# Analyzing Acceptor-like State Distribution of Solution-Processed Indium-Zinc-Oxide Semiconductor Depending on the In Concentration

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## Abstract

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## 1. Introduction

_{Th}.

_{s}and the drain voltage. Conversely, when a model for the bandgap state is not defined, the DOS distribution can be extracted by observing the changes in the drain current with respect to the external energy. Because of the significantly lower hole mobility compared to electrons in n-type semiconductors such as IZO TFTs, estimating the DOS distribution towards the valence band under the Fermi energy E

_{F}is difficult. However, the distribution of acceptor-like states above E

_{F}can be easily analyzed using thermal energy.

_{F}shift. Because the electrical conductivity and threshold voltage of IZO TFTs are closely associated with these doping characteristics, the doping effect, which depends on the In molarity ratio and the quantitative extraction of the DOS distribution, is crucial for solution-processed IZO TFTs. Furthermore, a precise understanding of the DOS distribution can facilitate the interpretation of the electrical instability caused by charge trapping/detrapping in solution-processed IZO TFTs.

## 2. Materials and Methods

_{3}(NO

_{3})

_{3}∙xH

_{2}O) and zinc nitrate hydrate (Zn

_{2}(NO

_{3})

_{2}∙xH

_{2}O) in 2-methoxyethanol (CH

_{3}O(CH

_{2})

_{2}OH), also known as the 2-ME solvent. The In:Zn molar ratios used in the preparation of the IZO solutions are listed in Table 1. The prepared solution, according to the ratios listed in Table 1, was spin-coated onto a p-type Si wafer with a sputtered 100 nm thick SiN

_{x}gate dielectric. The resulting coating formed an IZO semiconductor layer with a thickness of approximately 20 nm. The source/drain electrodes were fabricated through thermal deposition, and the finger-type structure had a W/L ratio of 2000 μm/80 μm. The detailed fabrication process for the electrical characteristics of solution-processed IZO TFTs can be found in previous studies [26,27].

_{G}= −20 V to 40 V with a drain voltage V

_{D}= 20 V. The transfer characteristics of all devices were measured up to 240 °C from RT at 5 °C intervals, and the temperature was increased at a rate of 5 °C per min.

## 3. Simple Charge Approximation

_{G}, and the distribution of acceptor-like states over the Fermi energy, E

_{F}, corresponds to the number of excited carriers per unit of induced energy. The calculation method in this study for the acceptor-like state distribution is based on the approach proposed by Lang et al., which extracts the DOS from the relationship between the gate voltage and excited carrier density [32,33,34].

_{a}(E) = N

_{shallow}(E) + N

_{deep}(E), and the induced free carrier density n(E) can be expressed as the integral of the product of the acceptor-like state and the Fermi–Dirac function:

_{a}(E), it can be assumed that f(E) = 1 and n(E) = ∫N(E) dE. In Figure 2c, the activation energy E

_{a}represents the energy required to place electrons from E

_{F}to E

_{C}, and by surface band bending y(x), E

_{a}can be expressed as

_{aFB}is the activation energy in the flat-band configuration. The equation for the activation energy was obtained from an Arrhenius plot.

_{D0}is a prefactor representing the initial ln I

_{D}converging with respect to the activation energy at a certain temperature. Based on the extracted activation energy, a brief result for the semiconductor DOS can be obtained by differentiating the density of free carriers as follows:

_{D}is constant under saturated conditions, the drain current of the IZO is determined by the surface potential and temperature. Thus, the drain current induced by thermal energy can be expressed as

_{d}denotes the electric field between the source and drain, i.e., ξ

_{d}= −V

_{D}/L. A

_{DS}is the cross-sectional area of the drain current and is given by A

_{DS}= W × d

_{s}, where d

_{s}is the channel thickness. It is assumed that the channel of the IZO TFT is sufficiently formed with a thin layer of semiconductor, approximately 20 nm in thickness. To compare the voltage-driven current characteristics with the thermal energy, the drain current of the TFT can be summarized as

