Modeling and visualization of carrier motion in organic films by optical second harmonic generation and Maxwell-displacement current

Since the discovery of conducting organic materials, organic devices have attracted much attention in electronics. Among them are organic light emitting diodes, organic field effect transistors, organic memory devices and so forth. In these electronic devices, organic semiconductors are used as active layers to realize their own device function, on the basis of general semiconductor device physics [96]. 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, intrinsic carrier density is quite low in active organic layers. As a result, carrier injection process makes a dominant contribution. We can see such examples in organic field effect transistors and organic light emitting diodes, whose device performance are governed by the carrier injection process. This situation is very similar to the carrier transport in dielectric materials. Accordingly, it is a very effective way to directly measure electric field distribution changes in active layers in these organic devices for analyzing and modeling carrier behaviors. This is a dielectric physics approach that is helpful for analyzing carrier injection and transport of dielectric materials [4, 5, 9]. As already described in section 2, EFISHG measurement is capable of detecting an electric field formed in organic devices due to static electric fields by an external applied DC voltage and time-varying electrostatic field by injected carriers. 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 explored [81, 97], and the electric field distribution before hole injection is shown to be in good agreement with the distribution analyzed using the rigorous solution of the Laplace field of the electrode system of OFETs [98, 99]. Furthermore, the electric field distribution originated from injected carriers has been determined from the EFISHG measurements, and it has been shown that the charge distribution along the OFET channel is basically determined based on a Maxwell–Wagner model that accounts for carrier accumulation at the interface between the gate-insulator/active organic layer interface [98–101].

Figure 8 shows a typical example of the EFISHG measurement carried out for top-contact pentacene OFETs with Au source and drain electrodes [98]. Under the condition of no carrier injection of the OFETs, EFISHG is shown to be activated to satisfy the rigorous solution of the Laplace equation of a three-electrode system of the OFETs [98, 99], as shown in figure 8(a). On the other hand, under the condition of hole-injection, the intensity of EFISHG decreases due to the space charge field formed along the channel by injected holes, as shown in figure 8(b) [97, 99]. Using equations (8) and (9), the carrier distribution along the channel is determined using the EFISHG measurement, as plotted in figure 8(b). These results show that carrier accumulation along the channel is governed by the Maxwell–Wagner effect, and the distribution is basically determined based on a Maxwell–Wagner model [84, 102, 103]. Our further EFISHG study shows that the carrier distribution along the channel in the steady-state that follows a solution of a classical differential equation of current that describes the continuity of carrier transport along the channel, which is modeled based on a transmission line model, as an extension of the Maxwell–Wagner model [100, 104]. 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 [100, 104]

$$\begin{eqnarray}&&V(x)={{V}_{0}}\sqrt{1-\frac{x}{L}}\,\,\text{with}\,\,V(0)={{V}_{0}}\,\,\text{and}\,\,V(L)=0,\end{eqnarray} \tag{ 11 }$$

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

$$\begin{eqnarray}&&E(x)=\frac{{{V}_{0}}}{2\sqrt{L(L-x)}}.\end{eqnarray} \tag{ 12 }$$

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EFISHG probes this electric field distribution well, and generates the signals that follow equation (8) with equation (12), where $E(0)$ of equation (8) is replaced by the $E(x)$ of equation (12).

As described above, it is clear that EFISHG is available for probing the steady-state carrier distribution along the channel of OFETs. By the way, some organic materials show ambipolar behavior, which means that electrons and holes are allowed to enter into materials from the electrodes. In the field of electrical insulation engineering, this carrier behavior is called double-injection [4]. Consequently probing electron and hole injection, and their distribution in organic devices is also important. For example, for organic light emitting device application, double carrier injection, i.e. electron and hole injection, is a key for device operation. Using ambipolar organic light emitting transistors (OLETs) with an active layer of the green-light-emitting polymer of poly(9,9-dioctylfluorene-alt-benzothiadiazole)(F8BT), which has a photo luminescent peak at a wavelength of 560 nm, the EFISHG measurement has been employed using a laser beam with a wavelength of 840 nm [79, 101]. Of course, for the EFISHG experiment, we need to remove the influence of photoluminescence, by using a band pass filter so that we can probe the EFISHG that is generated at a wavelength of 420 nm only. The EFISHG experiments showed that there is actually a zero-potential position in the channel, which corresponds to the meeting point of electrons and holes for the electroluminescence [101].

