The Mechanism of the Photostability Enhancement of Thin-Film Transistors Based on Solution-Processed Oxide Semiconductors Doped with Tetravalent Lanthanides

Abstract

The applications of thin-film transistors (TFTs) based on oxide semiconductors are limited due to instability under negative bias illumination stress (NBIS). Here, we report TFTs based on solution-processed In₂O₃ semiconductors doped with Pr⁴⁺ or Tb⁴⁺, which can effectively improve the NBIS stability. The differences between the Pr⁴⁺-doped In₂O₃ (Pr:In₂O₃) and Tb⁴⁺-doped In₂O₃ (Tb:In₂O₃) are investigated in detail. The undoped In₂O₃ TFTs with different annealing temperatures exhibit poor NBIS stability with serious turn-on voltage shift (ΔV_on). After doping with Pr⁴⁺/Tb⁴⁺, the TFTs show greatly improved NBIS stability. As the annealing temperature increases, the Pr:In₂O₃ TFTs have poorer NBIS stability (ΔV_on are −3.2, −4.8, and −4.8 V for annealing temperature of 300, 350, and 400 °C, respectively), while the Tb:In₂O₃ TFTs have better NBIS stability (ΔV_on are −3.6, −3.6, and −1.2 V for annealing temperature of 300, 350, and 400 ℃, respectively). Further studies reveal that the improvement of the NBIS stability of the Pr⁴⁺/Tb⁴⁺:In₂O₃ TFTs is attributed to the absorption of the illuminated light by the Pr/Tb4f ⁿ—O2p⁶ to Pr/Tb 4f ⁿ⁺¹—O2p⁵ charge transfer (CT) transition and downconversion of the light to nonradiative transition with a relatively short relaxation time compared to the ionization process of the oxygen vacancies. The higher NBIS stability of Tb:In₂O₃ TFTs compared to Pr:In₂O₃ TFTs is ascribed to the smaller ion radius of Tb⁴⁺ and the lower energy level of Tb 4f ⁷ with a isotropic half-full configuration compared to that of Pr 4f ¹, which would make it easier for the Tb⁴⁺ to absorb the visible light than the Pr⁴⁺.

1. Introduction

Oxide semiconductors, such as InGaZnO₄ (IGZO) [1,2,3,4,5], have drawn considerable attention for the advantages of relatively high mobility, large-area processability, good uniformity, high transparency to visible light, etc. [6] In particular, the extremely low off current (I_off) makes it attractive in energy-saving devices that require long stand-by time [7]. However, a critical technical issue remains to be solved for better device applications of the thin-film transistors (TFTs) based on oxide semiconductors. Although oxide semiconductors are highly transparent in the visible range, they suffer from serious threshold voltage (V_th) change under negative bias illumination stress (NBIS) even when illuminated by visible light with smaller photon energies than their bandgaps [8,9,10,11,12]. Although the NBIS instability of the oxide TFTs have been studied intensively over the past decade, no consensuses have been reached on the mechanism of the NBIS instability [6].

Our previous work shows that the doping of tetravalent lanthanides (Ln)—praseodymium (Pr⁴⁺) and terbium (Tb⁴⁺)—can improve the NBIS stability of the oxide TFTs greatly [13]. However, the insightful effects of the tetravalent lanthanides on photostability of the oxide TFTs is still unclear. In this paper, the differences between Pr⁴⁺ and Tb⁴⁺ doped oxide semiconductors are compared in detail, and new experiments and analysis (such as low-temperature measurements) are carried out to give a more insightful understanding of the mechanism of the NBIS instability of oxide TFTs and the intrinsic effect of Pr⁴⁺/Tb⁴⁺ on the electrical and optical properties of oxide TFTs.

2. Experimental Section

2.1. Precursor Solutions

The oxide semiconductor films were deposited by spin-coating and thermal decomposition of precursor solutions. A 0.2 M In₂O₃ solution was prepared by dissolving indium nitrate hydrate ((In(NO)₃·nH₂O), Sigma-Aldrich, Tianhe District, Guangzhou, China) in deionized water. The Ln:In₂O₃ precursor solutions were synthesized by dissolving indium nitrate hydrate ((In(NO)₃·nH₂O), Sigma-Aldrich, Tianhe District, Guangzhou, China) and lanthanides nitrate hydrate (Pr/Tb(NO)₃·nH₂O, Aladdin, Industrial Co., Shanghai, China) in deionized water, which was optimized to the total concentration of metal ion of 0.2 M and In/Ln molar ratio of 19:1. All the precursor solutions were stirred vigorously for 12 h at room temperature and filtered through a 0.22 μm syringe filter before spin-coating.

