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By applying nonequilibrium Green’s functions (NEGF) in combination with the density functional theory (DFT), we investigate the electronic transport properties of gated phenalenyl molecular devices with two different contact geometries. The calculated results show that electronic transport properties of the two different devices can be modulated by external transverse gates. When the molecule contacts the Au electrodes through two second-nearest sites, the current-voltage (
*I*-
*V*) characteristic curves are symmetric and suppressed by the gate electrodes. However, a rectifying behavior will occur when the electrodes connect the molecule on both sides, one second-nearest site and one third-nearest site, respectively. Mechanisms for such phenomena are proposed and these findings suggest a new opportunity for developing molecular devices.

Since the use of individual molecules as functional electronic devices was suggested in 1974 [

Phenalenyl, a stable organic radical with high symmetry, and its derivatives have attracted much attention for the intriguing properties such as the electrical, optical, and magnetic properties [

The geometries of the device proposed in this work are illustrated in

configuration. The sulfur atom is chosen to be located at the hollow site of the gold triangle and the Au-S distance is 2.0 Å, which is a typical Au-S distance. M1 and M2 correspond to the two different contacted geometries. In our calculations, the exchange-correlation potential is described by the Perdew-Burke-Ernzerhof parameter of the generalized gradient approximation (GGA.PBE). A single-ζ (SZ) atomic orbital basis set is employed for Au atoms and double-ζ plus polarization (DZP) basis set is adopted for the rest. Before calculating the electron transport properties of the device, all atoms in the channel region are relaxed with a force tolerance of 0.05 eV/Å. The geometrical optimizations and all the calculations are performed using the Atomistix ToolKit (ATK), which is based on fully self-consistent non-equilibrium Green’s function (NEGF) and density functional theory (DFT). According to NEGF formulas, the source-drain current I_{sd} through the system is obtained by Landauer-Büttiker formula,

I s d = 2 e h ∫ T ( E , V s d ) [ f ( E − μ L ) − f ( E − μ R ) ] d E (1)

where T(E, V_{sd}) is the transmission coefficient of the system at energy E under the source-drain bias (V_{sd}), μ L ( R ) and f ( E − μ L ( R ) ) are the chemical potential and Fermi function of the left (right) electrode, respectively. For simplicity, the average Fermi level E_{f} of the system is set to zero, thus the current is in fact the integral area of transmission curve inside the bias window [−eV/2, eV/2]. The transmission spectrum covers the integrated transmission coefficients T(E,V,k) over the 2D Brillouin zone of incident wave vectors k, T ( E , V ) = 1 Ω ∫ Ω ˜ d k T ( E , V , k ) , where Ω is the area of the reference unit cell surface.

f ( E − μ ) = 1 / { 1 + exp [ ( E − μ ) / ( k B T t e m p ) ] } (2)

The Fermi-Dirac distribution function, k_{B} is Boltzmann constant, and T_{temp} is the temperature. Furthermore, an additional gate voltage (V_{g}) is applied on the molecule to extend the device’s function. From

The self-consistently calculated I-V characteristics for the molecular device in the M1 configuration under the bias range from 0 V to 1.5 V with the gate voltage (V_{g}) setting to different values 0.0 V, 2.0 V, 4.0 V, 8.0 V and 12.0 V are shown in _{sd} region, the gated currents increase gradually slower than that of V_{g} = 0.0 V, which seems the I-V curves are suppressed by the gate electrodes. We present the transmission coefficients at E_{f} are 0.7742, 0.4406, 0.3759, 0.4439 and 0.0884 for V_{g} = 0.0 V, 2.0 V, 4.0 V, 8.0 V and 12.0 V via V_{sd} = 0.0 V, respectively, and it could be found that the transmission coefficients applied gate voltages obviously reduced, which are against the device transport, leading to the suppressed I-V curves in

