Probing and modeling of carrier motion in organic devices by electric-field-induced optical second-harmonic generation

As described in Sect. 2, we can measure the electric field distribution in organic devices and carrier motion in organic devices among others by probing the nonlinear polarization that generates EFISHG. Firstly, we discuss some examples and then show how carrier behaviors are modeled on the basis of experimental results.

Since the discovery of conducting organic materials, organic devices have attracted much attention in electronics. Among them are OLEDs, OFETs, and organic memory devices. In these electronic devices, organic semiconductor materials are used as active layers to realize their own device function, which are designed on the basis of general semiconductor device physics.³²⁾ However, the carrier injection and transport mechanisms in actual organic devices are not so simple, owing to the dielectric nature of active organic layers. Basically, the intrinsic carrier density is quite low in active organic layers. As a result, the function of devices with such layers is rather different from that of general semiconductor devices, and most organic devices are governed by the carrier injection process. We can see such examples of the device function of OFETs and OLEDs among others. Consequently, it is a very effective way to directly measure the electric field distribution in these devices for analyzing and modeling carrier behaviors on the basis of the dielectric physics approach.^33,34) As already described in Sect. 2, EFISHG measurement can be used to detect electric fields formed in organic devices. Keeping in mind this idea, the electric field distribution formed along the channel of pentacene-OFETs has been measured. The electric field distribution formed in the pentacene-OFETs before and after hole injection into the channel has been well probed,^35,36) where the electric field distribution before hole injection is in good agreement with the distribution analyzed by the rigorous solution of the Laplace equation. That is, the experimental electric field distribution well agrees with that determined theoretically by assuming the potentials of a three-electrode system of OFETs. Furthermore, the electric field distribution that originated from carriers has been determined from EFISHG measurements, and it has been shown that the charge distribution along the OFET channel is basically determined on the basis of the Maxwell–Wagner (MW) model, which describes carrier accumulation at the interface between two different materials. For OFETs, this model accounts for carrier accumulation and distribution on the gate-insulator/active organic layer interface.³⁴⁾ Figure 2 shows the EFISHG measurement of top-contact pentacene-OFETs with the Au source and drain electrodes.³⁶⁾ Under the condition of no carrier injection, EFISHG is shown to be activated to satisfy the rigorous Laplace solution of a three-electrode system of the OFETs,³⁷⁾ as shown in Fig. 2(a). On the other hand, under the condition of hole injection, the intensity of EFISHG decreases owing to the space charge field formed along the channel by injected holes, as shown in Fig. 2(b). Because we know the relationship between EFISHG intensity and electric field [see Eqs. (2) and (3)], it is easy to determine the carrier distribution along the channel, as plotted in Fig. 3.³⁶⁾ These results show that carrier accumulation along the channel is governed by the MW effect, and the distribution is basically determined on the basis of the MW model.^34,35) Our further EFISHG study shows that the carrier distribution along the channel in the steady state follows a solution of the classical differential equation of current, which describes continuity of carrier transport along the channel, and which is modeled on the basis of a transmission line model, as an extension of the MW model.^38–40) Analytical results show that the potential distribution along the channel is not linear, but it changes on satisfying the square root dependence along the channel, as shown below:

$$\begin{equation} V(x) = V_{0}\sqrt{1 - \frac{x}{L}}\quad \text{with}\ V(0) = V_{0}\ \text{and}\ V(L) = 0, \end{equation} \tag{ 6 }$$

where x = 0 and L represent the edge of the source and the drain electrodes, respectively. Accordingly, the electric field distribution is given as

$$\begin{equation} E(x) = \frac{V_{0}}{2\sqrt{L(L - x)}}. \end{equation} \tag{ 7 }$$

