Dual spin filtering and negative differential resistance effects in vanadium doped zigzag phosphorene nanoribbons with different edge passivations Open Access

The successful exfoliation of graphene from graphite has opened up a new era for thin-film materials science, especially nanomaterials. Monolayer black phosphorous, also known as phosphorene, was successfully fabricated by mechanically exfoliating from bulk black phosphorus in 2014.¹ As we all know, phosphorene is a direct bandgap semiconductor and maintains high electronic mobility.^2–4 Moreover, phosphorene-based field-effect transistors (FETs) have been fabricated by Li et al.⁵ Their high charge-carrier mobility (1000 cm² V⁻¹ s⁻¹) and drain current modulation (10⁵) indicate promising applications in nanoelectronic devices.^6–8 Despite that the mobility in graphene is orders of magnitude larger than that in phosphorene,⁹ the on/off ratio of graphene is inferior to that of phosphorene. Thus, phosphorene is more suitable for exploitation in multifunctional nanoelectronic devices than graphene.^{6–8,10–12}

The magnetic, electronic, and transport properties of phosphorene and phosphorene nanoribbons (PNRs) have been investigated practically,^13–17 and the electronic transport properties of phosphorene and PNRs are the hot spots of these research studies. Notice that pure phosphorene or PNRs are nonmagnetic, which greatly limits their application in spintronic devices.^18–20 To overcome the disadvantage and broaden their application in spintronic devices, many researchers try various methods. For instance, the manipulation of the magnetic properties of PNRs has been widely investigated by doping with impurity atoms,^21–25 changing the types of edge passivation,^{15,20,26–28} or applying the external field in different directions.^13,29,30 These investigations suggest excellent candidates for spintronic devices with spin filter,^6,31–34 current switch,^11,35–37 rectification,^38,39 and negative differential resistance (NDR) effects in the future based on PNRs.^{32,34,40–42} In the report by Hashmi and Hong,⁴³ they studied the effect of transition metal atom doped phosphorene on the electronic properties systematically, and the half-metallicity was found in V and Fe doped phosphorene. In addition, Zhu et al.⁴⁴ also proposed that when zigzag and armchair blue phosphorene nanoribbons are doped with transition metals, they could be transformed from semiconductors to metals or half-metals. Substitutional doping with metal atoms has been an effective method to tailor the pristine properties of phosphorene and PNRs. Our previous investigation has shown that the zigzag PNRs (ZPNRs) can be tuned from nonmagnetic metals to magnetic metals or half-metals by different doping positions of V atoms, and the V-doped ZPNRs (V-ZPNRs) have potential applications as multi-functional spintronic devices.⁴⁵ 

Recently, extensive efforts have also been devoted to the investigation of electronic properties of ZPNRs with different edge passivations. Sun et al.⁴⁶ clarified that edge passivation makes ZPNRs more stable, and when ZPNRs are passivated by non-metallic atoms, the non-metallic atoms play a key role in the regulation of electronic properties. What is more, Sidike et al.²⁷ investigated how the different edge saturations, including H, Li, O, and Co atoms, affect the transport properties of the ZPNRs, and Shi et al.²⁸ revealed that ZPNRs with oxygen-saturated edges are antiferromagnetic (AFM) or ferromagnetic (FM) semiconductors with spin density localized at two ribbon edges. Ren et al.¹⁴ found that the half-metal phase can be controlled by the edge functional groups in ZPNRs. These research studies demonstrate that edge passivation is one of the most feasible ways to change the electronic and transport properties.

In this paper, we focus on the influence of different edge passivations on the electronic and transport properties of V-ZPNRs based on density functional theory (DFT). For V-ZPNRs, the energy level has a spin split between spin-up and spin-down channels near the Fermi level, which indicates that they are magnetic. Furthermore, we calculate the current–voltage curves and transmission spectra of several V-ZPNR based devices with different edge passivations; both dual spin filtering and NDR effects are obtained. These findings imply that the ZPNRs hold great promise in spintronics, i.e., building NDR devices, dual spin filters, or dual spin diodes.

The Atomistix ToolKit (ATK) software package based on density functional theory combined with nonequilibrium Green’s function is used to optimize the geometry and calculate the electronic transport properties.^37,47 This software package has been widely used in the study of nanostructures. The criterion for the convergence of the structure optimization is that the force acting on each atom is less than 0.01 eV/Å. Then, to solve the Kohn–Sham equation, the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) function is used for the exchange–correlation potential,⁴⁸ and the basis function sets adopt the double-zeta polarized (DZP). In addition, 1 × 1 × 100 in the x, y, and z directions is used for k-point sampling in the contracted Brillouin zone, and the transport direction is along the z-direction. The mesh cutoff energy is set to 150 Rydberg. To avoid spurious interactions due to the periodic boundary conditions, a vacuum region of 15 Å along the x and y directions is introduced. After the geometry optimization, the lattice constants for our monolayer phosphorene are $a=3.29Å,b=4.56Å$⁠, which are in good agreement with other theoretical calculations.^18,25

The nanoscale devices based on V-ZPNRs that are passivated by different atoms are drawn in Fig. 1(a). The left (right) region of blue shadow denotes the unit cell as the left (right) electrode, which is the ZPNRs with a width of 6 (marked as 6ZPNRs). The central scattering region is composed of the 6-fold expansion of the unit cell. The red atoms on the two edges represent H, halogen (F and Cl), O, and S atoms. For clarity, the side view of the unit cell is shown in Fig. 1(b).

