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

Abstract

We demonstrate the effect 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-off current ratio, are effectively tuned by controlling sub-gap DOS distribution in a-IGZO TFTs.

1. 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.

2. 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 (N_C) and valence band (N_V) effective DOS are calculated using Equations (1) and (2).

$$N_C=2{\left(\frac{2\pi M_{C}kt}{h^2}\right)}^{\frac{3}{2}},$$

(1)

$$N_V=2{\left(\frac{2\pi M_{V}kt}{h^2}\right)}^{\frac{3}{2}},$$

(2)

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 × 10¹⁸ cm⁻³ eV⁻¹ and 2.4 × 10²¹ 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).

$$G_{TA}\left(E\right)=N_{TA}{e}^{\frac{\left(E-E_C\right)}{W_{TA}}},$$

(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).

$$G_{TD}\left(E\right)=N_{TD}{e}^{\frac{\left(E_V-E\right)}{W_{TD}}},$$

(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).

$$G_{GA}\left(E\right)=N_{GA}{e}^{\left[-{\left(\frac{\left(E-E_{GA}\right)}{W_{GA}}\right)}^2\right]},$$

(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).

$$G_{GD}\left(E\right)=N_{GD}{e}^{\left[-{\left(\frac{\left(E-E_{GD}\right)}{W_{GD}}\right)}^2\right]},$$

(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).

$$V_O{}^X\to V_O{}^{+2}+2e,$$

(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. Simulation parameters for the a-indium-gallium-zinc (IGZO) thin-film transistors (TFTs).

Parameter	Value	Unit	Description
µn	15	cm2 V−1·s−1	Electron mobility
µp	0.1	cm2 V−1·s−1	Hole mobility
NTA	1 × 1018	cm−3 eV−1	Density of tail states at conduction band
NTD	1 × 1020	cm−3 eV−1	Density of tail states at valence band
NGD	5 × 1016	cm−3 eV−1	Density of Gauss donor-like states
NGA	5 × 1016	cm−3 eV−1	Density of Gauss acceptor-like states
WTA	0.08	eV	Characteristic decay energy of acceptor-like tail states
WTD	0.06	eV	Characteristic decay energy of donor-like tail states
WGD	0.1	eV	Characteristic decay energy of donor-like Gauss states
WGA	0.2	eV	Characteristic decay energy of acceptor-like Gauss states
EGD	2.7	eV	Energy corresponding to the peak for donor-like Gauss states
EGA	0.5	eV	Energy corresponding to the peak for acceptor-like Gauss states
NC	5 × 1018	cm−3 eV−1	Effective density of states for conduction band
NV	2.4 × 1021	cm−3 eV−1	Effective density of states for valance band
EG	3.05	eV	Energy band
Xe	4.16	eV	Electron affinity
MC	0.34 Mo	Kg	Effective mass of conduction band
MV	21 Mo	Kg	Effective mass of valence band
ɛs	10ɛo	Fm−1	Dielectric constant
n	1015	cm−3	Electron carrier concentration

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.

$$G_{BBT}\left(F\right)=\frac{q^2{F}^2{m}_r{}^{\frac{1}{2}}}{18\pi \hslash E_G{}^{\frac{1}{2}}}{e}^{\left(-\frac{\pi m_r{}^{\frac{1}{2}}{E}_G{}^{\frac{3}{2}}}{2\hslash qF}\right)},$$

(8)

F, m_r, q, and E_G are the local electric field, conduction band effective mass, elementary charge, and bandgap energy, respectively.

3. Results and Discussion

Figure 2a shows the N_TA versus energy (E). The N_TA varies from 1 × 10¹⁸ to 5 × 10¹⁹ 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 × 10¹² to 2.27 × 10¹² A and low μ_sat from 11–7.9 cm² 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.

$$I_D={\mu }_{sat}·C_{ox}\left(\frac{W}{2L}\right){\left(V_G-V_{th}\right)}^2,$$

(9)

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 $\sqrt{I_D}$–V_G transfer curve.

$$G_{rad}=\frac{a\sqrt{I_D}}{a{V}_G}={\left({\mu }_{sat}·C_{ox}\left(\frac{W}{2L}\right)\right)}^{\frac{1}{2}}.$$

(10)

$G_{rad.max}$ 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.

$$\frac{I_{on}}{I_{off}}=\frac{I_D|V_G=40V}{I_D|V_G=-20V}.$$

(11)

Third, μ_sat is critical for evaluating device performance in the I_D–V_G transfer curve at the saturation region in the $\sqrt{I_D}$–V_G transfer curve.

$${\mu }_{sat}=\left(\frac{1}{C_{ox}}\right)\left(\frac{2L}{W}\right){\left(G_{rad.max}\right)}^2.$$

(12)

Fourth, V_th is also necessary for evaluating device performance in the I_D–V_G transfer curve at the saturation region in the $\sqrt{I_D}$–V_G transfer curve.

$$V_{th}=V_G-\frac{\sqrt{I_D}}{G_{rad.max}}.$$

(13)

Fifth, S is concerned with the low power device parameter at the saturation region in the I_D–V_G transfer curve.

$$S=\frac{a{V}_G}{a\log \left(I_D\right)}=\frac{1}{{\mu }_{sat}·C_{ox}\left(\frac{W}{2L}\right)}.$$

(14)

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 = 10¹⁸ 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.

Figure 3a shows the N_GA–E. The variation of N_GA is from 10¹⁶ to 5 × 10¹⁷ by five intervals. 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 × 10¹² to 2.93 × 10¹² A and low μ_sat from 10.4 to 9.8 cm² 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 0.05Ѿ0.3 eV at N_GA = 5 × 10¹⁶ cm⁻³ eV⁻¹ and 0.3–0.6 eV in E_C–E at N_GA = 5 × 10¹⁶ 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 × 10¹⁸ to 10²⁰ cm⁻³ eV⁻¹ and 0.03 to 0.06 eV at N_TD = 10²⁰ 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].

Figure 4a shows the N_GD–E. The range of N_GD is from 5 × 10¹⁶ to 10¹⁸ 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 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 × 10¹² to 3.9 × 10¹² A and high μ_sat from 9.9 to 10.4 cm² 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.

4. 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.