Gate-Modulated Conductance of Extended Conjugation in Atomically

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C: Physical Processes in Nanomaterials and Nanostructures

Gate Modulated Conductance of Extended Conjugation in Atomically Arrayed Molecular Assemblies Isaac W. Moran, and Kenneth R. Carter J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 08 Feb 2019 Downloaded from http://pubs.acs.org on February 8, 2019

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The Journal of Physical Chemistry

Gate Modulated Conductance of Extended Conjugation in Atomically Arrayed Molecular Assemblies Isaac W. Moran*,† and Kenneth R. Carter Polymer Science and Engineering Department, University of Massachusetts Amherst, Conte Center for Polymer Research, 120 Governors Drive, Amherst, Massachusetts 01003.

ABSTRACT

Within molecular electronics, the molecular scale transistor provides a compelling and central device. While substantial efforts have been expended on this subject, current embodiments typically involve cumbersome gating with non-intuitive routes for integration. In this theoretical study we examined the efficacy of combining a new molecular architecture with the wellestablished atomic resolution of the Si(100)2x1 hydride terminated surface to provide a molecular scale modulation scheme that is conceptually easier to integrate. A series of alkyl substituted carbazoles: ethylcarbazole, butylcarbazole, hexylcarbazole, and decylcarbazole, operating in the - motif provided the transport conduit through extended conjugation of - stacking upon assembly along the Si(100)2x1 dimer row. It was found that alkyl substituent

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lengths greater than 4 methylene units (butylcarbazole) effectively isolated the extended conjugation from the underlying substrate by preventing tunneling due to breakdown at terminal alkyl chains and coupling of eigenstates between the -stack and silicon crystal. These findings were corroborated by systematically stepping through the alkyl substitution length and noting the distribution of eignstates for all peaks in the corresponding transmission spectrum of -stacked wires as well as by plotting the zero-bias resistance against wire length. The resistance plots demonstrated a single, molecularly isolated, tunneling type scaling factor β for hexyl through decylcarbazole. In contrast, an inflection point was observed for the shorter ethyl and butylcarbazole indicating a transition to dual, substrate routed, conduction pathways in these cases. Further investigation of device response to localized gate potentials demonstrated that substituent lengths greater than 6 methylene units (hexylcarbazole) could block eignestate coupling between the -stack and substrate for gate potentials in the range of -4 to 1.5 V. This degree of isolation supported a modulation factor of over a 106x in conductance. These results suggest that elongating the  group in crystalline organized - assemblies may support transistor modulation by exploiting the underlying substrate as an easily integrated gate.

INTRODUCTION The pursuit of molecular scale electronics remains a promising and heavily investigated field. Characterization of electrical transport through single molecular conductors is well documented and has revealed intriguing relationships between structure and conductance.1–3 Inherit in all systems of this scale is the general relationship between resistance and length of the conduction path for tunneling electrons which takes the form of R = R0e(βn).

(1)


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Here R is the resistance of a system of length n, with intrinsic coefficient R0 and decay parameter β.4 Variations in β can be informative with respect to tunneling pathways. From this body of knowledge has come the rise in theoretical and experimental single molecule equivalents of standard logic devices such as diods5, switches6, and transistors7, as well as new quantum mechanical capabilities like negative differential resistors8 and spin-filters.9 Out of these examples, the transistor stands as the most critical for logic execution. While promising developments in metal/molecule/metal junction type transistors have recently been achieved7, the integration of such architectures are likely hampered by uncertainty of molecular orientation, conformation, bonding, and presence of unintended entities influencing molecular transport.4 These issues are well addressed by arranging molecules on the hydride terminated Si(100)2x1 surface as demonstrated by high resolution STM characterization of surface bound molecules.10,11 In particular, molecular assemblies on this surface adopt a registration that matches the underlying atomic spacing.

Such assemblies are commonly generated by

propagation of molecular chemisoption along Si(100)2x1 dimers rows. The mechanism typically involves generation of a Si dangling bond which homolytically couples to unsaturated groups on impinging molecules. The resulting carbon centered radical abstracts a neighboring hydrogen within the same dimer row thus regenerating a Si dangling bond which continues to propagate the growth of lines along the surface. Each molecule is precisely spaced at 3.8 Å from its neighbors and this spacing is insensitive to thermodynamics or structural characteristics of the adsorbate. Indeed, if aromatic functional molecules are atomically arranged along dimers of the Si(100)2x1 substrate, the resulting - overlap leads to extended -conjugation along the assembly. This one dimensional delocalization of electrons is considered to provide a suitable conduit for electron transport. Earlier computational studies have predicted this behavior12 and