As mentioned in section 2, it is possible to probe carrier motion by means of the TRM-SHG. Using the electrode system illustrated in figure 7, i.e. top-contact pentacene FETs with a Au source and drain electrodes, TRM-SHG measurement has been carried out using OFETs with a channel length of 40 µm. Here the pentacene was deposited at room temperature, i.e. around 20 °C. Figure 9(a) shows the TRM-SHG image in the channel region of the pentacene FET with a 500 nm thick SiO₂ gate insulator, where the SHG image was obtained along with carrier motions after a step positive voltage was applied. That is, a positive voltage V_pulse = 70 V was applied to the source electrode with respect to the gate and drain electrodes that were electrically shorted and grounded, i.e. V_ds = V_gs =  −70 V. At $\tau$ = 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 the Laplace electric field E₀, parallel to the channel, is formed only around the source electrode. Interestingly, as is clearly shown in the image, the emission band of the SHG signal gradually moves in the channel from the source to drain electrode. The visualized emission band motion, which starts from the source electrode, evidently indicates hole-injection from the Au-source electrode. That is, the pentacene FET shows a p-type semiconductor behavior, where the majority of carriers are holes injected from the source electrode and the carrier mobility is 0.1–0.2 cm² V⁻¹ s⁻¹. Note that the SHG image appears only in the region within a radius of around 150 µm, owing to the spot size of the laser (see the region indicated by a circle in figure 9(a)). To further clarify the hole transport mechanism across the channel, we plotted the SHG peak position with respect to elapsed time, as shown in figure 9(b) [37, 82, 105]. From figures 9(a) and (b), it is clear that holes travel in the direction from the source Au electrode to the drain electrode, on satisfying the square root time dependence [105, 106]. This time dependence reflects the interface charge propagation process (see figure 9(b) and [100, 107]), and well supports a Maxwell–Wagner effect model that is employed for analyzing transient carrier behaviors along the OFET channel. This is also well supported by a transmission line model that is basically based on the extension of the Maxwell–Wagner model. In physics, carriers propagate along the interface between the gate insulator and active layer, and this situation is roughly described as the interface accumulated charge, ${{Q}_{s}}={{C}_{g}}\left({{V}_{\text{gs}}}-{{V}_{\text{th}}}-\frac{{{V}_{\text{ds}}}}{2}\right)$, spreads with a velocity of $v=\mu \overline{V}/L$, and is thus illustrated by using a RC ladder circuit [100]. Here ${{C}_{g}}$ is the gate capacitor and ${{V}_{\text{th}}}$ is the threshold voltage. ${{V}_{\text{gs}}}$ is the applied gate-source voltage and ${{V}_{\text{ds}}}$ is the applied drain-source voltage and $\overline{V}$ ($\approx {{V}_{\text{gs}}}-{{V}_{\text{th}}}-{{V}_{\text{ds}}}/2$) is the average voltage for carrier drift in the FET channel region. In more detail, the transit time ${{t}_{\text{tr}}}\left(=L/v\right)$ is approximately given by [100]

$$\begin{eqnarray}&&{{t}_{\text{tr}}}\approx \frac{{{L}^{2}}}{\mu \left({{V}_{\text{gs}}}-{{V}_{\text{th}}}-\frac{{{V}_{\text{ds}}}}{2}\right)}.\end{eqnarray} \tag{ 13 }$$

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Here $\mu$ is carrier mobility, and $L$ is channel length. Equation (13) suggests that the carrier migrates into the channel region on satisfying the square root time dependence. The computer simulation based on a classical drift-diffusion equation supports this prediction [106–109].

On the other hand, under the application of a negative step voltage, the position of the SHG peak does not move, and the SHG signals are only concentrated around the edge of the source electrode during the measurement. Results suggest that electron injection is minor and this process is negligible [26, 110].

