Unveiled Influence of Sub‐gap Density of States on Low‐Frequency Noise in Si‐Doped ZnSnO TFTs: Does Correlated Mobility Fluctuation Model Suffice?

The presence of low‐frequency noise (LFN) in amorphous oxide semiconductor (AOS) thin‐film transistors (TFTs) is of utmost concern, prompting extensive investigations into the analysis of LFN. However, prior research endeavors have tended to overlook the significance of the sub‐gap density of states (DOS) in the LFN analysis, resulting in an incomplete comprehension. To bridge this knowledge gap, the influence of sub‐gap DOS is demonstrated on LFN in Si‐doped ZnSnO (SZTO) thin‐film transistors (TFTs) under various conditions. The SZTO TFTs is intentionally subjected to positive bias stress and hot carrier stress in order to control the sub‐gap DOS and investigate how this change affects the LFN characteristics. It is revealed that the non‐uniform energetic distribution of sub‐gap DOS induces bias‐dependent excess noise in the SZTO TFTs. Additionally, self‐recovery behavior after the HCS is observed, accompanied by a commensurate reduction in 1/f noise. These empirical observations provide evidence that the conventional correlated mobility fluctuation model used to explain LFN in AOS TFTs is insufficient and underscores the critical importance of considering subgap DOS when analyzing LFN of AOS TFTs.


Introduction
[3] AOSs have exceptional visible transparency of over 80% across the visible range, low processing temperature, high electron mobility over 10.0 cm 2 V −1 s, good uniformity, and high on-current to DOI: 10.1002/aelm.202300515off-current ratio. [4,5][12][13] LFN refers to the random fluctuations in electrical current or voltage that occur at frequencies below 100 kHz.These fluctuations are primarily caused by defects or traps in gate oxide that affect the transport of charge carriers in fieldeffect transistors (FETs) or TFTs.The study of LFN is significant for understanding the fundamental physics of device operation, as well as for evaluating device performance and reliability.[16][17][18][19][20][21][22][23][24][25][26] In these previous studies, the carrier number fluctuation (CNF) model that reflects the carrier trapping/detrapping process to/from gate oxide is mainly used to explain the LFN characteristics of the AOS TFTs.However, the CNF model often fails to fully explain the LFN characteristics of AOS TFTs because the model is originally based on field-effect transistors (FETs) with single-crystalline Si (c-Si). [10]Accordingly, the correlated mobility fluctuation (CMF) model, [19,21,22,[24][25][26] Hooge's mobility fluctuation (HMF) model, [20] contact noise, [24,25] and generation-recombination (G-R) noise [20] have been used to complement the CNF model and describe the deviation in LFN characteristics of AOS TFTs.Table 1 provides a summary of previous studies that have analyzed the LFN characteristics of AOS TFTs and their attempts to interpret the deviations from the CNF model.[29] The sub-gap DOS in AOS refers to the distribution of energy levels available for electrons to occupy within the band gap of the material.It is widely recognized that the sub-gap DOS significantly influences the electronic properties of AOS, including carrier mobility and conductivity. [27]owever, only a very few studies have explored the relationship between sub-gap DOS and LFN in AOS TFTs, and these studies have not established a clear correlation between the two.Instead, they only suggest a vague connection. [18,22,23][29] It has been reported that the sub-gap DOS exhibits significant variations under bias stress, suggesting that LFN properties are also expected to change.Therefore, examining the LFN characteristics under the influence of bias stress can help identify the relationship between sub-gap DOS and LFN.However, relevant studies on this topic are currently limited and further investigation is required to shed light on this relationship.
The present study addresses this issue by investigating the LFN characteristics of amorphous Si-doped ZnSnO (a-SZTO) TFTs under positive bias stress (PBS) and hot carrier stress (HCS).The power spectral density (PSD) of the device is measured at various bias conditions by changing the gate-to-source (V GS ) voltages in each stress condition.It is demonstrated that with an increase in V GS , Fermi-level (E F ) approaches the conduction band (E C ), and thus the corresponding sub-gap DOS strongly affects the LFN characteristics of the SZTO TFTs.An abnormal volcano-shaped 1/f noise behavior with respect to the change in V GS demonstrates that the conventional CNF with CMF model fails to fully grasp the LFN characteristics of the AOS TFTs.Furthermore, the self-recovery behavior of sub-gap DOS and corresponding decrease in 1/f noise provides additional evidence that the sub-gap DOS strongly affects the LFN of the AOS TFTs.Our findings complement existing LFN analyses by identifying the missing link between sub-gap DOS and LFN characteristics, contributing to the further development of reliable AOS TFTs.