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were later supported by experimental work showing extended -conjugation in styrene13 and benzophenone10 assemblies. To some extent, modulation of extended -conjugation has been demonstrated through creation of neighboring dangling bonds13 or modeled by theoretically implementing electron withdrawing/donating groups.14 Yet, when considered as a platform for molecular electronics, challenges are anticipated with this monolayer on Si(100)2x1 arrangement. Specifically, coupling between the molecular wire and underlying Si are anticipated to hinder device operation.15 Guo et al's15 earlier description of this system type surmised that greater separation of the molecular states might decouple them from the substrate and allow gate modulation. Accordingly, in this study we sought to determine if the installation of molecular spacing groups would in fact decouple extended -conjugation and in doing so, allow modulation of transport by a proximal gate. We describe here in, a theoretical investigation of molecular structure that achieved complete isolation of extended conjugation in molecules arranged on the Si(100)2x1 surface. The molecular motif chosen for this study comprises a series of alkyl substituted carbazoles. The alkyl substituent provides a point of attachment and serves as a molecular dielectric by separating the transport conduit, formed by -stacked carbazole rings, from the Si substrate.

Using this alkyl substituted

carbazole motif, we determined that a spacer length of 4 methylene units was adequate to completely isolate the -stack from an un-biased substrate. Molecularly isolated conductance was supported by single values of scaling factor β in wire length resistance plots as well as eigenstate plots localized exclusively on the carbazole rings. We further extended the investigation by demonstrating how the isolated molecular eigenstates could be modulated by an underlying gate. Such an arrangement may provide the basis for


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simplified molecular transistor integration. Throughout the study, electron transport through test structures was determined using the well-established non-equilibrium Green’s Function – density functional theory (NEGF-DFT) method. METHODS Test structures for this study closely emulated those employed by Guo et al.15 As in those reports, our structure consisted of two Al electrodes flanking a central scattering region containing free-standing or surface bound -stacked - molecules. The bound versions were bonded to a Si(100)2x1 crystalline slab though alkyl chains. Unique to our study was the choice of aromatic moiety and the variation in alkyl chain length representing the “” region. Our aromatic group of choice was the carbazole ring due to its propensity to -stack and the relative ease of alky substitution at the nitrogen. Scheme 1. Molecular structure for alkyl substituted carbazoles bonded to the silicon hydride surface. Index m = 1 for ethyl, 3 for butyl, 5 for hexyl, 7 for octyl, and 9 for decyl.

N

m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


H Si

Si

Accordingly, the alkyl carbazoles described in this investigation are quite synthetically accessible. Representative molecular structures are depicted in Scheme 1.

The formalism

adopted in this study labels test structures as alkylcarbazole(n), where alkyl is either ethyl, butyl, hexyl, octyl or decyl and n represents the number of alkyl carbazoles stacked between the


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electrodes. Device structures with -stacked wires of length n = 6 are displayed in Figure 1. A complete device layout, illustrating the left and right electrode regions and central scattering region for ethylcarbazole(6) is depicted in Figure 2.


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Figure 1. Structures for - transport devices. Each transport structure is composed of six alkyl carbazole molecules arrayed between Al leads which extend infinitely to the left and right. Panel a) shows a free standing ethylcarbazole(6) stack, while panels (b-f) show assemblies on a Si(100)2x1 crystalline substrate with increasing length of the alkyl substituent from b) ethyl, c) butyl, d) hexyl, e) octyl, and f) decyl. Geometry optimization of - molecules on the Si(100)2x1 crystalline surface was conducted in two steps. First single, isolated versions of each - molecule were geometry optimized by applying local density approximation (LDA) with a Vosko Wilk Nussair (VWN)16,17 correlation and a Dirac Block exchange function. Calculations were deemed converged after the local force dropped below 0.05 eV/Å. The optimized molecular structures were then positioned on a two layer Si(100)2x1 unit cell, Table S1-S4. A second geometry optimization was then run on the composite -/Si(100)2x1 structure. Here, we assumed the Si(100) crystal lattice would retain its bulk structure so the coordinates for Si and H atoms in the unit cell were fixed, while the - molecule was allowed to relax.


