# A Semi-Analytical Extraction Method for Interface and Bulk Density of States in Metal Oxide Thin-Film Transistors

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{it}) as functions of the front and back-side surface potentials, in which the electric field at the back side is assumed to be zero [15]. Therefore, it is essential to develop analytical methods for extracting both the interface DOS and the bulk DOS of TFTs.

## 2. Extraction Method

_{s}) and the back interface potential (Ψ

_{b}) are respectively labeled. Poisson’s equation is given by

_{free}(x) and n

_{trap}(x) are the free electron concentration and localised trapped electron concentration, respectively.

_{s}) is the surface charge concentration, and ρ(Ψ

_{b}) is the back interface charge concentration. Equations (3) and (4) can be further rearranged as

_{s}) considering the effect of the back interface potential can be expressed as

_{0}is the characteristic length of the potential distribution. Note that the assumption for Equation (8) will be confirmed by the numerical solution of Poisson’s equation in Appendix A and the device simulation in Section 3. Substituting Equation (8) into Equations (5)–(7), we have

_{g}(V

_{gs}) is gate capacitance at some V

_{gs}, C

_{ox}is the gate oxide capacitance per unit area, and Q

_{g}is the charge per unit area at the gate electrode

_{s}and V

_{gs}can be obtained by integrating Equation (12) over V

_{gs}:

_{fb}is the flat band voltage.

_{i}) can be expressed by an integration of n

_{free}(x) over x.

_{s}is the thickness of the active layer, n

_{0}is the flat band electron concentration, and V

_{t}is the thermal voltage (kT/q). On the other hand, Q

_{i}can also be obtained from the transfer characteristics of TFT at low V

_{ds}.

_{0}can be extracted from Equation (15) equal to Equation (16) at the condition of flat band, i.e., Ψ

_{s}= 0 and V

_{gs}= V

_{fb}. Then, x

_{0}at some V

_{gs}can be calculated from Equation (15) equal to Equation (16) by numerical integration.

_{g}+ Q

_{o}+ Q

_{s}= 0, where Q

_{o}is the effective interface charge per unit area at the gate insulator, one obtains

_{it}) can be calculated by differentiating Q

_{0}with respect to Ψ

_{s}

_{F}

_{0}is the bulk Fermi level of the active layer, which is calculated from the relationship of n

_{0}to E

_{F}

_{0}:

_{C}is the effective density of states in the conduction band with a typical value of 5 × 10

^{18}cm

^{−3}[18].

_{s}given by Equation (14) and the surface charge concentration ρ(Ψ

_{s}) given by Equation (9), the bulk density of states can be given by [17]

_{s}with respect to V

_{gs}is obtained from the C

_{g}–V

_{gs}characteristics of TFTs by Equation (14). Secondly, x

_{0}can be calculated from the current characteristics of TFTs by using Equations (15) and (16). Thirdly, ρ(Ψ

_{s}), Q

_{s}, and Q

_{o}will be subsequently obtained by Equations (9), (11), and (17), respectively. Finally, the interface density of states (N

_{it}(E)) and the bulk density of states (N

_{bt}(E)) can be extracted by Equations (18) and (20), respectively. As a result, the extraction method may be easily realised step by step as seen from the above extraction procedure.

## 3. Results and Discussion

_{2}) was deposited by plasma-enhanced chemical vapor deposition (PECVD). A 30 nm IZO active layer is deposited by using a radio frequency (RF) magnetron system with the segregated target of IZO (In

_{2}O

_{3}:ZnO = 1:1). Then, an etch stopper layer (ESL) SiO

_{2}is deposited by PECVD to protect the active layer. Finally, a 200nm Mo is formed by sputtering as S/D electrodes. The channel length and width of IZO TFTs are determined by layout and patterned by the conventional lithographic techniques.

