Numerical Study of Sub-Gap Density of States Dependent Electrical Characteristics in Amorphous In-Ga-Zn-O Thin-Film Transistors

: We demonstrate the e ﬀ ect of the sub-gap density of states (DOS) on electrical characteristics in amorphous indium-gallium-zinc (IGZO) thin-ﬁlm transistors (TFTs). Numerical analysis based on a two-dimensional device simulator Atlas controlled the sub-gap DOS parameters such as tail acceptor-like states, tail donor-like states, Gauss acceptor-like states, and Gauss donor-like states in amorphous IGZO TFTs. We conﬁrm accuracy by exploiting physical factors, such as oxygen vacancy, peroxide, hydrogen complex, band-to-band tunneling, and trap-assisted tunneling. Consequently, the principal electrical parameters, such as the threshold voltage, saturation mobility, sub-threshold swing, and on-o ﬀ current ratio, are e ﬀ ectively tuned by controlling sub-gap DOS distribution in a-IGZO TFTs.


Introduction
Thin-film transistors (TFTs) have received significant attention because of the rapid development of displays, sensors, computing, radiofrequency tags, and analog signal processing [1][2][3][4][5][6]. Specifically, TFTs based on metal-oxide, organic, and low-dimensional materials have advanced, achieving high electrical performances, optical transparency, and mechanical flexibility [7][8][9][10]. Among the various next-generation material-based TFTs, amorphous oxide semiconductor (AOS) TFTs based on multi-components exhibit high uniformity because of their high mobility, amorphous phase, and high transparency and flexibility [11][12][13]. Indium-gallium-zinc (IGZO) TFTs are the most representative AOS TFTs because of the advantages of carrier concentration controllability, electrical characteristics stability, and process compatibility with present fabrication [14][15][16]. A challenging issue in IGZO TFTs is enhancing electrical performance to drive high-quality active-matrix electronics, such as organic light-emitting diodes, micro light-emitting diodes, and high-resolution displays and sensors. To enhance the electrical performance of IGZO TFTs, many studies on IGZO TFTs exist, and oxygen vacancy (OV), peroxide (PO), and hydrogen complex (HC) models have been suggested [17][18][19][20]. However, progress has been insufficient to fully understand the change of electrical characteristics induced by the sub-gap density of states (DOS), even though sub-gab DOS distributions are highly related to the electrical characteristics of AOS TFTs.
In this study, we controlled sub-gap DOS distribution in variables such as tail acceptor-like states (N TA ), tail donor-like states (N TD ), Gauss donor-like states (N GA ), and Gauss acceptor-like states (N GD ). Therefore, we use Silvaco's two-dimensional device simulator Atlas to examine the effect of sub-gab DOS distributions on electrical characteristics. Consequently, the results show that the characteristics of electrical parameters, such as the threshold voltage (V th ), saturation mobility (µ sat ), sub-threshold swing (S), and on-off current ratio (I on /I off ), significantly affect the sub-gap DOS distribution.

Simulation Methodology
For the AOS IGZO TFT simulation, top-contact bottom-gate staggered structure was used in this study (Figure 1a). In the simulation, indium tin oxide (ITO) and aluminum (Al) were used for the gate and the source and drain electrodes, respectively. The work functions of ITO and Al are 4.7 eV and 4.33 eV, respectively. The lengths of both source and drain are 1 µm, and the gate length is 10 µm. The thickness of the electrodes is 50 nm. The gate insulator is a 100-nm-thick SiO 2 , and the active layer material is IGZO. The channel width and length are 100 µm and 10 µm, respectively. The affinity and bandgap of the IGZO parameters are 4.16 eV and 3.05 eV, respectively, and the conduction band (N C ) and valence band (N V ) effective DOS are calculated using Equations (1) and (2). In this study, we controlled sub-gap DOS distribution in variables such as tail acceptor-like states (NTA), tail donor-like states (NTD), Gauss donor-like states (NGA), and Gauss acceptor-like states (NGD). Therefore, we use Silvaco's two-dimensional device simulator Atlas to examine the effect of sub-gab DOS distributions on electrical characteristics. Consequently, the results show that the characteristics of electrical parameters, such as the threshold voltage (Vth), saturation mobility (μsat), sub-threshold swing (S), and on-off current ratio (Ion/Ioff), significantly affect the sub-gap DOS distribution.

