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Electronic transport properties of T-shaped silicene nanoribbons
Author’s Accepted Manuscript Electronic transport properties of T-shaped silicene nanoribbons A. Ahmadi Fouladi
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S1386-9477(16)30741-X http://dx.doi.org/10.1016/j.physe.2016.10.040 PHYSE12629
To appear in: Physica E: Low-dimensional Systems and Nanostructures Received date: 13 July 2016 Revised date: 23 September 2016 Accepted date: 24 October 2016 Cite this article as: A. Ahmadi Fouladi, Electronic transport properties of Tshaped silicene nanoribbons, Physica E: Low-dimensional Systems and Nanostructures, http://dx.doi.org/10.1016/j.physe.2016.10.040 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Electronic transport properties of T-shaped silicene nanoribbons A. Ahmadi Fouladi∗ Department of Physics, Sari Branch, Islamic Azad University, Sari, Iran
Abstract Based on the tight-binding model and a generalized Green’s function method, we theoretically investigated the electron transport properties of T-shaped silicene nanoribbons (TsSiNRs) structure composed of an armchair SiNR (ASiNR) with a sidearm connected to two semi-infinite ASiNR leads. In particular, we demonstrated that the transport properties sensitively depend on the sidearm width and length. Besides, we found that the metal to semiconductor transition occurs with the increase of the spin-orbit interaction (SOI) strength. The effect of the external perpendicular electric field on electron transport is also investigated and it is found that potential energy causes to the decrease of the energy gap leading to semiconductor to metallic transition. Keywords: T-shaped silicene nanoribbon, Electronic transport, Green’s function method, Spin-orbit interaction 1. Introduction Graphene, a two-dimensional (2D) honeycomb carbon lattice, has aroused great attention in the recent years due to it’s unique physical properties and applications in nanoelectronic devices. The application potentials of graphene stimulates considerable interest to explor other 2D honeycomb structures formed by group IV elements, such as germanene and silicene. Silicene, a monolayer of silicon with a hexagonal lattice structure, has been recently synthesized on various substrates [1, 2, 3]. The atomic structure of ∗
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silicene is similar to graphene, but it has a buckled structure [4] and relatively large spin-orbit interaction (SOI) [4], so it can become a good candidate for spintronic applications [5, 6]. Furthermore, the possible compatibility of silicene with current silicon-based semiconductor technology has attracted enormous interest of researches [5]. For constructing a silicene-based nanoelectronic device, the ability to modulate the electronic properties of silicene is absolutely required. The investigations show that the energy gap of silicene and silicene nanoribbons (SiNRs) can be tuned by applying external conditions such as electric field[7, 8, 9, 10, 11, 12], chemical functionalization with hydrogen and halogen elements[13, 14, 15], disorder[7], defect[16, 17, 18, 19], and strain [11, 20, 21, 22]. Electronic and transport properties of the SiNRs have been widely studied theoretically in the recent years [7, 8, 17, 23, 24, 25, 26, 27]. SiNRs have two types similar to graphene nanoribbons (GNRs): armchair and zigzag. Similar to GNRs, the armchair-edge SiNRs (ASiNRs) can be classified into three types with widths N = 3n, 3n + 1, 3n + 2 (where n is a positive integer). The ASiNRs with 3n + 2 are all metallic, while the others are semiconducting. The zigzag-edge SiNR (ZSiNR) becomes half metal under a transverse electric field [5]. By connecting ZSiNRs and ASiNRs, people can design and prepare silicene-besed nanojunctions of various shapes. These structures offer a wide range of possible applications since one can fine tune electronic properties by merely changing the size and geometry. In the present work, we theoretically investigated the electron transport properties of T-shaped SiNRs (TsSiNRs) structure consisting of a metallic ASiNR connected to a sidearm by the use of generalized Green’s function method based on tight-binding model in Landauer-B¨ uttiker formalism. The dependence of the density of states and the transmission probability for the TsSiNR structure on the sidearm width and length, SOI strength and external perpendicular electric field have been studied. 2. Model and method Here we describe our method based on a TsSiNR model consisting of an ASiNR with a sidearm connected to two semi-infinite metallic ASiNR leads, as depicted in Fig. 1. Using the tight-binding model, the Hamiltonian for
2
Figure 1: Schematic view of a TsSiNR structure composed of an ASiNR with a sidearm connected to two semi-infinite ASiNR leads of width nw . ns and nl , respectively, represent the width and length of the sidearm. The silicon atoms belong the two distinct sublattices, A and B.
