Tuneable Current Rectification Through a Designer Graphene Nanoribbon

Unimolecular current rectifiers are fundamental building blocks in organic electronics. Rectifying behavior has been identified in numerous organic systems due to electron‐hole asymmetries of orbital levels interfaced by a metal electrode. As a consequence, the rectifying ratio (RR) determining the diode efficiency remains fixed for a chosen molecule‐metal interface. Here, a mechanically tunable molecular diode exhibiting an exceptionally large rectification ratio (>105) and reversible direction is presented. The molecular system comprises a seven‐armchair graphene nanoribbon (GNR) doped with a single unit of substitutional diboron within its structure, synthesized with atomic precision on a gold substrate by on‐surface synthesis. The diboron unit creates half‐populated in‐gap bound states and splits the GNR frontier bands into two segments, localizing the bound state in a double barrier configuration. By suspending these GNRs freely between the tip of a low‐temperature scanning tunneling microscope and the substrate, unipolar hole transport is demonstrated through the boron in‐gap state's resonance. Strong current rectification is observed, associated with the varying widths of the two barriers, which can be tuned by altering the distance between tip and substrate. This study introduces an innovative approach for the precise manipulation of molecular electronic functionalities, opening new avenues for advanced applications in organic electronics.


Introduction
Quantum electron transport through single molecules offers the possibility of replicating functionalities of electronic devices with customized organic elements.Such a basic idea is the foundation of organic electronics, as launched by the seminal proposition of Aviram and Ratner for a molecular structure behaving as a diode. [1]ystematic measurements found that nonlinearities in electronic conductance are ubiquitous in molecular systems, [2] owing to their discrete orbital level alignment. [3,4]urthermore, the flexible character of molecules offers novel schemes of current rectification, e.g., related to induced conformational changes. [5,6]To date, singlemolecule-based rectifiers are mostly small soluble molecules [2] and offer limited in situ control over key characteristics like their current rectification ratio (RR) [7][8][9] or rectification direction. [10]n recent years, the combination of in-solution synthesis of organic precursor molecules with thermally-driven onsurface synthesis strategies (OSS) [11] successfully integrated different functionalities in single graphene nanoribbons (GNRs).Designer GNR architectures were synthesized incorporating sharp donor-acceptor interfaces, [12,13] quantum dots, [14,15] magnetic units, [16,17] or even luminescence active elements. [18,19]In these complex systems, sharp potential barriers were precisely inserted through the shape, [13,15] the atomic substitution of heteroatoms [12,20] or by attaching functional groups, [21] and their functionality was corroborated by precision spectroscopic measurements utilizing scanning tunneling microscopy.[28][29][30][31] In this article, we demonstrate the extraordinary current rectification of an atomically precise engineered GNR diode exhibiting a large mechanically tunable RR (>10 5 ), which can be controlled over several orders of magnitude and also be biasreversed.The GNR consists of a narrow armchair graphene nanoribbon (a seven-atom wide armchair GNR, 7AGNR) containing a single unit of substitutional diboron dopant inside (2B).The boron-doped GNR (2B-GNR) is synthesized on a Au(111) surface  [20] originating from the symmetric and antisymmetric linear combination of the topological boundary states.The spins in the two O2B orbitals are aligned.b) Sketch of the ribbon's band structure projected into a finite-sized molecule in real space.The VB and CB are confined into two separate segments by the 2B-unit resulting in quantum well states.Different segment lengths result in different band onset energies.The topological boundary state emerges around the 2B-unit inside the band gap.c) dI/dV spectra for a 2B-GNR (red, z = 5.8 nm) and a pristine 7AGNR (blue, z = 6 nm).The two dominant features V − and V + are present in both systems and attributed to resonant band transport, while the two peaks V − 2B and V + 2B appear between the band transport peaks V − and V + only in the doped system, as shown enlarged in the inset.The red curve is shifted vertically by 5 nS for easier comparison.Left: Sketch of the ribbon suspended between tip and substrate with the tip retraction z and the tip-2B-unit distance d 2B indicated.d) Lewis structure of a borylated ribbon segment and STM topography image of the 2B-GNR (V = −300 mV, I = 30 pA).The red cross indicates the position from where the ribbon was lifted.
by diluting a small amount of borylated bisbromo-trianthracene organic molecules with the bianthracene precursors normally used to form 7AGNRs. [14,20] The diboron unit induces two singlyoccupied states of topological origin [20] localized at either side of the dopant.The two states mix forming a doubly-degenerate in-gap bound state extending to both sides of the 2B dopant (Figure 1a). [20,32]This boron-induced in-gap state is half occupied with two electrons.Consequently, it appears split into the occupied (O2B) and unoccupied (U2B) spectral levels shown in Figure 1b, which enable hole and electron resonances for the electrical transport, respectively.Importantly, the 2B-dopant is also a potential barrier for the frontier bands of the 7AGNR, [14] which are then split into two segments and laterally confined to form quantum well states (VB nT and VB nS , n = 1, 2, 3,… in Figure 1b).In our experiments, we investigated quantum transport through a 2B-GNR suspended between the tip and the surface of an STM and found fingerprints of unipolar hole transport at both bias polarities.Our results reveal a mechanism for asymmetric hole transmission governed by the relative lengths of the two 7AGNR segments, defined by the tip-substrate distance.This mechanism forms the basis of the observed tunable current rectification.