Simulation Methodology
For the AOS IGZO TFT simulation, top-contact bottom-gate staggered structure was used in this study (Figure 1a). In the simulation, indium tin oxide (ITO) and aluminum (Al) were used for the gate and the source and drain electrodes, respectively. The work functions of ITO and Al are 4.7 eV and 4.33 eV, respectively. The lengths of both source and drain are 1 µm, and the gate length is 10 µm. The thickness of the electrodes is 50 nm. The gate insulator is a 100-nm-thick SiO2, and the active layer material is IGZO. The channel width and length are 100 µm and 10 µm, respectively. The affinity and bandgap of the IGZO parameters are 4.16 eV and 3.05 eV, respectively, and the conduction band (Nc) and valence band (Nv) effective DOS are calculated using Equations (1) and (2). In this study, we assumed that the effective mass of the electron and hole are 0.34 MO and 21 MO [21]. The values calculated using Equations (1) and (2) are 5 × 10 18 cm −3 eV −1 and 2.4 × 10 21 cm −3 eV −1 , respectively. This study assumed that localized states and NGD are equal. We also assumed that the electron carrier concentration is partially ionized from NGA using the OV model. Figure 1(b) presents the reference sub-gap DOS consisting of NTA, NTD, NGA, and NGD. Each formula follows the sub-gap DOS model [21]. The NTA distribution equation (GTA (E)) in the sub-gap DOS is (3).
where E is the electron energy, EC is the conduction band edge energy, NTA is the sub-gap DOS at E−EC, and WTA is the characteristic decay energy. The NTD distribution equation (GTD (E)) in the subgap DOS is given by Equation (4). In this study, we assumed that the effective mass of the electron and hole are 0.34 M O and 21 M O [21]. The values calculated using Equations (1) and (2) are 5 × 10 18 cm −3 eV −1 and 2.4 × 10 21 cm −3 eV −1 , respectively. This study assumed that localized states and N GD are equal. We also assumed that the electron carrier concentration is partially ionized from N GA using the OV model. Figure 1b presents the reference sub-gap DOS consisting of N TA , N TD , N GA , and N GD . Each formula follows the sub-gap DOS model [21]. The N TA distribution equation (G TA (E)) in the sub-gap DOS is (3).
where E is the electron energy, E C is the conduction band edge energy, N TA is the sub-gap DOS at E−E C , and W TA is the characteristic decay energy. The N TD distribution equation (G TD (E)) in the sub-gap DOS is given by Equation (4).
where E V is the valence band edge energy, N TD is the sub-gap DOS at E−E V , and W TD is the characteristic decay energy. The N GA distribution equation (G GA (E)) in the sub-gap DOS is given by Equation (5).
where E GA is the N GA energy peak, N GA is the Gaussian acceptor-like states at E GA −E in the sub-gap DOS, and W GA is the characteristic decay energy. The N GD distribution equation (G GD (E)) in the sub-gap DOS is given by Equation (6).
where E GD is the N GD energy peak, N GD is Gaussian donor-like states at E−E GD in the sub-gap DOS, and W GD is the characteristic decay energy. In the semiconductor based on Si and compound case, N GD is located near E V , but in the AOS case, N GD is positioned near E C because the N GD position changes the Madelung potential effect of the OV model [17]. The OV model demonstrates the N GD moves from a deep trap state to localized states because of the Madelung potential. Furthermore, the electrons are generated by removing oxygen bonding. The OV model is associated with Equation (7).
