Insertion of methylene groups into functional molecules for high thermal stability and superior functionality of single-molecule transistors: a first-principles study†

Miku Furushima *^a, Mitsuharu Uemoto ^a, Dongbao Yin ^b, Seiichiro Izawa ^b, Ryo Shintani ^c, Yutaka Majima ^b and Tomoya Ono ^a
aDepartment of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, Kobe, Hyogo 657-8501, Japan. E-mail: furushima@eedept.kobe-u.ac.jp; Tel: +81-78-803-6497
^bLaboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Kanagawa 226-8503, Japan
^cDivision of Chemistry, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan

First published on 20th August 2024

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1 Introduction

One of the strategies to realize high-speed operation, high-degree integration, and low energy consumption for electronic computing systems is to develop smaller devices.¹ This strategy, which has the ultimate goal of realizing transistors with a single molecule, is attracting growing interest these days.^2–4 Single-molecule transistors, as the term implies, are transistors in which a single molecule is used as a channel to cross-link the source and drain electrodes, and the channel current is controlled by the gate electrodes nearby.

There are several methods of fabricating single-molecule junctions, such as the mechanically controllable break junction method,⁵ electromigration,⁶ and the scanning tunneling microscopy break junction method.^7,8 However, for practical applications, many electrodes with nanoscale gaps should be fabricated simultaneously and these methods, in which human efforts should be put into an every single junction one by one, are unsuitable. Recently, Majima's group has developed a suitable technique by combining lithography⁹ and electroless Au plating (ELGP).^10,11 In this method, electrode nanogaps have been fabricated simultaneously with 17-Å-scale precision since 2012,¹¹ and channel molecules are expected to cross-link the electrodes.

One of the candidates for cross-linking channel molecules is a π-conjugated highly fused oligosilole derivative with two biphenyl groups (Bph; shown in Fig. 1a)¹² mainly for the following reasons:

• Its conductivity originating from the rigid π-conjugated system,^13,14

• The spontaneous strong bonding of S atoms on both sides of the Bph molecule to Au electrodes,¹⁵

• The stability of the backbone structure derived from Si atoms,

• The possible effect of lowering Fermi level pinning^16,17 by biphenyl groups, and

• The matching of the molecule length and the electrode nanogap, which possibly results in a self-assembled cross-linking structure.

The present method developed by Lee et al.¹⁸ and Yin et al.¹⁹ achieved several improvements, but the yield of the two-side-bonded structure is not sufficient. That is, it is important to realize a high thermal stability of the structure in which thiol groups on both sides of the molecule bond to the electrodes.

To increase the stability, the strict matching of the molecule length and the nanogap, which is a challenging undertaking in the ELGP method, is required. Therefore, another method of flexibly adjusting the molecule length, especially that providing flexibility for the molecule length with a spontaneous matching system, is required. In this paper, on the basis of first-principles calculations, a method providing flexibility for the molecule length by inserting methylene groups between edge thiols and biphenyls is suggested and discussed, as illustrated in Fig. 1b. A single σ bond is easy to rotate and thus has a high degree of freedom of rotation. On the other hand, the extent of the increase in stability and the change in the performance of a transistor are unknown. In this study, first, the stability of both-side-bonded structures is discussed with respect to the energy stability of the Bph molecule and the methylene-inserted Bph molecule (Bph–CH₂ molecule). Second, electronic states are determined by density functional theory (DFT) calculations.²⁰ Then, the local density of states (LDOS) and the ballistic electronic transmission²¹ are obtained. From the results, the applicability of inserting methylene groups is confirmed where both higher stability and sufficient on currents are revealed.

