Operation Mechanisms of Flexible RF Silicon Thin Film Transistor under Bending Conditions

Abstract

We fabricate a flexible silicon thin-film transistor (TFT) on a plastic substrate as a key component and representative example to analyze the major influencing factors of flexible devices under bending conditions. Experimental and two-dimensional device modeling results reveal that bending radius and device dimensions have a significant influence on the radio-frequency (RF) performance of the flexible silicon nanomembrane (SiNM) TFT under bending conditions. Carrier mobility and electric field extracted from the model, together with theoretical analysis, were employed to study the performance dependence and the operation mechanisms of the bended TFTs. The carrier mobility and electric field are increased monotonically with larger bending strains, which lead to better RF performance. They also showed a consistent change trend with different device parameters (e.g., gate length, oxide thickness). Flexible SiNM TFTs with a smaller gate length and a larger gate dielectric thickness are shown to have better RF performance robustness with bending strains. The analysis provides a guideline for the study of flexible electronics under bending conditions.

1. Introduction

Flexible electronics have received extensive attention in recent years because of their outstanding characteristics of bendability, foldability, and lightweight. Flexible electronics are now widely used in many new-rising areas [1,2,3,4,5,6,7,8,9,10]. In particular, the concept of the Metaverse makes wearable devices, flexible smart sensors, and electronic skins attract great interest [11]. With the development of transferable single-crystal SiNMs, flexible TFTs have become an essential and fundamental element for most of the flexible applications [12,13,14,15,16,17,18,19,20,21,22,23].

These flexible applications often need to operate under bending conditions, and thus the performance variations of flexible devices with bending strains are of great concern. While the flexible TFTs are the most essential components, the influencing factors and operation mechanisms of the TFTs under mechanical bending conditions are yet to be investigated. Researchers have been trying to study the performance of different types of flexible devices with bending strains [24,25,26,27,28,29,30,31,32]. However, these studies were most focused on the direct current regime and applied experimental characterizations or equivalent circuit modeling to analyze the performance variations of bended devices [33,34,35,36,37]. In addition, these studies were mainly about the monotonicity between the flexible device and bending radius.

Equivalent circuit modeling was usually used in traditional work, while two-dimensional device modeling was used in our proposed work. A small signal strain equivalent circuit model was employed for calculations and analysis of the TFT device in traditional work, where the source resistance can be obtained by model parameter extraction [24,28,37]. Then the relationship between source resistance and device performance was analyzed. Other device parameters, such as carrier mobility or electric field distribution, cannot be directly calculated or analyzed by this method. During this work, carrier mobility and electric field can be extracted from the model through Silvaco’s process simulators Athena and Atlas. It was clearer to show the carrier mobility and electric field variations under bending conditions and with different device structure parameters. Additionally, a standard fabrication process for the TFTs was applied to the model in our work, which was identical to the device fabrication processes, including the same device structure, ion implantations, annealing, etc. This helped to better investigate the device’s underlying mechanism.

In this work, it was found that the flexible SiNM TFTs have good RF performance robustness under bending conditions, and performance variations of flexible SiNM TFTs with bending strains were also related to the device dimension. Firstly, the flexible SiNM TFTs were fabricated on plastic substrates, and the RF characteristics of the flexible SiNM TFTs under different bending conditions were measured. Then Silvaco’s process simulators Athena and Atlas were used to analyze the dominant influencing factors of the flexible SiNM TFTs with different device dimensions under different bending conditions with model calculations of the carrier mobility and electric field. The SiNM TFTs with smaller gate lengths and larger gate dielectric thickness indicated better RF performance robustness with bending strains. The analysis was helpful for the design and application of flexible electronics under bending conditions.

2. Device Fabrication and Simulation

The main fabrication processes of the flexible silicon thin film transistor on plastic substrate were as follows [37]. First, high-dosage and high-energy ion implantations and high-temperature furnace annealing (950 °C) were conducted to form the source/drain (S/D) regions. Next, the top silicon template layer was patterned into 45 μm wide strips and then immersed in 49% aqueous hydrofluoric acid to remove the buried oxide (BOX) layer. The silicon nanostrips were then transferred onto a 225 μm thick polyethylene terephthalate (PET) substrate. Finally, the stack layers of SiO and Ti/Au were formed for the gate dielectric and gate metal. Figure 1a shows the finished gigahertz flexible SiNM TFTs on a PET substrate. Figure 1b shows the cross-section schematic of the flexible double-gate TFT (effective channel length is 1.5 μm, width is 40 μm).