The Landauer–Büttiker formula is a formula to describe the transport properties in a nanosystem. By connecting the current in the device with the transmission coefficient in the scattering region, the current is as follows:

where μ_L,R = E_F ± eV/2 are the electrochemical potentials of the left and right electrodes in terms of the common Fermi energy E_F. E is the energy of the electron, f_L(R) (E, μ) is the equilibrium Fermi distribution for the left (right) electrode, and T^↑(↓) (E, V) is the transmission probability for electrons transferring from the left to the right electrode with energy E and bias voltage V, which is defined as

where $GRA$ represents the retarded (advanced) Green function of the center region and Γ_L(R) is the coupling matrix of the left (right) electrode.

First, the band structure and total density of states (TDOS) of pristine and V atom doped ZPNRs have been calculated, which are shown in Fig. 2. For pristine ZPNRs, there is no obvious spin splitting of the energy level between spin-up and spin-down channels, and two subbands come across the Fermi level. This shows that the pristine ZPNRs are nonmagnetic metals. These results are in excellent agreement with other studies.^18,25 Compared with the case of pristine ZPNRs, the band structures with spin polarization are found in V-ZPNRs and two spin channels of the TDOS are asymmetric, which indicates that the V-doped ZPNRs show magnetism. To give a detailed analysis of why V-ZPNRs are spin polarized while pristine ZPNRs are not, we plot their spin difference density, which is shown in Figs. 2(c) and 2(f), respectively. It is clear that there is no distribution of spin difference density in pristine ZPNRs, while the spin difference density of V-ZPNRs is localized at the V atom, which indicates that the V atom is able to induce exchange interaction in the doped system and lead to the magnetism.

Then, we focus on the study of V-doped ZPNRs by different edge passivation types. As is known, structural stability is of great significance to experimental synthesis and practical applications. To find the stability of V-ZPNRs passivated by nonmetallic atoms, such as H, O, S, F, and Cl at two edges (signed by V-ZPNR_H, V-ZPNR_O, V-ZPNR_S, V-ZPNR_F, and V-ZPNR_Cl, respectively), we calculate their formation energy E_form, which is defined as E_form = E_total − E_V-ZPNR − 2E_X, where E_total is the total energy of the V-ZPNR terminated with the nonmetallic atoms, E_V-ZPNR is the total energy of the V-ZPNR with bared edges, and E_X is the energy of an isolated atom X (H, O, S, F, and Cl), and all units are in eV. The results show that formation energies for V-ZPNR_H, V-ZPNR_O, V-ZPNR_S, V-ZPNR_F, and V-ZPNR_Cl are −7.87, −14.86, −9.22, −13.18, and −6.34 eV, respectively. As we know, the negative value for the edge formation energy means that this structure is formed by an exothermal process, and the lower edge formation energy suggests a more stable structure. Therefore, we can conclude that all structures are stable. This suggests that these ribbons might be fabricated in the experiment.

The electronic properties of V-ZPNRs passivated by different nonmetallic atoms, including the band structure, total density of states (TDOS), and project density of states (PDOS), are displayed in Fig. 3. To illustrate the influence of different edge passivation types on electronic properties, the projected density of states (PDOS) is used to reflect the contribution of edge and passivation atoms to the TDOS. For comparison, the band structure, TDOS, and PDOS of bared V-ZPNRs are shown in Fig. 3(a). It can be seen that the density of states projected on edge P atoms shows clear peaks near the Fermi level, which means that the metallic characteristics of bared V-ZPNRs also originate from the edge states. To demonstrate the effect of the edge states visually, the Bloch state is also calculated in Fig. 3(a). The κ point is selected at the intersection site of a spin-up subband and the Fermi level. We can see that the Bloch state is not only localized at the V atom but also localized at the edge atoms. This means that the metallicity is related to the edge states.

