Density of trap states in a polymer field-effect transistor

It has become important to obtain a detailed understanding of charge carrier transport in organic field-effect thin-film transistors (TFT).^1–6 The measurement of the density of trap states (DOS) in organic TFTs is one of the key steps in understanding and describing carrier transport phenomena.^7–12 Previous work by Lang et al.⁷ and Kalb et al.^9,10 have used only the above-threshold characteristics to calculate the DOS of an organic single crystal semiconductor. This approach may work fairly well for single crystals in which the density of trap states is small. In polymer field-effect transistors, as well as other thin-film transistors in which there is a lot of disorder, sub-threshold conduction plays an important role even at fairly high gate voltages and must be part of the analysis. In this letter, we describe an approach which combines sub-threshold response as well as above threshold response in determining the density of trap states. We will show that this method is much more accurate for polymer and other disordered semiconductor based field-effect transistors.

Polymer transistors have received a lot of attention in the past two decades due to their unique properties and potential for use in displays and large-area electronics.^13–17 Co-polymers based on the diketopyrrolopyrrole (DPP) core are particularly promising on account of their relatively large mobilities, often exceeding 2 cm²/V s.^18–25 In this paper, we will employ data from DPP-based field-effect transistors to illustrate our method of calculating the DOS.

Data from the thiophene-flanked DPP copolymer with thienylene-vinylene-thienylene (PDPP-TVT) TFT is used for analysis.¹⁸ The chemical structure of PDPP-TVT and the device structure of the TFT are shown on Figs. 1(a) and 1(b), respectively. N-doped silicon was used as gate, with 290 nm thermally grown SiO₂ dielectric layer. The dielectric layer gave a value of capacitance per unit area (C_i) of 12 nF/cm². PDPP-TVT film was spin coated on octadecyltrichlorosilane (OTS) self-assembled monolayer (SAM) treated surface and annealed under an inert atmosphere at 200 °C for 30 min. The Ti/Au (2.5 nm/45 nm) source/drain electrodes were deposited on the polymer layer by thermal evaporation. The electrical characteristics of the TFT were measured at both 300 K and 273 K, using a semiconductor parameter analyzer in a cryogenic probe station. The channel width (W) and length (L) of the TFT is 1000 μm and 50 μm, respectively.

The transfer curves of PDPP-TVT TFT at a drain-source voltage V_DS = −10 V are shown in Fig. 2. First, we extracted threshold voltages (V_T) from a linear drain current (I_D) vs. a gate-source voltage (V_GS) plot to define sub-threshold and above-threshold regimes. V_T at 300 K and 273 K are −35.6 V and −37.6 V, respectively. In previous work from other groups, there was no specified method for identifying the sub-threshold regime.⁷ The Sub-threshold Swing (S.S.) was used to calculate the constant interface trap states density.^10,26 This method works quite well for single crystal organic TFTs which typically have a relatively small number of deep trap states. In thin-film transistors, there are typically three regimes of conduction: (i) Diffusion-limited sub-threshold conduction possessing an exponential current-voltage relationship; (ii) Drift-limited sub-threshold regime in which the current-voltage relationship is a power law,²⁷ and (iii) The above threshold region. The presence of a significant drift-limited sub-threshold regime is a characteristic of disordered semiconductor based TFTs and must be taken into consideration in determining the density of trap states. PDPP-TVT TFT clearly possess a wide range in which there is a non-linear semi-log I_D vs. V_GS relationship in sub-threshold regime. This range is the drift-limited regime associated with deep trap states, similar to amorphous Si TFTs.²⁸ A methodology to properly consider this conduction regime (with its unique characteristics) in the extraction of the DOS is needed for polymer TFTs.

