⇦Chinese Physics Letters, 2018, Vol. 35, No. 1, Article code 017201 Electron Transport Properties of Two-Dimensional Monolayer Films from Au-P-Au to Au-Si-Au Molecular Junctions * Dou-Dou Sun(孙豆豆), Wen-Yong Su(苏文勇)**, Feng Wang(王锋), Wan-Xiang Feng(冯万祥), Cheng-Lin Heng(衡成林) Affiliations School of Physics, Beijing Institute of Technology, Beijing 100081 Received 28 September 2017 *Supported by the National Natural Science Foundation of China under Grant Nos 11374033, 11774030, 51735001 and 61775016, and the Fundamental Research Funds for the Central Universities under Grant No 2017CX10007.
**Corresponding author. Email: suwy@bit.edu.cn Citation Text: Sun D D, Su W Y, Wang F, Feng W X and Heng C L 2018 Chin. Phys. Lett. 35 017201 Abstract We investigate the electronic-transport properties of two-dimensional monolayer films from Au-P-Au molecular junction to Au-Si-Au molecular junction using elastic scattering Green's function theory. In the process of replacing the P atoms with Si atoms every other line from the middle of monolayer blue phosphorus molecular structure, the substitution of Si atoms changes the properties of Au-P-Au molecular junction significantly. Interestingly, the current value has a symmetric change as a parabolic curve with the peak appearing in Au-Si$_{1}$P$_{1}$-Au molecular junction, which provides the most stable current of 15.00 nA in a wide voltage range of 0.70–2.70 V. Moreover, the current–voltage characteristics of the structures indicate that the steps tend to disappear revealing the property similar to metal when the Si atoms dominate the molecular junction. DOI:10.1088/0256-307X/35/1/017201 PACS:72.90.+y, 73.23.-b © 2018 Chinese Physics Society Article Text The successful exfoliation of graphene provides wide applications in electronic and thermoelectric devices. However, the zero band gap of graphene cannot realize the logic switch, which limits its applications in semiconductor and optoelectronic devices.[1] Thus other new two-dimensional materials have attracted significant attention in the past few years, such as silicene, germanene, boron nitride sheet, transition metal dichalcogenides and phosphorene.[2-10] Very recently, the representative silicene and phosphorene with a graphene-like honeycomb lattice have opened up renewal fields of nanoelectronics and nanophotonics. Monolayer silicon has been successfully achieved in experiments.[2,3] Blue phosphorus, a novel phase of phosphorus, has been obtained by half-layer-by-half-layer growth on a GaN substrate theoretically,[11] which displays a wide fundamental band gap and shares its high stability and mobility.[12-14] Although monolayer silicon and phosphorus have excellent features, some researchers believe that their compounds may exist with better properties. Huang et al.[15] have predicted and theoretically found several semiconducting Si$_{x}$P$_{y}$ monolayers, which can be stable only at the stoichiometry of $y/x \ge 1$ and can give the lowest negative formation enthalpies when $y/x=1$. Our previous work of Gao et al.[16] have investigated the electronic-transport properties of the predicted monolayer and bilayer Si$_{1}$P$_{1}$ molecular junctions, which found that monolayer Si$_{1}$P$_{1}$ molecular junction can output a stable current of 20 nA, and the bilayer Si$_{1}$P$_{1}$ molecular junctions can provide the higher current of 42 nA, respectively. Inspired by the unusual and promising characteristics of Si$_{1}$P$_{1}$ than their constituent parents,[15,16] and the little research on the compounds Si$_{x}$P$_{y}$, we are eager to explore how the electronic-transport properties change from blue phosphorus to silicon phosphide (Si$_{1}$P$_{1}$). In this Letter, we not only focus on the electronic-transport properties of the monolayer films from Au-P-Au to Au-Si$_{1}$P$_{1}$-Au molecular junctions, but also study that from Au-Si$_{1}$P$_{1}$-Au to Au-Si-Au molecular junctions. The conversion between molecular junctions is accomplished by replacing the P atoms with Si atoms every other line from the middle of blue phosphorus molecular structure. It is found that the current value is variable in the transformation process, which increases first and then decreases like a parabola with the lines of Si atoms increasing. It is noteworthy that the Au-Si$_{1}$P$_{1}$-Au (6 lines of Si atoms) not only provides the highest current value (the peak of the parabola), but also outputs the most stable current within the wide voltage range of 0.70–2.70 V, which verifies the rationality of our previous research.[16] A set of quantum chemistry calculation methods constitute the theoretical framework.[17-25] In the above methods, the molecular device consists of three parts: source electrode (S), drain electrode (D) and extended molecule (M), as shown in Fig. 1. The electrode of source (drain) and the extended molecule are treated with an effective mass approximation and hybrid density functional theory,[17,18,20] respectively. Through the line up of their effective Fermi levels, the extended molecule is in equilibrium with the source and the drain. Owing to the molecule being only a small perturbation to electrodes, the Fermi level of the electrodes can serve as the Fermi level of the whole equalizing molecular device, which we can set the middle of the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the finite system at the position of Fermi level in electrodes. Thus our methods not only have the advantage of bulk electrode parameters, but also conquer the shortage of the finite system.