_{ox}is the gate oxide capacitance in F/cm

^{2}, and the thickness of the gate dielectric, d

_{ox}, is 100 nm. By applying the V

_{D}= V

_{G}− V

_{Th}for the saturation current, and considering that the equations for the drain current I

_{D}(E) and I

_{D}(V

_{G}) are the same, the following summary can be made:

_{a}. It can be expressed as:

_{D}= 20 V was determined in the transfer curve in Figure 3, specifically in the saturation region. This was due to the relatively high leakage current of the fabricated IZO TFTs, which leads to increased external factors in the linear region [27]. Although there were some variations, the current of the IZO TFTs increased significantly with increasing temperature, and the TFT with the lowest In molarity ratio exhibited the largest increase in current. The increase in the off-state current was significantly greater than that in the on-state current. At high temperatures, control of the gate voltage is lost, resulting in only on-state characteristics. In the case of IZO TFTs with a high In molarity ratio in Figure 3b, carrier saturation is observed over the entire gate voltage range, and electric field saturation between source and drain occurs at temperatures above 160 °C, making measurements impossible. The increase in the TFT current with increasing temperature can be attributed to the carriers induced by the thermal energy and enhanced conductivity.

_{x}gate dielectric, specifically the influence of the initial charge state, and it is speculated that they are activated at temperatures above 60 °C and the charges escape through the gate electrode. In the temperature range of 60 to 160 °C, the characteristics of the TFTs from the off-state to the on-state were observed overall, and the maximum variation in activation energy was observed in the range of 70 to 110 °C. Carriers induced by thermal energy or surface bending accumulate in the TFT channel starting from the flat-band condition. The flat-band voltage of the TFT can be defined as the point at which the current begins to transition from the off-state to the on-state in the Arrhenius plot. However, the measured activation energy in this range was unexpectedly much larger (approximately 8–10 times) than the theoretical background. This can be explained by the trapped charge modifying the initial conditions of the current characteristics with respect to the gate voltage under thermal equilibrium at RT [35,36,37]. This electrical behavior was alleviated, particularly at temperatures above 160 °C as shown in the red region, where the influence of gate voltage decreased. At 240 °C (kT

_{T=240°C}= 0.0442 eV) in the range of −20 V to 40 V with V

_{D}= 20 V, a relatively reasonable activation energy was measured, and this was defined as the activation energy by converting the data to results at 90 °C.

_{a}in Figure 4c when V

_{G}= −20 V. Figure 5c illustrates the results of the extracted activation energy (E

_{a}) and the flat band voltage (V

_{FB}) values as a function of the In molarity ratio. The normalization conditions for Figure 5a,b were calculated using the following equation:

_{aFB}, was extracted from the maximum E

_{a}value in Figure 5a,b, and the corresponding gate voltage was defined as the flat-band voltage, V

_{FB}. The hatched region in Figure 5a,b represents the range below V

_{FB}and corresponds to the off-state in the depletion region where the minimum drain current I

_{DS}< 10

^{−13}A. As mentioned, activation energy values deviating significantly from the expected values at T = 90 °C were normalized using the flat band energy at T = 240 °C and a gate voltage of −20 V. The E

_{a}and V

_{FB}characteristics of the IZO TFTs exhibit a monotonic decrease with respect to the In molar ratio as shown in Figure 5c. The inversely proportional relationship between the activation energy and gate voltage indicates that the activation energy decreases as the gate voltage increases.