From Figs. 3(b)–3(f), we can see that the nonmetallic atoms can effectively modulate the electronic properties of V-ZPNRs. As same as the bared V-ZPNR, both V-ZPNR_O and V-ZPNR_S exhibit magnetic metallic characteristics. From their PDOS, we can see that these characteristics mainly originate from edge P atoms and the terminated atoms. The related Bloch states are also calculated, which is shown that the states are not only localized at the V atom but also localized at the terminated atoms. Furthermore, we find that the PDOS of edge P atoms and terminated atoms has similar peaks and characters in the vicinity of the Fermi level. This means that there is a strong hybridization between them. Compared with V-ZPNR_O, V-ZPNR_S has more subbands passing through the Fermi level. We predict that the conductivity of V-ZPNR_S will be much stronger than that of V-ZPNR_O. As manifested in Figs. 3(d)–3(f), the V-ZPNRs passivated by H or halogen (F and Cl) atoms exhibit magnetic semiconductor characteristics with the bandgaps of 0.135, 0.057, and 0.035 eV. Their PDOS shows that the terminated atoms (H, F, and Cl) have little contribution to the conduction band minimum (CBM) and valence band maximum (VBM). From their Bloch states, we find that there is little existence of wave function distribution for the edge atoms, which is different from V-ZPNR_O and V-ZPNR_S. Therefore, the edge passivation can effectively adjust the electronic properties of V-ZPNRs, which can convert them from the magnetic metal to magnetic semiconductor.

In addition, we investigate the transport properties of the edge-passivated V-ZPNR. Figure 4 presents the spin-resolved current–voltage (I–V) curves and spin polarization of several devices for a parallel configuration (PC: the left and right electrodes keep the same spin direction) and antiparallel configuration (APC: the left and right electrodes keep different spin directions) from −1.0 to 1.0 V. For clarity, we also plot the I–V curves of the bared V-ZPNR in Figs. 4(a) and 4(b). It can be seen that both spin-up and spin-down currents have similar trends in the PC and APC. No matter positive or negative bias, the currents generally increase with the voltage, and there is a slight vibration in the high bias range. To quantify the spin-filtering effects of the devices, the spin polarizability (SP) is calculated using |(I_up − I_dn)/(I_up + I_dn)| × 100% at non-zero bias and |(T_up − T_dn)/(T_up + T_dn)| × 100% at zero bias. We find that the obtained spin polarizability is lower than 40%. However, from Figs. 4(e)–4(j), we find that, after saturating the dangling bonds with different atoms at two edges, their polarizability is significantly improved as high as 100%, which is an efficient spin-filter.

The I–V curves of devices based on V-ZPNRs passivated by O or S atoms are drawn in Figs. 4(c) and 4(d). To confirm that whether the current of V-ZPNR_S is larger than that of V-ZPNR_O, we plot their I–V curves together for comparison. It can be seen that the current of V-ZPNR_S is three times larger than that of V-ZPNR_O in the PC and four times larger in the APC. This means that changing the edge passivation types can adjust the magnitude of the current.

Figures 4(e)–4(j) present the I–V curves of devices based on V-ZPNR_H, V-ZPNR_Cl, and V-ZPNR_F in the PC and APC. From the calculated results, there are several important features that can be visible clearly: (1) They all show obvious spin-filtering behavior, in both the PC and APC. The difference is that in the PC, the spin-up current is significantly larger than the spin-down current within our calculated bias range. However, in the APC, under the negative bias, the spin-up current has relatively large values, but the case is opposite when the voltage is positive. In Figs. 4(e) and 4(g), their I–V characteristics are similar, so we take V-ZPNR_Cl in the PC as an example. It can be found that its spin-down current is completely suppressed in the entire bias range, while the case of spin-up current is opposite. Thus, the spin polarization is steadily high up to 100% from 0.1 to 1.0 V in the PC. In the APC, their spin polarization can also reach 100% under high bias. (2) The devices reveal obvious negative differential resistance behaviors. Figure 4(h) displays that from 0.6 to 1 V, as the voltage increases, the spin-down current decreases. (3) For the case of V-ZPNR_H and V-ZPNR_Cl in the APC, the spin-up and spin-down currents are filtered unidirectionally, so the devices act as a dual spin filter or a dual spin diode, which is essential in the use of spintronic devices. That is to say, we can obtain pure spin current by simply changing the voltage direction. A positive bias is applied, and the spin-up current is zero and is in the “off” state, while the spin-down current is in the “on” state. On the contrary, under a negative bias, the spin-up current is conductive, while the spin-down one is blocked. (4) When both edges are passivated by Cl or F atoms, the spin-up current in the APC increases slowly, which indicates that it cannot open a large current under a low bias, leading to the threshold voltage of 0.3 V. The bias controlled spin-polarized current will be applied to the spin field-effect transistors.

