Source: https://pubs.rsc.org/-/content/articlehtml/2018/mh/c7mh00489c
Timestamp: 2019-04-24 17:47:18+00:00

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Organic semiconductors are intensively studied as promising materials for the realisation of low-cost flexible electronic devices. The flexibility requirement implies either performance stability towards deformation, or conversely, detectable response to the deformation itself. The knowledge of the electromechanical response of organic semiconductors to external stresses is therefore not only interesting from a fundamental point of view, but also necessary for the development of real world applications. To this end, in this work we predict and measure the variation of charge carrier mobility in rubrene single crystals as a function of mechanical strain, applied selectively along the crystal axes. We find that strain induces simultaneous mobility changes along all three axes, and that in some cases the response is higher along directions orthogonal to the mechanical deformation. These variations cannot be explained by the modulation of intermolecular distances, but only by a more complex molecular reorganisation, which is particularly enhanced, in terms of response, by π-stacking and herringbone stacking. This microscopic knowledge of the relation between structural and mobility variations is essential for the interpretation of electromechanical measurements for crystalline organic semiconductors, and for the rational design of electronic devices.
The common interpretation of the electrical response of organic semiconductor crystals to mechanical stress relies on the assumptions that (i) deformation affects charge mobility mostly along the strained direction, and (ii) compressive strain increases mobility via a reduction of intermolecular distances and the associated increase of electronic overlap, with tensile stress producing the opposite effect. Herein we demonstrate how this interpretation is oversimplified, by means of multiscale modelling predictions and experimental measurements. For the latter, an original configuration is adopted, where a single crystal field effect transistor is assembled on top of a flexible polymeric cantilever. In particular, our simulations reveal that uniaxial strain conditions can give rise to unusual responses, namely mobility hardly changing or even decreasing while compressing. Moreover, both calculations and experiments show that the electro-mechanical responses along the directions exhibiting higher mobility and closer packing are strongly coupled: if strain is applied along one axis, mobility strongly varies also along the other axis. This neat fundamental understanding of the influence of crystal deformation on electrical characteristics widens the design range of organic electromechanical systems, by suggesting configurations in which mechanical deformation and electrical response are applied or measured in orthogonal directions.
Fig. 1 (a) Crystal lattice orientation of rubrene according to Witte's notation.11 (b) Graphical representation of |ra| (left) and |rb| (right) intermolecular distances, sketched as arrows. (c) Scheme showing an example of the two conditions applied during molecular dynamics simulations: uniaxial strain (ε) and uniaxial stress (σ). Arrows indicate compression or expansion. (d) Calculated intermolecular distances between first neighbours along the two in-plane crystalline directions |ra| and |rb| in the case of uniaxial strain (top panels) and uniaxial stress (bottom panels).
Indeed, the complexity of the problem suggests that, for the time being, only punctual studies on a given material can provide the desired structure (strain)–property (mobility) relationship. Here, we describe such an attempt for rubrene, where we couple modern computational techniques28,31 to a novel experimental setup. Since previous experimental studies on pentacene demonstrated that not only the variation of cell parameters but also grain morphology can affect the response to strain,32,33 we focus on single crystal34 devices and simulations as a way to eliminate the latter effect. A multiscale simulation protocol is used to predict both the mechanical properties of rubrene from stress–strain curves and the corresponding variations of charge carrier mobility. Theoretical results are compared to experimental values obtained using field effect transistors (FETs) produced by lamination of single crystals on top of a cantilever beam35–37 (cantiFETs), and recording their electrical response to strain in real time.
The values in line with bulk and Young moduli reported for crystalline oligoacenes.19,38 From the matrix elements of C, the reduced elastic coefficients for in-plane stress ii = Cii − Cic2/Ccc (with i = a, b) and their anisotropy ratio were also calculated and compared with recent measurements and calculations.39,40 The values reported in Table 1 show a broad agreement with published theoretical and experimental values, substantiating the reliability of the predictions made through our computational protocol. We note that our calculations, as well as the ones in ref. 39 and the measurements in ref. 40, indicate two negative Poisson's ratios (νca and νac, see the ESI†).
