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采用非平衡格林函数结合密度泛函理论探讨了以锯齿型石墨烯纳米带为电极、2-苯基吡啶分子为中心区的分子器件电子输运性质. 分析I-V特性及透射谱随偏压的变化表明, 电极弯折能够调控器件负微分电阻特性, 使器件峰值电压(Vp)减小、电流峰谷比(PVR)增大, 当电极弯折角度为15°时, 器件获得低峰值电压(0.1 V)、高电流峰谷比(12.84)的负阻特性. 平衡态下器件的透射谱、态密度、散射态实空间分布图及投影态密度解释了器件负阻特性被调控源于电极弯折使器件中心分子与电极间的波函数交叠发生变化, 导致两者间耦合减弱. 弱耦合下外加偏压后, 器件的透射系数因能级移动和偏压的变化而产生大幅波动, 使器件在低偏置电压处即出现大的透射系数, 产生峰值电流Ip, 降低了器件的Vp, 且增大了PVR值, 其所获得的低Vp、高PVR的负阻特性在低功耗分子电子领域具有潜在的应用前景.Combining non-equilibrium Green’s function with density functional theory, we study the electronic transport properties of the molecular devices comprised of 2-phenylpyridine and zigzag graphene nanoribbon (ZGNR) electrodes. The I-V characteristics and transmission coefficients under external voltage biases are analyzed, and the results show that the negative differential resistance (NDR) is effectively adjusted by the bending of ZGNR electrode, which reduces the peak voltage (Vp) and increases the peak-valley ratio (PVR) of the device. When the electrode bending angle is 15°, the PVR of device M2 is a maximum value of 12.84 and Vp is 0.1 V, which is low enough for practical applications. The transmission spectra, the density of states and the real-space scattering state distribution at Ef of device under zero bias explain that the weaker coupling between the molecules and the electrodes is caused by the bending of the ZGNR electrode, which might be responsible for the adjustability of NDR. The analysis shows that the bending of the electrode changes the electronic structure between the 2-phenylpyridine molecule and the ZGNR electrode, and then changes the wave functions overlap between them, the coupling between the molecule and the electrodes gets weaker. An external bias can induce the level to shift. The transmission coefficient for the weaker coupling between the molecules. The electrodes can fluctuate wildly from level to level, and large NDR effect under very low bias is obtained with the variation of external bias. Therefore, for highly symmetric molecular devices, the electronic transport properties can be effectively adjusted by changing the coupling between the central molecule and the electrodes. Our investigations indicate that the 2-phenylpyridine molecular device with ZGNR electrodes may have potential applications in the field of low-power dissipation molecules device.
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Keywords:
- negative differential resistance /
- electrode bending /
- non-equilibrium Green’s function /
- density functional theory
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图 1 2-苯基吡啶分子器件结构图, 图中所示θ为石墨烯电极弯折角度
Fig. 1. Structure diagram of the 2-phenylpyridine molecular device, θ represented to the bending angle of the graphene electrode.
图 3 器件M1—M4在偏置电压为+0.1 V, +0.2 V, +0.5 V, +0.6 V, +0.8 V和+1.0 V时的透射谱图, 红色虚线为Ef能级, 蓝色线为偏压窗区间
Fig. 3. Transmission spectra of M1−M4 under the bias voltage of +0.1 V, +0.2 V, +0.5 V, +0.6 V, +0.8 V and +1.0 V, the red dashed line represented to the Fermi level, the blue line represented to the bias window interval.
图 4 平衡态下(Vb = 0)器件M1—M4的透射谱图, 红色虚线为Ef能级
Fig. 4. Transmission spectra of device M1−M4 under zero bias (Vb = 0), the red dotted line represented to the Fermi level.
图 5 平衡态下(Vb = 0)器件M1—M4的态密度图(a)及Ef处的实空间散射态分布图(b)
Fig. 5. Density of states (a) and the real-space scattering states distribution at Ef (b) under zero bias (Vb = 0) of device M1−M4.
表 1 器件M1−M4的Ip, Iv, PVR和Vp
Table 1. Ip, Iv, PVR and Vp of devices M1−M4.
