Device Physics of Contact Issues for the Overestimation and Underestimation of Carrier Mobility in Field-Effect Transistors

Chuan Liu, Gongtan Li, Riccardo Di Pietro, Jie Huang, Yong-Young Noh, Xuying Liu, and Takeo Minari

Phys. Rev. Applied 8, 034020 – Published 22 September 2017

Abstract

Very high values of carrier mobility have been recently reported in newly developed materials for field-effect transistors (FETs) or thin-film transistors (TFTs). However, there is an increasing concern of whether the values are overestimated. In this paper, we investigate how much contact resistance a FET or TFT can tolerate to allow the conventional current-voltage equations, which is derived for no contact resistance. We contend that mobility in transistors with resistive contact can be underestimated with the presence of the injection barrier, whereas mobility in transistors with gated Schottky contact can be overestimated by more than 10 times. The latter phenomenon occurs even in long-channel devices, and it becomes more severe when using low- $k$ dielectrics. This is because the band bending and injection barrier experience a complicated evolution on account of electrostatic doping in the semiconducting layer; thus, they do not follow a capacitance approximation. When the band bending is weak, the accumulation is as weak as that in the subthreshold regime. Accordingly, the carrier concentration nonlinearly increases with the gate field. This mechanism can occur with or without exhibiting the “kink” feature in the transfer curves, which has been suggested as the signature of overestimation. For precision, carrier mobility should be presented against gate voltage and should be examined by other recommended extraction methods.

Received 9 March 2017

DOI:https://doi.org/10.1103/PhysRevApplied.8.034020

Physics Subject Headings (PhySH)

Electrical properties Organic electronics Transport phenomena

Devices Field-effect transistors Organic semiconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Chuan Liu^1,*, Gongtan Li¹, Riccardo Di Pietro², Jie Huang¹, Yong-Young Noh³, Xuying Liu⁴, and Takeo Minari⁴

¹State Key Laboratory of Optoelectronic Materials and Technologies, Guangdong Province Key Laboratory of Display Material and Technology, School of Electronics and Information Engineering, Sun Yat-sen University, Guangzhou 510275, People’s Republic of China
²Hitachi Cambridge Laboratory, Cambridge CB3 0HE, United Kingdom
³Department of Energy and Materials Engineering, Dongguk University, 30 Pildong-ro, 1 gil, Jung-gu, Seoul 04620, Republic of Korea
⁴International Centre for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan

^*Corresponding author. liuchuan5@mail.sysu.edu.cn

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Vol. 8, Iss. 3 — September 2017

