Controlling the electronic transport properties of the tetrapyrimidinyl molecule with atom modified sulfur bridge

Abstract

The effect of the modified sulfur bridge on the I–V characteristics of a two-probe system of tetrapyrimidinyl molecules and Au electrodes is explored based on density functional theory with nonequilibrium Green's function. Five modified sulfur bridges with H, N or O atoms are considered. The two-probe system demonstrates a switch behavior when the sulfur bridge is modified with the H atom, and negative differential resistance behavior when modified with N or O. The analysis for the mechanism of the various properties has been presented with the highest occupied molecular orbital, lowest unoccupied molecular orbital and the transmission spectra.

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1. Introduction

With an aim to find a possible way to solve the miniaturization problem of traditional silicon based devices, investigations on the electronic structure and charge transfer of molecular devices are developing at an accelerating pace in the recent years. In the last several years, there has been a large growth of research effort in nanotechnology; various molecular devices have been made to realize the functions existing in microelectronic devices. So far, many interesting device properties, such as switching,^1–4 rectifying behavior,^5–8 negative differential resistance (NDR) behavior,^9–12 field effect transistors,^13,14 and spin filters^15,16 have been demonstrated at the real molecular level. NDR behavior is a property of the electrical circuit in which current decreases with the increase in voltage over certain voltage ranges. Since Esaki's discovery in 1958,¹⁷ the NDR effect has motivated a wide range of theoretical and experimental investigations from the fundamental aspects of electron transport to all possible applications.^18–21 The different contact types also affect the characteristics of current–voltage (I–V) curves.^22,23 All these facts indicate that the contact mode plays a key role in the determination of the electron-transport mechanism. Therefore, to provide a repeatable environment to make precise measurements of a wide variety of molecules is highly desirable. Unfortunately, achieving such an experimental environment is not an easy task. Here, we theoretically investigate the I–V curves induced with the sulfur bridge modified by H, N and O atoms. Five contact modes with different modified bridges are considered. To fully understand the electronic transport properties, we analyze the I–V behavior with the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) and transmission spectra.

2. Model and method

Before the quantum transport properties are determined, the stable geometrical structure of the tetrapyrimidinyl molecule is optimized using the first-principles DFT method implemented in the DMol³ software package.²⁴ The exchange–correlation energy is calculated by generalized gradient approximation (GGA) with parameterization of Perdew–Burke–Ernzerhof (PBE).²⁵ The energy convergence tolerance is 10⁻⁵ Ha, with the force on each atom being less than 5.0 × 10⁻⁴ Ha Bohr⁻¹. Frequency analysis is performed to validate the energetic stability of the molecule. Vibrational spectra are obtained in harmonic approximation using finite displacement to obtain the force constant matrix. The maximum change allowed in any Cartesian coordinate is set to 0.002 Å to obtain accurate geometries. The structure of the molecule in transport property calculations is determined by geometry optimization and vibration frequency analysis. The considered molecular architectures are illustrated schematically in Fig. 1. The modified bridges are thiol (–S), hydrogen sulfur (–SH), nitrogen sulfur (–SN), and oxygen sulfur (–SO). The contact modes with these bridges are represented by M1–M5, respectively. The modified atoms on the sulfur bridge result in different contact modes. As shown in Fig. 2, the –SH bridge is similar to thiol. However, the –SN and –SO bridges are obviously different from that of thiol, which results in the various I–V properties. Each layer of gold electrodes is represented by a 3 × 3 supercell with the periodic boundary conditions so that it imitates bulk metal structures. The geometrical optimizations and the electronic transport properties are calculated by the ab initio code package Atomistix ToolKit (ATK),²⁶ which is based on the combination of DFT with the NEGF technique, and the method has been used by several groups for a variety of applications and is well documented. In our calculations, the exchange–correlation potential is described by the Perdew–Burke–Ernzerhof parameterization of the generalized gradient approximation (GGA.PBE). Single-zeta plus polarization (SZP) basis set for gold atoms and double-zeta plus polarization (DZP) basis set for other atoms are adopted. The Hamiltonian, overlaps, and electronic densities are evaluated in a real space grid defined with a plane wave cut off of 150 Ry to achieve a balance between calculation efficiency and accuracy.

Fig. 1 Two-probe system of the tetrapyrimidinyl molecule with the modified sulfur bridges. M1–M5 represent the different contact modes. The modified atoms on the sulfur atom have not been shown in the figure (the light yellow spheres represent the anchoring points). The white, gray, blue and golden spheres represent H, C, N and Au atoms.