Device Fabrication and Material Characterization
In this study, we employ a-SZTO as the channel material and adopt a bottom gate configuration with a staggered structure.ZTO has gained attention as an alternative to IGZO due to its environmentally friendly nature, as it does not contain any toxic elements like indium or gallium. [32]Moreover, the introduction of Si doping into the ZTO material enhances the reliability of TFTs by reducing defects associated with oxygen vacancies. [33]Figure 1a presents a three-dimensional schematic of the device utilized in this study.Figure 1b shows the cross-sectional transmission electron microscopy (TEM) image of the SZTO TFT.The channel width and length are 250 and 50 μm, respectively.The fabrication process is explained in the Experimental and Figure S1 (Supporting Information).In Figure 1c, X-ray photoelectron spectroscopy (XPS) depth profile of the SZTO film is presented, revealing the presence of O1s, Si2p, Sn3d5, and Zn2p3 atoms.This result confirms the successful deposition of the SZTO film.Figure 1d shows X-ray diffraction (XRD) patterns of the SZTO film.With the exception of the peaks at around 23 and 34 degrees, which originate from the substrate, no other diffraction peaks corresponding to a crystalline phase are observed in the XRD spectra, indicating the stable amorphous state of the SZTO film.

Electrical Characteristics and LFN Characteristics of SZTO TFTs
Figure 2a shows the transfer characteristics (I D -V GS ) of the fabricated SZTO TFTs measured at various temperatures (Ts) with V DS set at 0.1 and 5.0 V.In both cases, the TFTs exhibit hysteresisfree behavior.A slight increase in on-current (I on ) and a negative shift in the threshold voltage (V th ) are observed with an increase in temperature.This behavior is attributed to the presence of donor-like states near the E C , caused by oxygen vacancies. [34]owever, due to the Si doping, the fabricated SZTO TFTs display a low concentration of oxygen vacancies, resulting in relatively mild temperature dependence of the device.A detailed explanation regarding the impact of Si doping on oxygen vacancy concentration can be found in our previous study. [33]    The inset shows the subgap DOS of the SZTO. [33]g) measurement.The bold line in each figure represents the average value obtained from five PSD measurements.Figure S3a (Supporting Information) demonstrates the repeatability of the PSD measurements by showing the sampled S ID /I D 2 at 10 Hz for the five PSD measurements.The devices exhibit 1/f  noise behavior, where  represents the slope of the logarithmic relationship between S ID and f ( = − ∂ln(S ID )/ ∂ln(f)).[16][17][18][19][20][21][22][23][24][25][26] The CNF model is expressed as [14][15][16] S ID with where g m is the transconductance, S Vfb is the PSD of flat band voltage fluctuation, q is the electron charge, N T is the volume trap density, C OX is the gate oxide capacitance per unit area, and  is the oxide tunneling attenuation distance.To assess whether the LFN characteristics of the SZTO TFT can be explained by conventional CNF model, the S ID /I D 2 sampled at 10 Hz is plotted with respect to I D , and its correlation to (g m /I D ) 2 is examined, as shown in Figure 3b.The S ID /I D 2 and (g m /I D ) 2 exhibit similar behavior to I D , except for the high I D region.Figure S3b  The deviation in the high I D region of FETs, including AOS TFT, has been analyzed using the CMF, which incorporates the term (1 2 in the right hand of Equation ( 1). [21,22]ere,  c represents the Coulomb scattering parameter, and μ eff corresponds to the effective carrier mobility.The CMF model accounts for the fluctuation in carrier mobility resulting from trapped charges in the defects of the gate oxide.In n-channel FETs, the  c is negative (positive) in the presence of an acceptorlike trap (donor-like trap). [35]Figure 3c shows the gate voltage fluctuation (S VG = S ID /g m 2 ) plotted against I D /g m .The positive slope in the plot indicates that the  c is positive.By using  c value of 8.1 × 10 5 the deviation from the CNF model in