Perfect rectifying behavior induced by AA-P₂ dopants in armchair silicene nanoribbon devices

Abstract

The band structures and electronic transport properties of AA-P₂-doped armchair silicene nanoribbons (ASiNRs), with two phosphorus atoms substituting two adjacent silicon atoms in the same sublattice A, were investigated by applying density-functional theory in combination with the non-equilibrium Green’s function method. The results proved that the adjustment of the location of AA-P₂ dopants in 7-ASiNRs gives rise to semiconducting and metallic characteristics of systems. The low-bias negative differential resistance behaviors appeared to be symmetrical in AA-P₂-doped ASiNR devices. However, the symmetry of negative differential resistance behaviors gradually declined with doping AA-P₂ from the center to the edge of the nanoribbons. In addition, a striking rectifying behavior can be found. These outstanding properties indicate the potential application of SiNRs in nanodevices.

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1 Introduction

Since a stable two-dimensional (2D) graphene monolayer was first fabricated in 2004, it has become a research focus due to its high electron mobility, resulting from Dirac cones in the energy band structures.^1,2 This outstanding characteristic motivated enough enthusiasm to explore graphene-like nanostructures. In terms of graphene itself, especially graphene nanoribbons (GNRs), the electronic properties need to be modulated by a controllable approach in the process of its practical application. Deliberately introducing defects and impurities is an effective way to change the electronic properties. A broad range of experimental and theoretical research has reported that boron (B) and nitrogen (N), the first choice doping elements, behave like n-type and p-type dopants in GNRs resulting in the modification of electronic structures.^3–8

Recently, a silicon analogue of graphene, named silicene, has attracted extensive attention. The epitaxial single-layer silicene sheets were successfully synthesized on Ag,⁹ ZrB₂,¹⁰ Au and Ir surfaces.^11,12 This breakthrough has realized the connection between monolayer 2D nanostructures with traditional silicon technology. Silicene, unlike graphene, is a low-buckled honeycomb lattice, which is attributed to a behavior in between that of sp² and sp³ hybridization.¹³ Therefore, silicene not only has similar electronic properties to those of graphene, but also has some more superior characteristics, such as a large spin–orbit interaction,¹⁴ quantum spin Hall effect,¹⁵ valley-polarized metallic phase,¹⁶ mechanically tunable bandgap,^17–19 and so on. Using a first principles method, band structure calculations indicated the silicene is a semimetallic nano-material with zero bandgap at the Fermi level.^20–23 Therefore, many studies on silicene were devoted to the opening of the energy bandgap. The synthesis of quasi-one-dimensional silicene nanoribbons (SiNRs) effectively has broken the bottleneck. Experimentally, SiNRs with a width of 1.6 nm and a length of a few hundred nm have been synthesised on an Ag(110) surface.^24,25 In addition, the theoretical calculation has also demonstrated that there are two types of SiNRs, zigzag-edged SiNRs (ZSiNRs) and armchair-edged SiNRs (ASiNRs). The ZSiNRs always exhibited metallic properties without being limited by the ribbon width, while ASiNRs exhibited metallic or semiconducting properties depending on the ribbon width.^26,27 The synthesis of SiNRs opened up a new opportunity for field effect transistors,^28,29 photoluminescence detectors,³⁰ and spintronic devices etc.³¹

Different from GNRs, not only can B and N insert into the Si crystal lattice, but aluminum (Al), phosphorus (P) and sulfur (S) can also be easily incorporated into SiNRs.^32,33 Sivek’s group studied the effect of impurities (containing B, N, Al and P dopants) on the structural, electronic, and magnetic properties of silicene, which suggested that B, N, and P atoms behave like acceptors and Al atoms as donors for silicene.³⁴ Moreover, the effect of B/N pair doping on the electronic properties of SiNRs was investigated by Zhang et al., and the results revealed that the B/N pair can adjust the bandgap by tuning the B/N pair doping site in ASiNRs.³⁵ However, regarding P pair doping in SiNRs, no literature has been published. In the present work, we predicted a reasonable way to tune the electronic and transport properties of SiNRs by doping two P atoms into the same silicene superlattice, which are marked as red atoms in Fig. 1(a), defined as AA-P₂. We achieved a transition between metallic and semiconducting characteristics in the ASiNRs by changing the location of the AA-P₂ dopants. Additionally, we observed low-bias negative differential resistance (NDR) and striking rectifying behaviors in AA-P₂-doped ASiNRs.