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Figure 2. Complete device layout for ethylcarbazole(6) structure with leads of Al atoms extending infinitely left and right from boxes with a central scattering region composed of finite Al leads flanking ethylcarbazole(6) bonded to a underlying silicon hydride slab. Electrodes used in transport calculations were generated by first constructing a Al(100) fcc crystal with supercell dimensions a=6, b=6, c=2. A carbazole molecule was then placed coplanar with the ab crystal face and minimization of the carbazole geometry was carried out while constraining the Al atoms. The optimized carbazole-on-Al structure was refined for device integration by eliminating Al atoms in the 6 x 6 supercell peripheral to the area inscribed by the carbazole ring. The remaining electrode constituted a 3 x 3 Al nanowire cross-section. This step ensured isolation of extended Al electrodes from interaction with the underlying Si(100)2x1 substrate. The reduced Al-carbazole complex was then taken as a template for interfacing Al leads with optimized free standing and surface bound alkyl carbazole systems. It is noted that the final device architecture, involving unpassivated, free floating Al nanowires, may impose transport perturbations such as interface charging under biased conditions and would certainly be experimentally prohibitive. Consequently, the scope of this study was limited to transport under non-biased conditions limiting the influence of such interface effects. In addition, a functionally comparable architecture might in fact be synthesized by employing vapor-liquid-solid growth of core-shell nanowires which have recently produced low dimensional, atomic scale metalsemiconductor heterostructures.18 Electrode interfaced - structures formed the basis for devices characterized by transmission calculations in this study. To generate devices of varying length, unit cells of optimized alkyl carbazole molecules, free standing, or on a Si(100)2x1 bilayer were replicated n times to generate -stacks of length = n. All remaining dangling bonds on replicated Si slabs were capped


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with H. Then Al electrodes were interfaced with terminal carbazole units and extended to form leads. To emulate the effect of gating on these systems, a theoretical metal gate of dimensions (15 x 2 x 23) Å3 was installed 0.68 Å below the Si(100)2x1 slab. For gated transmission calculations, a specific voltage was assigned to the metallic slab (typically between 0 and 10V), and transmission calculations were run under the influence of the gate potential. Transmission calculations were carried out with non-equilibrium Green's function formalism and density functional theory (NEGF-DFT) using self-consistent periodic boundary conditions in the TranSIESTA code.19,20 Gate potentials were imposed following procedures set forth in TranSIESTA which involve defining an external potential whose extra charge is compensated by the self-consistent loop to ensure charge neutrality.21 Local density approximation (LDA) was used for exchange correlations. Within the device configuration, 301 k-points were used in the z direction to generate high resolution transmission spectra. Only 101 k-points were used in the z direction for gated devices. Each atom type (Si, H, C, N, Al) was described with double- polarized numerical orbitals and norm-conserving pseudopotentials.22


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RESULTS AND DISCUSSION Transmission spectra for several different systems containing substituted carbazole structures in the scattering region are depicted in Figure 3. Each plot contains peaks for transmission near the Fermi level (Ef = 0, as reference) and major peaks are labeled as an eigenstate located on either the -stack, the Si substrate, or both. Corresponding molecular orbital plots are displayed in Figure S1-S6 (Supporting Information).

1.2

(a): Al-EthylCarbazole(6)_FreeStanding-Al (ring)

2.5

(ring)

(ring) (ring)

(ring) (ring)

1.0

(ring) (ring)

(both)

(ring) (ring)

(both) (both)

(ring)

(ring) Transmission

(ring) Transmission

(b): Al-EthylCarbazole(6)-Al

(ring) (ring) 2.0

0.8

0.6

(both)

1.5

(ring) (substrate)

1.0

0.4

0.5

0.2

0.0 -3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.0 -3.0

3.0

-2.5

-2.0

-1.5

-1.0

-0.5

Energy (eV)

1.6

(c): Al-ButylCarbazole(6)-Al

1.4

(ring)

(ring)

1.0

Transmission

Transmission

(ring)

(ring)

(ring) (ring)

(ring)

0.8

(ring)

(ring)

(ring)

0.6

(ring)

(ring)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.0 -3.0

3.0

-2.5

-2.0

-1.5

-1.0

-0.5

Energy (eV)

1.2

(ring) (ring)

(ring) (ring)

1.0

Transmission

(ring)

2.0

2.5

3.0

(ring)

(ring) (ring)

(ring)

(ring)

(ring)

(ring) (ring)

(ring)

(ring) 0.6

(ring) (ring)

(ring) 0.4

(ring)

(ring)

0.2

1.5

0.8

(ring)

(ring)

1.0

(ring)

(ring)

0.4

(ring) (ring)

(ring)

(ring)

0.6

0.5

(f): Al-DecylCarbazole(6)-Al

(ring)

(ring)

0.8

0.0 Energy (eV)

(e): Al-OctylCarbazole(6)-Al

(ring)

(ring)

(ring)

0.2

0.2

-2.0

(ring)

(ring)

(ring)

(sub)

-2.5

3.0

(both)

0.4

0.4

0.0 -3.0

2.5

(sub)

0.6

1.0

2.0

(ring)

(ring)

(ring)

0.8

1.2

1.5

(ring)

(ring)

(ring)

1.0

(ring) (ring)

1.0

0.5

(d): Al-HexlCarbazole(6)-Al

1.2

1.2

0.0 Energy (eV)

1.4

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(ring)

(ring)

0.2

(ring) 0.0 -3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 -3.0

-2.5

-2.0

Energy (eV)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Energy (eV)