the high I D region can be compensated.Figure S3d (Supporting Information) shows that the CNF with CMF model successfully explains the LFN characteristics of the SZTO TFT.However, it is worth noting that this  c value is too high, raising valid concerns regarding the validation of the CMF model's applicability.Here, we claim that the observed deviation should be attributed to the existence of sub-gap DOS rather than the CMF.The rationale behind this claim will be demonstrated and validated in our research.16][17][18][19][20][21][22][23][24][25][26] This assumption is often applicable to c-Si-based FETs. [36,37]However, in AOS, there are defects within the channel exist known as sub-gap DOS, which exhibit a significant variation in distribution across different energy levels, as illustrated in Figure 3d-2. [27,28]hese sub-gap DOS have been reported to affect the electrical properties of AOS TFTs, such as SS, I on , and V th . [28]It is unreasonable that sub-gap DOS, which is known to have a great influence on the performance of the AOS TFT, is not considered in analyzing the LFN characteristics.One approach to analyze these effects is to examine the bias-dependent behavior of N T in AOS TFTs using the CNF model.In the case of a uniform energy distribution across the energy space, the N T extracted from the CNF model should remain constant regardless of V GS .However, this is not the case when the traps are non-uniformly distributed.Depending on the magnitude of V GS , the energy levels of the defects contributing to the 1/f noise vary.As V GS increases, E C approaches to E F , and the corresponding energy level becomes dominant in governing the 1/f noise behavior of the device due to the changes in the band structure, as depicted in Figure 3e.Kushwaha et al. reported that the presence of non-uniform trap distribution in the energy space should be considered even in the case of c-Si-based FETs, such as highly scaled-down Fin-FET, whose variation in fin shape can induce the non-uniform trap distribution. [38]The FinFET exhibits a larger trap density at the weak-inversion region (low I D region); thus, excess noise is observed in the low I D region.With an increase in V GS , the excess noise disappears as the non-uniform distribution function approaches one in the strong inversion region (high I D region).Considering the presence of DOS, it becomes crucial to account for non-uniformity in the energy space when analyzing LFN in AOS TFTs.In the case of SZTO, various states exist from the E V to E C , including the donor-like tail states (g TD ), oxygen vacancy defect states (g O ), silicon defect states (g Si ), acceptor-like deep states (g DA ), and acceptor-like tail states (g TA ), as depicted in the inset of Figure 3f. [33,39]Note that the parameter values for calculating sub-gap DOS is shown in Table S1 (Supporting Information).Figure 3f shows the N T versus I D of the SZTO TFTs.Note that the N T s are extracted using the CNF model at f = 10 Hz, without employing the CMF model.The N T increases with increasing V GS , indicating that a higher trap density near the energy level close to the E C .Note that, within the measured I D ranges, the g DA and g TA come into play due to the formation of the E F in proximity to E C in the AOS.The increase in N T with V GS can be attributed to the presence g TA whose DOS increases towards E C .
where N TA and T TA denote the density and the characteristics temperature of tail states, respectively.
To extract the relationship between the relative energy of the E C and the V GS , it is important to accurately map the E C to the V GS by matching the corresponding gate voltage (V CBM ).This relationship can be extracted using the following equation: where A is the conducting channel area, N C is the DOS in the E C , μ eff is the effective mobility, and E is the electrical field.Figure 3g shows the accurate energy distribution: E F -E C with respect to V GS .
The detailed procedure for extracting the relationship between E C and V GS is described in Figure S4 and Note S1 (Supporting Information).