Unipolar Transport Through the 2B-State
We performed two-terminal electronic transport measurements in GNRs suspended between the tip and a Au(111) substrate of a low-temperature scanning tunneling microscope [17,20,27] as sketched in Figure 1c.To reach this configuration, the STM tip is positioned above one termination of the ribbon (e.g., over the red cross in Figure 1d), and gently approached toward the substrate until a bond between tip and ribbon forms.Upon retracting the STM tip, the ribbon is partially lifted from the substrate, creating the two-terminal transport configuration.Since the ribbons are semiconducting, their linear conductance for small voltage biases drops exponentially with increasing tip substrate distance z, with a decay constant that is characteristic of co-tunneling through the GNR bandgap. [27]o study the transport through a single 2B-dopant group, we retracted the ribbon to a tip height z larger than d 2B , the spacing between the 2B site and GNR's end.Close to z ∼ d 2B , the detachment of the 2B moiety from the surface is detected in STS spectra as a faint Kondo resonance. [20]A dI/dV spectrum recorded above this point reveals two sharp peaks, V − and V + in Figure 1c.They correspond to the onset of resonant band transport through the 7AGNR segments of the suspended ribbon as they are equally observed for a pristine 7AGNR lifted to a similar tip height (blue plot in Figure 1c).
In the 2B-GNRs, we observed additional spectral features between the band transport resonances.For the ribbon in Figure 1c, these in-gap features consist of two weaker dI/dV peaks at V − 2B = −0.5 V and V + 2B = 1.07 V, shown in the figure's inset.At the retraction height of z = 5.8nm > d 2B , the 2B moiety lies in the freestanding segment of the ribbon and provides an exponentially localized state, which is decoupled from tip and substrate by the two pristine GNR segments and located in the ribbon's band gap (as in Figure 1b).In this configuration, electrical transport proceeds in a double-barrier fashion, where a fraction V (0 <  < 1) of the tip-substrate bias V drops between tip and 2B-state, and the rest (1-)V between boron moiety and substrate, i.e.,  quantifies the electrostatic coupling.The position of the V ± 2B peaks in the spectra depends on the energy alignment of the 2B-states with respect to the chemical potential of the system ( and ′ for the occupied and unoccupied state in Figures 1b and 2b) and on the value of .Specifically, , , and ′ determine if the electrical transport is ambipolar (both O2B and U2B drive carriers at either polarity) or unipolar (resonant transport flow through only one of these states at either polarity). [33,34]o decipher the transport mechanisms behind the two ingap resonances, we modified  by increasing the tip height, i.e., increasing the size of the 2B-substrate barrier, and studied changes in the dI/dV spectra.In Figure 2a, we plot a set of dI/dV spectra recorded in the range 2.1 nm < z < 8.3 nm as a color map that pictures the peak evolution with z.The position of both peaks V − 2B and V + 2B shifts with z toward more negative values, while their spacing is rather constant (see Supporting Information for a detailed discussion).Note that the amplitude of V − 2B is fairly constant during retraction, while V +
We modeled the z-dependency of the position of both V 2B peaks by assuming that the fraction of potential drop  scales with the ratio z/d 2B , as in a parallel plate capacitor.Figure 2b details the conditions for resonant transport in the different transport configurations, which lead to analytical expressions for the z-dependence of the V − 2B and V + 2B peaks (see Supporting Information for details).Using these expressions, we fitted in Figure 2c the peak positions V − 2B and V + 2B from Figure 2a with the ambipolar (blue line) and unipolar (red line) resonant transport model.Both models perfectly reproduce the z-dependence of V − 2B , which represents hole transport via the occupied 2B-state, i.e., the O2B + resonance.However, the energy shift of the V + 2B peak with z is only reproduced in the case of unipolar transport, while the ambipolar behavior results in an opposite height dependence.The unipolar transport model even reproduces accurately a minute non-linearity observed only in the shift of V + 2B .Therefore, we attribute both V − 2B and V + 2B peaks to unipolar hole transport through the O2B + resonance, and discard resonant electron tunneling through the (negative ion) state U2B − .The unipolar transport model also provides analytical expressions for the electrostatic coupling , with the elementary charge e.We used these expressions to obtain the value of these two quantities at each value of z from the experimental data available, without further assumptions (Figure 2d).We find that  decreases monotonously with increasing z.This agrees with the continuous increase of the 2B-surface barrier width, which increases 1 − , as the tip retracts. [35]Accordingly, a second GNR with the 2B-unit closer to the tip by ≈ 0.9 nm (orange symbols in Figure 2d, refer to Figure S2, Supporting Information, for the conductance map) shows a similar decay of  with z but with a ≈ 5% smaller value.Furthermore, the energy  + of the O2B + hole resonance also shifts away from the Fermi level with increasing z (Figure 2d), from ≈ −300 to −400meV.We attribute the shift of  + to the reduction of the Au(111) surface-induced hole doping of the GNR [36] as the ribbon is lifted from the surface. [30]

