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Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor
Superlattices and Microstructures xxx (2016) 1e6
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor Khurshed A. Shah*, M. Shunaid Parvaiz Nanomaterials Research Laboratory, Department of Physics, Govt. Degree College for Women, K. P. Road, Anantnag-192101, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 September 2016 Accepted 27 September 2016 Available online xxx
The CNTFETs are the most promising advanced alternatives to the conventional FETs due to their outstanding structure and electrical properties. In this paper, we report the I-V characteristics of zig-zag (4, 0) semiconducting coaxial carbon nanotube field effect transistor (CNTFET) using the non-equilibrium Green's function formalism. The CNTFET is co-doped with two, four and six boron-nitrogen (BN) atoms separately near the electrodes using the substitutional doping method and the I-V characteristics were calculated for each model using Atomistic Tool Kit software (version 13.8.1) and its virtual interface. The results reveal that all models show negative differential resistance (NDR) behavior with the maximum peak to valley current ratio (PVCR) of 3.2 at 300 K for the four atom doped model. The NDR behavior is due to the band to band tunneling (BTBT) in semiconducting CNTFET and decreases as the doping in the channel increases. The results are beneficial for next generation designing of nano devices and their potential applications in electronic industry. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Coaxial CNTFET Negative differential resistance Non-equilibrium Green's function BN co-doping Band to band tunneling
1. Introduction Carbon nanotubes (CNTs) form a new class of materials with a wide spectrum of potential applications owing to their unique transport characteristics and single dimensionality [1]. Since their discovery in 1991 [2], CNTs are being continuously studied in order to compete with the growing demand of small size, fast computing and low power consumption nanodevices. Due to the shrinking limitations of conventional field effect transistors (FETs), new devices like CNT based FETs are expected to be used at large scale in order to overcome the scaling limitations of silicon FETs [3,4]. It is to mention that the first CNTFETs were fabricated in the year 1998 and their performance was analyzed [5,6]. CNTs are of great importance when employed in devices due to their various advantages like; (a) due to the one dimensional nature of density of states, the scattering phase space is greatly reduced which gives the high on-current in semiconducting CNTFETs, (b) the absence of surface dangling bond states in one dimensional CNTs improves gate control with negligible gate leakage, (c) short channel effects of CNTFET devices are suppressed due to the one dimensional character of carbon nanotubes [7]. The transfer properties of CNTs can be easily modified by doping and the variation in the conductivity depends upon the dopant positions and level of doping [8]. The doped CNT when used as a channel in FET gives astonishing results and therefore significant research is going on to understand the CNT transistor operations and to enhance their performance [9,10].
* Corresponding author. E-mail address: [email protected] (K.A. Shah). http://dx.doi.org/10.1016/j.spmi.2016.09.037 0749-6036/© 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037
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Moreover, it has been shown that most of the CNTFETs operate like that of non-conventional schottky barrier transistors [11,12] having different behavior than MOSFET like transistors. Also the progress in doping of CNTFETs is going on for their better performance [13,14]. Efforts are being made to uncover the unique properties like negative differential resistance (NDR) behavior in CNTFET [15]. NDR was discovered by Esaki in 1958 [16] and is one of the excellent properties due to its potential applications in various electronic devices. The NDR and its different mechanisms in CNTs were described in the many recent reports [17e19]. Although different types of CNTFETs, based on geometry (Back-gated CNTFET [5], Top-gated CNTFET [20]) and electrodes (Schottky-barrier CNTFET [11,21e23], Partially gated CNTFET [21,24], Source/Drain doped CNTFET), have been studied but in this paper, we report the electronic transport characteristics of BN co-doped coaxial CNTFET at different BN doping concentrations. We have used a zig-zag (4, 0) CNT as a channel in a coaxially metal gated FET. The CNT is separately doped with 2, 4 and 6 BN atoms and the corresponding transport characteristics were obtained for the comparative studies. This type of research has not been done till now to the best of our knowledge. 