By the way, carrier injection is governed by the electrode materials and semiconductors. Accordingly the film preparation condition is very important, and we can prepare pentacene layers that exhibit ambipolar behavior by controlling the substrate temperature during the deposition of the pentacene layers. Figure 10(a) shows the ${{I}_{\text{ds}}}$–${{V}_{\text{gs}}}$ characteristics of pentacene FET with a 500 nm thick SiO₂ gate insulator, where the pentacene film was deposited at a substrate temperature of 70 °C and the channel length is 50 $\mu \text{m}$. An ambipolar behavior is seen in the ${{I}_{\text{ds}}}$–${{V}_{\text{gs}}}$ characteristics. That is, both electrons and holes serve as carriers, depending on the applied ${{V}_{\text{gs}}}$. By employing the TRM-SHG experiment, we get the relationship between the position of the carrier front with elapsed time by applying the step voltage ${{V}_{\text{gs}}}$. The results show that the hole mobility is much higher than the electron mobility, i.e. about 100 times higher, as portrayed in figures 10(b) and (c) [111]. With consideration of these results, we can visualize the double carrier injection process that leads to recombination between electrons and holes injected from the source and drain electrodes. Figure 11 shows the TRM-EFISHG experiment, where a negative step voltage of V_dg =  −100 V was applied on the drain electrode with respect to the gate, and at the same time a positive step voltage of V_sg = +100 V was applied on the source electrode. As can be seen in the images of figure 11, double carrier injection followed by the electron–hole recombination is clearly demonstrated. At the time corresponding to carrier recombination, a bright band is seen due to the formation of a high electric field between the electrons and holes injected into the channel from the drain and source electrodes, respectively.

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As shown in figure 11, the TRM-EFISHG measurements allow us to visualize the double carrier transport process, i.e. double carrier injection and recombination. Consequently, this technique is available for studying the electro-light emitting process that starts from double carrier injection leading to carrier recombination, and also for visualizing the process that leads to the pre-electrical breakdown in devices.

Further we should note that carrier propagation is dependent on the interfacial film condition of the channel, e.g. carrier traps, morphology, etc. Equation (8) with equation (9) suggests that TRM-SHG is available for monitoring the contribution of the surface states of the channel. To confirm the potentiality of the TRM-SHG measurements, similar experiments were carried out for pentacene-FETs with a 100 nm thick poly-methylmethacrylate (PMMA) layer on the surface of the gate SiO₂ insulator [112, 113]. The SHG intensity is concentrated in the front region of the propagating SHG profile [112]. Results indicate that the space-charge field distribution is being formed along the channel due to the trapping of holes. Analysis based on a carrier trap model accounts well for the TRM-SHG experiments. That is, TRM-SHG is effective to probe the interface states of the channel region.

It is also noteworthy that the activation of EFISHG is material dependent, due to the material dependent parameter ${{\chi}^{(3)}}(2\omega ;0,\omega ,\omega)$ with angular frequency $\omega$ in equation (8). Consequently, probing carrier motion in one of the layers in multi-layer systems is possible. Actually, we have already demonstrated the detection of such carrier motions in OFETs with an active layer of double-layer system, e.g. OFETs with a C60/pentacene active layer, etc [71, 114, 115], where the hole carrier transport in the pentacene layer and electron carrier transport in C60 were selectively probed by choosing appropriate wavelengths of incident laser, which activate pentacene at 1120 nm and C60 at 1000 nm, respectively. That is, we can directly probe carrier motions in one of the multilayers by choosing an appropriate incident laser wavelength. The EFISHG measurement for pentacene/C60 OFETs showed that electrons are actually transported in the C60 layer, etc.

Carrier transport is strongly dependent on the film preparation condition, crystallinity of deposited films, and so forth. There are many film preparation methods, such as dipping, spin-coating, evaporation, and others. Accordingly the anisotropic property is induced in deposited films, and the organic film shows the anisotropic carrier transport property; carrier transport along the long-molecular axis direction is different from transport perpendicular to the long-molecular axis direction. Evaluating the anisotropic carrier behavior is very important for device technology, and also for understanding the carrier transport mechanism. By using the TRM-EFISHG measurement, we can visualize the anisotropic carrier transport behavior in organic thin films by using a round shape electrode system [116]. Figure 12(a) shows the visualized SHG images by holes into poly[(9,9-dioctylfluorenyl-2,7-diyl)-co-bithiophene]) (F8T2)-films from the edge of the round shape Au electrode. Here the F8T2 films were prepared using the floating film transfer method (FTM). As we can see in the set of figures (see figures 12(a-1)–(a-3)), the spreading speed of holes from the edge of the round shape electrode is totally directional dependent on the film. As we can see in the distorted SHG image of injected holes around the Au edge of electrode, carrier spreading is seen along the FTM direction, i.e. parallel to the molecular long-axis direction of F8T2. On the other hand, the visualized carrier behavior of holes in pentacene films deposited by thermal evaporation is isotropic, as shown in figures 12(b-1)–(b-3). In this way, we can evaluate the anisotropic carrier behaviors by using the TRM-EFISHG microscopic images [116, 117].