器件 Ip/μA Iv/μA PVR Vp/V 负阻特性电压区间 M1 1.73 0.83 2.08 0.6 [+0.6 V, +1.0 V] M2 1.67 0.13 12.84 0.1 [+0.1 V, +0.5 V] M3 1.60 0.31 5.16 0.2 [+0.2 V, +0.6 V] M4 0.99 0.17 5.82 0.1 [+0.1 V, +0.6 V] 
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表 2 平衡态下器件电极和中心分子在Ef处投影态密度值及其在总态密度降低值的贡献
Table 2. Projected density of states under zero bias (value and percentage in M1−M4) on electrode and 2-phenylpyridine at Ef.
器件 总态密度 ZGNR电极态密度 吡啶分子态密度 态密度降低值的贡献 原值 较M1降低值 原值 较M1降低值 原值 较M1降低值 ZGNR电极 吡啶分子 M1 1520.7666 — 1423.8923 — 96.8743 — — — M2 (M1-M2) 998.2693 522.4973 933.4124 490.4799 64.8569 32.0174 93.9% 6.12% M3 (M1-M3) 830.7494 690.0172 771.0848 652.8075 59.6646 37.2097 94.6% 5.39% M4 (M1-M4) 763.5156 757.251 702.3966 721.4957 61.119 35.7553 95.2% 4.72%
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表 3 器件M1—M4在零偏压、+0.1 V, +0.2 V, +0.6 V和+1.0 V下散射态实空间分布图, 色坐标参考图5(b)
Table 3. Real-space scattering state distribution of devices M1−M4 under zero bias, +0.1 V, +0.2 V, +0.6 V and +1.0 V, all the figures share the same color bar given in Fig. 5(b).
器件 Vb = 0 V Vb = 0.1 V Vb = 0.2 V Vb = 0.5 V(M2)
Vb = 0.6 V
(M1, M3, M4)Vb = 1.0 V M1 
M2 M3 M4
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[1] Joachim C, Gimzewski J K, Aviram A 2000 Nature 408 541
Google Scholar
[2] Shi X Q, Zheng X H, Dai Z X, Wang Y, Zeng Z 2005 J. Phys. Chem. B 109 3334
Google Scholar
[3] Wang S C, Lu W C, Zhao Q Z, Bernholc J 2006 Phys. Rev. B 74 195430
Google Scholar
[4] Guo C, Wang K, Zerah Harush E, Hamill J, Wang B, Dubi Y, Xu B Q 2016 Nat. Chem. 8 484
Google Scholar
[5] Ryu T, Lansac Y, Jang Y H 2017 Nano Lett. 17 4061
Google Scholar
[6] Lyo I W, Avouris P 1989 Science 245 1369
Google Scholar
[7] Kaneda M M, Messer K S, Ralainirina N, Li H, Leem C J, Gorjestani S, Woo G, Nguyen A V, Figueiredo C C, Foubert P, Schmid M C, Pink M, Winkler D G, Rausch M, Palombella V J, Kutok J, McGovern K, Frazer K A, Wu X, Karin M, Sasik R, Cohen E E W, Varner J A 2016 Nature 539 437
Google Scholar
[8] Long M Q, Chen K Q, Wang L L, Zou B S, Shuai Z 2007 Appl. Phys. Lett. 91 233512
Google Scholar
[9] Yuan S D, Wang S Y, Mei Q B, Ling Q D, Wang L H, Huang W 2014 J. Phys. Chem. C 118 617
Google Scholar
[10] Mathews R H, Sage J P, Sollner T C L G, Calawa S D, Chen C L, Mahoney L J, Maki P A, Molvar K M 1999 Proc. IEEE 87 596
Google Scholar
[11] Broekaert T P E, Brar B, van der Wagt J P A, Seabaugh A C, Morris F J, Moise T S, Beam E A, Frazier G A 1998 IEEE J. Solid-State Circuits 33 1342
Google Scholar
[12] Brown E R, Söderström J R, Parker C D, Mahoney L J, Molvar K M, McGill T C 1991 Appl. Phys. Lett. 58 2291
Google Scholar
[13] Chen J, Reed M A, Rawlett A M, Tour J M 1999 Science 286 1550
Google Scholar
[14] Li J, Duan Y, Zhou Y, Li T, Zhao Z, Yin L W, Li H 2017 RSC Adv. 7 53696