where the neutrality charge is X, the two-plus charge is +2, the OV state is V O , and e is the electron. Therefore, the V O state level is changed by filling or discharging electrons using the Madelung potential. Therefore, N GD would change from deep trap states to localized states. Furthermore, the PO model shows that excess oxygen induces an O-O bonding and identifies changed localized state levels. Thus, the N GD energy level should change in the localized state regime under the PO model [18]. Furthermore, the HC model illustrates that coupling metal atoms and light hydrogen atoms induces various energy levels [19]. Consequently, coupling at various energy levels would change the sub-gap DOS and Fermi level. Therefore, these variable models should demonstrate varying sub-gaps DOS by chemical atomic bonding or breaking. Thus, various parameters in the sub-gap DOS using the models should be applied in the simulation to observe the changes in the electrical characteristics in this study. Table 1 shows other parameters required for simulation. For accurate simulation, the generation-recombination mechanisms tarp-assisted tunneling (TAT) associated with band-to-band (BBT) and Pool-Frenkel Barrier Lowering (PFBL) models must be used [21,22]. The BBT and TAT models [23] should change the generation rate.
F, m r , q, and E G are the local electric field, conduction band effective mass, elementary charge, and bandgap energy, respectively.  Figure 2a shows the N TA versus energy (E). The N TA varies from 1 × 10 18 to 5 × 10 19 cm −3 eV −1 by five intervals. Figure 2b shows that the transfer curve is changing with the N TA . It presents the log scaled I D -V G curve by sweeping V G from −20 V to 40 V at V D = 40 V of a-IGZO TFTs from each N TA . Thus, electrical performance such as low I on /I off from 5 × 10 12 to 2.27 × 10 12 A and low µ sat from 11-7.9 cm 2 V −1 ·s −1 , high V th from 0.35-4.5 V, and high S from 128-438 mV dec −1 would be worse. We extract electrical parameters by analyzing the transfer curves. We take advantage of specific equations to extract parameters. First, I D is given by Equation (6) at the saturation region in the I D -V G transfer curve.

Results and Discussion
where W is the device width, L is the channel length, and C ox is the semiconductor insulator. Second, the G rad.max of the maximum gradient concept is used to extract µ sat and V th at the saturation region in the G rad.max is the maximum gradient value. Furthermore, to evaluate the device performance, the I on /I off is critical at the saturation region in the I D -V G transfer curve.
Third, µ sat is critical for evaluating device performance in the I D -V G transfer curve at the saturation region in the Fourth, V th is also necessary for evaluating device performance in the I D -V G transfer curve at the saturation region in the Fifth, S is concerned with the low power device parameter at the saturation region in the Finally, the concept of V on should be used to evaluate the changing electrical property exactly at the saturation region in the I D -V G transfer curve. Note that these phenomena are matched to the multiple trapping and release (MTR) model [24]. Thus, many N TA would interfere with the path of the electron. We elucidate the reasons by investigating the electron concentration distribution in the channel (Figure 2c). The results show that N TA is associated with lowering the electron concentration from top to bottom in the channel because of trapping electrons. Therefore, the N TA would be disturbed to move electrons using the MTR effect. Furthermore, we also ran the simulation in relation to W TA . The variation of W TA is 0.08-0.14 eV at N TA = 10 18 cm −3 eV −1 . However, no change in electrical properties was observed in this study. Therefore, N TA is more important than W TD regarding its effect on electrical performance.
Fifth, S is concerned with the low power device parameter at the saturation region in the ID-VG transfer curve.