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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 [130]. Using an energy diagram of the molecules, e.g. HOMO and LUMO states, (highest occupied molecular orbital and lowest unoccupied molecular orbital, respectively) much research has been carried out for improving device performance [131]. Ideas of using low work function electrodes, depositing dipolar layers on the surface of electrodes, utilizing multilayer systems comprising hole- and electron-transport, electroluminescent layers, and so forth have been presented [131, 132]. These important ideas are well accepted to achieve high-performance OLED devices [133]. However, owing to the ambiguities of energetics at the organic-metal and organic-organic interfaces, the carrier behavior in OLED devices is 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 electroluminescence (EL). Hence, one of the most effective ways is to directly probe carrier motion in OLED devices. Probing carrier behaviors in combination with charge accumulation at the interface is particularly important, because the Maxwell–Wagner effect suggests carrier accumulation at the interface of layers, and this accumulation contributes to form the space charge field. Consequently, EFISHG measurement coupled with the Maxwell–Wagner model analysis is very helpful for this purpose [28, 29, 89, 134, 135]. Making use of the TRM-EFISHG experiments on double layer OLEDs with N,N'-di-[(1-naphthyl)-N,N'-diphenyl]-(1,10-biphenyl)-4,4'-diamine ($\alpha$-NPD) and tris (8-hydroxy-quinolinato) aluminum(III) (Alq3) layers by applying a step voltage showed well the charging and discharging of carriers on electrodes and carrier transit across the $\alpha$-NPD and Alq3 layers, and the non-reversal charging and discharging processes resulted from the different carrier behaviors accompanied by ordinary green EL [29, 89].

To analyze carrier behaviors of OLED devices, EFISHG measurement is carried out by laser irradiation with a wavelength of 820 nm, in order to selectively measure the electric field formed in the $\alpha$-NPD layer by probing the SHG $I(2\omega)$ with a wavelength of 410 nm [28]. Upon application of the external voltage ${{V}_{\text{ex}}}(t)$, the electric field across the $\alpha$-NPD layer ${{E}_{1}}$ varies with time, on satisfying the following relation:

$$\begin{eqnarray}&&{{E}_{1}}(t)=\frac{{{C}_{2}}}{{{C}_{1}}+{{C}_{2}}}\cdot {{V}_{\text{ex}}}(t)\cdot \frac{1}{{{d}_{1}}}-\frac{{{Q}_{s}}(t)}{{{C}_{1}}+{{C}_{2}}}\cdot \frac{1}{{{d}_{1}}}+{{E}_{1}}_{b}\end{eqnarray} \tag{ 14 }$$

Here ${{C}_{1}}$ and ${{C}_{2}}$ are the capacitance of the $\alpha$-NPD layer and Alq3 layer, respectively, ${{d}_{1}}$ is the thickness of the $\alpha$-NPD layer. ${{E}_{1}}_{b}$ is the electric field caused by the work function difference etc, which corresponds to other terms in equation (8). ${{Q}_{s}}(t)$ is the interface charge accumulated at the interface between $\alpha$-NPD and Alq3 layers owing to the Maxwell–Wagner effect. The EFISHG is given by equation (8) with ${{E}_{1}}(t)$ of equation (14), instead of $E(0)$. That is, the generated EFISHG changes on satisfying equation (14), showing that interface charge ${{Q}_{s}}(t)$ is accumulated with a response time governed by the Maxwell–Wagner relaxation time.