2.2. Device Fabrication

A bottom-gate and top-contact structure was used to fabricate Ln:In₂O₃ TFT, as shown in Figure 1. First, a 300-nm-thick Al:Nd alloy film was deposited onto a glass substrate by sputtering and patterned by wet etch, followed by an anodization process to form a 200-nm-thickness Nd:AlO_x gate dielectric layer on the surface of Al:Nd film [14]. Next, an ultraviolet light irradiating for a long time was used to treat a part (channel area) of the Nd:AlO_x surface with a stencil shadow mask in order to form a hydrophilic surface in the channel area. The Ln:In₂O₃ precursor films were deposited onto the wettable area irradiated by UV by spin-coating the precursor solutions at 2000 rpm for 5 s and 6500 rpm for 40 s, followed by drying at 40 °C and thermal annealing at 300/350/400 °C for 1 h in an air condition. Then, the Al source and drain electrodes were deposited on the Ln: In₂O₃ layer by thermal evaporation and defined the channel area with 800 μm width (W) and 200 μm length (L) by using a stencil shadow mask. Finally, the devices were post-annealed at 300 °C for 1 h in an air condition.

2.3. Characterization of Films and Devices

The electrical characteristics of the TFTs were measured using a semiconductor parameter analyzer system in conjunction with a probe station in a vacuum condition. The NBIS stability was tested by monitoring evolutions of the transfer curves of the TFTs as a function of the stress time under gate bias stresses of −20 V combined with white LED irradiation (250 Lux). The crystallization characteristics of the films were determined by X-ray diffraction (XRD) experiments. The chemical shift of different elements was characterized by the X-ray Photoelectron Spectroscopy (XPS).

3. Results and Discussion

3.1. TFT Characteristics

The transfer curves of the In₂O₃, Pr:In₂O₃, and Tb:In₂O₃ TFTs with different annealing temperature are shown in Figure 2a–c, respectively. All the TFTs showed increases on the current (I_on) and off current (I_off) with increasing annealing temperatures, which reflects that the channels became more conductive as the annealing temperature increased. Compared to those of the Pr:In₂O₃ and Tb:In₂O₃ TFTs, the In₂O₃ TFTs displayed higher I_off, more negative V_th, and more sensitivity to the annealing temperature, which reflects that both Pr and Tb can reduce the free carriers. The saturation mobility (μ_sat) of TFTs were calculated using Equation (1).

The properties of the In₂O₃, Pr:In₂O₃, and Tb:In₂O₃ TFTs are summarized in

Table 1. Summary of the properties of the Pr/Tb:In₂O₃ TFTs with different annealing temperatures.

	T (°C)	μ (cm2·V−1·s−1)	SS (V/dec)	Vth (V)	Ion/Ioff	ΔVon under NBIS (V)
In2O3	300	16.6	0.27		5.6 × 107	Bias dependent
	350	24.5	0.55		2.9 × 107	Bias dependent
	400	23.4	0.68		6.8 × 106	Bias dependent
Pr:In2O3	300	5.0	0.11	1.8	8.4 × 109	−3.2
	350	6.1	0.14	1.5	3.0 × 107	−4.8
	400	10.1	0.13	0.4	5.1 × 107	−4.8
Tb:In2O3	300	4.7	0.12	2.6	3.7 × 109	−3.6
	350	13.4	0.17	1.2	1.8 × 108	−3.6
	400	18.2	0.15	1.4	6.9 × 107	−1.2