Finally, the concept of Von should be used to evaluate the changing electrical property exactly at the saturation region in the ID-VG transfer curve. Note that these phenomena are matched to the multiple trapping and release (MTR) model [24]. Thus, many NTA would interfere with the path of the electron. We elucidate the reasons by investigating the electron concentration distribution in the channel (Figure 2c). The results show that NTA is associated with lowering the electron concentration from top to bottom in the channel because of trapping electrons. Therefore, the NTA would be disturbed to move electrons using the MTR effect. Furthermore, we also ran the simulation in relation to WTA. The variation of WTA is 0.08-0.14 eV at NTA = 10 18 cm −3 eV −1 . However, no change in electrical properties was observed in this study. Therefore, NTA is more important than WTD regarding its effect on electrical performance.  Figure 3a shows the NGA-E. The variation of NGA is from 10 16 to 5 × 10 17 by five intervals. Figure  3b shows that the transfer curve is changing with NGA. It presents the log scaled ID-VG curve by sweeping VG from −20 V-40 V at VD = 40 V of IGZO TFTs from each NGA. Therefore, electrical performance, such as low Ion/Ioff from 4 × 10 12 to 2.93 × 10 12 A and low μsat from 10.4 to 9.8 cm 2 V −1 ·s −1 , high Vth from 0.5 to 2.5 V, high Von from 0.5 to 2.5 V, and high S from 128 to 316 mV dec −1 , would be worse. Thus, this work investigates some electrical properties. First, both NTA and NGA negatively affect electrical performance under the MTR model. Second, the NTA significantly changes the Ion/Ioff.   Figure 3b shows that the transfer curve is changing with N GA . It presents the log scaled I D -V G curve by sweeping V G from −20 V-40 V at V D = 40 V of IGZO TFTs from each N GA . Therefore, electrical performance, such as low I on /I off from 4 × 10 12 to 2.93 × 10 12 A and low µ sat from 10.4 to 9.8 cm 2 V −1 ·s −1 , high V th from 0.5 to 2.5 V, high V on from 0.5 to 2.5 V, and high S from 128 to 316 mV dec −1 , would be worse. Thus, this work investigates some electrical properties. First, both N TA and N GA negatively affect electrical performance under the MTR model. Second, the N TA significantly changes the I on /I off . However, the N GA significantly changes the positive shift V th . If we employ the N TA in this study, the acceptor-like traps should increase around the end of the E C . Therefore, the electrons should be trapped and released more easily by the N TA around the end of the E C when the device is operated. However, if we employ the N GA in this study, the acceptor-like traps increase around the E GA because N GA is not located at the edge of E C . This means that electrons are trapped in acceptor-like states, but in the N GA case, electrons must have more energy to be emitted because they are not located near E C when the device is operated. Finally, other condition studies also run simulations of parameters, such as W GA and E GA , with ranges of 0.05 lectronics 2019, 8, x FOR PEER REVIEW 6 of 10 owever, the NGA significantly changes the positive shift Vth. If we employ the NTA in this study, the cceptor-like traps should increase around the end of the EC. Therefore, the electrons should be rapped and released more easily by the NTA around the end of the EC when the device is operated. owever, if we employ the NGA in this study, the acceptor-like traps increase around the EGA because GA is not located at the edge of EC. This means that electrons are trapped in acceptor-like states, but n the NGA case, electrons must have more energy to be emitted because they are not located near EC hen the device is operated. Finally, other condition studies also run simulations of parameters, such s WGA and EGA, with ranges of 0.05Ѿ0.3 eV at NGA = 5 × 10 16 cm −3 eV −1 and 0.3-0.6 eV in EC-E at NGA 5 × 10 16 cm −3 eV −1 . However, these did not change the electrical performance. The results show that t is critical to reduce the amount of NTA and adjust the EGA control position for making higherformance AOS IGZO TFTs. We also simulated the NTD and WTD in the sub-gap DOS, ranging from × 10 18 to 10 20 cm −3 eV −1 and 0.03 to 0.06 eV at NTD = 10 20 cm −3 eV −1 . However, these did not change the lectrical performance because, in this case, the IGZO channel layer is a large bandgap and NTD is far rom the EC point. Therefore, the NTD near EV does not affect electrical performance when the device s operated. However, if high energy is injected, such as photons, it should release electrons in the tates, and the electrons released from NTD to EC should change the electrical performance [25].  , and high S from 172 to 744 mV dec −1 , would be better and worse, respectively. Note that the istribution of NGD affects the electrical performance, such as a bad S and negative-shift Vth. Therefore, GD is related to trapping electrons and associated with electron generation in the channel more easily 0.3 eV at N GA = 5 × 10 16 cm −3 eV −1 and 0.3-0.6 eV in E C -E at N GA = 5 × 10 16 cm −3 eV −1 . However, these did not change the electrical performance. The results show that it is critical to reduce the amount of N TA and adjust the E GA control position for making high-performance AOS IGZO TFTs. We also simulated the N TD and W TD in the sub-gap DOS, ranging from 5 × 10 18 to 10 20 cm −3 eV −1 and 0.03 to 0.06 eV at N TD = 10 20 cm −3 eV −1 . However, these did not change the electrical performance because, in this case, the IGZO channel layer is a large bandgap and N TD is far from the E C point. Therefore, the N TD near E V does not affect electrical performance when the device is operated. However, if high energy is injected, such as photons, it should release electrons in the states, and the electrons released from N TD to E C should change the electrical performance [25]. However, the NGA significantly changes the positive shift Vth. If we employ the NTA in this study, the acceptor-like traps should increase around the end of the EC. Therefore, the electrons should be trapped and released more easily by the NTA around the end of the EC when the device is operated. However, if we employ the NGA in this study, the acceptor-like traps increase around the EGA because NGA is not located at the edge of EC. This means that electrons are trapped in acceptor-like states, but in the NGA case, electrons must have more energy to be emitted because they are not located near EC when the device is operated. Finally, other condition studies also run simulations of parameters, such as WGA and EGA, with ranges of 0.05Ѿ0.3 eV at NGA = 5 × 10 16 cm −3 eV −1 and 0.3-0.6 eV in EC-E at NGA = 5 × 10 16 cm −3 eV −1 . However, these did not change the electrical performance. The results show that it is critical to reduce the amount of NTA and adjust the EGA control position for making highperformance AOS IGZO TFTs. We also simulated the NTD and WTD in the sub-gap DOS, ranging from 5 × 10 18 to 10 20 cm −3 eV −1 and 0.03 to 0.06 eV at NTD = 10 20 cm −3 eV −1 . However, these did not change the electrical performance because, in this case, the IGZO channel layer is a large bandgap and NTD is far from the EC point. Therefore, the NTD near EV does not affect electrical performance when the device is operated. However, if high energy is injected, such as photons, it should release electrons in the states, and the electrons released from NTD to EC should change the electrical performance [25].  Figure 4a shows the NGD-E. The range of NGD is from 5 × 10 16 to 10 18 cm −3 eV −1 by five intervals. Figure 4b shows the transfer curve changes with NGD. It shows sweeping VG from −20 to 40 V at VD = 40 V of IGZO TFTs from each NGA. Thus, the electrical performances, such as low Von from 0.85 to −3.4 V, and high S from 172 to 744 mV dec −1 , would be better and worse, respectively. Note that the distribution of NGD affects the electrical performance, such as a bad S and negative-shift Vth. Therefore, NGD is related to trapping electrons and associated with electron generation in the channel more easily by VO. Therefore, if the NGD increases, S deteriorates, and Vth changes in a negative shift. We elucidate  Figure 4a shows the N GD -E. The range of N GD is from 5 × 10 16 to 10 18 cm −3 eV −1 by five intervals. Figure 4b shows the transfer curve changes with N GD . It shows sweeping V G from −20 to 40 V at V D = 40 V of IGZO TFTs from each N GA . Thus, the electrical performances, such as low V on from 0.85 to −3.4 V, and high S from 172 to 744 mV dec −1 , would be better and worse, respectively. Note that the distribution of N GD affects the electrical performance, such as a bad S and negative-shift V th . Therefore, N GD is related to trapping electrons and associated with electron generation in the channel more easily by V O . Therefore, if the N GD increases, S deteriorates, and V th changes in a negative shift. We elucidate more detailed reasons by examining the electron concentration distribution (Figure 4c). From the top to the bottom pictures, we find that the electrons gathered more easily on the channel by the condition N GD at the saturation region of the simulated IGZO TFTs V D = 40 V and V G = 0 V. Note that these results illustrate a tendency by the OV model. Therefore, the oxygen concentration must be controlled, and the N GD level via the PO and OV models must be adjusted.  (Figure 4c). From the top to the bottom pictures, we find that the electrons gathered more easily on the channel by the condition NGD at the saturation region of the simulated IGZO TFTs VD = 40 V and VG = 0 V. Note that these results illustrate a tendency by the OV model. Therefore, the oxygen concentration must be controlled, and the NGD level via the PO and OV models must be adjusted.  