3D-printed graphene/polymer structures for electron-tunneling based devices

Designing 3D printed micro-architectures using electronic materials with well-understood electronic transport within such structures will potentially lead to accessible device fabrication for ‘on-demand’ applications. Here we show controlled nozzle-extrusion based 3D printing of a commercially available nano-composite of graphene/polylactic acid, enabling the fabrication of a tensile gauge functioning via the readjustment of the electron-tunneling barrier width between conductive graphene-centers. The electronic transport in the graphene/polymer 3D printed structure exhibited the Fowler Nordheim mechanism with a tunneling width of 0.79–0.95 nm and graphene centers having a carrier concentration of 2.66 × 1012/cm2. Furthermore, a mechanical strain that increases the electron-tunneling width between graphene nanostructures (~ 38 nm) by only 0.19 Ǻ reduces the electron flux by 1e/s/nm2 (from 18.51 to 19.51 e/s/nm2) through the polylactic acid junctions in the 3D-printed heterostructure. This corresponds to a sensitivity of 2.59 Ω/Ω%, which compares well with other tensile gauges. We envision that the proposed electron-tunneling model for conductive 3D-printed structures with thermal expansion and external strain will lead to an evolution in the design of next-generation of ‘on-demand’ printed electronic and electromechanical devices.


Results
shows the depth profiling of device 1 where the G-peak position spatial mapping and the spectra were obtained at different heights, and we observed: (a) the intensity of Raman signal from the photodetector reduces as we scan deeper into the composite (the focal plane it moved into the composite from the surface), www.nature.com/scientificreports/ and 2,692 ± 1 cm −1 ) bands, and (c) the arrangement of the graphene platelets is random (see supplementary information); however, its interface with PLA is consistent. The decrease in Raman signal intensity with depth ( Fig. 1) is attributed to the absorption of the scattered light by the material that the light passes through before reaching the objective lens. It is known that different amounts of polymer dopes graphene differently to change its Raman peak positions 22,23 . The Raman G-peak position (scale: 1,570 to 1585 cm −1 ) is maintained at different depths in the printed graphene/PLA structure, (even at 80 m deep) (Fig. 1); this implies that the relative concentration of graphene with respect to interfaced-PLA remains nominally unchanged. Further, since the composite is conductive (further explained in the next section), the graphene-network is percolating, implying that the microscale composition of graphene is also uniform. The Raman mapping also shows that the arrangement of graphene sheets at every depth-section is random with similar coverage of graphene ( Fig. 1 and supplementary figure). Importantly, the printing process does not modify the dispersion of graphene within the PLA matrix.
When the measurements were made at different depths, we confirmed that graphene exists at every depth. However, since graphene is a large nanomaterial (several microns in lateral size), its presence in a composite cannot be uniform in the micron scale. We found that its composition is uniform in the 50 × 50 micron 2 area-scale.
Using the Tuinstra and Koenig 24 relationship, the graphitic size of the samples were calculated using the I D / I G intensity ratio: where L a is the in-plane correlation length or cluster diameter, C ′ ( ) is the variable scaling coefficient, I(D), and I(G) are the intensity of D and G peak, respectively. C ′ ( ) ∼ 19.22 nm was calculated according to Cançadoa et al. 25 , I(D), and I(G) was obtained from the Raman graph (from the integration of the area under the curve), indicating that the ordered graphitic region with sp 2 hybridized carbon atoms in the graphene sheets is in the order of 37.75 ± 2.42 nm (L a ). In addition, using the relationship 26 : as h is the Planck's constant, Pos(G) is the position of the G peak (derived from the Lorentz fitting), Pos(G) 0 is the position of the G peak without doping, Ŵ is the dimensionless electron-phonon coupling for the LO phonons where v F is fermi level velocity (1.1 × 10 6 m/s), and n is the carrier concentration. Equations 2 and 3 were solved in Matlab using the values from the Raman spectra, obtaining the value of the carrier concentration average of 2.63*10 12 /cm 2 . This order of magnitude of doping is consistent with that of other graphenic composites. Equations 2 and 3 are derived for graphene with large number of sp 2 hybridization of carbon atoms (infinite sp 2 carbon lattice); however, the relatively sp 2 domain size of graphene in this study is ~ 37.75 nm (or ~ 54,000 sp 2 carbon atoms per domain). Therefore, the validity of these equations and the derived charge density is limited. The electron transport for the percolating network of the 3D printed structure of device 1 was studied using a cryo-probe-station under vacuum (0.75 mTorr), acquiring the current-voltage (I-V) data of device 1 at different temperatures. Figure 2 shows the I-V characteristic of the device measured at 75 K, 100 K, 125 K, 150 K, 175 K, and 200 K.
To obtain the overall transport thermal-barrier of the 3D printed devices for electron transfer between graphene platelets, we applied Arrhenius Law to fit the I-V data. This was done to determine the mechanism that most appropriately describes the electron transport (electron tunneling or thermal hopping) (shown in Supplementary v4Information) : where Ea is the thermal barrier height, k B is the Boltzmann constant, and T is the temperature (details of this calculation are shown in supplementary information). Using the I-V (Fig. 2a) data obtained at different temperatures under high vacuum (0.75 mTorr) and fitting the impedance with the Arrhenius equation (Fig. 2b) we found the thermal barrier height of 0.15 meV. This is smaller than k B T at room temperature (25 meV). Since thermal emission occurs with thermal barriers higher than k B T at room temperature, the mechanism of carrier transportation for this device is electron tunneling 37,38 . Electron-tunneling is a phenomena that occurs when the electron potential is below the barrier height and therefore, can occur at low-electrical fields (or low electron potentials) as shown by Nakatsuji et al. 39 , Takayanagi et. al. 40 , Wang et. al. 41 , and Nakatsuji et al. 42 .
In this work, the thermal expansion equation applied on the interparticle polymer layers governs the tunneling distance: where a 0 and a are the average tunneling distance at zero-Temperature and at any other temperature, and is the thermal expansion coefficient. 48 Combing with the FNET equation with Eq. 5, we get www.nature.com/scientificreports/ where m is the mass of an electron, t is the FNET constant, and is the tunneling barrier height. Since the electron must dissociate from graphene before tunneling into the next graphene platelet, the tunneling barrier is assumed to be graphene's work function: 4.85 eV. Fitting the data, as shown in Fig. 2c, the tunneling distance at absolute zero temperature was found to be 0.78 nm (calculation-details are provided in Supplementary Information). The strain was induced on device 2 (the channel length, width, and height are 8 mm, 0.8 mm, and 0.4 mm respectively, and the electrode dimensions are 2 × 3 × 6 mm 3 ) by a motion controller driver and the strain analysis of the 3D printed graphene/PLA structure was performed. Here, the device was fixed on a lever with the motioncontroller driver pushing on the graphene/PLA to generate strain, and two electrodes were connected to the edges of the devices, as shown in Fig. 3. The strain percentage was calculated via: where ε is the strain, l 0 is the length of the device at rest (with no strain applied), and h is the bending-distance after strain is applied. Details of this calculation and a figure to illustrate it is shown in the Supplementary Information.
The I-V measurements on the strained device were performed for different values of strain (Fig. 4). The electron-transport on this device also follows FNET, and it was combined with the strain equation to obtain:

