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Analysis of Transient Currents in Organic Field Effect Transistor: The Time-of-Flight Method Martin Weis,† Jack Lin, Dai Taguchi, Takaaki Manaka, and Mitsumasa Iwamoto* Department of Physical Electronics, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan ReceiVed: August 31, 2009; ReVised Manuscript ReceiVed: September 23, 2009
The transient current generated from an organic field effect transistor (OFET) is analyzed, and the modified time-of-flight (TOF) method is employed for evaluating the carrier mobility of the pentacene OFET. Analysis shows that the displacement current rises up before carriers reach the drain, and the inflection points of the transient currents represent the transport time of carriers across the channel. TOF experiments performed on OFETs with various channel lengths L show an increase of the transit time in proportion to L2/(Vgs - Vth), suggesting that the interface charging propagation regulates the carrier transport. The obtained TOF mobility has good correspondence with the steady-state FET mobility. The study of the charge propagation through the OFET is one of the challenges of present applied physics.1 The reason dwells not in potential applications only but also in the deep understanding of the carrier behaviors in organic solids.2-5 In the past, the research was focused on the current-voltage (I-V) and capacitance-voltage (C-V) characteristics at various biassing and stress conditions. Already, some important observations were pointed out, (i) the presence of an accumulation layer on the organic semiconductor-gate insulator interface,6 (ii) major contribution of injected carriers to the current,7 and (iii) subsequent high contact resistance.6 The quality of the OFET device has been judged using the carrier mobility, evaluated mostly from the drain current in the steady state. However, understanding of the transient behavior of OFET is needed for potential high-frequency applications. This motivated us to develop a technique available for analyzing carrier behaviors in the transient state,8 and the idea of using modified time-of-flight (TOF) burgeoned.9 The setup was based on the detection of the transient current induced by excess charge injected from the source electrode and propagated through the channel to the drain electrode. Although the TOF technique has been already employed,9-11 the analysis of the TOF currents generated from OFET has been carried out simply based on the TOF analysis used for films sandwiched between two electrodes. Hence, in this letter, we return to the theoretical background of the TOF and apply developed analysis to the OFET experiment. Results help us to understand the physical meaning of the transit time ttr recorded by the TOF method. The transient currents in pentacene OFET are analyzed, and the interface charging propagation is confirmed. Furthermore, the contact resistance and the carrier mobility are evaluated. Let us first consider the origin of the transient currents. For times shorter than the transit time (t < ttr), before charges reach the opposite electrode, only the displacement current is recorded; for longer ones (t > ttr), the conductive current is observed. For * To whom correspondence should be addressed. † On leave from Slovak Academy of Sciences, Bratislava, Slovakia.
10.1021/jp908381b CCC: $40.75
simplicity, we assume the nondispersive transport process,13 but it can be extended to the dispersive transport case without losing the underlying physics.14 In the metal-insulator-metal (MIM) structure, the TOF current is mainly generated by carriers traveling at constant velocity under constant external electric field Eext ) V/d (d: film thickness). Thus, the delay time is directly tr ) d2/µV (µ: mobility). On the other hand, in the OFET device, an electric field formed by applied bias is not constant, owing to the three-electrode system. Hence, the carrier velocity in OFET changes at the transient state. The carrier transfer is regulated by the semiconductor-gate insulator interface charge propagation15 when carriers are continuously supplied from the source electrode. The transport time reflects the charge injection, accumulation, and transport processes represented by the charging time tch and transit time ttr. Here, the discrepancy in processes and delay times must be explained; (i) carrier injection is followed by charging of the source-gate electrode system, denoted as the charging time tch; (ii) at the same time, accumulated charge propagation happens along the channel, simultaneously charging the channel, and it is designated as transit time ttr. Note that although processes (i) and (ii) seem to be independent, they are connected to each other via the internal field. However, as a first approximation, we assume processes (i) and (ii) in series, that is, the total transport time ttp consists of charging time and transit time and is equal to the delay time between the pulse application and start of the conductive current flow. Before carriers reach the drain, the displacement current should be generated by a change of induced charge on the drain electrode. According to Green’s reciprocity theorem, for a single charge q being placed in the channel at a position jx, we describe induced charge on the drain electrode qD by using the local potential V(xj), defined as the potential established in the OFET in the absence of injected carriers (Laplace field), and it is given by qD ) -qV(xj)/V. In contrast to the MIM structure, here, the displacement current is strongly positionally dependent on V(xj). 2009 American Chemical Society
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J. Phys. Chem. C, Vol. 113, No. 43, 2009
Letters
Figure 1. Ideal transient current generated in the (a) MIM and (b) OFET structure, where it is assumed (b) without and (c) with charging of the channel.
