Localized Tail States and Electron Mobility in Amorphous ZnON Thin Film Transistors

The density of localized tail states in amorphous ZnON (a-ZnON) thin film transistors (TFTs) is deduced from the measured current-voltage characteristics. The extracted values of tail state density at the conduction band minima (Ntc) and its characteristic energy (kTt) are about 2 × 1020 cm−3eV−1 and 29 meV, respectively, suggesting trap-limited conduction prevails at room temperature. Based on trap-limited conduction theory where these tail state parameters are considered, electron mobility is accurately retrieved using a self-consistent extraction method along with the scaling factor ‘1/(α + 1)’ associated with trapping events at the localized tail states. Additionally, it is found that defects, e.g. oxygen and/or nitrogen vacancies, can be ionized under illumination with hv ≫ Eg, leading to very mild persistent photoconductivity (PPC) in a-ZnON TFTs.

less sensitive to bonding angle disorder. This can yield a high density of localized tail states near the CBM in a-ZnON (see Fig. 1c). For a TFT with a-ZnON channel, the field-effect mobility is strongly affected by the presence of the localized tail states. This can be explained with trap-limited conduction theory (i.e. multiple trapping and thermal release events) (see Fig. 1c,d) 5,14 . One of the ways to reduce the localized tail state density is by thermal annealing, resulting in higher mobility (up to 110 cm 2 /V-s) reported in Ref. 8.
In this paper, we extract the density of localized tail states in a-ZnON TFTs, using current-voltage characteristics of the device. The extracted values of tail state density at the CBM (N tc ) and characteristic energy (kT t ) are about 2 × 10 20 cm −3 eV −1 and 29 meV, respectively, thus kT t > kT (i.e. thermal energy) at T = 300K. This implies that trap-limited conduction is dominant at room temperature. In addition, it is found that the extracted field-effect mobility and its gate voltage-dependence are strongly dependent on the pre-factor 1/(α + 1), where α = 2(kT t /kT-1) for kT t > kT. Here, we derived a more accurate field-effect mobility expression, using the proposed self-consistent extraction method. Also, a weak persistent photoconductivity in a-ZnON TFTs with Mo electrode is observed under visible light illumination, suggesting ionization of defects, such as oxygen and/or nitrogen vacancies, located near the VBM. To check the effect of electrode on leakage current and PPC, we replaced the Mo with Cr for electrodes. It is found that the leakage current slightly increases, but the effect of illumination is maintained, suggesting the PPC is arising from a change in the intrinsic property of the channel layer.

Results and Discussion
Localized Tail States. Since the current-voltage (I-V) characteristics of the TFT are largely determined by the density of localized states, e.g. tail states in the channel layer, the density of localized states can be retrieved from the measured terminal characteristics [15][16][17] . As a first step, the free carrier density (n free ) is extracted from the measured I-V characteristics. Note that linear characteristics of the drain current vs. gate voltage (I DS -V GS ) are required rather than saturation regime characteristics 16,17 , Here, μ band is the band mobility of the ZnON layer (note that this is a constant and the main unknown), ε S the permittivity of a-ZnON (which is about 11ε 0 , where ε 0 is vacuum permittivity), kT the thermal energy, W the channel width, L the channel length, and V DS the drain voltage. Also, the carrier density Here, 'e' denotes a free electron released into conduction band. In (a), ϕ B is the potential barrier height at the grain boundary in poly-crystalline ZnO. In (b), ϕ B is the potential barrier height due to compositional disorder in amorphous InGaZnO. (d) Schematic diagram to describe trap-limited conduction associated with the localized tail states. Here, n free and n trap denote free and trapped carrier densities at band tail states, respectively.