10

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Figure 3. Scattering region transmission spectra for six different, -stacked, alkyl carbazole structures as depicted in Figure 1. The peaks are labeled according to where the molecular orbital is located, either on the -stacked rings (ring), the silicon substrate (sub), or spread over both (both). The energy axis is in reference to the aluminum electrode Fermi level of -3.72 eV. The first system analyzed was a free standing stack of six ethylcarbazole molecules between Al electrodes, Figure 1a. This simplified arrangement only offers a conduction path through the ethyl substituted -stacked carbazole rings. Accordingly, the transmission spectrum, depicted in Figure 3a, contains a few groupings of nearly discrete peaks for occupied and unoccupied energy levels on either side of the Fermi level. With transport restricted entirely to the isolated -stack, a band gap of 2.90 eV was calculated which compares well with 2.28 eV reported for napthyl12 and 4.0 eV for the smaller benzene.15 In this particular structure, the occupied peaks centered around -1.45 eV, likely support the bulk of transport at low bias as they are closest to the Fermi level. Introducing the presence of a Si(100)2x1 slab to which the ethyl substituted carbazole rings are covalently attached (Figure 1b) generated a multitude of new peaks in the occupied and unoccupied regions of the resulting transmission spectrum. Most of the new peaks appear in the unoccupied energy levels, but an increase in peaks between -2 and -3 eV of the occupied region is also apparent. These new peaks can be attributed to transmission pathways that involve conduction through the Si slab as is corroborated by MO projections for these energy levels (Figure S2). As seen by Guo15, when only separated by a relatively short ethyl group spacer, the -stack is significantly coupled to the underlying Si substrate. Therefore transmission can occur through several pathways including states isolated on the -stack, states spread over the -stack


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and substrate, and states isolated to the substrate as demonstrated in Figure 4. The enhanced conduction imparted by the substrate reduced the band gap to approximately 1.35 eV with the unoccupied region situated closest to the Fermi level. Accordingly, transport in this case is anticipated to occur predominantly through the unoccupied states. Further comparison can be drawn to Guo's substituted benzene on Si(100)2x1 system in that the occupied peaks retained much of the same shape and distribution as observed in the occupied peaks of the isolated ethylcarbazole(6) device. Perhaps most striking is the characteristic, isolated peak at 0.325 eV attributed to a transmission pathway situated exclusively on the Si substrate. A similar peak arrangement was seen in the ethylbenzene system15 with a characteristic peak at 0.6 eV attributed to a substrate sequestered state.


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Figure 4. Scattering states for ethylcarbazole(6) demonstrating transmission pathways through a) the -stack (-1.42 eV peak in Figure 3b), b) both the -stack and substrate (-2.62 eV peak in Figure 3b), and c) the underlying substrate (0.32 eV peak in Figure 3b). Lengthening the alkyl spacer by two carbons, from ethyl to butyl, caused a notable disruption in the hybridization between molecular orbitals on the ring and substrate. As seen in Figure 3c, the transmission spectrum for six butylcarbazole units bonded to the Si substrate has a set of unoccupied peaks reminiscent of the isolated ethylcarbazole(6) stack where in both cases transport is supported exclusively by extended -conjugation. The band gap is also widened to 2.20 eV when ignoring the very minor peak at 0.355 eV. The broadened band gap is a direct result of decoupling the conduit through the carbazole rings from that available in the Si substrate. Still, conduction can occur through the Si substrate as evinced by MOs for


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transmission states at 1.44 and 1.76 eV (Figure S3f,g). The isolated, but distinct substrate pathway is likely the result of tunneling from the electrodes through the butyl spacers on each terminal unit demonstrating that this length of sigma spacer is sufficient to prevent hybridization between -conjugation and Si substrate states, but not tunneling between electrodes and substrate. More to the point, if the intention is to restrict transmission to -conjugation states, then a butyl sigma spacer is insufficient due to tunneling through the terminal units. Further increasing the alkyl spacer to six carbon units generated even more isolation of the stack from the underlying substrate. With a hexyl substituent, transmission peaks in the occupied region were very similar to those calculated for the free standing ethylcarbazole(6) system indicating that conduction is highly relegated to the -stack with very little tunneling to, or hybridization with, the Si substrate. Here the band gap broadens back to approximately 2.9 eV, again similar to the free standing structure. It is apparent that a small degree of coupling between the conduction pathways remained as evidenced by the hybrid molecular orbital for the unoccupied peak at 2.95 eV (Figure S4q). Transmission spectra for systems with the longest alkyl substituents, octyl and decyl, contain peaks solely attributed to conduction through the -stack. Here again, the occupied peaks matched that of the hexyl substituted system and were nearly the same as the free standing ethyl substituted system indicating similar conduction pathways in all 3 systems. Band gaps in both cases were about ~3.2 eV, larger even than the free-standing system. This expansion in band gap can be attributed to the loss of a ring based transmission pathway at ~1.76 eV which was seemingly disrupted by the longer alkyl substituents.


