Charge Trapping and Emission Properties in CAAC-IGZO Transistor: A First-Principles Calculations

The c-axis aligned crystalline indium-gallium-zinc-oxide field-effect transistor (CAAC-IGZO FET), exhibiting an extremely low off-state leakage current (~10−22 A/μm), has promised to be an ideal candidate for Dynamic Random Access Memory (DRAM) applications. However, the instabilities leaded by the drift of the threshold voltage in various stress seriously affect the device application. To better develop high performance CAAC-IGZO FET for DRAM applications, it’s essential to uncover the deep physical process of charge transport mechanism in CAAC-IGZO FET. In this work, by combining the first-principles calculations and nonradiative multiphonon theory, the charge trapping and emission properties in CAAC-IGZO FET have been systematically investigated. It is found that under positive bias stress, hydrogen interstitial in Al2O3 gate dielectric is probable effective electron trap center, which has the transition level (ε (+1/−1) = 0.52 eV) above Fermi level. But it has a high capture barrier about 1.4 eV and low capture rate. Under negative bias stress, oxygen vacancy in Al2O3 gate dielectric and CAAC-IGZO active layer are probable effective electron emission centers whose transition level ε (+2/0) distributed at −0.73~−0.98 eV and 0.69 eV below Fermi level. They have a relatively low emission barrier of about 0.5 eV and 0.25 eV and high emission rate. To overcome the instability in CAAC-IGZO FET, some approaches can be taken to control the hydrogen concentration in Al2O3 dielectric layer and the concentration of the oxygen vacancy. This work can help to understand the mechanisms of instability of CAAC-IGZO transistor caused by the charge capture/emission process.


Introduction
Benefited from the high mobility and good large-area uniformity, indium-galliumzinc-oxide (IGZO) has received a lot of attention since it was discovered in 2004 [1]. After years of development, this material is making its entry into the display industry, thanks to its better performance than amorphous silicon [2][3][4][5]. Recently, a new crystalline oxide semiconductor called c-axis aligned crystalline IGZO (CAAC-IGZO) has also caught the attention of researchers. Field-effect transistors (FETs) with the CAAC-IGZO channel layer exhibit an extremely low off-state leakage current (~10 −22 A/µm) [6,7], which helps to further reduce the leakage power in-memory application. More importantly, the mobility of the CAAC-IGZO FET doesn't degrade at high temperatures [8]. In terms of the potential advantages of extremely low power, high mobility, capacitorless architecture and backend-of-line (BEOL) compatibility [9][10][11], the CAAC-IGZO FET has promised to be an ideal candidate for DRAM applications [7,12,13].
Despite its benefits, the instability of CAAC-IGZO FETs greatly limits their application. These instabilities are mainly reflected in the drift of the threshold voltage when curve of the FET negatively, while PBS shifts it positively. To clearly explain the mental performance of IGZO transistors, a great deal of possible mechanisms ha proposed [14][15][16][17][18][19], for instance, charge trapping processes at the interfaces and/o dielectric, the creation and impact of deep traps in active layer, the absorption of or water molecules at the channel interface, the removal of oxygen interstitials, the of electrons by oxygen vacancies, the reduction of peroxide concentration, and the tion and diffusion of hydrogen, and so on. However, due to the complexity of the tric layer and semiconductor layer, the origin of the bias instabilities in CAAC-IGZ is still controversial. On the other hand, thanks to the sensitivity of the transistors ous factors, such as the deposition conditions, annealing conditions and gate-d material, it is difficult to isolate the impact of different origins on reliability. There better develop high-performance CAAC-IGZO FETs for DRAM applications, it's e to uncover the deep physical process of charge transport mechanisms in CAAC FETs.
In this work, we systematically investigate the charge trapping and emission ties in CAAC-IGZO FETs based on a first-principles calculations. Then, by combin nonradiative multiphonon theory, the trapping process properties of several intri fects in CAAC-IGZO stack with Al2O3 dielectric have been discussed in detail. Fina influence of charge trapping process on the reliability of devices has also been di under positive bias stress (PBS) and negative bias stress (NBS).

