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The spin filtering effect and negative differential behavior of the graphene-pentalene-graphene molecular junction: a theoretical analysis

  • Barnali Bhattacharya
  • Rajkumar Mondal
  • Utpal SarkarEmail author
Original Paper
  • 153 Downloads
Part of the following topical collections:
  1. International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB-2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday

Abstract

Density functional theory (DFT) combined with nonequilibrium Green’s function (NEGF) formalism are used to investigate the effects of substitutional doping by nitrogen and sulfur on transport properties of AGNR-pentalene-AGNR nanojunction. A considerable spin filtering capability in a wide bias range is observed for all systems, which may have potential application in spintronics devices. Moreover, all model devices exhibit a negative differential effect with considerable peak-to-valley ratio. Thus, our findings provide a way to produce multifunctional spintronic devices based on nitrogen and sulfur doped pentalene-AGNR nanojunctions. The underlying mechanism for this interesting behavior was exposed by analyzing the transmission spectrum as well as the electrostatic potential distribution. In addition, a system doped with an odd number of dopant shows a rectifying efficiency comparable to other systems. The above findings strongly imply that such a multifunctional molecular device would be a useful candidate for molecular electronics.

Graphical abstract

The graphene-pentalene-graphene molecular junction

Keywords

Density functional theory Spin filtering effect Negative differential effect Molecular junction Rectification ratio 

Introduction

The molecular electronics field [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] has achieved tremendous attention over the last two decades, and the reduction in size of molecular devices has become a major challenge for the scientific community. After the prediction of first molecular rectifier [1], molecular nanojunction and nanostructured systems are attracting growing interest as a new technological platform for electronic devices, such as rectifiers [1, 3, 4, 5, 6, 7, 8, 9], field effect devices [10], spin filters [11, 12, 13, 14, 15, 16], switching devices [17], and negative differential resistance (NDR) based devices [5, 8, 9, 11, 13, 14, 16, 17], etc. A capable approach for constructing molecular electronic devices is that of choosing molecules with intrinsic functionality. Many relevant experimental [3, 17] and theoretical [2, 10, 11, 12, 13, 14] works have been reported in this concern. Some molecular junctions are found to be promising candidates for next-generation electronic devices because of the amazing properties of spin transport [13, 14, 15, 16] through them where electrical current is controlled by the manipulation of spin of the electron. Various strategies [18, 19, 20] have been proposed for designing a single-molecule junction keeping in mind that the problem of intermolecular interactions should be avoided and the size of junction should be reduced. Improvement of molecular junction, in terms of size reduction, response, etc., is the most difficult task and depends on two major factors: choosing the appropriate molecule as well as contact moiety for molecular junction. Besides overall structure, spin configuration, position of the terminal atoms of electrode surface, and distance between the electrodes play a vital rule [21, 22, 23, 24]. Moreover, the molecular junction becomes magnetic molecule junction (MMJ) when a nonmagnetic molecular bridge is placed between two ferromagnetic electrodes [25, 26]. Pentacene is one such molecule that is very promising in organic thin-film transistors [27, 28], and a recent study [29] showed that functionalized pentacene–graphene nanojunctions are potential candidates in spintronic devices due to their spin-resolved transport properties with negative differential resistance behavior. Pyridine-linked (PDL) molecules [30, 31] have attracted enormous concern due to their exciting electrical properties. Biferrocene-based molecular junctions [32] have also been investigated due to their spin filtering capability. In addition, n-polyacene molecules sandwiched between Ni electrodes have been studied to show their spin filtering efficiency (SFE) [15].

It is clear from the previous study that carbon-based materials, such as graphene [33] and carbon nanotube [34], having flexible electronic properties are well adopted contact moiety for designing molecular junctions as they can be directly synthesized at the contact region. Graphene is found to be a well adapted electrode substance over metal for molecular junction as the electronic coupling in metal−organic interfaces are complicated and do not follow simple rules [30, 35]. It means that molecular level alignment between different metal-organic junctions cannot be understood by simply considering the difference in work function. Local interactions also play a crucial role in molecular level alignment [35]. Moreover, it is difficult to achieve a perfect atomic interface for metal organic junction, and so it results in high contact resistance for the device [5]. The planar-structured graphene may overcome this difficulty [5, 7, 22] as they can be directly used as electrodes in molecular devices. Graphene electrodes are employed in organic field-effect transistors [36, 37] and organic photovoltaic solar cells [38] due to their high conductivity and transparency. Graphene nanoribbons are a more accurate choice for electrodes in comparison to two dimensional (2D) graphene and are used as electrodes in molecular electronic devices for spin injection [7, 14]. Armchair graphene nanoribbons (AGNRs) show semiconducting properties [39, 40] and the band gap depends on the width of the ribbon, while the zigzag graphene nanoribbons (zGNRs) are metallic in nature [41]. Recent theoretical and experimental studies [42, 43] prove that the armchair graphene nanoribbons (AGNRs) are more stable than zigzag graphene nanoribbons (zGNRs). Moreover, ferromagnetism occurs in armchair GNR [44], which makes it a suitable electrode material for magnetic molecular junction. Numerous recent studies mainly concentrated on electron transport and the magnetic anisotropy in a single-electron transistor consisting of molecules placed between two armchair electrodes.