the ASiNR can be written as follows [28]: λSO z c†iα cjα + i √ νij c†iα σαβ cjβ 3 3 ij α ij αβ † 2 − i λR γij c†iα (σ × d 0ij )zαβ cjβ + Ve ξi ciα ciα 3 i
H = −t
(1)
ij αβ
where c†iα (cjβ ) denotes the creation (annihilation) operator of an electron with spin polarization α(β) at site i(j). ij and ij stand for the nearestneighbor and next nearest-neighbor pairs in the lattice, respectively. The first term of Eq. 1 represents the usual nearest-neighbor hopping integral with a transfer energy t = 1.6 eV [28]. The second and the third terms represent the effective intrinsic spin-orbit interaction (SOI) and the intrinsic Rashba SOI, respectively. σ = (σx , σy , σx ) is the Pauli matrix with νij = +1 (νij = −1) if the next-nearest neighbor hopping is anticlockwise (clockwise) with the respect to the positive z-axis, γij = +1 (γij = −1) and ξi = +1 (ξi = −1) for A(B) site. λSO = 3.9 meV and λR = 0.7 meV are the effective d SOI and Rashba SOI parameters, respectively [28]. d 0ij = |d ij | is the unit ij vector parallel to the vector d ij connecting the two sites i and j in the same sublattice, and Ve is the potential energy created by applying an external 3
perpendicular electric field. To investigate the electronic transport through the TsSiNR junction, we used a generalized Green’s function method. To proceed, the Green’s function of the TsSiNR junction is given by G(E) = [(E + iη)I − H − ΣL (E) − ΣR (E)]−1 ,
(2)
where η → 0+ , I is the identity matrix and ΣL(R) is the self-energy of the left (right) SiNR electrode due to the coupling of the TsSiNR structure with left and right SiNR electrodes that can be calculated by the recursive method described by Sancho and co-workers [29]. Within the Landauer-B¨ uttiker framework, the transmission function, average density of state (ADOS) and the local density of state (LDOS) can be expressed by the following equations [30]: (3) T (E) = T r[ΓL (E) G(E)ΓR (E)G† (E)]. ADOS(E) = −(1/N π)T r[Im(G(E))]
(4)
LDOS(E) = −(1/π)Im(G(E)).
(5)
here ΓL(R) = i(ΣL(R) − Σ†L(R) ) is the coupling function of the left (right) electrode. 3. Results and discussion According to the formalism described in Section 2, we have investigated the electron transport properties of TsSiNR junction. During the computation we use λSO = 3.9 meV (Ve = 0), except for Fig. 4 (Fig. 5) where λSO (Ve ) is varying. Figure 2(a) shows the transmission probability as a function of the electron energy with different sidearm widths of TsSiNR (ns ) for nw = 11, na = 4 and nl = 6. For the perfect ASiNR, the transmission probability exhibits the staircase-like characteristics (not shown here). It can be seen that the transmission probability has diminished from perfect ASiNRs because of the addition of the sidearm. Also, the transmission states symmetrically appear at the two sides of the Dirac point (E = 0). As the width of the sidearm increases, the transmission states from the positive and negative energy side move towards the Dirac point and the new resonance states appear near the Dirac point. Besides, in the presence of the sidearm there are some transmission dips which are character of anti-resonance states. These anti-resonance 4
Figure 2: (a) The transmission probability as function of energy in TsSiNR junction with nw = 11, na = 4, nl = 6 and different ns : ns = 6 (solid curve), ns = 12 (short dashed curve), ns = 18 (short dash-dotted curve). The spatial-resolved LDOS of TsSiNR junction at the transmission zero dips with (b) ns = 6, E = 550 meV ; (c) ns = 12, E = 454 meV and (d) ns = 18, E = 393 meV .