The particular variation tendency of I-V curve after applying gate voltages can be interpreted in terms of transmission spectrum T(E) and spatial distribution of frontier molecular orbitals. As shown in _{g} increases, the transmission peaks flow to the low energy, and gradually move out of the bias window. That means the currents are decreasing, as we all know that the current is determined by T(E, V) in the bias window. At V_{g} = 0.0 V, within the bias window, there is a broaden transmission peak around the Fermi level derived from the LUMO (0.162 eV) level, which is the main transmission channel in this device. When V_{g} increases to 2.0 V, the broaden transmission peak is divided into some small and low peaks, and all the peaks are moving to the low energy, in this case, the HOMO resonance is closer to E_{f}, as the main transmission channel. To further add the gate voltage to 8.0 V, the HOMO resonance is moving out of the bias window, and while V_{g} = 12.0 V, the

broaden transmission peaks are completely out of the bias window, except for some smaller and lower peaks. For this reason, currents are suppressed when we add the positive gate voltages. But from this figure we also can see another molecular orbitals are moving closer to E_{f} as the gates adding, which means if we further add the gate voltages, the current will not depressed enormously for the other resonance will move into the bias window as the main transmission channel.

The self-consistent calculated I-V characteristic for M2 device under the bias range from −2.0 V to 2.0 V with the gate voltage (V_{g}) setting to different values 0.0 V, 2.0 V, 4.0 V, and 8.0 V are shown in

bias due to the currents are almost the same. The inserted figure shows the rectification ratio, a ratio of the currents under positive and negative voltages for the same bias magnitude ( R R = I ( V ) / | I ( − V ) | ) . The forward (backward) rectification is defined according to the rectification ratio R > 1 (R < 1). Obviously, while 0.0 V < V_{sd} < 0.8 V, the rectification ratios are depressed gradually as the gates adding, and the biggest rectification ratio reaches 2.7 at a bias of 0.3 V as V_{g} = 0.0 V. While V_{sd} > 0.8 V, the rectification ratios are increased rapidly and intersect with the curve of V_{g} = 0.0 V as the added gates, and the rectification ratio reaches 2.8 at a bias of 2.0 V with V_{g} = 8.0 V. From this figure we can also see the rectification direction is inversed within the bias region of [0.06 V, 0.8 V] at the V_{g} = 8.0 V.

To understand the observed I-V curves and the rectification behaviors, we give the transmission spectrum T(E) and molecular projected self-consistent Hamiltonian (MPSH) of four frontier molecular orbitals HOMO-1, HOMO (the highest occupied molecular orbital), LUMO (the lowest unoccupied molecular orbital), and LUMO+1 at V_{sd} = 0.0 V for different V_{g}, as shown in _{f} are 0.0108, 0.0154, 0.0206 and 0.01563 for V_{g} = 0.0 V, 2.0 V, 4.0 V and 8.0 V, respectively, so the currents vary approximately linearly in low V_{sd} regions. It is notable that the HOMO resonances are closer to E_{f}, therefore, HOMO is the main transmission channel in this device. _{sd} regions. Although LUMO and LUMO+1 orbitals are always fully delocalized, for they are far away from E_{f} and cannot be excited in low V_{sd} regions to transport electrons.

_{g} = 8.0 V, the case is opposite to the former cases, there are more broaden and higher transmission peaks in the bias window under the negative bias and only two sharp and lower transmission peaks under the positive bias, which means exhibiting a reverse rectification under this bias.

V_{g} | HOMO-1 | HOMO | LUMO | LUMO+1 |
---|---|---|---|---|

0 V | ||||

2 V | ||||

4 V | ||||

8 V |

In conclusion, we have investigated the electronic transport properties of phenalenyl molecular with two different contact geometries via different gates. The theoretical results show that the I-V curves are symmetric and the currents are depressed as the applied gates adding with the M1 model. While with the asymmetric M2 model, the currents are asymmetric and the rectification behavior occurs, which means the asymmetric structure will lead to rectification phenomenon, and the rectifying behavior is different as the gates adding, all these findings could be helpful for application of the phenalenyl molecular in the future.

This work was supported by the Natural Science Foundation of Shandong Province (No.ZR2018LA012) and Doctoral Research Start-up Fund (No.2017BSZX03).

The authors declare no conflicts of interest regarding the publication of this paper.

Jiang, X.H., Liu, W. and Zhao, J.H. (2021) Electronic Transport Properties of Phenalenyl Molecular Devices via Gated Modulation. Journal of Applied Mathematics and Physics, 9, 503-514. https://doi.org/10.4236/jamp.2021.93035