Figure 5a shows the EGD-E. The range of EGD is from 2.3-2.9 eV for the EC-E. Figure 5b shows that the transfer curve is changing with EGD. It presents by sweeping VG −20 to 40 V at VD = 40 V of IGZO TFTs from each EGD. The electrical performances, such as high Ion/Ioff from 3.7 × 10 12 to 3.9 × 10 12 A and high μsat from 9.9 to 10.4 cm 2 V −1 ·s −1 , low Vth from 4.9 to 3.2 V, low Von from 0 to −2.2 V, and low S from 407 to 152 mV dec −1 , are shown. As the EGD approaches EC, the electrical performances are improved, but the slope of the transfer curve changes around 0 V, showing a non-ideal transfer characteristic. Therefore, optimized electrical characteristic requires moving up by controlling the localized states in donor-like states by O-O bonding and VO. For elucidating more detailed reasons, we investigated, as shown in Figure 5c. From the top to the bottom pictures, we find that the carrier concentration in the channel is high because EGD is located near EC more closely at VG = 0 V and VD = 40 V. Therefore, EGD is concerned with the carrier injection as a doping semiconductor by VO. Therefore, when EGD is located near EC, electrons are generated more easily. Therefore, the electrons are released rather than trapped, and the electrical performance could be improved.  Figure 5a shows the E GD -E. The range of E GD is from 2.3-2.9 eV for the E C -E. Figure 5b shows that the transfer curve is changing with E GD . It presents by sweeping V G −20 to 40 V at V D = 40 V of IGZO TFTs from each E GD . The electrical performances, such as high I on /I off from 3.7 × 10 12 to 3.9 × 10 12 A and high µ sat from 9.9 to 10.4 cm 2 V −1 ·s −1 , low V th from 4.9 to 3.2 V, low V on from 0 to −2.2 V, and low S from 407 to 152 mV dec −1 , are shown. As the E GD approaches E C , the electrical performances are improved, but the slope of the transfer curve changes around 0 V, showing a non-ideal transfer characteristic. Therefore, optimized electrical characteristic requires moving up by controlling the localized states in donor-like states by O-O bonding and V O . For elucidating more detailed reasons, we investigated, as shown in Figure 5c. From the top to the bottom pictures, we find that the carrier concentration in the channel is high because E GD is located near E C more closely at V G = 0 V and V D = 40 V. Therefore, E GD is concerned with the carrier injection as a doping semiconductor by V O . Therefore, when E GD is located near E C , electrons are generated more easily. Therefore, the electrons are released rather than trapped, and the electrical performance could be improved.

Conclusions
We have described the importance of key parameters of acceptor-like and donor-like states in sub-gap states. From the simulation model and related theories, this work clarified how the sub-gap DOS profile affects the electrical characteristics in the a-IGZO TFTs. Note that four controlled variables, namely, NTA, NGA, NGD, and EGD, significantly affected electrical performances such as Von, Vth, S, Ion/Ioff, and μsat. For acceptor-like traps, all electrical properties became worse because of the trapped electrons near the EC base on the MTR effect. For donor-like traps, some electrical properties such as S became worse because of localized states. Other electrical properties such as Vth and μsat improved because of the injected electrons based on the OV and PO models. In the future, we want to investigate the effect of more than four variables focused on in this work on electrical properties to exactly determine the significant role of controlling parameters on the improvement of the electrical properties in AOS TFTs.

Conclusions
We have described the importance of key parameters of acceptor-like and donor-like states in sub-gap states. From the simulation model and related theories, this work clarified how the sub-gap DOS profile affects the electrical characteristics in the a-IGZO TFTs. Note that four controlled variables, namely, N TA , N GA , N GD , and E GD , significantly affected electrical performances such as V on , V th , S, I on /I off , and µ sat . For acceptor-like traps, all electrical properties became worse because of the trapped electrons near the E C base on the MTR effect. For donor-like traps, some electrical properties such as S became worse because of localized states. Other electrical properties such as V th and µ sat improved because of the injected electrons based on the OV and PO models. In the future, we want to investigate the effect of more than four variables focused on in this work on electrical properties to exactly determine the significant role of controlling parameters on the improvement of the electrical properties in AOS TFTs.

Conflicts of Interest:
The authors declare no conflict of interest.