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For these systems, transmission would likely occur through the occupied peaks centered at 1.45 eV which were nearest the Fermi level. While some hybridization between  and  orbitals was observed in the decylcarbazole(6) structure (eV = 2.34, Figure S6d), evaluation of the eigenstates verified that no tunneling or hybridization existed between the -stack and underlying substrate. By observing how transmission occurs in different systems as the number of molecular repeat units (system length) is increased we can understand how the architecture influences electron transport. An investigation of resistance scaling was carried out by determining R as a function of system length (number of stacked molecules) for a series of alkyl carbazoles. It is understood that resistance, R, in these systems is simply the inverse of the conductance or R = 1/G, where G is the zero bias conductance given by G = TEFG0. Here, transmission at the Fermi level is represented by TEF, and the conductance quantum is represented by G0 = 2e2/h. As mentioned earlier, R is also related to the system architecture through the scaling factor β in R = R0e(βn). Semilog plots of resistance vs. molecular repeat units (system length) are depicted in Figure 5. Each data set in Figure 5, represents a specific series of alkyl carbazole molecules attached to the Si(100)2x1 substrate with varying number of repeat units in the scattering region. In general, an exponential increase in R with repeat units was observed indicating tunneling transmission.


15


1.00E+14 Ethyl Butyl

1.00E+12

Hexyl Octyl

1.00E+10

Resistance (kΩ)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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β1(octyl, decyl)=3.50

β1(hexyl)=3.68

Decyl

β2(butyl)=0.613

1.00E+08 1.00E+06

β1(butyl)=3.68 β2(ethyl)=0.019

1.00E+04 β1(ethyl)=2.98

1.00E+02 1.00E+00 0

1

2

3

4 5 repeat unit (n)

6

7

8

9

Figure 5. Semi-log plot of zero-bias resistance for alkyl carbazole structures on Si(100)2x1 substrate. Each plot is labeled with a scaling factor (β) calculated for the corresponding alkyl spacer. The resistance plots for each version of alkyl carbazole structure clearly revealed the threshold points for decoupling of the -stack and underlying substrate based on alkyl substituent chain length. Initially, all systems generated a similar slope of scaling factor β ~ 3.0-3.5. This is reasonable considering a comparable scaling factor of 3.77 – 3.85 attained by Guo15 for ethylbenzene on Si(100)2x1. The larger ring area of carbazole likely accounts for the slight drop in resistance compared to benzene. For systems with longer alkyl separators, hexyl, octyl, and decyl, only one slope is observed, indicating a singular pathway for conduction throughout the range of repeat units investigated. The plots for shorter alkyl separators, ethyl and butyl, show two slopes (or two scaling factors (β1, β2)) illustrating inflection points where conduction transitioned from isolation in the -stack to transmission through both the -stack and the underlying Si substrate. Table 1 lists values for β1 and β2 from each system.


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Table 1. β1 and β2 values for alkylcarbazole structures on Si(100)2x1 Alkyl Substituent

β1, -stack transmission

β2, substrate transmission

ethyl

2.979

0.019

butyl

3.685

0.613

hexyl

3.549

N/A

octyl

3.505

N/A

decyl

3.502

N/A

When separated by the ethyl group, with only two carbon atoms, breakdown occurred after three molecular repeat units. This is in agreement with Guo's15 findings where breakdown for ethylbenzene occurred after 3 molecular repeat units. A transition in conductive pathways occurs at this point due to competitive resistance between the extended -conjugation conduit and the terminal alkyl chain conduit (electrode-to-alkylchain-to-Si slab). This concept is supported by the significant drop in β for longer systems as conduction through two pathways (-stack and Si slab) should have less resistance than the initial single pathway (-stack). The longer butyl group can support isolation up to 5 molecular repeat units after which coupling to the Si slab contributes to transmission due to competitive resistance in the -stack. Interestingly, β2 for the ethyl and butyl substituted systems were different even though this value should conceivably be dominated by transmission through the underlying substrate which was equivalent in both cases. The discrepancy is likely attributed to the degree of -stack/substrate coupling in each system. While a higher β2 of 0.613 for the butyl substituted carbazole system (in line with ethylbenzene for n > 3) probably indicates discrete transition from -stack conduction to substrate conduction, the much lower value of 0.019 for the ethyl substituted system