_{Th}with respect to the In molarity ratio, extracted under RT and T = 90 °C conditions. More detailed information on the characteristics, including the threshold voltage and field-effect mobility based on the In molarity ratio, can be found in the Supplementary Materials (Figures S4 and S5). In Figure 6a,b, the black dashed lines are extrapolated from the maximum slope of the square root graph, whereas the red dashed lines are extrapolated near the flat-band voltage. The yellow box in the figure represents the subthreshold region. Unlike single-crystal silicon-based MOSFETs, amorphous semiconductor TFTs operate under accumulated conditions without inversion. As shown in Figure 6a,b, the actual flat band voltage and threshold voltage of the IZO TFTs differed by approximately 4–5 V, regardless of the In concentration, suggesting the existence of a subthreshold region inferred from the flat band condition from the maximum flat band condition. Consequently, to describe the changes in the subthreshold voltage region more accurately, we defined the applied voltage using the gate voltage as V

_{F}(V

_{G}) = V

_{G}− V

_{Th}(V

_{G}), where V

_{Th}(V

_{G}) is the extrapolated threshold voltage at each gate voltage measurement point, that is:

_{m}is the transconductance of the square root of I

_{D}, g

_{m·max}is the maximum transconductance of the square root of I

_{D}, I

_{D·max}is the drain current at the point of g

_{m·max}, and V

_{G·max}is the gate voltage at the point of g

_{m·max}, respectively. The V

_{Th}characteristics at the temperatures T = RT and T = 90 °C are shown in Figure 6c, where the V

_{Th}values are determined by extrapolation from the maximum transconductance. The field-effect mobility, µ

_{FE}, calculated from the transconductance can be found in the Supplementary Material, Figure S5. V

_{Th}is approximately 1–5 V higher at T = 90 °C compared to the RT condition, and it ranges from 40% to 70% of the on-state current, regardless of the In molarity ratio. V

_{Th}decreased monotonically with increasing In molarity ratio, suggesting a similar mechanism to the characteristics observed for doping in single-crystal silicon semiconductors.

_{C}) and the corresponding characteristic energy kT

_{c}from the exponential distribution tangent at the point N

_{C}with respect to each In molarity ratio. In the graphs in Figure 7a,b, two band-tail state models are described: the shallow state (red dashed line) and the deep state (black dashed line) of the acceptor-like states. N

_{C_tail}and −1/kT

_{c_tail}correspond to the characteristics of the shallow state, mostly related to the In concentration. In Figure 7a,b, the black rectangles and blue circles represent the DOS distribution when using V

_{F}(V

_{G}) and fixed V

_{Th}values, respectively, and the yellow box indicates the DOS distribution in the subthreshold voltage region. As depicted in Figure 7a,b, employing linear extrapolation for V

_{F}(V

_{G}) allows a more comprehensive description of the DOS profile compared to using a fixed V

_{Th}, including the subthreshold voltage region. The magnitude of DOS at the conduction band edge N

_{C}is 9.59 × 10

^{18}for a low In molarity ratio of 0.0125 M, and it increases by approximately three orders of magnitude to 7.63 × 10

^{21}for a high In molarity ratio of 0.2 M. The characteristic energy kT

_{c}decreases from 488 meV to approximately 38 meV, and when converted to −1/kTc, it ranges from approximately 2.05 eV

^{−1}to 26.13 eV

^{−1}as shown in Figure 7c.

## 4. Meyer–Neldel Rule-Based Field-Effect Analysis

_{a}in the Arrhenius plot. The DOS analysis method based on the MN rule involves extracting the distribution of acceptor-like states by differentiating carriers with respect to the surface band-bending energy (y

_{s}) considering the applied external thermal energy condition. As defined in Equation (4), N(E) is a function of kT and y

_{s}, where the activation energy E

_{a}is influenced by the thermal and surface energies, i.e., E

_{a}= kT and E

_{a}(x) = E

_{aFB}− y(x). Additional definitions are required to simultaneously consider thermal and surface energies as variables in a single equation. The MN parameter A, which directly correlates with the activation energy, can be used to define the influence of temperature. More detailed explanations and calculation methods for characteristics based on the MN rule are available in the literature [38,39,40,41,42,43,44,45]. The calculation method for the acceptor-like state distribution based on the MN rule used in this paper is derived from the theory proposed by C. Chen’s research group [38].