The uniaxial strain condition represents the limiting case of a crystal laterally confined, clamped, or any other experimental setup preventing a molecular rearrangement along the cell vectors normal to strain. In a second series of simulations, we investigated instead the other limiting case, that of uniaxial stress, ideally corresponding to a rubrene crystal free to respond to applied stress with a lateral deformation according to its Poisson ratio elements (reported in Table S3, ESI†). Fig. 1 compares the variation of the in-plane intermolecular distances (|ra|, |rb|) under conditions of uniaxial strain or uniaxial stress. The linear variations of all plotted quantities confirm that the chosen interval of ±0.4% strain is located within the elastic regime. The main difference upon comparing the two series of simulations is the variation of the components of the intermolecular distances orthogonal to the strain direction. While in the case of uniaxial strain such terms show little to no dependence on strain, for uniaxial stress – especially along the a and b directions – the stress along one axis affects all intermolecular distances. Conversely the variation of |rc| is quite modest in the considered interval when stress is applied along a or b in line with the low magnitude of the corresponding stiffness matrix components C13 and C23 (for further details, see Fig. S3–S5, ESI†).
Fig. 2 Relative mobility variations Δμi as a function of strain, calculated along the i = a (a and b panels) and b (c and d panels) crystal axes. The dashed and full lines refer to the two different models for charge transport considered (q = 1 for band-like transport and q = 2 for hopping, respectively). Insets: Variation of intermolecular distances |ra| and |rb| between dimers along the same direction of the calculated mobility variation, as a function of strain. Error bars were estimated as the difference between the mobility parallel to the cell vectors and with a misalignment of 5° and are negligible for plots (a) and (b). Relative mobilities calculated along the out-of-plane direction c are reported in Fig. S7 and S8 (ESI†).
Uniaxial strain and uniaxial stress conditions result in striking differences, albeit in both cases the response is linear in the considered strain interval, and antisymmetric for tensile or compressive strains. Let us first consider the relative variation of mobility measured along the higher mobility axis, a, arising from the strain along the same axis. For uniaxial strain and uniaxial stress conditions, two opposite trends are observed (Fig. 2a). When uniaxial strain is applied along a, Δμa decreases by about 5% for a tensile strain of 0.4%. This trend alone can be easily rationalized by taking into account the change in the intermolecular distances ra and rb, since the electronic coupling (here Ja) is known to decrease exponentially with the increase of the intermolecular distance.27,53 Unexpectedly, when uniaxial stress conditions are applied (orange circles in Fig. 2a), Δμa is found to increase slightly with tension, yielding a positive mij coefficient which cannot be related to the changes in the intermolecular distances along a, as their average values along this direction are unchanged with respect to the uniaxial strain case (see Fig. 1c). The trend is not repeated when the strain is applied along b (Fig. 2b): in this case the two deformations have a very similar effect on Δμa, with the expected decreasing profile at increasing strain (positive values of mij). As for the mobility probed along the second in-plane direction b, for deformations along a and b, (Δμb in Fig. 2c and d) it follows qualitatively the same trend of the mobility along a.
For our system, we ruled out a major role of the fluctuations in intermolecular distances (recently suggested for explaining the increase of charge carrier mobility of a naphthobenzodithiophene upon compressive strain17) since the standard deviations of |ra|, |rb| and |rc| vary less than 1% in the considered strain interval (Fig. S2, ESI†). To fully understand the effect of the intermolecular fluctuations on the modulation of the transfer integral, it is useful to verify the values of the parameter ηi = Ji/si in the absence of strain, where si is the standard deviation of the Ji distribution, and as usual i = a, b, c. The smaller the value of η, the higher the impact of lattice dynamics on the transfer integral values.54–56 The three rubrene nearest neighbours are characterized by three distinct values of η: from our calculations they are 3.4, 2.0 and 1.6 for dimers along a, b and c respectively. All of them are large enough to indicate a weak or negligible dependence of the mobility on the amplitude of intermolecular vibrations, hence it is not expected that a strain-induced variation of si could significantly affect mobility values. In addition, we verified that imposing strain on the rubrene crystal does not modify this picture, since η changes very little upon strain (see Table S4, ESI†). As highlighted in Fig. 3, the variation of the average values of Ji actually originates from a shift of the whole distribution rather than a broadening (see also Fig. S7 and S8 and standard deviation and skewness values in Table S4, ESI†).
Fig. 3 Distributions of the absolute values of the instantaneous transfer integrals |Jta| and |Jtb| as a function of strain εii applied along the corresponding crystal axis: +0.4% (blue line), 0% (black line) and −0.4% (red line). (a) Uniaxial strain; (b) uniaxial stress conditions. Transfer integrals calculated along the out-of-plane direction c are reported in Fig. S7 (ESI†).
