# Explainable Artificial Intelligence (XAI) for Increasing User Trust in Deep
Reinforcement Learning Driven Autonomous Systems

Jeff Druce
Charles River Analytics
Cambridge, MA
<EMAIL_ADDRESS>
Michael Harradon
Charles River Analytics
Cambridge, MA
<EMAIL_ADDRESS>
James Tittle
Charles River Analytics
Cambridge, MA
<EMAIL_ADDRESS>

###### Abstract

We consider the problem of providing users of deep Reinforcement Learning (RL)
based systems with a better understanding of when their output can be trusted.
We offer an explainable artificial intelligence (XAI) framework that provides
a three-fold explanation: a graphical depiction of the systems generalization
and performance in the current game state, how well the agent would play in
semantically similar environments, and a narrative explanation of what the
graphical information implies. We created a user-interface for our XAI
framework and evaluated its efficacy via a human-user experiment. The results
demonstrate a statistically significant increase in user trust and acceptance
of the AI system with explanation, versus the AI system without explanation.

##  1 Introduction

Artificial intelligence is playing an increasingly prominent role in societies
throughout the world. The recent explosion in their popularity can arguably be
contributed to their dramatic increase in performance afforded by deep
learning (DL) architectures Deng (2014), and associated hardware advances
Schmidhuber (2015). E.g., computer vision has benefited from Convolutional
Neural Networks (CNNs) LeCun et al. (1995), resulting in near human level
perception for object identification, tracking, and segmentation. Natural
language processing has benefited from recurrent neural network architectures,
increasing performance in tasks such as machine translation Devlin et al.
(2018). Autonomous agents, such as those controlled by deep RL policy
networks, have been of particular importance. Deep RL architectures as
function approximators have demonstrated super-human performance in a variety
of Atari video game environments Mnih et al. (2015), and are showing promise
in arenas of high complexity such as StarCraft 2 Vinyals et al. (2019). This
high-performing autonomy motivates its widespread deployment in a variety of
applications.

However, a drawback of these high-performing neural network architectures, and
hence deep RL based systems, is that they are inherently black-box and offer
little insight into _why_ they produce the output they do Gunning (2017). Deep
learning architectures consist of a (typically large) number of cascading
mathematical operations mapping input to output. It is this large number of
operations that allows modeling complex, non-linear patterns in data. As a
consequence of these large number of operations, the aspects of the input that
were inflectional in formulating system output become blurred. In control
networks, where the output could govern the actions of highly impactful
systems (e.g., autonomous vehicles), the lack of explainability is worrisome.
Even more problematic, deep RL based systems have been shown to be highly
dependent on the exact structure of the input, producing wildly different
output with only small perturbations to the input Witty et al. (2018). Users
employing these system can be left with agents producing erratic behavior with
little indication as to why.

Explainable artificial intelligence (XAI) methods offer means to peer inside
the black-box of deep RL based systems. Many XAI methods have been developed
to offer explanations for DL systems including: saliency based-method
Selvaraju et al. (2017), local interpretable model approximations Ribeiro et
al. (2016), and activation propagation methods Bach et al. (2015). These
methods can be effective for providing users with information as to what
features in data-space were most influential in formulating system output
(e.g., an attention map highlighting the ears of a husky in a dog-cat
classification task). These methods are effective in helping explain _why_
black-box systems produce the output they do, but don’t necessarily foster
trust in the AI system.

##  2 Approach

In this work, we are concerned with engendering user trust in deep RL based
autonomous agents. Our domain of interest is the Atari game, Amidar. In this
game, a player navigates through a board collecting points for traversing
horizontal and vertical line segments, while avoiding enemies to prevent being
killed. The q-network we are considering, is a convolutional neural network
consistent with the architecture in Mnih et al. (2015), where the output is
the expected total discounted future reward for each action. An experience
memory mechanism is employed to mitigate the problems associated with
correlated data and non-stationary distributions.

The interest in conveying trustworthiness versus explaining low level actions
was motivated by the observation that our autonomous agent only performed well
in an environment that was virtually identical to what it had seen in
training. Specifically, we observed our q-network policy controlling the agent
produced extremely erratic behavior when small semantically meaningful
interventions to game environment were performed. E.g., when we removed a
single enemy from the game, the agent performed significantly worse on
average. This behavior was magnified the more enemies were removed. This
implied the agent had not learned a robust strategy for the game, but was
simply using the enemies as a "signal" as to how to act; a more detailed
analysis is available in Witty et al. (2018).

With this potential brittleness in mind, in order to build trust in a deep RL
based system, we argue that not only information on how well the system is
currently performing is necessary, but also how well it is generalizing away
from its training set. Therefore, we consider two key metrics: 1) the state
Value Estimate Error (VEE); and 2) the distance to the nearest training sample
(DNTS). The output of the underlying deep q-network responsible for the system
output is the total discounted future reward for each available action. Thus,
we can convey the performance of the system by comparing its output against
the actual reward accumulated by the agent. I.e., a low VEE implies the agent
has an understanding of the current state value, and a high error means it
erroneously estimated the value of the state. DNTS provides a notion of how
similar the DL _perceives_ the current environment is relative to a sample
from training Mandelbaum and Weinshall (2017). A low-distance implies the
agent considers this as something similar to what it has seen in training, and
a large distance corresponds to something not similar to what it has seen in
training. Therefore, the DNTS metric gives the user a sense of how well the
system is generalizing away from its training set. More details on these
metrics are provided in Section 3.

We evaluate the effectiveness of our XAI system with an 18-subject user study.
Subjects were broken into two groups, those with our XAI system, and those
without. Those without the interface showed a statistically significant
decrease in user trust and acceptance of the AI system. As an additional
study, we gave questions which tested the users mental model of the AI. We
presented this as a prediction task; the results of this case were
inconclusive.

##  3 Conveying Trustworthiness

At the core of approach is conveying information to a user as to whether they
can trust the actions of an agent’s underlying policy network. To convey
trustworthiness, we explore how the underlying $Q$ network is performing in
its current environment, how well the agent performs in a variety of scenarios
similar to the current environment, and present an analysis to the user.

###  3.1 Metrics

Deep RL q-networks are typically function approximators, consisting of deep
neural networks, where the function they are approximating estimates the value
of the current state. Specifically, they act as control policies which can be
greedily used (although stochasticity is often incorporated, especially in
training to foster exploration) to produce agents that gain as much reward as
possible. The total discounted reward, denoted by $Q^{*}$, and can be defined
recursively as:

$Q^{*}(s,a)=r(s,a)+\gamma\max_{a^{\prime}}Q^{*}(s_{t+1},a^{\prime})$ (1)

where $r$ is the reward, and $s$ is the state, and $a$ is the action. The deep
network defining the $Q$ function is trained (via stochastic gradient decent)
to minimize the error between the estimated total discounted future reward,
and the actual reward. Therefore, to convey a notion of the underlying
network’s performance, we chose to provide information on how well the agent
estimates its state (versus, e.g., the total points achieved, or any number of
other performance metrics Poole and Mackworth (2010))– which we refer to as
Value Estimate Error (VEE). Mathematically, this can expressed as

$VEE=\sum_{t=N}^{\infty}|{Q^{*}(s_{t},a)}-V(s_{t})|,$ (2)

where $t$ indicates time, $N$ indicates the time index for the current game
sate, $s$ is the state, $a$ is the action, and $V$ is the actual discounted
future reward 111We note that this requires ”running forward” the episode
until completion along the course of the episode. This, of course, cannot be
done in real time. However, we note that the current cumulative discounted
reward could be calculated, and used instead. This is a matter we intend to
explore in future work.. When the value of this comparison variable is high,
the error in the policy network’s estimation implies it does not comprehend
its environment well; when the value is low, it tends to understand its
environment. Therefore, this variable provides an indication of how much the
user can trust the agent in the current environment. The value for an example
episode is plotted on the y-axis of the graph in Fig. 1.

