Potassium-Doped Graphene Nanoribbons for High-Specific

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Potassium-Doped Graphene Nanoribbons for High Specific Conductivity Wiring Jie Zhang, and Eric Fahrenthold ACS Appl. Nano Mater., Just Accepted Manuscript • DOI: 10.1021/acsanm.9b00327 • Publication Date (Web): 09 Apr 2019 Downloaded from http://pubs.acs.org on April 11, 2019

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ACS Applied Nano Materials

Potassium-Doped Graphene Nanoribbons for High Specific Conductivity Wiring Jie Zhang and Eric P. Fahrenthold∗ Department of Mechanical Engineering, University of Texas, Austin, TX 78712 * E-mail: [email protected] Phone: 512-471-3064. Fax: 512-471-8727

Abstract Carbon based conductors and metal-carbon composites have attracted much recent research interest, as candidates for the future replacement of copper wiring in a variety of applications. The development of nanocarbon based electrical wiring with high mass specific conductivity is of particular interest in weight sensitive applications such as aerospace vehicle design. Although recent experimental research suggests that doped graphene may offer fundamental improvements in specific conductivity, some important properties of interest cannot be measured directly, including the effects of dopants on the conductance of interfaces (junctions) in multi-layer graphene. Recent computational research has developed the first general ab initio model of doped graphene nanoribbon (GNR) based electrical conductors, including the combined effects of doping density, doping distribution, GNR overlap, junction conductance, junction cascades, and electron mean free path on the specific conductivity of doped graphene nanowires. The general modeling approach has been applied to potassium-doped graphene; the results are consistent with published experimental data, and identify nanoscale features which limit macroscale conductor performance. Keywords: graphene, nanoribbons, doping, potassium, modeling

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Introduction The development of improved carbon based electrical conductors for wires and cabling, 1,2 integrated circuits, 3,4 chemiresistive sensing, 5,6 and other applications is the focus of much recent research. Experimental research has demonstrated the potential of some carbon based conductors to achieve mass specific conductivities which exceed that of copper. 7 In recent work complementary improvements in current carrying capacity 8 have also been made. In mass sensitive applications, such as aircraft wiring, interest in carbon based conductors is motivated in large part by potential improvements in specific conductivity. The approach most widely employed to improve specific conductivity is doping. Published experimental work 9 suggests that n-doping with alkali metals (K, Na, Li) or p-doping with halogens (I, Cl, Br), either directly or as components of larger dopant molecules, offers the most promising route to high specific conductivity. Of the alkali metals and halogens studied to date, the most promising dopants appear to be potassium and iodine. Conductivity enhancement due to potassium doping can be very high, 10,11 and significant conductivity improvements have been reported for experiments employing iodine doping. 7,12 The vast majority of experimental research on nanocarbon conductors has studied carbon nanotube (CNT) based wiring. Despite considerable success in improving the conductivity of CNT based wiring, the development of high specific conductivity CNT based wiring has proven to be very difficult. Recent computational work on CNT based wiring 13,14 indicates that dopant distribution effects, variations in electrical properties with CNT diameter, parasitic mass effects for multiwall tubes, and the conductivity properties of doped CNT interfaces (junctions) are the most important factors limiting the mass specific performance of CNT based wiring. Note that for the CNT bundles which typically make up the tested cables, direct measurement of the effects of these variables on mass specific conductivity is not possible. Difficulties encountered in the development of CNT based wiring and advances in the fabrication of graphene based films and fibers appear to be encouraging experimental research on alternative graphene based nanocarbon conductors. 11,15 The published fabrication process for potassium-doped films is briefly described as follows. 15 Graphene film (GF) was first prepared by depositing graphene