2 Method

The structures and total energies of Bph and Bph–CH₂ molecules in vacuum and between two Au(111) electrodes with a gap length of 47.66 Å are obtained. The supercell sizes are 14.71 × 16.98 × 65.00 ų and 14.71 × 16.98 × 53.92 ų when in vacuum and between two electrodes, respectively. The obtained atomic geometries between the two electrodes are shown in Fig. 2. During ionic relaxation, the positions of all Au ions and cell shapes are fixed. The binding energy E_B of the molecules and electrodes is defined as

EB = 3 × Eele + Emol − Elink − 2 × EH/ele,	(1)

where E_ele, E_mol, E_link, and E_H/ele are the total energies of electrodes, molecules, the cross-linking system, and a system of a H atom adsorbed on an electrode, respectively. DFT calculations²⁰ are carried out using the Vienna ab initio Simulation Package.²² The pseudopotential generated by the projector augmented wave method²³ is used to describe electron–ion interactions. The Perdew–Burke–Ernzerhof functional within the general gradient approximation is employed.²⁴ The plane-wave basis set is used with a cutoff energy of 500 eV. Γ-centered 2 × 2 × 1 k-point sampling is performed for x-, y-, and z-directions, where z is the direction of the channel current. Ionic relaxation is performed until the norms of all the forces on the ions except Au become lower than 0.05 eV Å⁻¹.

The LDOSs of the channel molecules between the electrodes shown in Fig. 2 are calculated under the following conditions using the RSPACE code,^25,26 which employs the real-space finite-difference method²⁷ in the framework of DFT. The periodic boundary conditions are imposed on all directions of the supercell. The electron–ion interactions are described using norm-conserving pseudopotentials²⁸ of Troullier and Martins.²⁹ The exchange–correlation interaction is treated within the local density approximation (LDA).³⁰ Integration over the Brillouin zone is carried out using the Γ point. The supercell size is the same as the ionic relaxation condition for the molecules between two electrodes and the grid spacing in real space is taken to be 0.20 × 0.18 × 0.19 ų. The self-consistent field calculation is continued until the change of the total energy becomes lower than 2.72 × 10⁻⁵ eV, the common value as a threshold. Note that we confirmed that this grid spacing is fine enough for the electronic states to converge. The LDOS along the z-axis (the long axis of the molecules) is visualized. The LDOS is defined as

	(2)

where E is the energy level, x, y, and z are the Cartesian coordinates, Ψ_i and ε_i are, respectively, the wavefunction and its eigenvalue of the i-th eigenstate, α is the smearing factor set to 135.1 eV⁻², and N is the normalization factor .

On the basis of the calculated electronic structure mentioned above, the electron transport properties of the molecule junction are investigated. The overbridging boundary-matching method^25,31,32 in the framework of DFT is adopted for transport property calculations. The models for such calculations are shown in Fig. 2, where the scattering region, which corresponds to the supercell to obtain the LDOS, is connected to the left (right) electrode on the left (right) side. The k-point mesh, the grid spacing, and the lateral length of the supercell in the electrode regions are chosen to correspond to those in the scattering region. Using the Kohn–Sham effective potential obtained under the periodic boundary condition, we computed the properties of the transport of the incident electrons originating from the left electrode under the semi-infinite boundary condition non-self-consistently³³ with energy values ranging from −0.8 eV to 2.0 eV in increments of 0.05 eV. It has been reported that this procedure is as accurate as that in the linear response regime but significantly more efficient than performing computations self-consistently on a scattering-wave basis. The transmission spectra are plotted using the transmission coefficients and group velocities obtained by the overbridging boundary-matching method.

3 Results and discussion

When the molecules are placed between the electrodes, each S atom locates near a bridge site of the first layer of Au(111) with chemical bonding. Moreover, the molecule long axis is almost vertical to the surfaces of the electrodes. The E_B values are −1.46 and −0.41 eV for Bph and Bph–CH₂ molecules, respectively. The main reason why the E_B of the Bph–CH₂ molecule is 1.05 eV higher than that of the Bph molecule is the distortion of the thiol groups in the anchor region, which form bonds to the electrodes. When a S atom locates at a bridge site, the natural angle of a S–C bond to the surface normal is about 60°, as revealed by a DFT study of the benzene thiolate bonding on Au(111).³⁴ Therefore, the Bph molecule, which is rigid between S atoms at the both-side edges, cannot locate perpendicular to the surface without any distortion. Such an inevitable distortion can be found in the cross-linking structure in Fig. 2a. On the other hand, the Bph–CH₂ molecule, which has flexible methylene groups at the edges because of its easy rotation, can locate with the natural angle without any distortion. The structure in Fig. 2b also shows the chemical bonding with less distortion.