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Figure 1
Under- or overestimation of carrier mobility due to contact resistance (linear regime): Gate dependence of (a) resistance ( $R_{C}$ , $R_{CH}$ ), (b) drain current ( $I_{D S}$ ), and (c) extracted field-effect mobility by Eq. (2) when setting $μ_{0} = 1 {cm}^{2} V^{- 1} s^{- 1}$ . For comparison with disordered semiconductors, extracted field-effect mobility by Eq. (2) when setting $μ_{0} = μ_{1} (V_{G} - V_{th})^{β}$ : $β = 0.1$ (d) and $β = 0.3$ (e). The channel width $W$ and length $L$ are, respectively, equal to 1000 and $100 μ m$ . $C_{i}$ is the unit area gate capacitance, which is equal to $1 \times 10^{- 8} F / {cm}^{2}$ .
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Figure 2
Injection barrier and miscalculation of field-effect mobility (saturated regime): Schematic of (a) device structure, (b) energy levels of metal-semiconductor contact, and (c) density of states of the semiconductor in a 2D calculation. In (c), the DOS of the disorder-free semiconductor is shown as black curves, whereas the DOS for localized, tail states for disordered semiconductors is shown as red curves. The transfer curves and field-effect mobility are plotted against $V_{G}$ when the work-function equals (d),(g) 4.25, (e),(h) 4.40, or (f),(i) 4.80 eV. For TFTs with disorder-free semiconductor, the curves are shown in (d)–(f) and the set mobility (constant) are shown in blue dashes for a reference. For TFTs with disordered semiconductors, the curves are shown in (g)–(i) and the mobility (nonconstant) calculated in Ohmic contact are shown in blue dashes for a reference. The data are obtained by TCAD 2D calculation and the devices operated in the saturated regime.
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Figure 3
Evolution of band bending in semiconductors: (a) Position for showing band bending in the transistor, and the coordinates of points $a$ , points $b$ , points $c$ , and points $d$ are ( $10 μ m$ , 0 nm), ( $10 μ m$ , 39 nm), ( $90 μ m$ , 39 nm), and ( $90 μ m$ , 0 nm), respectively; $V_{1}$ is at $x = 11.0 μ m$ and $y = 39.0 nm$ . The effect of $V_{G}$ on the valence band or HOMO level in the band diagram: (b) Ohmic contact; work function equals 4.8 eV, and (c) non-Ohmic contact; work function equals 4.25 eV. (d) Voltage drop in the barrier region and channel region. (e) Injection from source electrodes to the semiconductors, and the valance band or HOMO level next to the electrode, depending on the gate voltage. The schematic representations in (b), (c), and (e) are plotted according to the results of the TCAD 2D calculations.
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Figure 4
Transition of operation modes in transistors: Injected hole concentration (mobile carriers) in the channel ( $x = 11 μ m$ , $y = 40 nm$ ) at different $V_{G}$ for TFTs with a disorder-free semiconductor (a) and disordered semiconductor (b). (c) At a large ( $V_{G} = - 70 V$ ), the potential distribution from the source ( $x = 15 μ m$ , $y = 0 nm$ ) to the bottom of the active layer ( $x = 15 μ m$ , $y = 39 nm$ ) for various work-function values. (d) Transfer curves of a TFT with disorder-free semiconductor in a semilog scale by 2D calculation (dots) and the fitting by Eq. (2) (lines). The reference curve is plotted using the data of Ohmic contact ( $WF = 4.8 eV$ ). The transistors work in the TFT mode or in the SBT mode. (e) The same data in the linear scale. The data of devices with a metal work function of 4.25 eV are plotted in blue; those with a metal work function of 4.40 eV are plotted in red.
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Figure 5
Low- $k$ dielectric, long channel devices, and examples of presenting mobility: (a) Devices with non-Ohmic contact ( $WF = 4.4 eV$ ) and with different dielectric constant $k$ , indicating that overestimation of mobility can be even more dominant in device operation with a low- $k$ dielectric (the intrinsic value is $7.0 {cm}^{2} V^{- 1} s^{- 1}$ ). (b) Devices with non-Ohmic contact ( $WF = 4.25 eV$ ) in different channel lengths, indicating that long channel devices still suffer from a miscalculation of mobility. (c) An example for presenting the carrier mobility of a transistor with an injection barrier ( $WF = 4.45 eV$ ) in the linear regime. (d) An example for presenting the carrier mobility of the same transistor in the saturated regime. The value extracted by the $G$ function is obtained from output curves ( $V_{G} = - 70 V$ , $V_{D S} = 0$ to $- 70 V$ ; cf. Supplemental Material).
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Figure 6
Mobility curves of nonideal FETs or TFTs: Constant (black line) or power-law mobility (gray line); gradual decaying mobility in the transistor with resistive contact or surface or phonon scattering of carriers (red line, underestimated in the linear regime if the former); sharp peak mobility in the transistors with gated Schottky contacts, and the device transits from the SBT mode to the TFT mode (blue line, probably overestimated); exponentially increased mobility in the transistor with gated Schottky contact, and the device works in the SBT mode (purple line, needs verification and overestimated if in the SBT mode). The values for each curve are normalized to the maximum of each.
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