Effects of Bias Stress on DOS and the Corresponding Change in LFN Characteristics
Although the findings presented in the previous section suggest the potential influence of sub-gap DOS on the LFN characteristics of AOS TFTs, additional evidence is required to establish the clear relationship between sub-gap DOS and LFN properties in AOS TFTs.In AOS TFTs, it has been reported that bias stress can induce a significant change in the sub-gap DOS. [28]Therefore, in this section, we delve into the effects of different types of bias stresses (PBS and HCS) on the 1/f noise behavior.By investigating these effects, we aim to further demonstrate the connection between sub-gap DOS and LFN characteristics in AOS TFTs.This investigation will provide additional support for our claim that the analysis of LFN in AOS TFTs should take into account the presence of sub-gap DOS.

Effects of PBS
To begin, we examine the impact of PBS on the electrical properties and LFN characteristics of SZTO TFTs. Figure 4a shows the I D -V GS of the SZTO TFTs with varying PBS time (t PBS ).With an increase in t PBS , the V th of the device undergoes a positive shift.Note that other electrical properties, such as SS, I on , and μ eff remain largely unaffected.Figure 4b shows the V th shift (ΔV th ) versus PBS time.Note that the V th of the device is extracted at I D = 100 nA by using the constant current method.The positive shift in V th arises from the trapping of electrons in the channel into the gate dielectric.Figure 4c-1,c-2 show the S ID /I D 2 versus f of the device before and after the PBS (t PBS = 3000 s) is applied.Figure 4d show the S ID /I D 2 sampled at 10 Hz versus I D for the device before and after the PBS.Interestingly, unlike the pristine device, the S ID /I D 2 and (g m /I D ) 2 of the device under PBS not only exhibit the deviation at the high I D region but also at the low I D region.Here, it is important to note that the CMF model cannot explain such deviation because the CMF model can mainly explain the deviation at the high I D region. [40]Figure 4e shows the N T of the pristine device and device after 3000 s of HCS.An increase in the magnitude of N T at the low I D region is observed, which corresponds to the energy level of g DA .During the PBS, excessive oxygen in SZTO diffuses into the interface between the gate oxide and channel, increasing the g DA .The increase in S ID /I D 2 in the low I D region can only be explained by considering the non-uniform energy distribution of the N T .This observation further supports the influence of subgap DOS on the AOS TFTs in LFN analysis, suggesting that the analysis of LFN should consider the presence of sub-gap DOS in these devices.As shown in Figures S5a,b, the application of short-time of PBS does not change the LFN characteristics of the SZTO TFTs.This can be attributed to the relatively low density of oxygen vacancies in SZTO, which imparts robustness to PBS. [39]he introduction of an appropriate quantity of silicon suppresses the diffusion of oxygen into the gate insulator due to the stronger bond between Si and O atoms. [33]This enhancement significantly contributes to the stability of the PBS process by preventing the formation of electron traps both within the gate insulator and at its interface.Figure 4f shows the full-scan XPS spectra of the SZTO film.Although the change in the LFN characteristics by the PBS (t PBS 3000 s) demonstrates the relationship between the sub-gap DOS and LFN characteristics of SZTO TFTs, further evidence is required to confirm their relationship conclusively.