Figures 13 and 14 show, respectively, EL and EFISHG measurements under application of an AC square voltage to the ITO/$\alpha$-NPD /Alq3/Al OLEDs [136, 137]. Two kinds of AC square voltage waveforms are chosen, one with no DC components (square voltage a), and the other with DC components (square voltage b). As figure 13 shows, EL is generated in accordance with the applied AC square voltage, where the generation is dependent on the applied frequency and also the waveform. In more detail, the EL intensity gradually decays with the increase of the frequency of the applied AC square voltage, and reaches a minimum at the frequency corresponding to the carrier transit time of the Alq3 layer. Interestingly, the EL intensity again increased by the application of further higher frequency AC square voltages, relying on the DC component of the AC square voltages [138–140]. Results suggest the presence of two EL modes, where the space charge field caused by the interface charge makes a significant contribution. That is, in the low frequency region, accumulated holes at the interface suppress hole injection and lead to the decrease of the EL intensity activated by the recombination of holes and electrons injected from opposite electrodes. On the other hand, in the high frequency region the accumulated holes assist electron injection and result in the increase of EL intensity activated by the recombination of the interfacial accumulated holes and injected electrons from Al electrode. However this is merely speculation, and we need to make clear the presence of this space charge field caused from accumulated interface charges and its contribution. For this purpose the EFISHG measurement is useful. Figure 14 shows the EFISHG measurements in the low frequency region, where two kinds of AC square voltage waveforms are chosen, i.e. one with no DC component (square voltage a), the other with a DC component (square voltage b) [136–138]. From the top to bottom, the applied external voltage, ${{V}_{\text{ex}}}(t)$, generated EFISHG intensity $I\left(2\omega \right)$, electric field ${{E}_{1}}(t)$ and accumulated interface charge ${{Q}_{s}}(t)$ are plotted. Here the generated EFISHG intensity $I\left(2\omega \right)$ is plotted by $\sqrt{I\left(2\omega \right)}$ with consideration of the relation between the electric field and the generated EFISHG (see equation (8)). ${{Q}_{s}}(t)$ is calculated using the Gauss law of equation (7) with the EFISHG equation (8). Under the AC voltage application with no DC component (square voltage a), in region A, ${{Q}_{s}}$ is zero, in prior to voltage application ${{V}_{\text{ex}}}$ = +20 V. In region B, external voltage ${{V}_{\text{ex}}}$ = +20 V induces charges on the ITO and Al electrodes with a circuit response time ${{t}_{\text{RC}}}$($=RC$) $\sim$ 10⁻⁷ s, and forms an electric field in the α-NPD layer as high as ${{E}_{\text{RC}}}=$ 5.6  ×  10⁵ V cm⁻¹. After that, in region C, holes are injected from the ITO to α-NPD layer and electrons are injected from the Al to Alq3 layer for radiative EL recombination. The holes smoothly transport in the α-NPD layer (hole mobility: ${{\mu}_{h}}\sim$10⁻⁴ cm² V⁻¹s⁻¹) but electrons go through the Alq3 layer slowly (electron mobility: ${{\mu}_{e}}\sim$ 10⁻⁵ cm² V⁻¹s⁻¹), due to the imbalance of hole and electron transport in the layers. As the result, holes accumulate excessively at the α-NPD/Alq3 interface, and the electric field in the α-NPD layer decreases. The EFISHG shows that the electric field actually decreases from ${{E}_{\text{RC}}}=$ 5.6  ×  10⁵ V cm⁻¹ to ${{E}_{Qs}}=$ 4.8  ×  10⁵ V cm⁻¹ at ${{t}_{\text{d}}}=$ 10⁻⁵ s due to excess hole accumulation ${{Q}_{s}}=$ 6.5  ×  10⁻⁸ C cm⁻².On the other hand, under AC voltage application with a DC component (square voltage b), electrode charges are induced on the ITO and Al electrodes and holes accumulated excessively at the α-NPD/Alq3 interface, in a way similar to the carrier processes under the square voltage a. However, excess holes stay at the α-NPD/Alq3 interface in regions A and E $Q_{s}^{0}$= 3.0  ×  10⁻⁸ C cm⁻², as evidenced by the EFISHG measurement. These results support the prediction that there are accumulated holes at the interface, and these charges suppress hole injection in the low frequency region and lead to the decrease of the EL intensity. Using the EFISHG results, we can carry out a similar discussion on the presence of interface charge and its contribution, in terms of the EL in the high frequency region [137, 140]. In this way, we can monitor dynamical carrier behaviors in charging and discharging processes in EL devices, by means of EFISHG.

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It is noteworthy that electroluminescence has received much attention as one of the pre-breakdown phenomena in the field of electrical insulation engineering for the past decade, where the main research interest is to detect very weak EL signals for the diagnostics of insulators. However, using EFISHG provides a new way for the detection of the pre-breakdown phenomena because carrier motions leading to carrier recombination can be monitored, as shown in figure 15 [141].

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Ferroelectric polymers are widely used as memory materials, where the copolymer of vinylidene fluoride (VDF) and trifluoroethylene (TrFE), P(VDF-TrFE) stands out as its bistable and remanent polarization can be repeatedly turned-over by an external electric field [142, 143]. Recently, ferroelectric polymers have also been used in electronic devices such as organic field effect transistors (OFETs) [144, 145] and organic photovoltaic cells (OPVs) [146, 147], where a strong internal electric field induced in the active layer of these devices by 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 deeply studied in terms of the turn-over of the spontaneous polarization of ferroelectric layers [148, 149]. For 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 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 means of electrical measurements such as displacement current measurement (DCM) using a ramp voltage [150, 151], but these are no longer sufficient to account for carrier behaviors in a variety of organic semiconductor devices being utilized with ferroelectric P(VDF-TrFE) layers. Using EFISHG probes, the electric field change induced in organic devices with a ferro-electric layer gives much information on the carrier behavior in these devices [152–154].