Computation Methodology
To uncover the charge trapping and emission properties, a general FET is sel a prototype device. Figure 1 shows the illustration of the carrier trapping pro CAAC-IGZO FET with active layer of CAAC-IGZO and gate dielectric of Al2O3. T principles calculations were utilized based on the density functional theory (DFT first-principle plane-wave pseudopotential method. All calculations were perfor the Vienna Ab Initio Simulation Package (VASP) software [20]. The projector aug wave (PAW) [21] pseudopotential was used to describe the interactions between cleus and valence electrons. The generalized gradient approximation (GGA) w Perdew-Burke-Ernzerhof (PBE) functional was selected to model the exchange an lation interactions [22]. The cut-off energy for the wave function was set to 500 structural models were fully relaxed using the conjugate gradient algorithm u atomic force was less than 0.01 eV/Å. The hybrid functional of Heyd-Scuseria-Ernzerhof (HSE06) was used to ensure the accuracy of bandgap calculation and avoid the small bandgap under GGA-PBE function [23]. 30% and 15% of PBE were replaced with Hartree-Fock function in the calculation of Al 2 O 3 Materials 2023, 16,2282 3 of 17 and IGZO, respectively. To avoid overestimation of metal d bands, the GGA+U method was used to include an on-site Coulomb correlation interaction between the localized metal d electrons [24]. The parameters of U = 8.0 eV, 8.0 eV, 8.0 eV and under PBE function and U = 3.5 eV, 4.0 eV, 4.0 eV under HSE06 function were selected for In 3d, Ga 3d and Zn 3d orbitals, respectively. Figure 2 shows the crystal model of α-Al 2 O 3 and CAAC-IGZO. Al 2 O 3 as a gate dielectric is often grown by ALD to form an amorphous structure. However, Choi et al. [25] confirmed that the features of native defect in Al 2 O 3 are not strongly dependent on the phase, and the results in the α-Al 2 O 3 are representative and applicable to an amorphous structure. The optimized lattice parameters for the perfect α-Al 2 O 3 crystal are a = b = 4.767 Å and c = 13.028 Å, which are good agreement with the experimental values with a = b = 4.656 Å and c = 13.140 Å [26]. To simulate the defects, a supercell of 2 × 2 × 1 with 120 atoms was used. The optimized lattice parameters for the perfect CAAC-IGZO crystal are a = b = 3.345 Å and c = 26.083 Å, which are good agreement with the experimental values with a = b = 3.2948 Å [27] and c = 26.071 Å [28]. To reduce the interaction of defects in the a-b plane, a supercell with 112 atoms was used. The supercell was obtained by setting lattice vectors to (420), (040), and (221) for the IGZO crystal and reducing the lattice constant c to one-third [29]. To have an insight into the capture process of the CAAC-IGZO FETs with Al 2 O 3 dielectric, a variety of different intrinsic defects are considered, which may widely exist and have been suggested as the cause of reliability issues [30][31][32][33][34][35] in oxide semiconductor materials, for instance, oxygen vacancy (V O ), oxygen interstitial (O i ), hydrogen interstitial (H i ), hydrogen substituted oxygen (H O ) and hydroxyl interstitial ((OH) i ), and so on. Here, the defect of Ho can be regarded as a coexistence of H i and V O . And the defect of (OH) i can be regarded as a coexistence of H i and O i . In IGZO crystalline, because of the different chemical environment from nearby metal atoms, four kinds of oxygen vacancy will be created by removing the selected oxygen atoms, as well as two kinds of oxygen interstitial, as shown in Figure 2b. [23]. 30% and 15% of PBE were replaced with Hartree-Fock function in the calculation of Al2O3 and IGZO, respectively. To avoid overestimation of metal d bands, the GGA+U method was used to include an on-site Coulomb correlation interaction between the localized metal d electrons [24]. The parameters of U = 8.0 eV, 8.0 eV, 8.0 eV and under PBE function and U = 3.5 eV, 4.0 eV, 4.0 eV under HSE06 function were selected for In 3d, Ga 3d and Zn 3d orbitals, respectively. Figure 2 shows the crystal model of α-Al2O3 and CAAC-IGZO. Al2O3 as a gate dielectric is often grown by ALD to form an amorphous structure. However, Choi et al. [25] confirmed that the features of native defect in Al2O3 are not strongly dependent on the phase, and the results in the α-Al2O3 are representative and applicable to an amorphous structure. The optimized lattice parameters for the perfect α-Al2O3 crystal are a = b = 4.767 Å and c = 13.028 Å, which are good agreement with the experimental values with a = b = 4.656 Å and c = 13.140 Å [26]. To simulate the defects, a supercell of 2 × 2 × 1 with 120 atoms was used. The optimized lattice parameters for the perfect CAAC-IGZO crystal are a = b = 3.345 Å and c = 26.083 Å, which are good agreement with the experimental values with a = b = 3.2948 Å [27] and c = 26.071 Å [28]. To reduce the interaction of defects in the a-b plane, a supercell with 112 atoms was used. The supercell was obtained by setting lattice vectors to (420), (040), and (221) for the IGZO crystal and reducing the lattice constant c to one-third [29]. To have an insight into the capture process of the CAAC-IGZO FETs with Al2O3 dielectric, a variety of different intrinsic defects are considered, which may widely exist and have been suggested as the cause of reliability issues [30][31][32][33][34][35] in oxide semiconductor materials, for instance, oxygen vacancy (VO), oxygen interstitial (Oi), hydrogen interstitial (Hi), hydrogen substituted oxygen (HO) and hydroxyl interstitial ((OH)i), and so on. Here, the defect of Ho can be regarded as a coexistence of Hi and VO. And the defect of (OH)i can be regarded as a coexistence of Hi and Oi. In IGZO crystalline, because of the different chemical environment from nearby metal atoms, four kinds of oxygen vacancy will be created by removing the selected oxygen atoms, as well as two kinds of oxygen interstitial, as shown in Figure 2b.

Formation Energy and Transition Level
As mentioned above, the CAAC-IGZO FETs may be affected by a variety of defects. To identify which defects have an impact on the FET, the formation energy of all kinds of defects will be discussed firstly. The formation energy of defect can be obtained as [37], where represents the total energy of a supercell with the defect in the cell, is the total energy for a perfect supercell, is the number of atoms removed from or added to the supercell to form a defect, is the chemical potentials of oxygen and