_{D0}can be calculated from the current characteristics in the Arrhenius plot using the equation ln I

_{DS}= ln I

_{D0}− Ea/kT, where ln I

_{DS}vs. 1/kT represents the y-intercept at x = 0. The MN parameter A, defined from I

_{D0}, is derived from Equation (3).

_{D00}represents the MN constant. The MN parameter A is a variable determined by the temperature and y(x) is a variable influenced by the applied voltage. At low temperatures, the electrical behavior of the IZO TFTs resembled the characteristics in the subthreshold region above the flat-band voltage. At high temperatures, the electrical behavior of the IZO TFTs resembled that in the overthreshold voltage region. By determining the MN parameters in the subthreshold and overthreshold voltage regions, the thermal energy factor can be incorporated into Equation (11). Substituting Equations (3) and (11) into this relationship, the equation for the drain current as a function of the gate voltage can be obtained as follows:

_{a}(x) = E

_{aFB}− y(x), the drain current equation can be transformed into a function of x, as follows:

_{FB}= I

_{D00}· exp[(A − β) · E

_{aFB}]. To establish the relationship between the charge density and the electric field induced by the surface potential under the applied gate voltage, Poisson’s equation can be employed:

_{s}and ε

_{0}are the dielectric constant of the IZO semiconductor and permittivity of vacuum, respectively. By considering the electric field at a distance x from the semiconductor gate dielectric interface and utilizing the following definition, the relationship between the electric field and the induced carrier density can be derived.

_{s}) = 0 and dy(d

_{s})/dx = 0 at the top of the semiconductor surface d

_{s}, and y(0) = V

_{F}and dy(x)/dx = −ξ

_{s}(x). Substituting x with y as a function of Equation (13), under the dy

_{s}/dx condition in Equation (16), and rearranging according to I

_{D}(V

_{GS})/I

_{FB}− 1, we can express it as:

_{ins}is the dielectric constant of the gate dielectric, and d

_{ins}is its thickness. To simplify the calculation, we assume that y

_{s}is much smaller than V

_{GS}− V

_{Th}. The applied voltage V

_{F}follows the previously mentioned V

_{F}(V

_{GS}) = V

_{GS}− V

_{Th}(V

_{GS}) condition from a simple charge approximation. From Equation (18), V

_{F}can be expressed as follows:

_{s}, we obtain:

_{s}and V

_{F}, substituting Equation (18) into Equation (17), and differentiating with respect to V

_{F}, we obtain the equation for transconductance:

_{s}), we can obtain the relationship between transconductance dI

_{D}/dV

_{F}and n(y

_{s}).

_{s}from the relationship between V

_{F}and y

_{s}, we rearrange Equation (21) for dV

_{s}/dV

_{F}and substitute Equation (18), which results in the following expression:

_{s}on the left side can be approximated using an iteration based on the results obtained by substituting V

_{F}and I

_{D}(V

_{F}) on the right side. Using the calculations performed thus far, the final distribution of the acceptor-like state density N(E) can be obtained as follows:

_{D0}and flat-band current values as functions of the applied gate voltage in the IZO TFTs. More detailed results for I

_{D0}as a function of the In concentration are provided in the Supplementary Materials (Figure S7). In Figure 8a,b, V

_{FB}and V

_{Th}are determined using a simple charge approximation. The hatched region represents the depletion region and the yellow box indicates the subthreshold region. The speculated value of I

_{FB}in Figure 8c is inferred from the off-state current in the transfer characteristics. While an approximate value of I

_{FB}was estimated from the transfer characteristics, the I

_{FB}values shown in Figure 8c are approximations obtained through the calculations in Equations (22) and (24). As shown in Figure 8a,b, the approximate MN prefactor I

_{D0}exhibits an inverse relationship with the gate voltage and decreases significantly with increasing In molarity ratio.