Current Rectification
A striking feature of the conductance map in Figure 2a is that, at negative voltage, the dI/dV amplitude of O2B + hole resonance remains rather constant during the whole retraction, even for separations as large as z = 8 nm.However, the amplitude of the resonance at positive bias voltage decreases monotonously with z.To quantify this, we compare in Figure 3a the linear conductance G(V, z) of the V ± 2B resonances.The values of the negative ) |I|-V-curves taken from z = 4.9 nm (bright red curve) to 6.7 nm (dark red curve) in steps of Δz = 0.3 nm.At negative bias, the onset current remains approximately constant.In stark contrast, the onset current at positive bias reduces exponentially.Note that the onset current at negative bias (I ≈ −20 pA) slightly increases resulting in constant linear conductance.c) Sketch of the VB-extension of the one-level unipolar transport model for the GNR suspended between tip (left) and substrate (right).The tip-O2B + distance is determined by the chemical structure of the ribbon, i.e., a constant tunneling barrier width, while the O2B + -substrate distance changes with z resulting in a variable tunneling barrier width.Hole tunneling from tip (V < 0) or substrate (V > 0) to the O2B + hole resonance limits the tunneling rate, resulting in a constant (z-dependent) transmission for V < 0 (V > 0).The finite voltage drop across the 2B-state brings the valence band in the second ("grey") segment of the ribbon closer to the O2B + resonance, facilitating the fast hole relaxation into to the second electrode.
bias conductance G(V − 2B , z) (filled circles) remain fairly constant during the whole tip retraction.On the other hand, G(V + 2B , z) decreases exponentially (open circles), and changes by six orders of magnitude during the 4 nm retraction, with decay constant  + = 3.4 ± 0.1 nm −1 .The ratio of resonant conductance G(V + 2B )∕G(V − 2B ) (defined as resonant RR) changes by six orders of magnitude over the observed z interval (from ≈ 10 3 to 10 −3 ), showcasing a widerange in situ-tunability of the GNR's diode character, exceeding other tunable devices. [6,7,37]Notably, the forward bias direction reverses at z = 5.7 nm.At this elevation, the diboron unit lies around the midpoint of the tip-surface gap.The inversion of rectification direction has so far only been achieved by chemical modifications to the employed molecule, [9] further evidencing our extraordinary ability of mechanical control over the rectification behavior of the molecular diode.
The corresponding current-bias traces recorded in the range 4.9 nm ⩽ z ⩽ 6.7 nm (Figure 3b) reveal sharp current onsets upon reaching resonance conditions, followed by a constant current plateau.While for negative bias the current plateau amounts to I ≈ 20 pA independently of z, at positive bias the current value is strongly sensitive to z.A non-resonant RR, defined as RR nr = |G(V)/G(− V)|, quantifies the diode character of the borylated GNR in an alternative way.A RR nr in the range of 10 5 − 10 3 is reached at low bias voltage (±0.5 V) and z < 5.5 nm.
To rationalize the large current rectification in the unipolar transport via the 2B-state, we consider the tunneling channel opened by the O2B + resonance (see Figure 3c).As evidenced in Figure 2, hole transport proceeds through the 2B-state when the positive-ion state O2B + aligns with either tip's (V < 0) or substrate's (V > 0) chemical potential.At negative bias, hole tunneling from the tip is the rate-limiting process (blue arrow in Figure 3c bottom), which remains constant with z because the width d 2B of the tip-2B barrier is fixed.At positive bias, the ratelimiting step is hole tunneling from the substrate through the GNR barrier (blue arrow in Figure 3c top), which increases with z.Therefore, conductance at positive bias decreases exponentially as the ribbon is lifted.The presence of the two segments of GNR valence band at ≈ 200 mV below the 2B-state reduces the apparent height of the barrier for hole tunneling and enables tunneling over large distances. [29,30]Additionally, a finite voltage drop across the 2B-state can alter the relative alignment of the two valence bands with respect to the O2B state, potentially lowering the height of the "second" tunneling barrier further and, thus, facilitating the fast relaxation of the hole into the second electrode at either bias polarity (grey arrows in Figure 3c).
Elevating the bias beyond resonant transport through the 2Bstate enables resonant band transport at V + and V − .The dI/dV peaks V + and V − , and the peaks V + 2B and V − 2B exhibit essentially identical energy shift with z, evidencing that the band resonances found at higher bias correspond to unipolar resonant transport via the VB (V ± in Figure 2a, see also Supporting Information for a detailed discussion).Most importantly, this enables efficient current rectification for bias voltage up to 1 V.The corresponding current plateau of 2 nA at negative bias voltage is accessible over a large z-interval and exhibits RR nr > 10 6 , exceeding values of reported molecular diodes. [38,39]