The twist of biphenyl groups is also affected by the distortion. The biphenyl twist angle θ values, defined as the twist angle between the planes that include six C atoms of each benzene ring as shown in Fig. 3, are 27° (30°) and 40° (40°) for the left-side (right-side) of Bph and the left-side (right-side) of Bph–CH₂, respectively. The angle θ of the free biphenyl molecules in the gas phase is 45°,³⁵ which indicates that θ approaches the angle of free biphenyl molecules for Bph–CH₂ because of the less distortion and rotational degree of freedom derived from inserted methylene groups. The effect of twist angle θ on the electronic states and the transport properties will be discussed later.

For a qualitative discussion on transport properties, the LDOSs of Bph and Bph–CH₂ models are shown in Fig. 4a and c, respectively. For both molecules, the LDOS in the region where |z| < 15 Å shows several horizontal bands corresponding to molecular orbitals (MOs), as is also shown in the contour curved lines in Fig. 4a and c. Such electronic states based on MOs can be clearly identified by converting the LDOS to one-dimensional profiles of density of states (DOS) of channel molecule regions. The DOS of the channel molecule region (|z| < 15 Å), defined as

	(3)

where z_min = −15 Å and z_max = 15 Å, are shown in Fig. 4b and d. These profiles exhibit several peaks originating from MOs. The levels of HOMO−1, HOMO, LUMO, and LUMO+1 of the isolated molecule calculated using the Becke three-parameter Lee–Yang–Parr functional^36–38 are shown in Table 1, where the HOMO (LUMO) is the highest occupied (lowest unoccupied) MO and the notation −1 (+1) represents the next level below (above). Considering the trend of LDA, which underestimates the band gaps, MOs, LDOS, and DOS are consistent. These MO band structures are expected to contribute to the transmission of electrons via resonant tunneling,³⁹ which will also be discussed later with the transport properties.

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The ballistic transmittance of electrons in the range of E = −0.8–2.0 eV is calculated and shown in Fig. 4b and d. The transmittance spectrum of the Bph molecule shows two peaks above and two peaks below the Fermi level (E_F). The transmittance spectrum of the Bph–CH₂ molecule exhibits two peaks above and two peaks below E_F. The peaks below E_F are dominant for both molecules considering the transmission. These peak structures are consistent with our experimental results (see also Section S1 in the ESI†). A π-conjugated highly fused oligosilole molecule with terphenyl and phenyl groups (Tph–ph) and its methylene-inserted derivative (Tph–ph–CH₂), which resemble Bph and Bph–CH₂, respectively, show several transmission peaks and nontransmissive band gaps. This consistency suggests the reliability of both theoretical and experimental results.

The energy levels of the transmission peaks in Fig. 4b and d roughly correspond to the MOs shown in the backbone regions in LDOS in Fig. 4a and c and in DOS in Fig. 4b and d. This result suggests that MOs function as transport paths of resonant tunneling,³⁹ as briefly mentioned above. Moreover, interpeak regions have almost zero transmission, especially for the Bph–CH₂ model. This may make it easy to control the channel current by applying gate biases.

The heights of the HOMO and HOMO−1 peaks of the Bph–CH₂ molecule are 4% and 700% of those of the Bph molecule, respectively.⁴⁰ We find that the transmission of Bph–CH₂ can be increased and decreased. From the obtained spectra, the channel currents are estimated using the following equation:

	(4)

where I₀ is the constant of proportionality and E = −0.8 eV corresponds to the drain bias of −0.8 V. The channel current ratio of Bph–CH₂ to Bph, I_Bph–CH2/I_Bph, of 0.20 is sufficiently large in spite of the insulating properties of methylene groups.

The channel current estimated above is sufficient, but we would like to seek for a higher value. For this purpose, the mechanism of the transmission peak height change is analyzed and discussed. In this paper, we focus on the insulating methylene groups, the twist of biphenyl groups, and the electronic states of biphenylthiol and biphenylmethanethiol which are the moieties at the edges.

Methylene groups, more generally alkyl groups, were revealed to be insulating.⁴¹ For Bph, the π-conjugated system is thought to be located on the area of five- or six-membered rings sharing π-electrons and π-electron-like lone pair electrons of S atoms.⁴² For Bph–CH₂, however, the π-conjugated system lies on only the area between the two biphenyl groups. Inserted methylene groups may have lowering effects on transmissions.