Formation Energy and Transition Level
As mentioned above, the CAAC-IGZO FETs may be affected by a variety of defects. To identify which defects have an impact on the FET, the formation energy of all kinds of defects will be discussed firstly. The formation energy of defect can be obtained as [37], where E q de f ect represents the total energy of a supercell with the defect in the cell, E per f ect is the total energy for a perfect supercell, n i is the number of atoms removed from or added to the supercell to form a defect, µ i is the chemical potentials of oxygen and hydrogen atom/ion, q represents the number of electrons transferred from or to electron reservoirs [38,39], E f refers to the Fermi level relative to the valence band maximum energy (VBM, E v ) position in a perfect supercell. The correction term, ∆V, is referred to as the electrostatic potential that is far from the defect in the supercell with respect to the perfect supercell of the same size. Otherwise, in order to determine the position of the defect level in the band gap, one can calculate the transition level. Based on Equation (1), the position of the Fermi level at which the formation energy of charge states q equals to the formation energy of charge states q' was defined as transition level ε(q/q') [37].
Generally, by using the charged formation energy and transition level, one can clearly understand the stability of defect and the relative position of defect level in the bandgap from an energy perspective. Figure 3 shows the formation energy of each defect under O-rich conditions In this work, the Fermi level of IGZO channel is set at 0.2 eV below E C in the absence of an electric field, which is a reasonable assumption [2,40]. From in Figure 3a, as compared with the other oxygen vacancies in IGZO, Vo 1, being nearby an In atom and Zn atom, exhibits the lowest formation energy. This result indicates that Vo 1 may exist more stably in IGZO than other oxygen vacancies, which is attributed to the weak bonding between In atom and O atom. It is noting that unlike the role of oxygen vacancies in a-IGZO and some transition metal oxides [31,41], oxygen holes do not act as n-type electron donors in CAAC-IGZO. In contrast, the formation energy of interstitial oxygen does not depend significantly on the metal ions in its vicinity. More importantly, our calculations also show the most stable charge states for each intrinsic defect in IGZO and Al 2 O 3 without an electric field. In the absence of electric field, the Fermi level is 0. hydrogen atom/ion, represents the number of electrons transferred from or to electron reservoirs [38,39], refers to the Fermi level relative to the valence band maximum energy (VBM, ) position in a perfect supercell. The correction term, ∆ , is referred to as the electrostatic potential that is far from the defect in the supercell with respect to the perfect supercell of the same size. Otherwise, in order to determine the position of the defect level in the band gap, one can calculate the transition level. Based on Equation (1), the position of the Fermi level at which the formation energy of charge states q equals to the formation energy of charge states q' was defined as transition level ε(q/q') [37].
Generally, by using the charged formation energy and transition level, one can clearly understand the stability of defect and the relative position of defect level in the bandgap from an energy perspective. Figure 3 shows the formation energy of each defect under O-rich conditions In this work, the Fermi level of IGZO channel is set at 0.2 eV below in the absence of an electric field, which is a reasonable assumption [2,40]. From in Figure 3a, as compared with the other oxygen vacancies in IGZO, Vo1, being nearby an In atom and Zn atom, exhibits the lowest formation energy. This result indicates that Vo1 may exist more stably in IGZO than other oxygen vacancies, which is attributed to the weak bonding between In atom and O atom. It is noting that unlike the role of oxygen vacancies in a-IGZO and some transition metal oxides [31,41], oxygen holes do not act as n-type electron donors in CAAC-IGZO. In contrast, the formation energy of interstitial oxygen does not depend significantly on the metal ions in its vicinity. More importantly, our calculations also show the most stable charge states for each intrinsic defect in IGZO and Al2O3 without an electric field. In the absence of electric field, the Fermi level is 0.2 eV below and the most stable charge states for intrinsic defects (VO, Oi, Hi, HO and (OH)i) in IGZO, are 0, −2, +1, +1 and −1, respectively. And the most stable charge states for intrinsic defects (VO, Oi, Hi, HO, and (OH)i) in Al2O3, are also 0, −2, +1, +1 and −1, respectively. These charged defects will form a charged center in oxide and lead to the fixed oxide charge, and then significantly influence the electrical characteristics of transistor. As a result, Hi and HO defects will lead to positive fixed oxide charge, while Oi and (OH)i will result in a negative fixed oxide charge.  Figure 4 shows the band alignment and transition level of defects in Al2O3/IGZO system. In general, the transition levels reveal which defects undergo electron capture or emission. With the position of the Fermi level changes in the presence of electric field, the defects will capture electrons when the Fermi level is higher than the transition level as well as emission electrons when the Fermi level is lower than the transition level. Therefore, if the transition level is closer to the Fermi level, the defect is a more efficient center    Figure 4 shows the band alignment and transition level of defects in Al 2 O 3 /IGZO system. In general, the transition levels reveal which defects undergo electron capture or emission. With the position of the Fermi level changes in the presence of electric field, the defects will capture electrons when the Fermi level is higher than the transition level as well as emission electrons when the Fermi level is lower than the transition level. Therefore, if the transition level is closer to the Fermi level, the defect is a more efficient center for electron capture or emission under the electric field. In Figure 4, one can see that the transition level ε (+1/−1) of H i in Al 2 O 3 is 0.52 eV above the Fermi level of CAAC-IGZO which is closer to the Fermi level, as compared with the transition level ε (+1/−1) of H O in Al 2 O 3 which is 2.14 eV above Fermi level. This result suggests that the defect H i in Al 2 O 3 gate dielectric is probable effective electron trap center for CAAC-IGZO channel under PBS. The reason is that when a positive bias voltage is applied, the bandgap of the gate dielectric is shifted downwards, thus allowing the process of electron capture more likely to occur in H i defects in Al 2 O 3 gate dielectric. The detailed schematics for electron trapping process under PBS can be seen in Figure 5a. In contrary, the transition levels ε (+2/0) of Vo in CAAC-IGZO and ε (+2/0) of Vo in Al 2 O 3 are distributed at −0.73~−0.98 eV and 0.69 eV below the Fermi level of CAAC-IGZO, respectively. The transition level ε (+2/0) for Vo in CAAC-IGZO and Al 2 O 3 is closer to the Fermi level, as compared with other defects.