2. Models and methods In this paper we modeled a zig-zag (4, 0) SWCNT channel surrounded by a metallic region which acts as a transistor gate. The two ends of the SWCNT channel form the transistor source and drain terminals. The whole assembly acts like a coaxial CNTFET with left electrode connected to the source and the right electrode connected to the drain while the scattering region is surrounded by the metallic gate as shown in Fig. 1. The coaxial or cylindrical geometry makes this device symmetric in angular direction which simplifies the electron transport calculations and permits self-consistent electrostatics [25,26]. All the modelling and simulation process is done using Atomistic Tool Kit Software (Version 13.8.1) [27] and its graphical interface. The CNTFET channel is co-doped with 2, 4 and 6 BN atoms near the source and drain terminals by substituting the carbon atoms of the Zig-Zag (4, 0) SWCNT as shown in Fig. 2 (a, b, c) respectively. In 2 atom doped model one boron atom is doped near the source and one nitrogen atom is doped near the drain, a similar methodology is adopted for other models. In this study, the drain-source current is calculated as a function of drain-source voltage in the range of 0e2 V at a given gate voltage (0.0 V, 0.1 V, 0.2 V, 0.3 V, 0.4 V) for each CNTFET model respectively. All the three models consist of carbon atoms with the bond length of 1.42 Å. The central region consists of 128 atoms while both the electrodes are made up of 28 carbon atoms each with ten percent of their length considered as scattering region in order to cover the scattering loses. The simulation was done according to extended huckel theory (EHT) combined with Non-equilibrium Green's Function (NEGF) formalism for transport calculations. The electrodes were kept at the temperature of 300 K. In order to have proper sampling, the values for the set of k-points were chosen to be 1, 1, 100 with the density mesh cut-off put at 20 Hartee. The NEGF method is used for device modelling with the assumption that energy levels are sufficiently delocalized [28]. This provides the appropriate self-consistent field for electronelectron interactions, besides the single particle approach is used for simulations which is based on Landauer-Buttiker formalism. 3. Simulation results The simulations were done using the Atomistic Tool Kit (version 13.8.1) software. In order to study the electronic transport properties of BN co-doped CNTFET, the transmission spectra was analyzed by plotting the IV and conductance curves at different doping concentrations. Fig. 3 (a, b, c) shows the IV and conductance curves of two, four and six atom BN co-doped CNTFETs respectively at zero gate voltages. Similar graphs were also plotted for gate voltages ranging from 0.1 to 0.4 V which are not included here, keeping in view the interest of the reader. Besides this we have calculated the drain-source current at different gate voltages and the variation of the drain current with applied voltage is shown in Fig. 4 (a, b, c).
Fig. 1. Geometrical presentation of Coaxial CNTFET.
Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037
K.A. Shah, M.S. Parvaiz / Superlattices and Microstructures xxx (2016) 1e6
3
Fig. 2. Source and Drain Terminals of Co-axial CNTFET showing Boron and Nitrogen atoms (a) 2 atom doped (b) 4 atom doped (c) 6 atom doped.
From the results it is clear that the zig-zag (4, 0) CNT based FET shows Negative Differential Resistance (NDR) at 300 K. The possible mechanism behind the observed NDR effect is the band to band tunneling (BTBT) due to the appropriate distribution of acceptor and donor like states as the function of energy. The boron doping induces p-type character while as the nitrogen doping induces n-type character in the nanotube thus forming the donor-acceptor like states. BTBT is possible when the field along the channel is able to shift the conduction and valence bands in the order of semiconductor energy gap. Since in this paper we have used semiconducting nanotube as a channel and BN doping has been introduced which makes the BTBT feasible by proper shifting and aligning the conduction and valence bands with respect to the Fermi level, as is previously reported in case of chemical doping of nanotubes [29,30]. From Figs. 3 and 4, it is clear that as the drain-source voltage is increased, the current increases at first but after a further increase in current BTBT gets suppressed due to low gate to drain voltage which gives rise to NDR region. At high drain-source voltages, the current increases rapidly and then decreases again showing small NDR regions. This is due to the fact that high VDS BTBT becomes independent of drain-source voltage, thus increasing current rapidly. After that with further increase in drain-source voltage, the field becomes such that the electronic states shift away from the Fermi level, resulting in the decrease in current. Furthermore in Figs. 3 and 4, it is also observed that the NDR effect does not show much variation with the changing gate voltages at low bias. This is because the gate is wrapped around over the entire tube length so the tunneling condition cannot be disrupted by the gate voltage once the doping is done. The four atom doped model shows the maximum PVCR of 3.2 as compared to other models. The six atom doped model has PVCR of 2.1 which could be attributed to the fact that as doping increases the conduction band edge lowers or the valance band edge raises reducing the net band gap. This reduction is called bandgap narrowing [31] which changes the tunneling barrier heights and in turn increases the tunneling current. Thus the PVCR increases from two atom doped CNTFET model to
Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037
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Fig. 3. I-V & dI/dV curves of BN co-doped CNTFET (a) Two atom doped (b) Four atom doped (c) Six atom doped.
Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037
K.A. Shah, M.S. Parvaiz / Superlattices and Microstructures xxx (2016) 1e6
5
Fig. 4. Id Vs Vds curves for BN co-doped CNTFET (a) Two atom doped (b) Four atom doped (c) Six atom doped.
four atom doped model and then decreases with further increase in doping concentration. These results show that 4 atom BN co-doped CNTFET is the best for electronic applications. 4. Conclusion Electronic transport properties of BN co-doped coaxial CNTFET are studied at different doping concentrations. The results give insight into the NDR effect in the given CNTFET due to BTBT which depends upon the appropriate alignment of valence and conduction bands. At first the PVCR increases from two atom doped model to four atom doped model and then decreases as the doping concentration is increased because of bandgap narrowing. The maximum PVCR of 3.2 was observed for the four atom BN co-doped CNTFET model. Thus our results elucidate the NDR behavior in the realm of nano dimensions which provides a link to next generation design. The results are very important for potential nanoelectronic applications like amplifiers, oscillators, digital logic and memories. Acknowledgement The authors greatly acknowledge the financial support by University Grants Commission (UGC), New Delhi (grant No: 42768/2013) which enables this study to occur. References [1] I. Deretzis, A. La Magna, Nanotechnology 17 (2006) 5063. [2] S. Iijima, Nature 354 (1991) 56.
Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037
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Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor Khurshed A. Shah*, M. Shunaid Parvaiz Nanomaterials Research Laboratory, Department of Physics, Govt. Degree College for Women, K. P. Road, Anantnag-192101, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 September 2016 Accepted 27 September 2016 Available online xxx
The CNTFETs are the most promising advanced alternatives to the conventional FETs due to their outstanding structure and electrical properties. In this paper, we report the I-V characteristics of zig-zag (4, 0) semiconducting coaxial carbon nanotube field effect transistor (CNTFET) using the non-equilibrium Green's function formalism. The CNTFET is co-doped with two, four and six boron-nitrogen (BN) atoms separately near the electrodes using the substitutional doping method and the I-V characteristics were calculated for each model using Atomistic Tool Kit software (version 13.8.1) and its virtual interface. The results reveal that all models show negative differential resistance (NDR) behavior with the maximum peak to valley current ratio (PVCR) of 3.2 at 300 K for the four atom doped model. The NDR behavior is due to the band to band tunneling (BTBT) in semiconducting CNTFET and decreases as the doping in the channel increases. The results are beneficial for next generation designing of nano devices and their potential applications in electronic industry. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Coaxial CNTFET Negative differential resistance Non-equilibrium Green's function BN co-doping Band to band tunneling
1. Introduction Carbon nanotubes (CNTs) form a new class of materials with a wide spectrum of potential applications owing to their unique transport characteristics and single dimensionality [1]. Since their discovery in 1991 [2], CNTs are being continuously studied in order to compete with the growing demand of small size, fast computing and low power consumption nanodevices. Due to the shrinking limitations of conventional field effect transistors (FETs), new devices like CNT based FETs are expected to be used at large scale in order to overcome the scaling limitations of silicon FETs [3,4]. It is to mention that the first CNTFETs were fabricated in the year 1998 and their performance was analyzed [5,6]. CNTs are of great importance when employed in devices due to their various advantages like; (a) due to the one dimensional nature of density of states, the scattering phase space is greatly reduced which gives the high on-current in semiconducting CNTFETs, (b) the absence of surface dangling bond states in one dimensional CNTs improves gate control with negligible gate leakage, (c) short channel effects of CNTFET devices are suppressed due to the one dimensional character of carbon nanotubes [7]. The transfer properties of CNTs can be easily modified by doping and the variation in the conductivity depends upon the dopant positions and level of doping [8]. The doped CNT when used as a channel in FET gives astonishing results and therefore significant research is going on to understand the CNT transistor operations and to enhance their performance [9,10].
