Nonthermal Equilibrium Process of Charge Carrier Extraction in Metal/Insulator/Organic Semiconductor/Metal (MIOM) Junction

: This paper presents the concept and experimental evidence for the nonthermal equilibrium (NTE) process of charge carrier extraction in metal/insulator/organic semiconductor/metal (MIOM) capacitors. These capacitors are structurally similar to metal/insulator/semiconductor/(metal) (MIS) capacitors found in standard semiconductor textbooks. The difference between the two capacitors is that the (organic) semiconductor/metal contacts in the MIOM capacitors are of the Schottky type, whereas the contacts in the MIS capacitors are of the ohmic type. Moreover, the mobilities of most organic semiconductors are signiﬁcantly lower than those of inorganic semiconductors. As the MIOM structure is identical to the electrode portion of an organic ﬁeld-effect transistor (OFET) with top-contact and bottom-gate electrodes, the hysteretic behavior of the OFET transfer characteristics can be deduced from the NTE phenomenon observed in MIOM


Introduction
Organic semiconductors (OSs) exhibit very low conductivities without chemical doping; however, with the injection of dopants they exhibit high conductivities. This characteristic has been employed in the fabrication of organic field-effect transistors (OFETs), which has been extensively studied in recent years. These devices are used not only for practical applications but also for the determination of mobility in OSs [1][2][3]. Figure 1a shows the typical structure of a top-contact bottom-gate-type OFET in which the source (S)/drain (D) electrodes are formed on an OS film fabricated on a film of insulator (INS) and gate (G) electrodes. Figure 1b shows a capacitor composed of metal 1 (M1)/INS/OS/metal 2 (M2). The metal/insulator/organic semiconductor/metal (MIOM) capacitor is identical to the electrode portion of the OFET.
MIOM capacitors are equivalent to metal/INS/semiconductor/(metal) (MIS) capacitors found in standard textbooks [4] when OS/M2 contacts form an ohmic junction. However, when the OS/M2 contact forms a Schottky junction, charge carrier extraction based on nonthermal equilibrium (NTE) processes frequently occurs. This behavior is significantly different from that of the MIS capacitors. This NTE charge extraction process can be one of the origins of the hysteresis behavior in the transfer characteristics of OFETs [5][6][7][8][9][10][11]. However, detailed experiments on MIOM capacitors have not been conducted yet. In this study, we theoretically and experimentally describe a model of the NTE process of charge extraction [12,13]. This model was derived from several studies based on accumulated charge measurements (ACM) [12][13][14][15][16][17][18][19] to determine the electron and hole injection barriers in OS films. The ACM allowed us to estimate the potential distribution in the OS based on experimental data. The obtained values of the injection barriers were approximately consistent with those obtained using ultra violet photoelectron spectroscopy [20,21], this study, we theoretically and experimentally describe a model of the NTE process of charge extraction [12,13]. This model was derived from several studies based on accumulated charge measurements (ACM) [12][13][14][15][16][17][18][19] to determine the electron and hole injection barriers in OS films. The ACM allowed us to estimate the potential distribution in the OS based on experimental data. The obtained values of the injection barriers were approximately consistent with those obtained using ultra violet photoelectron spectroscopy [20,21], photoemission yield spectroscopy [22,23], inverse photoelectron spectroscopy [24], and low-energy inverse photoelectron spectroscopy [25]. Therefore, we believe that the validity of the model has been confirmed in previous studies on ACM. The components of the two electrodes are not always the same. Note that the MIOM capacitor is identical to the electrode portion of the OFET. The panel (b) was reproduced with permission [13]. Copyright © 2021, AIP Publishing. Figure 2 shows the calculations of potential distribution in the OS layer when a bias voltage, Vbias, is applied to an MIOM capacitor, with a hole injection barrier of 0.4 eV for the Schottky junction between the OS and M2. These calculations assume that there are no charge-capturing dopants in the OSs. This assumption is considered reasonable for OSs in which doping is difficult. Figure 2a-d show the potential diagrams of the thermal equilibrium (TE) state obtained by solving the Poisson-Boltzmann equation [13]. As there is a Schottky barrier at the OS/M2 interface, no charge is injected when Vbias is low (Figure 2b). The device operates as a capacitor with a series capacitance (C0) of the OS layer (COS) and INS layer (CINS), that is, C0 = CINSCOS/(CINS + COS). At this stage, the total accumulated charge Qtotal is the same as the interface charge Q0 between the OS and M2, that is, Qtotal = Q0 = C0Vbias. With an increase in Vbias, the gap between the Fermi level of the M2 electrode and the highest occupied molecular orbital (HOMO) near the INS decreased and holes were injected into the OS layer (Figure 2c,d). Consequently, the OS layer near the INS layer exhibited band bending owing to the accumulated holes. The degree of band bending increased as the amount of hole injection increased. However, this band bending is limited to the vicinity of the INS/OS interface, and the approximate shape of the potential curve in the OS layer is dominated by Q0 at the OS/M2 interface. The HOMO level of the OS at the OS/M2 interface was pinned by the Fermi level of M2 and did not exceed this level. Thus, once the holes were injected, most of the voltage applied to the capacitor decreased within the insulator layer.  Figure 2 shows the calculations of potential distribution in the OS layer when a bias voltage, V bias , is applied to an MIOM capacitor, with a hole injection barrier of 0.4 eV for the Schottky junction between the OS and M2. These calculations assume that there are no charge-capturing dopants in the OSs. This assumption is considered reasonable for OSs in which doping is difficult. Figure 2a-d show the potential diagrams of the thermal equilibrium (TE) state obtained by solving the Poisson-Boltzmann equation [13]. As there is a Schottky barrier at the OS/M2 interface, no charge is injected when V bias is low (Figure 2b). The device operates as a capacitor with a series capacitance (C 0 ) of the OS layer (C OS ) and INS layer (C INS ), that is, C 0 = C INS C OS /(C INS + C OS ). At this stage, the total accumulated charge Q total is the same as the interface charge Q 0 between the OS and M2, that is, Q total = Q 0 = C 0 V bias . With an increase in V bias , the gap between the Fermi level of the M2 electrode and the highest occupied molecular orbital (HOMO) near the INS decreased and holes were injected into the OS layer (Figure 2c,d). Consequently, the OS layer near the INS layer exhibited band bending owing to the accumulated holes. The degree of band bending increased as the amount of hole injection increased. However, this band bending is limited to the vicinity of the INS/OS interface, and the approximate shape of the potential curve in the OS layer is dominated by Q 0 at the OS/M2 interface. The HOMO level of the OS at the OS/M2 interface was pinned by the Fermi level of M2 and did not exceed this level. Thus, once the holes were injected, most of the voltage applied to the capacitor decreased within the insulator layer. Furthermore, we considered the charge extraction from this state by decreasing Vbias. If charge extraction occurs in the TE, it is the reverse of the charge injection case, with charge extraction at the INS/OS interface and then at the OS/M2 interface. However, as the electric field applied to the sample is still directed from the M2 electrode to the INS side, whether this TE reverse process occurs depends on carrier diffusion. If carrier diffusion is unlikely, the electric field in the OS, which is proportional to Q0, decreases rapidly before the charge is extracted from the INS/OS interface. This is the case for the NTE model [13]. When Q0 is slightly reversed, the charge at the INS/OS interface immediately begins to move because of the influence of the electric field. Therefore, the holes near the INS/OS interface are continuously extracted, whereas Q0 remains near zero, as shown in Figure  2e,f. Consequently, the initial state is achieved. In the NTE model, the potential in the NTE state is semiempirically reproduced based on the potential calculation in the TE state, considering the series of processes described above. States (e) and (f) are not in the TE but are kept metastable by the electric field. If an ohmic junction is formed at the OS/M2 interface, no such metastable state occurs, because the electric field near the OS/M2 interface is negligible. In other words, the formation of such a metastable state is unique to MIOM capacitors with Schottky junctions at the OS/M2 interface.