Fig. 1 (a) Structural parameters for silicene. The red atoms denote the same superlattice. (b) Schematic illustration of the supercell of C–E configuration. The labeled capital letters stand for different doping sites forming different types of AA-P₂ dopants. Golden, white, and lilac atoms indicate silicon, hydrogen, and phosphorus atoms, respectively. (c) The relationship of the total energy for AA-P₂-doped 7-ASiNRs, showing that the total energy has diminished in the A–B′ configuration, which has the lowest total energy.

2 Models and methods

In this paper, the electronic band structures and transport properties were investigated for AA-P₂-doped ASiNRs, adopting density functional theory (DFT) combined with the non-equilibrium Green function (NEGF) method. After a test calculation, we only considered the ASiNRs as our object of study, as the location of AA-P₂ doping had no effect on the metallic character of the ZSiNRs. As everyone knows, each superlattice contains two different lattice structures, as shown by the positions of the red and golden atoms in Fig. 1(a), which were defined as “A” and “B”. On the basis of the location and direction of the AA-P₂ dopants, we mainly considered two different models. The first model, (I) AA-P₂⊥ASiNRs, showed that two P atoms perpendicular to the armchair line were inserted into the same superlattice “A” of the ASiNRs, and were marked as A–C, B–D, C–E from edge to center. Model (II) AA-P₂∠ASiNRs, showed that two P atoms perpendicular to the diagonal armchair line were inserted into the same superlattice “A” of ASiNRs, and were marked as C–D, B–C, A–B from center to edge. Fig. 1(b) shows a diagram of the C–E structure of the ASiNRs, in which two P atoms substituted silicon atoms (labeled by capital letters) and formed AA-P₂-doped ASiNRs in a supercell consisting of three unit cells. The edge silicon atoms were inactivated by hydrogen. Compared with GNRs, the study found that the bandgap of SiNRs also depended on the width of the ribbon, while GNRs had larger bandgaps than SiNRs with the same ribbon width. So, bandgap variation for SiNRs was separated into three types, namely N = 3n + 1, 3n and 3n − 1, with n being an integer.³⁶ In addition, the bandgap decreases along with an increase in the width of the nanoribbons, resulting from a quantum confinement effect (QCE).^37,38 Trivedi et al. proved that the 3n + 1 type of SiNRs have large bandgaps compared to the 3n and 3n − 1 types.³⁹ Therefore, we chose the width of AA-P₂-doped ASiNRs with seven dimer lines (N = 7).

The geometric structure optimization and electronic band structure calculation were performed using the Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA) package.^40,41 The generalized gradient approximation (GGA) parameterized by Perdew Burke Ernzerhof (PBE) was adopted for the exchange-correlation potential.⁴² To achieve the balance between calculation accuracy and flexibility, full structural optimizations were carried out by 10 × 1 × 1 Monkhorst–Pack k point sampling until the residual forces on the atoms were less than 0.02 eV Å⁻¹ and the difference in total energy was less than 10⁻⁵ eV. In the self-consistent total-energy calculations, the Brillouin zone (BZ) was sampled using 23 × 1 × 1 Monkhorst–Pack k points. The cutoff energy was set to 200 Ry. The atomic orbital basis set was the double-ζ plus polarization (DZP) basis set.