_{D0}graph as a function of the activation energy and MN parameter A with respect to the In molarity ratio. The complete extraction results of MN parameter A for the entire In concentration range are summarized in Supplementary Material Figure S8. The MN parameter A in Figure 9a,b indicates the slopes obtained by differentiating ln I

_{D0}in terms of E

_{a}and can be defined in two regions. The region where I

_{D0}corresponds to the subthreshold region is depicted within the yellow box, whereas the region from the edge of the yellow box to 0 eV represents the overthreshold voltage region. Results: A in the two regions was defined based on the average slopes in each region as A

_{_subthreshold}and A

_{_overthreshold}. A1 and A2 in Figure 9a,b refer to A

_{_subthreshold}and A

_{_overthreshold}, respectively. As mentioned earlier, the value of E

_{a}in Equation (11) is a function of bias and temperature. Since we cannot simultaneously use two variables in a single equation like Equation (12), we will specify the value of A to incorporate the temperature factor. In this case, the A

_{_subthreshold}value represents the influence at low temperatures, while the A

_{_overthreshold}value represents the influence at high temperatures. By doing so, we can specify the thermal energy at low and high temperatures and ultimately calculate the shallow/deep state distribution based on the bias. The atypical magnitude of negative A, especially at high temperatures and high In concentrations in Figure 9b, can be attributed to the electrical behavior of a slight drain current decrease in the saturation region, which is associated with the percolation theory. As shown in Figure 9c, depending on the In molarity ratio, A

_{_subthreshold}in the subthreshold region shows relatively little variation, ranging from 25.85 to 19.48 eV

^{−1}. However, A

_{_overthreshold}exhibits significant variation, ranging from 14.38 to −39.38 eV

^{−1}in the overthreshold voltage region. It is important to note that, while the MN parameter A was estimated from Figure 9a,b, the exact values of A were subsequently obtained based on the calculations.

_{s}as a function of the applied gate voltage V

_{F}, the surface free carrier density n(y

_{s}) in terms of y

_{s}, and the maximum surface band bending of y

_{s}with respect to the In molarity ratio. Moreover, detailed analysis results regarding the In molarity ratio can be found in Figure S9 of the Supplementary Materials. The blue squares in Figure 10a,b represent the characteristics in the subthreshold voltage region, whereas the red circles represent the characteristics in the overthreshold voltage region. The y

_{s}–V

_{F}graph was derived using Equation (24), and the n(y

_{s})–y

_{s}graph was extracted using Equation (22). The values of y

_{s}obtained from Equation (24) were iteratively derived until an error of 0.1% was achieved. Furthermore, the modified I

_{FB}value, I

_{FB}’ = 100 × I

_{FB}, was used in Equation (23). The interpretation of the corrected results was based on the analysis of E

_{a_FB}using a simple charge approximation. Without using a correction factor of 100, y

_{s}for low In, 0.0125 M, changed from 1.845 to 2.597 eV, and y

_{s}for high In, 0.2 M, changed from 1.066 eV to 1.435 eV. Furthermore, if the uncorrected I

_{FB}were applied, the carrier density n(y

_{s}) at the degenerated states would increase by a factor of 10

^{2}, resulting in the DOS at the conductor band edge N

_{C}reaching levels as high as 10

^{25}cm

^{−3}·eV

^{−1}. Using the correction factor, the interpretation of the IZO semiconductor characteristics can be considered theoretically reasonable. As shown in Figure 10c, for an applied gate voltage of V

_{G}= 40 V, the maximum surface band bending y

_{s}decreased with increasing In molarity ratio and closely resembled the result of E

_{a_FB}in the subthreshold region as depicted in Figure 3c. The characteristics of y

_{s}in the region above the threshold voltage can be understood as a decrease in activation energy with a significant amount of thermal energy. This thermal energy, which is represented by the MN parameter A in the equation, plays a role in reducing the activation energy during the TFT operation.