Concept of NTE Process of Charge Extraction
In the following section, experimental evidence supporting this model is presented. Furthermore, we considered the charge extraction from this state by decreasing V bias . If charge extraction occurs in the TE, it is the reverse of the charge injection case, with charge extraction at the INS/OS interface and then at the OS/M2 interface. However, as the electric field applied to the sample is still directed from the M2 electrode to the INS side, whether this TE reverse process occurs depends on carrier diffusion. If carrier diffusion is unlikely, the electric field in the OS, which is proportional to Q 0 , decreases rapidly before the charge is extracted from the INS/OS interface. This is the case for the NTE model [13]. When Q 0 is slightly reversed, the charge at the INS/OS interface immediately begins to move because of the influence of the electric field. Therefore, the holes near the INS/OS interface are continuously extracted, whereas Q 0 remains near zero, as shown in Figure 2e,f. Consequently, the initial state is achieved. In the NTE model, the potential in the NTE state is semiempirically reproduced based on the potential calculation in the TE state, considering the series of processes described above. States (e) and (f) are not in the TE but are kept metastable by the electric field. If an ohmic junction is formed at the OS/M2 interface, no such metastable state occurs, because the electric field near the OS/M2 interface is negligible. In other words, the formation of such a metastable state is unique to MIOM capacitors with Schottky junctions at the OS/M2 interface.

Displacement Current Measurement
In the following section, experimental evidence supporting this model is presented.