Fig. 2 Snapshots for the bridging position. (a) Only S atom; (b) modified with H atom; (c) modified with N atom; (d) modified with O atom.

According to NEGF formulas, the current in the two-probe system can be obtained with the Landauer–Büttiker formula:

where μ_l(r) is the chemical potential of the left (right) electrode, f(E − μ_l(r)) is the Fermi distribution function of electrons in the left (right) electrode, and T(E,V) is the transmission coefficient at energy E and bias V, which can be obtained by the following formula:

T(E,V) = T_r[Γ_l(E)G^R(E)Γ_l(E)G^A(E)] (2)

where G^R(E) and G^A(E) are the retarded and advanced Green's functions, respectively, of the central scattering region, is the line width function, and are the self-energies of the central scattering region, which contain all the effects of the electrodes. The transmission coefficient T(E) can be decomposed into the contribution of n eigen channels:

For the system in equilibrium state, the equilibrium conductance can be obtained by the transmission coefficient T(E) at the Fermi level E_f,

G = G₀T(E_f) = G₀∑T_n (4)

where G₀ = 2e²/h is the conductance quantum (7.748091733 × 10⁻⁵ S). More details for the method can be found elsewhere.^27,28

3. Results and discussion

The current–voltage characteristics of the tetrapyrimidinyl molecule with contact modes of M1–M5 are presented in Fig. 3. From the figure, it can be seen that the transport properties of the molecular devices are strongly dependent on the contact modes. It is noted that the contact mode of the M1 tetrapyrimidinyl molecule connects to the two Au electrodes with two unmodified sulfur bridges. The I–V curve of the contact mode displays symmetry for both the positive and the negative biases. It will be used for a reference to analyze the effect of the other modified bridges with different atoms.

Fig. 3 Calculated I–V curves for each contact mode.

To show the characteristics of the I–V curves, we calculated the rectification ratios and presented them in Fig. 4. The rectification effects of M2 and M3 and the NDR behaviors of M4 and M5 are obviously displayed in the figure. It is helpful for us to discuss them in detail in the following sections.

Fig. 4 Calculated rectification ratios for each contact mode.

3.1 Switch behaviors caused by the H-modified sulfur bridge

The current of M2 is very small until −1.5 V, then starts to rise steadily with the negative bias, and remains small all the time on the positive bias. Carefully checking the I–V curve with M3, one can see it is an approximate mirror image of that with M2, although the tetrapyrimidinyl molecule is not symmetrical in the direction of the axis. As a result, the current occurs on the larger positive bias. This result shows that the present characteristic of the I–V curve is mainly determined by the bridge but not by the molecule itself. Both cases can be used as molecular switches, and the only difference is that the closed status depends on different directions of bias. Comparing the results with that of M1, one can recognize that the effect of the modified atom is responsible for the change in the I–V curves.

The new characteristics of the I–V curve for M2 can be understood with the transmission spectra shown in Fig. 5. In the range of low bias, the transmission peak under positive bias has not entered the bias window, therefore there is no current. The transmission peak begins to enter the bias window after −1.4 V under positive bias, so current starts to rise. Fig. 5 shows that the main part of a transmission peak is outside of the right threshold of the bias window, therefore the current can continue to increase if the bias keeps increasing. As such, the currents of M2 and M3 in Fig. 3 show no threshold.

Fig. 5 Transmission spectra from 1.3 to 1.8 V for M2. The red dotted line indicates positive bias, and the black solid line indicates negative bias. The region between two blue dotted lines represents the bias window.

This phenomenon can be understood through molecular projected self-consistent Hamiltonians (MPSHs) shown in Fig. 6. It is known that the coupling between the electrodes and molecule are especially important to the electronic transport properties, therefore, the present MPSHs include not only the molecule but also two surface layers of electrodes (the first layer of left and right electrodes). The LUMO of M2 has a high level of localization above the Fermi level and no delocalized electronic density; the electrons cannot tunnel through the LUMO. From Fig. 6, one can find that the localization of the HOMO remains at a low level below −1.4 V. However, the delocalization is obvious at −1.4 V, which makes the electrons able to tunnel easily through the HOMO, therefore, the current increases sharply. Moreover, the delocalization remains with the bias increase, so the current remains at a high level. As for M3, in which the H modified S bridge is placed between the molecule and other electrode, the similar HOMO and LUMO behavior can be observed from Fig. 7. Because the structure of tetrapyrimidinyl is not symmetrical, the I–V curves of M2 and M3 are not absolute mirror images, but obviously demonstrate the effect of the H modified bridge on the I–V curves.