To further verify the physical mechanism of peculiar I–V curves in the spintronic devices, we plot the transmission spectrum as a function of energy level and bias voltage for devices based on V-ZPNR_O, V-ZPNR_S, and V-ZPNR_Cl in Fig. 5. From Figs. 5(a)–5(d), we can see that for the devices based on V-ZPNR_O and V-ZPNR_S, the transport spectra near the Fermi level maintain high values under zero bias in both the PC and APC. When a bias is applied, the currents increase rapidly as the expansion of the bias window. Moreover, it is noticed that the transmission coefficient of V-ZPNR_S in the bias window is far more than that of V-ZPNR_O, which explains that the current of V-ZPNR_S is much larger than that of V-ZPNR_O. From the transmission spectrum of V-ZPNR_S in the PC and APC, we can see that the area of the spin-up and spin-down transmission spectra gradually decreases from 0.6 to 1.0 V, indicating the obvious NDR effect.

From Fig. 5(e), we can see that, for the device of V-ZPNR_Cl in the PC, there is almost no transmission spectrum of spin-down within the entire bias window, which indicates that the spin-down current is suppressed. However, more and more spin-up transmission coefficients enter the bias window with the increase in positive bias voltage, resulting in increasing spin-up current. Therefore, high spin polarization is obtained. Moreover, we notice that, when the bias voltage is higher than 0.4 V, the values of the spin-up transmission spectrum decrease instead. A obvious zero transport gap (ZTG) enters the bias window, which results in the decrement of the spin-up current and the appearance of the NDR effect. Then, we pay attention to the case of the APC in Fig. 5(f). For the spin-up transport spectrum, there is no transmission spectrum under the entire positive bias, resulting in hardly any spin-up transport channels and nearly zero spin-up currents under positive bias. However, within the negative bias window, when the negative bias greater than 0.3 V is applied, the large transmission peaks come into the bias window and bring about a large number of transport channels, which explains the rapid rise of the spin-up current when the negative bias voltage exceeds 0.3 V. Moreover, for the device based on V-ZPNR_Cl in the APC, it is worth noting that the characteristic of the spin-up transport spectrum under the positive (negative) bias is the same as the spin-down transport spectrum under the negative (positive) bias. That is to say, combining the transmission spectrum in positive and negative bias voltages, one can know the dual spin filtering and dual spin diode effects in the device in the APC.

Finally, in order to give a vivid physical picture of the dual spin filtering effects and NDR behaviors in the device based on V-ZPNR_Cl, we plot the spin-resolved transport spectra associated with the local density of state (LDOS) in the APC around the Fermi level, which is shown in Fig. 6. According to the Landauer–Büttiker equation, we know that the integral area of the transport spectrum in the bias window corresponds to the magnitude of the current. From Fig. 6(a), we observe that at −0.6 V, the spin-up transport spectrum has visible high transmission peaks, but there are no transmission peaks for spin-down, which results in almost zero spin-down currents. However, as the bias goes to −0.8 V in Fig. 6(c), the reduction of the integral area of the spin-up transport spectrum is accompanied by the occurrence of the NDR effect. In addition, it can be seen from Fig. 6(b) that at 0.6 V, the spin-down current is suppressed, which is opposite to the characteristic at −0.6 V, thus forming an excellent dual spin filter. From the LDOS in Figs. 6(e)–6(l), we can see that at −0.6 V, the spin-up state extends to the whole scattering region, while the spin-down state is only localized in the right central scattering region. This means that the spin-up currents are the “on” states and the spin-down currents are the “off” states. In addition, we notice that the situation of LDOS at ±0.8 V is similar to that at ±0.6 V. Therefore, it can be concluded that the device based on V-ZPNR_Cl exhibits interesting transport characteristics as follows: When a positive bias is applied to the device, a spin-down current is obtained, and when a negative bias is applied, we can obtain a spin-up current. This discovery means that the device can act as a dual spin filter or a dual spin diode. By controlling the direction of the magnetic and electric fields, the current and spin orientation can be adjusted.

In summary, the electronic and transport properties of V-ZPNRs by different edge passivations have been studied using the first-principles study based on density functional theory combined with nonequilibrium Green’s function. The band structures and density of states show that the undoped ZPNRs are nonmagnetic, while the V-ZPNRs exhibit significant magnetic. The conductivity of V-ZPNRs can be adjusted effectively by different edge passivation types. Moreover, the devices based on V-ZPNR_H, V-ZPNR_F, and V-ZPNR_Cl exhibit dual spin filter effects and NDR behaviors. The spin polarization can reach up to 100% stably in a wide bias range. In brief, the proposed devices show a variety of important properties of spintronics, such as NDR behaviors and dual spin filter effects, which is of great significance for the development of spintronic devices based on phosphorene nanoribbons.

This work was supported by the National Natural Science Foundation of China (Grant No. 11604090) and the Program for Innovative Teams of Outstanding Young and Middle-aged Researchers in the Higher Education Institutions of Hubei Province (Grant No. T2020014).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding authors upon reasonable request.