The above discussions motivated us to design a molecular nanojunction with a pentalene molecule linked to an armchair nanoribbon via acetylenic linkage. Pentalene (C8H6) is an organic semiconductor that can be viewed as two fused cyclopentadiene rings. We chose the pentalene molecule as polycyclic conjugated systems bearing carbocyclic five-membered rings, such as fluorenes [45] and indenes [46] have attained much interest because of their use in organic electronic devices. Recently, pentalene derivatives revealed promise in organic thin-film transistors [47], field-effect transistors [48]. In addition, transition-metal-pentalene sandwich clusters show their efficiency toward molecular junction formation [49], which also motivates our present study. We also investigated the modification of transport properties due to doping as doping effectively changes the other properties of the nanostructured system, including electronic [50, 51, 52, 53, 54], optical [51, 52, 55], and capacitive [54, 55, 56]. It has been reported that BN doped graphene nanoribbon [8] shows its strong rectifying efficiency and NDR effect. Theoretical studies reflect the perfect spin filtering effect and NDR behavior of phosphorus-doped zigzag graphene nanoribbons [57] and sulfur-passivated graphene nanoribbons [58].

In this paper, we calculate the transport properties of an AGNR-pentlene- AGNR device using density functional theory (DFT) method combined with nonequilibrium Green’s function (NEGF) formalism. We explored the modulation of electronic properties and spin-polarized current due to substitutional doping by nitrogen/sulfur with different concentration and predicted noticeable spin filtering efficiency of our modeled device. Furthermore, negative differential resistance effect was found with a small rectifying efficiency for these devices, which suggests their possible use in molecular electronics.

Calculation details

To maintain the good connectivity between the electrode and central scattering region, the entire system is optimized until the net force on each atom is less than 0.01 eV/Å. Optimization of all structures is performed using the conjugated gradient algorithm within the framework of the density functional theory as implemented in the SIESTA package [59]. The generalized gradient approximation (GGA) in Perdew-Burke-Ernzernhof (PBE) [60] form was used as the exchange-correlation functional and norm-conservative Troullier–Martins pseudo-potentials (PP) [61] with double-zeta-plus polarization function (DZP) basis set were employed for representing the valence and core electrons. The cutoff energy is set to 300 Ry and a 1×1×10 k-points sampling is used throughout the calculation and the electronic temperature is maintained at 300 K.

After optimization, the transport properties of these systems were calculated by using the TranSIESTA module within the SIESTA software package, which uses density functional theory (DFT) combined with the nonequilibrium Green’s function (NEGF) formalism [62, 63]. In transport calculation, under a certain bias voltage, the Landauer–Buttiker formula [64] is used to describe the spin-polarized current through the scattering region:
$$ I\left({V}_b\right)=\frac{e}{h}{\int}_{-\infty}^{\infty }T\left(E,{V}_b\right)\left[{f}_L\left(E,{\mu}_L\right)-{f}_R\left(E,{\mu}_R\right)\right] dE $$
where fL/R is the equilibrium Fermi–Dirac distribution functions for left (right) electrode and μL/R is the electrochemical potential for left (right) electrode, which can be related to the bias voltage as eVb = μL − μR. The transmission function T(E, Vb) for the the scattering region is obtained by the following formula:
$$ T\left(E,{V}_b\right)= Tr\left[{\varGamma}_L{G}^R{\varGamma}_R{G}^A\right] $$
where ΓL/R are coupling strength of the left (right) electrode and GR/A is the retarded (advanced) Green’s function of the scattering region.