cpl-35-1-017201-fig1.png
Fig. 1. Schematic diagram of a molecular junction.
Our theoretical calculation comes from the work of Wang et al.,[20] with the elastic scattering approach based on the original work of Mujica et al.[21] and similar to the works of Datta et al.[22,23] The Hamiltonian of the finite system can be expressed as $H_{\rm f}|\eta \rangle=\varepsilon _\eta|\eta \rangle$, $|\eta \rangle $ is the eigenstate of $\varepsilon _\eta$. Under $\varepsilon _\eta$, only the coupling potential between the electrode and the molecular of the system has an important effect on the conductance of the molecular device, which can be calculated by $$\begin{align} V_{SJ} =\,&\sum\limits_\nu \langle S^\nu|H|J^\nu\rangle\\ =\,&\sum\limits_\nu \sum\limits_{S_i,J_i} a_{S_i}^\nu a_{J_i}^\nu \langle \phi _{S_i}|H|\phi_{J_i} \rangle.~~ \tag {1} \end{align} $$ Equation (1) is the coupling potential between the layer of $S$ in the source and the layer of $J$ in the molecule, where $\langle \phi _{S_i}|H|\phi _{J_i} \rangle$ is the interaction between the base vector of the two atoms. We assume that the molecular devices are arranged along the $Z$-direction, if electrons are scattered from the initial position $\sum |{\xi _i} \rangle$ in the source to the final position $\sum |\xi'_m \rangle$ in the drain, the transition matrix element of the system can be written based on elastic scattering Green's function theory as[20,24,25] $$\begin{align} T_{\xi'\xi}^\eta =\,&\sum\limits_{i,m} \sum\limits_{J,K} V_{\xi'_mK} g_{KJ}^\eta V_{J\xi _i}\\ &+\sum\limits_{i,m} \sum\limits_{D\ne \xi'_{\rm m},J} V_{\xi'_m} g_{DJ}^\eta V_{J\xi _i}\\ &+\sum\limits_{i,m} \sum\limits_{K,S\ne \xi _i} {V_{\xi'_m}} g_{KS}^\eta V_{S\xi _i},~~ \tag {2} \end{align} $$ where $K$ and $D$ are the layers of $K$ and $D$ of the molecule and drain electrode, respectively, $g_{\rm KJ}^\eta$ is the distribution function of carrier conductance on energy, $i$ and $m$ are the atomic positions of the source and drain, respectively. In the one-dimensional electron system, the electrons in state $k$ from source transfer to the state $q$ of the drain can be described by a transition matrix element $T$, when the external bias $V_{\rm D}$ is applied, the current density $i_{\rm 1D}^{[17-19]}$ and $T$[17,26] can be written as $$\begin{align} i_{\rm 1D} =\,&\frac{2\pi e}{\hbar}\sum\limits_{k,q} {|T|} ^2[f(E_k-eV_{\rm D})\\ &-f(E_q)]\times \delta (E_k -E_q),~~ \tag {3} \end{align} $$ $$\begin{align} T(E_i)=\,&\sum\limits_J \sum\limits_K V_{SJ} V_{KD} \sum\limits_\eta \frac{\langle {J} |\eta\rangle \langle \eta |K \rangle}{z_i -\varepsilon _\eta},~~ \tag {4} \end{align} $$ where $E_k$ and $E_q$ are the initial state energy and the final state energy respectively, $J=1,2,\ldots,N$ and $K=1,2,\ldots,N$ run over all atomic sites, 1 and $N$ are two end sites where the molecule and the electron reservoirs are connected, $V_{SJ}$ and $V_{KD}$ are the coupling between sites $J(K)$ and reservoirs $S(D)$, and $\langle {J} |\eta\rangle \langle \eta | K\rangle$ as two overlapping matrix elements represent the delocalization of $|\eta \rangle$. Parameter $z$ is a complex variable which can be expressed as $z=E_i+i{\it \Gamma}_i$, where $E_i$ is the observed energy in the scattering process, which corresponds