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demonstrates -stack/substrate coupling supporting high transmission through this dual pathway structure. For alkyl chains of 6 carbons or longer, breakdown did not occur over the repeat unit range investigated. This indicates that, at least for - molecular wires of these lengths, transmission would occur exclusively though the -stack and remain decoupled from the underlying Si slab. The identification of highly isolated - systems with significant system length opens up the possibility to fabricate modulated devices which support transistor functionality. An example architecture is described below, utilizing a theoretical gate. Verification of isolated transmission pathways opens up the potential for device architectures. Accordingly, if transmission is restricted to the -stack, then it might be possible to perturb that transmission by localized gating without incurring tunneling or other forms of leakage current. Effective modulation of the transmission would be very enabling with respect to molecular device design. To explore this concept we constructed two transistor type devices by placing a theoretical metallic gate below the silicon substrate of two - structures composed of either ethylcarbazole(6) or decylcarbazole(6) assembled on a Si(100)2x1 slab as seen in Figure 6. To ensure that the devices were outside the regime of competitive resistance, 6 repeats were used in each system.


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Figure 6. Transistor device structures for - molecular devices composed of a) ethylcarbazole(6) or b) decylcarbazole(6). A theoretical metallic gate is position directly below the Si(100)2x1 slab in each device. It was anticipated that the ethylcarbazole(6) device, with multiple transmission pathways, would operate more like a metallic conductor where gate bias could push the valence and conduction bands around, but there would always be some band close to, or aligned with, Fermi level. The decylcarbazole(6) structure, on-the-other-hand, characterized by a sequestered -stack conduit, was considered more analogous to a semi-conductor where band gaps could be adjusted


19


Page 20 of 30

by gate bias to significantly alter transmission. For each modeled device structure, the gate voltage was swept from -10 to 10 V. At each step, calculations were done to determine the transmission spectrum (Figure 7, Figure 8) and corresponding eigenestates (Figure S7 to S14 for ethylcarbazole(6), Figure S15 to S22 for decylcarbazole(6)). The transmission spectrum at each voltage was used to determine the conductance as plotted in Figure 9.


20

Page 21 of 30

1.6

(a): Al-EthylCarbazole(6)-Al, Vg = -10.0V

2.0

(both)

(both)

(both)

1.6

(sub)

1.2

(sub)

(sub)

(sub)

(sub)

(sub)

0.8

(sub) (sub)

(both) (sub)

(sub)

(sub)

(both)

1.4

Transmission

Transmission

1.0

0.6

(b): Al-EthylCarbazole(6)-Al, Vg = -7.0V

1.8

1.4

(sub)

1.2 1.0 0.8

(sub) (both) (both) (ring) (sub) (sub) (both)

0.6 0.4

(both)

0.2 0.0 -3.0

-2.5

-2.0

-1.5

-1.0

-0.5

(sub) (sub)

(sub)

0.0

(sub)

1.8

(sub)

(sub) (sub)

0.4

(sub)

0.2

0.5

1.0

1.5

2.0

2.5

0.0 -3.0

3.0

-2.5

-2.0

-1.5

-1.0

-0.5

(c): Al-EthylCarbazole(6)-Al, Vg = -4.3V

2.0

(sub)

0.5

1.0

1.5

2.0

2.5

3.0

(d): Al-EthylCarbazole(6)-Al, Vg = -1.4V (both)

1.8 1.6

1.4

(both)

1.4

(both) (sub)

(both) (both)

(sub)

(both)

(sub)

(sub)

Transmission

1.2 Transmission

0.0 Energy (eV)

1.6

1.0

(both)

0.8 0.6

(both)

1.2

(both)

1.0

(sub) (ring)

0.8

(sub) (both)

(ring)

(sub)

(both) (ring)

0.4

(ring) 0.2

(sub)

(sub)

0.6 (both)

0.4

0.2

0.0 -3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.0 -3.0

3.0

-2.5

-2.0

-1.5

-1.0

-0.5

Energy (eV)

2.5

(sub) (sub) (both) (both)

Energy (eV)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Energy (eV)

(e): Al-EthylCarbazole(6)-Al, Vg = 1.4V

2.5

(f): Al-EthylCarbazole(6)-Al, Vg = 4.3V

(sub) 2.0

(sub)

(both)

(both)

(ring)

2.0

(both)

(both)

1.5

(sub)

(ring) (both)

1.0

(sub)

(both)

(both) (sub) (both) (both)

(sub)

(both)

Transmission

Transmission

(both) (both)

(sub)

(both)

1.5

(ring) (both)

(ring)

1.0

(ring) (sub) 0.5

0.5

0.0 -3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

(sub)

0.0 -3.0

3.0

-2.5

-2.0

-1.5

-1.0

-0.5

(g): Al-EthylCarbazole(6)-Al, Vg = 7.0V

3.0

1.5

(both) (sub)

(ring)

(both)

(sub)

1.5

2.0

2.5

3.0

2.5

(sub) (both)

