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

## Abstract

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.

## Introduction

Graphene—a single-atom-thick sheet of carbon atoms arranged in a hexagonal honeycomb lattice1—has gained considerable attention due to its exceptional mechanical2, electrical3, and thermal properties4. Compounding on these properties, graphene’s chemical and physical stability has led to numerous applications, including nanoelectronics, biomedical applications such as biosensors, antibacterial, drug delivery, cell imaging, tissue engineering, and energy storage applications in batteries5,6. Graphene and its derivatives include graphene oxide (oxygenated graphene), graphane (hydrogenated graphene), and fluorographene (fluorinated graphene). Graphene oxide is one of the most widely studied chemical derivatives of graphene because of its water solubility and fast, scalable synthesis. A fast-evolving research-field is the 2D and 3D printing of nanomaterials, including graphene oxide and its composites. 3D printing, which became an important research area in the 1980s, can significantly improve fabrication of microelectronic devices and other constructs for various fields due to the ability of on-demand manufacturing, at reduced cost in comparison to other fabrication techniques.

Further, the applications of 3D printing has evolved into the fields of biomedicine7,8, and sensors9,10,11,12,13. There is also an increasing number of applications in electrochemical systems such as supercapacitors, electrodes, electrochemical, batteries, and water splitting using 3D printing14. The Black Magic filament (used in this work) has been previously used for photoelectrochemical sensors, supercapacitor, and electrodes15,16,17. This PLA based filament has 8 wt% of graphene18. In this work, we show that electronic devices with graphene-composite can be 3D printed for device evaluation and strain gauge application. These electronic devices constructs can potentially have applications in wearable electronics where flexibility is essential19,20,21.

Here, we outline the electron-transport properties (transport-barrier, average tunneling distance, carrier concentration, graphene nanostructures size, electron flux) of 3D printed devices made from graphene/PLA filaments, and the effect of temperature and strain on these properties.

## Results

Figure 1 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), (b) there is no relatively change with depth to the position of the D, G and 2D (1,341 ± 3 cm−1, 1,580 ± 1 cm−1, 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 positions22,23. 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 micron2 area-scale.

Using the Tuinstra and Koenig24 relationship, the graphitic size of the samples were calculated using the ID/IG intensity ratio:

$$\frac{I\left( D \right)}{{I\left( G \right)}} = \frac{{C^{\prime } \left( \lambda \right)}}{{L_{a} }}$$
(1)

where La is the in-plane correlation length or cluster diameter, $$C^{\prime } \left( \lambda \right)$$ is the variable scaling coefficient, I(D), and I(G) are the intensity of D and G peak, respectively. $$C^{\prime } \left( \lambda \right)\sim 19.22$$ 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 sp2 hybridized carbon atoms in the graphene sheets is in the order of 37.75 ± 2.42 nm (La). In addition, using the relationship26:

$$\overline{h} \Delta Pos \left( G \right)_{{E_{F} }} = \frac{{\lambda_{{\Gamma }} }}{2*\pi }\left[ {\left| {E_{F} } \right| + \frac{{\overline{h}Pos\left( G \right)_{0} }}{4} ln\left| {\frac{{E_{F} - \overline{h}Pos\left( G \right)_{0} }}{{E_{F} + \overline{h}Pos\left( G \right)_{0} }}} \right|} \right]$$
(2)

as $$\overline{h}$$ 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, $$\lambda_{{\Gamma }}$$ is the dimensionless electron–phonon coupling for the LO phonons at $${\Gamma }$$ (the value used was 0.0326), and $$E_{F}$$ is the Fermi energy distribution of doping. It is important to note that several different values of Pos(G)0 have been reported in the literature (See Supporting Information) with an average value of 1583.67 cm−127,28,29,30,31,32,33,34,35. Using Eq. 2 and the values of the G peak positions for the different depths, we found the different values of EF (0.21 eV). The doping concentration was calculated using36:

$$\left| {E_{F} \left( n \right)} \right| = \overline{h}\left| {v_{F} } \right|\sqrt {\pi n}$$
(3)

where $$v_{F}$$ is fermi level velocity (1.1 × 106 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*1012/cm2. 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 sp2 hybridization of carbon atoms (infinite sp2 carbon lattice); however, the relatively sp2 domain size of graphene in this study is ~ 37.75 nm (or ~ 54,000 sp2 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 (IV) 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) :

$$\left( {\frac{I}{V} \upmu {\text{ exp}}\left( { - \frac{{E_{a} }}{{K_{B} T}}} \right)} \right)$$
(4)

where Ea is the thermal barrier height, kB 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 kBT at room temperature (25 meV). Since thermal emission occurs with thermal barriers higher than kBT at room temperature, the mechanism of carrier transportation for this device is electron tunneling37,38. 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.