where x is the distance from the front channel interface along the channel depth, and ϕ the channel potential along x. Based on Equations (2) & (3), the carrier densities can be connected to gate voltage using a charge balance Equation: E(x = 0) = C ox (V GS − V Te ). Here, C ox is the gate-insulator capacitance and V Te is an effective threshold voltage which can be represented as [1/V GS + 1/V T ] −1 for V GS > 0 and V T > 0, where V T is a threshold voltage to be extracted with a linear extrapolation at a linear regime. This yields the following, Squaring Equation (4) and taking its first derivative with respect to the surface potential ϕ (x = 0) = ϕ S , n trap can be obtained as, Based on Equations (1), (4), and (5), the density of tail states (N tail (E)) can be given as the first derivative of Equation (5), where E F0 is the Fermi level at flat band (see the Supplementary Information for more detailed derivation procedure). Based on the above extraction method, the density of localized tail states was retrieved using a-ZnON TFTs with W = 50 μ m and L = 10 μ m. Here, the linear I DS − V GS characteristics were measured at a small V DS (e.g. 0.01 V and 0.1 V), as seen in Fig. 2(a,b) shows output characteristics for different V GS (see also Figure S2 in the Supplementary Information). The basic parameter to be extracted from each I-V curve is V T . The V T values of these two cases (V DS = 0.01 V and 0.1 V) are 4.4 V and 4.3 V, respectively. The other unknown parameters, μ band and C ox are 110 cm 2 /V-s and 19 nF/cm 2 , respectively 8 . Here, μ band can be the maximum achievable mobility and the C ox value was calculated using a thickness of 300 nm and measured permittivity of ~6.5ε 0 for the gate insulator Si 3 N 4 . Using these parameters and Equations (1-6), the carrier densities (n free and n trap ) and density of tail states (N tail (E)) were extracted as seen in Fig. 3a,b, respectively. As indicated in Fig. 3b, the tail states (i.e. gap states near the E C ) can be approximated as an exponential distribution [14][15][16] , Here, N tc is the tail state density at E = E C (i.e. conduction band minima), and kT t is the characteristic energy of the tail state. Applying Equation (7) into the plot shown in Fig. 3b, N tc and kT t values were extracted as 2 × 10 20 cm −3 eV −1 and 29 meV, respectively.

Electron Mobility.
To incorporate the effect of tail states into the field effect mobility (μ FE ), the trap-limited conduction theory is employed, Here, n free (with Boltzmann's approximation for |E F − E C | > kT) and n trap (for kT t > kT) are represented analytically as a function of Fermi level (E F ) 16,17 , respectively, as follows, where N C is an effective free carrier density [cm −3 ]. Note that the N C value of ZnON is about 2 × 10 18 cm −3 , which is calculated with an electron effective mass ~0.2 m 0 10,11 , where m 0 is the electronic rest mass. With Equations (9) & (10), Equation (8) can be rewritten as a function of E F , assuming n free < n trap , Here, E F − E C (= E F0 + qϕ S − E C ) can be given as a solution of Equation (4), replacing V Te by V T just for the above-threshold regime, Using Equations (11) & (12), Equation (11) can be represented as a function of V GS , following a power law, where α = 2(kT t /kT − 1). Note that ξ is a prefactor independent on V GS . As seen in Equation (13), the field-effect mobility (μ FE ) is a function of V GS , and linked with localized tail states in terms of the exponent (α ) and constant (ξ ) in the power law. Along with Equation (13), the current-voltage relation can be derived based on a drift transport equation, and approximated with the condition, V GS − V T  V DS (i.e. linear approximation), as follows, Due to the presence of the exponent (α ) and gate-voltage dependence in the μ FE expression seen in Equation (13), the first derivative of Equation (15) with respect to V GS (i.e. transconductance (g m )) is given as follows, Note that the first term of Equation (16) cannot be zero since μ FE is a function of V GS . So, the conventional way to get μ FE seems to be insufficient and inconsistent. In Equation (16), the first derivative of μ FE is shown and can be expanded with Equation (13), as follows, With Equation (17), Equation (16) can be rewritten as follows, From Equation (18), μ FE is now given as follows, As can be seen in Equation (19), due to the presence of α associated with localized tail states, the mobility can be reduced by the ratio of 1/(α + 1). Here, we defined the parameter '1/(α + 1)' as the mobility scaling factor due to trapping events in the localized tail states. So, the conventional way yields an over-estimated value and hence an inconsistency. So, we believe that Equation (19) provides a more accurate μ FE (V GS ) while capturing the effects of localized tail states with the parameter α . Using Equation (19), μ FE (V GS ) was extracted using the retrieved value of kT t seen in Table 1. In addition, the following equation can also be defined to explain the portion of trapping (ψ ) as, This can be used as a measure of how trapping significantly affects the electron mobility. As shown in Fig. 4(a), μ FE (at V GS = 9 V) is about 30.2 cm 2 /V-s for V DS = 0.01 V which is reduced by 21% (i.e. ψ = 0.21) compared to the conventional extraction route where μ FE is considered as a constant (38.4 cm 2 /V-s without considering α ), i.e. μ gm . Note that we also tested the proposed mobility extraction method for V DS = 0.1 V. It is found that there is a discrepancy less than 1% compared to the case of V DS = 0.01 V, as summarized in Table 1. Here, we believe that the case of V DS = 0.01 V provides higher accuracy compared to V DS = 0.1 V since a smaller V DS is always better to satisfy the assumption that V GS − V T  V DS , relating to Equation (15).
