⇦Chinese Physics Letters, 2017, Vol. 34, No. 2, Article code 027201 Electron Transport Properties of Two-Dimensional Si$_{1}$P$_{1}$ Molecular Junctions * Rui-Fang Gao(高瑞方), Wen-Yong Su(苏文勇)**, Feng-Wang(王锋), Wan-Xiang Feng(冯万祥) Affiliations School of Physics, Beijing Institute of Technology, Beijing 100081 Received 1 November 2016 *Supported by the National Natural Science Foundation of China under Grant No 11374033.
**Corresponding author. Email: suwy@bit.edu.cn Citation Text: Gao R F, Su W Y and Feng F W X 2017 Chin. Phys. Lett. 34 027201 Abstract We focus on two new 2D materials, i.e., monolayer and bilayer silicon phosphides (Si$_{1}$P$_{1})$. Based on the elastic-scattering Green's function, the electronic-transport properties of two-dimensional monolayer and bilayer Au-Si$_{1}$P$_{1}$-Au molecular junctions are studied. It is found that their bandgaps are narrow (0.16 eV for a monolayer molecular junction and 0.26 eV for a bilayer molecular junction). Moreover, the calculated current-voltage characteristics indicate that the monolayer molecular junction provides constant output current (20 nA) over a wide voltage range, and the bilayer molecular junction provides higher current (42 nA). DOI:10.1088/0256-307X/34/2/027201 PACS:72.90.+y, 73.23.-b © 2017 Chinese Physics Society Article Text Since Aviram et al.[1] first proposed a conceptual model of a molecular rectifier, molecular electronic devices have attracted a great deal of attention due to their promising applications[2] in many fields, such as optoelectronics[3,4] and mechanical strain.[5,6] The successful exfoliation of monolayer graphene promotes the development of two-dimensional (2D) molecular devices.[7] However, the zero bandgap in nature limits its applications.[8] Therefore, researchers have committed to exploring new 2D semiconducting materials in the last few years. For instance, monolayer silicon[9-14] and monolayer black phosphorus[8,15-17] have been achieved. The artificial monolayer silicon has a large energy gap at the Dirac point and favors a detectable quantum spin Hall effect.[9-14] The monolayer black phosphorus exhibits a widely tunable and direct bandgap, high carrier mobility and remarkable in-plane anisotropic electrical, optical and phonon properties.[15-20] Although 2D silicon and black phosphorus have been achieved, it is interesting whether or not the silicon phosphide exists. Huang et al.[21] discovered several 2D semiconducting silicon phosphide (Si$_{x}$P$_{y}$) molecules theoretically, which are stable only at the stoichiometry of $y/x \ge 1$. By comparison, they found that Si$_{x}$P$_{y}$ molecules of the $P-6m2$ structure with the stoichiometry of $y/x=1$ gave the lowest negative formation enthalpies ($\Delta H$).[21] Meanwhile inspired by graphene, based on $P-6m2$ Si$_{1}$P$_{1}$ molecules, we assume a new monolayer Si$_{1}$P$_{1}$. Through the first principle calculation, we find that its molecular orbit is blank over a wide scope. This inspired us to predict that the monolayer silicon phosphide (Si$_{1}$P$_{1}$) molecules have some novel properties. Therefore, we study the electronic transport properties of monolayer (what we have assumed is new monolayer Si$_{1}$P$_{1}$) and bilayer ($P-6m2$ Si$_{1}$P$_{1}$) gold-Si$_{1}$P$_{1}$-gold molecular junctions by first principle theory. It is found that the monolayer and bilayer gold-Si$_{1}$P$_{1}$-gold molecular junctions show excellent electrical performance through theoretical calculation, especially the monolayer molecular junctions, which will output stable current over a wide voltage range, and might be applied to molecular current regulator devices, while the bilayer molecular junctions provide higher current. The calculation theory has developed from a set of quantum chemistry calculation methods.[22-26] In the approach, the molecular junction system is divided into three regions: the source electrode (S), the drain electrode (D) and the molecule (M), as shown in Fig. 1. The position of the molecule is between the source and drain electrode. The source and the drain are described by an effective mass approximation (EMA),[22-24] and the extended molecule is treated with hybrid density functional theory level.