In the above threshold region, the slope of the log (I_D) vs. log (V_G) curve is expected to be 1, since the drain current varies linearly with gate voltage. In the sub-threshold drift-limited region, the current voltage characteristics are given by

where V_FB is the flat band voltage from the transfer curve, β is a pre-factor, and α is the power law factor that can be determined from the log (I_D) vs. log (V_G) characteristics. These are illustrated in Fig. 3 for two different temperatures. Fig. 3(a) shows the log (V_GS–V_FB) dependent log (I_D) in sub-threshold regime. We used the turn-on voltage as a V_FB, where the sign of (ΔI_D/ΔV_GS) is changed. The dependence of log (V_GS–V_T) on log (I_D) in the above threshold regime is also shown in Fig. 3(b). It is obvious that the slopes in each regime, which indicate the power law factor in the TFT drain current equation, are greatly different. From Fig. 3(a), the drift-limited power law factors for 300 K and 273 K were 4.63 and 3.65, respectively. In addition, from Fig. 3(b), the above threshold regime power law factors for 300 K and 273 K were 1.04 and 1.10, respectively. The slope in the above threshold regime was very close to unity, which means that the TFT operated in the linear region. However, the drift-limited regime power law factor was much larger than its counterpart of the above threshold regime, which indicates not only the existence of a substantial number of deep trap states but also the necessity of a different mobility calculation method for the drift-limited regime, rather than the conventional linear field-effect mobility extraction.

To more accurately determine both activation energy and density of deep trap states, we create a composite mobility vs. gate voltage characteristic that spans both the sub-threshold and above threshold regimes. These regimes have different current voltage characteristics: For the linear region, the field-effect mobility is described by Eq. (2) over the full operating range

This set of values is used for the calculation of activation energy in previous works.^10–12 We call it a linear model in the remainder of this paper.

In the drift-limited mobility regime, the current voltage characteristics are given by Eq. (1). β is defined to satisfy the continuous transition of mobility at V_GS = threshold voltage. This method of analysis of the sub-threshold drift-limited region has been employed by Nathan et al.²⁷ We refer to this mobility model as the linear/drift model hereafter. The results of calculated mobilities based on the two models are shown in Fig. 4(a).

In high mobility organic and polymer TFTs, the principal charge transport mechanism is multiple trap and release (MTR).^2,29 According to the MTR model, the activation energy (E_A) can be calculated from the field-effect mobility, as described by the following equation:

where k is the Boltzmann constant and T is the temperature. From the activation energy data, it is possible to calculate the density of trap states based on Lang's method⁷ 

where q is the elementary charge and a is a gate voltage independent effective accumulation layer thickness. In this case, a = 10 nm is used.

The calculated activation energy and the density of trap states based on the linear and linear/drift model are shown in Figs. 4(b) and 4(c), respectively. For the activation energies in the sub-threshold regime, the linear model gives smaller values than the linear/drift model. In addition, there are some points where the slope is unnaturally changed in the linear model case. This difference in activation energy translates to a more significant change in the density of trap states. Contrary to the continuous curve of the linear/drift model calculation, the linear model results in a hump, which is an artifact. Such features may convey the impression that there is a local peak in the density of states, leading possibly to erroneous interpretations of charge transport data. There is a significant difference in the magnitude of the density of states calculated by the two methods for a wide range of energies. We note that previous work on sub-threshold behavior in TFTs did not include the calculation of the density of trap states. We believe that the approach we have demonstrated is very suitable for use in analyzing TFT data for a number of disordered semiconductors.

In summary, we have demonstrated a method of calculating the density of trap states in a disordered semiconductor thin-film transistor. Our approach combines sub-threshold drift-limited region operation and above threshold operation to yield an accurate, artifact-free density of states profile. The density of states profile is extracted from the mobility versus gate voltage characteristic that extends from the above threshold region into the sub-threshold drift region. We illustrated the method by analyzing data from PDPP-TVT TFT. Such methods of analysis are inherently better suited for disordered and polycrystalline semiconductor based TFTs and can also be used for single crystal TFTs.

This work was based upon work supported primarily by the National Science Foundation Nanosystems Engineering Research Center on Nanomanufacturing Systems for Mobile Computing and Mobile Energy Technologies (NASCENT) - NSF EEC Grant No. 1160494 and by the ECCS Division of the National Science Foundation under grant ECCS-1407932. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. This work is also supported by the Research Grant of Kwangwoon University. The chemical synthesis work was carried out at IMRE, Singapore which was supported by A*STAR.