The VEE by itself is not completely telling as to how well the agent is
trustworthy. For example, if the VEE is low, but the current game state is
something the agent has seen many time in training, the agent may not be
robust. Conversely, if the current game state is extremely dissimilar from
what the agent has seen in training, and the VEE is high, it does not
necessarily imply the agent is not somewhat generalized.

To introduce a notion of how well the underlying policy network has
generalized, we introduce the Distance to Nearest Training Sample (DNTS)
metric. Rather than do a comparison of the current game state to states
directly in data space (i.e., the RBG image tensors), we calculate the
$\ell_{2}$ distance of the feature embedding in the penultimate layer (the
second to last layer). This is motivated by the fact that distances in the
original domain would not reflect the _semantic_ difference in the data. E.g.,
for two game states, if the board games were identical (same ladders filled,
and enemy locations), except for the agent location, the $\ell_{2}$ distance
between them would be the same for any agent location. The feature embedding
layer however, is effectively the "featurized" version of the data according
to the q-network. Therefore, looking at the distance in this space, allows a
comparison of the q-networks perception of the game state. Mathematically, it
can be written as:

$DNTS(s_{N})=\min_{s*\in\mathcal{S}}||\mathcal{F}(s*)-\mathcal{F}(s_{N})||_{2}^{2}$
(3)

where $s_{N}$ is the current state, $\mathcal{F}(\cdot)$ is the feature
embedding of the q-network, and $\mathcal{S}$ is the collection of all game
states in the training buffer. Together, these metrics can be combined to give
the user a sense of how well the agent is estimating the current state value
relative to how similar the game states are to what it has seen in training.
We present the information in a 2-D graph that is "traced-out" along the
course of gameplay. This is shown in Fig. 1.

###  3.2 Creating Similar Scenarios

A primary motivation for conveying trustworthiness of autonomous agents was
observing that agents were in fact very brittle with respect to their input
differing from their training environments. A consequence of this was that a
user of the system would be left with an erroneous mental model of the AI.
E.g., in our Amidar environment, the agent appeared to allude enemies with
sophisticated strategies such as "hiding" in a position waiting for the
enemies to pass, or dodging into nearby levels. This can result in an observer
hallucinating that the agent has learned complex strategic tactics. To
mitigate this problem, we provide the user with an analysis of how the agent
would perform on _intervened_ game states. That is, on game states that are
similar and still semantically meaningful (i.e., the game rules/appearance is
preserved), but differ in some way. To show an analysis of how the agents will
respond in a similar (but different) environment, we chose the following
interventions: adding vertical line segments between horizontal levels,
filling in line segments, and moving the agent location on the board.(see
Section 3.3, and Fig. 1).

We perform interventions by creating an emulator that creates Amidar game
state. These high-level interventions to the game were enabled by having
access to the Atari Toolbox Tosch et al. (2019). For consistency, the same
renderer that generated the game environment during training, also rendered
the manipulated environments.

Figure 1: Our explanation interface for Amidar. Figure 2: The user-interface
for Amidar without explanation.

###  3.3 The User Interface

A user-interface (UI) can be an effective tool in establishing user trust in a
software system Klein and Shortliffe (1994); Carlson et al. (2014). For our
XAI system, we created a user-interface (UI) with six major components (see
Fig. 1).

  1. 1.

Agent selection For our initial framework, we let this be a selection of 3
agents, each trained in an Amidar environment with different game-board
characteristics. The first agent was trained on an unmodified Amidar game-
board. The second agent was trained on an Amidar board which contains random
ladders connecting two horizontal levels (traversable by the agent and
enemies). The third agent was trained on an Amidar game-board where the player
had a randomized starting position. This is to verify our approach is
applicable to different autonomous agents for Amidar.

  2. 2.

Agent description A brief description of how the agent was trained. E.g.,
agent Alice has been trained in a scenario where some ladders have been
randomly added in its environment.

  3. 3.

Live game stream After the user selects an agent, the live video of the game
progressing is displayed.

  4. 4.

Agent performance characterization The 2D-figure traces out the agent’s VEE
and DNTS metrics (see Section 3.1 along the course of the game.

  5. 5.

Narrative explanation Narrative statements which provide a textual
interpretation of the VEE and DNTS;

  6. 6.

"What If" scenarios Indicate performance on how the agent _would_ play if
particular interventions were performed. For each intervention, a green border
indicates the agent would have received over 75% of the mean reward for the
agent playing games with no interventions; a red border indicates the agent
would have scored below 75%. The first intervention type is "Add Line
Segment", this intervention consists of adding a vertical line segment
connecting two horizontal levels in a game-board. The second intervention is
"Fill Ladder Segment", this intervention consists of filling or "painting" a
line segment (this occurs when an agent traverses any point on the game-
board). The third intervention is "Move Player", which consists of
transporting the agent to another legal position on the game-board (player is
never placed directly in a place where they will be immediately killed).

##  4 User Study

###  4.1 Evaluation Design

The evaluation design includes two tasks:

  * •

Acceptance Testing. Participants watch 3 agents perform in 12 video sequences
either with or without explanations, and afterwards complete a questionnaire
on system acceptance.

  * •

System Prediction. Participants view 36 (freeze-frame) Amidar game states, and
are asked to predict system performance for each of the 3 agents.

An overview for the participant workflow design for the evaluation can be seen
in Fig. 3. Participants were run in groups of 4, unless a scheduled
participant did not arrive for the session, and all participants in a group
participated in the same condition—either explanation or no explanation.
Participants were informed that they would be viewing an automated agent play
a simple video game, and that their task was to view the system output over 36
sequences, and then assess whether they thought the automated agent should or
should not be accepted as useful. The participants in the Explanation UI
condition were given an additional training session of approximately 15
minutes during which the main elements of the Explanation Interface were
described using numerous examples, and participants were able to ask questions
about interface functionality. Because of the simplicity of the interface in
the No Explanation UI condition, the training for those participants was less
than five minutes, but participants also had the opportunity to ask any
questions about interface functionality before the study began. Fig 1 shows
the Explanation Interface for the AMIDAR game playing agent and Fig. 2 shows
the control interface.

Figure 3: Workflow for our experiment.

###  4.2 Experiment Results

After the acceptance testing task, all participants were given both trust and
user acceptance questionnaires. In addition, explanation satisfaction
(Hoffman, Mueller, Klein, and Litman, 2018) and usability/usefulness
questionnaires were administered to participants in the Explanation Interface
condition. All questionnaires used a five point Likert scale, and only
included positive statements about either the autonomous system or the XAI
interface so that higher scores always indicated more positive user
assessments of the autonomous system, and the XAI interface.

Below are the questions answered by the subjects (note the Liker scale was 1
through 5, with 1 being "Strongly Disagree", and 5 being "Strongly Agree"):

Trust Questions

  1. 1.