Fermi level (eV) Formation Energy (eV)
The results indicate that the oxygen vacancies in CAAC-IGZO active layer and Al 2 O 3 gate dielectric are likely to be the electron emission center under NBS, due to the bandgap of gate dielectric shifting upwards thus allowing the process of electron emission. Figure 5b shows the schematics of electron emission process under NBS in detailed. The properties of electron capture or release in these defects will be discussed in more detail in the following.
which is closer to the Fermi level, as compared with the transition level ε (+1/−1) of HO in Al2O3 which is 2.14 eV above Fermi level. This result suggests that the defect Hi in Al2O3 gate dielectric is probable effective electron trap center for CAAC-IGZO channel under PBS. The reason is that when a positive bias voltage is applied, the bandgap of the gate dielectric is shifted downwards, thus allowing the process of electron capture more likely to occur in Hi defects in Al2O3 gate dielectric. The detailed schematics for electron trapping process under PBS can be seen in Figure 5a. In contrary, the transition levels ε (+2/0) of Vo in CAAC-IGZO and ε (+2/0) of Vo in Al2O3 are distributed at −0.73~−0.98 eV and 0.69 eV below the Fermi level of CAAC-IGZO, respectively. The transition level ε (+2/0) for Vo in CAAC-IGZO and Al2O3 is closer to the Fermi level, as compared with other defects. The results indicate that the oxygen vacancies in CAAC-IGZO active layer and Al2O3 gate dielectric are likely to be the electron emission center under NBS, due to the bandgap of gate dielectric shifting upwards thus allowing the process of electron emission. Figure 5b shows the schematics of electron emission process under NBS in detailed. The properties of electron capture or release in these defects will be discussed in more detail in the following.    for electron capture or emission under the electric field. In Figure 4, one can see that the transition level ε (+1/−1) of Hi in Al2O3 is 0.52 eV above the Fermi level of CAAC-IGZO which is closer to the Fermi level, as compared with the transition level ε (+1/−1) of HO in Al2O3 which is 2.14 eV above Fermi level. This result suggests that the defect Hi in Al2O3 gate dielectric is probable effective electron trap center for CAAC-IGZO channel under PBS. The reason is that when a positive bias voltage is applied, the bandgap of the gate dielectric is shifted downwards, thus allowing the process of electron capture more likely to occur in Hi defects in Al2O3 gate dielectric. The detailed schematics for electron trapping process under PBS can be seen in Figure 5a. In contrary, the transition levels ε (+2/0) of Vo in CAAC-IGZO and ε (+2/0) of Vo in Al2O3 are distributed at −0.73~−0.98 eV and 0.69 eV below the Fermi level of CAAC-IGZO, respectively. The transition level ε (+2/0) for Vo in CAAC-IGZO and Al2O3 is closer to the Fermi level, as compared with other defects. The results indicate that the oxygen vacancies in CAAC-IGZO active layer and Al2O3 gate dielectric are likely to be the electron emission center under NBS, due to the bandgap of gate dielectric shifting upwards thus allowing the process of electron emission. Figure 5b shows the schematics of electron emission process under NBS in detailed. The properties of electron capture or release in these defects will be discussed in more detail in the following.

Electronic Properties of Charge Capture/Emission Process
According to the analysis of the transition levels above, one can determine that H i in Al 2 O 3 is the possible electron capture center and V O in both Al 2 O 3 and CAAC-IGZO is the possible electron emission center. To clearly understand the electronic properties of Al 2 O 3 and CAAC-IGZO with different defects and charge states during the charge transition process, we calculated the density of states (DOS) of Al 2 O 3 and CAAC-IGZO with different defects and charge states, respectively. Figure 6 shows the DOS and the local charge density of hydrogen interstitial in Al 2 O 3 dielectric layer. It is found in Figure 6a that, when the charge state in Al 2 O 3 with the defects is +1, the protonated hydrogen forms a hydroxide ion with the oxygen ion, at which there is no sub-state in the bandgap. When H + i captures an electron and forms H 0 i , the hydrogen-oxygen bond will be broken and the hydrogen atom moves to the middle of the aluminum ion, as shown in Figure 6b. In this case, a new sub-state DOS arises and is distributed at 3.2 eV above VBM, which is composed of H orbitals and O orbitals. When H 0 i captures an electron and forms H − i , the aluminum ion moves closer to the H atom. The sub-state DOS distributed at 2.6 eV above VBM, composed of H orbitals and O orbitals, which is 0.6 eV lower than H 0 i .