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oxide sheets (from an aqueous suspension) on a Teflon substrate, followed by air drying, acid reduction, high temperature annealing, and mechanical compression. In the second step, potassium dopant was applied to the GF using a two-zone vapor transport method: (a) the GF and the potassium were placed in separate zones of a glass tube under an argon atmosphere, then (b) the sealed tube was heated, using two electric heating sleeves to independently specify the temperatures of the GF and potassium zones of the reaction tube. Control of the temperature difference between the two reaction tube zones allowed for the production of both monolayer and bilayer films doped by intercalated potassium. Although the electrical properties of graphene have been widely studied, 16,17 no published work has developed and compared with experiment a multiscale ab initio model of doped graphene nanoribbon (GNR) based conductors. This paper describes computational research investigating the potential of potassium-doped GNRs as the base material for improved electrical conductors. It estimates the combined effects of doping density, doping distribution, GNR overlap, junction conductance, junction cascades, and mean free path on the macroscale specific conductivity of doped nanowires. Of central interest are differences in the response of armchair and zigzag GNRs to dopant treatments, parasitic mass effects, and the conductivity properties of doped GNR junctions. The modeling results are compared with published experimental measurements of the specific conductivity of potassium-doped graphene films and fibers, and conclusions are presented which may assist future experimental research.

Computational methods The computational modeling procedure used in this paper consists of three steps: • The first step models the effects of dopant on GNR conductance, for both armchair and zigzag GNRs. Armchair GNRs with the edge number seven (7-aGNR) possess the largest band gap, and were therefore chosen for the analysis of doping effects. Zigzag GNRs with the edge number six (6-zGNR) were chosen for the analysis in order to compare armchair and zigzag nanoribbons of similar width. • The second step models the effects of dopant on nanoribbon junction conductance. The

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junction calculations are limited to the 6-zGNR case. • The third step combines the nanoribbon and junction modeling results with mean free path data from the literature, to formulate a nanowire model suitable for use in estimating macroscale conductor performance. The ab initio calculations made in the first two steps employ models which are periodic in the transmission direction; a vacuum space of length 30 ˚ A was specified in the orthogonal directions in order to avoid neighbor interactions. The junction models were set up by first relaxing two parallel GNRs, then deleting an integer number of unit cells on opposite ends of the GNRs in order to obtain the desired junction overlap. The equilibrium and conductance calculations were made using the ab initio code suite SIESTA, 18 which includes the electronic transport code TranSIESTA. 19 The equilibrium analysis employed density functional theory while the transport analysis employed a non-equilibrium Green’s function method. All of the models were relaxed until the default SIESTA force tolerance criterion of 0.04 eV/˚ A was reached. The calculations employed a double-zeta polarized basis set, with a local density approximation (LDA) 20 in the relaxation phase and a local spin-density approximation (LSDA) in the transport phase. The energy cutoff for the real space mesh was set to 300 Ry, and k-point grids of 3 × 3 × 5 and 3 × 3 × 20 were used for the scattering region and for the electrodes respectively. Van der Waals forces were not modeled but are of interest for future work. In the section which follows, the electrical performance of the nanoconductors is described using Landauer formulas for the zero bias conductance (G) at the Fermi energy (Ef ), G↑ = G0 T ↑ (Ef ),

G↓ = G0 T ↓ (Ef ),

G0 = 2

e2 h

(1)

where T ↑ (E) and T ↓ (E) are the spin up and spin down transmissions at the energy E, e is the charge on an electron, h is Planck’s constant, and G0 is the quantum unit of conductance.

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Results and Discussion The modeling results are discussed in the following sequence. The first subsection presents computational results for the ballistic conductance of doped GNRs, as a function of dopant mass loading; included is a discussion of doping mechanisms suggested by density of states, charge density difference, and HOMO-LUMO (highest occupied molecular orbital-lowest unoccupied molecular orbital) plots. The second subsection presents computational results for the ballistic conductance of nanoribbon junctions. The third subsection presents computational results for the nanowire model, comparing the modeling results to published experimental data. Doped nanoribbon models. This subsection describes the computed electrical properties of the doped GNRs, both armchair and zigzag, including transmission, density of states, and charge density difference plots at two different dopant mass loadings. A total of four potassium-doped nanoribbon configurations were modeled. They are shown in Figure 1, and include armchair and zigzag GNRs analyzed at doping densities of one dopant atom per two unit cells (denoted here by ‘1/2’) and one dopant atom per three unit cells (denoted here by ‘1/3’). The dopant atoms are distributed along the GNR centerline, with one atom per two unit cells being the highest doping density for which a uniform line of potassium atoms was found to be a stable equilibrium state. Note that this result is consistent with published experiments, 23 which indicate that the highest doping density for potassium atoms arranged on a graphene surface is one dopant per two carbon hexagons, in a structure which corresponds to that of KC8 . The potassium atoms were initially separated from the GNR surface by distance of 4.00 ˚ A; at equilibrium the average standoff for the potassium atoms in the four configurations was 2.52 ˚ A. The equilibrium standoff distance computed here for GNR was slightly less than that reported 24 for potassium interaction with graphite, estimated in previous work to be 2.81 ˚ A. Transmission plots for the potassium-doped GNRs are shown in Figure 2, where conductance values at the Fermi Energy are highlighted. In the armchair (7-aGNR) case, doping at the low density (1/3) increases the conductance value from zero to 2G0 , while doping at the high density produces no further increase in conductance. In the zigzag (6-zGNR) case, doping at the low density (1/3) increases the conductance value from zero to 2G0 , while doping at the high density produces

