Reply to: Safe practices for mobility evaluation in field-effect transistors and Hall effect measurements using emerging materials

replying to: V. Bruevich & V. Podzorov. Nature Electronics https://doi.org/10.1038/s41928-024-01154-8 (2024)

In response to our recent Article¹, Bruevich and Podzorov² raised concerns regarding the extraction of mobility from our perovskite thin-film transistor (TFT) transfer curves, potential Joule effects in our TFTs, and the differences between the estimated Hall and TFT hole concentration/mobility. Here we provide a response and additional details about our work.

Bruevich and Podzorov² recalculate the mobility based on raw data from our original Article (Fig. 1d in ref. ¹). They use the reliability factor based on the nonlinearity in the |I_DS|^1/2–(V_GS) curve to extract the mobility, which is often described for organic thin-film transistors (OTFTs)³. However, the adopted mode is typically suited to a highly ordered semiconductor, where linear transfer curves are expected, with constant carrier mobility. The applicability of linear evaluation for the extraction of mobility in polycrystalline disordered semiconductor systems has been discussed previously⁴. The nonlinearity in the V_GS–I_DS characteristics of halide perovskites may also originate from aspects other than those of conventional OTFTs. For example, the crystallization process in the three-dimensional (3D) Sn²⁺-perovskite channel is difficult to control, resulting in a complex film surface environment and contact interface, both of which influence the V_GS–I_DS linearity. Furthermore, for perovskite semiconductors with electronic polarization and high dielectric constants, the electron–phonon interaction can induce nonlinearities^4,5, as reported in other semiconductor systems with high dielectric constants or disorder^6,7,8.

Therefore, whether the approach proposed by Bruevich and Podzorov can be used as the standard method for perovskite TFT mobility extraction remains questionable, and new considerations or modifications for the mobility evaluation might be needed in the future. Assuming that this method is suitable, we analysed the data measured in the linear transfer characteristics (|I_DS|–(V_GS)) (Fig. 1a). The results suggest a mobility of 42 cm² V⁻¹ s⁻¹ with a reliability factor of 80%.

Fig. 1: Transfer characteristics of CsSnI₃-based TFTs.

a, Logarithmic (black solid line, left axis) and linear plots (circle scatter, right axis) of one CsSnI₃-based TFT measured in the linear regime. b, Transfer curves of one CsSnI₃-based TFT as a function of scanning speed. Note, a slightly lower on-state current caused by slower scan speeds is reasonable due to the increased charge trapping.

Regarding the potential non-equilibrium effects caused by high Joule power, the effect is expected to be negligible. In Fig. 3a,b of our original paper, the long-term continuous switching and transfer curve measurement can be seen to be highly consistent. Meanwhile, the device character is independent of the V_GS sweep rate (Fig. 1b). However, a specific investigation of the Joule heating effect on perovskite TFTs is an interesting topic for future work.

Using the TFT threshold voltages reported in ref. ¹, Bruevich and Podzorov² estimate the hole concentration to be 2.5 × 10¹⁸ cm⁻³ and the film conductivity to be 1.8 S cm⁻¹. However, comparing hole concentrations obtained from TFT transfer characteristics and Hall measurements can be problematic. Due to band bending at the interface, as well as the non-uniform carrier distribution within the TFT films, directly dividing by thickness can lead to inaccuracy⁹. Additionally, the estimated hole concentration and film conductivity are too high for a transistor channel to show efficient on–off current modulation^10,11. Bruevich and Podzorov note that the Sn²⁺ perovskites exhibit high hole concentrations due to the p-doping effect. This is only true for pristine Sn-based perovskite, which is not suitable as a channel semiconductor. Thus, a hole suppressor (such as 10 mol% SnF₂) is used to reduce the excessive hole concentrations for TFT applications. For example, a quantitative study has demonstrated that doping 10 mol% SnF₂ into Sn²⁺-perovskite films can substantially reduce the hole density from 10¹⁹ to ~10¹⁶ cm⁻³ (ref. ¹²). In our study, we used 10 mol% SnF₂ and Pb as hole suppressors and excess CsI to reduce the self-p-doping effect for the high TFT on/off current ratio and mobility.

Based on the hole concentration values, the Hall mobility of 0.5 cm² V⁻¹ s⁻¹ calculated by Bruevich and Podzorov appears to be too low. Such a low film mobility would make it impossible to achieve high-mobility transistors, even with the TFT mobility of 13 cm² V⁻¹ s⁻¹ recalculated by Bruevich and Podzorov. Various characterization methods have demonstrated that 3D Sn²⁺-based polycrystalline perovskite films possess high mobilities because of the intrinsically small hole effective masses and low Fröhlich interactions^13,14,15. With Hall measurements, µ_Hall is mainly determined from fundamental film scattering, such as grain-boundary and impurity scattering (bulk transport). For the TFT µ_FE, charge-carrier transport under a gate bias is mainly confined near the semiconductor/dielectric interface. Such transport is much more sensitive to the hole traps existing in the bandgap near the valence and maximum, as well as to the interface roughness/defects of the gate dielectric and semiconductor layers. Generally, the TFT µ_FE is reported to be lower than µ_Hall, and this difference has been widely discussed for different semiconductors^{16,17,18,19,20,21}. The degree of difference between the device µ_FE and film µ_Hall may depend on the device optimization.

Although our initial devices did not show ideally optimized characteristics—notable hysteresis, for example—in such cases we generally extracted the mobility from the forward scan, as charge trapping during the forward scan can lead to a false, high mobility if extracted using the reverse scan. Nevertheless, we appreciate the value of this discussion, as well as the importance of developing safe practices for mobility evaluation with high-performance TFTs based on emerging halide perovskite semiconductors. In our recent Perspective²² we provided a detailed discussion on safely reporting perovskite TFTs and extracting mobilities. Besides the consideration of V_GS–I_DS linearity, the gate leakage, dielectric capacitance evaluation and other issues also need to be considered.