Electronic Properties of Charge Capture/Emission Process
According to the analysis of the transition levels above, one can determine that Hi in Al2O3 is the possible electron capture center and VO in both Al2O3 and CAAC-IGZO is the possible electron emission center. To clearly understand the electronic properties of Al2O3 and CAAC-IGZO with different defects and charge states during the charge transition process, we calculated the density of states (DOS) of Al2O3 and CAAC-IGZO with different defects and charge states, respectively. Figure 6 shows the DOS and the local charge density of hydrogen interstitial in Al2O3 dielectric layer. It is found in Figure 6a that, when the charge state in Al2O3 with the defects is +1, the protonated hydrogen forms a hydroxide ion with the oxygen ion, at which there is no sub-state in the bandgap. When H captures an electron and forms H , the hydrogen-oxygen bond will be broken and the hydrogen atom moves to the middle of the aluminum ion, as shown in Figure 6b. In this case, a new sub-state DOS arises and is distributed at 3.2 eV above VBM, which is composed of H orbitals and O orbitals. When H captures an electron and forms H , the aluminum ion moves closer to the H atom. The sub-state DOS distributed at 2.6 eV above VBM, composed of H orbitals and O orbitals, which is 0.6 eV lower than H .  Figure 7 shows the DOS and the local charge density of oxygen vacancies in Al2O3 dielectric layer. One can see that, when the defects are in the charge state of 0, the electrons are mainly present in the oxygen vacancies. The sub-state DOS distributes at 2.7 eV above VBM, which is composed of Al orbitals and O orbitals. When V emits an electron and forms V , the aluminium ion moves slightly outward from the oxygen vacancy. The substate DOS distributes at 4.1 eV above VBM, which is 0.9 eV higher than V , as shown in Figure 7b. On the other hand, the electron emission process for the oxygen vacancy from V to V is very similar to that from V to V process, again with the aluminum ion moves slightly outward from the oxygen vacancy. The sub-state DOS distributes at 5.4 eV above VBM, which is 1.1 eV higher than V .   Figure 8 shows the DOS and the local charge density of oxygen vacancies in the CAAC-IGZO active layer. As can be seen in Figure 8 that the electronic properties of four kinds of oxygen vacancies are similar. When the defects are in the charge state of 0, the electrons are mainly present in the oxygen vacancies. The sub-state DOS distributes at 1.6 eV above VBM. For the oxygen vacancies from V and V , the sub-state DOS is mainly composed of In orbitals and O orbitals, while for and V , the sub-state DOS is composed of both Ga orbitals, Zn orbitals and O orbitals. When V emits an electron and forms V , the metal ions move outward from the oxygen vacancy. The sub-state DOS distributes at about 2 eV above VBM, which is 0.4 eV higher than V . Similarly, the electron emission process for the oxygen vacancies from V to V also arises with the outward movement of metal ions. The sub-state DOS is distributed near the Conduction Band Minimum (CBM).

Kinetics of Charge Capture/Emission Process
To uncover the kinetics of the charge capture/emission process in CAAC-IGZO FETs, it is crucial to know the activation barrier of the transition process. However, the transition level mentioned above only considers the equilibrium energy relationship between the two-defect charge states and ignores the deformation of the defect site when the charge state is changing. Physically, changes in defect configuration and electron-phonon coupling alter the activation barrier of the charge capture/emission process and will significantly influence the kinetics of the charge capture/emission process. In order to better understand the kinetics of the charge capture/emission process, it is essential to further consider the relationship between the defect formation energy and configuration. The theoretical model used in this work is called as nonradiative multiphonon theory (NMP) [42,43], which has been proven to correctly describe the charge trapping of oxide defects in transistors [44].

Kinetics of Charge Capture/Emission Process
To uncover the kinetics of the charge capture/emission process in CAAC-IGZO FETs, it is crucial to know the activation barrier of the transition process. However, the transition level mentioned above only considers the equilibrium energy relationship between the two-defect charge states and ignores the deformation of the defect site when the charge state is changing. Physically, changes in defect configuration and electron-phonon coupling alter the activation barrier of the charge capture/emission process and will significantly influence the kinetics of the charge capture/emission process. In order to better understand the kinetics of the charge capture/emission process, it is essential to further consider the relationship between the defect formation energy and configuration. The theoretical model used in this work is called as nonradiative multiphonon theory (NMP) [42,43], which has been proven to correctly describe the charge trapping of oxide defects in transistors [44].

Nonradiative Multiphonon Transition Process
Generally, if a defect is neutral in state and negatively charged in state , the atomic equilibrium configuration is different in each state. Here, the different states are denoted by and . Since the real motion of atoms is highly complex, one usually uses a single reaction coordinate to hold all 3N coordinates of the N atoms under consideration. The total energy consists of contributions from the ionic system, the electronic system, and a coupling term in each state. The coupling term describes the shift in the equi-