Displacement Current Measurement
The simplest experimental technique for detecting the NTE process during charge extraction is the displacement current measurement. Figure 3a shows the experimental setup. In this experiment, holes (or electrons) were injected through the Schottky barrier at the OS/M2 interface by applying a positive (or negative) V bias at V off for a long period. The injected holes (or electrons) were extracted using voltage sweeps. The simplest experimental technique for detecting the NTE process during charge extraction is the displacement current measurement. Figure 3a shows the experimental setup. In this experiment, holes (or electrons) were injected through the Schottky barrier at the OS/M2 interface by applying a positive (or negative) Vbias at Voff for a long period. The injected holes (or electrons) were extracted using voltage sweeps.    Figure 3b shows a typical example of the displacement current used for hole extraction during the TE [13]. The sample used was n-Si/SiO2 (100 nm)/pentacene (50 nm)/Au. A sample behaved as a series capacitor if no charge was injected into (or extracted from) the OS layer. In that case, the displacement current is given by −I = −C0dVbias/dt, which is indicated by a dotted line in the figure. Here, C0 is the series capacitance of the INS and OS layers, as previously mentioned. If a current was observed above the dotted line, the accumulated charge near the INS/OS interface was extracted. In the pentacene sample (Figure 3b), the charge accumulated near the INS/OS interface was immediately extracted when the applied positive bias was reduced. This is direct evidence of the TE-type charge extraction in this sample. At V off = −3 and −6 V, V bias = V off is insufficient to inject electrons (a). The threshold of the decrease in displacement current is due to the hole injection from M2 to the OS (b,c). At V off = −9, −12, −15, −18, and −21 V, the time dependence of the displacement current is almost the same, and the displacement current at t < 6.5 ms is approximately −C 0 A. This is the direct evidence indicating electron injection by V off (d) and the NTE process of electron extraction (d)→(e). As the voltage drops in the OS layer at V bias = V off are almost the same owing to the electron accumulation near the INS/OS interface, the thresholds of the current decrease are also almost the same. After the electrons are extracted (e)→(f), holes are subsequently injected (f)→(g). Figure 3b shows a typical example of the displacement current used for hole extraction during the TE [13]. The sample used was n-Si/SiO 2 (100 nm)/pentacene (50 nm)/Au. A sample behaved as a series capacitor if no charge was injected into (or extracted from) the OS layer. In that case, the displacement current is given by −I = −C 0 dV bias /dt, which is indicated by a dotted line in the figure. Here, C 0 is the series capacitance of the INS and OS layers, as previously mentioned. If a current was observed above the dotted line, the accumulated charge near the INS/OS interface was extracted. In the pentacene sample (Figure 3b), the charge accumulated near the INS/OS interface was immediately extracted when the applied positive bias was reduced. This is direct evidence of the TE-type charge extraction in this sample. Figure 3c shows a typical example of the displacement current used for hole extraction during the NTE. The sample was n-Si/SiO 2 (100 nm)/metal-free phthalocyanine (H 2 Pc, 52 nm)/Au. The displacement current was close to C 0 dV bias /dt up to approximately t = 0.5 ms, and then increased sharply. This confirms that NTE charge extraction occurred, indicating that only the electric field in the OS layer changed in the first stage and that the holes injected at V bias = V off were extracted after the electric field inside the sample almost disappeared.
Currently, it is unclear whether charge carriers were extracted via the TE or NTE processes. However, considering the model shown in Figure 2, we believe that TE charge extraction was enhanced by diffusion processes and tended to occur when the carrier density or mobility was high. For the pentacene/Au sample, TE charge extraction was observed in many of the tested samples [13,15]; however, NTE charge extraction was also observed in some samples [18]. Figure 3d shows the electron extraction experiment for p-Si/SiO 2 (70 nm)/H 2 Pc (44 nm)/Au [12]. Care must be taken when analyzing the data because the hole injection barrier was considerably lower than the electron injection barrier in H 2 Pc/Au. Figure 4 shows a potential diagram derived from the TE and NTE models to explain Figure 3d. In the case of V off = −3 and −6 V, an electric field was generated in the OS layer, but no electrons were injected into the OS. A negative interfacial charge Q 0 was generated at the OS/M2 interface because of the electric field (Figure 4a). When V bias increased in the positive direction, Q 0 decreased and eventually reversed, followed by hole injection. That is, a displacement current reflecting the change in Q 0 was observed initially. Subsequently, a displacement current owing to hole injection was observed (Figure 4b,c).
In the case of V off ≤ −9 V, electron injection at V bias = V off occurred (Figure 4d). In this V off region, the time at which the displacement current began to decrease was almost constant at 6.5 ms (Figure 4e). This is because the voltage drop across the OS became constant when the electrons were injected. Therefore, it was possible to determine whether the electrons were injected by V off based on the obtained experimental data. Although electrons were injected by V off , the displacement current at the beginning of the voltage sweep was by C 0 dV bias /dt. This indicated that the injected electrons were not extracted at the beginning of the voltage sweep, suggesting that NTE electron extraction occurred in this sample.