Fig. 6 Highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) corresponding to an applied bias of −1.2 to −1.6 V of M2.

Fig. 7 Highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) corresponding to an applied bias of 1.2 to 1.6 V of M3.

3.2 Negative differential resistance behavior with N (or O)-modified sulfur bridges

Fig. 3 shows that the current for M4 reaches a peak value at 1.38 V, then decreases suddenly with further increase in the bias, while for M5, the peak values appear at 1.14 V although the peak is lower than that of M4. Therefore, obvious NDR behaviors are demonstrated for both the bridges, and the strongest NDR behavior appears in M4.

Transmission spectra from 1.1 V to 1.6 V for M4 are shown in Fig. 8. There is a transmission peak in the bias window at 1.1 V, and the peak strengthens gradually with the increase of the applied positive bias. However, when the bias reaches 1.6 V, the resonance peak in the bias window keeps broadening but there is a drop in the peak value. As a result, the current drops to a lower value, and NDR behavior appears but is less obvious. To quantitatively demonstrate the NDR effect, we have calculated the peak-to-valley ratio parameter (PVR) for the I–V curves of the M4 and M5 where NDR is obvious. The PVRs are 5.21 for M4 and 1.84 for M5, which shows that the NDR effects are sensitive to the modified atoms. Fig. 8 shows no transmission peak from the bias window, therefore the current cannot increase, despite the bias increasing. Thus, the currents of M4 and M5 in Fig. 3 show threshold.

Fig. 8 Transmission spectra from 1.1 to 1.6 V for M4. The black solid line indicates negative bias. The region between two blue dotted lines represents the bias window.

We show the HOMO of M4 in Fig. 9. It is found that the delocalization of the HOMO becomes obvious after 1.4 V, where the current also increases obviously as shown in Fig. 2. However, the delocalization begins weakening after 1.6 V, which decreases the transmission ability of M4. Carefully checking the MPSH in Fig. 9, one can find that the LUMO always has no contribution to the charge transmission. The NDR behavior only depends on the variation of charge distribution on the HOMO. We can therefore conclude that the mechanism of the NDR behavior is the effect of bias voltage on HOMO, but not the additional effect of LUMO as is the case of the twisting diphenyldipyrimidinyl system.²⁹ M5 demonstrates a similar situation to that of M4, however, the peak shows less significant changes. The mechanism is also similar to that of M4. Comparing the I–Vs of M4 and M5 with those of M2 an M3, one can see that the modified bridges –SN and –SO have greater impact on the I–V properties. Carefully examining Fig. 2, we find the N atom is closer to the electrode than the S atom, which implies that it completely changes the contact mode when compared with the –S bridge. Therefore, the NDR behavior of the I–V is the most obvious. In the case of the –SO bridge, both the O and S atoms are close to the electrode, and contribute to the charge transmission. Therefore, the change of I–V for M5 is weaker than that of M4. One also can find from Fig. 2 that the H atom slightly varies the contact mode of the S bridge. Therefore, the changes of the I–V curves of M2 and M3 are much smaller in comparison to those of M4 and M5. This means the geometries of the sulfur bridges significantly affect the transmission properties of the two-electrode systems, as the geometrical torsions between the molecular rings play significant roles in the rectification properties.²⁹

Fig. 9 Highest occupied molecular orbital (HOMO) corresponding to an applied bias of 1.3 to 1.8 V of M4.

4. Conclusions

We have obtained the I–V characteristics for the tetrapyrimidinyl molecule with different bridge radicals based on density functional theory and non-equilibrium Green's function method. It is found that the two-probe system of the tetrapyrimidinyl molecule appears to have a switching effect when the sulfur bridge is modified with H atom and significant NDR behavior when the bridge is modified with N or O atoms. These results show that the I–V characteristics of the two-probe system can be controlled by modifying the atoms on the sulfur bridge. The delocalization changes of HOMO, which result from the modified atoms, are responsible for the various the I–V characteristics of the two-probe system. These findings can contribute to the design of various functional molecular devices using the idea of modifying the atoms on the sulfur bridge.

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant nos NSFC-11174117 and NSFC-11374132.

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