Nonradiative Multiphonon Transition Process
Generally, if a defect is neutral in state V 1 and negatively charged in state V 2 , the atomic equilibrium configuration is different in each state. Here, the different states are denoted by e 1 and e 2 . Since the real motion of atoms is highly complex, one usually uses a single reaction coordinate e to hold all 3N coordinates of the N atoms under consideration. The total energy consists of contributions from the ionic system, the electronic system, and a coupling term in each state. The coupling term describes the shift in the equilibrium positions and the change of the vibrational frequencies. In most case, the energy-coordinate relationship can be approximated as a quadratic function for small displacement. This simplification can reasonably reflect the essence of the capture process [45]. Another simplification is first-order approximation [45,46], which assumes that only one vibrational mode contributes to the electronic transition process. Based on these approximations, the relationship of total energy to reaction coordinates is usually written as [44], where e is the reaction coordinate with the local equilibrium position e i , M is the effective mass of the 'defect molecule' [47], ω i is the vibrational frequency of mode i and E i represent the potential energy of states.
In terms of the relationship of energy to reaction coordinates in Equation (2), one can obtain the relationship of a nonradiative multiphonon transition process, as shown in Figure 9a. In the regular operation of the transistor, photons are not available, which means the increase of energy should only rely on many phonons during the transition process. In Figure 9a, E 12 and E 21 are the electron capture and emission energy barriers, respectively. λ 12 and λ 21 are the reorganization energies that reflects the strength of electron-phonon coupling, respectively. When an electric field is present at the location of the defect, the total energy difference between two states changes from E 2 -E 1 to E 2 -E 1 by qV ox . For defects in the gate dielectric Al 2 O 3 , V ox is the potential difference at the defect from the interface. For defects in IGZO channel, V ox is the surface potential at the location of defects. Besides, the capture energy barrier and emission energy barrier also change to E 12 and E 21 , as shown in Figure 9b. Then, the rates of transition between two states can be given [44], here, N c is the effective DOS in CBM, n is the electron density of active channel, v th is the thermal velocity of the electron, σ is the capture cross-section, k is the Boltzmann constant, and T is the absolute temperature. According to Equation (3), the effective capture/emission times and the probability of two states occupying at the moment with the infinity of t are given, here, effective time constant τ 0 incorporates the N c , v th and σ, and is weakly dependent on bias and temperature [48].
where is the reaction coordinate with the local equilibrium position , is the effective mass of the 'defect molecule' [47], is the vibrational frequency of mode i and represent the potential energy of states.
In terms of the relationship of energy to reaction coordinates in Equation (2), one can obtain the relationship of a nonradiative multiphonon transition process, as shown in Figure 9a. In the regular operation of the transistor, photons are not available, which means the increase of energy should only rely on many phonons during the transition process. In Figure 9a, and are the electron capture and emission energy barriers, respectively. and are the reorganization energies that reflects the strength of electronphonon coupling, respectively. When an electric field is present at the location of the defect, the total energy difference between two states changes from to -by . For defects in the gate dielectric Al2O3, is the potential difference at the defect from the interface. For defects in IGZO channel, is the surface potential at the location of defects. Besides, the capture energy barrier and emission energy barrier also change to and , as shown in Figure 9b. Then, the rates of transition between two states can be given [44], here, is the effective DOS in CBM, is the electron density of active channel, is the thermal velocity of the electron, is the capture cross-section, is the Boltzmann constant, and is the absolute temperature. According to Equation (3), the effective capture/emission times and the probability of two states occupying at the moment with the infinity of t are given, here, effective time constant incorporates the , and , and is weakly dependent on bias and temperature [48]. Figure 9. Relationship of total energy to reaction coordinate of nonradiative multiphonon transition process without electric field (a) and with an electric field (b). V 1 and V 2 represent the neutral state and negative charge state of the defect, respectively. V 2 represents the negative charge state of defect when an electric field is present. E 12 is the electron capture energy barrier, and E 21 is the electron emission energy barrier. The vibrational energy of the system is modeled by E 12 and E 21 .
Then, the relationship of total energy to coordinates is estimated by using a DFT method. The energy expression of charged state V 1 and charged state V 2 can be expressed as, here, E V 2 (e 1 ) and E V 1 (e 2 ) can be also calculated to define the quadratic function. The coefficient 1 2 Mω 2 i can be extracted from the parabolic potential energies.