For mechanical bending tests, the small-signal RF performance was measured for the SiNM TFTs mounted on the curvature mold with an Agilent E8364A performance network analyzer using Cascade GSG probes. Figure 1c shows an example photo of the bending test setup. The flexible SiNM TFT was mounted on bending test fixtures with different radii of 77.5 mm, 38.5 mm, and 21 mm. With Figure 1d and Equation (1), the tensile strains were calculated to be 0.16%, 0.33%, and 0.6%, respectively:

$$Strain(\%)=\frac{\Delta L}{L+\Delta L}=\frac{1}{\frac{2R}{\Delta R}+1}$$

(1)

where R is the radius of the curvature mold, $\Delta R$ is the thickness of the bended SiNM TFT, $L$ is the reference length, and $\Delta L$ is the elongation under tensile strain condition. To analyze the operation mechanism of SiNM TFTs under bending strains, Silvaco’s process simulators Athena and Atlas were used to model the RF performance of the flexible SiNM TFTs with different device structures under various bending conditions [26]. The same fabrication processes and parameters of SiNM TFT were applied to the model, including the same device structure, ion implantations, annealing condition, etc. [38].

Mechanical parameters of the flexible SiNM TFT have been assigned to silicon (Young’s modulus 169 GPa, Poisson ratio 0.28), silicon oxide (Young’s modulus 75 GPa, Poisson ratio 0.2), and metal electrodes (Young’s modulus 70 GPa, Poisson ratio 0.33), respectively. Doping has little effect on the mechanical parameters of silicon. Therefore, the same stress parameters were applied to the entire silicon region. The metal stress parameter and the gate oxide stress parameter were assigned to the electrodes and gate oxide, respectively. Figure 1e shows the schematic cross-section structure and doping concentration of the flat and bended TFTs.

3. Results and Discussion

Bending tests were carried out for the flexible SiNM TFTs, and the applied tensile strains were ~0.16%, ~0.33%, and ~0.6%, respectively. Figure 2a–d showed the current gain (H₂₁) and power gain (G_max) of the flexible SiNM TFT with no strain and 0.6% strain, respectively. The results indicate good agreement between the model and experimental results, indicating the accuracy of the model for the bended TFTs.

More importantly, Figure 2e,f showed that H₂₁ and G_max of the flexible SiNM TFTs increased monotonically with larger bending strains. Some studies attribute the RF performance changes of flexible devices with strains to the variation of carrier mobility [39,40]. Therefore, the carrier mobility of n+ doped regions in the model was extracted by Silvaco’s process simulator Atlas to investigate the underlying mechanism.

Figure 3a showed that the carrier mobility of the n+ doped regions increased by 5.83% with strains up to ~0.60%. When the carrier mobility of the n+ doped regions increased, the resistivity of the sources (n+ doped) decreased, leading to smaller source resistance and thus better RF performance. In addition, Figure 3a–c showed the change percentage of carrier mobility, H₂₁, and G_max of the flexible SiNM TFTs with larger bending strains, indicating a nonlinear increase in the change with larger strain.

To better understand this phenomenon, the electric field of the channel of the flexible TFTs was investigated, since the electric field also had an influence on the effective carrier mobility. The electric field contained a lateral and vertical electric field. The bending tests had little effect on the vertical electric field. Therefore, the lateral electric field was the main influencing factor. When the flexible SiNM TFTs were bended, the distance between drain and source became smaller, leading to a larger lateral electric field in the channel (Figure 3d). Additionally, the increase of electric field became less with larger strain, which was consistent with the change trend of mobility, H₂₁, and G_max. In addition, a large electric field at a larger bending strain may result in the saturation of carrier drift velocity and thus a smaller increase in carrier mobility with a larger strain. Consequently, the RF performance of the flexible TFTs increased monotonically with larger bending strains, while the change in the increase percentage became smaller as the strain was larger.

