Bias-dependent Contact Resistance in Rubrene Single-Crystal Field-Effect Transistors

We report a systematic study of the bias-dependent contact resistance in rubrene single-crystal field-effect transistors with Ni, Co, Cu, Au, and Pt electrodes. We show that the reproducibility in the values of contact resistance strongly depends on the metal, ranging from a factor of two for Ni to more than three orders of magnitude for Au. Surprisingly, FETs with Ni, Co, and Cu contacts exhibits an unexpected reproducibility of the bias-dependent differential conductance of the contacts, once this has been normalized to the value measured at zero bias. This reproducibility may enable the study of microscopic carrier injection processes into organic semiconductors.

Improvements in the material control of organic thin films occurred during the past decade are enabling the reproducible, low-cost fabrication of organic field-effect transistors (FETs) with mobility values in the range 0.1 -1 cm 2 /Vs [1]. These values are sufficient for the development of new applications in the field of plastic electronics [2]. However, the fabrication of high-quality electrical contacts for organic transistors has not witnessed comparable progress [3], and low-quality contacts are now starting to pose limits to the performance of organic FETs. Specifically, with mobility values in between 0.1 and 1 cm 2 /Vs, the contact resistance -typically larger than 1 kOhm cm even in the best devices-limits the transistor performance as soon as the channel length becomes smaller than ≃ 10µm [4], preventing the possibility of device downscaling. The irreproducibility of the contact resistance makes the situation even worse: for gold-contacted pentacene thin-film FETs, for instance, the spread in contact resistance values was recently observed to exceed three orders of magnitude (from 2 kOhm cm to more than 1 MOhm cm) [5]. The current lack of understanding of the microscopic carrier injection [6] processes from a metal electrode into an organic semiconductor does not help us to determine the causes of the observed irreproducibility and more systematic experiments are needed to explore the performance of different metals as contact materials. Here we report systematic transport measurements of rubrene (C 42 H 28 ) single crystal FETs with electrodes made of five different metals (Ni, Co, Cu, Au, Pt). All the transistors have been fabricated with a sufficiently short channel length, so that the total device resistance is entirely dominated by the contacts. By studying more than 250 contact-dominated devices we have collected enough statistics to determine the average contact resistance, its spread in values, as well as its bias dependence. We find significant differences between the different metals. In particular, for Nickel -which exhibits the lowest resistance-the spread is only a factor of two, for Cobalt and Copper slightly more than one order of magnitude, * a.molinari@tnw.tudelft.nl and for Gold more than three orders of magnitude (Platinum seems to behave similarly to Gold, but the number of devices tested was not sufficient to make more quantitative statements). We also find that for Ni, Cu, and Co (but nor for Au and Pt) the bias dependence of the contact resistance normalized to the resistance measured at zero-bias exhibits an excellent reproducibility, and can be interpreted in terms of two back-to-back Schottky diodes connected in series. Our results suggest that organic single-crystal FETs with Ni, Co, and Cu contacts may be suitable for the investigation of the microscopic carrier injection processes at a metal/organic interface.
Some of the metals (i.e., Cu and Co) investigated here have not been used previously for the fabrication of organic FETs. In fact, the vast majority of past experiments have relied on noble metal electrodes, especially gold, whose choice is motivated by the high value of their work-function and by the stability against oxidation in air. These criteria, although plausible, have never been thoroughly investigated. Our recent and un-expected finding of record low contact resistance in devices with Nickel electrodes (100 Ωcm) [7] clearly underscores the importance to explore a broader class of materials.
The rubrene single crystal FETs are fabricated by lamination of thin (≈ 1µm thick), free-standing crystals grown by vapor phase transport, onto a highly doped Si substrate, covered by a 200 nm thick thermally grown SiO 2 layer with pre-defined metal electrodes (see Ref. [8]). The contacts are fabricated by means of electronbeam lithography, evaporation and lift-off and their geometry is chosen so that many FETs with channel length varying from 200 nm to 50 µm can be fabricated on the same crystal (see inset in Fig. 1). Our earlier studies have shown that the room-temperature carrier mobility in rubrene single-crystal FETs with SiO 2 gate dielectric is narrowly spread around 4 cm 2 /Vs [9], which allows us to estimate the maximum channel length L for which the channel resistance can be neglected with respect to the contact resistance. Specifically, for FETs with Nickel contacts (whose resistance is normally lower than 1 kOhm cm) we have confined our measurements to devices with L smaller than 2 µm. For devices with electrodes made of the other materials, where the contact resistance is higher, devices with channel lengths up to ≃ 20µm have also been used. With the channel resistance being negligible in all cases, the device resistance corresponds to the total contact resistance (i.e., to the sum of the source and drain resistances). Fig. 1 shows the I − V characteristics of a Cu-contacted FET with L = 5µm, measured [10] at different values of the gate voltage (much larger than the threshold voltage). The curves are essentially independent of the gate voltage and exhibit a very pronounced non-linear increase of the source-drain current at low bias. These I − V characteristics are markedly different from those of conventional transistors where the resistance is dominated by the channel, as illustrated in the inset of Fig. 1. A nonlinear and gate-voltage independent I−V curve similar to that shown in Fig. 1 has been observed in short-channel devices fabricated with all the different metal electrodes, and to analyze this behavior in more detail we look at the differential conductance dI/dV of the devices (obtained by numerical differentiation of the I − V curves; see Fig. 2a). In the differential conductance plots, the non-linearity present in the I −V characteristics produces a narrow peak around zero bias on a voltage scale comparable to kT /e, with the precise value being different for the different metals.