Charge Transition Process in Al 2 O 3
By analyzing the nonradiative multiphonon process, one can discuss the kinetics of the charge transition process. Next, the interstitial hydrogen defect in Al 2 O 3 gate dielectric will be discussed, which is a possible electron capture center under PBS in terms of the calculation of the transition levels. Since the capture of electrons by defects has a certain time constant, the probability of a defect capturing two electrons at the same time is very low. Firstly, the charge capture processes from H + i to H 0 i and H 0 i to H − i will be analyzed, respectively. Figure 10 shows the total energy as a function of the reaction coordinates for the hydrogen interstitial in the Al 2 O 3 dielectric layer and the energy barrier of the transition process. As can be seen in Figure 10a,b that for the transition process from H + i to H 0 i , the reorganization energy λ 21 required is very high based on the method in Figure 9, reaching to 3.42 eV. The high reorganization energy indicates that the system has a strong electron-phonon coupling in this capture process. Otherwise, combined with the DOS's results in Figure 6, it is found that the vibrational mode of the hydrogen-oxygen bond contributes to this electron capture process. Since the H 0 i state has a higher equilibrium energy, the capture barrier will become relatively high, reaching to~1.8 eV. According to Equation (5), this barrier will result in a low capture rate k 12 . As V ox increases from 0V to 2V, the capture barrier decreases linearly from 1.8 eV to 0.3 eV. Then the capture rate will increase exponentially. For the transition process from H 0 i to H − i in Figure 10c,d that, the reorganization energy λ 21 is obviously different from that from H + i to H 0 i . The different reorganization energy indicates that the vibrational modes contribute differently to the electronic transition process in the two processes. According to the DOS's results, one can find that the vibrational mode of the adjacent aluminum ion around the hydrogen interstitial contributes to the H 0 i to H − i process, which is different for the process from H + i to H 0 i . At the same time, although the equilibrium energy while the probability of defects in H − i state increases significantly, according to Equation (5). The capture barrier is basically equal to 0 eV, which means that the electron capture time τ c from H 0 i to H − i is basically equal to τ 0 . Overall, for the H + i defect in the Al 2 O 3 gate dielectric, when V ox is greater than 0.52 V, the Fermi level is higher than the transition level ε (+1/−1), and the equilibrium energy of H − i is lower than H + i , which means that the probability of defects in the state of −1 is higher than that in the state of +1. The electron capture of defects is a favorable energy process. However, the capture barrier is very high (about 1.4 eV), which makes the capture rate of H + i to be very slow. After the electron capture is happened and H 0 i is formed, the defect will generate electron capture again quickly by a capture time τ 0 and forms H − i . As V ox is continuously increased, the capture time τ c from H + i to H 0 i will decline exponentially. These kinetic properties suggest that the electron capture process of hydrogen interstitial in Al 2 O 3 is relatively slow at low voltage, but rapidly increases at high voltage, and eventually form the negative charge center in the gate dielectric oxide. Overall, for the H defect in the Al2O3 gate dielectric, when V is greater than 0.52 V, the Fermi level is higher than the transition level ε (+1/−1), and the equilibrium energy of H is lower than H , which means that the probability of defects in the state of −1 is higher than that in the state of +1. The electron capture of defects is a favorable energy process. However, the capture barrier is very high (about 1.4 eV), which makes the capture rate of H to be very slow. After the electron capture is happened and H is formed, the defect will generate electron capture again quickly by a capture time and forms H . As V is continuously increased, the capture time from H to H will decline exponentially. These kinetic properties suggest that the electron capture process of hydrogen interstitial in Al2O3 is relatively slow at low voltage, but rapidly increases at high voltage, and eventually form the negative charge center in the gate dielectric oxide.
Next, we will discuss the transition process of oxygen vacancjes in the Al2O3 gate dielectric, which is a possible electron emission center under NBS based on the transition levels mentioned above. Similarly, we analyzed the emission process from V to V and from V to V , respectively. Figure 11 shows the total energy as a function of the reaction coordinate for the oxygen vacancies in the Al2O3 dielectric layer and the energy barrier of the transition process. As can be seen in Figure 11a,c that, for the two transition processes, the reorganization energies are relatively close, suggesting that the vibrational Next, we will discuss the transition process of oxygen vacancjes in the Al 2 O 3 gate dielectric, which is a possible electron emission center under NBS based on the transition levels mentioned above. Similarly, we analyzed the emission process from V 0 O to V + O and from V + O to V 2+ O , respectively. Figure 11 shows the total energy as a function of the reaction coordinate for the oxygen vacancies in the Al 2 O 3 dielectric layer and the energy barrier of the transition process. As can be seen in Figure 11a,c that, for the two transition processes, the reorganization energies are relatively close, suggesting that the vibrational modes contribute to the electronic transition process, which may be the same in both processes. Combining with the DOS's results, one can obtain that the vibrational modes of the adjacent aluminum ion around oxygen vacancies contribute to the electron emission process. According to Figure 11b, for the transition process from V 0 O to V + O , the emission barrier decreases from 1.0 eV to 0 eV as V ox increases from 0 V to 2 V. In Figure 11d, for the transition process from V + O to V 2+ O , the emission barrier decreases from 0.5 eV to 0 eV as V ox increases. And as V ox is greater than 1.4 V, the emission barrier increases slightly. crease in the emission barrier, while the emission time for the transition process from V to V gradually converges to and begins to increase as is greater than 1.4 V. As a result, these kinetic properties suggest that the rate of electron emission process from the oxygen vacancies in Al2O3 increases as the voltage increases, and finally forms the positive charge center in the gate dielectric oxide.

Charge Transition Process in CAAC-IGZO
Finally, we will discuss the electron emission process of the oxygen vacancies in the CAAC-IGZO active layer. Figure 12 shows the total energy as a function of the reaction coordinate for the oxygen vacancies in the CAAC-IGZO active layer and the energy barrier of the transition process, respectively. Based on the results mentioned above, four kinds of oxygen vacancies in CAAC-IGZO are similar. Here, we only discuss the transition process of V . As can be seen in Figure 12a,c that, for the electron emission processes from V to V and from V to V , the reorganization energies are very close. The results imply that the vibrational modes contribute to the electronic emission process, which may be the same in both processes. The DOS's results also display that the vibrational O , which represents a significantly lower emission time τ e for the process from V + O to V 2+ O . As |V ox | increases further, the emission time τ e for the transition process from V 0 O to V + O decreases rapidly due to a further decrease in the emission barrier, while the emission time τ e for the transition process from V + O to V 2+ O gradually converges to τ 0 and begins to increase as V ox is greater than 1.4 V. As a result, these kinetic properties suggest that the rate of electron emission process from the oxygen vacancies in Al 2 O 3 increases as the voltage increases, and finally forms the positive charge center in the gate dielectric oxide.