states are related to the destructive interference between propagating states along the SiNR and the bound states localized in the sidearm region. The dips with zero transmission probability are associated to quasi-bound states. In Figs. 2(b)-2(d) we plot the spatial-resolved LDOS of TsSiNR structure at the transmission zero dips with ns = 6, E = 550 meV ; ns = 12, E = 454 meV and ns = 18, E = 393 meV , respectively (see inset of Fig. 2(a)). For ns = 6 the electrons are strongly confined in the middle region of the SiNR and sidearm, as shown in Fig. 2(b). With the increase of the ns the intensity of electron confinement at the middle region of SiNR decreases and the localized states at the sidearm edges gradually increase. In Fig. 3(a), we show the dependence of the transmission probability on the sidearm lengths of TsSiNR (nl ) for nw = 11, na = 4 and ns = 6. It is seen that the transmission peaks and dips are narrowed and shift toward the Dirac point as the nl increases. 5
Figure 3: (a) The transmission probability as a function of energy in TsSiNR junction with nw = 11, na = 4, ns = 6 and different nl : nl = 4 (solid curve), nl = 6 (short dashed curve), nl = 8 (short dash-dotted curve), nl = 10 (short dotted curve). The spatial-resolved LDOS of TsSiNR junction at the transmission peaks with (b) nl = 4, E = 147 meV ; (c) nl = 6, E = 125 meV ; (d) nl = 8, E = 100 meV and (e) nl = 10, E = 84 meV .
Besides, the transmission function has non-zero value for nl = 4 at the Dirac point. As the nl is increased to 10, the transmission function reaches to zero at the Dirac point leading to metal-semiconductor transition. Figures 3(b)3(e) present the graphs of the spatial-resolved LDOS of TsSiNR structure at the transmission peaks with nl = 4, E = 147 meV ; nl = 6, E = 125 meV ; nl = 8, E = 100 meV and nl = 10, E = 84 meV , respectively. It is seen that the state contributing to the transmission peak is strongly distributed the edges of sidearm. The LDOS at the edges of sidearm increases with the nl increases and hence, the transmission peaks are narrowed. In Fig. 4(a) the effect of effective SOI parameter (λSO ) on the transmission probability of the TsSiNR junction with nw = 11, na = 4, nl = 3 and ns = 6 is investigated. 6
Figure 4: (a) The transmission probability and (b) ADOS as function of energy in TsSiNR junction with nw = 11, na = 4, nl = 3, ns = 6 and different λSO : λSO = 0 (solid curve), λSO = 0.1 t0 (short dashed curve), λSO = 0.2 t0 (short dash-dotted curve).
One finds the transmission zero dips are seen at the energies E = ±143 meV for λSO = 0. The increase of the λSO results in the dips becoming broader and move toward the Dirac point. These dips can be seen at the energies E = ±123 meV for λSO = 0.1 t0 . In fact the change of the λSO causes the modulation of Hamiltonian of the junction and hence, the position of these dips, which corresponds to eigen-energies of the quasi-bound states, alters. These dips completely disappear for λSO > 0.17 t0 . Furthermore, there is no energy gap for the system with λSO = 0 and the increase of the λSO causes appearance of an energy gap for the system. Consequently, the metal to semiconductor transition occurs. In fact, with the increase of the λSO , the ADOS at the Dirac point decreases, as shown in Fig. 4(b). We have shown that the LDOS for the sites of TsSiNR at the Dirac point is strongly suppressed with the increase of the λSO (not shown here). We now investigate the response of the electronic transport properties of the TsSiNR junction in the presence of an external perpendicular electric field. Figure 5(a) shows 7
Figure 5: (a) The transmission probability as function of energy in TsSiNR junction with nw = 11, na = 4, nl = 8, ns = 6 and different Ve : Ve = 0 (solid curve), Ve = 0.02 t0 (short dashed curve), Ve = 0.04 t0 (short dash-dotted curve), Ve = 0.06 t0 (short dotted curve). The spatial-resolved LDOS of TsSiNR junction at the Dirac point (E = 0) with (b) Ve = 0 ; (c) Ve = 0.02 t0 ; (d) Ve = 0.04 t0 and (e) Ve = 0.06 t0 .