Effects of HCS
In order to further establish the relationship between the sub-gap DOS and LFN characteristics in AOS TFTs, the effects of HCS on the SZTO TFTs are investigated.Figure 5a-1-a-4 show the I D -V GS of the SZTO TFTs at different HCS times (t HCS s).The V GS and V DS are set at 20 and 40 V, respectively, for HCS. Figure 5b shows the combined I D -V GS of the devices under different t HCS s.Subsequent to HCS, significant degradation of electrical properties is observed, including an increase in SS and a decrease in I on .Notably, a hump is observed at t HCS = 10 and 150 s, which disappears at t HCS = 300 s. Figure 5c-1-c-3 show the S ID /I D 2 versus f measured at different t HCS values.A substantial increase in 1/f noise is observed, and the S ID /I D 2 exhibits very abnormal behavior with an increase in V GS .Specifically, for t HCS = 10 and 150 s, the devices exhibit a volcano-shaped behavior where the S ID /I D 2 increases with V GS in the low I D region, then decreases with further increase in V GS in the high I D region, as summarized in Figure 5d.We want to emphasize that this behavior cannot be explained without the consideration of sub-gap DOS in the CNF model.To confirm that the volcano-shaped noise behavior is not limited to a single device, the PSD of another device is measured at different t HCS values.Figures S6a,b show the S ID /I D 2 versus f of the SZTO TFTs after the t HCS of 10 and 300 s, respectively.The volcano-shaped behavior is also observed in this device, demonstrating the reproducibility of this phenomenon.
Figure 6a shows the N T as a function of I D for different t HCS values.A peak in N T is observed around I D ≈2 μA, indicating the generation of a narrow and shallow trap located between the g TA and g DA .These specific DOS are referred to as needle defect states (g N ), [41] whose DOS is modeled as (5) During the initial stage of HCS, a significant number of N N is generated with a small value of W N .With an increase in t HCS , the peak value of N T is slightly decreased due to Joule heat (JH) caused by the large I D flowing through the channel during the HCS.However, with an increase in t HCS the N is increased.It has been reported that the hump disappears with an increase in W N , resulting in a further decrease of I on , 41 which can be clearly shown in Figure 5b.Note that if the width of this acceptor-like Gaussian state exceeds 0.1 eV, no hump is formed. 41Figure S6c shows the N T versus I D of the device shown in Figure S5a,b (Supporting Information) as a parameter t HCS , exhibiting similar behavior across different devices.
Moreover, the behavior of N T with respect to HCS exhibits fdependent characteristics.Figure 6b-1-b-3 show the N T versus f of the SZTO TFTs subjected to different times of HCS.Here, it is important to note that the N T in Figure 6a,b cannot be regarded as exact value of sub-gap DOS because this extraction is based on CNF model.Nonetheless, sub-gap DOS value extracted by multifrequency CV method closely align with the values that is extracted from the LFN measurement.Figure 6c shows the slope of the plot in Figure 6b versus I D .After a long HCS period (t HCS = 300 s), the slope remains constant irrespective of V GS .However, for t HCS = 10 s, the slope varies depending on V GS .Specifically, the slope is much larger in the low I D region, demonstrating that the generation of N T by the HCS at the early stage mainly occurs at the high f domain in the low V GS region.With an increase in V GS , the difference of N T between the low and high f domains is decreased.This frequency dependency can stem from the tunneling depth between the carriers and defects. [37]HCS more readily affects the shallow traps near the channel during the early stages, while the population of deep traps located farther from the channel also increases with t HCS .Through LFN spectroscopy, not only the energy distribution but also the location distribution can be analyzed.
One might argue that the increase in N T is caused by the damaged gate oxide rather than an increase in DOS.This speculation is reasonable because the hot carriers generated during the HCS can not only alter the DOS but also degrade the gate oxide (SiO 2 ).However, this speculation can be refuted by examining the long-term reliability of the device.Figure 6d illustrates the I D -V GS of the SZTO TFTs subjected to HCS and five days after.The devices are stored at room temperature, and the temperature and humidity conditions during the five-day period are shown in Figure S7a (Supporting Information).A negative shift in V th and an increase in I on are observed after five days.Figure S7b (Supporting Information) shows the S ID /I D 2 versus f of the SZTO five days after the HCS measured at different V GS s. Figure 6e-1,e-2 show the S ID /I D 2 versus f for the HCS-damaged and the devices measured five days later.The PSDs show a significant decrease after five days.Figure S7c (Supporting Information) shows the ratio between the PSD of devices with HCS damaged and five days after in low and high V GS .Two interesting phenomena are observed: 1) The S ID /I D 2 decreases more prominently at low V GS , indicating that the N T generated far from the E C is more easily recovered.2) The S ID /I D 2 decreases more prominently at the low f region, indicating that deep traps are more easily restored compared to shallow traps.Figure 6f shows the N T versus I D for the HCS-damaged device and the device measured five days later.It is evident that the needle defects are cured, and the presence of tail states is reflected in the LFN characteristics.However, it should be noted that the g TA is not fully recovered and still exhibits a value approximately three times larger than that of the pristine device.Figure 6g schematically illustrates the change in DOS due to HCS (red lines) and self-recovery behaviors (green lines).
These results provide confirmation that the changes in the LFN characteristics due to HCS are indeed associated with the DOS, not the damaged gate oxide.If the gate oxide is damaged by hot carriers, the damage would be relatively permanent and not self-recoverable within a five-day period.In contrast, the selfrecovery behavior of the DOS after bias stress has been reported.It appears that the needle defects and tail states are related to defects such as zinc interstitials. [42,43]When highly energetic electrons accumulate at the interface under the positive gate and drain bias, they can create positively charged zinc interstitials by colliding with AOS atoms and breaking weak bonds.These interstitials can then act as shallow donor-like states. [42]However, it is worth noting that the zinc-related shallow donor-like states can be recovered, as has been shown in previous studies. [44]This is because zinc interstitials have a low migration barrier at room temperature, allowing them to move and be cured with relatively low thermal energy.