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a further increase in conductance to 3G0 . The transmission distributions for the potassium-doped GNRs show an apparent left shift, as compared to that for the undoped GNR, consistent with ntype doping. In both the armchair and zigzag GNRs, potassium doping moves the Fermi level across the band gap, changing the GNRs from semiconducting to metallic (example band gap diagrams and data are provided in the Supporting Information). Note that only in the case of the armchair GNR at the highest doping density do the transmission plots show any differences between the spin up and spin down transmission distributions. The spin-averaged Fermi energy conductance results for the four modeled configurations are summarized in Figure 3. The underlying conductance change mechanisms associated with potassium doping are illustrated by the density of states (DOS) and charge density difference plots shown in Figures 4 and 5. The shaded and cross-hatched regions in Figure 4 indicate the spin up and spin down partial density of states (PDOS) plots for potassium; they contribute significantly to the states at the Fermi energy only in the high density doping configurations. In both the armchair and the zigzag case, doping shifts the DOS distributions to the left and (on average) increases the DOS at energies near the Fermi level. The charge density difference distributions shown in Figure 5 are defined by

∆Q = QK+GN R − QGN R − QK

(2)

where QK+GN R is the total charge density of the doped system, with QGN R and QK the corresponding charge densities for the GNR and the dopant atoms. Note that all three charge densities are computed using the same set of atomic coordinates. In both the armchair and the zigzag cases, Figures 5a through 5d show that the potassium dopant atoms act as electron donors; since all four plots use the same scale, those figures also indicate the relative effectiveness of the dopant atoms in establishing low scattering pathways for the charge carriers. The total charge transfers for both the armchair and the zigzag cases, at both doping levels, are listed in Table 1. The effects of potassium doping on the HOMO-LUMO orbital structure of graphene are illustrated in Figures 5e and 5f, which compare the spin-up HOMO-LUMO plots for pristine 6-zGNR graphene to those for 6-zGNR graphene doped at density 1/2. Table 2 lists the associated HOMOLUMO energy gaps. The effects of doping are two-fold: first the HOMO-LUMO energy gaps are

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greatly reduced, second the HOMO-LUMO overlap is dramatically improved. Both of these effects are generally associated with improved conductance. In summary, the potassium-doped GNRs exhibit the following properties: • The potassium atoms n-dope the armchair and the zigzag GNRs. • The potassium atoms transform the GNRs from semiconducting to metallic. • The potassium atoms increase the total DOS in the vicinity of the Fermi energy, although only at the highest modeled doping concentration do the dopant atoms contribute significantly to the DOS at the Fermi energy. • In the zigzag GNR case, differences between the spin up and spin down DOS and PDOS are negligible, at both doping densities. • In the armchair GNR case, at the lower doping density, differences between the spin up and spin down DOS are significant while differences between the spin up and spin down dopant PDOS are negligible. • In the armchair GNR case, at the higher doping density, differences between the spin up and spin down DOS and differences between the spin up and spin down dopant PDOS are both substantial. Doped nanoribbon junction models. Recognizing that macroscale wiring must be fabricated from a collection of many GNR components, this subsection considers the effects of potassium doping on GNR junctions. Only 6-zGNR junctions were modeled, at the higher of the two doping densities discussed in the preceding section. Previous modeling work on both nanotube 13,26 and GNR junctions 27,28 has suggested that junction conductance can be a sensitive function of nanoconductor overlap, and that low junction conductance can severely limit carbon nanowire performance. Hence the effects of potassium doping on GNR junction conductance, as a function of GNR overlap, is of central interest. The doped junction configuration modeled here is shown in Figure 6a. In all cases the dopant atoms were initially positioned above the center of a carbon hexagon. Starting from a configuration