I understand how the Automated Game Player works – its goals, actions and
output.

  2. 2.

The Automated Game Player is reliable. It plays the game in a consistent
manner.

  3. 3.

It is easy to follow what the Automated Game Player does.

  4. 4.

I am able to predict how the Automated Game Player will play the game (Its
actions are predictable.)

  5. 5.

I am able to judge when I should trust and not trust the Automated Game
Player.

  6. 6.

I am confident in the Automated Game Player. I feel that it performs well.

  7. 7.

The Automated Game Player UI will have a positive effect on my performance
when it comes to understanding Agent capabilities.

  8. 8.

I can trust the Automated Game Player UI.

User Acceptance Questions

  1. 1.

The Automated Game Player User Interface would be a useful aid in
understanding how an Automated player will perform in different game
conditions

  2. 2.

The Automated Game Player User Interface enables a person to understand how
the automated player will perform in different game conditions more quickly
and efficiently.

  3. 3.

The Automated Game Player User Interface enables a person to understand how
the automated player will perform in different game conditions better than
they could on their own.

  4. 4.

The Automated Game Player User Interface is easy to use

Fig. 4 a) shows a greater average Trust score for the Explanation UI condition
(3.32) compared to the No Explanation UI condition (2.6). A statistical
hypothesis test indicated this difference was not significant (t (df 10) =
1.71, p = .058). Fig. 4 b) shows a greater average User Acceptance score for
the Explanation UI condition (4.02) compared to the No Explanation UI
Condition (2.67). A statistical hypothesis test indicated this difference was
significant (t (df 10) = 2.72, p = .03). Based on the 5-point Likert scale, an
average user response should be 3, and therefore the results in Fig. 4 c)
indicate that the average Usability/Usefulness (4.01) and Explanation
Satisfaction scores (3.53) are both higher than the neutral scale value. We
hypothesized that the Explanation Interface would provide users with a richer
mental model of the AI classifier, which would lead to a higher percent
correct on the prediction task. However, the results in Fig. 4 d) show only
slightly greater Prediction

Figure 4: Workflow for our experiment.

##  5 Conclusions and Future Work

The results of the evaluation confirm that our XAI system did indeed increase
user trust and acceptance of the AI system. This finding is both supported
from qualitative questionnaires, as well as statistical results from
quantitative questions. Given the brittle nature of the black box AI systems,
this result is encouraging that user’s value on information as to the
trustworthiness of AI systems. However, the results are not exceedingly
positive, with improvements barely outside of a single standard deviation.
Specifically, the perception of prediction correctness did not significantly
increase with explanations. This implies the users perhaps did not learn a
significantly better mental model for the autonomous system.

Several research directions naturally follow from this work. First, we would
like to consider a more complex domain, necessitating a more sophisticated
deep RL policy network. For example, in many critical tasks, AIs will not act
autonomously, but act as trusted partners in a human-machine collaboration.
Providing an XAI framework for this hybrid task to check for increase
efficiency would be interesting. Additionally, the manner in which the VEE was
calculated(see 3.1), could be improved. E.g., we could use the cumulative
error up until the current point in time (rather than "artificially" rolling
out the episode until completion). A study as to the effectiveness of this
approximation would be of interest.

#### Acknowledgments

The authors would like to thank Amanda DiFiore for her valuable contributions
during data collection. This research was developed with funding from the
Defense Advanced Research Projects Agency (DARPA). This material is based on
research sponsored by the Air Force Research Lab (AFRL) under agreement number
FA8750-17-C-0118. The U.S. Government is authorized to reproduce and
distribute reprints for governmental purposes notwithstanding any copyright
notation thereon. The views, opinions and/or findings expressed are those of
the author and should not be interpreted as representing the official views or
policies of the Department of Defense or the U.S. Government.

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.tifpng.pngconvert #1 .tif

#  MoRe Electrodes with 10-nm Nanogaps for Electrical Contact to Atomically
Precise Graphene Nanoribbons

Damian Bouwmeester<EMAIL_ADDRESS>Kavli Institute of Nanoscience,
Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands
Talieh S. Ghiasi  Kavli Institute of Nanoscience, Delft University of
Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands  Gabriela Borin Barin
nanotech@surfaces Laboratory, Empa, Swiss Federal Laboratories for Materials
Science and Technology, 8600 Dübendorf, Switzerland  Klaus Müllen  Max Planck
Institute for Polymer Research, 55128 Mainz, Germany  Pascal Ruffieux
nanotech@surfaces Laboratory, Empa, Swiss Federal Laboratories for Materials
Science and Technology, 8600 Dübendorf, Switzerland  Roman Fasel
nanotech@surfaces Laboratory, Empa, Swiss Federal Laboratories for Materials
Science and Technology, 8600 Dübendorf, Switzerland  Department of Chemistry,
Biochemistry and Pharmaceutical Chemistry, University of Bern, Freiestrasse 3,
CH-3012 Bern, Switzerland  Herre S.J. van der Zant  Kavli Institute of
Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The
Netherlands

###### Abstract

Atomically precise graphene nanoribbons (GNRs) are predicted to exhibit
exceptional edge-related properties, such as localized edge states, spin
polarization, and half-metallicity. However, the absence of low-resistance
nano-scale electrical contacts to the GNRs hinders harnessing their properties
in field-effect transistors. In this paper, we make electrical contact with
9-atom-wide armchair GNRs using superconducting alloy MoRe as well as Pd (as a
reference), which are two of the metals providing low-resistance contacts to
carbon nanotubes. We take a step towards contacting a single GNR by
fabrication of electrodes with a needle-like geometry, with about 20 nm tip
diameter and $10$ nm separation. To preserve the nano-scale geometry of the
contacts, we develop a PMMA-assisted technique to transfer the GNRs onto the
pre-patterned electrodes. Our device characterizations as a function of bias-
voltage and temperature, show a thermally-activated gate-tunable conductance
in the GNR-MoRe-based transistors.

###### keywords:

Graphene nanoribbons; Electronic properties; Substrate transfer; Field effect
transistor; Metal-semiconductor contacts; Superconducting electrodes

Figure 1: PMMA membrane GNR transfer method. (i) Au(111) on mica 9-AGNR growth
substrate. (ii) PMMA membrane on PDMS placed on a glass slide. (iii) Aligned
placement of the PMMA membrane onto the GNR growth substrate. The stage is
heated to 130 ∘C to promote stronger adhesion of the PMMA membrane to the GNR
growth substrate. (iv) Delamination of the mica layer in 30% HCl. (v) Gold
etching in KI/I2 for 5 to 10 minutes followed by rinsing and soaking overnight
in DI water. (vi) GNRs on PMMA membrane after drying in ambient conditions
(vii) Stamping of the PMMA membrane onto the target substrate, followed by
annealing at 150 ∘C. (viii) Target substrate with PMMA-covered GNRs after GNR
transfer

## Introduction

Graphene nanoribbons (GNRs) are a quasi-1D analogue of graphene. Although
graphene is classified as a 2D semimetal, a combination of quantum confinement
and electron-electron interactions make GNRs semiconducting 1, 2, 3. The
electronic band gap of GNRs scales inversely with their width and depends on
their edge structure 2. This tunable band gap is a property that is of
interest for field-effect transistors (FETs) 4, 5 and optoelectronics 6.
Moreover, GNRs exhibit edges and ends that can host localized spin-polarized
states 1, 7, 8 which is interesting for spintronic applications. Since the
electronic properties of GNRs are sensitive to their width and edge structure,
edge disorder and width variation at the atomic level result in hopping
transport within the ribbon 9, which significantly suppresses their intrinsic
electronic/spintronic properties 10.