Comments on Previous Studies
Through our systematic investigation of bias stress effects on the LFN characteristics of SZTO TFTs, we have successfully confirmed the importance of considering the non-uniform energy distribution in AOS TFTs for LFN analysis.The specific manifestation of excess noise can vary based on factors such as the gate oxide and the channel material.Nevertheless, the core assertion of this study would remain unchanged.The type of gate oxide (whether it's SiO 2 , HfO 2 , Al 2 O 3 , etc.) leads to distinctions in both the interface traps at the channel-gate oxide junction and the bulk traps within the gate oxide itself.However, even under these circumstances, the exchange of carriers to and from the sub-gap DOS persists.Consequently, the excess noise originating from these sub-gap DOS remains a prominent factor.In scenarios where the channel material differs, the characteristics of sub-gap DOS also diverge.Both the energy distribution and concentration of sub-gap DOS exhibit significant discrepancies depending on the material type.This disparity in energetic distribution results in variations in the appearance of excess noise across different operating regions.To illustrate, when the excess sub-gap DOS exists well below the E C , the excess noise stemming from the DOS is observed in the I D region.Conversely, in situations where there is a notable concentration of DOS near the E C , as in the case of this study, the excess noise would become apparent in the high I D region.Furthermore, the magnitude of the excess 1/f noise that originates from the sub-gap DOS is directly influenced by the concentration of the DOS.However, the central assertion that accounting for excess noise arising from sub-gap DOS is crucial for analyzing the LFN characteristics of AOS TFTs remains highly significant.
This discovery allows for a reevaluation of previous studies on the LFN characteristics of AOS TFTs.For instance, Kim et al. conducted an analysis of the LFN characteristics in IGZO TFTs in relation to DOS. [22] However, their results have not been properly addressed and can be reinterpreted based on the nonuniform energy distribution of DOS. Figure S8a (Supporting Information) shows the I D -V GS of the IGZO TFTs. Figure S8b (Supporting Information) shows the S ID /I D 2 sampled at 10 Hz versus I D of the pristine and damaged (V GS = V DS = 20 V).The deviation of the PSD from the CNF model is corrected by using the CMF model ( C of 10 5 Vs C −1 ), as in most of the previous studies. [21,24,25]Accordingly, the deviation of the S ID /I D 2 from (g m /I D ) 2 in the high I D region could be corrected.However, such a high value of  C is unrealistic, as it typically falls below ≈1 × 10 4 Vs C −1 in most cases. [35]Instead, this behavior can be attributed to the higher density of tail states as the E F approaches closer to the E C , consistent with the energy distribution of DOS presented in Figure S8d.It should be noted that there is a discrepancy between the N T extracted from the 1/f noise and DOS, which appears to be caused by the f-dependent behavior of N T .Many studies analyzing the LFN characteristics of AOS TFTs, including reference [21], have explained the deviation of 1/f noise from the CNF model using the CMF model.However, it is insufficient to simply fit the results by using a positive value of  C .Instead, the nonuniform energy distribution arising from the DOS should be considered.In this study, we provide the rationale for why this analysis is necessary and present the method to validate the results.