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with one unit cell overlap, the GNR overlap was increased in one unit cell increments to a maximum of nine, in order to obtain the spin averaged junction conductance results plotted in Figure 6b (differences between the spin up and spin down conductance results were negligible). Although junction performance generally improved with overlap, comparison of the junction modeling results with the doped nanoribbon performance summarized in Figure 3 suggests that, for the range of overlaps modeled here, junction conductance may severely limit carbon nanowire performance. Figure 6c shows DOS and PDOS plots for pristine and potassium-doped 6-zGNR junctions at a four unit cell overlap (example HOMO-LUMO plots for doped and undoped junctions are provided in the Supporting Information). Overall the junction modeling results indicate that: • The potassium atoms n-dope the zigzag GNR junctions. • The potassium atoms transform the GNR junctions from semiconducting to metallic. • The potassium atoms make only modest contributions to the total DOS in the vicinity of the Fermi energy. • Neither the junction DOS nor the dopant PDOS show significant differences between the spin-up and spin-down conductance. • Doped junction conductance is lower, by a factor of approximately four, than doped nanoribbon conductance, when compared at the same doping density. The junction dopant spacial distribution modeled here approximates that described in published experiments 11,15 measuring the performance of graphene sheets doped by intercalated potassium. However, previous work on nanocarbon conductors 13 has indicated that doping effectiveness may be strongly dependent on dopant distribution, suggesting that the study of alternative dopant distribution patterns is an appropriate focus for future computational work. Nanowire model. The ballistic conductance calculations presented in the last two sections provide transmission properties essential for the construction of a macroscale model of the performance of potassium-doped GNR conductors. The other essential modeling inputs are a geometry model for the ‘nanowire’ and scaling information, since the quantum calculations are made at the nanoscale. This subsection extends previous work 13 (focused on CNT based nanowires) to the

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GNR based nanowire case, adopting the simplest possible set of geometric and scaling assumptions needed to estimate the macroscale (experimentally measured) performance of doped graphene based conductors. The nanowire modeling results are presented in the form of an expected macroscale performance range, recognizing that macroscale carbon conductors consist of bundles or assemblies of nanowires, as opposed to a uniform crystal. The assumed geometry model for the GNR nanowires consists of a string of end overlapped (Figure 6a) nanoribbons. Note that a segment of length L, resistance R, and mass per unit length b of any one dimensional conductor may be used to compute specific conductivity (M ) m

M=

L b R m

(3)

The length of the modeled nanowire segment is the mean free path (LM F P ) of an electron in graphene, and the mass per unit length of the nanowire is determined by the GNR mass per unit b GN R , the dopant mass per unit length m b D , the fractional overlap of the nanoribbons (φ) length m b AD ) due to the junctions: at the junctions, and the added dopant mass per unit length (m

b = (1 + φ) m b GN R + m bD + φm b AD m

(4)

b GN R = 59.2 amu/˚ b D = 7.92 amu/˚ b AD For the nanowires modeled in this paper, m A, m A, and m

is zero. The fractional overlap is the fraction of the mean free path over which the doped GNRs are end overlapped, at the junctions. The larger the overlap, the greater the cohesive strength of the macroscale conductors; however overlaps also introduce parasitic mass, reducing the specific conductivity of the macroscale conductor. The resistance (R) of the modeled nanowire segment is computed using R−1 = M IN [GN , GJ ]

(5)

where GN and GJ are the ballistic conductance values for the doped nanoribbon and doped junction respectively, obtained from the transmission calculations presented in the last two subsections. A M IN function is needed to correctly represent the physics of electron wave transmission in the nanowire, with the lower of the nanoribbon and junction conductances determining current flow