to the energy of the transmitting electron from reservoir $S$ to scattering region, and the Fermi golden rule determines the escape rate ${\it \Gamma}_i$. Then the current of the whole molecular junction can be calculated by $I_{\rm 1D}=i_{\rm 1D}$. In the two-dimensional electron system, the current density can be described as[18-20,26-28] $$\begin{align} i_{\rm 2D}=\,&\frac{2\pi e}{\hbar}\int_{\rm eV}^\infty \int_0^\infty {\rho _{\rm 1D}} (E_x)dE_x|T|^2 \\ &\cdot[f(E_x+E_z -eV_{\rm D})-f(E_x\\ &+E_z)]n_{\rm 1D}^{\rm S} (E_z)n_{\rm 1D}^{\rm D} (E_z)dE_z, \\ \rho _{\rm 1D} (E)=\,&r_S N_{\rm 1D}(E),~~ \tag {5} \end{align} $$ where $\rho _{\rm 1D} (E)$ and $N_{\rm 1D} (E)$ are the densities of states per length per electron volt of the source and the one-dimensional (1D) density of state per length per electron volt, respectively, $E_z$ is the kinetic energy of the transmitting electron in the $z$ direction, $n_{\rm 1D}^{\rm S} (E_z)$ and $n_{\rm 1D}^{\rm D} (E_z)$ are the one-dimensional density of states of the source and drain electrodes, respectively,[26-28] and $r_S$ is the average radius of the conduction electron, then the current of the whole system of molecular junctions can be obtained by $I_{\rm 2D}=Ai_{\rm 2D}$ ($A$ is equal to $r_S$). Figures 2(a)–2(d) illustrate several representative models of the monolayer films from Au-P-Au molecular junction to Au-Si-Au molecular junction with 2, 4, 6 and 8 lines of Si atoms, respectively, which have honeycomb lattices similar to graphene but with surface puckered structures. We transfigure the models by atomic substitution that Si atoms replace P atoms every other line from the middle of blue phosphorus molecular structure until the Si atoms occupy the entire molecular structure. The Au-Si$_{1}$P$_{1}$-Au molecular junction emerges when the lines of Si atoms are 6, as shown in Fig. 2(c). The role of the hydrogen atoms is to saturate the Si and P bonds. The orbital energy and orbital density of states are calculated by the Gaussian 09 software package.[29] In this study we take the B3LYP method[17] that represents the hybrid density functional theory and the basis set is LanL2DZ. Then the electron transport properties of the extended molecules are calculated using the QCME (quantum chemistry for molecular electronics) program.[30] Its working principle is to read out the output file of Gaussian 09 and to extract the description related to the electronic structure, including the overlaps. Based on this input of controllable bias voltage and ambient temperature, we can calculate the value of the electron transport properties such as the electronic transition probability, the change of current and conductance with bias voltage. The temperature $T$ is 300 K in our calculation.
cpl-35-1-017201-fig2.png
Fig. 2. The top and side views of several representative structures from Au-P-Au molecular junction to Au-Si-Au molecular junction with the replacement of Si atoms every other line from the middle of blue phosphorus molecular structure. Here (a)–(d) represent the lines of Si atoms to be 2, 4, 6 and 8, respectively. Au, Si, P and H atoms are represented by yellow, gray, orange and white spheres, respectively. The Au atoms on two sides are source (S) and drain (D) electrodes, respectively.