_{gs}) from −10 V to 10 V with the step of 0.1 V at the condition of V

_{ds}= 0.1 V. The C–V characteristics are measured by superimposing the AC voltage signal (amplitude = 200 mV, frequency = 1 kHz) to DC gate bias in the condition of source and drain electrodes connected together. Note that those measurements are done at room temperature in the dark air ambient. It is thought that the DOS distribution of AOS TFTs remains unchanged at different temperatures [10]. Figure 2a shows the transfer characteristics of IZO TFTs (W/L = 20 μm/10 μm). The threshold voltage, the field-effect mobility, sub-threshold swing (SS), and on/off current ratio (I

_{on}/I

_{off}) of the pristine TFTs are extracted to be 1.8 V, 12.36 cm

^{2}/(V·s), 0.23 V/dec, and 1 × 10

^{7}, respectively. V

_{fb}is extracted as 0.6 V from the I–V characteristics following the method developed by Migliorato et al. [19]. n

_{0}is extracted as 3.84 × 10

^{16}cm

^{−3}by (15) when Ψ

_{s}= 0, i.e., V

_{gs}= V

_{fb}. Figure 2b shows the C

_{g}–V

_{gs}characteristics of the devices at the frequency of 1 kHz, which are measured with source and drain electrodes combined together. Note that the frequency of 1 kHz for the AC signal may be low enough to make the TFTs work in the quasi-static conditions. Figure 3 shows the surface potential (Ψ

_{s}) with respect to V

_{gs}from (14) based on the C–V characteristics and the value of V

_{fb}. Figure 2c shows the micrograph of IZO TFTs with W/L = 20 μm/10 μm.

_{gs}= 2.0 V, V

_{ds}= 0.1 V. It is found that the proposed Equation (8) can fit the simulated potential distribution well. Note that at other values of Vgs including that at the subthreshold region, the simulated potential distributions are also found to be well fitted by Equation (8) with different values of x

_{0}. As a result, Equation (8) may be reasonable and correct for reproducing the potential distribution of the thin active layer. Furthermore, based on the I–V characteristics and the surface potential distribution as seen in Figure 3, the value of x

_{0}can be extracted from Equation (15) equal to Equation (16), as shown in Figure 5. It is found that the value of x

_{0}tends to vary slowly when V

_{gs}is larger than the threshold voltage, because the variation of Q

_{i}changes more slowly for TFTs working in the above-threshold region.

_{C}, while it linearly increases with the increase of energy close to E

_{C}at the exponent coordinate. Then, the interface DOS of AOS TFTs may be divided into two parts: constant deep states and exponential tail states, i.e.,

_{iD}is the density of deep states, N

_{iT}is the density tail states at the conduction edge, and E

_{iT}is the characteristic energy of tail states. For details, N

_{iD}/N

_{iT}is extracted by extrapolating the deep/tail states to E = E

_{C}, and E

_{iT}is extracted from the slope of log(N

_{it}) versus (E − E

_{C}) for the tail states. The extracted values are N

_{iD}= 1.3 × 10

^{12}cm

^{−2}eV

^{−1}, N

_{iT}= 2.9 × 10

^{12}cm

^{−2}eV

^{−1}, E

_{iT}= 0.08 eV. Obviously, the interface DOS distribution can be used to characterise interface quality and the reliability of AOS TFTs [20,21].

_{C}, while it quickly increases with the increase of energy close to E

_{C}at the exponent coordinate. It is found that the bulk DOS may be a superposition of exponential deep states and exponential tail states, i.e.,

_{bD}/N

_{bT}is the density of deep/tail states at the conduction edge and E

_{bD}/E

_{bT}is the characteristic energy of deep/tail states, of which the extraction method is similar to that of interface DOS as described above. The extracted values are N

_{bD}= 6.0 × 10

^{16}cm

^{−3}eV

^{−1}, E

_{bD}= 5.0 eV, N

_{bT}= 6.5 × 10

^{17}cm

^{−3}eV

^{−1}, and E

_{bT}= 0.10 eV. Such double exponential distribution for the bulk DOS can also be seen in other previously reported works [8,9,10,11]. For details, the deep states in AOSs may derive from oxygen deficiency, while the tail states originate from the variation of In–O–metal bonding angles [22].