On-surface, bottom-up chemical approaches have enabled the synthesis of a
variety of GNRs from molecular precursors with structural precision on the
atomic level 11, such as armchair 11, zigzag 12, chevron 11,
staggered/topological 13, 14, metallic 15 and substitutionally doped GNRs 16.
The electronic properties of these GNRs have mostly been studied by scanning
tunneling microscopy. Characterization of the intrinsic electronic properties
of the GNRs in electronic circuits has been comparatively limited by high
contact resistances, limited chemical stability of the edges, and short GNR
length below typical source-drain contact distances.

Low-resistance Ohmic electrical contacts are important for obtaining large on-
state currents in FET devices, as well as for studying the intrinsic transport
properties of GNRs. However, making consistent, low-resistance electrical
contact to atomically-precise GNRs is challenging due to their on-surface
synthesis with typical 1-nm width that leads to large band gaps (of the order
or $1$ eV). Their typical length scale also results in a small contact area,
of the order of $10$ $\mathrm{nm}^{2}$. Recently, there have been considerable
efforts to electrically contact atomically precise armchair-edge GNRs by
electrodes made of graphene 17, 18, 19, 20, carbon nanotubes(CNTs) 21,
palladium 5, 22, 23, 24 and gold 25. These studies, however, are still limited
compared to the detailed characterization of a large variety of contacts to
CNTs 26, 27. Even though CNTs structurally differ from GNRs by the absence of
edges, small diameter (less than $1.0$ nm) CNTs are the closest system to
atomically precise GNRs due to their similar band structure and considerable
band gap (larger than $0.8$ eV) 28.

For the case of semiconducting CNTs, Schottky barriers are formed at the
metal-CNT interfaces, the size of which depends on the chosen contact metal
and the diameter of the nanotube. The presence of Schottky barriers results in
a contact resistance that increases as the temperature is decreased. For CNTs,
a distinction is often made between physisorption and chemisorption 29, 30, as
well as p-type (high work function) and n-type (low work function) electrical
contacts 27. Typically, n-type contacts form with metals that are prone to
oxidation (Al, Sc, Y, Ti), while p-type contacts can be made with noble metals
(Au, Pt, Pd), as well as Ni, Co, Mo and W.

Two of the metals that stand out for making low-resistance electrical contacts
with small or absent Schottky barriers to CNTs are Pd 31, 32 and Mo 33/MoRe
alloy 34, 35. Pd contacts to 9- and 13-atom-wide armchair GNRs (9-AGNRs and
13-AGNRs) have already been studied in a short-channel FET geometry by Llinas
et al. 5, who found that transport in their devices was limited by tunneling
through a Schottky barrier at the contacts. Nevertheless, their Pd-contacted
9-AGNR FETs with a $\textrm{high-}\upkappa$ HfO2 gate dielectric have a large
on-state current ($>1$ $\upmu$A), as well as an on-off ratio of $10^{5}$.
Mo/MoRe on the other hand is of interest as it is a superconducting metal,
which may be used to induce superconductivity in GNRs by the superconducting
proximity effect 36 at cryogenic temperatures. In a weakly transparent
electrical contact, the superconducting energy gap can be used to perform
tunneling spectroscopy of the GNRs, while a highly transparent contact would
allow for utilizing GNRs in Josephson junctions.

Here, we further explore MoRe and Pd contacts to 9-AGNRs by studying their
current-voltage characteristics at various temperatures. In particular, we
compare two distinct electrode geometries that have the potential to
respectively address many GNRs in parallel, and single GNRs. With the aim of
contacting single 9-AGNRs, an electrode design was made that minimizes gap
width. Here we fabricate needle-like MoRe and Pd nanogap electrodes with a
minimum width of $\sim 20$ nm and spacing of 6-15 nm. The smaller gap spacing
achieved for this geometry could also enable addressing shorter GNRs. The
polymer-free transfer method was attempted on this geometry, resulting in
broken MoRe nanowires due to etching. In order to preserve the  more fragile
needle-like nanogaps and the contact geometry from etchants used in polymer-
free GNR-transfer recipes, here we develop a PMMA-membrane-assisted technique
for the transfer of the 9-AGNR films, based on the PMMA fishing transfer
technique introduced by Martini et al. 17. This technique keeps the electrodes
intact by preventing direct contact with any liquid and allows for controlled
handling and $\sim 1\leavevmode\nobreak\ \upmu$m precise placement of the GNRs
onto the electrical contacts using micro-manipulators. Our transfer method
offers the additional advantage of using a stretched and clamped PMMA film,
which could reduce wrinkling and folding. With this technique, we fabricate
10-nm nanogap MoRe and Pd devices and we investigate and compare their
performance. We show that the 10-nm Pd nanogap devices have a few orders of
magnitude higher conductance, which suggests that a Pd/MoRe bilayer thin film
would be a better contact material for the realization of functional
superconducting GNR devices.

## Results

The 9-AGNRs were grown by on-surface synthesis37, discussed in detail in the
methods section. The average length of the 9-AGNRs used in this work is 45 nm.

The two distinct electrode geometries used here to address the GNRs are the
wide-nanogap and needle-like geometries. The wide-nanogap geometry consists of
a pair of $2\leavevmode\nobreak\ \upmu$m long parallel wires, separated by
approximately 30 nm. This geometry was made to address transport through many
GNRs in parallel. The needle-like nanogap geometry consists of two opposing
nanowires that are cuspated at a 30∘ angle, separated by less than 15 nm. This
geometry minimizes the contact area and thus, increases the chance of making
contact with a single GNR. The fabrication of these two electrode geometries
is discussed in detail in the methods section.

Prior to the GNR transfer, the nanogap electrodes were characterized by
recording the current versus bias voltage ($IV$ characteristic) in the bias
range of -1 to 1 V. Only devices that were found to be electrically open
(resistance $\geq$ 1 T$\Omega$ at 1 V) were used in this study. The transfer
of the GNRs onto wide MoRe nanogaps was performed by a polymer-free method 38.
For the needle-like MoRe and Pd nanogap devices, we resorted to a
polymethylmethacrylate (PMMA) membrane-based transfer method, because the gold
etchant destroys the MoRe and Pd nanowires. The procedure for making the PMMA
membrane for the GNR transfer is detailed in the methods section.

As this PMMA-membrane transfer method has not yet been applied to GNRs, we
discuss it in detail, following the steps illustrated in Fig. 1. In the first
step, the PMMA-PDMS stamp held on a glass slide (ii) is brought in contact
with the GNR film, grown on a Au-mica substrate (i), using micromanipulators
of a transfer stage, shown in (iii). After the contact of the PMMA membrane
and the GNR film, the stage is heated to 130 ∘C to promote stronger adhesion.
The stack of PDMS-PMMA-GNR-Au(111)-mica held on the glass slide is then put
into 30% HCl until the mica is delaminated from the Au film, depicted in (iv).
The glass slide is then rinsed and soaked in DI water three times, before
leaving it to dry in ambient conditions. As shown in (v), KI/I2 gold etchant
is next drop-casted onto the Au film with a pipette and left for 10 minutes to
fully etch the 200 nm Au film. The GNR-PMMA-PDMS stack is then rinsed and
soaked in DI water overnight to remove residual iodine stains. After drying in
ambient conditions(vi), the PMMA membrane is perforated around the PDMS using
a needle to allow for its easier detachment from the PDMS stamp in the next
step. The PMMA-GNR film is brought into contact with the pre-fabricated
electrodes at the transfer stage, heated up to 150 ∘C to improve adhesion
(vii). In the final step, the glass slide-PDMS stamp is retracted, leaving the
PMMA-covered GNR film on the electrodes (viii). After the transfer, the
devices were post-annealed for 30 minutes at 150 ∘C to reflow the PMMA layer
which would increase the chance of making better contact with the GNR film.