. Although the In₂O₃ TFTs had higher mobility, they exhibited large hysteresis in the transfer curves between forward and reverse gate sweeps, which suggests that the In₂O₃ TFTs were in a rather unstable state even annealed at 400 °C. For Pr:In₂O₃ TFTs, the mobility increased slightly from 5.0 to 6.1 cm²·V⁻¹·s⁻¹ as the annealing temperature increased from 300 °C to 350 °C; when the annealing temperature further increased to 400 °C, the mobility increased largely to 10.1 cm²·V⁻¹·s⁻¹. For Tb:In₂O₃ TFTs, the mobility at 300 °C annealing temperature was only 4.7 cm²·V⁻¹·s⁻¹, which was a bit lower than that of the Pr:In₂O₃ TFTs. As the annealing temperature increased to 350 °C, the mobility increased significantly to 13.4 cm²·V⁻¹·s⁻¹, which was much higher than that of the Pr:In₂O₃ TFTs. When the annealing temperature further increased to 400 °C, the mobility further increased to as high as 18.2 cm²·V⁻¹·s⁻¹. It can be briefly summarized that, at a low annealing temperature (300 °C), the Pr:In₂O₃ TFT and Tb:In₂O₃ TFT showed little difference on mobility, but at high annealing temperature (350/400 °C), the Tb:In₂O₃ TFTs had much higher mobilities than the Pr:In₂O₃ TFTs.

3.2. Film Structures

As known, in solution-processed oxide semiconductors, increasing annealing temperature is good for reducing the chemical residues and hence increasing the mobility, which is consistent with the results summarized in Table 1 [15]. For TFTs with the same annealing temperature (350 or 400 °C), the higher mobility of the Tb:In₂O₃ TFTs compared to that of the Pr:In₂O₃ TFTs may be attributed to the smaller ions radius of the Tb ions compared to the corresponding Pr ions. Unlike most of the other elements, lanthanides with larger atomic numbers have smaller ion radii due to the lanthanide contradiction, so Tb has a smaller ion radius (0.92 Å for Tb³⁺, and 0.76 Å for Tb⁴⁺) than Pr (0.99 Å for Pr³⁺, and 0.85 Å for Pr⁴⁺). Therefore, the ion radius of Tb is closer to that of In³⁺ (0.80 Å) compared to those of Pr, which may result in being easier to incorporate into the In₂O₃ lattice of Tb than Pr. The structures of the solution-processed Pr:In₂O₃ and Tb:In₂O₃ films annealed at different temperature were characterized by XRD experiments, as shown in Figure S1. All of the films showed a relatively strong diffraction peak around 30.6°, which is close to the (222) of the bixbyite In₂O₃, and a weak diffraction peak around 35.2°, which is close to the (400) of the bixbyite In₂O₃. Both Pr:In₂O₃ and Tb:In₂O₃ films exhibited better crystallinity as the annealing temperature increased. The 300 °C-annealing Tb:In₂O₃ film exhibited a much stronger (222) diffraction peak than the 300 °C-annealing Pr:In₂O₃ one. For the films annealed at higher temperatures (350 and 400 °C), there were no clear differences in the (222) diffraction peaks between Pr:In₂O₃ and Tb:In₂O₃, but the Tb:In₂O₃ showed a stronger (400) peak than the Pr:In₂O₃. Interestingly, the diffraction peak of the Pr:In₂O₃ film was almost in the same position as that of In₂O₃ film, while the diffraction peak of the Tb:In₂O₃ film exhibited an apparent left shit (~0.2°) compared to the standard (222) diffraction peak of the pure In₂O₃. The result implied that the Tb ions (at least some of them) may incorporate into the In₂O₃ lattice (causing lattice expansion) while most of the Pr ions may not incorporate into the In₂O₃ lattice (still In₂O₃ phase after Pr doping). Compared to the Pr:In₂O₃ with separated phases of PrO_x and In₂O₃, the Tb:In₂O₃ with Tb incorporated into the In₂O₃ lattice is better for carrier transport, which may result in higher mobility.