Results and discussion

Model structure

Our model device contains three parts, namely the left electrode (LE), right electrode (RE), and central scattering region (SR), which is coupled to two semi-infinite leads, i.e., LE and RE (presented in Fig. 1a). Pentalene was chosen as the scattering molecule to see the nature of electron transport through it. To make the scattering region periodic, the pentalene molecule is coupled with armchair graphene fragment at both ends via acetylenic linkage such that the electronic structure of the scattering region resembles the electronic structure of other one dimensional (lD) structures [65] to some extent. Here acetylenic linkage is used as a linker between molecule and GNR fragment to extend the π-conjugation of the pentalene molecule as π-extended pentalene molecules are fairly stable [66]. The carbon atoms at the edges of the graphene fragment end with hydrogen atoms (sp2 type) in order to eliminate the dangling bonds. The left and right electrodes are modeled by a semi-infinite replica of the armchair graphene nanoribbon (AGNR) extending along the transport direction (Z-direction). Keeping the LE and RE the same, we also consider a nitrogen or sulfur substituted pentalene molecule as a core of scattering region (as shown in Fig. 1 and Fig. S1 in supplementary material). The doping concentration is varied and the transport properties of the materials were calculated via a two probe model. The suitable doping site has been checked in terms of energy and found that N and S atoms both favor to substitute sp2 hybridized carbon atoms rather than sp3 hybridized carbon atoms (see Fig. S2 in supplementary material).
Fig. 1

a Representative device model for AGNR-pentalene-AGNR nanojunction showing two electrodes and the scattering region; b device model for N/S-substituted pentalene-AGNR nanojunction. Here gray, white, blue ball represents carbon, hydrogen, and dopant (N/S) atom respectively

To verify the feasibility of our model device, we checked the thermodynamic stability of these materials in terms of formation energy (Table S1) and found it to be small positive for the entire model device. The substitution process (N/S doping) is endothermic in nature, but their small magnitudes (< 1) indicate the possibility of their synthesis. An N-substituted system is more stable than an S-substituted system as the formation energy is comparatively small for N-substituted systems (except the 4 N/S-doped model). For highest dopant concentration (4 N/S-doped pentalene), S-substitution is more favorable than N-substitution. The stability gradually decreases with increasing concentration.

Doping-induced modification in the electronic structure

As band structures significantly affect transport properties, we presented the band structure and total density of states (TDOS) of electrode as well as scattering region (Fig. 2 and Fig. S3). An armchair graphene nanoribbon is a direct band gap semiconductor with band gap value 1.52 eV located at Γ-point (see Fig. 2a), which is consistent with a previous study [67]. The overlap of band for both spin channels confirms the zero net magnetization of the electrode.
Fig. 2

The bandstructure and density of states (DOS) of electrode and scattering region a AGNR electrode b pristine pentalene-1D system c 4N-doped pentalene-1D system d 4S-doped pentalene-1D system. Fermi energy is shifted to 0.00 eV

