Self‐Assembly of Organic Semiconductors on Strained Graphene under Strain‐Induced Pseudo‐Electric Fields

Abstract Graphene is used as a growth template for van der Waals epitaxy of organic semiconductor (OSC) thin films. During the synthesis and transfer of chemical‐vapor‐deposited graphene on a target substrate, local inhomogeneities in the graphene—in particular, a nonuniform strain field in the graphene template—can easily form, causing poor morphology and crystallinity of the OSC thin films. Moreover, a strain field in graphene introduces a pseudo‐electric field in the graphene. Here, the study investigates how the strain and strain‐induced pseudo‐electric field of a graphene template affect the self‐assembly of π‐conjugated organic molecules on it. Periodically strained graphene templates are fabricated by transferring graphene onto an array of nanospheres and then analyzed the growth and nucleation behavior of C60 thin films on the strained graphene templates. Both experiments and a numerical simulation demonstrated that strained graphene reduced the desorption energy between the graphene and the C60 molecules and thereby suppressed both nucleation and growth of the C60. A mechanism is proposed in which the strain‐induced pseudo‐electric field in graphene modulates the binding energy of organic molecules on the graphene.

by mixing 1 mL of 5 × 10 −3 M PEI in ethanol and 50 mL of DI water. [3]Finally, the doped graphene film was transferred to an NS array.

C60 deposition.
C60 was deposited using the same methodology as previously employed. [4]Organic molecular beam deposition (OMBD) was used to deposit C60 (Aldrich Chemicals, 99.99% purity) in ultra-high vacuum (UHV, 10 -8 Torr).The substrate temperature was kept at room temperature, and the deposition rate was 0.1Å/s.

Calculation of Diffusion Equation
The following diffusion equation is calculated by Finite-Difference-Method using MATLAB: where   60 is surface concentration of C60 ad-molecules,  ⃗ is the diffusion flux of C60 molecules, (, ) is diffusivity,  C 60 (, ) is the lifetime of C60 ad-molecules, and  is the deposition rate. was assumed to be constant,  = 1.185 × 10 −8 / 2 •  which is equivalent to 0.1Å/s.where  avg is the average diffusion coefficient over the whole space and  amp is the amplitude.(Figure S3b).Because of blunt tips, the curvature of NS and G/NS-array obtained from AFM might be different from the real cases, especially when  is small.As  becomes larger than 39 nm,   of G/NS-array surface started to be larger than the radius of curvature of the bare NS surface (Figure S3c).From this information, we concluded that graphene had conformal contact with NS when  ≤ 39 nm.Compared with Figure S3a,  = 39 nm corresponds to sin.The areal fraction of graphene conformally contact with NS (  ) is equal to the ratio of 3 ×  initial to the area of a hexagonal unit cell (   ) shown in Figure S3a, that is,   = (3 ×  initial )/ unit cell ).The areal fraction of graphene conformally contact with NS is 0.096 and corresponding polar angle  is 18.8°.
The area of deformed graphene on a NS is  contact = 2 2 (1 − cos) and the initial area of the same region before the deformation is  initial =  2 sin 2 .Here, we assumed that initial graphene before deformation is perfectly flat.This is a highly plausible assumption because very stiff and thus flat PMMA/graphene layer first covers the NS-array, then the deformation of graphene begins with the removal of PMMA layer.So, the applied biaxial strain in graphene can be calculated using the equation, The strain in graphene is determined by the competition between the strain energy from the deformation of graphene and the adhesion energy of graphene contact with NS; The increase in energy due to the tensile strain in graphene is compensated by the decrease in energy due to the adhesion energy between graphene and SiO2 surface. [5]The sum of strain energy and van der Waals interaction energy of graphene per one nanosphere is approximately given as, where  2 = 340 / is Young's modulus of graphene, [6] and  ̃vdW the interaction energy between graphene and SiO2, which is reported to be 0.45 J/m 2 . [7]At equilibrium,  =   is the polar angle that minimizes ().
Figure S3d shows () as a function of .As a result, the minimum is at   = 19.6°.At the equilibrium, the strain at the apex region is calculated to be 2.98% according to Eq. S5, and the calculated   is 0.102.Lastly, the average biaxial strain of whole area of graphene, which corresponds to the strain in graphene measured by Raman spectroscopy, is calculated to be    = 0.30%.The calculated   ,   and average strain are all numerically consistent with the experimental values (18.8°, 0.096, 0.30%, respectively).Though the model to describe the strain in graphene on NS-array is oversimplified, the numerical agreements of the simple analytical model with the experimental values strongly implies that biaxial strain around 3% is indeed present at the apex region of G/NS-array.To verify our observation that C60 nucleation was nearly absent at the apex regions of the G/NS-array, we used contact-mode AFM to scan the upper half of an apex region. [8]Normal force of 5nN was applied to prevent any damage to the graphene with conventional tip cantilever (CDT-CONTR, force constant 0.5 N/m).If a C60 thin film was present, a corresponding step height would be observed in the height image of the apex region after the scanning process.Figure S7 shows height images of graphene at the apex region before and after the scanning; no step height was observed.The observation that C60 readily nucleates at the apexes of bare NS-array also excludes the effects of wetting transparency and surface morphology of graphene on the self-assembly of C60 molecules.Therefore, we conclude that the strain-induced pseudo-electric fields are responsible for the specific nucleation and growth of C60 on the free-standing regions.In contrast to the C60/graphene system, the pentacene/graphene system does not exhibit charge transfer upon adsorption because the lowest unoccupied molecular orbital (LUMO) level of pentacene is considerably higher than the EF of graphene by 1.2-1.3eV. [9]Because of the large energy gap between the LUMO level of pentacene and the EF of graphene, charge transfer between pentacene and graphene is expected to be absent, even when graphene is subjected to a moderate tensile strain (a few %).
As shown in Figure S13a, no preferential nucleation or growth of C60 was observed in the free-standing regions of the G/NS-array.Therefore,  apex/rest was estimated to be 1.47, indicating the absence of discernible nucleation or growth of C60 in the apex regions, as compared with the free-standing regions.Therefore, the binding energy of pentacene on a graphene/NS-array should be independent of the strain field in the graphene. [10]hat of C60, is expected upon the adsorption of NTCDA molecules.In contrast to pentacene, preferential nucleation and growth were observed in the freestanding regions. apex/rest was 0.09.