3.3. NBIS Instabilities

To further investigate the effect of Pr/Tb on the TFT properties, the stability of the TFTs were characterized under NBIS with a negative V_G stress of −20 V combined with an illumination stress of 250-Lux white LED light. Figure 3 shows the transfer curve evolutions of different TFTs as a function of the stress time during NBIS. The V_on shift (ΔV_on, defined by the gate voltage shift at I_D = 10⁻⁸ A) under 3600 s NBIS are summarized in Table 1. The In₂O₃ TFTs with different annealing temperatures exhibited poor NBIS stability with large ΔV_on (the actual ΔV_on of the In₂O₃ TFTs was much larger than the measured ΔV_on, as discussed below). After doping with Pr/Tb, the TFTs showed greatly improved NBIS stability. Surprisingly, the Pr:In₂O₃ and the Tb:In₂O₃ TFTs exhibited different temperature-dependent trends. As the annealing temperature increased, the Pr:In₂O₃ TFTs had poorer NBIS stability (ΔV_on were −3.2, −4.8, and −4.8 V for annealing temperature of 300, 350, and 400 °C, respectively), while the Tb:In₂O₃ TFTs had better NBIS stability (ΔV_on were −3.6, −3.6, and −1.2 V for annealing temperatures of 300, 350, and 400 ℃, respectively).

It should be noted that the V_on of all the undoped-In₂O₃ TFTs with different annealing temperatures reached the negative limit of −20 V (the voltage of the stressing gate bias) after 3600 s NBIS, which means that the actual ΔV_on of the undoped-In₂O₃ TFTs was much larger than the measured ΔV_on. To confirm the dependence of the V_on shift limit on the stressing gate bias, the TFTs were characterized under NBIS with a more negative stressing gate bias of −30 V combined with an illumination stress of 250-Lux white LED light. Figure S2 shows the evolutions of the transfer curves of different TFTs under −30 V NBIS as a function of the stress time. The ΔV_on of the In₂O₃ TFTs under −30 V NBIS were much larger than those under −20 V NBIS, and the negative limit of the V_on of the In₂O₃ TFTs after NBIS is close to −30 V. Thus, the NBIS instability of the In₂O₃ TFTs were much more serious than measured. In contrast to the undoped In₂O₃ TFTs, the Pr/Tb:In₂O₃ TFTs did not show much difference for ΔV_on under −30 V NBIS, as shown in Figure S3.

3.4. Oxygen Vacancies

It has been reported that the decrease in V_O concentration of the IGZO can improve the NBIS stability effectively [16]. Compared to the IGZO, the In₂O₃ has much higher V_O concentration. Although the lanthanide doping can reduce the V_O concentration and suppress the free carrier generation of the In₂O₃, the V_O concentration is still much higher than that of the IGZO. Here, the large improvement of NBIS stability after Pr/Tb doping is not mainly due to the reduction of the V_O concentration, because there are no direct relationships between the NBIS stability and the V_O concentration [13,17,18]. For example, the Pr:In₂O₃ had much higher V_O concentration than Tb:In₂O₃ (see Figure 4) for annealing temperature of 300 ℃, but it did not exhibit much difference in NBIS stability compared with Tb:In₂O₃. The In₂O₃ doped with another lanthanide element gadolinium (Gd, which has low electronegativity and large metal–oxide bonding energy that is comparable to those of Pr and Tb) had a low V_O concentration, but the Gd:In₂O₃ TFT had poor NBIS stability with ΔV_on of as large as −13.9 V [13] for Pr:In₂O₃ annealed at 400 °C, the V_O concentration reduced greatly compared to the one annealed at 300 °C, but its NBIS stability was not as good as the one annealed at 300 °C. Thus, the reduction of V_O concentration is not the main reason for the large improvement of NBIS stability after Pr/Tb doping.

3.5. Temperature-Dependent Performances

To further investigate the intrinsic mechanism of the NBIS stability, the NBIS stability measurements were performed at different temperatures (from 78 K to 295 K). Figure 5 shows the ΔV_on evolution of the different TFTs under NBIS, and Figure S4 shows the corresponding evolutions of the transfer curves of different TFTs under NBIS. All of the TFTs showed decreasing I_on with decreasing measuring temperature, which implies that trap-limited conduction (TLC) becomes dominant at a low temperature. In oxide semiconductors, both TLC and percolation conduction (PC) exist (see Figure 6) [19,20]. In TLC, the electrons are subjected to multiple trapping events in the localized tail states below the conduction band edge (E_m), and the transport between tail states is via the variable range hopping (VRH) [20]. At this low temperature, the electrons are more likely to be trapped in the localized tail states due to the lack of sufficient thermal energy, thus the mobility decreases as the measuring temperature decreases. As a result, the conductivity of the oxide semiconductors reduces greatly at a low temperature, which is consistent with the reduction of the I_on of the TFTs at low temperatures (see Figure S4).