The transport property calculations were performed using the TRANSIESTA-C package.^40,41,43 The standard equation for voltage transmission spectra was used:

T(E, V) = Tr[Γ_L(E, V)G(E, V)Γ_RG^†(E, V)

where G is the Green’s function of the contact region, Γ_L/R is the coupling matrix, and V is the applied voltage bias. The computational formula for current can be used, namely the Landauer–Büttiker formula:
where μ_L and μ_R are the electrochemical potentials for the two electrodes and T(E, V) is the transmission coefficient at energy E and bias voltage V.⁴³

3 Results and discussion

Unlike planar graphene sheets, the stable structure of the silicene sheet was buckled as shown in Fig. 1(a), and we can predict higher surface activity due to the sp² and sp³ mixed hybrid lattice structure. After the structure optimization, the Si–Si bond lengths varied from 2.26 Å at the edge to 2.28 Å at the center and the Si–H bond length was about 1.51 Å. The calculated total energy of the AA-P₂-doped ASiNRs systems is presented in Fig. 1(c) which shows a lowest total energy in the A–B′ system (−734.5 eV). The results clearly show that the A–B′ configuration was the most stable structure. The difference in the negative total energies of these AA-P₂-doped systems is small, which implies that the AA-P₂-doped systems are all relatively stable. Obviously, in Fig. 1(c), the configurations of A–C and A–B were more favorable energetically than the others, suggesting that the AA-P₂ doping style was more likely to occur at the edge of the nanoribbons. Considering that the P atoms were incorporated at the edge of the A–C system, the lengths of the Si–H and P–Si bonds were 1.46 Å and 2.25 Å respectively, shorter than the edge Si–H and Si–Si bond lengths of 1.51 Å and 2.26 Å respectively, leading to a slight local deformation in the system. Moreover, when the exotic P atoms gradually moved closer to the center, the P–Si bond lengths were also slightly shorter than the initial Si–Si bond (2.26 Å), which demonstrates a stronger interaction between P and Si atoms.

The electronic band structures of AA-P₂-doped ASiNRs were investigated using periodic boundary conditions and are plotted in Fig. 2(a)–(c), corresponding to pristine 7-ASiNR, AA-P₂⊥ASiNR and AA-P₂∠ASiNR systems, respectively. The perfect 7-ASiNRs exhibited typical semiconducting characteristics with a bandgap of 0.52 eV between the π and π* bands at the Γ point in Fig. 2(a), which was consistent with 0.57 eV reported by Trivedi et al.³⁹ Similar to GNRs, impurity atoms in SiNRs also obviously changed the site of the bands shown in Fig. 2(b) and (c). We found that inserted AA-P₂ dopants caused a shift of Fermi level (E_F) into the conduction band and made the overall bands move down, which suggested that two extra electrons from the AA-P₂ dopants formed local states within the region of the conduction band. On the other hand, the introduction of AA-P₂ impurities not only changed the site of the bands, but also can modulate the bandgap of SiNRs. Due to the insertion of AA-P₂ dopants into ASiNRs, the P atoms generated two new impurity subbands between the π and π* bands, which indicated that the P atoms acted as donors. As for the AA-P₂⊥ASiNR systems shown in Fig. 2(b), AA-P₂ dopants provided an extra two electrons for ASiNRs and the bandgaps obviously decreased along with the location of the AA-P₂ dopants from edge to center. For example, the A–C system maintained a bandgap of about 0.08 eV. However, for the B–D and C–E systems, two new subbands touched each other and intersected with E_F so that the bandgap disappeared, and the systems display typical metallic features. More interesting was that impurity states in the vicinity of E_F were more delocalized with the location of P atoms from edge to center. Moreover, for AA-P₂∠ASiNR systems, as AA-P₂ dopants were introduced from the center to the edge of the nanoribbon, the two subbands were so slightly separated until they completely displayed a bandgap of about 0.21 eV in the A–B′ configuration. As a result, by changing the location of the AA-P₂ dopants in the 7-ASiNRs, the semiconducting and metallic characteristics of the systems can be obtained. As far as we know, the location-dependent electronic properties observed here are in reasonable agreement with related theories about graphene nanoribbons.^44,45

Fig. 2 (a)–(c) Band structure of pristine 7-ASiNR, AA-P₂ vertical doped ASiNRs and AA-P₂ diagonal doped ASiNRs, repectively. The Fermi level is set to zero, marked by the red dotted line. The red and blue bands represent the impurity subbands from AA-P₂ dopants in 7-ASiNRs.