Conclusion
In this study, we have conducted a comprehensive investigation of LFN characteristics in a-SZTO TFTs and established the relationship between the LFN and DOS in AOS TFTs.Our findings challenge the conventional understanding of LFN behavior in AOS TFTs, which often relied on the supplementation of the CNF model with the CMF model using a positive value of  C to explain deviations at high I D regions.Through our analysis of PBS and HCS effects on SZTO TFTs, we have demonstrated that the non-uniform energy distribution of DOS plays a crucial role in understanding the V GS -dependent 1/f noise behavior.The observed volcano-shaped normalized drain current PSD resulting from the HCS-induced generation of needle defects cannot be adequately explained by the CNF model supplemented with the CMF model.Furthermore, the self-recovery behavior of NT provides clear evidence that the DOS is responsible for the excess noise in AOS TFTs.These findings have significant implications for the advancement of AOS TFTs, as they highlight the necessity of considering the influence of DOS on LFN characteristics.This study opens up new avenues for researchers to explore the underlying physics of LFN in AOS TFTs and develop more accurate models for predicting their behavior.By incorporating the understanding of non-uniform energy distribution in DOS, future studies can improve the design and optimization of AOS TFTs for various applications.

Experimental Section
Fabrication Process of SZTO TFTs: In this study, a p + -Si substrate with a 100 nm SiO 2 layer obtained through thermal oxidation was utilized as the substrate.Prior to deposition, the substrate underwent ultrasonic cleaning in acetone, methanol, and deionized water for 10 min each.The amorphous Si-doped ZnSnO (a-SZTO) films were deposited at a temperature of 20 °C using a radio-frequency magnetron sputtering technique.The sputtering process involved using sputtering power of 50 W, a working pressure of 6 mTorr, and an argon gas flow rate of 40 sccm.The channel layers were formed through standard photolithography and wet etching methods, utilizing SnO etchant for the wet-etching process.Subsequently, annealing was performed in an air environment within a furnace for 2 h at a temperature of 500 °C.For the source and drain electrodes, titanium (10 nm) and aluminum (40 nm) were deposited using E-beam and thermal evaporation, respectively.
LFN Measurement: A semiconductor parameter analyzer (B1500A) was utilized, low noise current amplifier (SR570), and signal analyzer (35670A) to measure the PSD.The measurement procedure was conducted as follows: The B1500A supplied the V GS and V DS , and the output current from the SZTO TFTs was connected to the SR570 to convert the current fluctuation into a voltage fluctuation.The 35670A was then used to convert the dynamic signal from the SR570 to PSD.To verify the validity of the CNF model, the PSD of the device was measured at various V GS values while maintaining a fixed V DS value (0.1 or 5.0 V).This study utilized I D values ranging from ≈200 nA to 1 μA to investigate the validity of the CNF model.Since the device's magnitude was small, the measurement system's noise floor needs to be confirmed.The current amplifier's low noise mode (SR570 manufacturer specifications) had a noise floor of 4 × 10 −27 A 2 Hz −1 , which was much lower than the device noise, ensuring that the PSDs measured in this study were not affected by the measurement system's noise floor.Furthermore, the limited bandwidth of the circuit may cause spectral distortion of the devices' PSD.However, the SR570's internal circuitry preserves both the signal's amplitude and phase.With sensitivities of 100 nA, 1 μA, and 10 μA, the SR570's rated bandwidths in low noise mode were 2, 20, and 200 kHz, respectively.Therefore, considering the limited frequency range (f ≤ 1.6 kHz) used in this study, there would be no spectral distortion.
Figure S2a,b (Supporting Information) show the I D -V GS of the nine SZTO TFTs measured at V DS values of 0.1 and 5.0 V, respectively.The output characteristics (I D -V DS ) of the device measured at different Ts are shown in Figure 2b.