It could also be seen from Figure 5 and Figure S4 that all devices displayed decreasing ΔV_on with decreasing temperature. Surprisingly, when the measuring temperature decreased to 78 K, the pure In₂O₃ TFT showed little ΔV_on after 3600 s NBIS, while the Pr:In₂O₃ and Tb:In₂O₃ TFTs exhibited positive ΔV_on of +1.0 V and +0.8 V, respectively. For comparison, the stability under negative bias stress (NBS) without light illumination were tested at room temperature, as shown in Figure S5. Only the pure In₂O₃ TFTs showed obvious ΔV_on of −3.2 V after 3600 s NBS at room temperature (while the Pr/Tb:In₂O₃ TFTs exhibited neglectable ΔV_on). The results reflect that the NBIS instability is a combined effect of light illumination and temperature (thermal activation), as well as gate bias. The energy of the white LED light (or blue light) is not enough to activate the deep donates (such as V_O) near valance band maximum (VBM) at low temperature (78 K), which is contrary to the concept that the activation energy of the subgap state formed by V_O is lower than the energy of the blue LED light.

3.6. Mechanisms of NBIS Instability

Over the past decades, considerable research efforts have been made to understand the native defects/impurities present in oxide semiconductors, but the origin of the unintentional n-type conductivity and/or the NBIS instability of the oxide TFTs is still a subject of debate [21,22,23,24,25,26,27,28,29,30]. Specifically, defect formation and carrier generation, electron localization/transient behavior, as well as carrier scattering in an amorphous state are all far from being fully understood. However, there seems to be an undeclared consensus that the V_O is the major defect in n-type oxide semiconductors. Very recent studies show that V_O likely acts as both shallow and deep donors in In₂O₃ [21,22]. The localized valence tail states or the subgap states near VBM, which are determined not only by their density but also by the degree of localization (structural defects in the amorphous state), contribute to the optical absorption within the visible range, i.e., from 1.5 eV to 3 eV [17]. Under combined stress of light illumination, temperature, and negative gate bias, some of the V_Os will be excited, delocalized free electrons to the conduction band [23,24,25,26,27]. The transition of the V_O ground state to singly charged oxygen vacancy (Vo¹⁺) or doubly charged oxygen vacancy (Vo²⁺) excited states causes spontaneous outward relaxation. The relaxation for V_O to Vo²⁺ is strong because of the electrostatic repulsion of the two positive charges in Vo²⁺ (e.g., the four nearest In neighbors of the Vo²⁺ in In₂O₃ significantly relax outward by 9.3%, 9.6%, 7.7%, and 13%) [21]. The strong relaxation causes a very slow V_O ionization/recombination process, which leads to a very long decade time of the photocurrent [28,29]. However, since the highest energy of the white LED light (the blue light, ~2.7 eV) is high enough for exciting some of the less-deep V_O states directly at low temperatures, the V_O ionization model cannot fully explain why the In₂O₃ TFTs exhibited little ΔV_on at a low temperature (78 K).

Flewitt and Powell proposed a defect transition model to interpretate why the ΔV_on is the combined effect of light illumination, temperature, and negative gate bias. According to the model, the electron donor defect (D_e) can transfer to the neighboring n-coordinated oxygen atom [O(―M)_n] via oxygen interstitials (O_i) with the help of holes, forming a positively charged defect (D_h²⁺) at the site of the original O(―M)_n: [30].

The energy barrier for oxygen vacancy migration via O_i for pure In₂O₃ is about 0.71 eV, which accounts for the requirement for the thermalization energy (certain temperature) to activate the V_Os. Under negative gate bias, the conduction band tails are depleted of electrons, which suppresses Equation (3). However, as the bias is insufficient to pull the Fermi level down through the large number of D_e states, the localized valence band tail states can never be accumulated with holes, so Equation (2) is also suppressed. Only under light illumination combining with negative gate bias are holes in the valence band tail created, allowing the hole quasi-Fermi level to be pulled towards the valence band [30]. This permits Equation (2), and D_h states may be created at the expense of D_e states. Therefore, it is only the combination of photon illumination with energies sufficient to lead to hole generation in valence band tail states and certain temperature with thermalization energy higher than the energy barrier for oxygen vacancy migration as well as negative gate bias that will lead to the negative ΔV_on, as observed experimentally.