As revealed from Fig. 2b, the pristine pentalene-1D system is a direct band semiconductor with energy band gap 0.18 eV located at zone boundary (Z-point). The valence band maxima (VBM) and conduction band minimum (CBM) are basically pyπ and pyπ* band respectively as observed from projected band study (Fig. S4). The energy states around the Fermi level (both CB and VB) are basically contributed by py orbital (Fig. 2b (ii)) of C atom, which is perpendicular to the σ-bond that binds the constituent atoms in the xz-plane. Although the nitrogen doping in graphyne and graphene [52, 68] is similar to electron doping, in the case of the pentalene-1D system, N-doping acts as p-type doping and results an electron-hole asymmetry that can clearly be observed from its band diagram and density of states (Fig. 2c (ii) and Fig. S3). The electron-hole asymmetry shifts the Fermi level toward lower energy (Fig. 2c, Fig. S3 and Table S2) as compared to the pristine pentalene-1D system. In addition, the π and π* bands of the pristine system (contributed by only C atom) undergo an upward shift without suffering an abrupt modification in their shape but have a slightly larger gap between them located in Z-point (Table S2 and Fig. S5). Although for the 1N/2N-doped pentalene-1D system, the π and π* undergo a negligible shift, the Fermi level still remains in between them and the system behaves as a direct band gap semiconductor. With increasing dopant concentration (3N/4N-doped pentalene-1D system) an upward shift of π and π* increases and crosses the Fermi level. Thus, the 3N/4N-doped pentalene-1D system behaves as a p-type semiconductor. Moreover, for highest dopant concentration (4N-doped pentalene-1D system), localized bands are observed at (near) the Fermi level, which appears as a sharp peak in the DOS plot (Fig. 2c). The well dispersed localized band at the Fermi level arises from the C atom and is observed for both spin channels, while the dispersionless impurity band endorsed by N atom appears at the Fermi energy (below the Fermi level) for down spin channel (for up spin channel). It is evident from the DOS plot for up spin that the sharp peak at Fermi energy is contributed by the py orbital of the C atom only, whereas for down spin the py orbital of both C and N atoms contribute to it. The downward shift of Fermi level increases with increasing dopant concentration and follows the trend 1N < 2N < 3N < 4N. When 4C is substituted by 4N, the gap is increased to 0.13 eV (0.06 eV) for up spin (down spin). Moreover, the spin splitting near Fermi level is increased with increasing concentration. Contrary to N-doping, S-doping acts as an electron doping (n-type doping) and shifts the Fermi level toward higher energy (Fig. 2d and Fig. S6, Table S2) as compared to the pristine pentalene-1D system. Due to S-doping, the π and π* band (blue color) of the pristine system undergoes a downward shift with/without having any gap between them at zone boundary. For odd number of S-atoms, a large gap is observed between the π and π* band, but for even number of S-atoms, a small gap is observed between the π and π* band. The downward shift of the π and π* band (upward shift of Fermi level) increases with increasing dopant concentration and follow the trend 1S < 2S < 3S < 4S. However, at the Fermi level, a huge gap is observed at Γ-point, with the exception of the 1S-doped pentalene-1D system. Thus, the S-doping altered the band gap position from Z-point to Γ-point compared to the pristine pentalene-1D system, but preserved direct gap semiconducting properties with enhancing band gap (0.82 eV → 0.92 eV) and zero magnetic moment. The absence of energy states at the Fermi level in the corresponding DOS plot ensures the semiconducting nature of the S-doped pentalene-1D system. Again the contribution of the S atom around the Fermi level is negligible compared to the C atom. For the 1S-doped pentalene-1D system, the π* band crosses the Fermi level having slightly larger gap between them located in Z-point and this system behaves as an n-type semiconductor (Fig. S3). The corresponding DOS plot shows a sharp peak at the Fermi level.

Current-voltage characteristics

The current-voltage (I-V) characteristics of our modeled AGNR-pentalene-AGNR based two-terminal devices are presented in Fig. 3. It is evident from the I-V curve that all considered devices exhibit a transport gap near the Fermi level (Fig. S7), which arises due to the band gap of the AGNR semi-infinite lead (1.52 eV) and acts as a threshold in the current voltage characteristics, i.e., up to ±1.52 V of bias voltage, the current is too feeble (nearly zero). However, the intensity of the current is dictated by the band gap of the scattering region. The current is low for the S-doped device and is comparable with the pristine device below bias voltage 1.80 V; afterward, the current gets suppressed compared to the pristine system. This behavior can be explained in terms of the band gap of the scattering region. Due to S-doping, the band gap or the gap between two π-bands enhances more than ~4.50 times that of the pristine one and current decreases markedly. For the N-doped device, the current is comparable with the pristine device up to 4.00 V; later the current noticeably decreases for 3N/4N-doped pentalene-device, but for 1N/2N-doped pentalene-device the current is comparable (even slightly larger) with the pristine one. The N-doping slightly increases the gap between two π-bands compared to the pristine one, as a consequence of which the current decreases for the 3N/4N-doped pentalene-device. The slight increase in current for the 1N/2N-doped pentalene-device cannot be explained in terms of band gap.
Fig. 3

Current-voltage characteristic of a AGNR-pentalene-AGNR device b AGNR-1N-doped pentalene-AGNR device c AGNR-2N-doped pentalene-AGNR device d AGNR-3N-doped pentalene-AGNR device e AGNR-4N-doped pentalene-AGNR device f AGNR-1S-doped pentalene-AGNR device g AGNR-2S-doped pentalene-AGNR device h AGNR-3S-doped pentalene-AGNR device i AGNR-4S-doped pentalene-AGNR device