Discussion
In conclusion, we demonstrate 3D printed structures of graphene/PLA, applicable as components of on-demand electronic devices. We show the operation of a tensile gauge functioning via the modification of electron-tunneling width between graphenic-centers. For the graphene/PLA system, the thermal barrier to electron transport was 150 µeV (much smaller than energy at room temperature), and the electron tunneling distance was 0.78 nm at cryo-temperature and 0.95 nm at room temperature. The mechanical strain that increases the electron-tunneling width between graphene nanostructures (~ 38 nm) by an average of 0.19 Angstrom reduces the electron flux from 18.51 to 19.51 e/s/nm 2 for the 3D-printed heterostructure. Our work shows that a 3D printable filament with a network of 2D nanomaterials (with low percolation threshold) within the polymer matrix can be building blocks for on-demand electronic devices.

Methods
In this report, we fabricated two different devices for investigating the effects of temperature (device 1) and mechanical strain (device 2) on the electrical conductivity of the 3D printed graphene/PLA nano-composite structures. The devices were designed in Autodesk Inventor and loaded to the CTC Bizer series Dual Nozzle 3D Printer (0.4 mm nozzle size, 1.75 mm filament size (GRPHN-PLA, Black Magic 3D), Printer setting: stagetemperature at 60 °C, and extruder temperature at 190 ̊ C) for device-fabrication. The schematic of the mechanism to 3D printed devices is shown in Fig. 5. The printing time for the graphene/PLA structure of device 1 was 9 min (18 min for the PLA support structure), the channel length, width, and height are 8 mm, 1 mm, and 0.4 mm respectively, and the electrode dimensions are 5 × 5 × 5 mm 3 . (Follow the same process for device 2). The structure and spatial distribution of graphene in the printed composite devices were characterized employing confocal Raman spectroscopy (WITEC Alpha-300-RA system with 532 nm incident laser and 100X objective lens). The Raman spectra of the devices also provided information on the doping levels of the graphene as well as the size of the ordered graphitic regions.