[23,26] The extended molecule is in equilibrium with the source and the drain through the line up of their effective Fermi levels. Because the molecule is only a small perturbation to electrodes, a convenient method is to set the middle of the HOMO–LUMO gap of the finite system at the position of the electrodes' Fermi level (HOMO is the highest occupied molecular orbital, and LUMO is the lowest unoccupied molecular orbital). Therefore, our approach utilizes the advantage of bulk electrode parameters and overcomes the shortcomings of the finite models. We assume that the molecular device is aligned along the $z$ direction. Based on the elastic-scattering Green's function theory, electrons in a state $k$ of source have a transition matrix element $T$ to go the state $q$ of the drain. When the electrode is made of an atomic wire, it can be treated as a one-dimensional electron system. When an applied voltage $V_{\rm D}$ is introduced, the total current density is[23-25] $$\begin{align} i_{\rm 1D}=\,&\frac{2\pi e}{\hbar}\sum\limits_{k,q} {|T|} ^2[f(E_k -eV_{\rm D})\\ &-f(E_q)]\times \delta (E_k -E_q),~~ \tag {1} \end{align} $$ where $E_{k}$ is the initial state energy, $E_{q}$ is the finial state energy, and $T$ is the transition matrix element, which could be written as[23,30] $$\begin{align} T(E_i)=\sum\limits_J {\sum\limits_K {V_{\rm JS}}} V_{\rm DK} \sum\limits_\eta {\frac{\langle J| \eta \rangle \langle \eta| K \rangle}{z_i -\varepsilon _\eta}},~~ \tag {2} \end{align} $$ where $J$ and $K$ run over all atomic sites, which are denoted as $1,2,{\ldots},N$, with sites 1 and $N$ being two end sites of a molecule which connects with two electron reservoirs, and $V_{\rm JS}$ ($V_{\rm DK}$) represents the coupling between atomic site $J(K)$ and reservoirs $S(D)$.[23] Orbital $|\eta \rangle$ is the eigenstate of the Hamiltonian ($H_{\rm f}$) of a finite system that consists of the molecule sandwiched between two clusters of metal atoms: $H_{\rm f}|\eta \rangle =\varepsilon _\eta|\eta \rangle$. The product of two overlapping matrix elements $\langle J|\eta \rangle \langle \eta|K \rangle$ represents the delocalization of orbital $|\eta \rangle$. Here parameter $z$ is a complex variable, $z=E_i +i{\it \Gamma}_i$, with $E_{i}$ being the energy at which the scattering process is observed, therefore it corresponds to the energy of the transmitting electron when it enters the scattering region from reservoir S. The escape rate ${\it \Gamma}_i$ is determined by the Fermi Golden rule. The accompanied research[23-26] should be consulted for further details of $T$.
cpl-34-2-027201-fig1.png
Fig. 1. Schematic diagram of a molecular junction.
When the electrode is made of a metal film, it can be treated as a two-dimensional electron system. In the two-dimensional situation, the current density can be described as[24-30] $$\begin{align} i_{\rm 2D}=\,&\frac{2\pi e}{\hbar}\int_{eV}^\infty {\int_0^\infty {\rho _{\rm 1D} ({E_x})dE_x}}|T|^2[f(E_x\\ &+E_z -eV{}_{\rm D})-f(E_x\\ &+E_z)]n_{\rm 1D}^{\rm S} (E_z)n_{\rm 1D}^{\rm D} (E_z)dE_z,\\ \rho _{\rm 1D} (E)=\,&r_{_{\rm S}} N_{\rm 1D} (E), \end{align} $$ where $\rho _{\rm 1D}(E)$ is the density of states per length per electron volt of the source, $N_{\rm 1D} (E)$ is the one-dimensional density (1D) of state per length per electron volt, $r_{_{\rm S}}$ is defined as the radius of a sphere whose volume is equal to the volume per conduction electron,[24-30] $E_{z}$ is the kinetical energy in the $z$-direction, and $n_{\rm 1D}^{\rm S}(E_z)$ and $n_{\rm 1D}^{\rm D} (E_z)$ are the 1D density of states (DOS) of the source and the drain, respectively. The current through the molecular junctions can be computed by the relationship $I_{\rm 2D}=A i_{\rm 2D}$, where $A$ is equal to $r_{_{\rm S}}$. Then the conductance is obtained by $$ G=\frac{\partial I_{\rm 2D}}{\partial V}. $$ In Fig. 2, two different models (named as monolayer molecular junction and bilayer molecular junction) of Au-Si$_{1}$P$_{1}$-Au molecular junctions are shown. The monolayer and bilayer Si$_{1}$P$_{1}$ molecules have honeycomb lattices like graphene but with surface puckered structures. The unsaturated Si and P bonds are saturated with hydrogen atoms. In Fig. 2(b), two monolayer molecular junctions are adsorbed by Si–Si bonds. The two layers are $Pm$ of symmetry with respect to the central plane.