2.0

(sub) (sub)

(both)

0.5

(both) (both)

(ring) 1.5

(ring) (ring) (both)

(ring) 1.0

0.0 -3.0

1.0

(h): Al-EthylCarbazole(6)-Al, Vg = 10.0V

(both)

(ring)

1.0

0.5

(both)

(both) (both) (both)

Transmission

2.0

(both)

0.0 Energy (eV)

Energy (eV)

2.5

(both) (both)

(sub)

(ring)

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(sub) (sub)

(both) (both)

(sub) (sub)

0.5

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 -3.0

-2.5

-2.0

Energy (eV)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Energy (eV)


21


Page 22 of 30

Figure 7. Scattering region transmission spectra for the ethylcarbazole(6) transistor device depicted in Figure 6a. Each plot represents a specific gate voltage from -10 to 10 V. The peaks are labeled according to where the molecular orbital is located, either on the -stacked rings (ring), the silicon substrate (sub), or spread over both (both). The energy axis is in reference to the aluminum electrode Fermi level of -3.73 eV.


22

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1.2

(a): Al-DecylCarbazole(6)-Al, Vg = -10.0V

0.6

(ring) 0.5

(ring)

0.8

0.4 Transmission

Transmission

(b): Al-DecylCarbazole(6)-Al, Vg = -7.0V

(ring)

1.0

0.6

0.3

(ring)

(ring)

(both)

(ring) (ring) (ring)

0.2

0.0 -3.0

-2.5

(ring)

(ring)

(ring) (ring)

(ring)

-2.0

-1.5

0.1

(ring)

(ring)

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-2.5

-2.0

-1.5

-1.0

-0.5

(c): Al-DecylCarbazole(6)-Al, Vg = -4.3V

0.7

0.5

1.0

1.5

2.0

3.0

(ring)

(both)

(ring)

(ring) (ring)

Transmission

(ring)

(ring)

0.5

(ring)

(ring) 0.6

2.5

(d): Al-DecylCarbazole(6)-Al, Vg = -1.4V

0.6

1.0

Transmission

0.0 Energy (eV)

(ring)

0.8

(ring)

(ring)

(ring)

0.0 -3.0

3.0

(ring)

Energy (eV)

1.2

(ring)

0.2

0.4

0.4

(ring)

0.3

0.4 0.2

(ring)

(ring) 0.2

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.0 -3.0

3.0

-2.5

-2.0

-1.5

-1.0

-0.5

Energy (eV)

(e): Al-DecylCarbazole(6)-Al, Vg = 1.4V (ring)

(ring)

1.6

(ring)

(ring) (ring)

Transmission

2.0

2.5

3.0

(ring)

(ring) (ring)

(ring)

1.2 1.0

(ring)

(ring)

(ring) 0.4

1.5

(ring)

(ring)

(ring) (ring)

(ring) (ring) (ring) (ring)

(ring)

(ring) 0.6

1.0

(ring)

1.4

(both)

1.0

0.8

0.5

(f): Al-DecylCarbazole(6)-Al, Vg = 4.3V

(ring)

(ring)

0.0 Energy (eV)

Transmission

1.2

(ring)

(ring)

0.1

0.0 -3.0

(both)

(ring) (ring)

0.8 0.6

(ring) 0.4

(ring) (ring)

0.2

(ring)

(ring)

0.2 0.0 -3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.0 -3.0

3.0

-2.5

-2.0

-1.5

-1.0

-0.5

Energy (eV)

1.4

(g): Al-DecylCarbazole(6)-Al, Vg = 7.0V

1.0

1.4

(both) (ring)

(ring)

(ring) (ring)

1.0

Transmission

(ring) (ring)

0.6

0.6

0.4

0.2

0.2

-1.5

-1.0

-0.5

0.0

2.0

2.5

3.0

(both)

(ring)

(ring)

0.5

1.0

1.5

2.0

2.5

3.0

0.0 -3.0

(ring) (ring)

(ring)

(ring)

(ring)

0.8

0.4

-2.0

1.5

(h): Al-DecylCarbazole(6)-Al, Vg = 10.0V

(ring)

(ring)

-2.5

1.0

1.2

(ring) (ring)

0.8

0.0 -3.0

0.5

(both)

(both)

(ring) (ring)

0.0 Energy (eV)

1.2

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(ring)

(ring)

(ring)

-2.5

-2.0

Energy (eV)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Energy (eV)


23


Figure 8. Scattering region transmission spectra for the decylcarbazole(6) transistor device depicted in Figure 6. Each plot represents a specific gate voltage from -10 to 10 V. The peaks are labeled according to where the molecular orbital is located, either on the -stacked rings (ring), the silicon substrate (sub), or spread over both (both). The energy axis is in reference to the aluminum electrode Fermi level of -3.71 eV.