the transmission probability as function of the energy with different potential energy Ve for the TsSiNR junction with nw = 11, na = 4, nl = 8, ns = 6. It is interesting to note that the transmission zero dips completely disappear in the presence of external perpendicular electric field. As it can be seen, the transmission gap decreases and a semiconductor to metallic transition occurs when Ve is increased form 0 to Ve = 0.06 t0 . Moreover, the transmission dip at the Dirac point turned into the transmission peak for Ve > 0.056 eV that can be clearly seen from the LDOS of the structure. Figures 5(b)-(e) show the spatial-resolved LDOS of the TsSiNR junction for the Dirac point with Ve = 0, Ve = 0.02 t0 , Ve = 0.04 t0 and Ve = 0.06 t0 , respectively. One can find that the intensity of the LDOS in the sidearm edges is considerably enhanced, 8
and the localized states turned into the extended states by increasing Ve . It is noticed that the TsSiNR junction composed of the zigzag SiNR components shows the metallic behavior, and the metal to semiconducting transition does not occur by changing the geometry of the system and the strength of the SOI (not shown here). So it is more favorable to fabricate switching devices by using the TsSiNR junction composed of the armchair SiNR components. 4. Conclusion In summary, using the generalized Green’s function technique based on the tight-binding model and the Landauer-B¨ uttiker formalism, we have numerically investigated the electron transport properties of the TsSiNR structure, in which the perfect ASiNR with a sidearm connected to metallic ASiNR leads. Our results show that the electron transport characteristics can be remarkably modulated by TsSiNR sidearm width and length, spin-orbit interaction strength and applying an external perpendicular electric field. We have shown that the position of the transmission function dips and peaks can be controlled by the above parameters. Results show that the variation of sidearm width can create new transmission states around the Dirac point. Besides, with the increase of sidearm width, the LDOS of the quasibond states related to the transmission zero dips decreases at the middle region of TsSiNR and gradually increases in the sidearm edges. We have also demonstrated that the LDOS at the edges of sidearm increases and the transmission peaks and dips are narrowed and shift toward the Dirac point as sidearm length increases. Furthermore, with the increase of sidearm length, the transmission probability reaches to zero at the Dirac point leading to metal-semiconductor transition. We found that the ADOS at the Dirac point decreases with the enhance of the the effective SOI parameter (λSO ) and then, the metal to semiconductor transition occurs. Applying an external perpendicular electric field can cause a disappearance of the transmission zero dips, and by increasing of that, the LDOS of the sidearm edges at the Dirac point drastically increases and hence, the transmission gap decreases and semiconductor to metallic transition occurs. These results represent an important insight into the understanding of electron transport through the SiNRs, which are a necessary requirement for the progress of silicene based nanoelectronic devices.
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S1386-9477(16)30741-X http://dx.doi.org/10.1016/j.physe.2016.10.040 PHYSE12629
To appear in: Physica E: Low-dimensional Systems and Nanostructures Received date: 13 July 2016 Revised date: 23 September 2016 Accepted date: 24 October 2016 Cite this article as: A. Ahmadi Fouladi, Electronic transport properties of Tshaped silicene nanoribbons, Physica E: Low-dimensional Systems and Nanostructures, http://dx.doi.org/10.1016/j.physe.2016.10.040 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Electronic transport properties of T-shaped silicene nanoribbons A. Ahmadi Fouladi∗ Department of Physics, Sari Branch, Islamic Azad University, Sari, Iran
Abstract Based on the tight-binding model and a generalized Green’s function method, we theoretically investigated the electron transport properties of T-shaped silicene nanoribbons (TsSiNRs) structure composed of an armchair SiNR (ASiNR) with a sidearm connected to two semi-infinite ASiNR leads. In particular, we demonstrated that the transport properties sensitively depend on the sidearm width and length. Besides, we found that the metal to semiconductor transition occurs with the increase of the spin-orbit interaction (SOI) strength. The effect of the external perpendicular electric field on electron transport is also investigated and it is found that potential energy causes to the decrease of the energy gap leading to semiconductor to metallic transition. Keywords: T-shaped silicene nanoribbon, Electronic transport, Green’s function method, Spin-orbit interaction 1. Introduction Graphene, a two-dimensional (2D) honeycomb carbon lattice, has aroused great attention in the recent years due to it’s unique physical properties and applications in nanoelectronic devices. The application potentials of graphene stimulates considerable interest to explor other 2D honeycomb structures formed by group IV elements, such as germanene and silicene. Silicene, a monolayer of silicon with a hexagonal lattice structure, has been recently synthesized on various substrates [1, 2, 3]. The atomic structure of ∗