Resonant Phonon and Quantum Well States
The peaks V − 2B and V + 2B are accompanied by a set of satellites (Figure 4) with equidistant energy spacing, which originates from unipolar resonant tunneling through vibronic states. [34,40]The features show a characteristic amplitude pattern indicating that the same Franck-Condon coefficients govern the vibronic modes independent of the voltage polarity.Fitting the satellite peak's energy by a linear regression (inset of Figure 4a), we obtain the excitation energy eV ±  at positive and negative bias.with their satellite structure.The equidistant spacing is the fingerprint of vibronic modes. [34,40]The inset shows the linear regression fitted to the relative peak voltages for negative (filled circles) and positive (open circles) bias.The obtained slopes are indicated.As the vibronic states undergo the same gating as O2B, the unipolar transport model can be applied.We obtain  = 0.65 ± 0.01 and E  = 20.1 ± 0.6 meV.Note, that the relative peak intensities for both bias polarities are almost identical in agreement with unipolar transport.b) dI/dV spectra at selected z.The calculated voltages VB 2T for quantum well resonances of the confined VB are indicated by vertical lines.Spectra are offset vertically for clarity.The inset sketches the first two quantum well states of the quantized VB in the particle-in-a-box model.
The vibronic structure follows the same gating as the 2B resonances.Therefore, we can apply the set of equations from the unipolar model discussed above to determine the fundamental vibrational energy E  and the corresponding  for every z.For example, we find that E  amounts to 20.1 ± 0.6 meV and  = 0.65 ± 0.01 at z = 5.82 nm.We find that  decays with tip retraction in a similar fashion as for the 2Bstates, while E  remains constant with z (see Figure S5, Supporting Information).This excludes that E  corresponds to bending or torsional vibrations of the whole free-standing segment.Instead, as we discuss in the Supporting Information (Figures S5 and S6, Supporting Information), these peaks most probably correspond to a vibrational mode of the boron moiety.
The confinement of the VB by the 2B-state gives rise to higher order quantum well modes inside the ribbon [14] (Figure 1b and inset Figure 4b).Quantum well modes of 7AGNRs were spatially resolved by scanning tunneling spectroscopy. [14,41]The sharp transport resonances V − and V + , associated to the zeroorder quantum well mode of the VB, are traced through a series of dI/dV spectra of the 2B-GNR (VB 1T in Figure 4b).Using a simple particle-in-a-box model (see Supporting Information for details), we estimate the voltage at which the transport resonance corresponding to the second quantum well mode VB 2T between tip and 2B-state is expected (Figure 4b).Spectral resonances found above V − and V + in the dI/dV spectra reproduce accurately the voltages obtained from the particle-in-a-box model confirming the access to quantum well modes of the confined VB via unipolar resonant transport.