The band tail states not only affect the electron mobility but also affect bias instability. Indeed, it is known that the density of band tail states determines the rate of instability creation, e.g. threshold voltage shift (Δ V T ). The Δ V T as a function of time (t) is defined by the following relation 18 , Here, V Stress is the bias stress, V T0 the pre-stress threshold voltage (~4.3 V), and t 0 the characteristic time constant. In particular, β is a power-law exponent, which is proportional to the tail state density (N tc , cm −3 eV −1 ), So the following relation can be deduced, where ξ is a constant in the dimension of cm 3 eV. To extract the values of β and t 0 , the I-V characteristics were measured after applying 20 V bias stress for each stress period, as seen in Fig. 4b. Based on this, the Δ V T as a function of time is retrieved, as seen in the inset of Fig. 4b, yielding β ~ 0.34 and t 0 ~ 10 8 sec.
Here, it is found that the value of β is smaller compared to a-Si TFTs ~ 0.4 18 . As can be seen in Equation (22), this can be explained with a smaller N tc of a-ZnON TFTs ~ 2 × 10 20 cm −3 /eV compared to a-Si TFTs ~ 10 22 cm −3 /eV 19 .
Persistent Photoconductivity. Additionally, we performed computations of the density of states (DOS) in a-ZnON. Figure 5 shows the computed total DOS and projected DOS (PDOS) onto Zn, O, and N atoms for a-ZnON. Note that the fabricated a-ZnON film composition has been measured with the Rutherford backscattering spectrometry (RBS) (see the Supplementary Information). As shown in Fig. 5a, it is clear that the N forms the VBM, and is located from − 1.8 eV to 0 eV. This implies that oxygen defects (e.g. vacancies and interstitials), viewed as the origin of the PPC, are filled with N. Also, the band-gap is about 0.75 eV, as indicated in Fig. 5, suggesting that photon energies in the range from 0.75 eV ~ 2.55 eV may not give rise to the PPC in a-ZnON. To check this, we measured the drain current as a function of time (i.e. I DS -time plot) when V GS = 0 V and V DS = 0.01 V under illumination with 550 nm wavelength light (equivalent to 2.25 eV photon energy, hv), as seen in Fig. 6a. Here, the maximum optical power P 0 is ~0.1 mW/cm 2 . As shown in Fig. 6b, the drain current (~2.3 × 10 −10 A) under P 0 is increased by 2 times more than that (~1.2 × 10 −10 A) under 0.5P 0 . This suggests that the drain current under illumination is associated with excess carrier generation, which is linearly proportional to incident optical power, rather than electron trapping into gate insulator. After removal of illumination (after t = 80 s), the drain current is almost recovered, thus the examined a-ZnON is optically very stable. However, we find a small difference (i.e. I PPC ~ 3.4 × 10 −11 A) between the initial (I DS ~ 9.1 × 10 −11 A) and final (I DS ~ 1.25 × 10 −10 A) stages. Thus, persistent photoconductivity (PPC) still exists, albeit mild as seen in Fig. 6b, implying that some of the excess electrons are generated from optically irreversible states. So, the PPC may be associated with some of the unfilled oxygen defects (O D ). Besides oxygen-related defects, we also consider nitrogen-related defects (N D ), such as nitrogen vacancies (N V ), which exist especially at the vicinity of the valence band maxima [20][21][22] . Under illumination, they can also be ionized as N V 0 → N V n+ + ne -, where n is an integer, e.g. 1 ~ 3 20,22 . Since these constitute negative U-defects, the ionization process is irreversible even after removal of light, thus giving rise to the mild PPC 22 . These defects, collectively denoted as D 0 , can be ionized under illumination (D 0 → D n+ + ne − ), relocating to the vicinity of the E C 10,11,[20][21][22][23][24][25] . This maintains the increased Fermi level (E F ) even after illumination, as  Here, light pulse