The asymmetric behavior of current for up and down spin channel is clearly evident from the I-V curve for all modeled devices. The current corresponding to down spin is larger than that of the up spin one in the considered bias range. As bias increases, the spin-resolved current for up and down spin increases. This indicates the spin filtering behaviors of all systems, which can be confirmed from the (I − I) plot (Fig. S8), where I and I stand for up spin current and down spin current respectively. We can quantify the spin filtering behaviors of all systems by calculating the spin filtering efficiency (SFE) in considered bias range for which it can be defined as SFE = (I − I)/(I + I), where I and I stand for up spin current and down spin current respectively. At zero bias, the SFE can be defined as (T(Ef) − T(Ef))/(T(Ef) + T(Ef)) where T(Ef) and T(Ef) represents spin up and spin down transmission coefficient at Fermi level. To compare the spin filtering behavior of all considered systems, we plotted the SFE as a function of bias as depicted in Fig. S9. In the pristine pentalene device, SFE is steady and about ~33.33% in the bias ranges from (1.00 V to 7.00 V) and (−1.00 V to −7.00 V) indicating a stable SFE. When N is doped in the device, the SFE value highly changes in the voltage range 2.20 V → −2.20 V for high concentration of dopant (3N/4N), while for low N concentration (1N/2N-doped pentalene-device) the SFE value is steady (about 33.40%) and resembles the pristine pentalene-device. In the case of 3N-doped pentalene-device, the SFE value is very high (80.00 → 98.00%) in the bias range from −0.40 V → 0.60 V and the SFE is almost 98.00% at zero bias. Thus, a perfect spin filtering effect can be expected for the 3N-doped pentalene-device in that bias range. With increasing bias voltage, SFE value decreases first then increases to 76.20% (60.10%) at 1.60 V (−1.60 V). Later, SFE value again decreases and finally reaches platform (~33.00 to ~35.00%). For the 4N-doped pentalene-device at 0.00 V the SEF is almost −77.40% then a sudden fall in SEF is observed between the bias ranges (0.20 V to 0.60 V) and (−0.20 V to −0.60 V). In this bias range, the SFE value is too low and about 0.10 → 2.00%. The SFE value rises to peak (54.00 → 55.00%) at ±0.80 V, and afterward decreases until the bias approaches ±1.20 V. The SFE values highly fluctuate in the bias range from (1.40 V to 1.80 V) and (−1.40 V to −1.80 V). The fluctuations in SEF get minimized in higher voltage, ranges from (2.00 V to 7.00 V) and (−2.00 V to −7.00 V) and appear more or less stable (Fig. S9). Close inspection shows that there still exists some fluctuation, and in this bias range, the SEF value is highest for the 4N-doped pentalene-device and even greater than that of the pristine pentalene-device. The SFE for the S-doped device is almost the same as that of the pristine system and found to be constant in the bias range from (0.20 V to 7.00 V) and (−0.20 V to −7.00 V), except the 1S-doped pentalene-device.

The superiority of the S-doped device over the pristine device is that the SEF value in the low region is also steady, implying their stable spin filtering efficiency. For the 1S-doped pentalene-device, the SFE value rapidly changes in the bias range −2.20 V to 2.20 V. At zero bias the SFE value is almost 50%, but up to ±0.4 V the SFE value decreases for positive bias and increases for negative bias. With further increase of bias voltage in the negative direction, the SFE value declines gradually up to −1.40 V, then again increases to ~87.50% at −1.80 V. After that the SFE values eventually decrease and reach more or less steady state (the SFE values vary from 28.00 → 32.00%). However, for +ve bias voltage at 0.60 V the SFE value becomes almost 100.00%, inferring perfect spin filtering efficiency. Then a sudden fall in SEF value (45.00%) is observed at 0.80 V followed by a fluctuation of SFE value within the bias range 1.00 V to 1.80 V (SFE value fluctuate between 80.00 to 9.00%). With further increases in +ve bias voltage, the SFE value starts increasing and finally reaches a merely stable value. One interesting observation is that fluctuation of the SFE value in the low bias region is observed only for those system in which π (π*) bands cross the Fermi level and the gap between the π and π* band is situated in either CB or VB (n-type semiconductor or p-type semiconductor).

All considered devices are found to exhibit negative differential resistance (NDR) behavior besides their spin filtering capability (Table S3). In order to illustrate the NDR phenomenon, the peak−to–valley ratio (PVR) is defined as the ratio of Imax and Imin within a certain range of bias voltage. It is clearly revealed from Table S3 and Fig. 3a that in the pristine system the current for both spins increases gradually with increasing bias voltage and reaches a maximum at ±4.80 V. Thereafter, current decreases with further increase of bias voltage up to ±5.40 V, thus leading to a negative differential resistance (NDR) behavior. Corresponding PVR value is 1.12 (1.11) for positive (negative) bias voltage. In the second NDR region the difference between peak current and valley current is maximum, and appears in the bias range (6.20 V → 6.80 V) as well as (−6.20 V → −6.80 V) and the corresponding PVR is 1.23 (1.22) for positive (negative) bias voltage. In addition to these NDR phenomenons, a minor drop of current was observed at 5.80 V for which current difference with its preceding one (5.60 V) is too low and can be neglected.