EFISHG enables the probing of this electric field distribution and generates the signals that follow Eq. (3) with the relation Eq. (7), where E(0) in Eq. (3) is replaced with E(x) in Eq. (7). Figure 4(a) shows the plots of calculation (solid line) and experimental results (symbols) of the normalized electric field of the conduction carriers in the channel region of OFET in the on-state.³⁷⁾ The calculation is based on the rigorous solution of the differential equation, but a small difference is identified in experimental electric intensity and the calculated result of the electric field of the charged layer (indicated by solid lines), possibly owing to the presence of trapped carriers that contribute to the additional electric field [see Eq. (4)]. Figure 4(b) shows the electric field distribution obtained from SHG experiment plotted in the log–log scale, and the line represents the linear fit, suggesting the square root dependence of electric field along the channel [see Eq. (7)].

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

As has been described above, it is clear that EFISHG measurement can be used for probing the steady-state carrier distribution along the channel of OFETs. Some organic materials show ambipolar behaviors,³²⁾ which means that electrons and holes can enter into materials from electrodes. In the field of electrical insulation engineering, this carrier behavior is called double injection.³⁾ Consequently, probing injected electrons and holes and determining their distribution in organic devices are also important.^35,37) For example, for organic light-emitting device applications, simultaneous electron and hole injection is a key to device operation. Using ambipolar organic light-emitting transistors (OLETs) with an active layer of the green-light-emitting polymer poly(9,9-di-n-octylfluorene-alt-benzothiadiazole) (F8BT), which has a photoluminescent peak at the wavelength of 560 nm, EFISHG measurement has been employed using a laser beam of 840 nm wavelength.^41–43) For the experiment, we need to remove the effect of photoluminescence using a band pass filter so that we can probe EFISHG at a wavelength of only 420 nm.

Figure 5(a) shows the structure of OLETs, where electron and hole transfer into the active layer from opposite electrodes is essential to emitting light. Figure 5(b) shows an image of electroluminescence (EL) from the F8BT OLETs, which is generated from the channel region and it is visualized as a bright band using a CCD camera.⁴²⁾ This emission band represents the meeting point of electrons and holes followed by recombination for EL, but this image does not directly show the distribution of holes and electrons along the channel. An EFISHG image shown in Fig. 5(c) clarifies this situation, because EFISHG is proportional to the electric field, as given by Eq. (3). Therefore, we can map the carrier distribution along the channel experimentally using the Gauss law [Eq. (2)]. Figure 6 shows the potential profile reconstructed from the EFISHG experiment.⁴²⁾ Closed circles represent the results, and we can see that there is a zero-potential position in the channel. It is easy to understand that electrons and holes accumulate, depending on the polarity of potentials. Interestingly, this distribution is in good agreement with the theoretical carrier distribution that is derived by solving an one-dimensional continuity equation for the current density J, in the same way as in the derivation of Eqs. (6) and (7). In this derivation, it is assumed that electrons and holes dominate carrier conduction, depending on the zero-potential position. That is, the idea of zero-potential position clearly developed from the study of ambipolar OFETs by EFISHG measurement.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