To further investigate the electromechanical response of rubrene, single crystals under mechanical strain were electrically characterized, in a transistor configuration, and the relative variations of drain-current with strain were compared to the calculated mobility changes discussed above. Different approaches exist to characterize the electrical properties of single crystals under stress and strain. The most common one uses flexible arrays of transistors, although new setups have recently appeared in the literature. For instance, Wu et al.23 measured the variations of rubrene work function by Kelvin probe force microscopy (KPFM) under different tensile strain by using thermal expansion of PDMS and silicon substrates. Here we apply a new method based on an Organic Field Effect Transistor (OFET) embedded in a suspended organic micro-cantilever, henceforth called cantiFETs, first described by Rao et al.35 and improved recently by Thuau et al., who fabricated highly sensitive electro-mechanical transducers using piezoelectrically-gated OFETs.37 In the present work, single crystal rubrene FETs are integrated in organic MEMS plastic cantilevers. By bending the flexible cantilever, controlled and uniform strains can be applied to the embedded transistors, thus enabling the accurate evaluation of the electromechanical properties of organic semiconductors (Fig. 4). The triangular shape is chosen to induce a uniform longitudinal stress in the crystal when a force is applied at the free-end of the cantilever.57 The rubrene crystal is positioned near the clamping region of the cantilever, in order to minimize bending-induced strain along the cantilever width direction (Fig. S10, ESI†). Then the applied force at the cantilever free-end induces uniaxial tensile strain in rubrene crystals along the cantilever length direction since in the width direction it is almost clamped. As a consequence, the intermolecular distance along a specific axis on rubrene single crystals is changed in a controllable fashion, as schematized in Fig. 4a. While monitoring the drain current of the transistor for different applied strain values, the electromechanical response of rubrene is characterized accurately and reversibly (Fig. 4d).
Fig. 4 Field effect transistors (FET) produced by lamination of single crystals on top of a cantilever beam (cantiFET), (a) 3D representation of a cantiFET. The top scheme represents the cantilever at rest, while at the bottom the cantilever is bent, inducing a uniaxial tensile strain along the b-axis of the crystal. (b) Architecture of the cantiFETs: a plastic substrate made of polyethylene naphthalate (PEN) is used as a support layer of the suspended cantilever. The integrated OFETs consist of an aluminum (AL) bottom gate electrode, a polystyrene (PS) gate dielectric, and gold (Au) source/drain top electrodes. (c) Typical forward and reverse transfer curve of a rubrene cantiFET at Vds = −50 V along the a-axis, recorded in the absence of strain. (d) Real time measurement of drain current along the b-axis in a device subjected to different tensile strains applied along the b-axis at Vds and Vgs equal to −50 V, showing the reversible behaviour of the cantiFET response.
In practice, different mechanical and electrical configurations were tested experimentally, as shown in Fig. 5. Fig. 5 shows the results obtained for each device configuration: for all setups, the drain current, directly proportional to the mobility (see the ESI† for details), decreases when increasing tensile strain, as predicted by simulations in uniaxial strain conditions (cf.Fig. 2 and Table 2). The experimental results on the one hand validate the trends obtained by molecular dynamic simulations and, on the other hand, demonstrate the impact of strain on the mobility of rubrene using an original approach based on OFET-embedded MEMS configurations.
Fig. 5 Experimental relative variation of mobility as a function of strain magnitude and direction of application and measurement. Mobility variations were obtained assuming proportionality with drain current values in the saturation regime (see the ESI† for details). The inset pictures schematize the different setups: (a) strain applied along the a-axis and drain current measured along the same axis; (b) strain applied along b and current measured along a; (c) strain applied along a and current measured along b; (d) strain applied along b and current measured along b. Horizontal error bars represent the standard deviation on the determination of strain from the deflection profiles, while vertical error bars correspond to the standard deviation of the current calculated over three repeated measurement cycles.
Controlled uniaxial tensile strain is applied to rubrene single crystals, simultaneously measuring the induced variation of current, using an original setup based on an organic field effect transistor embedded in a suspended polymeric micro-cantilever37 (Fig. 4a and b). Considering its reduced cost and ease of fabrication, this setup represents an excellent mechanical platform to characterise accurately the electrical properties of organic materials. Contrary to previous reports of an elastic-to-plastic transition occurring via thermal expansion on a poly(dimethylsiloxane) substrate at a strain of 0.05%,29 the registered response is elastic and reversible in the strain range considered (up to 0.18%, Fig. 4d). Quantitatively, the relative variation of current is negative, coherent with recent experiments exploiting wrinkling instabilities,15 and more pronounced when measured along the b-axis (Fig. 5b and d) than along the a-axis (the direction of higher mobility) (Fig. 5a and c). Interestingly, the effect is qualitatively independent of the direction of the application of the strain, revealing a strong coupling between the two in-plane directions of rubrene crystals and a microscopic mechanism more elaborate than the mere reduction of the electronic couplings caused by the increase of the intermolecular distances along the direction of application of strain. Rubrene crystals then appear to be more sensitive to strain when compared to TIPS-pentacene58 or alkylthiophenes,17 as suggested by their higher electromechanical sensitivity and stiffness.