* Corresponding author. E-mail address: [email protected] (K.A. Shah). http://dx.doi.org/10.1016/j.spmi.2016.09.037 0749-6036/© 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037
2
K.A. Shah, M.S. Parvaiz / Superlattices and Microstructures xxx (2016) 1e6
Moreover, it has been shown that most of the CNTFETs operate like that of non-conventional schottky barrier transistors [11,12] having different behavior than MOSFET like transistors. Also the progress in doping of CNTFETs is going on for their better performance [13,14]. Efforts are being made to uncover the unique properties like negative differential resistance (NDR) behavior in CNTFET [15]. NDR was discovered by Esaki in 1958 [16] and is one of the excellent properties due to its potential applications in various electronic devices. The NDR and its different mechanisms in CNTs were described in the many recent reports [17e19]. Although different types of CNTFETs, based on geometry (Back-gated CNTFET [5], Top-gated CNTFET [20]) and electrodes (Schottky-barrier CNTFET [11,21e23], Partially gated CNTFET [21,24], Source/Drain doped CNTFET), have been studied but in this paper, we report the electronic transport characteristics of BN co-doped coaxial CNTFET at different BN doping concentrations. We have used a zig-zag (4, 0) CNT as a channel in a coaxially metal gated FET. The CNT is separately doped with 2, 4 and 6 BN atoms and the corresponding transport characteristics were obtained for the comparative studies. This type of research has not been done till now to the best of our knowledge. 2. Models and methods In this paper we modeled a zig-zag (4, 0) SWCNT channel surrounded by a metallic region which acts as a transistor gate. The two ends of the SWCNT channel form the transistor source and drain terminals. The whole assembly acts like a coaxial CNTFET with left electrode connected to the source and the right electrode connected to the drain while the scattering region is surrounded by the metallic gate as shown in Fig. 1. The coaxial or cylindrical geometry makes this device symmetric in angular direction which simplifies the electron transport calculations and permits self-consistent electrostatics [25,26]. All the modelling and simulation process is done using Atomistic Tool Kit Software (Version 13.8.1) [27] and its graphical interface. The CNTFET channel is co-doped with 2, 4 and 6 BN atoms near the source and drain terminals by substituting the carbon atoms of the Zig-Zag (4, 0) SWCNT as shown in Fig. 2 (a, b, c) respectively. In 2 atom doped model one boron atom is doped near the source and one nitrogen atom is doped near the drain, a similar methodology is adopted for other models. In this study, the drain-source current is calculated as a function of drain-source voltage in the range of 0e2 V at a given gate voltage (0.0 V, 0.1 V, 0.2 V, 0.3 V, 0.4 V) for each CNTFET model respectively. All the three models consist of carbon atoms with the bond length of 1.42 Å. The central region consists of 128 atoms while both the electrodes are made up of 28 carbon atoms each with ten percent of their length considered as scattering region in order to cover the scattering loses. The simulation was done according to extended huckel theory (EHT) combined with Non-equilibrium Green's Function (NEGF) formalism for transport calculations. The electrodes were kept at the temperature of 300 K. In order to have proper sampling, the values for the set of k-points were chosen to be 1, 1, 100 with the density mesh cut-off put at 20 Hartee. The NEGF method is used for device modelling with the assumption that energy levels are sufficiently delocalized [28]. This provides the appropriate self-consistent field for electronelectron interactions, besides the single particle approach is used for simulations which is based on Landauer-Buttiker formalism. 3. Simulation results The simulations were done using the Atomistic Tool Kit (version 13.8.1) software. In order to study the electronic transport properties of BN co-doped CNTFET, the transmission spectra was analyzed by plotting the IV and conductance curves at different doping concentrations. Fig. 3 (a, b, c) shows the IV and conductance curves of two, four and six atom BN co-doped CNTFETs respectively at zero gate voltages. Similar graphs were also plotted for gate voltages ranging from 0.1 to 0.4 V which are not included here, keeping in view the interest of the reader. Besides this we have calculated the drain-source current at different gate voltages and the variation of the drain current with applied voltage is shown in Fig. 4 (a, b, c).