The twist angle of biphenyl groups can also be the origin of the transmission lowering. Biphenyl groups, which have π-conjugated electronic structures, are most conductive when it is flat and quantitatively, conductivity is proportional to cos²θ.^43–45 As mentioned above, because of the rotational freedom of inserted methylene groups, the angle θ of Bph–CH₂ approaches 45°, the value of an isolated biphenyl molecule, which has steric hindrance between H atoms. The relation of the trade-off of increasing the stability and decreasing the conductivity by the rotational degree of freedom of methylene groups is suggested.

The two factors mentioned above cannot explain the increase of HOMO−1 transmission by methylene insertion. To understand the origin of this, the relation between the changes of the electronic states and conductivities is discussed. Comparing the LDOSs in Fig. 4a and c, the regions of biphenyl groups (|z| = 10–20 Å) exhibit a difference. That is, for Bph, the energy level of the relatively high-ρ area (E = −0.5 to 0.0 eV) is higher than HOMO−1 (E = −0.60 eV), while for Bph–CH₂, the level of the relatively high-ρ area is almost equal to HOMO−1 (E = −0.60 eV). To understand the origin of this difference, the orbital energies of the biphenylthiol and biphenylmethanethiol molecules are calculated and summarized in Table 2 (see also Section S2 in the ESI† for computational details). The latter biphenylmethanethiol molecule has a 0.5 eV higher E_F and thus the orbital energies with respect to E_F are 0.5 eV lower comparing those from the biphenylthiol molecule. These shifts, especially the shift of HOMO−1, are in agreement with the difference of LDOS. These facts suggest that methylene insertion increases the transmission of HOMO−1 via adjusting the E_F of the biphenyl moiety.

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We find the effect of insulating alkyl groups and furtherly the two nontrivial effects on the transport properties. One is the effect via the twist of biphenyl groups and the other is the effect via the orbital energy shift of edge moieties. These findings indicate that conductivity can be controlled by chemically modifying the biphenyl moieties. Examples of such chemical modifications include control of the twist angle by adding alkane bridges as shown in Fig. 5b and control of the orbital energies of edge moieties to match that of the backbone structure by introducing functional groups such as electron-donating methyl groups or an electron-withdrawing halogen as shown in Fig. 5c and d. The increase of the yields and conductivities upon these modifications is our future topic.

4 Conclusion

We found that the Bph–CH₂ molecule with the both-side-bonded structure is more stable in energy than the Bph molecule and methylene group insertion can be the method of designing a single-molecule transistor with sufficient on current. The binding energy of the Bph–CH₂ model is 1.05 eV larger than that of the Bph model, indicating the stability of the both-side-bonded structure. The origin of the difference in binding energy is the distortion of the bonding network around S atoms. The Bph–CH₂ model has higher rotational degrees of freedom resulting in smaller distortions. The LDOSs show horizontal band structures, confirming that the transmission originates from resonant tunneling. The magnitudes of transmission can be larger or smaller depending on the MOs. The estimated on current of Bph–CH₂ is 20% that of Bph, indicating the sufficient on current of Bph–CH₂. The factors that change the peak heights in the transmission spectra are insulating methylene groups, twist angles of biphenyl groups affected by the molecule distortion, and the E_F values of the edge moieties. These findings are a guide for increasing not only the yield but also the transmission.

Data availability

A part of the data was obtained from the RSPACE code, which is not available due to legal confidential requirements.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was partially financially supported by MEXT as part of the “Program for Promoting Researches on the Supercomputer Fugaku” (Quantum-Theory-Based Multiscale Simulations toward the Development of Next-Generation Energy-Saving Semiconductor Devices, JPMXP1020200205) and also supported as part of the JSPS KAKENHI (JP22H05463), JST CREST (JPMJCR22B4), and JSPS Core-to-Core Program (JPJSCCA20230005). The numerical calculations were carried out using the computer facilities of the Institute for Solid State Physics at The University of Tokyo and the supercomputer Fugaku provided by the RIKEN Center for Computational Science (Project ID: hp230175).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4nj02610a

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