Email address: [email protected]
Preprint submitted to Physica E
April 13, 2017
silicene is similar to graphene, but it has a buckled structure [4] and relatively large spin-orbit interaction (SOI) [4], so it can become a good candidate for spintronic applications [5, 6]. Furthermore, the possible compatibility of silicene with current silicon-based semiconductor technology has attracted enormous interest of researches [5]. For constructing a silicene-based nanoelectronic device, the ability to modulate the electronic properties of silicene is absolutely required. The investigations show that the energy gap of silicene and silicene nanoribbons (SiNRs) can be tuned by applying external conditions such as electric field[7, 8, 9, 10, 11, 12], chemical functionalization with hydrogen and halogen elements[13, 14, 15], disorder[7], defect[16, 17, 18, 19], and strain [11, 20, 21, 22]. Electronic and transport properties of the SiNRs have been widely studied theoretically in the recent years [7, 8, 17, 23, 24, 25, 26, 27]. SiNRs have two types similar to graphene nanoribbons (GNRs): armchair and zigzag. Similar to GNRs, the armchair-edge SiNRs (ASiNRs) can be classified into three types with widths N = 3n, 3n + 1, 3n + 2 (where n is a positive integer). The ASiNRs with 3n + 2 are all metallic, while the others are semiconducting. The zigzag-edge SiNR (ZSiNR) becomes half metal under a transverse electric field [5]. By connecting ZSiNRs and ASiNRs, people can design and prepare silicene-besed nanojunctions of various shapes. These structures offer a wide range of possible applications since one can fine tune electronic properties by merely changing the size and geometry. In the present work, we theoretically investigated the electron transport properties of T-shaped SiNRs (TsSiNRs) structure consisting of a metallic ASiNR connected to a sidearm by the use of generalized Green’s function method based on tight-binding model in Landauer-B¨ uttiker formalism. The dependence of the density of states and the transmission probability for the TsSiNR structure on the sidearm width and length, SOI strength and external perpendicular electric field have been studied. 2. Model and method Here we describe our method based on a TsSiNR model consisting of an ASiNR with a sidearm connected to two semi-infinite metallic ASiNR leads, as depicted in Fig. 1. Using the tight-binding model, the Hamiltonian for
2
Figure 1: Schematic view of a TsSiNR structure composed of an ASiNR with a sidearm connected to two semi-infinite ASiNR leads of width nw . ns and nl , respectively, represent the width and length of the sidearm. The silicon atoms belong the two distinct sublattices, A and B.
the ASiNR can be written as follows [28]: λSO z c†iα cjα + i √ νij c†iα σαβ cjβ 3 3 ij α ij αβ † 2 − i λR γij c†iα (σ × d 0ij )zαβ cjβ + Ve ξi ciα ciα 3 i
H = −t
(1)
ij αβ
where c†iα (cjβ ) denotes the creation (annihilation) operator of an electron with spin polarization α(β) at site i(j). ij and ij stand for the nearestneighbor and next nearest-neighbor pairs in the lattice, respectively. The first term of Eq. 1 represents the usual nearest-neighbor hopping integral with a transfer energy t = 1.6 eV [28]. The second and the third terms represent the effective intrinsic spin-orbit interaction (SOI) and the intrinsic Rashba SOI, respectively. σ = (σx , σy , σx ) is the Pauli matrix with νij = +1 (νij = −1) if the next-nearest neighbor hopping is anticlockwise (clockwise) with the respect to the positive z-axis, γij = +1 (γij = −1) and ξi = +1 (ξi = −1) for A(B) site. λSO = 3.9 meV and λR = 0.7 meV are the effective d SOI and Rashba SOI parameters, respectively [28]. d 0ij = |d ij | is the unit ij vector parallel to the vector d ij connecting the two sites i and j in the same sublattice, and Ve is the potential energy created by applying an external 3
perpendicular electric field. To investigate the electronic transport through the TsSiNR junction, we used a generalized Green’s function method. To proceed, the Green’s function of the TsSiNR junction is given by G(E) = [(E + iη)I − H − ΣL (E) − ΣR (E)]−1 ,
(2)
where η → 0+ , I is the identity matrix and ΣL(R) is the self-energy of the left (right) SiNR electrode due to the coupling of the TsSiNR structure with left and right SiNR electrodes that can be calculated by the recursive method described by Sancho and co-workers [29]. Within the Landauer-B¨ uttiker framework, the transmission function, average density of state (ADOS) and the local density of state (LDOS) can be expressed by the following equations [30]: (3) T (E) = T r[ΓL (E) G(E)ΓR (E)G† (E)]. ADOS(E) = −(1/N π)T r[Im(G(E))]
(4)
LDOS(E) = −(1/π)Im(G(E)).