cpl-34-2-027201-fig2.png
Fig. 2. (Color online) The top view and side view of structures of Au-Si$_{1}$P$_{1}$-Au molecular junctions (monolayer for (a) and bilayer for (b)). Au, Si, P, and H atoms are represented by yellow, gray, orange, and white spheres, respectively. The Au atoms on the left and right side are source (S) and drain (D) electrodes.
The calculations of structural optimization and electronic structure are carried out at the hybrid density functional theory (DFT) B3LYP[22,23] where the basis set is LANL2DZ using the Gaussian 09 package.[31] Then the $I$–$V$ characteristics of the monolayer and bilayer Au-Si$_{1}$P$_{1}$-Au molecular junctions are calculated by the quantum chemistry for the molecular electronic (QCME) program.[32]
Table 1. The calculated orbital energies of HOMO, LUMO and the total energy of the monolayer Si$_{1}$P$_{1}$ molecule and molecular junction, the bilayer Si$_{1}$P$_{1}$ molecule and molecular junction at the B3LYP level. The unit is eV.
HOMO LUMO Total energy
Monolayer Si$_{1}$P$_{1}$ molecule $-$6.35 $-$2.57 $-$10248.50
Monolayer molecular junction $-$5.99 $-$5.83 $-$32168.76
Bilayer Si$_{1}$P$_{1}$ molecule $-$5.32 $-$3.48 $-$19436.32
Bilayer molecular junction $-$5.76 $-$5.50 $-$63286.15
In Table 1, we compare the energies of HOMOs, LUMOs, and total energy of the monolayer Si$_{1}$P$_{1}$ molecule and molecular junction, bilayer Si$_{1}$P$_{1}$ molecule and molecular junction. Energy gaps between the HOMO and LUMO of the molecular junctions are less than their corresponding molecule, therefore the position of the conductance channel moves forward. The decrease of energy gap between HOMO and LUMO leads to a higher conduction ability. Fermi levels are at $-$5.91 eV for the monolayer molecular junction and $-$5.63 eV for the bilayer molecular junction, respectively.
cpl-34-2-027201-fig3.png
Fig. 3. (Color online) The density of states and the molecular orbits of Au-Si$_{1}$P$_{1}$-Au molecular junctions (monolayer for (a) and bilayer for (b)). The density of states is denoted by the red line. The occupied orbitals and the virtual orbitals are represented by the green line and the blue line, respectively.