Fig. 1. Geometrical presentation of Coaxial CNTFET.
Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037
K.A. Shah, M.S. Parvaiz / Superlattices and Microstructures xxx (2016) 1e6
3
Fig. 2. Source and Drain Terminals of Co-axial CNTFET showing Boron and Nitrogen atoms (a) 2 atom doped (b) 4 atom doped (c) 6 atom doped.
From the results it is clear that the zig-zag (4, 0) CNT based FET shows Negative Differential Resistance (NDR) at 300 K. The possible mechanism behind the observed NDR effect is the band to band tunneling (BTBT) due to the appropriate distribution of acceptor and donor like states as the function of energy. The boron doping induces p-type character while as the nitrogen doping induces n-type character in the nanotube thus forming the donor-acceptor like states. BTBT is possible when the field along the channel is able to shift the conduction and valence bands in the order of semiconductor energy gap. Since in this paper we have used semiconducting nanotube as a channel and BN doping has been introduced which makes the BTBT feasible by proper shifting and aligning the conduction and valence bands with respect to the Fermi level, as is previously reported in case of chemical doping of nanotubes [29,30]. From Figs. 3 and 4, it is clear that as the drain-source voltage is increased, the current increases at first but after a further increase in current BTBT gets suppressed due to low gate to drain voltage which gives rise to NDR region. At high drain-source voltages, the current increases rapidly and then decreases again showing small NDR regions. This is due to the fact that high VDS BTBT becomes independent of drain-source voltage, thus increasing current rapidly. After that with further increase in drain-source voltage, the field becomes such that the electronic states shift away from the Fermi level, resulting in the decrease in current. Furthermore in Figs. 3 and 4, it is also observed that the NDR effect does not show much variation with the changing gate voltages at low bias. This is because the gate is wrapped around over the entire tube length so the tunneling condition cannot be disrupted by the gate voltage once the doping is done. The four atom doped model shows the maximum PVCR of 3.2 as compared to other models. The six atom doped model has PVCR of 2.1 which could be attributed to the fact that as doping increases the conduction band edge lowers or the valance band edge raises reducing the net band gap. This reduction is called bandgap narrowing [31] which changes the tunneling barrier heights and in turn increases the tunneling current. Thus the PVCR increases from two atom doped CNTFET model to
Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037
4
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Fig. 3. I-V & dI/dV curves of BN co-doped CNTFET (a) Two atom doped (b) Four atom doped (c) Six atom doped.
Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037
K.A. Shah, M.S. Parvaiz / Superlattices and Microstructures xxx (2016) 1e6
5
Fig. 4. Id Vs Vds curves for BN co-doped CNTFET (a) Two atom doped (b) Four atom doped (c) Six atom doped.
four atom doped model and then decreases with further increase in doping concentration. These results show that 4 atom BN co-doped CNTFET is the best for electronic applications. 4. Conclusion Electronic transport properties of BN co-doped coaxial CNTFET are studied at different doping concentrations. The results give insight into the NDR effect in the given CNTFET due to BTBT which depends upon the appropriate alignment of valence and conduction bands. At first the PVCR increases from two atom doped model to four atom doped model and then decreases as the doping concentration is increased because of bandgap narrowing. The maximum PVCR of 3.2 was observed for the four atom BN co-doped CNTFET model. Thus our results elucidate the NDR behavior in the realm of nano dimensions which provides a link to next generation design. The results are very important for potential nanoelectronic applications like amplifiers, oscillators, digital logic and memories. Acknowledgement The authors greatly acknowledge the financial support by University Grants Commission (UGC), New Delhi (grant No: 42768/2013) which enables this study to occur. References [1] I. Deretzis, A. La Magna, Nanotechnology 17 (2006) 5063. [2] S. Iijima, Nature 354 (1991) 56.
Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037
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Please cite this article in press as: K.A. Shah, M.S. Parvaiz, Negative differential resistance in BN co-doped coaxial carbon nanotube field effect transistor, Superlattices and Microstructures (2016), http://dx.doi.org/10.1016/j.spmi.2016.09.037