(5)
here ΓL(R) = i(ΣL(R) − Σ†L(R) ) is the coupling function of the left (right) electrode. 3. Results and discussion According to the formalism described in Section 2, we have investigated the electron transport properties of TsSiNR junction. During the computation we use λSO = 3.9 meV (Ve = 0), except for Fig. 4 (Fig. 5) where λSO (Ve ) is varying. Figure 2(a) shows the transmission probability as a function of the electron energy with different sidearm widths of TsSiNR (ns ) for nw = 11, na = 4 and nl = 6. For the perfect ASiNR, the transmission probability exhibits the staircase-like characteristics (not shown here). It can be seen that the transmission probability has diminished from perfect ASiNRs because of the addition of the sidearm. Also, the transmission states symmetrically appear at the two sides of the Dirac point (E = 0). As the width of the sidearm increases, the transmission states from the positive and negative energy side move towards the Dirac point and the new resonance states appear near the Dirac point. Besides, in the presence of the sidearm there are some transmission dips which are character of anti-resonance states. These anti-resonance 4
Figure 2: (a) The transmission probability as function of energy in TsSiNR junction with nw = 11, na = 4, nl = 6 and different ns : ns = 6 (solid curve), ns = 12 (short dashed curve), ns = 18 (short dash-dotted curve). The spatial-resolved LDOS of TsSiNR junction at the transmission zero dips with (b) ns = 6, E = 550 meV ; (c) ns = 12, E = 454 meV and (d) ns = 18, E = 393 meV .
states are related to the destructive interference between propagating states along the SiNR and the bound states localized in the sidearm region. The dips with zero transmission probability are associated to quasi-bound states. In Figs. 2(b)-2(d) we plot the spatial-resolved LDOS of TsSiNR structure at the transmission zero dips with ns = 6, E = 550 meV ; ns = 12, E = 454 meV and ns = 18, E = 393 meV , respectively (see inset of Fig. 2(a)). For ns = 6 the electrons are strongly confined in the middle region of the SiNR and sidearm, as shown in Fig. 2(b). With the increase of the ns the intensity of electron confinement at the middle region of SiNR decreases and the localized states at the sidearm edges gradually increase. In Fig. 3(a), we show the dependence of the transmission probability on the sidearm lengths of TsSiNR (nl ) for nw = 11, na = 4 and ns = 6. It is seen that the transmission peaks and dips are narrowed and shift toward the Dirac point as the nl increases. 5
Figure 3: (a) The transmission probability as a function of energy in TsSiNR junction with nw = 11, na = 4, ns = 6 and different nl : nl = 4 (solid curve), nl = 6 (short dashed curve), nl = 8 (short dash-dotted curve), nl = 10 (short dotted curve). The spatial-resolved LDOS of TsSiNR junction at the transmission peaks with (b) nl = 4, E = 147 meV ; (c) nl = 6, E = 125 meV ; (d) nl = 8, E = 100 meV and (e) nl = 10, E = 84 meV .
Besides, the transmission function has non-zero value for nl = 4 at the Dirac point. As the nl is increased to 10, the transmission function reaches to zero at the Dirac point leading to metal-semiconductor transition. Figures 3(b)3(e) present the graphs of the spatial-resolved LDOS of TsSiNR structure at the transmission peaks with nl = 4, E = 147 meV ; nl = 6, E = 125 meV ; nl = 8, E = 100 meV and nl = 10, E = 84 meV , respectively. It is seen that the state contributing to the transmission peak is strongly distributed the edges of sidearm. The LDOS at the edges of sidearm increases with the nl increases and hence, the transmission peaks are narrowed. In Fig. 4(a) the effect of effective SOI parameter (λSO ) on the transmission probability of the TsSiNR junction with nw = 11, na = 4, nl = 3 and ns = 6 is investigated. 6
Figure 4: (a) The transmission probability and (b) ADOS as function of energy in TsSiNR junction with nw = 11, na = 4, nl = 3, ns = 6 and different λSO : λSO = 0 (solid curve), λSO = 0.1 t0 (short dashed curve), λSO = 0.2 t0 (short dash-dotted curve).