_{C_s}and N

_{C_d}, correspond to the characteristics of the shallow and deep states, respectively, whereas the characteristic energies kT

_{c_s}and kT

_{c_d}represent the slopes of the shallow and deep state characteristics. As shown in Figure 11c, the N

_{C_s}value increases from 1.93 × 10

^{18}eV

^{−3}cm

^{−3}to 2.77 × 10

^{21}eV

^{−3}cm

^{−3}with respect to the In molarity ratio, while the kT

_{c_s}value decreases from approximately 280 meV to 40 meV.

_{C}depending on the calculation methods are summarized in Table 2. As shown in Table 2, the calculated results demonstrate a similar magnitude for both approaches. However, it’s important to note that the simple charge approximation method may lead to inaccuracies and fluctuation, especially in the deep state region. This is attributed to drawing two tangents from the one distribution in the calculation. On the other hand, the advantage of the MN Rule-based field-effect analysis over the charge sheet approximation method is its theoretical foundation and accuracy based on parameters such as the conductivity dI

_{D}/dV

_{F}with respect to the gate voltage. It provides a more detailed DOS distribution from the deep to the shallow states. This is because MN constant, A, has been appropriately characterized into subthreshold and overthreshold regions. As a result, the extracted DOS distribution characteristics obtained from the two methods were similar, with an exponential increase in N

_{C}and a linear decrease in E

_{a_FB}with respect to the In molarity ratio. As mentioned above in the atomic bonding structure model, the atomic bonding structure of Zn–O or In–O is determined by factors such as the charge density of metal cations and the atomic sizes. In case of solution-processed IZO semiconductors, the amorphous random network structure is determined by Zn–O bonding, and depending on the In concentration In atoms replace Zn atoms. The enhanced electrical conductivity of IZO semiconductors has been empirically confirmed [26,27]. By replacing the ionic bonding of Zn

^{2+}with the ionic bonding of In

^{3+}, the In–O bonding structure can act as donor, and free electrons are generated through the reaction of the dangling bond D

_{InO}

^{−}

`→`D

_{InO}

^{0}+ e

^{−}. These free electrons can improve the conductivity of the IZO semiconductor. Based on the fundamentals of the solution-processed IZO semiconductor, the DOS distributions were calculated quantitatively, revealing an increase in weak, dangling bonds and oxygen vacancies within the In–O atomic bonding structure. This led to a significant increase in the number of donors near the conduction band edge. The DOS extraction method presented in this study is applicable to a wide range of amorphous semiconductor materials and is effective in predicting the precise position of the Fermi energy. This provides a versatile approach that can be employed to understand the electronic properties and device performances of various material systems.

## 5. Conclusions

## Supplementary Materials

_{G}-sqrt(I

_{D}) graphs for extracting the threshold voltage of solution-processed IZO TFTs. (a–g) Graphs represent the results for different In molarity ratios, with the yellow region indicating the subthreshold voltage region. (h) V

_{Th}results for various In molarity ratios are shown at RT and T = 90 °C. Figure S5. Field-effect mobility, µ

_{FE}, characteristics as a function of gate voltage with respect to the In molarity ratio. Figure S6. (a–g) The DOS distribution calculated using the simple charge approximation method. Each (a–g) graph corresponds to a different In molarity ratio, and the tangent lines represent the exponential distribution models of the shallow (band tail) states and deep states, respectively. (h) Graph showing the variation in N

_{C}and −1/kT

_{c}with respect to the In molarity ratio. N

_{C}represents the DOS value at E

_{C}, and T

_{C}represents the characteristic temperature. Figure S7. (a–g) Graphs of the MN prefactor (I

_{D0}) as a function of gate voltage. Each graph represents the results for different In molarity ratios, and the hatched area and yellow area correspond to the region below the flat band voltage and the subthreshold voltage region, respectively. (h) Flat band current values according to the In molarity ratio. The flat band current values were extracted from the off-state current of the transfer curves. Figure S8. (a–g) The In(I

_{D0}) and MN constant, A, as a function of activation energy. Each graph represents the characteristics for different In molarity ratios. (h) The MN constant, A, in the subthreshold voltage region and overthreshold voltage region with respect to the In molarity ratio. Figure S9. (a–g) Graphs of V