Google Scholar
[15] Zhang J, Qin Z, Yao K L 2017 Chem. Phys. Lett. 688 89
Google Scholar
[16] Wang Q, Li J W, Wang B, Nie Y H 2018 Front. Phys. 13 138501
Google Scholar
[17] Min Y, Zhong C G, Yang P P, Yao K L 2018 J. Phys. Chem. Solids 119 238
Google Scholar
[18] Yao A L, Dong Y J, Wang X F, Liu Y S 2019 Appl. Nanosci. 9 143
Google Scholar
[19] Yang Z X, Pan J L, Cheng X, Xiong X, Ouyang F P 2019 J. Appl. Phys. 126 104501
Google Scholar
[20] Berg J, Bengtsson S, Lundgren P 2000 Solid-State Electron. 44 2247
Google Scholar
[21] Chen W, Li H, Widawsky J R, Appayee C, Venkataraman L, Breslow R 2014 J. Am. Chem. Soc. 136 918
Google Scholar
[22] Mahendran A, Gopinath P, Breslow R 2015 Tetrahedron Lett. 56 4833
Google Scholar
[23] Xu B, Tao N J J 2003 Science 301 1221
Google Scholar
[24] Marmolejo-Tejada J M, Velasco-Medina J 2016 Microelectron. J. 48 18
Google Scholar
[25] Celis A, Nair M N, Taleb-Ibrahimi A, Conrad E H, Berger C, de Heer W A, Tejeda A 2016 J. Phys. D Appl. Phys. 49 143001
Google Scholar
[26] Capozzi B, Xia J, Adak O, Dell E J, Liu Z F, Taylor J C, Neaton J B, Campos L M, Venkataraman L 2015 Nat. Nanotechnol. 10 522
Google Scholar
[27] Van Dyck C, Geskin V, Cornil J 2014 Adv. Funct. Mater. 24 6154
Google Scholar
[28] Li J, Li T, Zhou Y, Wu W K, Zhang L N, Li H 2016 Phys. Chem. Chem. Phys. 18 28217
Google Scholar
[29] Zang J, Ryu S, Pugno N, Wang Q, Tu Q, Buehler M J, Zhao X 2013 Nat. Mater. 12 321
Google Scholar
[30] Lee S M, Kim J H, Ahn J H 2015 Mater. Today 18 336
Google Scholar
[31] Xie Y, Chen Y, Wei X L, Zhong J 2012 Phys. Rev. B 86 195426
Google Scholar
[32] Song Q C, An M, Chen X D, Peng Z, Zang J F, Yang N 2016 Nanoscale 8 14943
Google Scholar
[33] Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15
Google Scholar
[34] Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169
Google Scholar
[35] Taylor J, Guo H, Wang J 2001 Phys. Rev. B 63 245407
Google Scholar
[36] Landauer R 1970 Philos. Mag. 21 863
Google Scholar
[37] Büttiker M 1988 Phys. Rev. B 38 9375
Google Scholar
[38] Datta S 1995 Electronic Transport in Mesoscopic Systems (Cambridge: Cambridge University Press) pp117–174
[39] Pshenichnyuk I A, Coto P B, Leitherer S, Thoss M 2013 J. Phys. Chem. Lett. 4 809
Google Scholar
[40] Stokbro K, Taylor J, Brandbyge M, Mozos J L, Ordejón P 2003 Comput. Mater. Sci. 27 151
Google Scholar
[41] Thygesen K S, Jacobsen K W 2005 Chem. Phys. 319 111
Google Scholar
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Google Scholar
[43] Wang S D, Sun Z Z, Cue N, Xu H Q, Wang X R 2002 Phys. Rev. B 65 125307
Google Scholar
[44] Jalabert R A, Stone A D, Alhassid Y 1992 Phys. Rev. Lett. 68 3468
Google Scholar
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