One finds the transmission zero dips are seen at the energies E = ±143 meV for λSO = 0. The increase of the λSO results in the dips becoming broader and move toward the Dirac point. These dips can be seen at the energies E = ±123 meV for λSO = 0.1 t0 . In fact the change of the λSO causes the modulation of Hamiltonian of the junction and hence, the position of these dips, which corresponds to eigen-energies of the quasi-bound states, alters. These dips completely disappear for λSO > 0.17 t0 . Furthermore, there is no energy gap for the system with λSO = 0 and the increase of the λSO causes appearance of an energy gap for the system. Consequently, the metal to semiconductor transition occurs. In fact, with the increase of the λSO , the ADOS at the Dirac point decreases, as shown in Fig. 4(b). We have shown that the LDOS for the sites of TsSiNR at the Dirac point is strongly suppressed with the increase of the λSO (not shown here). We now investigate the response of the electronic transport properties of the TsSiNR junction in the presence of an external perpendicular electric field. Figure 5(a) shows 7
Figure 5: (a) The transmission probability as function of energy in TsSiNR junction with nw = 11, na = 4, nl = 8, ns = 6 and different Ve : Ve = 0 (solid curve), Ve = 0.02 t0 (short dashed curve), Ve = 0.04 t0 (short dash-dotted curve), Ve = 0.06 t0 (short dotted curve). The spatial-resolved LDOS of TsSiNR junction at the Dirac point (E = 0) with (b) Ve = 0 ; (c) Ve = 0.02 t0 ; (d) Ve = 0.04 t0 and (e) Ve = 0.06 t0 .
the transmission probability as function of the energy with different potential energy Ve for the TsSiNR junction with nw = 11, na = 4, nl = 8, ns = 6. It is interesting to note that the transmission zero dips completely disappear in the presence of external perpendicular electric field. As it can be seen, the transmission gap decreases and a semiconductor to metallic transition occurs when Ve is increased form 0 to Ve = 0.06 t0 . Moreover, the transmission dip at the Dirac point turned into the transmission peak for Ve > 0.056 eV that can be clearly seen from the LDOS of the structure. Figures 5(b)-(e) show the spatial-resolved LDOS of the TsSiNR junction for the Dirac point with Ve = 0, Ve = 0.02 t0 , Ve = 0.04 t0 and Ve = 0.06 t0 , respectively. One can find that the intensity of the LDOS in the sidearm edges is considerably enhanced, 8
and the localized states turned into the extended states by increasing Ve . It is noticed that the TsSiNR junction composed of the zigzag SiNR components shows the metallic behavior, and the metal to semiconducting transition does not occur by changing the geometry of the system and the strength of the SOI (not shown here). So it is more favorable to fabricate switching devices by using the TsSiNR junction composed of the armchair SiNR components. 4. Conclusion In summary, using the generalized Green’s function technique based on the tight-binding model and the Landauer-B¨ uttiker formalism, we have numerically investigated the electron transport properties of the TsSiNR structure, in which the perfect ASiNR with a sidearm connected to metallic ASiNR leads. Our results show that the electron transport characteristics can be remarkably modulated by TsSiNR sidearm width and length, spin-orbit interaction strength and applying an external perpendicular electric field. We have shown that the position of the transmission function dips and peaks can be controlled by the above parameters. Results show that the variation of sidearm width can create new transmission states around the Dirac point. Besides, with the increase of sidearm width, the LDOS of the quasibond states related to the transmission zero dips decreases at the middle region of TsSiNR and gradually increases in the sidearm edges. We have also demonstrated that the LDOS at the edges of sidearm increases and the transmission peaks and dips are narrowed and shift toward the Dirac point as sidearm length increases. Furthermore, with the increase of sidearm length, the transmission probability reaches to zero at the Dirac point leading to metal-semiconductor transition. We found that the ADOS at the Dirac point decreases with the enhance of the the effective SOI parameter (λSO ) and then, the metal to semiconductor transition occurs. Applying an external perpendicular electric field can cause a disappearance of the transmission zero dips, and by increasing of that, the LDOS of the sidearm edges at the Dirac point drastically increases and hence, the transmission gap decreases and semiconductor to metallic transition occurs. These results represent an important insight into the understanding of electron transport through the SiNRs, which are a necessary requirement for the progress of silicene based nanoelectronic devices.
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