As mentioned in Sect. 2, it is possible to probe carrier motion by TRM-SHG measurement. Using top-contact pentacene-OFETs with the Au source and drain electrodes, TRM-SHG measurement was carried out. Here, the channel length of the OFET is 40 µm. Figure 7(a) shows an image of TRM-SHG from the channel of pentacene-OFET with a 500-nm-thick SiO₂ gate insulator, where the SHG image was obtained including carrier motions after a positive voltage pulse was applied. That is, the positive voltage pulse V_pulse = 70 V was applied to the source electrode with respect to the gate and drain electrodes that were shorted and grounded, i.e., V_ds = V_gs = −70 V. At τ = 0 ns, the laser pulse coincides with the rising edge of the voltage pulse, and SHG signals are found near the edge of the source electrode, indicating that the Laplace electric field E₀ parallel to the channel is formed only around the source electrode. Interestingly, as it is clearly shown in the image, the emission band of the SHG signal gradually moves in the channel from the source electrode to the drain electrode with time. The visualized emission band motion starting from the source electrode is the direct evidence of hole injection from the Au source electrode. That is, pentacene-OFET shows a p-type behavior, where the majority of carriers are holes injected from the source electrode and the carrier mobility is in the range of 0.1–0.2 cm² V⁻¹ s⁻¹. Note that the SHG image is confined in the region within a radius of approximately 150 µm, owing to the spot size of the laser [see the region indicated by a dashed circle in Fig. 7(a)]. To further clarify the hole-transport mechanism across the channel, we plotted the SHG peak position with respect to the elapsed time, as shown in Fig. 7(b).⁴⁴⁾ From Figs. 7(a) and 7(b), it is clear that holes travel in the direction from the source Au electrode to the drain electrode, satisfying the square root time dependence.^45,46) This time dependence reflects the interface charge propagation process [see Fig. 7(b) and Ref. 39], and well supports the RC ladder circuit model that is employed for analyzing transient carrier behaviors along the OFET channel.^32,39,40) On the other hand, under the application of negative pulse voltage, the position of the SHG peak never moves; the SHG signals are concentrated around the edge of the source electrode during the measurement, suggesting that electron injection is prohibited.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

It is instructive here to note that carrier propagation is dependent on the interfacial condition of the channel formed on the surface of the gate insulator, e.g., the presence of carrier traps. Equation (4) suggests that TRM-SHG measurement can be used for monitoring the contribution of the surface states of the channel. To confirm the potentiality of TRM-SHG measurement, an experiment was carried out using pentacene-OFETs with a 100-nm-thick poly(methyl methacrylate) (PMMA) layer on the surface of the gate SiO₂ insulator. Figures 8(a) and 8(b) show the results of the experiment carried out under the same experimental conditions as those for results shown in Fig. 7(a), where SHG is concentrated in the front region of the propagating SHG profile.⁴⁷⁾ This result indicates that the space-charge field E_s formed along the channel is due to trapped holes and moving holes. Analysis based on a carrier trap model well accounts for the results. That is, TRM-SHG measurement is effective for probing interface states of the channel region. Furthermore, note that we can probe the effect of nanoparticles and dipoles on the carrier injection and transport by using the TRM-SHG measurements.^48,49)

Zoom In Zoom Out Reset image size

As shown in Fig. 5, electrons and holes have a significant contribution in ambipolar OLETs. To understand the details of the carrier mechanism of EL, it is very informative to simultaneously probe the dynamical electron and hole carrier behaviors that lead to EL, after the electron and hole injection starts at the source and drain electrodes, respectively. Also, probing hole and electron motion simultaneously would be useful for understanding the electrical breakdown of materials⁵⁰⁾ and the recombination of injected carriers in organic devices.³⁰⁾ TRM-SHG measurement has the potentiality for visualizing electron and hole carrier motion simultaneously. Our group has already visualized such carrier motion in OFETs, by applying positive and negative pulse voltages to the source and drain electrodes with respect to the gate electrode. Also, we should note that the activation of SHG is material-dependent, owing to the material-dependent parameter $\chi ^{(3)}(2\omega ;0,\omega ,\omega )$ with the angular frequency ω in Eq. (3). Consequently, probing carrier motion in one of the layers in multilayer systems is possible. Actually, we demonstrated the detection of such carrier motions in OFETs with an active layer in a double-layer system, e.g., OFETs with a C60/pentacene active layer.^51–55) Furthermore, visualization of two-dimensional planar carrier motion in EFISHG measurement allows us to probe anisotropic carrier motions in organic layers, and this observation provides a new way for characterizing anisotropic carrier transport in organic thin films by employing a round-shaped electrode in the EFISHG measurement.⁵⁶⁾