Charge Transition Process in CAAC-IGZO
Finally, we will discuss the electron emission process of the oxygen vacancies in the CAAC-IGZO active layer. Figure 12 shows the total energy as a function of the reaction coordinate for the oxygen vacancies in the CAAC-IGZO active layer and the energy barrier of the transition process, respectively. Based on the results mentioned above, four kinds of oxygen vacancies in CAAC-IGZO are similar. Here, we only discuss the transition process of V O2 . As can be seen in Figure 12a,c that, for the electron emission processes from V 0 O to V + O and from V + O to V 2+ O , the reorganization energies are very close. The results imply that the vibrational modes contribute to the electronic emission process, which may be the same in both processes. The DOS's results also display that the vibrational modes of the adjacent metal ion around oxygen vacancy contribute to the electron emission process. The lower reorganization energy represents a weaker electron-phonon coupling of the oxygen vacancies in the CAAC-IGZO active layer, as compared with the defect transition process in Al 2 O 3 . In Figure 12b, one can see that for the transition process from V 0 O to V + O , the emission barrier decreases rapidly from 1.0 eV to 0 eV as |V ox | increases slightly at |V ox | being greater than 1.6 V. In Figure 12d, for the transition process from V + O to V 2+ O , the emission barrier decreases from 0.6 eV to 0 eV as |V ox | increases and begins to increase when |V ox | is greater than 1.2 V. The emission barrier is approximately 0.2 eV, as |V ox | is equal to 2 V.
13 of 17 modes of the adjacent metal ion around oxygen vacancy contribute to the electron emission process. The lower reorganization energy represents a weaker electron-phonon coupling of the oxygen vacancies in the CAAC-IGZO active layer, as compared with the defect transition process in Al2O3. In Figure 12b, one can see that for the transition process from V to V , the emission barrier decreases rapidly from 1.0 eV to 0 eV as | | increases slightly at | | being greater than 1.6 V. In Figure 12d, for the transition process from V to V , the emission barrier decreases from 0.6 eV to 0 eV as | | increases and begins to increase when | | is greater than 1.2 V. The emission barrier is approximately 0.2 eV, as | | is equal to 2 V. Overall, for the V defect in the CAAC-IGZO active layer, when V is greater than 0.73 V. the Fermi level is below the transition energy level ε (+2/−0), the defects undergo the electron emission as a favorable energy process. At that point, the emission barrier for the transition process from V to V is about 0.25 eV. Subsequently, the V defect is | | Overall, for the V 0 O defect in the CAAC-IGZO active layer, when V ox is greater than 0.73 V. the Fermi level is below the transition energy level ε (+2/−0), the defects undergo the electron emission as a favorable energy process. At that point, the emission barrier for the transition process from V 0 O to V + O is about 0.25 eV. Subsequently, the V + O defect is then emitted again with a much lower emission energy of about 0.1 eV. As |V ox | increases further, the emission time τ e for the transition process from V 0 O to V + O decreases rapidly to τ 0 and begins to increase at |V ox | greater than 1.6 V, while the emission time τ e for the transition process from V + O to V 2+ O converges to τ 0 and begins to increase at |V ox | greater than 1.2 V. These kinetics properties suggest that the rate of the electron emission process increases with the increasing voltage, then begins to slow down when the voltage reaches about 1.6 V, and finally forming a positive charge center in the active layer.

Instability Effects in IGZO Device Induced by Charge Capture/emission Process
As mentioned above, the instability of the CAAC-IGZO FETs is mainly reflected in the drift of the threshold voltage under NBS and PBS. To uncover the instability, we then discuss the instability effects in IGZO devices induced by the charge capture/emission process. General speaking, the change of defect charge state caused by the charge capture/emission process will leave a new positive or negative charge center in oxide semiconductors and gate dielectric, which can be observed macroscopically as a change of fixed oxide charge per area (Q ox ) and affects the electrical performance of the device. The relationship of the threshold voltage drifts with Q ox is described as [44], here, C ox is the capacitance per area of gate dielectric. Universally, the capture/emission process of the oxygen vacancies does not quickly follow the gate bias change, which will be experimental recorded as a BTI effects. Under PBS, the electron capture process of hydrogen interstitial in the Al 2 O 3 dielectric layer will decrease the value of Q ox , and then induce a positive drift of the threshold voltage. In a 2T0C DRAM cell, this PBS-induced positive drift occurs within the write transistor and read transistor of the write operation and results in lower open-state current and slower write operations. In addition, the large capture barrier and capture time of the process from H + i to H 0 i will cause a small drift of the threshold voltage at lower temperatures and low positive gate bias voltage. The experiment displays that the Al 2 O 3 gate dielectric with 1.1% hydrogen concentration may result in a positive but small ∆V th at 25 • C under PBS [33]. While the trap level E t tested by IPE measurements is 0.69 eV above the Fermi level, which is similar to our results. However, the ∆V th will become negative as the temperature raising. The reason is that under higher stress, trapped hydrogen in the gate-dielectric is released, diffuses to IGZO layer. To overcome the instability, some approaches can be taken to control the hydrogen concentration in Al 2 O 3 dielectric layer, such as replacing water with ozone as a precursor for ALD of the gate dielectric.
Under NBS, the electron emission process of the oxygen vacancies in the Al 2 O 3 dielectric layer and CAAC-IGZO active layer will lead to the increase of Q ox , and then induce a negative drift of the threshold voltage. In a 2T0C DRAM cell, the NBS-induced negative drift occurs within the write transistor of the read operation and results in larger off-state current and shorter retention time. Generally, the transistor is in off-state under a negative gate bias. The phenomenon of the negative drift of the threshold voltage will be observed when transistor is in on-state again and one can find a hysteresis of the currentvoltage curve. To better understand the phenomenon of the negative drift of the threshold voltage induced, one firstly need to distinguish between the different contributions of the oxygen vacancies in the Al 2 O 3 dielectric layer and CAAC-IGZO active layer to the threshold voltage drift, respectively. According to the calculations, the behavior of the oxygen vacancies in the Al 2 O 3 dielectric layer and CAAC-IGZO active layer is essentially similar. However, it should be noted, that V ox is the surface potential at the defect for the active layer and the potential difference at the defect for the dielectric layer. It is well known that when the gate bias of transistor is below the threshold voltage, more voltage will fall on