1.00E+00

EthylCarbazole(6) 1.00E-02

DecylCarbazole(6)

1.00E-04

Conductance (S)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 30

1.00E-06 1.00E-08 1.00E-10 1.00E-12 1.00E-14 -10

-8

-6

-4

-2

0

Gate Bias (V)

2

4

6

8

10

Figure 9. Conductance in gated - molecular devices as a function of gate voltage for structures composed of ethylcarbazole(6), (■) and decylcarbazole(6), (●). In general, for the ethylcarbazole(6) structure, little modulation of conductance was seen (Figure 9, squares) which likely results from lack of an isolated transmission conduit. While gate bias did adjust the orbital distributions around the Fermi level, it did not impose a notable energy barrier to transmission. This is likely due to the availability of multiple transmission pathways involving the Si substrate. In the region of negative gate bias, transmission was supported by redistribution of the HOMO orbitals over the Fermi level, Figure 7a-c. Positive gate bias shifted orbitals in the other direction, consequently distributing the LUMOs over the Fermi level, Figure 7e-h. The dip in conductance around Vg = -4.3 to -1.4 V can be attributed to a small energy


24

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barrier of ~0.25 to 0.4 eV established by retraction of the LUMOs away from the Fermi level, Figure 7c-d. For the decylcarbazole(6) structure, in contrast to the ethyl counterpart, a significant modulation of conductance was observed along the sweep of gate voltage (Figure 9, circles). In fact, the conductance spanned over 6 orders of magnitude for this range of gate voltage. Here positive gate bias creates a significant separation between the Fermi level and both the HOMO and LUMO bands, thus decreasing overall conductance (Figure 8e-g). It should be noted that the decane alkyl dielectric maintained complete isolation of the -stack only between -1.4 and 4.3 V (Figure S18-S20). For voltages outside this range tunneling appeared in some of the scattering state norms (Figure S19p). However, within the -1.4 to 4.3 V voltage range, switching to negative bias increased the decylcarbazole(6) device conductance by a factor of 106 over positive gate bias. Under these fields, the valence bands were promoted sufficiently close to the Fermi level to allow a substantial increase in transmission. Accordingly, it seems probable that transmission in a decylcarbazole(6) structure could be modulated substantially by gate voltage without incurring any form of gate leakage for biases in the range of -1 to 4 V. It is thus suggested that proper isolation of the -stack by an adequate alkyl chain dielectric imparts the possibility for - molecular structures to operate as true transistor devices. It should be noted that these observations concern systems modeled at 0 K. Deviations from the reported behavior at higher temperatures may arise due to phonon scattering. CONCLUSIONS Altogether, we have investigated the influence of molecular structure on transport properties for assemblies on the Si(100)2x1 surface. Geometry optimization of Si(100)2x1 bound alkyl-


25


Page 26 of 30

substituted carbazoles demonstrated that these systems adopt confirmations supporting extended -conjugation through -stacking of the carbazole rings. Band gaps within these conduits were found to be sensitive to the degree of coupling with the underlying Si crystal which was in turn dictated by the methylene spacer group length. Examination of molecular eignenstates and path length resistance for these systems revealed a threshold in alkyl spacer length capable of completely isolating orbitals of the -stack from those of the substrate. Gate modulation of a coupled ethylcarbazole(6) and an isolated decylcarbazole(6) -stack yielded highly contrasting behavior. While little modulation occurred in the substrate coupled ethylcarbazole(6) system, stack isolation in decylcarbazole(6) supported a range in conductance spanning 6 orders of magnitude. However, it was observed that gate tunneling may occur for gate potentials outside the range of -1 to 4 V. This theoretical demonstration of gate modulated transport in isolated molecular pathways assembled on the Si(100)2x1 surface by simple gate architectures suggests that established transistor layouts may in fact be implemented on the molecular scale. The ability to construct integrated devices on this scale offers further evidence that this substrate may be an ideal platform for molecular electronics.

SUPPORTING INFORMATION Supporting Information. Cartesian coordinates for unit cell alkyl carbazoles on Si(100)2x1 slabs. Scattering state wavefunction norms for major peaks in transmission spectra of alkylcarbazole(6)s from Figure 3, 7 and 8.


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AUTHOR INFORMATION Corresponding Author *[email protected] *[email protected] Present Addresses †Draper Labs, 555 Technology Square, Cambridge, MA. ACKNOWLEDGMENTS This research was in part supported by the UMass Center for Hierarchical Manufacturing (CHM) and NSF Nanoscale Science and Engineering Center (DMI-0531171). We thank Daniel Valencia of Draper Labs for informative consultation on numerical methods used for transport calculations. REFERENCES (1)

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Gate-Modulated Conductance of Extended Conjugation in Atomically

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