OLEDs have attracted much attention in electronics. Basically, an OLED is an injection-type device with two different electrodes that are separated by an organic multilayer system. Using the energy diagram of molecules, e.g., HOMO and LUMO states, many research studies have been carried out to improve device performance. Ideas of using low-work-function electrodes, depositing dipolar layers on the surface of electrodes, and utilizing multilayer systems comprising hole and electron transport, and electroluminescent layers among others have been presented.^30,72–74) These important ideas for achieving high-performance OLED devices are well accepted. However, owing to the ambiguities of energetics at the organic–metal and organic–organic interfaces, electron and hole behaviors in OLED devices are still not fully understood. To clarify the details, we need to pay attention to carrier injection from electrodes, carrier transport across active layers, and charge accumulation and recombination at the interface, which lead to EL. Hence, one of the most effective ways is to probe directly carrier motion in OLED devices. In particular, probing carrier behaviors simultaneously with charge accumulation at the interface is very important. EFISHG measurement can be applied for this purpose. It is instructive here to note that the MW effect well accounts for the charge accumulation at the interface between two adjacent materials;^31,34) thus, the analysis of organic EL devices as a MW effect element in combination with the EFISHG measurement is helpful.⁷⁵⁾

The EFISHG experiments on the indium zinc oxide (IZO)/N,N'-di-[(1-naphthyl)-N,N'-diphenyl]-(1,10-biphenyl)-4,4'-diamine (α-NPD)/tris(8-hydroxy-quinolinato) aluminum(III) (Alq3)/LiF/Al structure OLED device showed good charging and discharging of carriers on electrodes and carrier transit across α-NPD and Alq3 layers, and nonreversal charging and discharging processes resulted from the different carrier behaviors accompanied by EL. Briefly, a rectifying behavior was observed for the devices together with the enhancement of ordinary green EL from the Alq3 layer under forward bias condition (IZO positive). Figures 9(a)–9(d) respectively show the transient EFISHG intensity I(2ω) and EL intensity under application of a square wave voltage of V_ex = 5 V.⁷⁵⁾ The SHG I(2ω) with a wavelength of 410 nm is selectively generated from the α-NPD layer by laser irradiation with a wavelength of 820 nm. Figure 9(b) shows the electric field in α-NPD, E₁, plotted using Eq. (3). In Fig. 9, regions 1–3 and 4–6 respectively correspond to charging and discharging processes. In region 1, E₁ increases with a response time τ_RC of 7 × 10⁻⁸ s. This value agrees well with the R_sC^* = 7.7 × 10⁻⁸ s with a lead resistance R_s of 170 Ω and a series capacitance $C^{*} = C_{1}C_{2}/(C_{1} + C_{2})$ of 4.5 × 10⁻¹⁰ F (C₁: capacitance of α-NPD layer, C₂: capacitance of Alq3 layer). E₁ at the end of region 1 was estimated from the SHG intensity as 2.7 × 10⁵ V/cm, and corresponded well to the Laplace electric field determined from the ratio of C₁ to C₂ as $E_{1} = C_{2}/(C_{1} + C_{2})\cdot V_{\text{ex}}/d_{1}$. Here, d₁ is the thickness of α-NPD. Over the entire region 1, no EL enhancement was observed. These results show that region 1 reflects electrode charging by V_ex. In region 2, SHG I(2ω) and E₁ are nearly constant, and no EL enhancement was observed. In region 3, E₁ decays with a relaxation time of 2 × 10⁻³ s, and finally saturates. This evidently shows that positive charge Q_s is accumulated at the α-NPD/Alq3 interface. Note that this charge accumulation is due to the MW effect, and it is accompanied by the EL enhancement. At the end of region 3, the electric field is E₁ = 2.2 × 10⁵ V/cm, and the accumulated charge density is calculated as Q_s = 6.8 × 10⁻⁸ C/cm². The relaxation time corresponds well to the MW relaxation time of a double-layer system τ_MW = 2 × 10⁻³ s. Regions 4–6 are discharging processes. In region 4, E₁ decreases with the time constant τ_RC = 7 × 10⁻⁸ s, in the same way as in region 1. This result indicates that the charge induced on electrodes at the end of region 1 is discharged through the external circuit. On the other hand, Q_s (> 0) remains at the α-NPD/Alq3 interface, which gives rise to electric fields $E_{1} = - Q_{\text{s}}/(C_{1} + C_{2})\cdot 1/d_{1} < 0$ and $E_{2} = + Q_{\text{s}}/(C_{1} + C_{2})\cdot 1/d_{2} > 0$. At the end of region 4, the electric field saturated at E₁ = −3.1 × 10⁴ V/cm, suggesting that most of the charge Q_s remain at the interface. The enhanced EL intensity is nearly constant over the entire region 4. In region 5, the electric field E₁ in the α-NPD layer decreases and finally reaches E₁ = 0, while the enhanced EL intensity does not change. In region 6, E₁ = 0 but EL gradually decays with relaxation time τ = 3 × 10⁻⁴ s. As described above, in actual devices, charging and discharging processes are nonreversible, that is, the relaxation time τ_MW = 2 × 10⁻³ s for charging, whereas τ_MW = 5 × 10⁻⁶ s for discharging. The nonreversal behavior is mainly due to the difference in the contribution of the electric field arising from accumulated charges at the interface. In the charging process, accumulated positive charges hinder hole injection from ITO electrodes via the α-NPD layer. On the other hand, in the discharging process, accumulated positive charges assist electron injection from the Al electrode via the Alq3 layer. This model well accounts for two EL modes generated in these sandwich-type EL devices, depending on the frequency of the applied square voltage.^76–80) As mentioned above, we can monitor dynamical carrier behaviors in charging and discharging processes in EL devices by EFISHG measurement.