Furthermore, the dimensions of the gate and the dielectric layer could also have an impact on the bending robustness of the flexible TFTs. First, the operation mechanism of the bended TFTs with different gate lengths (1.3, 1.5, and 1.7 μm) was investigated. From Figure 4a, it was observed that with the same gate length, H₂₁ increased with larger bending strains. More importantly, with the same bending strain, H₂₁ increased more with a larger gate length. The change rate of H₂₁ of the SiNM TFTs, with gate lengths up to 1.7 μm, was nearly 12%. The result indicated that the RF performance of the SiNM TFTs under bending conditions was not only affected by bending strains but also related to the gate length. One reason was explained as follows. The cutoff frequency of the TFTs can be expressed as:

$$f_T=\frac{1}{2\pi }\frac{1}{\frac{C_{gs}+C_{gd}}{g_m}+C_{gd}\left(R_s+R_d\right)}$$

(2)

where R_s was the source resistance, R_d was the drain resistance, and C_gd was the gate drain capacitance, respectively. Source resistance and gate drain capacitance were the two main influencing factors for H₂₁ of the SiNM TFTs. With a larger gate length, gate drain capacitance was larger. Therefore, when the bending tests were carried out for the flexible SiNM TFTs, a larger gate drain capacitance will increase the change of the source resistance according to Equation (2). Therefore, with a similar decrease of R_s and R_d with larger bending strains, the f_T (or H₂₁) had more change. The other reason was related to the electric field of the bended TFTs (Figure 4b). Figure 4b clearly showed that the electric field near the channel of SiNM TFTs with a short gate length (1.3 μm) changes less than it does with a long gate length (1.7 μm). The electric field in the channel of the bended TFT with a smaller gate length changed less than that with a larger gate length. The small change rate of the electric field meant the carrier mobility changed less, and thus the SiNM TFTs would have good RF performance robustness. Overall, the flexible SiNM TFTs with smaller gate lengths showed better RF performance robustness under bending conditions than those with larger gate lengths.

The influence of gate dielectric thickness on the RF performance of the bended SiNM TFTs was also investigated (Figure 4c). From Figure 4c, it was observed that, with the same gate dielectric thickness, H₂₁ increased with larger bending strains. More importantly, with the same bending strain, H₂₁ increased more with a thinner gate dielectric layer. The change rate of H₂₁ in the SiNM TFTs with gate dielectric thickness up to 23 nm was nearly 18%. The results showed that H₂₁ had a smaller change with a thicker gate dielectric layer. This can also be explained by Equation (2), where a thinner gate dielectric leads to a larger gate drain capacitance. This will increase the change in the source resistance and thus more change for H₂₁. In addition, Figure 4d showed that the carrier mobility of the SiNM TFTs with a thicker gate dielectric layer changed less. A small change rate of carrier mobility means that the SiNM TFTs have good RF performance robustness. Consequently, the flexible SiNM TFTs with larger gate dielectric thickness had better RF performance robustness under bending conditions. The results in Figure 4 also verified that there was no convergence or singularity problem with the model. Compared to the equivalent circuit modeling or physical device model, two-dimensional device modeling can better show the underlying mechanism. By two-dimensional device modeling, the device structure parameters (e.g., channel length, oxide material, and thickness) can be directly modified to show the device’s performance. Furthermore, the two-dimensional device modeling can exhibit the performance prediction on different bending conditions or device structures, which cannot be realized by traditional modeling.

The performance of flexible SiNM TFTs has been continuously improved. However, there are still limitations to further improving the repeatability and reliability of the flexible devices. For the modeling and analysis of flexible electronics, investigations on the device’s performance with different environmental parameters, such as humidity and high- and low-temperatures, are yet to be conducted. Based on the individual device modeling, accurate modeling for flexible integrated circuits is also a future research direction.

4. Conclusions

In conclusion, flexible single-crystalline silicon nanomembrane (SiNM) thin film transistors were fabricated on plastic substrates. The RF performance of the SiNM TFTs with various dimensions was investigated under different bending conditions. Experimental and two-dimensional device modeling results revealed that the bending strain and the device dimensions had a significant influence on the RF performance of the bended SiNM TFTs under bending conditions. The RF performance of the flexible TFTs increased monotonically with larger bending strains, while the change in the increase percentage became smaller as the strain was larger. Carrier mobility and electric field extracted from the model, together with theoretical analysis, were employed to study these performance dependences and the operation mechanisms of the bended TFTs. The carrier mobility and electric field were increased monotonically with larger bending strains, which led to better RF performance. They also showed a consistent change trend with different device parameters (e.g., gate length, oxide thickness). The flexible SiNM TFTs with smaller gate lengths or larger gate dielectric thickness had better RF performance robustness under bending conditions. The results provided a useful guideline for the design and application of flexible TFTs under bending conditions.