_{F}–y

_{s}and y

_{s}–n(y

_{s}) as a function of In molarity ratio. The red y-axis represents the values of n(y

_{s}). (h) The maximum value of y

_{s}at V

_{G}= 40 V as a function of In molarity ratios. Figure S10. (a–g) The DOS distribution calculated using the MN rule-based field-effect analysis method. (a–e) represent the graphs for different In molarity ratios. The tangent lines in the graphs depict the exponential distribution models for shallow states and deep states. (h) Graphs showing the characteristics of shallow states and deep states, represented by N

_{C}and kT

_{c}, respectively, as a function of In molarity ratio.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic illustrating (

**a**) the band gap state of the amorphous IZO semiconductor, (

**b**) the atomic bonding structure of the amorphous random network in the IZO semiconductor, and (

**c**) the energy band diagram of the IZO semiconductor, including the band gap states.

**Figure 2.**(

**a**) Schematic illustration depicting the device structure of a solution-processed IZO TFT and the measurement atmosphere of the vacuum chamber. (

**b**) Acceptor-like state distribution of an IZO semiconductor. (

**c**) Energy band diagram of a metal-gate dielectric-IZO semiconductor illustrating the key energy levels.

**Figure 3.**Transfer characteristics of solution-processed IZO TFT according to the measurement temperatures. (

**a**) Transfer curves with 0.0125 M of In molarity and (

**b**) 0.2 M of In molarity. The various colored lines in graphs (

**a**,

**b**) depict the results measured at temperatures ranging from RT to 240 °C. (

**c**) On-state drain current as a function of In molarity ratio at RT and 240 °C.

**Figure 4.**Arrhenius plots of solution-processed IZO TFTs with (

**a**) 0.0125 M of In molarity ratio and (

**b**) 0.2 M. The different colored lines in graphs (

**a**,

**b**) show the measurement results with respect to the gate voltage ranging from −20 V to 40 V. (

**c**) The extracted activation energy is at T = 240 °C with respect to In molarity.

**Figure 5.**(

**a**) Normalized activation energy versus gate voltage graph with 0.0125 M of In molarity and (

**b**) 0.2 M of In molarity. (

**c**) Activation energy and flat band voltage as a function of the In molarity ratio.

**Figure 6.**Square root of the drain current versus gate voltage for solution-processed IZO TFTs (

**a**) with In 0.0125 M and (

**b**) 0.2 M, where the black dashed line represents the tangent at V

_{G.max}, while the red dashed line represents the tangent at the gate voltage near V

_{FB}. The yellow region in graphs (

**a**,

**b**) represents the subthreshold voltage region. (

**c**) The threshold voltage graph in terms of the In molarity ratio at RT and 90 °C.

**Figure 7.**Calculated band gap state distribution and characteristic temperature of solution-processed IZO semiconductors from the conduction band to the Fermi energy level. (

**a**) The DOS distribution with 0.0125 M of In molarity and (

**b**) 0.2 M of In molarity. The yellow region in graphs (

**a**,

**b**) corresponds to the E

_{aFB}-E

_{a}, defined from the Ea extracted from the subthreshold voltage region. (

**c**) The density of band tail state at the E

_{C}and properties of the slope with respect to the In molarity.

**Figure 8.**The MN prefactor I

_{D0}graph as a function of the gate voltage (

**a**) at 0.0125 M of In molarity and (

**b**) at 0.2 M of In molarity. The yellow region in graphs (

**a**,

**b**) corresponds to the subthreshold voltage region. (

**c**) The estimated and measured flat band current characteristics in accordance with the In molarity ratio.

**Figure 9.**The characteristics of the MN prefactor and MN parameter A graph depending on the activation energy at (

**a**) 0.0125 M of In molarity ratio and (

**b**) 0.2 M of In molarity ratio. The yellow region represents the E

_{a}in the subthreshold voltage region. (

**c**) The MN parameter A in the subthreshold voltage region and overthreshold voltage region with respect to the In molarity ratio.