In order to compare the contact properties of FETs contacted with the five different metals we have carefully analyzed the reproducibility of the measured differential resistance. We find that the level of reproducibility depends on the specific metal used. The differential conductance measured on two different short-channel goldcontacted FETs is shown in Fig. 2b, which illustrates the poor reproducibility of these devices. In fact, for Au contacts (and similarly for Pt) the bias dependence of the differential conductance exhibits large differences in different samples and a zero-bias peak is observed only in a few devices. At the same time, the absolute value of the resistance measured at low bias is spread over three orders of magnitude (see Fig. 2c).
The situation is very different for Ni-, Co-, and Cu- contacted transistors. Fig. 3 and 4 show the differential conductance curves for many FETs with Nickel and Copper electrodes, normalized to the zero bias value. Re-markably, all curves fall nearly on top of each other, indicating a good reproducibility of the bias dependence of the contact resistance. The histograms shown in the insets of Fig. 3 and 4 quantify the reproducibility in the absolute (zero-bias) value of the contact resistance. For Nickel the absolute value of the contact resistance exhibit a good reproducibility: for the majority of devices dV /dI(V = 0) = 500 ± 250 Ωcm; for the few devices for which dV /dI(V = 0) > 1000 Ωcm the larger resistance is likely to originate from an imperfect lift-off process during the electrode fabrication, causing a poor adhesion of the crystal to the metal surface. For Copper -and similarly for Cobalt (data not shown)-, the spread in contact resistance is between one and two orders of magnitude (still considerably smaller than for Gold). This larger spread makes the reproducibility of the bias dependence in devices with Co and Cu contacts even more surprising.
Overall, it is a remarkable finding that materials such as Ni, Co, and Cu, whose surface oxidizes during fabrication, lead to an enhanced reproducibility. We now take a first step in interpreting the experimental data, by modeling our devices as two oppositely biased Schottky diodes connected in series (corresponding to the metal/organic and organic/metal interfaces at the source and drain contacts). The simplest expression for the current through a diode [11] reads: where n is the so-called ideality factor and I 0 is taken to be constant (i.e., independent of V ). The resulting I − V curve for two back-to-back diodes I − V curve then is: The continuous lines in Fig. 3 and 4 are plots of the differential conductance calculated by differentiating this equation, from which we see a qualitative agreement between the data and the back-to-back Schottky diode picture. The reproducibility of the data is sufficient to discriminate quantitatively between the behavior of Nickel, for which the width of the peak corresponds to an ideality factor of n ≃ 3, and for Copper, where n ≃ 1. The deviation at high bias -i.e., the fact that the measured differential conductance is higher than what is expectedoriginates from having assumed that I 0 is a constant, whereas in reality I 0 depends on bias. Within conventional models of metal/semiconductor interfaces the bias dependence of I 0 may originate from different microscopic phenomena, such as a bias-induced lowering of the Schottky barrier (i.e. the Schottky effect), diffusion limited transport, tunneling, etc. [11]. The reproducibility of the bias-dependent is therefore crucial to determine which of these microscopic phenomena dominates the behavior of charge injection at metal/organic interfaces.
In conclusion, we have investigated the contact resis- tance of organic transistors, with electrodes made of five different metals, including materials such as Cu and Co that had not been previously used. Our results show that Ni, Cu, and Co enable a superior reproducibility of the contact characteristics as compared to metals used in the past. This good reproducibility suggests the possibility to use FETs contacted with these metals for the study of microscopic processes of carrier injection into organic semiconductors. Financial support from FOM, NanoNed, and NWO (Vernieuwingsimpuls) is gratefully acknowledged.