For electron-tunneling within this thermally-expandable network, we included a thermal-expansion equation with the Fowler Nordheim electron tunneling (FNET) Eq. 37,38,43,44,45,46. Consistently, Connelly et al. also employed the Fowler–Nordheim Model for electron transport within their 3D printed structure47.

In this work, the thermal expansion equation applied on the interparticle polymer layers governs the tunneling distance:

$$\frac{a}{{a_{0} }} = 1 + {\text{a}} \times {\text{T}}$$
(5)

where a0 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

$$I = I_{0} + t {\exp}\left( {\left( {\frac{{2\left( {2m\emptyset } \right)^{\frac{1}{2}} }}{{\overline{h}}}} \right)a_{0} *\left( {1 + {\text{a}} \times {\text{T}}} \right)} \right)$$
(6)

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 mm3) 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 motion-controller 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:

$$\varepsilon = \frac{{\left( {2{\text{* sin}}^{ - 1} \left( {\frac{{{\raise0.7ex\hbox{{l_{0} }} \!\mathord{\left/ {\vphantom {{l_{0} } 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{2}}}}{{\left( {\frac{{l_{0}^{2} }}{8h} + \frac{h}{2}} \right)}}} \right)} \right)* \left( {\frac{{l_{0}^{2} }}{8h} + \frac{h}{2}} \right) - l_{0} }}{{l_{0} }} \times 100$$
(7)

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 IV 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:

$$I = I_{0} + t\exp \left( { - \left( {\frac{{2\left( {2m\emptyset } \right)^{\frac{1}{2}} }}{{\overline{h}}}} \right)a_{0} \times \left( {1 + \frac{{\text{e}}}{100}} \right)} \right)$$
(8)

where the tunneling barrier (ϕ) is kept as the work function of graphene (4.85 eV). Fitting the above equation with the current versus the strain data (Fig. 4, regression = 0.994) provides the tunneling distance at rest at room temperature to be 0.95 nm (calculations shown in Supplementary Information). This indicates that the device can be used as a strain gauge. Extrapolating from the equation for electron-tunneling with thermal expansion (Eq. 6) for the tunneling distance at room temperature, we get 0.95 nm, consistent with the result from the strain equation (Eq. 8). The electron flux $$(e_{f} = I/(e.A_{cross - section} ))$$ on device 2 between the graphene sheets under 0% strain is 18.51 e/s/nm2, and the electron flux under 2.038% strain is 19.51 e/s/nm2; this shows that increasing the electron tunneling width between the nanostructures by just 0.19 Angstrom the electron flux reduces by 1 e/s/nm2 through the polylactic acid junctions in the 3D-printed heterostructure. Also, for our device, the change in resistance is expressed as $$(\frac{{R_{0} - R}}{{R_{0} }})$$, where $$R_{0}$$ is the resistance of the unstrained device (ε = 0%), R is the strained device (ε = 2.038%). This value is 5.28 ± 0.15%. This results in the response sensitivity, $$(\frac{{R_{0} - R}}{{R_{0} }}){/}(\% Strain)$$, of 2.59 Ω/Ω%. Other works have reported similar response sensitivity values: Tian et al.49 reports ~ 0.12 Ω/Ω%, Bae et. al.50 reports ~ 0.3 Ω/Ω%, Xu et. al.51 reports 1 Ω/Ω%, Wang et. al.52 reports ~ 3 Ω/Ω%, and Jinlong et. al.53 reports ~ 4 Ω/Ω%.

## 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/nm2 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: stage-temperature 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 mm3. (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.

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## Acknowledgements

VB acknowledges financial support from National Science Foundation (Grants: CMMI-1503681 and CMMI-1030963), Office of Naval Research (N00014-18-1-2583) and University of Illinois at Chicago. This research is supported in part by the NSF—Graduate Research Fellowship Program for DCCF under the Grant No. 1444315.

## Author information

Authors

### Contributions

V.B. led the work. D.C.C.F. and D.L. performed the 3D printing experiments. D.C.C.F. performed the Raman spectroscopy and electromechanical measurements. D.C.C.F. and V.B. analyzed the data and wrote the manuscript.

### Corresponding author

Correspondence to Vikas Berry.

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Carvalho Fernandes, D.C., Lynch, D. & Berry, V. 3D-printed graphene/polymer structures for electron-tunneling based devices. Sci Rep 10, 11373 (2020). https://doi.org/10.1038/s41598-020-68288-5

• Accepted:

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• DOI: https://doi.org/10.1038/s41598-020-68288-5

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