## 4. Conclusions

_{iD}= 1.3 × 10

^{12}cm

^{−2}eV

^{−1}, N

_{iT}= 2.9 × 10

^{12}cm

^{−2}eV

^{−1}, and E

_{iT}= 0.08 eV. Additionally, the bulk DOS is extracted as the superposition of exponential deep states and exponential tail states with N

_{bD}= 6.0 × 10

^{16}cm

^{−3}eV

^{−1}, E

_{bD}= 5.0 eV, N

_{bT}= 6.5 × 10

^{17}cm

^{−3}eV

^{−1}, and E

_{bT}= 0.10 eV. Furthermore, the device simulation is performed by a 2D device simulator to verify the extracted values of interface DOS and bulk DOS. It is found that there is a good agreement between simulation results and the measured transfer and output characteristics of IZO TFTs. Hence, the proposed extraction method for interface and bulk DOS may be valuable for characterising metal oxide TFTs due to the advantages of being semi-analytical and fast. Since the proposed extraction method is directly deduced from Poisson’s equation, it may also be applied in other types of TFTs, such as a-Si:H TFTs, polysilicon TFTs, or organic TFTs.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

_{free}(x) and n

_{trap}(x) may be expressed as

_{s}is obtained from (14). E

_{s}is the surface electric field of the active layer, which is obtained from the relationships ${\epsilon}_{ox}{V}_{ox}/{t}_{ox}={\epsilon}_{s}{E}_{s}$ and ${V}_{gs}={\phi}_{ms}+{\psi}_{s}+{V}_{ox}$, where V

_{ox}is the voltage across the oxide and Φ

_{ms}is the work function difference between the gate and active layer semiconductor.

_{bt}(E) at the condition of V

_{gs}= 1.0 V. It is shown that the numerical results of potential distribution may be reproduced well by (8). It is further found that the numerical results of potential distribution at other V

_{gs}can also be fitted well by (8) with different x

_{0}. Similarly, analytical complex exponential distributions of potential are also obtained by only taking into account either the free electrons [23] or the trapped electrons [12] in Poisson’s equation. In brief, Equation (8) may be a reasonable approximation for the potential distribution to achieve a good tradeoff between accuracy and simplicity.

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**Figure 1.**(

**a**) Cross-sectional view of indium zinc oxide thin-film transistors (IZO TFTs) with inverted staggered bottom gate structure; (

**b**) energy band diagram along the thin-film depth direction of IZO TFTs.

**Figure 2.**Experimental data of IZO TFTs (W/L = 20 μm/10 μm). (

**a**) Transfer characteristics; (

**b**) C

_{g}–V

_{gs}characteristics; (

**c**) The micrograph of the devices.

**Figure 3.**Ψ

_{s}versus V

_{gs}obtained by (14) based on the capacitance–voltage (C–V) characteristics.

**Figure 6.**Extracted interface density of states (DOS) as a function of E − E

_{C}from the proposed method (symbols) and results fitted by (21) (solid lines).

**Figure 7.**Extracted bulk DOS as a function of E − E

_{C}from the proposed method (symbols) and results fitted by (22) (solid lines).

**Figure 8.**Experimental data (symbols) and simulated results (solid lines) of IZO TFTs with W/L = 20 μm/10 μm. (

**a**) Transfer characteristics; (

**b**) output characteristics.

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**MDPI and ACS Style**

Chen, W.; Wu, W.; Zhou, L.; Xu, M.; Wang, L.; Ning, H.; Peng, J.
A Semi-Analytical Extraction Method for Interface and Bulk Density of States in Metal Oxide Thin-Film Transistors. *Materials* **2018**, *11*, 416.
https://doi.org/10.3390/ma11030416

**AMA Style**

Chen W, Wu W, Zhou L, Xu M, Wang L, Ning H, Peng J.
A Semi-Analytical Extraction Method for Interface and Bulk Density of States in Metal Oxide Thin-Film Transistors. *Materials*. 2018; 11(3):416.
https://doi.org/10.3390/ma11030416

**Chicago/Turabian Style**

Chen, Weifeng, Weijing Wu, Lei Zhou, Miao Xu, Lei Wang, Honglong Ning, and Junbiao Peng.
2018. "A Semi-Analytical Extraction Method for Interface and Bulk Density of States in Metal Oxide Thin-Film Transistors" *Materials* 11, no. 3: 416.
https://doi.org/10.3390/ma11030416