Figure 3a- 1 -a- 3
show the drain current normalized PSD (S ID /I D 2 ) as a function of frequency (f) for the device measured at different V GS values with V DS fixed at 5.0 V during the PSD

Figure 2 .
Figure 2. a) Transfer characteristics (I D -V GS ) of the fabricated SZTO TFTs measured at different temperatures.The V DS is set at 0.1 and 5.0 V. b) Output characteristics (I D -V DS ) of the device measured at different temperatures (b-1) T = 20 °C, b-2) T = 40 °C, b-3) T = 60 °C, and b-4) T = 80 °C).

Figure 3 .
Figure 3. a) Drain current normalized PSD (S ID /I D 2 ) versus frequency (f) of the device measured at different values of V GS (a-1) I D = 205 nA, a-2) I D = 775 nA, a-3) I D = 3.29 μA)).b) S ID /I D 2 sampled at 10 Hz and (g m /I D ) 2 versus I D .c) Gate voltage fluctuation (S VG = S ID /g m 2 ) versus I D /g m .Schematic energy diagram of d-1) c-Si with uniform trap distribution and d-2) AOS with non-uniform trap distribution.e) DC-measured I D -V GS characteristics (solid line) and the I D and V GS values during the five times of PSD measurements (open square symbols).The inset shows the corresponding energy level.f) N T versus I D of the SZTO TFTs.The inset shows the subgap DOS of the SZTO.[33]g) E F -E C versus V GS .
shows the S ID /I D 2 sampled at 10 Hz and (g m /I D ) 2 versus I D , while the V DS is fixed at 0.1 V. Figure S3c shows the three sets of PSD measurements in this condition.Regardless of the V DS values, a discrepancy between the S ID /I D 2 and (g m /I D ) 2 is observed in the high I D region.
Figure 3e also presents the DC-measured I D -V GS characteristics (solid line) and the I D and V GS values during the five times PSD measurements (open square symbols).The solid line and open square symbols align well, indicating negligible drift effects during the measurement.

Figure 4 .
Figure 4. a) I D -V GS of the SZTO TFTs with the change of PBS time (t PBS ).b) Vth shift (ΔV th ) versus PBS time.S ID /I D 2 versus f of the c-1) pristine device c-2) device after t PBS of 3000 s. d) S ID /I D 2 sampled at 10 Hz versus I D of the device before and after the PBS.e) N T of the pristine device and device after 3000 s of HCS.f) Full-scan XPS spectra of SZTO film.

Figure 5 .
Figure 5.I D -V GS of the a-1) pristine SZTO TFT, SZTO TFTs with a-2) t HCS = 10 s, a-3) t HCS = 150 s, and a-4) t HCS = 300 s, respectively.b) Combined I D -V GS of the devices under different t HCS s. S ID /I D 2 versus f measured at t HCS of c-1) 10 s, c-2) 150 s, and c-3) 300 s. d) N T versus I D as a parameter of t HCS .

Figure 6 .
Figure 6.a) N T versus I D of the devices as a parameter of t HCS .N T versus f of the SZTO TFTs with b-1) t HCS = 10 s, b-2) t HCS = 150 s, and b-3) t HCS = 300 s. c).Slope in N T versus f plot as a function of I D in different t HCS .d) I D -V GS of the SZTO TFTs applied to HCS and five days after.S ID /I D 2 versus f of the e-1) HCS-damaged and e-2) five days after SZTO TFTs.(f) N T versus I D of the HCS damaged and five days after SZTO TFTs.g) Schematic diagram of subgap DOS evolution under HCS and self-recovery.

Table 1 .
Previous studies on LFN analysis of AOS TFTs.