The mechanism of electron transport in extended molecules is that the energy of the incident electrons from the source raises with the increase of the external bias $V_{\rm D}$. The electrons can tunnel through the conduction orbits and reach the drain electrode easily when its energy is higher than the energy of conduction orbits, which leads to a sharp increase in the current. Then the current will be constant until the energy reaches the next conduction orbital. This process results in the quantized steps in the current–voltage curves. Figures 3(a)–3(d) show the density of states (DOS) of the structure models mentioned in Fig. 2 corresponding to 2, 4, 6 and 8 lines of Si atoms, respectively. It is obvious that there are some peaks in each DOS picture, which means that there might be orbits for electronic transport with a rapid increase in current. The first two peaks are located at the HOMO and LUMO, respectively. The flats over a wide energy range represent no orbit, which we can deduce that the current would remain stable over the voltage range until the next DOS peak (conduction orbit). Then the steps of current will be formed. Figures 3(a)–3(c) reveal that the flats are obvious, particularly in Fig. 3(c) (Au-Si$_{1}$P$_{1}$-Au), which has the widest flat with the energy range from $-$4.16 eV to $-$2.55 eV and can be assumed that there would be a wide analogous step in the $I$–$V$ curve. Then the flat becomes narrow and almost disappears, as shown in Fig. 3(d), implying that the current might keep rising without obvious steps in the $I$–$V$ curve. Moreover, the DOS of Au-Si$_{1}$P$_{1}$-Au (Fig. 3(c)) is in agreement with our previous work.[16]
cpl-35-1-017201-fig3.png
Fig. 3. The density of states of several representative structures from Au-P-Au molecular junction to Au-Si-Au molecular junction mentioned in Fig. 2 corresponding to the lines of Si atoms to be 2, 4, 6 and 8, respectively.
cpl-35-1-017201-fig4.png
Fig. 4. The transmission spectra of several representative structures from Au-P-Au molecular junction to Au-Si-Au molecular junction with the lines of Si atoms being 0, 1, 2, 4, 6, 8, 10 and 12, respectively.
Whether the orbits in DOS peaks can really be conduction orbits also depends on the transmission. Figure 4 reveals the transmission spectra of structure models corresponding to 0, 1, 2, 4, 6, 8, 10 and 12 lines of Si atoms, respectively. The peaks indicate that there may be transport channels of electrons that will lead to a rapid increase in current. It is easy to find that the highest peak (the second peak in pink) appears in the structure with 6 lines of Si atoms (Au-Si$_{1}$P$_{1}$-Au), which will produce the maximum current. Then after the third peak, the transmission remains zero from 0.70 eV to 2.45 eV similar to the DOS curve in Fig. 3(c), yielding the stable current within the wide energy range. The transmission with 0, 1, 2 and 4 lines of Si atoms also remain zero within a wide range of 0.20–1.80 eV but have lower peaks. In addition, the transmission with 8, 10 and 12 lines of Si atoms show numerous lower peaks from 0.00 eV to 3.00 eV, which will lead to the lower current and narrow steps in the current–voltage curves.
cpl-35-1-017201-fig5.png
Fig. 5. The calculated current and conductance characteristics of several representative structures from Au-P-Au molecular junction to Au-Si-Au molecular junction with the lines of Si atoms being 0, 1, 2, 4, 6, 8, 10 and 12, respectively.