Figure 2: Room temperature characterization. a) SEM image of a 2 $\upmu$m wide
MoRe nanogap contact electrodes; The electrode seperation is 30 nm and the
scalebar is 400 nm. b) $IV$ curves of wide MoRe nanogap 9-AGNR devices. Each
color corresponds to a measurement performed on a different device. c)
Histogram of conductances of wide MoRe nanogap 9-AGNR devices. d) Map of
current versus bias voltage and temperature of a selected wide MoRe nanogap
9-AGNR device. e) Corresponding temperature dependence of the $IV$
characteristic extracted from d) for $T$ = 5, 50, 100, 150, 200, and 250 K. f)
Corresponding temperature dependence of the current at $V$ = 1 V extracted
from d). The inset shows the rescaled curve with a guide to the eye based on
the nuclear tunneling model.

Figure 3:  a) SEM image of a representative needle-like MoRe 10-nm nanogap
electrodes with a separation of roughly 10 nm; The scalebar is 100 nm. b) $IV$
curves of three MoRe 10-nm nanogap 9-AGNR devices. Each color corresponds to a
measurement performed on a different device. c) Gate voltage dependence of the
current at $V$ = 1 V of a selected MoRe 10-nm nanogap 9-AGNR device. The
arrows indicate the sweep direction of the gate voltage. d) Map of the current
versus bias voltage and temperature of the same device as in c) at a fixed
gate voltage of -2 V. e) Corresponding temperature dependence of the $IV$
characteristic extracted from d), shown for $T$ = 170, 200, 230, 260, 290, 320
and 350 K. f) Corresponding temperature dependence of the current at $V$ = 1 V
extracted from d). The inset shows the rescaled curve with a guide to the eye
based on the nuclear tunneling model.  Figure 4: a) Temperature dependence of
the $IV$ characteristic of a 10-nm Pd nanogap 9-AGNR device. b) Comparison of
the $IV$ curve of the most conductive 10-nm MoRe nanogap, shown as the blue
$IV$ curve in figure 3, and the $IV$ curve of the 10-nm Pd nanogap in Fig. 4a
at room temperature.

We first discuss the measurements of wide MoRe nanogap 9-AGNR devices, at room
temperature in vacuum. In Fig. 2 we show a representative SEM image of the
wide MoRe nanogap electrodes. For all devices, $IV$ curves were recorded in
the bias range from -20 to 20 mV, which we show together in Fig. 2. Out of the
22 devices onto which the GNR transfer was performed, 21 were found to be
conductive. All $IV$ curves are linear within the applied bias range, with
varying slopes. The electrical conductance ($G$) of the devices was extracted
by fitting the slope with a linear fit, resulting in the histogram of Fig. 2.
The majority of the devices show conductance in the range of 0.5-8 nS, with a
median of 1.3 nS. The standard deviation of $\mathrm{log}(G)$ is 0.95,
equivalent to a standard deviation in the conductance of $\sim$1 order of
magnitude. There are, however, also devices with a conductance smaller than 10
pS or larger than 10 nS, spanning over four orders of magnitude in total.

The temperature dependence of the $IV$ characteristics of one of the wide MoRe
nanogaps-GNR junctions is shown in Fig. 2 on a logarithmic scale (see SI,
section 1, for measurements of another device. Furthermore an $IV$ curve up to
4V taken at 100 mK can be found in the SI, section 2). The measured current at
a fixed bias voltage decreases with decreasing temperature, with a kink
observed at $80$ K. In Fig. 2, the $IV$ curves plotted for various
temperatures highlight the plateau-like feature at $T<100$ K, together with an
increase in the slope of the logarithm of the $IV$ curve with decreasing
temperature. In Fig. 2, the current at a bias voltage of 1 V is plotted versus
inverse temperature. In the high-temperature regime, an exponential decay is
found, which can be described by:

$I\ =\ C\ e^{-\frac{E_{\mathrm{a}}}{k_{\mathrm{B}}T}},$ (1)

where $C$ is a constant, $k_{\mathrm{B}}$ is the Boltzmann constant and
$E_{\mathrm{a}}$ is an activation energy. Below
$\frac{1}{k_{\mathrm{B}}T}=0.1$ $(\mathrm{meV})^{-1}$, equivalent to
$T\leavevmode\nobreak\ >\leavevmode\nobreak\ $80 K, the temperature-dependence
fit yields $E_{\mathrm{a}}\leavevmode\nobreak\ =\leavevmode\nobreak\ 17.8$
meV.

At lower temperatures, the log(current)-voltage curve does not follow the
exponential decay and instead flattens off. For this part, the scaling
analysis done by Richter et al. 25 for charge transport in 9-AGNR networks was
followed, which is based on a nuclear tunneling 39, 40, 41 model. We note that
an analysis based on the Richardson-Schottky and Simmons model was also
attempted. The bias voltage dependence could be fit, but we could not
simultaneously reproduce the temperature scaling. The nuclear tunneling model
instead gives an efficient description of the current versus bias voltage and
temperature. The equation describing the $IV$ characteristic in this model is:

$I\ =\ I_{0}\ T^{\alpha+1}\ \mathrm{sinh}(\frac{\gamma eV}{2k_{\mathrm{B}}T})\
|\Gamma(1+\frac{\alpha}{2}+i\frac{\gamma eV}{2\pi k_{\mathrm{B}}T})|^{2},$ (2)

where $I_{0}$ is a constant, $\alpha$ is a dimensionless dissipation
coefficient, $\gamma<1$ is the inverse of the number of hopping sites/voltage
divisions and $\Gamma$ is the gamma function. In the inset of Fig. 2, a
rescaling of the data in Fig. 2 has been made by plotting
$\frac{I}{T^{\alpha+1}}$ versus $\frac{eV}{k_{\mathrm{B}}T}$ on a log-log
scale. $\alpha=9$ was taken as a fixed parameter in the model to compare with
the results from Richter et al 25. When $\alpha$ is fixed, $\gamma$ determines
the transition from a thermally-activated regime, where
$\frac{I}{T^{\alpha+1}}$ is proportional to $\frac{eV}{k_{\mathrm{B}}T}$, to a
bias-driven regime, where $\frac{I}{T^{\upalpha+1}}$ scales as
$(\frac{eV}{k_{\mathrm{B}}T})^{\alpha+1}$. A guide to the eye is plotted for
$\gamma=0.378$, which shows reasonable agreement with the data. This
corresponds to a voltage division over an average of roughly $3$ segments
within a distance of 30 nm.