3.7. Effect of the CT Transition of Pr⁴⁺/Tb⁴⁺ on the Photo Stability

The great improvement in NBIS stability of the Pr/Tb:In₂O₃ TFTs is ascribed to the charge transfer (CT) transition of the Pr⁴⁺ and Tb⁴⁺. It is known that tetravalent lanthanide ions (Ce⁴⁺, Pr⁴⁺ and Tb⁴⁺) have low CT transition energies that have broad-band absorption [31,32,33]. Compared to Ce⁴⁺, whose CT transition absorption is in the UV range, the CT transistor of Pr⁴⁺ and Tb⁴⁺ have broad absorption in the visible range [13,31]. To identify the existence of Pr⁴⁺/Tb⁴⁺ in the Pr/Tb:In₂O₃ films, X-ray photoelectron spectroscopy (XPS) experiments were performed. Figure 7 shows the Pr3d and Tb3d spectra of the Pr/Tb:In₂O₃ films. The peaks were fitted according to the analysis reported elsewhere [34,35]. The parameters of the fitting peaks for Pr3d and Tb3d are summarized in Tables S1 and S2, respectively. The ratio of Pr⁴⁺/Pr³⁺ or Tb⁴⁺/Tb³⁺ were calculated by the peak areas. There is a clear trend of Pr⁴⁺/Pr³⁺ < Tb⁴⁺/Tb³⁺ at the same annealing temperature. The higher content of Tb⁴⁺ in Tb:In₂O₃ compared to that of Pr⁴⁺ in Pr:In₂O₃ may be one of the reason for the higher mobility and stability of Tb:In₂O₃ TFTs compared to those of Pr:In₂O₃ TFTs because Tb⁴⁺ has a smaller radius with an isotropic half-full 4f ⁷ configuration and a quenched orbital moment. It should be noted that the 4f ⁷ configuration has a large magnetic moment that may scatter the carriers and decrease the mobility. It should be noted that the properties of the solution-processed Pr/Tb:In₂O₃ differed from those of the vacuum-processed ones greatly. We will not compare the difference between vacuum-processed Pr and Tb doped In₂O₃ TFTs this time. The more insightful mechanisms of the difference between Pr and Tb doped In₂O₃ is still under investigated and will be reported in the future.

Figure 6 illustrates the CT transition process in Pr⁴⁺/Tb⁴⁺ doped In₂O₃. Initially, the system is at Point A on Parabola (4f ⁿ) corresponding with an electron at the top of the valence band and a Ln⁴⁺ ion (Ln4f ⁿ—O2p⁶). Under light illumination, the initial state transfers to Point B of the Ln³⁺ state (Ln4f ⁿ⁺¹—O2p⁵). Due to Ln³⁺ having a larger ionic radius than Ln⁴⁺, it relaxes outward and moves to Point C. Then, it transfers back to Parabola (4f ⁿ) via crossing relaxation (by thermal activation) where all luminescence is quenched [36,37,38]. It should be noted that the Ln4f ⁿ—O2p⁶ to Ln4f ⁿ⁺¹—O2p⁵ CT transition has smaller overall lattice expansion/contraction and shorter relaxation time compared to V_O ionization because of the Coulomb attraction between the hole (O2p⁵) and the transferred electron [17,36]. As a result, the Ln⁴⁺ can more easily absorb light than V_O. The results reveal that the improvement of the NBIS stability of the Pr/Tb:In₂O₃ TFTs is attributed to the absorption of the illuminated light by the Ln4f ⁿ—O2p⁶ to Ln4f ⁿ⁺¹—O2p⁵ CT transition and downconversion of the light to nonradiative transition with a relatively short relaxation time compared to V_O ionization. Minasian et al. reported that the partially occupied 4f states are lower in energy than the unoccupied 5d states and provide band gaps of 2.3 and 1.7 eV for PrO₂ and TbO₂, respectively [39]. The lower energy level of Tb 4f ⁷ compared to Pr 4f ¹ would make it easier for the Tb⁴⁺ to absorb the visible light than the Pr⁴⁺, which may be the main reason for the higher NBIS stability of Tb:In₂O₃ TFTs compared to Pr:In₂O₃ TFTs.