After analyzing the DOS and transmission spectra, we calculate the current and conductance characteristics, as shown in Fig. 5. The $I$–$V$ curves are consistent with the above analysis of DOS and transmission. The pink line (Au-Si$_{1}$P$_{1}$-Au) reveals the most stable step with the largest current of 15.00 nA from 0.70 V to 2.70 V, which is also in line with the result of our previous work[16] and shows its promising application in molecular devices outputting stable current. The lines of 0, 1, 2 and 4 also show an excellent stable step within a wide energy range but with very small current less than 2.00 nA. However, the lines of 8, 10 and 12 illustrate no obvious stable steps with the current continuing to rise along the winding road, and their current value is small as well. The gradual disappearance of the steps leads to the similar linear relationship revealed in $I$–$V$ curves, which can be considered as the metal-like properties. The transition from semiconductor to similar metal is related to the analysis of our another study.[31] Because Si is a group-IVA element, among which the graphene has excellent conductivity through the Dirac point with the valence and conduction band meet at one point. Thus the silicene when Si atoms dominate the molecular structure also has good conductivity though Si atoms are slightly weaker than C atoms (graphene). The conductance characteristics, such as the Au-Si$_{1}$P$_{1}$-Au shows three major peaks, the first peak is at 0.17 V, which is equivalent to the energy of DOS peak at about $-$4.63 eV (LUMO), where the conductance will increase rapidly. Thus the DOS peak at about $-$4.63 eV for the monolayer Au-Si$_{1}$P$_{1}$-Au molecular junction corresponds to the first conduction channel. Then there is no obvious peak from 0.70 V to 2.70 V determining the stable current within the wide range. The conductance characteristics of other structures have lower and more peaks than Au-Si$_{1}$P$_{1}$-Au molecular junction, verifying the analysis of transmission. Having studied the characteristics of the current and conductance of each film from Au-P-Au to Au-Si-Au molecular junctions, we find that there is an interesting curve of current values changing with the numbers of the lines of Si atoms at 1.0 V, as shown in Fig. 6. It is like a symmetrical parabola between the 4 and 9 lines. In addition, the peak of the parabola appears in the 6 lines, which signifies the Au-Si$_{1}$P$_{1}$-Au molecular junction could produce the maximum current value of 15.0 nA. The lowest point appears in the 2 lines and the minimum current is 0.6 nA. Furthermore, combined with the above mentioned results of Au-Si$_{1}$P$_{1}$-Au molecular junction, our calculations can provide a validation of our previous work.[16]
cpl-35-1-017201-fig6.png
Fig. 6. The current values at 1.0 V as a function of the lines of Si atoms of the monolayer molecules from Au-P-Au molecular junction to Au-Si-Au molecular junction.
In conclusion, based on nonequilibrium Green function theory and density functional theory, we have studied the electronic transport properties of the monolayer molecules from Au-P-Au to Au-Si-Au molecular junctions with a substitution of Si atoms for P atoms every other line. It is exciting to find that the current values change with the lines of Si atoms like a parabola, among which the Au-Si$_{1}$P$_{1}$-Au (6 lines of Si atoms) molecular junction not only occupies the peak of the parabola with the maximum current value of 15.0 nA, but also provides the most stable current within a wide voltage range of 0.70–2.70 V, which is expected to be used in steady flow devices in molecular circuits. In the changes of $I$–$V$ curves, the gradual disappearance of the steps shows a similar metal-like property. Moreover, our study enriches the research of the new 2D material Si$_{1}$P$_{1}$ and explores its more potential application in electronic devices. The method in the present study provides the theoretical basis for experimental research on Si$_{1}$P$_{1}$ and provides a new idea to explore the secrets of more 2D functional materials theoretically and experimentally. References High-frequency, scaled graphene transistors on diamond-like carbonValley polarized quantum Hall effect and topological insulator phase transitions in siliceneInduced ferromagnetism in one-side semihydrogenated silicene and germaneneHeavy-Hole States in Germanium Hut WiresTuning the Electro-optical Properties of Germanium Nanowires by Tensile StrainGraphene and boron nitride lateral heterostructures for atomically thin circuitryElectronics and optoelectronics of two-dimensional transition metal dichalcogenidesTunable Transport Gap in PhosphorenePhosphorene oxides: Bandgap engineering of phosphorene by oxidationThe Nature of the Interlayer Interaction in Bulk and Few-Layer PhosphorusHalf Layer By Half Layer Growth of a Blue Phosphorene Monolayer on a GaN(001) SubstrateTheoretical predictions on the electronic structure and charge carrier mobility in 2D Phosphorus sheetsElectronic Structures and Carrier Mobilities of Blue Phosphorus Nanoribbons and Nanotubes: A First-Principles StudyThermal properties of black and blue phosphorenes from a first-principles quasiharmonic approachSecond law and entropy production in a nonextensive systemElectron Transport Properties of Two-Dimensional Si 1 P 1 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 formalismElectronic conduction through organic moleculesConductance spectra of molecular wiresLength dependence of coherent electron transportation in metal–alkanedithiol–metal and metal–alkanemonothiol–metal junctionsTwo Possible Configurations for Silver–C 60 –Silver Molecular Devices and Their Conductance CharacteristicsCharging-induced asymmetry in molecular conductors
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