Supplementary Discussion 1
Additional effects of charge transfer between C60 and graphene on the nucleation behaviors of C60 thin films.
The charge transfer between C60 and graphene causes strong molecule-substrate attraction, which means the reduction of interfacial free energy of C60 thin film/graphene.It leads to  des =  ̅ vdW ( bi ) +  ̅ C ( 0 ,  bi ). (Eq.S8) The fitting parameter  = 0.25 was introduced to account for the reduction in  ̅ vdW due to the out-of-plane thermal vibration of the graphene surface.In this simplified model,  ̅ vdW was assumed to depend only on  bi .The estimation of  ̅ vdW ( bi ) = 1.1368 − 3.155  was derived from our DFT calculation results (Figure S12) and  ̅ C ( 0 ,  bi ) was calculated using Eq. 5 in the main manuscript.
The effect of the Coulombic interaction on the desorption energy (or binding energy) of C60 on graphene ( ̅ C / des , Figure S17) was estimated using Eq.S8.This calculation was performed under conditions in which the graphene was subjected to tensile strains of 0 and 3.1%.Consequently, the Coulombic interaction at a hole concentration of 2.5 × 10 12 cm −2 in graphene ( 0 =-2.5 × 10 12 cm −2 ) contributed 53 and 0.79% to the desorption energy for the 0 and 3.1% tensile strain conditions, respectively.It is important to note that the quantitative accuracy of our model is not guaranteed as it does not adhere to first-principles theory.

Figure S2 .
Figure S2.a) AFM phase images of G/NS-array before and after annealing in hydrogen atmosphere.b) RMS roughnesses Rq of height (left) and phase (right), and c) XPS C1s peaks before and after annealing in hydrogen atmosphere.

Figure S3 .
Figure S3.Schematic diagram and AFM data of topographic information on G/NS-array.a) Top and side view unit-cell of G/NS-array y. b) Overlap of cross-section image obtained from AFM height profile.c) The average radius of curvature of NS (white) and G/NS-array (green).d) Total energy of G/NS-array system per one nanosphere as a function of .

Figure S5 .
Figure S5.a) AFM height images (upper) and phase images (lower) of G/NS-array samples after C60 deposition for 40s.b) The fraction of the area of C60 islands at the apex regions in G/NS-array templates to the total area of C60 islands in G/NS-array samples.

Figure S6 .
Figure S6.AFM a) height and b) phase image of a 0.39 ML C60 thin film deposited on G/Flat SiO2.

Figure S7 .
Figure S7.AFM height images of an apex region of G/NS-array a) before and b) after contact-mode AFM process.Overlap cross-section before and after AFM scanning shows no difference of height profile.

Figure S9 .
Figure S9.Areal fraction of C60 islands at the apex regions in G/NS-array templates with a NS diameter of 200nm to the total area of C60 islands at the apex (orange), wrinkles (blue), and free-standing (red) regions in the G/NS-array as a function of the deposition time.

Figure S10 .
Figure S10.a) Raman single spectrum of G/Flat SiO2 with various doping levels.Red line (PEI) and blue line (TFSA) samples were doped using the underside doping method.b) Transfer characteristics of field-effect transistors fabricated with doped graphene.The transfer curves of TFSA-and PEI-contact samples were blue-and red-shifted, respectively, as compared to that of the pristine graphene device.The SiO2 thickness was 300 nm and the drain-source voltage was 0.01 V.The channel length and width were 40 and 1100 μm, respectively.

Figure S12 .
Figure S12.DFT simulation of the C60 adsorption energy on a graphene surface.a) Side and top views of the C60/graphene unit-cell used for the DFT simulation.b) Adsorption energy of C60 (Eads) as a function of the strain on perfectly flat graphene (black square) and curved graphene (red triangle).The radius of curvature was 100 nm.

Figure S14 .
Figure S14.Probability of electron transfer from unstrained graphene to a C60 ad-molecule.

Figure S16 .
Figure S16.a) Finite difference method (FDM)-modeled diffusivity of C60 on a G/NS-array with a diameter of 200 nm and b) calculated nC60(x,y) after 100 ns.

Table S1 .
DFT calculation of Eads (eV) as a function of the strain (%) and radius of curvature of graphene.The radius of curvature of 100 nm corresponds to that of 200 nm-diameter nanospheres.The radius of curvature of 37.8 and -86 nm correspond to curvatures of 0.026 and 0.01 nm -1 , respectively.(*: + andsigns indicate convex and concave, respectively).