The variation of charge carrier mobility as a function of compressive and tensile strain is predicted by calculations combining molecular dynamics, quantum chemistry, and charge diffusion models. The computational results are validated through the comparison of the stiffness tensor with previously published experimental and theoretical data39,40 (Table 1), notably indicating negative Poisson's ratios when stress and strain couple the a and c (out-of plane) crystal axes. The relative mobility changes under uniaxial strain conditions, calculated assuming incoherent transport (Fig. 2, blue lines, q = 2) match semi-quantitatively with measurements, with larger electromechanical sensitivities when strain is applied along the b-axis (∼20) with respect to the a-axis (∼10), independent of the direction of the measurement of the current (see Table 2). Taking into consideration the possibility of coherent transport (dotted lines in Fig. 2) yields as expected a reduced response to strain, that does not alter the qualitative picture and still captures the correct order of magnitude of the experimental mobility variations.
The calculations extend the scope of the OFET experiments by considering also the conditions of uniaxial stress, corresponding to an ideal case in which the two dimensions of the crystal perpendicular to the applied stress direction are let free to adapt so as to minimize lateral stresses according to the corresponding Poisson's ratios (Fig. 1c). While the predicted change in mobility is very similar for uniaxial stress and uniaxial strain applied along b (Fig. 2c and d), quite surprisingly the response changes in sign for uniaxial stress along a, i.e. the mobility increases for tensile strains and decreases for compressive strains (Fig. 2a and c), despite intermolecular distances behaving oppositely. This result underlines the importance of considering the exact mechanical setup in interpretation of electro-mechanical experiments, because (i) the effect of mechanical deformation might not always be readily translated into a predictable mobility change, and (ii) the actual conditions of the experiment, such as the substrate mechanical properties, adhesive behaviour, or clamping, might strongly affect the magnitude and sign of the electrical response of the device.
Concerning the microscopic nature of the electrical response, for rubrene it originates from the shift of the whole electronic coupling distribution upon strain (Fig. 3), and not from a change in their standard deviation caused by the suppression or enhancement of intermolecular vibrations as recently put forward for explaining strain-mobility trends for a benzodithiophene derivative.17 Despite the strong dependence of the electronic coupling on the intermolecular distances, their variation alone is sufficient to rationalize the electric response only for uniaxial strain conditions, and not for uniaxial stress ones. In the latter case, although the unambiguous variation of mobility is clearly generated by the rearrangement of the molecules upon strain, it appears to be the complex result of tiny yet collective variations of several inter/intra-molecular parameters that influence the electronic couplings and ultimately, the measured current.
In summary, a systematic study of the electromechanical response of rubrene crystals under strain has been carried out. The results show a considerable agreement between the mobilities calculated under uniaxial strain conditions, and the measured current changes in the cantiFETs upon controlled strain. The anisotropy of the rubrene crystal structure translates into an anisotropy in its strain response, and remarkably the strain applied along b has a major impact on mobility along the direction of fastest charge transport a, and vice versa, with larger effects when the mobility is measured along b. This investigation brings new fundamental understanding on the nature of rubrene electrical response upon device deformation, helping the realization of more efficient devices, and stimulating future investigations for a wide range of crystalline and amorphous organic semiconductors.
where the sum runs over the three types of neighbours with intermolecular distance vector , is a cell axis unit vector, and μ0 is a constant, and q is an exponent that depends on the charge transport mechanism.
We considered two neighbours along a, four along b, and four along c. The second type of neighbours along c,43 was not considered throughout this study. The squared electronic coupling in eqn (1) is consistent both with a Marcus-like localized hopping regime and with a partially delocalized picture, more appropriate for the intralayer transport in the ab plane.52 The relative changes in mobility were calculated using eqn (1)l along i = a, b, c and strains applied along j = a, b, c with respect to the same quantity at εjj = 0. The exponent q was set equal to 1 and 2, so as to encompass the expected behaviour of several transport mechanisms, and to let the reader easily guess the trends for other similar values of q which may appear in the different flavours of charge transport equations.46 Instantaneous transfer integrals Jt were also calculated for all dimers every 300 ps, and used to compute distributions as a function of strain (Fig. 3 and Fig. S7, S8, and averages |Jti| in Table S5, ESI†).