9-AGNR devices with needle-like 10-nm MoRe nanogaps are also characterized at
room temperature in vacuum. In Fig. 3 we show a representative SEM image of
the needle-like MoRe electrodes. The GNR film was transferred onto 32 pre-
fabricated nanogaps. The current is measured versus the applied bias voltage
up to 1 V. $IV$ curves of the conductive devices are shown together in Fig. 3.
Three devices are found to have a current above the noise level within this
range. The $IV$ curves are nonlinear with a maximum current of 1 to 5 pA. The
electrical characteristics of the two devices shown by the blue and orange
curves display an asymmetry in current versus the bias-voltage which is mostly
independent of the polarity of the source-drain contacts and can be explained
by a capacitive coupling of the source and drain electrodes to the GNRs (see
SI, section 3). The current through the junctions was also characterized
versus local bottom-gate voltage ($V_{\mathrm{gate}}$) at a fixed bias voltage
of $V$ = 1 V. This is shown in Fig. 3 for the device represented by the green
$IV$ curve in Fig. 3. The sweep directions of the gate voltage are indicated
by the arrows. The observed hysteresis (additional results on time dependence
in SI, section 4) in the trace and retrace gate-sweeps is similar to what has
been reported for 7-AGNR devices at room temperature in air 42, as well as in
vacuum for 5-AGNR and 9-AGNR devices for temperatures between 5 and 262 K 43.
Furthermore, the current is the largest at negative gate voltages, which is
indicative of p-type behavior of the 9-AGNR FETs.

Similar to the measurements on the wide-nanogap geometry, the $IV$
characteristic of the 10-nm nanogaps is measured versus temperature
(measurements of another device in SI, section 1). At a fixed
$V_{\mathrm{gate}}\leavevmode\nobreak\ =\leavevmode\nobreak\
-2\leavevmode\nobreak\ V$, $IV$ curves were first measured cooling down from
290 K to 160 K, below which the current gets smaller than the noise floor of
100 fA. To obtain additional information, $IV$ curves are also measured
warming up from 290 K to 350 K. The resulting curves are shown in Fig. 3 as a
colormap, with a few individual traces in Fig. 3. As observed in the wide-
nanogap MoRe GNR devices, the current decreases by orders of magnitude as the
temperature is lowered. In the needle-like MoRe devices, the asymmetry of the
current with bias voltage also increases as the temperature is decreased. In
contrast to what was observed in the wide-nanogap geometry in Fig. 2, the
slope of the log(current)-voltage characteristic is smaller in the 10-nm
nanogap devices. The temperature dependence of the current at a bias voltage
of 1 V versus inverse temperature is plotted in Fig. 3. Activation energies
are once again extracted by fitting the current versus temperature at $V=$ 1 V
using equation 1, which results in $E_{\mathrm{a}}=138$ meV for $T<290$ K and
$E_{\mathrm{a}}=454$ meV for $T>290$ K. The obtained $E_{\mathrm{a}}$ for the
MoRe 9-AGNR devices are an order of magnitude larger in 10-nm nanogap than
those found for the wide-nanogap geometry.

Finally, we measured the $IV$ characteristic of 9-AGNR devices with 10-nm
nanogap geometry made of the larger work function noble metal Pd as a function
of temperature. Pd is well-known for making low-resistance Ohmic electrical
contacts to CNTs, as well as GNRs 5, which makes it an excellent metal to
compare with MoRe as a reference. Out of the 32 devices onto which 9-AGNRs
were transferred, 2 were found to be electrically conductive. The $IV$ curves
at various temperatures for one device are shown in Fig. 4a (measurements of
another device in SI, section 1. Furthermore a nuclear tunneling scaling
analysis can be found in the SI, section 5). The $IV$ characteristic of the
selected Pd device is bias symmetric. The slope of the log(I)-V characteristic
is small, but larger than that measured for the MoRe 10-nm nanogaps. The
devices with Pd contacts show a weaker temperature dependence of the $IV$
characteristics than those with MoRe contacts (shown in Fig. 3). At $T=10$ K,
the current is still orders of magnitude above the noise level, with currents
up to $300$ pA at $1$ V bias voltage. In Fig. 4b the $IV$ characteristic of
the 10-nm Pd nanogap 9-AGNR device is compared with that of the most
conductive MoRe nanogap of the same geometry, at room temperature. The
conductance of the MoRe devices is four orders of magnitude smaller than the
Pd devices at a bias voltage of $1$ V.

## Discussion

In the $IV$ characteristics of wide-nanogap MoRe 9-AGNR devices, one thing
that stands out is the variation in conductance by 4 orders of magnitude. Some
variation is expected due to inherent uncertainty in the transfer method. The
GNRs are not globally aligned and may have lost local alignment during the
transfer. The numbers of GNRs present in the different devices varies due to
the inherent randomness of GNR film growth and positioning on the devices.
Improvements can be made with regard to the effect of GNR alignment by growing
and transferring globally aligned GNRs on Au (788) surfaces onto devices. In
this case the alignment can be also be monitored by polarized Raman
spectroscopy44. For 5-AGNR devices, aligned growth on Au (788) has been shown
to significantly improve the device yield and conductance23. The variation in
device conductance over orders of magnitude however points towards large
variation in GNR conductance. This could possibly be explained by oxidation or
inhomogeneity of the sputtered MoRe alloy contact, which would results in
additional tunnel barriers and spatially varying work functions. Another
possible explanation is that the gold etchant introduces a spatially non-
uniform doping profile over the devices, resulting in variable band alignment.

Another peculiarity is the kink at 80 K in Fig. 2, which is suggestive of a
change in the transport regime. The kink occurs at a voltage of approximately
$\pm$200 mV, for which $eV/k_{\mathrm{b}}T\approx 200\leavevmode\nobreak\
\mathrm{meV}\leavevmode\nobreak\ /\leavevmode\nobreak\ 6.6\leavevmode\nobreak\
\mathrm{meV}\approx 30$. This corresponds to the kink in the nuclear tunneling
scaling plot in the inset of Fig. 2. In the context of the nuclear tunneling
model, this suggests that the kink may be a transition from a thermally
dominated regime to a bias voltage-driven regime.

The fact that the temperature and voltage dependence of the wide-nanogap MoRe
9-AGNR devices can be described using a nuclear tunneling model is surprising,
considering the fact that the contact spacing is smaller than the average
length of the GNRs. The earlier study by Richter et al. 25 described a
possible hopping process from ribbon to ribbon. This suggests that either the
dominant transport path is through roughly $3$ GNRs or that the hopping
process occurs within single GNRs with a length scale between
$30\leavevmode\nobreak\ \mathrm{nm}\leavevmode\nobreak\ /\leavevmode\nobreak\
3=10$ nm and $45\leavevmode\nobreak\ \mathrm{nm}\leavevmode\nobreak\
/\leavevmode\nobreak\ 3=15$ nm. The hopping sites may be local trap states, in
which case the sub-sections in the GNR itself act as the charge transport
barrier. Such trap states could be present due to a multitude of possible
causes, such as overlapping of the GNRs due to rearrangement during substrate
transfer, iodine doping after the conventional wet transfer technique used for
the wide-nanogaps, as well as adsorbates or charge puddles 45, 46. If the
transport through our wide-nanogap MoRe devices is dominated by trap sites,
that may also explain the large variability in resistances. A sparse trap
density with random placement/barrier widths could result in a large variation
in conductance.

