility. From the equation, we know that the Gibbs free energy decreases as the thickness ratio decreases, and the capture of the trap to carrier decreases. At last, the mobility increases, and it is in agreement with Figure 6.

5. CONCLUSION In conclusion, the carrier mobilities of the organic semiconductors NPB and TPD with different thicknesses have been evaluated by IS. The mobility increases as the thickness increases. The XRD and AFM test showed that the increments of mobility are not influenced by molecular structure and film morphology. Considering that the interface layer acts as carrier trap and decreases the carrier mobility, we propose the interface trap free energy λTrap as dG = λ Trap·dA

From the above equation, Gibbs free energy decreases with the decrease of the interface thickness ratio, the capture of the trap to carrier decreases, and therefore, the mobility increases. From the point of device design and performance optimization, this work can offer an important reference and solve the problem of materials consumption.

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REFERENCES

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*Tel.: +8625 85866332. Fax: +86 25 85866332. E-mail: [email protected]. * E-mail: [email protected]. E

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