Zoom In Zoom Out Reset image size

Furthermore, note that EL has also received much attention as one of the prebreakdown phenomena of insulators in the field of electrical insulation engineering for the past 10 years, before the pioneering OLED work by Tang and Van Slyke,⁷²⁾ where the main research interest is to detect very weak EL signals for the diagnostics of insulators. EFISHG has an impact on the electrical insulation engineering community as a new method of detecting the prebreakdown phenomena of insulators as well as organic EL devices, because carrier motions leading to pre-electrical breakdown that results in EL can be probed before the EL as pre-breakdown phenomenon is initiated.⁵⁰⁾ This is also an advantage of using EFISHG measurement.

Ferroelectric polymers are widely used as memory materials, where the copolymer of vinylidene fluoride (VDF) and trifluoroethylene (TrFE), P(VDF–TrFE), stands out owing to its bistable and remanent polarization that can be repeatedly turned over by an external electric field.^81,82) Recently, ferroelectric polymers have also been used in electronic devices such as OFETs⁸³⁾ and organic photovoltaic cells (OPVs),⁸⁴⁾ where a strong internal electric field induced in the active layer of these devices by the spontaneous polarization of ferroelectric polymers is well utilized for efficient device operations. As a result, carrier behaviors in the active semiconductor layer, e.g., pentacene, have been extensively studied in terms of the turn over of the spontaneous polarization of the ferroelectric layer.^85–88) For the p-type pentacene-OFETs with a ferroelectric P(VDF–TrFE) gate insulator, hole/electron injection, transportation, charging, and discharging at the P(VDF–TrFE) gate insulator interface and so forth have been clarified in response to the turn over of the spontaneous polarization of the ferroelectric layer. Similarly, organic memory MIS diodes with a ferroelectric P(VDF–TrFE) insulator have been studied. These studies are mainly carried out by electrical measurements such as displacement current measurement (DCM), but these are no longer sufficient to account for carrier behaviors in a variety of organic semiconductors being utilized with ferroelectric P(VDF–TrFE) layers. With EFISHG, the electric field change induced in organic devices using a ferroelectric layer gives much information on the carrier behavior in these devices.