The positive ΔV_on under NBIS at a low temperature (78 K, see Figure 5 and Figure S4) of the Pr/Tb:In₂O₃ TFTs was ascribed to the further trapping of electrons by the Ln4f ⁿ⁺¹ exciting states. At a low temperature, most of the electrons are localized in the tail states that intersect the Parabola (4f ⁿ⁺¹), as shown in Figure 6. Under negative gate bias, these localized electrons are depleted and a part of them can further transit to Point C via the Parabola (4f ⁿ⁺¹). As a result, the density of the localized electrons decreases, which is the reason why Pr/Tb:In₂O₃ TFTs exhibited positive ΔV_on under NBIS at a low temperature.

3.8. Formatting of Mathematical Components

$$I_{\mathrm{D}}=\frac{W\mu C_{\mathrm{i}}}{2L}{\left(V_{\mathrm{G}}-V_{\mathrm{th}}\right)}^2$$

(1)

where C_i is the areal capacitance of the dielectric; V_th is the threshold voltage obtained by fitting the saturation region of I_D^1/2 versus V_G plots and extrapolating the fitted line to I_D = 0.

D_e + [O(—M)_n2+2h] → D_e+O_i+D_h²⁺ → O(—M)_n1 + D_h²⁺

(2)

D_h²⁺ + [O(—M)_n1+2e] → D_h²⁺+ O_i^2-+ D_e → O(—M)_n2 + D_e

(3)

4. Conclusions

In conclusion, TFTs based on solution-processed In₂O₃ semiconductors doped with Pr⁴⁺ or Tb⁴⁺ were investigated. It was found that both Pr⁴⁺ and Tb⁴⁺ can improve the NBIS stability greatly, but Tb⁴⁺ is better than Pr⁴⁺. The undoped In₂O₃ TFTs with different annealing temperatures exhibited poor NBIS stability with serious turn-on voltage shift. As the annealing temperature increased, the Pr:In₂O₃ TFTs had poorer NBIS stability (ΔV_on are −3.2, −4.8, and −4.8 V for annealing temperatures of 300, 350, and 400 °C, respectively), while the Tb:In₂O₃ TFTs had better NBIS stability (ΔV_on are −3.6, −3.6, and −1.2 V for annealing temperatures of 300, 350, and 400 °C, respectively). When the measuring temperature decreased to 78 K, the pure In₂O₃ TFT showed little ΔV_on after 3600 s NBIS, while the Pr:In₂O₃ and Tb:In₂O₃ TFTs exhibited positive ΔV_on of +1.0 V and +0.8 V, respectively. Further studies reveal that the negative ΔV_on under NBIS is the combining effect of photon illumination with energies sufficient to lead to hole generation in valence band tail states, a certain temperature with thermalization energy higher than energy barrier for oxygen vacancy migration, and negative gate bias that will lead to bending of the energy band. The improvement of the NBIS stability of the Pr⁴⁺/Tb⁴⁺:In₂O₃ TFTs is attributed to the absorption of the illuminated light by the Pr/Tb4f ⁿ—O2p⁶ to Pr/Tb 4f ⁿ⁺¹—O2p⁵ charge transfer (CT) transition and downconversion of the light to nonradiative transition with a relatively short relaxation time compared to ionization of oxygen vacancies. The positive ΔV_on of the Pr/Tb:In₂O₃ TFTs under low temperature (78 K) is attributed to the further trapping of electrons by the 4f ⁿ⁺¹ exciting states under negative bias. The higher NBIS stability of Tb:In₂O₃ TFTs compared to Pr:In₂O₃ TFTs is ascribed to the smaller ion radius of Tb⁴⁺ and the lower energy level of Tb 4f ⁷ compared to Pr 4f ¹, which would make it easier for the Tb⁴⁺ to absorb the visible light than the Pr⁴⁺. It is worth noting that two sets of devices were tested, and the results can be considered typical.