Rubrene crystals were grown using a physical vapour transport process. Commercial rubrene (Sigma-Aldrich) was placed inside a copper furnace as source material for crystal growth. Then, oxygen was removed from the furnace by means of Argon purge. The as-received rubrene was purified two times through physical vapour transport with an Argon flow of 30 ml min−1 and a heating temperature of 320 °C. Crystals were grown for several days before being collected and placed again in the same furnace, cleaned with isopropanol. In the third step, crystals were grown inside a glass furnace with an Argon flow of 15 ml min−1 and a heating temperature of 320 °C. The growth time was between 20 and 40 min in total, starting from room temperature. Crystals were collected and laminated manually on the cantilever using Microtools tips from MiTeGen, controlling the orientation of the crystal axes with respect to the electrodes. Only ultra-thin rubrene crystals with a thickness below 1 μm were used, since thicker crystals would otherwise delaminate from the substrate upon bending, owing to their higher rigidity.
Polyethylene naphthalate (PEN) square substrates of 2.25 cm2 and 50 μm-thick were patterned by xurography and cleaned in successive ultrasonic baths for 5 min each time (soaped water, deionized water, acetone, ethanol, isopropanol and deionized water). Then PEN substrates were thermally annealed at 180 °C for 2 hours. This curing allows the release of oligomers present on formation of the plastic surfaces. Aluminium was evaporated on PEN through shadow masks using an e-beam process so as to form the gate electrode (80 nm thick). Evaporation was performed under 1 × 10−6 mbar vacuum, with a deposition rate of 0.1 nm s−1. To spin coat the polystyrene (PS) gate dielectric layer, a solution was prepared by dissolving PS (280 000 g mol−1) into chlorobenzene at a concentration of 70 mg mL−1. The solution was stirred overnight before being filtered (PTFE 0.45 μm). 120 μL of PS was then spin coated (20 s at 500 rpm then 60 s at 2000 rpm) to obtain a 1.7 μm-thick gate dielectric layer. Right after the spin coating, each sample was annealed on a hot plate at 80 °C during 5 hours under vacuum. Then gold electrodes (60 nm thick) were deposited through shadow masks via thermal evaporation, with a deposition rate of 0.1 nm s−1 under 5 × 10−6 mbar vacuum, to pattern the source/drain electrodes. Finally, the triangular shape of the cantilevers was patterned by xurography. On top of this architecture, rubrene single crystals were laminated manually between gold electrodes, in order to control their orientation. The channel length L = 50 μm of the cantiFET coincides with the distance between the gold electrodes, while the width of the contact varies from crystal to crystal (120–750 μm).
The cantiFETs were first characterized electrically in the absence of strain. In particular, the transfer curves of the transistors were obtained by applying Vds = 50 V, with a typical example shown in Fig. 4c. The transistors showed hole mobilities in the range of 1.1 cm2 V−1 s−1, an ION/IOFF ratio of up to 106, and threshold voltages Vth ranging from 0 to −30 V. A vertical force was applied to the cantilever tip using a micromanipulator (MiBot from Imina Technologies SA, Fig. S11, ESI†). The deflection δ was obtained by measuring the position of the cantilever extremity from the video recording (Navitar camera). The corresponding strain on the top surface is then calculated as ε = hδ/Λ2, where h and Λ are respectively the thickness and the length of the cantilever.
As the applied strain was kept below 0.2% to ensure elastic deformation of the rubrene crystals, and in agreement with the theoretical predictions of variation of mobility of only a few percent, transfer curves did not show enough significant changes to accurately characterize the electromechanical behaviour of rubrene (cf. Fig. S12, ESI†). Instead of using the full transfer curve, we then monitored the real-time value of the drain current in the saturation regime, with Vgs and Vds equal to −50 V. Every ten seconds, a tensile strain was applied to the cantilevers, reaching a maximum value of 0.18% before the strain was released gradually (Fig. 4d). To account for the time drift of the drain current at each value of strain (see Fig. 4b), the baseline was corrected with a quadratic function.
This work in Bordeaux was funded by the French State grant ANR-10-LABX-0042-AMADEus managed by the French National Research Agency under the initiative of excellence IdEx Bordeaux program (reference ANR-10-IDEX-0003-02). We thank Dr Jérôme Cornil (UMons & FNRS, Belgium) for stimulating discussions.
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