**Figure 10.**Characteristics of surface band bending and free carrier density depending on the applied voltage and surface bending, respectively. (

**a**) The characteristics of solution-processed IZO TFT with 0.0125 M of In molarity and (

**b**) with 0.2 M. (

**c**) The maximum surface band bending at the subthreshold voltage region and overthreshold voltage region with respect to the In molarity ratio.

**Figure 11.**Extracted acceptor-like state distribution using MN Rule-based field-effect analysis. (

**a**) The DOS profile and fitting model of shallow/deep states at In 0.0125 M and (

**b**) at In 0.2 M. The red area in graphs (

**a**,

**b**) represents the DOS in the overthreshold voltage region. (

**c**) Density of shallow/deep states at the edge of the conduction band and their characteristic temperature results.

No. | In01 | In02 | In03 | In04 | In05 | In06 | In07 | In08 |
---|---|---|---|---|---|---|---|---|

Zn molarity (M) | 0.25 (fixed) | |||||||

In molarity (M) | 0 (non-operational) | 0.0125 | 0.025 | 0.05 | 0.1 | 0.125 | 0.15 | 0.2 |

In, Zn atomic weight ratio, In/Zn | 0 | 0.086 | 0.178 | 0.350 | 0.706 | 0.883 | 1.055 | 1.368 |

No. | N_{C}(cm ^{−3}·eV^{−1}) | In 0.0125 M | In 0.025 M | In 0.05 M | In 0.1 M | In 0.125 M | In 0.15 M | In 0.2 M |
---|---|---|---|---|---|---|---|---|

Simple charge approximation | N_{C_tail} | 9.59 × 10^{18} | 1.02 × 10^{20} | 8.01 × 10^{19} | 1.51 × 10^{20} | 1.53 × 10^{21} | 2.00 × 10^{22} | 7.63 × 10^{21} |

N_{C_deep} | 3.48 × 10^{18} | 4.19 × 10^{18} | 8.37 × 10^{18} | 3.42 × 10^{18} | 1.30 × 10^{18} | 2.60 × 10^{19} | 1.10 × 10^{19} | |

MN Rule field- effect analysis | N_{C_s} | 1.93 × 10^{18} | 4.57 × 10^{18} | 1.12 × 10^{19} | 1.41 × 10^{20} | 1.57 × 10^{20} | 2.68 × 10^{21} | 2.76 × 10^{21} |

N_{C_d} | 2.28 × 10^{17} | 7.03 × 10^{17} | 1.44 × 10^{18} | 1.61 × 10^{19} | 1.05 × 10^{19} | 5.25 × 10^{19} | 1.87 × 10^{20} |

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## Share and Cite

**MDPI and ACS Style**

Kim, D.; Lee, H.; Yun, Y.; Park, J.; Zhang, X.; Bae, J.-H.; Baang, S.
Analyzing Acceptor-like State Distribution of Solution-Processed Indium-Zinc-Oxide Semiconductor Depending on the In Concentration. *Nanomaterials* **2023**, *13*, 2165.
https://doi.org/10.3390/nano13152165

**AMA Style**

Kim D, Lee H, Yun Y, Park J, Zhang X, Bae J-H, Baang S.
Analyzing Acceptor-like State Distribution of Solution-Processed Indium-Zinc-Oxide Semiconductor Depending on the In Concentration. *Nanomaterials*. 2023; 13(15):2165.
https://doi.org/10.3390/nano13152165

**Chicago/Turabian Style**

Kim, Dongwook, Hyeonju Lee, Youngjun Yun, Jaehoon Park, Xue Zhang, Jin-Hyuk Bae, and Sungkeun Baang.
2023. "Analyzing Acceptor-like State Distribution of Solution-Processed Indium-Zinc-Oxide Semiconductor Depending on the In Concentration" *Nanomaterials* 13, no. 15: 2165.
https://doi.org/10.3390/nano13152165