In detail, the displacement of charge q along the OFET interface at a distance δx induces the drain charge δq16
δq ) -
q δx π(L - jx)
(1)
where L is the channel length. Hence, it is easy to expect that the displacement current depends on the carrier location jx and carrier velocity ∂xj/∂t. The generated current is not constant even when a single electron or hole travels at a constant speed, obviously different from the displacement current from the MIM structure. When carriers are continuously supplied from the source, the charge carrier density profile17 p ) p0[1 - x/(R(t)1/ 2)] develops along the semiconductor-gate insulator interface, as was already reported.17 Here, the constant R ) (2µV)1/2 describes the evolution with time. That is, the additional electric fieldgeneratedfromcarrierspropagatesalongthesemiconductor-gate insulator interface. Hence, the field in the channel is approximately given by E ) V/xj. As a result, the velocity has a nonconstant value Vofet ) (µV/2t)1/2. Therefore, using the abovementioned relations, we derive
ID )
∂qD poL √ttr /t 1 1 - √ttr /t )∂t 2ttr π( t /t - 1) 2 √ tr
(
)
(2)
It is interesting to point out that the first fraction in eq 2 has a meaning of steady-state current, that is, the average charge in the device transported in the transit time (q/ttr). This is identical to the displacement current of the MIM structure, I ) -(p0d/ ttr)(t/ttr) (constant carrier injection case t < ttr), which is shown in Figure 1 as line (a). The second fraction in eq 2 represents the effect of positional-dependent induced charge (see eq 1), and the third term illustrates the boundary condition of continuous charge injection. Note that in the MIM structure, the corresponding second term is unity, and the third term is t/ttr. The displacement current in three-electrode system of the OFET is time-dependent, and its time evolution is depicted in Figure 1 as line (b). Even though the electric field is dependent on the charge position in the channel (E ) V/xj), the observed effect is not due to the space-charge field generated by carriers.18 Here, it must be emphasized that the recorded TOF current represents
the sum of the displacement and conductive current. Omitting the displacement thus leads to the incorrect estimation of the transit time. In other words, the displacement current depicts the rising edge of the recorded TOF current. Hence, here still remains an estimation of the transit time in the experiment, where the steady-state current is still not established after charge carriers reach the drain electrode, possibly owing to the dispersive transport. Thus, the exponential-like relaxation process is expected, which corresponds with charging of the device. This behavior complicates extraction of the transport time from the recorded transit current, but it can be also included in the analysis (shown in Figure 1, line (c)). Considering the displacement current represented by eq 2, the current value always rises before carriers reach the drain electrode (t < ttr) and is zero when carriers have already reached the drain electrode (t > ttr). Additionally, we must note that the conductive current (for t > ttr) can be represented by the constant drain-source current (Ids) or by the approaching concave function in the case of the device charging. Hence, the inflection point of the recorded current represents the transport time. In other words, in contrast to the MIM structures where transit time is extracted by a cross section of the extrapolated polynomial-like transient current on the log-log scale,2,18 in the OFET, the inflection point represents the transport time. In the end, we must shortly mention the meaning of the transport time, which includes transit time as well as charging time. In detail, the charging time tch of the source-gate electrode system can be simply estimated as the time required for interface charging19
tch ) RcCg
(3)
by assuming the equivalent circuit model with the contact resistance Rc and gate insulator capacitance Cg. On the other hand, the transient time that we derived previously15 is given as
ttr )
L2 1 2 µ(Vgs - Vth)
(4)
where Vgs and Vth are gate-source and threshold voltages, respectively. Samples used in experiments were top-contact pentacene OFETs. Heavily doped Si wafers with a 100 nm thick thermal oxide (SiO2) insulating layer were used as the substrates. During the deposition of pentacene (100 nm in thickness), the pressure was kept at less than 10-4 Pa, and the deposition rate was fixed at 0.5 Å/s. Subsequently, gold electrodes (source and drain) of 100 nm thickness were deposited. The designed channel length/ width (L/W) were 40-100 µm/3 mm. The TOF experimental setup is shown in Figure 2. The gate and drain electrodes were grounded, and a square wave voltage from the function generator (WF1974) was applied on the source electrode. The transient current was measured by the voltage drop across the load resistance using the oscilloscope (Tektronix DPO2024). The load resistance (Rload ) 1 k Ω) was much smaller than the channel resistance; thus, the drain and gate had the same potential. For comparison, the prepared devices were measured by standard steady-state current-voltage analysis. All measurements were performed in a laboratory ambient atmosphere. Figure 2 illustrates a typical result on OFET for different channel lengths, where the zero time denotes the rising edge of the voltage pulse with an amplitude of V ) 20 V. It is obvious that the transient
Letters
Figure 2. Transient current through the OFET for various channel lengths; arrows illustrate positions of the transport times. The inset shows a schematic view of the experimental setup for the TOF technique.
J. Phys. Chem. C, Vol. 113, No. 43, 2009 18461 transport time with a nonzero value for zero channel length. This phenomenon is assigned to the charging time (i.e., accumulation of the charge below the source electrode) and estimated to be tch ) 2.4 µs; in accordance with eq 3, this corresponds to the contact resistance of Rc ) 160 kΩ. Additionally, the average mobility is evaluated from the slope (see eq 4) as µ ) 1.9 × 10-2 cm2/(V s). Even though this value is slightly higher than mobility from the steady-state measurement, it was reported that the mobility estimated for the transient case is higher than that in the steady state of the device.20 The reason probably dwells in the space-charge field, which is created in the steady state only and suppresses carrier injection and transport. In conclusion, the transient current in organic devices was studied by the TOF method. In the OFET structure, the displacement current rises as charges approach the drain electrode. By analysis of these results, we obtained mobility comparable with FET mobility. This shows reasonability of the developed approach and suggests the TOF experiment for the OFET structures as a tool for study of transient carrier behavior. References and Notes
Figure 3. Transport time versus the square of the channel length. The solid line represents a linear fit. The inset illustrates the transient current for channel length L ) 80 µm, where the arrow depicts the location of the transport time.
current starts to flow after a certain delay time which depends on the channel length. The following saturation of the current corresponds to the steady-state current with a difference of less than 5%. The steady-state measurements also revealed the threshold voltage of 25 V and the FET mobility of 1.4 × 10-2 cm2/(V s). On the basis of the above-mentioned discussion, we analyzed recorded transient currents (Figure 2). The transport times were evaluated by the inflection points, whose positions are depicted in the graph by arrows. Figure 3 depicts the dependence on the channel length which can separate carrier transport and accumulation represented by the transit and charging times, respectively. There is a remarkable linear dependence of the
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