For the single N-doped device with positive bias voltage (Fig. 3b), two prominent NDR phenomenon become visible between 4.80 V → 5.80 V and 6.20 V → 6.60 V respectively, and the corresponding PVR value is 1.17 and 1.24 for up and down spins respectively. However, for negative bias voltage, NDR behaviors appear between −5.00 V → −5.60 V, as well as between −6.20 V → −6.80 V, with PVR value of 1.08 and 1.35 respectively. In the 2N-doped system, the current increases monotonically in the bias range (0.00 V → ±5.00 V), except for a minor fall of current at ±4.20 V. Afterward, the current decreases with increasing bias up to ±5.60 V. Another prominent NDR region is observed in the bias range (6.20 V → 6.80 V), as well as between (−6.20 V → −6.80 V), having PVR value of 1.32 (1.31) for positive (negative) bias. For the 3N-doped pentalene-device, under both positive and negative bias, the first major NDR phenomenon is noticed in the voltage range (4.00 V → 5.00 V) and (−4.00 V → −5.00 V). In addition, other NDR phenomenon become noticeable within the bias voltage range (5.60 V → 6.60 V) and (−5.60 V → −6.60 V). For the +ve bias voltage, we obtained the PVR value of 1.35 for ↑ spin and 1.37 for ↓ spin; however, for –ve bias voltage, the PVR value is 1.27 for ↑ spin and 1.26 for ↓ spin. When we consider the 4N-doped pentalene-device, three major NDR regions are observed in the considered bias range. Besides, there are some minor falls of current at some specified voltage (±4.60 V). The first clearly visible NDR behavior emerged in the bias range (3.80 V → 5.00 V) and (−3.80 V → −5.00 V), whereas the second NDR phenomena is observed in the range (5.80 V → 6.80 V) and (−5.80 V → −6.80 V). We see that increasing N concentration shifted the first prominent NDR phenomenon toward the low voltage region (except the 2N-doped system). Next, we explore the tailoring of NDR phenomenon due to S-doping. For the single S-doped device, in positive bias voltage, up spin current exhibits a remarkable negative differential effect (NDR) within the bias range 5.40 V → 6.60 V with a PVR value 1.41, whereas down spin current exhibits NDR behavior in the region 5.20 V → 6.40 V with PVR value of 1.20. Conversely, up spin current under negative bias voltage shows an NDR region between −5.80 V → −7.00 V having PVR value of 1.49, while the NDR phenomenon becomes visible between −6.20 to −7.00 V with PVR value of 1.41 in the case of down spin current. Apart from these, some negligible falls in current were observed in the entire bias range. The 2S-doped pentalene-device exhibits three NDR regions for both positive and negative bias voltage. These three NDR regions occur between (4.00 → 4.40 V) and (−4.00 → −4.40 V), (5.40 → 6.00 V) and (−5.40 → −6.00 V), as well as (6.60 → 7.00 V) and (−6.60 → −7.00 V); among which the regions (5.40 → 6.00 V) and (−5.40 → −6.00 V) have the highest PVR value (1.52). For the 3S-doped pentalene-device, the occurrence of NDR behavior in the positive bias region is totally different from the negative bias region. Under positive bias voltage, NDR phenomenon appears in the bias voltage ranging from 4.00 V → 5.00 V and 5.60 V → 6.40 V, excluding a minor drop at 1.20 V → 1.40 V. Interestingly, the PVR value increases with increasing voltage, and the highest PVR value (1.59) is assigned to region 5.60 V → 6.40 V. However, for negative bias voltage, two NDR regions appear within voltage −5.40 V → −5.80 V, −6.40 V → −6.60 V; among which region −5.40 V → −5.80 V corresponds to the highest PVR value (1.51). There are two prominent NDR regions found in the I-V characteristics of the 4S-doped pentalene-device. Irrespective of the polarity of bias voltage, the first NDR phenomenon appears in the voltage range (4.00 V → 4.40 V) and (−4.00 V → -4.40 V) exhibiting the PVR value of 1.11 (1.13) under positive (negative) bias voltage. After 4.40 V, with further increase in forward voltage, the current increases rapidly up to 18.75 μA (37.45 μA) for up (down) spin at 5.20 V, then the current starts falling and reaches 11.22 μA (22.35 μA) for up (down) spin at 6.80 V. Now for negative bias voltage, after −4.40 V the current reaches a peak value of 18.54 μA (37.05 μA) for up (down) spin at −5.20 V, then decreases to 11.22 μA (22.35 μA) for up (down) spin at −6.80 V. Thus, an NDR region occurs between (5.20 V → 6.80 V) and (−5.20 V → -6.80 V) having a strong peak-to-valley ratio (PVR = ~1.67 for positive voltage and PVR = ~1.66 for negative voltage). Although some minor drops in current exist in this region, they are neglected as the difference in current is too low.