Conclusion
We have demonstrated the unipolar resonant transport through a boron-induced in-gap state embedded in a 7AGNR suspended between two metallic electrodes.The state is available for hole transport at both voltage polarities.This transport channel was predicted to show a large degree of spin polarization. [32]The asymmetric position of the quantum dot in the ribbon enables a large in situ tunable current rectification (RR>10 5 at V < 1 V) likely following a mechanism comparable to current rectification in asymmetric two-level molecules. [37,42,43]We are able to mechanically control the resonant RR by six orders of magnitude, including an inversion of forward bias direction.Furthermore, the presence of the boron moiety confines the valence band, creating quantum well states in the ribbon.We show that both ground and excited states of the quantized band are available for resonant electron transport.Our results extend the technological potential of atomically precise highconductance graphene nanoribbons and shine light on a novel approach for the manipulation of molecular electronic functionalities.

Experimental Section
The Au(111) substrate was prepared by sputtering the crystal with Neon ions for 10 min, followed by one annealing step at T = 740 K in ultra-high vacuum conditions (p < 10 −9 mbar) for 15 min.The ribbons were fabricated following the two-step on-surface synthesis via successive Ullmanncoupling and cyclodehydrogenation. [14,20,44] The samples were analyzed in situ in a home-built STM kept with liquid Helium at ≈6 K.The bias was applied to the substrate, while the tip was grounded.We used a PtIr tip.An atomically sharp apex termination by gold atoms was reached by controlled indention of the tip into the clean Au(111) substrate.Details on the lifting procedure to reach the two-terminal transport configuration are described in detail elsewhere. [20]The experimental data were prepared for presentation using WSxM [45] and the python matplotlib library. [46]Color maps use perceptual continuous color scales based on. [47]

Figure 1 .
Figure1.Molecular orbitals of a finite-sized free-standing 2B-GNR: a) Wavefunctions of the degenerate O2B[20] originating from the symmetric and antisymmetric linear combination of the topological boundary states.The spins in the two O2B orbitals are aligned.b) Sketch of the ribbon's band structure projected into a finite-sized molecule in real space.The VB and CB are confined into two separate segments by the 2B-unit resulting in quantum well states.Different segment lengths result in different band onset energies.The topological boundary state emerges around the 2B-unit inside the band gap.c) dI/dV spectra for a 2B-GNR (red, z = 5.8 nm) and a pristine 7AGNR (blue, z = 6 nm).The two dominant features V − and V + are present in both systems and attributed to resonant band transport, while the two peaks V − 2B and V + 2B appear between the band transport peaks V − and V + only in the doped system, as shown enlarged in the inset.The red curve is shifted vertically by 5 nS for easier comparison.Left: Sketch of the ribbon suspended between tip and substrate with the tip retraction z and the tip-2B-unit distance d 2B indicated.d) Lewis structure of a borylated ribbon segment and STM topography image of the 2B-GNR (V = −300 mV, I = 30 pA).The red cross indicates the position from where the ribbon was lifted.