is applied as described in the inset. (c) Possible density of states picture with respect to optical carrier generation mechanisms and PPC. Here, the generated electrons are denoted as 'e' , E F and E' F denote Fermi levels before and after illumination, respectively, and E V is the valence band maxima. (d) Schematic 3-D band diagram along the channel depth. Here, we show the effect of the positive gate bias on the recombination of ionized deficiency defects with induced electrons. described in Fig. 6c. Since we have a very mild PPC (see Fig. 6b), we should assume that the density of defects, including oxygen and nitrogen vacancies, is small, implying that the photocurrent under illumination mostly consists of electrons generated from the N 2p states in the valence band. In order to estimate the number of the ionized deficiency defects (N idd , cm −2 ), we may use the following relation, Using the values of the parameters extracted in the previous sections (e.g. I PPC = 3.4 × 10 −11 A, μ FE = 30.2 cm 2 /V-s, W/L = 5, V DS = 0.01 V), the N idd is retrieved as 1.43 × 10 8 cm −2 . To electrically remove these ionized defects, we employed a positive gate-pulse scheme 25 , as seen in Fig. 6b. This yields a fully recovered current level (I DS ~ 9.2 × 10 −11 A) which is similar to the current level before illumination. Hence, it is suggested that these ionized defects (D n+ ) were eliminated with the forced recombination with the electrons (ne − ) induced during the positive gate-pulse width (+ 10 V), i.e. D n+ + ne − → D 0 , as described in Fig. 6d. Here, the number of induced electrons (i.e. N e ≈ C ox × (10 − V T )/q ≈ 6.7 × 10 11 cm − 2 ) are much more than the N idd ~ 1.43 × 10 8 cm −2 , thus it is enough for a full recombination.
In addition, we replaced Mo with Cr for electrodes to check effects of metal on leakage current and PPC. Figure 7a shows the measured I DS vs. time for two devices with different metal electrodes, e.g. Mo and Cr, respectively. It is found that there is a small current difference before and after illumination for each case. And the difference (i.e. I PPC ) is almost the same as 0.034 nA. This implies that the choice of electrode metal doesn't affect the PPC. And the current difference between the Mo and Cr cases (Δ I DS ) is shown on the right-hand-side y-axis. It is found that this current difference is always approximately 0.1 nA, suggesting that the leakage current is changed globally regardless of illumination and PPC. This can be explained with the reduced barrier height at source side (qφ b ) due to a smaller work-function of Cr (~4.5 eV) compared to Mo (~4.6 eV), as shown in Fig. 7b,c. These results indicate that the choice of metal for electrodes does not affect the PPC.

Conclusions
In conclusion, the density of localized tail states in ZnON thin film transistors (TFTs) has been extracted using current-voltage characteristics of the TFTs. The extracted values of N tc and kT t are about 2 × 10 20 cm −3 eV −1 and 29 meV, respectively. Considering trap-limited conduction theory, the field-effect mobility expression has been derived and shown to be represented in terms of tail state parameters. In particular, the exponent (α ) has been strongly connected to the mobility through kT t which is a key measure of the degree of the disorder of the channel layer. This suggests that a reduction of kT t is needed to achieve higher mobility. Additionally, it has been revealed that the examined ZnON is optically very stable showing only weak PPC which is thought to be arising from ionization of defects, such as oxygen and/or nitrogen vacancies, located in vicinity of the valence band maxima. This happens equivalently in both ZnON TFTs with Mo and Cu electrodes, suggesting the PPC is associated with a change of the intrinsic property of the channel.