Some interesting findings from the above discussion are that: (a) NDR behavior becomes stronger with increasing dopant concentration, and for the same dopant concentration, NDR behavior is stronger for the S-substituted system than N-substituted system; (b) for all systems, peak-to-valley ratio is higher for the second NDR region, i.e., NDR behavior becomes stronger in high bias voltage with only the exception of the 3S-doped pentalene-device; (c) the NDR behavior is stronger under positive bias voltage than negative bias (except singly doped devices and the 3S-doped pentalene-device).

To explain the above interesting NDR phenomenon, we analyzed the electrostatic potential map, width, and strength of the transmission peak within the energy bias window. Energy bias window (EBW) is defined as the range between \( \raisebox{1ex}{$-{eV}_b$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \) to \( \raisebox{1ex}{$+{eV}_b$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \) and the current at any bias can be obtained by integrating the transmission function at that bias within the bias window. For convenience, the electrostatic potential map, transmission spectra, and density of states corresponding to some distinct bias voltage for the pristine pentalene-device up to voltage 6.20 V under positive bias is presented in Figs. 4 and 5. With the increase of bias voltage, the electrostatic potential of left and right electrodes gets redistributed, and the total density of states of the right electrode, RDOS, (total density of states of the left electrode, LDOS) shows its tendency to shift downward (upward) near the Fermi level.
Fig. 4

Electrostatic potential map of pristine pentalene-device at different bias voltage a 0.00 V, b 1.60 V, c 4.80 V, d 5.00 V, e 5.20 V, f 5.40 V, g 5.60 V, h 5.80 V, i 6.00 V, j 6.20 V

Fig. 5

Transmission spectra, LDOS, RDOS of pristine pentalene-device at different bias voltage a 0.00 V, b 1.60 V, c 4.80 V, d 5.00 V, e 5.20 V, f 5.40 V, g 5.60 V, h 5.80 V, i 6.00 V, j 6.20 V

The electrostatic map corresponding to zero bias (Fig. 4a) shows that potential is uniformly distributed all over the device, and corresponding transmission spectra, LDOS, RDOS (Fig. 4a) show a well defined gap at the Fermi level, which also clarifies the zero current at 0.00 V. Up to 1.60 V, the potential distribution is more or less uniform and there is no notable transmission peak within the EBW, which results in a feeble current in this range. The first distinguishable transmission peak within the EBW arises at 1.60 V (Fig. 5b) as a result of which current starts increasing noticeably from 1.60 V. The corresponding electrostatic map shows that the potential of the left electrode is slightly higher than the right electrode. Beyond 1.60 V the current starts increasing monotonically and continues up to 4.80 V attributed to the gradual growth of transmission function within the EBW. The corresponding electrostatic map at 4.80 V bias shows that potential of the left electrode is still higher than the right electrode as well as the width, and the strength of the transmission peak within the EBW (enclosed by purple dotted lines) increases as a result of which a significant current flows from the left to right electrode. Moreover, there is a strong overlap between LDOS and RDOS within the bias window, which enhances the current at 4.80 V. As the bias increases to 5.00 V (Fig. 4), the current starts to fall and continues up to 5.40 V. In this bias region, although the EBW increases, the width of transmission peak within the EBW (enclosed by blue dotted lines) remains more or less the same as that observed at 4.80 V. However, the strength of the peak has a small decreasing tendency. This is because within this bias range the overlap region of LDOS and RDOS remains the same. Moreover, in this region (5.00 V to 5.40 V), the electrostatic potential of the right electrode is higher than the left electrode (except 5.40 V) and thus creates a barrier; as a consequence there is NDR behavior. As the current increases at 5.60 V, the decreasing trend of transmission peak remains the same but the width of peak slightly increases with the EBW. In addition, the electrostatic potential of the left electrode is higher than the right electrode, which results in a small increase in current. Afterward, a minor drop of current was observed at 5.80 V; this happens as the electrostatic potential of the right electrode is higher than the left electrode but the transmission coefficient within the EBW is almost the same as the previous one (5.60 V). When the bias is larger than 5.80 V, the current starts increasing, and it continues to 6.20 V. In this bias region, the electrostatic potential of the left electrode is higher than the right electrode, which increases the current.