For the needle-like devices, the expected device yield, based on random
angular alignment only, is $30^{\circ}/180^{\circ}=1/6\approx 16\%$. This is
significantly larger than the observed yield, which suggests that there is a
mechanism that decreases the observed device yield. We identify two possible
mechanisms that could reduce device yield. Firstly, the probability of a GNR
to bridge the electrodes could be reduced by rearrangements of the GNR film.
Clustering/stacking of GNRs, variations in GNR density or the dissolution of
GNRs into the PMMA layer and contact defects such as surface oxidation could
reduce the device yield (See SI, section 6, for the Raman spectra on MoRe).
Secondly, the observed device yield can be lower than the number of devices
containing GNRs. We suspect the latter could be the case as the measured
devices are close to the lower limit of measurable conductances in our setup
($\sim 0.1$ pS)

The $IV$ characteristic of the needle-like MoRe nanogap 9-AGNR devices display
a significantly smaller slope of the log(current)-voltage characteristic. The
most likely explanation for this is the gate voltage of $-2$ V, applied to
improve the signal-to-noise ratio. In SI section 7, we show that the
normalized $IV$ curves get increasingly more linear as the gate voltage goes
from $0$ to $-4$ V. Another possible reason for the difference in linearity is
that the dominant transport mechanism for these junctions is different, as
transport can occur over a source-drain distance of only $6$ nm. This distance
is smaller than the segment length found for the wide-nanogap MoRe devices.

From the temperature dependence of the $IV$ characteristic at $1$ V, the
extracted $E_{\mathrm{a}}$ can be related to the band alignment of the contact
metal with the valence band of the GNR at p-type contacts. A lower
$E_{\mathrm{a}}$ implies better band alignment and a smaller Schottky barrier.
The $E_{\mathrm{a}}$ extracted for the MoRe-based 9-AGNR devices are an order
of magnitude larger in 10-nm nanogaps compared with that in wide nanogaps.
Note that for these devices, the used geometry, gate dielectric, and transfer
methods are different.

We believe it is unlikely that the geometry itself plays a significant role in
the band alignment on the metal surface. It is possible that the
high-$\upkappa$ HfO2 and Pt local gate influence the band alignment if the
GNR-metal contact is close to the oxide interface. The effective vacuum
($\upepsilon_{r}=1$) distance between the Pt and the GNR is about $0.5$ \- $1$
nm. For CNTs embedded in Pt, an expected p-doping of $0.75$ eV was found by
ab-initio calculations using a density functional theory + non-equilibrium
Green’s function simulation 47. Assuming a similar doping effect for GNRs over
a larger distance than the van der Waals gap of $0.33$ nm 48, the expected
doping is of the order of $0.33\leavevmode\nobreak\
\mathrm{nm}\leavevmode\nobreak\ /\leavevmode\nobreak\ 1\leavevmode\nobreak\
\mathrm{nm}\times(0.75\leavevmode\nobreak\ \mathrm{eV})=240$ meV, which is in
magnitude comparable to the observed mismatch in activation energies. This
would however result in a better valence band alignment of the GNRs in the
10-nm nanogap devices and lower activation energies, which is the opposite of
what was observed. Thus this explanation based on geometry can not explain our
observations.

The transfer method may also influence the MoRe/GNR contact by means of
doping. In particular, the gold etchant step, which produces iodine complexes,
is known to result in p-type doping of graphene 49. Nanoparticle gold residues
can also potentially introduce n-doping50. In the PMMA-membrane-based transfer
technique, no contact of the gold etchant with the electrode was made and a
considerably longer rinse and soak time, 8 to 24 hours versus 5 minutes, was
used after the gold etchant step. This could have resulted in a lower doping
level of the GNRs when compared to the conventional polymer-free wet transfer
(used for wide nanogaps) and consequently worsen the band-alignment with MoRe.
Besides, the GNRs are covered by PMMA after the membrane-transfer, which may
by itself influence the doping of the GNRs.

To get a better understanding of the quality of the MoRe-GNR contact, a
comparison with other contact metals is desirable. Activation energies are not
as widely reported in the literature as room temperature resistances 5, 17,
25, 19, 51. Thus, to compare with other devices, we use the room-temperature
resistance per unit of contact width as a benchmark, similar to what is done
for 2D materials 52. The conductance of needle-like MoRe devices with 10-nm
nanogaps is around 1 pS for a contact width of around 20 nm, while for the 2
$\upmu$m wide MoRe contacts an average conductance of approximately 1 nS was
found. This translates to a conductance per unit width of
$0.05\leavevmode\nobreak\ \mathrm{pS}/\mathrm{nm}$ and
$0.5\leavevmode\nobreak\ \mathrm{pS}/\mathrm{nm}$, respectively.

For comparison, our Pd 10-nm nanogaps exhibit a current of 1 nA at 0.1 V,
resulting in a conductance of 10 nS over the contact width of around 20 nm,
which translates to $500\leavevmode\nobreak\ \mathrm{pS}/\mathrm{nm}$. With
the sample contact geometry and PMMA-assisted GNR transfer technique, the
reference Pd nanogaps show significantly lower resistances than the MoRe ones.
Together with the reduced temperature dependence, this suggests that the band
alignment of the Pd work function with the 9-AGNR valence band is better. This
could have been partially expected based on the fact that the work function of
Pd ($5.12$ eV 53) is larger than the work function of MoRe ($4.6$ \- $4.96$ eV
54, 55) (See SI, section 8, for a schematic of the estimated band alignment).
Another possible explanation for a larger contact resistance for MoRe contacts
is the presence of a thin insulating layer on the MoRe surface. Although MoRe
alloys are known to have noble-metal-like properties, surface oxidation is yet
possible 56.

Recently, 9-AGNR devices with Pt wide-nanogap contacts have been studied at
room temperature 51. It was found that the devices made by PMMA-based GNR
transfer have a larger contact resistance than those made by polymer-free GNR
transfer. This results suggests that it is well possible that the difference
observed between the average conductance of the two types of MoRe devices
could similarly in part be an effect of the two different transfer methods.
For 1-$\upmu$m wide Pt contacts with 50 nm spacing, the reported average
conductance for the devices made with PMMA-based GNR transfer and with
polymer-free GNR transfer is $1.0\leavevmode\nobreak\ \mathrm{pS}/\mathrm{nm}$
and $100\leavevmode\nobreak\ \mathrm{pS}/\mathrm{nm}$, respectively.

As a final remark, we note that our MoRe contacts to GNRs show larger contact
resistances than expected based on studies on MoRe-CNT junctions, in which
resistances smaller than $1$ M$\Omega$ per nanotube were obtained 34, 35. A
possible explanation for this difference could be that in studies with CNTs,
nanotubes were grown or annealed at temperatures higher than $850$ ∘C on top
of the MoRe contacts, resulting in molybdenum-carbon end bonds. Since no such
annealing step was performed for our GNR devices, we do not expect chemical
bonds between the MoRe and the GNRs. Another possible explanation for the high
resistance of our 9-AGNR devices made with MoRe is that the work function of
MoRe is too low to achieve a good p-type contact, while it is closer to the
work function of graphene ($4.62$ \- $4.7$ eV 57, 58). This explanation is
supported by the ambipolar response in the gate dependence of our MoRe
devices, which we show in Fig. S5 and Fig. S6 in the SI. This suggests that
MoRe could still be a good contact metal for GNRs with smaller band-gaps, such
as 17-AGNRs 59, while larger band-gap GNRs are better contacted by high work
function metals such as Pd and Pt.