To investigate the effect of AA-P₂ dopants on the electronic transport properties in 7-ASiNRs, we calculated the electronic transport properties. First of all, we used the two-probe transport model of AA-P₂-doped ASiNR devices, typified by the D–E′ configuration, as shown in Fig. 3(a). The two-probe model consisted of left lead, scattering center region and right electrode, respectively. The scattering center region linked up with half-infinite AA-P₂-doped ASiNR electrodes and contained three supercells, each of which was in combination with three sequential silicon unit cells. The transmission spectra of the AA-P₂⊥ASiNR and AA-P₂∠ASiNR systems at the equilibrium state are plotted in Fig. 3(b) and (c). The conducting channels of the systems were promoted by introducing impurity bands, and small transmission gaps appeared at the E_F of the A–C and C–D′ systems compared with those of perfect 7-ASiNR. About 2G₀ (G₀ = 2e²/h) transmission peaks from the flat near the E_F appeared in A–B′, B–D and B–C′, which showed the visible metallic character. In particular, the peak at about 3G₀ appeared at the E_F of the C–E configuration in accordance with the electronic band structure of C–E. So, we reached the conclusion that changing the sites of the P atoms significantly altered the zero-bias transport properties with semiconducting and metallic characteristics in AA-P₂-doped ASiNRs.

Fig. 3 (a) Schematic of the two-probe transport model of the D–E′ configuration. The lilac atoms represent the position of the phosphorus atoms. The numbers on the left side indicate the width of the ASiNRs. (b) and (c) The transmission spectra of AA-P₂ vertical doped ASiNRs and AA-P₂ diagonal doped ASiNRs at the equilibrium state, respectively. The dot-dash line and shadowed parts denote the transmission spectra at positive and negative energies respectively.

In order to evaluate the transition between metal and semiconductor, and deeply explore the transport properties by changing the location of the AA-P₂ dopants in 7-ASiNRs, the current–voltage (I–V) characteristic curves of all AA-P₂-doped ASiNR devices are presented in Fig. 4(a) at the bias range from −1 to +1 V in steps of 0.1 V. The current of all devices increased rapidly to reach peak values first, then the currents decreased and fell to the lowest values with an increase of the bias, leading to good NDR behavior. As for AA-P₂⊥ASiNR systems, the magnitude of the current in the A–C device was significantly less than that of the B–D and C–E systems. Similarly, for AA-P₂∠ASiNRs, not only did the current decrease but also the symmetry of current was destroyed under the positive and negative voltage. On this basis, we can draw the conclusion that the NDR behaviors of AA-P₂-doped ASiNR devices depended on the location of the AA-P₂ dopants. In addition, the symmetry of the geometric structure was broken by doping the edge, thus weakening the conduction ability. Furthermore, it is interesting that the NDR effect generally appeared within high bias regions, while NDR behaviors in our devices can be observed at such a low bias (from 0.0 to 0.4 V), which reduced power consumption in the device design process. Although the edge doping of AA-P₂ reduced the current for the A–B′ system and weakened the NDR behavior, rectifying behaviors still can be observed. According to the basic definition of the rectifying ratio, R(V) = I(V)/I(−V), we plotted the rectifying ratio curves on AA-P₂-doped ASiNRs in Fig. 4(b). From the figure, we can see that the rectifying ratio of the B–D and B–C′ systems was almost 1 within the scope of the calculated bias. This means that the magnitude of the opposite current was almost the same for positive and negative bias. However, the A–B′ device appeared to have the biggest rectifying ratio of about 10 at 0.5 V. When the symmetrical structure of the system was broken, the magnitude of current decreased leading to the current of A–B′ being smaller than the others. The NDR behaviors still existed, however, the peak-to-valley ratio (PVR) in the positive bias region is larger than that in the negative bias region to exhibit a rectifying behavior. These outstanding behaviors indicate the potential application of AA-P₂-doped ASiNRs in nanomaterial-based devices.