Figure 2 .
Figure 2. Resonant bipolar transport through the 2B-state: a) Color map of dI/dV spectra at different tip substrate separation z.The transport resonances at V ±2B and V ± are clearly identified in the spectra for z > 3 nm.The dI/dV-signal in the top right corner has been amplified by a factor 5. A Kondo resonance (red square and inset, the color scale of the inset ranges from 0.2 to 8 nS) emerges at z = 2.8 nm upon detaching the 2B-unit from the substrate.[20]b) Comparison of unipolar transport through a single occupied energy level  and ambipolar transport through two energy levels  and ′.The conditions for resonant transport through the O2B + hole resonance  + (U2B − electron resonance  − ) are indicated for positive and negative voltage in both cases.See Supporting Information for a more detailed discussion.c) Simulated V − 2B and V + 2B as functions of z for the unipolar model (red dashed line) and the ambipolar model (blue dashed line) assuming the plate capacitor geometry and the experimental values of V − 2B and V + 2B (black crosses) extracted from (a).The inset sketches the plate capacitor model, from which follows  = d 2B /z.See Supporting Information for details on the simulation.d) Gating efficiency  and energy  + of the O2B + hole resonance for two 2B-GNR.The orange data points stem from a ribbon with the 2B-unit being ≈ 0.9 nm closer to the tip, i.e., smaller d 2B .

Figure 3 .
Figure 3. Current rectification through molecular asymmetry: a) Linear resonant conductance G(V ± 2B , z) through the O2B + hole resonance at negative (filled circles) and positive bias (open circles).The decay constants  − >5 = −0.04 ± 0.03 nm −1 (for z > 5 nm) and  + = 3.4 ± 0.1 nm −1 are obtained.The grey-shaded region corresponds to the data presented in panel (b).b) |I|-V-curves taken from z = 4.9 nm (bright red curve) to 6.7 nm (dark red curve) in steps of Δz = 0.3 nm.At negative bias, the onset current remains approximately constant.In stark contrast, the onset current at positive bias reduces exponentially.Note that the onset current at negative bias (I ≈ −20 pA) slightly increases resulting in constant linear conductance.c) Sketch of the VB-extension of the one-level unipolar transport model for the GNR suspended between tip (left) and substrate (right).The tip-O2B + distance is determined by the chemical structure of the ribbon, i.e., a constant tunneling barrier width, while the O2B + -substrate distance changes with z resulting in a variable tunneling barrier width.Hole tunneling from tip (V < 0) or substrate (V > 0) to the O2B + hole resonance limits the tunneling rate, resulting in a constant (z-dependent) transmission for V < 0 (V > 0).The finite voltage drop across the 2B-state brings the valence band in the second ("grey") segment of the ribbon closer to the O2B + resonance, facilitating the fast hole relaxation into to the second electrode.

Figure 4 .
Figure 4. Phonon and Quantum Well Excitations: a) V −2B and V + 2B with their satellite structure.The equidistant spacing is the fingerprint of vibronic modes.[34,40]The inset shows the linear regression fitted to the relative peak voltages for negative (filled circles) and positive (open circles) bias.The obtained slopes are indicated.As the vibronic states undergo the same gating as O2B, the unipolar transport model can be applied.We obtain  = 0.65 ± 0.01 and E  = 20.1 ± 0.6 meV.Note, that the relative peak intensities for both bias polarities are almost identical in agreement with unipolar transport.b) dI/dV spectra at selected z.The calculated voltages VB 2T for quantum well resonances of the confined VB are indicated by vertical lines.Spectra are offset vertically for clarity.The inset sketches the first two quantum well states of the quantized VB in the particle-in-a-box model.