Accumulated Charge Measurement
Another method to investigate NTE charge extraction is ACM [12,13]. Changes in the accumulated charge are observed in this experiment. As the theoretical calculation of the accumulated charge is much easier than that of the displacement current, the observed data are analyzed more easily in this experiment than in the displacement current measurement. Figure 5a shows the experimental scheme for the ACM. In this experiment, the states V bias = V off and V bias = V a + V off were alternately created to determine the amount of accumulated change Q acc (V a ) = Q total (V a + V off ) − Q total (V off ). Here, Q total (V bias ) is the amount of charge accumulated at the junction when the applied voltage is maintained at V bias for a long period. In the scheme shown in Figure 5a, long-term displacement current integration is necessary to determine Q acc (V a ). However, as it is affected by the current amplifier offsets and other factors, Q acc (V a ) is determined with high accuracy using a method called the voltage oscillation technique [14]. From the Q acc (V a ) obtained thus, the parameters ∆Q and V OS were obtained using the following equations: These two parameters are defined as follows. The first is ∆Q, where C 0 V a is the accumulated charge at the OS/M2 interface; therefore, this parameter is zero when no charge is injected (or extracted) by V a into the OS and shifts from zero when charge is injected (or extracted). In addition, V OS indicates the voltage drop inside the OS caused by V a according to Gauss's law. A feature of this experiment is that it is not dynamic, but static, and the experimentally obtained Q acc and V a as well as ∆Q and V OS are easy to compare with theoretical calculations that assume a quasistatic state.
These two parameters are defined as follows. The first is ΔQ, where C0Va is the accumulated charge at the OS/M2 interface; therefore, this parameter is zero when no charge is injected (or extracted) by Va into the OS and shifts from zero when charge is injected (or extracted). In addition, VOS indicates the voltage drop inside the OS caused by Va according to Gauss's law. A feature of this experiment is that it is not dynamic, but static, and the experimentally obtained Qacc and Va as well as ΔQ and VOS are easy to compare with theoretical calculations that assume a quasistatic state.  [12]. Copyright © 2023, Elsevier B. V. Panels (b,c) were reproduced with permissions [13]. Copyright © 2021, AIP Publishing. Figure 5b shows the experimental data for ΔQ vs. VOS for n-Si/SiO2/H2Pc/Au during hole injection. The calculations of the ΔQ-VOS plots, assuming the NTE model, are shown in Figure 5c. The variation in the potential curve corresponding to point ① is shown in  [12]. Copyright © 2023, Elsevier B. V. Panels (b,c) were reproduced with permissions [13]. Copyright © 2021, AIP Publishing. Figure 5b shows the experimental data for ∆Q vs. V OS for n-Si/SiO 2 /H 2 Pc/Au during hole injection. The calculations of the ∆Q-V OS plots, assuming the NTE model, are shown in Figure 5c. The variation in the potential curve corresponding to point 1 is shown in Figure 5d. This is the point where ∆Q shifts from zero, and according to calculations, a similar potential curve change occurs at point 1 '. For OSs that follow the NTE model, the ∆Q-V OS plot allows us to determine the charge injection barrier at the OS/M2 interface experimentally. In the case of H 2 Pc/Au, the hole injection barrier with approximately 0.2 eV was obtained from the plot [13].

Conclusions
The NTE charge extraction described in this study is a phenomenon specific to an MIOM capacitor, where a Schottky barrier exists between the OS/M2 contacts and where the mobility of the OS is not very high. Several MIOM capacitors satisfy the above two conditions; consequently, the NTE process of charge extraction appears to be a common phenomenon in both MIOM capacitors and OFETs. In the case of MIS capacitors and inorganic field-effect transistors, where ohmic contacts are formed between the semiconductor and the metal electrode, this NTE process does not occur. This process in OFETs is detrimental to transistor operation. Considering the mechanism of the process, the fabrication of ohmic contacts between the OS/M2 interface or the application of an OS with high mobility are the most effective ways to avoid this process. However, the NTE process may be useful in the application of OFETs, as memory devices. In addition, the NTE phenomenon can be used to determine the charge injection (extraction) barrier by means of ACM [12,13].
Author Contributions: This study was conceptualized by H.T. The formal analysis and methodology were provided by H.T. and T.O. Data curation was conducted by T.K. All authors have read and agreed to the published version of the manuscript.