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in the conductor. Note that this resistance calculation: (a) correctly captures the limiting case in which ‘perfect’ junctions are transparent to the electrons, and (b) avoids the scaling pitfall in which a large cascade of trivially imperfect nanoscale junctions would block macroscale current flow. The nanowire model just described was used to compute specific conductivity (M ) for ideal (φ = 0, negligible overlap) and nonideal (φ = 1, one hundred percent overlap) nanowires composed of the doped 6-zGNR conductors and junctions considered in this paper. Figure 7 compares the computed specific conductivity of ideal and nonideal nanowire models with the measured specific conductivity for three published experiments on potassium-doped graphene. The experimental configurations and specific conductivity test results are listed in Table 3. Adopting the mass specific conductivity of copper 29 as a reference (Mref = 6671.30 S m2 kg−1 ), Figure 7 plots the performance metric M/Mref . Note that the model calculations assume only one junction per mean free path with GJ = 0.623 G0 , and the mean free path is taken to be 500 nm. 30 The computed results indicate that an ideal potassium-doped 6-zGNR nanowire can improve upon the specific conductivity of copper by a factor of more than three. This suggests that doped GNR based conductors offer a viable alternative to doped CNT based conductors 13,26 in the development of high specific conductivity replacements for copper. However, as in the doped CNT conductor case, doped GNR conductors can be expected to show macroscale performance significantly less than the theoretical maximum, for several reasons: • narrow zigzag GNRs are very mass efficient conductors, other nanowire geometries (for example the monolayer and bilayer graphene ‘sheets’ described in published experimental work) may be less mass efficient; • not all dopant atoms can be expected to be well aligned and well distributed along the GNRs, reducing doping efficiency; and • large fractional overlaps may be required in order to produce conductors with acceptable mechanical strength. The significant fractional overlap (and the resultant parasitic mass) required to obtain acceptable mechanical strength is perhaps the biggest disadvantage of nanocarbon conductors, as compared to metals, where all of the conductor mass contributes to both conductance and mechanical strength.

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As indicated in Figure 7, the computed performance for a ‘nonideal’ conductor (fractional overlap of one, half the total carbon mass is parasitic) shows good agreement with published experiments which measured specific conductivity for monolayer and bilayer graphene sheets doped by intercalated potassium atoms. Since the doped graphene conductor configurations accessible with published experimental methods and the doped conductor configurations accessible (at practical computational costs) in ab initio modeling are not identical, the comparisons with experimental data shown in Figure 7 are approximate. Nonetheless, the results suggest that the ab initio based models developed here identify the most important structural features and material properties which control nanowire performance.

Conclusions Experimental research on nanocarbon conductors indicates that graphene is a viable candidate for the development of high specific conductivity wiring, and that doping by halogens or alkali metals offers the most promising route to mass specific electrical conductivities which exceed that of copper. Despite significant progress, experimental work has been hindered by the fact that important nanoscale characteristics of doped nanocarbon bundles are difficult to measure directly. Among these characteristics are the conductance effects of dopant atoms on individual nanocarbons and on nanocarbon junctions. The modeling results presented in this paper show good agreement with published experimental data for a nanowire model which appears to be representative of a cohesive conductor. The modeling results suggests several conclusions on the development of potassium-doped GNRs as high specific conductivity wiring: • Potassium is a very mass efficient dopant for both armchair and zigzag GNRs. • Doped zigzag GNRs appear to be the most promising conductors: at the higher dopant density considered in this paper, the benefits of potassium doping on zigzag GNRs continued to accrue, while the benefits of potassium doping on armchair GNRs appeared to saturate. • Improving the conductance of GNR junctions is critical, since junction conductance can severely limit nanowire performance.

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• Narrow, potassium-doped zigzag GNR conductors may offer specific conductivities as much as twice those measured for the potassium intercalated graphene sheets described in published experiments. • As compared to previous computational studies on doped carbon nanotubes, 26 the best case specific conductivity improvement offered by potassium doping of GNRs is similar to that offered by potassium doping of CNTs. Although the present work identifies some important focus areas for future experimental research, it considers only one dopant and a limited range of dopant densities, GNR widths, junction overlaps, and dopant distributions. Additional computational research is needed to consider alternative dopants and to investigate a wider range of nanowire parameters, evaluating the applicability of the suggested conclusions to a broader range of doped graphene conductor configurations.