Figure 10 shows a typical example of DCM measurements for MFM and MFSM [inset of Fig. 10(b)] devices, which were prepared on patterned IZO substrates.⁸⁵⁾ A P(VDF–TrFE) (72–28 mol %) layer of 200 nm thickness was spin-coated on the substrate, and then a pentacene layer (200 nm, for MFSM device) and gold electrode were thermally evaporated successively. For the DCM measurement, a ramp voltage was applied to the IZO electrode. Figure 10(a) shows the results of DCM for the MFM device. Two peaks (peaks 1 and 2) are clearly observed at symmetric positions at voltages corresponding to the coercive electric field E_c of 0.6 MV/cm, and show no dependence on sweeping frequencies of ramp voltage. These results suggest that the appearances of peaks 1 and 2 are due to the turn over of spontaneous polarization.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

On the other hand, for MFSM devices [Fig. 10(b)], three peaks A, B, and C are clearly observed. The appearance of the third peak, peak C, at the non-symmetric position of peak A is a typical characteristic of the MFSM device. Results suggest a two-step polarization reversal of the ferroelectric layer in the pentacene/P(VDF–TrFE) double-layer device. However, this is a mere speculation. For studying carrier behaviors with the turn over of polarization, it is very helpful to measure the electric field formed in pentacene and PVDF layers. Figure 11 shows the result of EFISHG measurement, where the electric field across the pentacene layer is recorded.⁸⁶⁾ Results clearly verify the proposed two-step polarization reversal process by the two different hysteresis loops: one loop is shown in Fig. 11 corresponding to peaks A and B, and the other loop corresponds to peak C. Results of EFISHG suggest that the interaction of interfacial charge and ferroelectric polarization is responsible for this two-step process. The two-step turn over strongly depends on organic semiconductor materials, where the interaction at the interface between the ferroelectric layer and the semiconductor layer is different.^87–91) EFISHG measurement probes well such differences and is available for the development of memory devices.

Zoom In Zoom Out Reset image size

There are many types of OSC, e.g., bilayer type and blended type. Among them, bulk heterojunction (BHJ) OSCs have been paid much attention in terms of their conversion efficiency. However, the basic mechanism of carrier behavior is so complex, and the development of techniques available for probing carrier behaviors in OSCs is anticipated, for obtaining a complete picture of carrier behaviors. In BHJ OSCs, electron donor and acceptor molecules are mixed to introduce a larger contacting area for creating excitons to be separated into electrons and holes efficiently. However, it is very speculative to identify carrier paths in such devices. The EFISHG measurement is very useful for investigating fundamental processes, not only in bilayer (double-active-layer) OSCs but also in blended-type OSCs.^55,92–100) The main reason is that the generation of the EFISHG depends on the material properties of the targeted sample. Consequently, it is possible to observe and study different material components in the BHJ layer individually by choosing two appropriate laser wavelengths. This is an advantage of EFISHG for the study of the carrier path in BHJ OSCs. For example, for OSCs codeposited with pentacene and C60, EFISHG measurement has been carried out at two laser wavelengths of 1000 and 860 nm, by which carrier behaviors inside the pentacene and C60 have been selectively probed. As a result, the two carrier paths for electrons and holes have been identified from the EFISHG response by the application of a laser pulse to the OSCs. That is, two types of electric field pointing in opposite directions are identified as a result of the selective probing of SHG activation from C60 and pentacene. Also, under open-circuit conditions, the transient process of the establishment of the open-circuit voltage inside the co-deposited layer has been directly probed in terms of the photovoltaic effect. Figure 12 shows an example of the EFISHG response. As we can see in the figure, we can identify the difference in the generation of EFISHG, suggesting two carrier paths in OSCs.⁹²⁾ The EFISHG provides an additional promising method for studying the carrier path of electrons and holes as well as the dissociation of excitons in BHJ OSCs.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

As mentioned above, EFISHG measurement can be applied to studying carrier behaviors in organic devices, including OFETs, OSCs, and OLEDs. Obviously, this method has potential applications in the study of carrier behaviors in inorganic devices.