Fig. 4 (a) Current–voltage (I–V) characteristics of AA-P₂-doped ASiNR devices with the bias voltage varying from −1.0 V to 1.0 V in a step of 0.1 V. (b) Rectification ratio as a function of the bias for AA-P₂-doped ASiNR devices from 0.1 V to 1.0 V.

To explain the strong rectification behavior, the bias-based transmission spectra are plotted in Fig. 5. As we know, the current was determined by the integral region in the bias windows from the Landauer–Büttiker formula. Furthermore, the interaction between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) was one of the important factors in influencing the conductivity of the systems. In other words, the smaller the distance between the two orbitals is, the stronger the conductance ability. For the B–C′ configuration in Fig. 5(a), the real integral areas were almost the same at biases with identical absolute values, such as ±0.4, ±0.5, ±0.6 and ±0.7 V. The gap between the HOMO and LUMO was nearly invariable at the equal absolute voltage values so that the rectifying ratio maintains a value of 1. As for the A–B′ configuration in Fig. 5(b), however, the integral areas and two orbitals were no longer symmetrical at the same bias absolute value, leading to the appearance of rectifying behavior, for which the biggest ratio was almost as much as 10 at 0.5 V. We can see the obvious transferring channels in the bias window at 0.5 V, while the transmission coefficients were almost zero in the bias window at −0.5 V. On the other hand, the gap between the HOMO and LUMO at 0.5 V was smaller than at −0.5 V. In consequence, the A–B′ device exhibited prominent rectifying behavior. The reason for this phenomenon is rooted in the doping effect of phosphorus atoms. It is well known that a phosphorus atom has one more electron than a silicon atom. When two silicon atoms at the same sublattice A were replaced by AA-P₂ in the A–B′ system, the additional electrons were injected into the system and the Fermi energy was pushed up slightly. In addition, the doping of phosphorus atoms was only performed on one side of the ASiNRs which made the distribution of electrons different on the two sides of the system. So, the A–B′ configuration showed a rectifying behavior like a p–n junction which was consistent with the previous rectifying mechanism.^46–48 We can predict that the unique electronic transport properties of the ASiNRs incorporated by AA-P₂ dopants could be very useful for designing silicene-based molecular devices.

Fig. 5 (a) and (b) Bias-dependent transmissions of B–C′ and A–B′ configurations from ±0.4 V to ±0.7 V in steps of 0.1 V. The dashed lines are bias windows and the green part denotes the real integral area of the bias window. The red and blue triangles represent the HOMO and LUMO, respectively.

4 Conclusions

The bandgap variation and transport properties of AA-P₂-doped 7-ASiNR devices were investigated by applying DFT combined with the NEGF method. Compared with the total energy between different types of AA-P₂-doped ASiNRs, the results made clear that the configurations with AA-P₂ dopants situated on the edge of ASiNRs, such as A–C and A–B′, were the most stable. The interesting thing was that semiconducting and metallic characteristics had been observed by changing the doping location of the AA-P₂ dopants in 7-ASiNRs. In addition, changing the location of P atoms inserted into ASiNRs will disrupt the distribution of electrons resulting in symmetric NDR and obvious rectifying behavior in low-bias regions. In particular, the rectifying ratio of the A–B′ configuration can reach up to 10 at 0.5 V. So, we predict that by adjusting the position of AA-P₂ dopants in ASiNRs, the transition between semiconducting and metallic characteristics can be realized, which provides a theoretical basis for the design of silicene-based electronic devices.

Acknowledgements

This work was supported by the National Basic Research (973) Program of China (Grant No. 2011CB932700), and the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province.

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