Acknowledgements This work was supported by the Office of Naval Research (Grant number N00014-16-2357). Computer time support was provided by the Department of Defense High Performance Computing Modernization Program (project ONRDC40983493) and the Texas Advanced Computing Center (project group number G-815029) at the University of Texas at Austin.

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Table 1: Charge transfer (|e|): potassium to graphene GNR type 6-zGNR 6-zGNR 7-aGNR 7-aGNR

Dopant density Charge transfer per dopant atom 1/3 0.748 1/2 0.449 1/3 0.772 1/2 0.694

Table 2: Computed HOMO and LUMO energies (eV) Configuration EHOMO 6-zGNR Pristine -4.328 6-zGNR + K@1/3 -3.349 6-zGNR + K@1/2 -3.499 7-aGNR Pristine -4.704 7-aGNR + K@1/3 -2.640 7-aGNR + K@1/2 -2.408

EFERMI -4.136 -3.299 -3.449 -3.995 -2.639 -2.396

ELUMO -3.966 -3.269 -3.414 -3.200 -2.611 -2.105

Table 3: Measured specific conductivity for potassium-doped graphene Experimental Graphene Dopant data source configuration configuration Liu et al. (2016) [11] fibers monolayer intercalation Zhou et al. (2017) [15] film monolayer intercalation Zhou et al. (2017) [15] film bilayer intercalation

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M/Mref 2.07 1.27 1.37

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Figure 1: Models of potassium-doped GNRs. (a) 7-aGNR at a doping density of 1/3; (b) 7-aGNR at a doping density of 1/2; (c) 6-zGNR at a doping density of 1/3; (d) 6-zGNR at a doping density of 1/2.

Figure 2: Computed transmission for potassium-doped GNRs. (a) 7-aGNR at doping densities of zero, 1/3, and 1/2; (b) 7-aGNR at at doping densities of zero, 1/3, and 1/2.

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Figure 3: Conductance at the Fermi energy for potassium-doped 7-aGNRs and 6-zGNRs.

Figure 4: DOS and PDOS plots for potassium-doped GNRs. (a) 7-aGNR at doping densities of zero, 1/3, and 1/2; (b) 6-zGNR at doping densities of zero, 1/3, and 1/2.

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Figure 5: Charge density difference (CDD) and HOMO-LUMO plots. (a) CDD for a 7-aGNR at a doping density of 1/3; (b) CDD for a 7-aGNR at a doping density of 1/2; (c) CDD for a 6-zGNR at a doping density of 1/3; (d) CDD for 6-zGNR at a doping density of 1/2; (e) spin up and spin down HOMO-LUMO for a pristine 6-zGNR, (f) spin up and spin down HOMO-LUMO for a potassium-doped 6-zGNR, doping density 1/2.

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Figure 6: Modeling of 6-zGNR junctions. (a) Schematic of a potassium-doped 6-zGNR junction, doping density 1/2; (b) spin-averaged junction conductance at a doping density of 1/2, as a function of the junction overlap (in 6-zGNR unit cells); (c) spin up and spin down DOS for a pristine 6-zGNR junction at an overlap of four unit cells, and spin up and spin down DOS and PDOS for a potassium-doped 6-zGNR junction, at a doping density of 1/2 and an overlap of four unit cells.

Figure 7: Comparison of the computed nanowire relative specific conductivity with published experimental data; model results are shown for ideal (φ = 0) and nonideal (φ = 1) potassiumdoped 6-zGNR nanowires, doping density 1/2; experimental results are shown for graphene films with monolayer intercalated potassium doping (Exp. A [15]), graphene films with bilayer intercalated potassium doping (Exp. B [15]), and graphene fibers with monolayer intercalated potassium doping (Exp. C [11]).

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Table of Contents Graphic

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Potassium-Doped Graphene Nanoribbons for High-Specific

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