Figure 16 shows a typical example of DCM measurements for metal-ferroelectric layer-metal (MFM) and metal-ferroelectric layer-semiconductor-metal (MFSM) (the inset of figure 16(a)) devices, which were prepared on patterned indium zinc oxide (IZO) substrates [30]. A P(VDF-TrFE) (VDF:TrFE = 72: 28 mol. %) layer with a thickness of 200 nm was spin-coated on the substrate, and then a pentacene layer (200 nm, for the MFSM device) and gold electrode were thermally evaporated successively. For the DCM measurement, a ramp voltage was applied on the IZO electrode. Figure 16(a) shows the results of the DCM for the MFM device. Two peaks (peaks A and B) are clearly observed at symmetric positions at voltages corresponding to the coercive electric field ${{E}_{c}}$ of 0.6 MV cm⁻¹, and show no dependence on the sweeping frequencies of the ramp voltage. These results suggest that the appearance of peaks A and B are due to the turn-over of spontaneous polarization.

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On the other hand, for MFSM devices, 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 ferro-electric layer in the pentacene/P(VDF-TrFE) double-layer device. However this is merely speculation. For studying carrier behaviors with the turn-over of polarization, it is very helpful to measure the electric field formed in pentacene and P(VDF-TrFE) layers. Figure 17 shows the result of EFISHG measurement, where the electric field across the pentacene layer is recorded [31]. Results clearly verify the proposed two step polarization reversal process by the two different hysteresis loops: one loop is in figure 17, corresponding to peak A and B, and the other loop corresponding to peak C [148]. Results of EFISHG suggest that the interaction of interfacial charge and ferroelectric polarization is responsible for this two-step process. It is noteworthy that the situation of the 2-step turn-over strongly depends on the organic semiconductor materials, where the interaction at the interface between the ferroelectric layer and semiconductor layer is quite different. For example, for P(VDF-TrFE) /C60/Au (or Al) double layer devices, only two peaks appear, but the peak position appears at quite different voltages from those of the P(VDF-TrFE) /pentacene /Au double layer device, owing to the potential drop across the C60 layers. Using the EFISHG measurement is an effective way for clarifying the contribution of organic semiconductor layers [153, 155].

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There are many kinds of organic solar cells (OSCs), e.g. bilayer type, blended-type, etc. Among them the bulk hetero-junctions (BHJs) OSCs have been paid much attention in terms of the conversion efficiency of OSCs. Using BHJs, an idea for the introduction of hole and electron blocking layers has also been developed. However the basic mechanism of carrier behavior is getting more and more complex. Thus the development of techniques available for probing carrier behaviors in OSCs is anticipated, for getting the whole picture of carrier behaviors.

In BHJs 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 the identification of carrier paths is very speculative in such devices. The EFISHG measurement is very useful to investigate fundamental processes, not only in bilayer (double active layer) OSCs but also in blended-type OSCs [156–160]. 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 carrier path in BHJ OSCs. For example, for OSCs co-deposited with pentacene and C60, EFISHG measurement has been carried out at two laser wavelengths of 1000 nm and 860 nm, by which carrier behaviors inside the pentacene and C60 have been selectively probed. As a result, the presence of two carrier paths for electrons and holes has been identified from the EFISHG response by application of a laser pulse to the OSCs [63]. The EFISHG provides an additional promising method to study the carrier path of electrons and holes as well as dissociation of excitons in BHJ OSCs [161, 162]. Furthermore, recently much attention has been focused on perovskite solar cells, where the dissociation of excitons is postulated to happen in the bulk of the solar cells. We believe that EFISHG can be employed to make clear the contribution of the internal electric field, and thus the technique is available for studying the carrier process.

As mentioned above, EFISHG is available for studying carrier behaviors in organic devices. Finally we should note that this method has a potentiality to study carrier behaviors in inorganic devices, such as amorphous silicon (a-Si) solar cells [163] and AlGaN/GaN high electron mobility transistors (HEMT) [164, 165].