To investigate electric structures of the two molecular junctions thoroughly, density of states (DOS), occupied orbitals and virtual orbitals of monolayer and bilayer molecular junctions are shown in Fig. 3. The energy of the incident electron in the source increases with the bias voltage ($V$). Once the energy is higher than the energy of the conduction orbit (there might be an orbit for electronic transport in the position of every DOS peak), the electrons will tunnel through the orbit easily and the current will increase sharply. The current will keep stable before the energy of the incident electron arrives at the energy of the next conduction orbit, which shows in steps in the current-voltage ($I$–$V$) curves. For example, the monolayer molecule junction, as shown in Fig. 3(a), presents no DOS peak from about $-$5.4 eV to $-$2.9 eV. This means that there is no orbit for electronic transport over a wide energy range. We thus deduce that the current would remain at the value over a wide voltage range until the next conduction orbit. The bilayer molecule junction, as shown in Fig. 3(b), presents no DOS peak from about $-$4.6 eV to $-$4.0 eV. That is, there would be an analogous step in the current-voltage ($I$–$V$) curve of the bilayer molecular junction but in a narrow voltage range. Figures 4(a) and 4(b) are the current and the conductance characteristics of monolayer and bilayer molecular junctions along with the bias voltage, respectively. The calculation of the current-voltage ($I$–$V$) curve confirms our above-mentioned analysis. In Fig. 4(a), the current of the monolayer molecular junction reaches the largest value at about 0.50 V, and then it remains at that value until 3.0 V, which makes it a significant promising candidate in the application to constant-output-current devices. The current of the bilayer molecular junction is higher than the monolayer molecular junction. The largest values are 20.28 nA for the monolayer molecular junction and 50.07 nA for the bilayer molecular junction, respectively. In Fig. 4(b), the first conductance peaks of monolayer and bilayer molecular junctions are at the voltage of 0.30 V and 0.13 V, respectively. At the voltages of 0.30 V and 0.13 V, their energies correspond to the DOS peak at about 5.60 eV for the monolayer molecular junction and the DOS peak at about 5.50 eV for the bilayer molecular junction. Therefore, the DOS peak at about 5.60 eV for the monolayer molecular junction and about 5.50 eV for the bilayer molecular junction correspond to their first conduction channels, respectively.
cpl-34-2-027201-fig4.png
Fig. 4. (Color online) The calculated current (a) and conductance (b) characteristics of monolayer and bilayer molecular junctions.
In summary, the electronic-transport properties of 2D monolayer and bilayer Au-Si$_{1}$P$_{1}$-Au molecular junctions are studied by means of a generalized quantum chemical approach. Based on the hybrid density functional theory, the structural is optimized and the electronic structure is calculated. The results of the current indicate that both of the monolayer and bilayer Au-Si$_{1}$P$_{1}$-Au molecular junctions have their own novel properties, such as the stable output current for the monolayer molecular junction and higher current for bilayer molecular junctions. The two novel 2D Au-Si$_{1}$P$_{1}$-Au molecular junctions will promote the development of molecular devices for constant-output-current electronic-device applications due to their low cost and better electrical performance. References Molecular rectifiersA brief history of molecular electronicsMolecular Junctions: Can Pulling Influence Optical Controllability?Direct Optical Determination of Interfacial Transport Barriers in Molecular Tunnel JunctionsElectric conductance of a mechanically strained molecular junction from first principles: Crucial role of structural relaxation and conformation samplingElectric Field Effect in Atomically Thin Carbon FilmsRediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronicsEvidence for Dirac Fermions in a Honeycomb Lattice Based on SiliconQuantum Spin Hall Effect in Silicene and Two-Dimensional GermaniumExperimental Evidence for Epitaxial Silicene on Diboride Thin FilmsLow-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tinQuantum Spin Hall Effect in GrapheneSilicene: Compelling Experimental Evidence for Graphenelike Two-Dimensional SiliconPhosphorene: An Unexplored 2D Semiconductor with a High Hole MobilityStrain-Induced Gap Modification in Black PhosphorusLayer-controlled band gap and anisotropic excitons in few-layer black phosphorusElectric field effect in ultrathin black phosphorusHigh-mobility transport anisotropy and linear dichroism in few-layer black phosphorusHighly anisotropic and robust excitons in monolayer black phosphorusSecond law and entropy production in a nonextensive systemFirst-Principles Study of Electrochemical Gate-Controlled Conductance in Molecular JunctionsQuantum chemical study of coherent electron transport in oligophenylene molecular junctions of different lengthsEffects of chemical and physical modifications on the electronic transport properties of molecular junctionsCurrent–voltage characteristics of single molecular junction: Dimensionality of metal contactsA quantum chemistry approach for current–voltage characterization of molecular junctionsElectron conduction in molecular wires. I. A scattering formalismTwo Possible Configurations for Silver–C 60 –Silver Molecular Devices and Their Conductance CharacteristicsCharging-induced asymmetry in molecular conductorsLength dependence of coherent electron transportation in metal–alkanedithiol–metal and metal–alkanemonothiol–metal junctions
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