For 9-AGNR devices with superconducting contacts, further advances could be
made by doping the 9-AGNRs or modifying the metal/9-AGNR interface by thermal
annealing. To reduce contact resistances with MoRe, GNRs with smaller band
gaps could also be considered. In addition, the effective work function of
superconductors such as MoRe, Nb or NbTiN could be increased, and thus brought
into better alignment with valence band of GNRs, by applying a thin coating of
Pd or Pt to their surface, e.g. in a hybrid Pd/MoRe heterostructure.

## Conclusion

9-atom-wide armchair GNRs were transferred onto pre-fabricated wide and 10-nm
MoRe nanogap contacts, as well as onto Pd electrodes with 10-nm nanogaps. To
facilitate GNR transfer onto chemically fragile electrodes, we introduce a
PMMA-membrane assisted transfer technique for the 10-nm MoRe nanogap contacts,
which allows for controlled handling and micron-precise placement of the GNR
film without exposing the electrodes to any liquid. We characterized the
conductance of the devices as a function of bias voltage and temperature. In
the devices, the electrical resistance increases with decreasing temperature.
The $T$-dependence of the $IV$ characteristics of the wide MoRe nanogap
devices can be described by a nuclear tunneling model with a dimensionless
dissipation coefficient $\alpha=9$ and $n=3$ hopping sites. This is despite
the average GNR size of 45 nm exceeding the electrode separation of 30 nm. In
comparison, the needle-like MoRe 10-nm nanogaps show a stronger $T$-dependence
of conductance with an order of magnitude larger activation energies. The
10-nm MoRe nanogaps also show field-effect response to the local gate,
indicating a p-type metal-semiconductor contact. Pd nanogaps show four orders
of magnitude higher conductance for the same bias voltage at room temperature
with smaller activation energies than MoRe nanogaps. That suggests the
possibility of using Pd/MoRe bilayer thin film electrodes for obtaining low-
resistance electrical contacts to GNRs for the realization of superconducting
metallic electrodes with a nano-scale geometry down to the limit of addressing
a single GNR.

### Methods

GNR synthesis. 9-AGNRs were synthesized from 3’,6’-diiodo-1,1’:2’,1”-terphenyl
(DITP) 37. Au(111)/mica (Phasis, Switzerland) surface was cleaned in ultrahigh
vacuum by two sputtering/annealing cycles: 1 kV Ar+ for 10 min followed by
annealing at 470 ∘C for 10 min. In the next step, the precursor monomer DITP
was sublimed onto the Au(111) surface from a quartz crucible heated to 70 ∘C,
with the substrate held at room temperature. After deposition of approximately
one monolayer DITP, the substrate was heated (0.5 K/s) to 200 ∘C for 10
minutes to activate the polymerization reaction, followed by annealing at 400
∘C (0.5 K/s) for 10 minutes to form the GNRs via cyclodehydrogenation.

Fabrication of contact electrodes. For all devices, 285 nm SiO2 on highly-
doped p-type Si substrates were cleaned in red fuming nitric acid for at least
5 min. prior to processing. This was followed by a 5 min. O2 plasma step at a
flow of 600 sccm and a power of 600 W in a barrel etcher prior to spin coating
of e-beam resist. For the wide-nanogap MoRe devices, the e-beam resist AR-P
6200.04 was spin-coated onto the substrates at 4000 RPM and baked at 185 ∘C
for 3 min., resulting in an 80 nm thick film.

The wide-nanogap geometry was written by an e-beam pattern generator at 100 kV
with a $200$ $\upmu$m aperture at a beam current of $800$ pA. The exposed
pattern was developed in pentyl acetate for 1 min., followed by a 5 s descum
in xylene 60 and a 30 s rinse in isopropyl alcohol, followed by N2 blow
drying. A 62:38 MoRe alloy was RF sputtered at an argon pressure of 15
$\upmu$bar and a power of 100 $W$ for 1 min to yield an approximately 20 nm
thick layer. Finally, metal lift-off was performed by soaking the samples in
the remover AR 600-71 at 70 ∘C, followed by a rinse in isopropyl alcohol and
N2 blow drying.

For the e-beam exposure of the needle-like nanogap pattern an overdose-
undersize (ODUS) procedure with a shape-proximity error correction algorithm
was performed 61, 62. The development was done in pentyl acetate developer
that was cooled to $-16$ ∘C in a freezer, as this has been shown to improve
contrast for resists that are exposed by polymer chain scission 63. Upon
overdosing to 1000 - 2000 $\upmu\mathrm{C\ cm^{-2}}$ the pattern, 6 - 10 nm
electrode separations result. The contact pads were kept further than 100
$\upmu$m from the nanogaps to minimize exposure by back-scattered electrons
and exposed at 600 $\upmu\mathrm{C\ cm^{-2}}$. MoRe was sputtered in the same
manner as described for the wide-nanogap contacts. 5 nm Ti and 12 nm Pd were
deposited by e-beam evaporation at a rate of $0.05$ nm/s and $0.1$ nm/s
respectively.

The MoRe needle-like electrodes were made on top of an evaporated 5 nm Ti + 10
nm Pt local bottom gate covered by a 12 nm thick HfO2 high-$\upkappa$
dielectric layer made by atomic layer deposition at 110 ∘C.

PMMA-membrane fabrication

The procedure for suspension and transfer of the PMMA membranes, based on the
technique by Kaverzin et al.64, is as follows; We start with spin coating a
thick layer of a water-soluble polymer, in this case, Elektra 92, onto silicon
oxide wafers. Next, a 1000 $\upmu$m thick layer of PMMA 950K was spin-coated
onto the Elektra 92 layer in two steps, baked at 180 ∘C for 1 min after each
step. A rectangular hole was cut in a piece of scotch tape, which was
subsequently pressed against the PMMA membrane on silicon. The scotch tape was
suspended over a beaker filled with DI water with the silicon piece submerged
to dissolve the Elektra 92. After the silicon piece detached from the PMMA
membrane, the membrane was rinsed and left to dry in ambient conditions. The
dry PMMA membrane was next stretched over a piece of Polydimethylsiloxane
(PDMS), placed on a glass slide.

##  1 Acknowledgments

This work was supported by the Netherlands Organisation for Scientific
Research (NWO/OCW), as part of the Frontiers of Nanoscience program. T.S.G.
also received funding from the European Union Horizon 2020 research and
innovation program under grant agreement no. 863098 (SPRING). G.B.B., P.R. and
R.F acknowledge the European Union Horizon 2020 research and innovation
program under grant agreement no. 881603 (GrapheneFlagship Core 3) and the
Office of Naval Research BRC Program under the grant N00014-18-1-2708. G.B.B.,
P.R. and R.F. also greatly appreciate the financial support from the Werner
Siemens Foundation (CarboQuant). This research was funded, in whole or in part
by the Swiss National Science Foundation under Grant No. 200020_182015. For
the purpose of Open Access, the author has applied a CC BY public copyright
license to any Author Accepted Manuscript version arising from this submission

## Supporting information

See the supporting information for an analysis of additional devices,
additional electrical characterization, Raman spectroscopy characterization of
the transferred 9-AGNR films, band diagrams and optical microscopy images of
the MoRe 9-AGNR devices.

## Author Declarations

### Conflict of Interest

The authors have no conflicts to disclose.

## Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon request.

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