The I-V characteristic of our model device is not perfectly antisymmetric in nature, i.e., not only the sign of current changes for positive and negative bias but also the magnitude. Some of our model devices (containing an odd number of dopant) show asymmetry in the I-V curve for positive and negative bias, indicating their voltage rectifying capability. In order to illustrate the rectifying capability, the rectification ratio is defined as RR(V) =  ∣ I/I+|. The forward or reversed rectification can be identify from the condition RR(V) < 1 (forward rectification) or RR(V) > 1 (reversed rectification). The rectification ratio of our model devices are plotted in Fig. 6 and Fig. S10. The rectifying capability of the pristine system and system doped with an even number of dopant are too low and this is due to the mirror symmetry of their structure. For example, the RR(V) plot of the pristine system (Fig. 6a) shows forward rectification in the low bias regime (0.20 V → 0.80 V) with a maximum RR(V) value of 0.40 and exhibits reversed rectification at 2.20 V and 2.60 V having a RR(V) value of 1.11. In contrast, the rectifying capability of a system doped with an odd number of dopant is comparable with another study of single diode [8], and their rectifying capability is notable in the low bias region but declines with increasing bias. Among them, the rectifying capability is highest for the S-doped pentalene-device, more specifically for the 1S-doped pentalene-device. For the 1N-doped pentalene-device, the forward rectification is observed in the bias region (0.20 V → 0.60 V), and thereafter it is reversed up to bias range 1.40 V. With further increase in bias voltage, the forward rectification region (1.60 V → 3.00 V) starts, followed by the reverse rectification region. The rectification is maximum (RR(V) = 3.45) at 0.80 V.
Fig. 6

Rectification ratio (RR(V)) of a AGNR-pentalene-AGNR device b Odd number of N-doped pentalene-AGNR devices c Odd number of S-doped pentalene-AGNR devices. The solid line and dotted line represent RR for up spin and down spin respectively

The maximum rectification of the 3N-doped pentalene-device is 2.90 at 1.60 V. The forward rectification and reversed rectification region appears successively through all bias but strongly from 0.00 V to 3.20 V. The rectification ratio of the 1S-doped pentalene-device shows that its rectifying capability is totally different for up and down spin current, which is not prominent in other devices. The rectification ratio is higher for the up spin channel having a maximum value of 8.58 at 1.20 V and comparatively lower for the down spin channel having the highest value of 4.65 at 0.40 V. This rectification ratio of the 1S-doped pentalene-device is comparable with another study [8], and the highest rectifying efficiency for up spin is even greater than that obtained for the p-n junction diode formed by doped GNRs (single diode). The 3S-doped pentalene-device shows a strong rectification ratio of 3.60 at 2.20 V. The rectifying capability of these systems may be used for designing nanoelectronic devices.

In brief, our proposed model devices exhibit noticeable NDR behavior along with spin filtering efficiency. In addition, the rectifying effect is observed in the junctions with an odd number of dopant atoms. Thus, a multifunctional molecular device can be realized.

Conclusions

The spin-dependent electronic transport properties of the doped AGNR-pentalene-AGNR nanojunction were determined by using the NEGF-DFT approach, and a noticeable spin filtering effect was observed in a broad bias range for all considered systems. Substitutional doping of the pentalene-system with nitrogen and sulfur creates an impurity state, which subsequently shifts the Fermi level upward/downward, and thus the substituted pentalene–graphene nanojunction behaves as an n-type/p-type semiconductor. The variation of transport properties with the increasing dopant concentration is well discussed. Our calculation reveals that among all these systems, NDR behavior is more prominent in S-substituted systems than N-substituted systems. The physical mechanism for this interesting NDR phenonmemon was discussed with the help of electrostatic potential distribution, overlap of DOS between left and right electrodes, and different transmission peak width and strength within the EBW. Further, the system doped with an odd number of dopant shows noticeable rectifying capability, and the maximum rectifying efficiency is observed in the 1S-doped pentalene-device. Our findings strongly imply that these proposed model devices behave as multifunctional molecular devices and would be useful candidates for molecular electronics.

Notes

Acknowledgments

We dedicated this work to celebrate the 60th birthday of Prof. Pratim K. Chattaraj. Miss Barnali Bhattacharya would like to thank CSIR for providing a fellowship.

Supplementary material

894_2018_3818_MOESM1_ESM.docx (4.5 mb)
ESM 1 (DOCX 4572 kb)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsAssam UniversitySilcharIndia

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