Negative-Differential-Resistance Devices Achieved by Band-Structure Engineering in Silicene under Periodic Potentials

Chang-Hung Chen, Wen-Wu Li, Yuan-Ming Chang, Che-Yi Lin, Shih-Hsien Yang, Yong Xu, and Yen-Fu Lin

Phys. Rev. Applied 10, 044047 – Published 18 October 2018

Abstract

An important development in modern electronics is the realization of band-structure engineering for the design of novel materials and devices. One possible way to realize band-structure engineering is by addition of periodic potentials to two-dimensional (2D) materials, such as graphene, to form a superstructure, known as a “superlattice.’ Unlike the band gap of graphene, the band gap of silicene can be tuned by an out-of-plane electric field owing to its unusual buckled structure. In this work, we use the designable band gap of silicene and the band structure of superlattices, together with the spin and valley degrees of freedom, to propose a design principle for optimizing the performance of spin- and valley-dependent negative-differential-resistance (NDR) devices using silicene superlattices. On the basis of the effective Hamiltonian formalism, we predict that the peak-to-valley current ratio could be larger than most recently reported results achieved by 2D materials, suggesting that the silicene superlattice is a good candidate for realizing NDR devices. The design principle proposed in this work could also be extended to other layered materials with tunable band gaps. This could pave the way for advanced material and device designs based on band-gap engineering of 2D materials.

Received 8 March 2018
Revised 21 June 2018

DOI:https://doi.org/10.1103/PhysRevApplied.10.044047

Physics Subject Headings (PhySH)

Electronic structure Topological phase transition Valleytronics

2-dimensional systems Devices Silicene Superlattices

Band structure methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Chang-Hung Chen^1,2,*,†, Wen-Wu Li^1,*, Yuan-Ming Chang², Che-Yi Lin³, Shih-Hsien Yang⁴, Yong Xu^5,‡, and Yen-Fu Lin^2,§

¹Key Laboratory of Polar Materials and Devices (Ministry of Education), Technical Center for Multifunctional Magneto-Optical Spectroscopy (Shanghai), East China Normal University, Shanghai 200241, China
²Department of Physics, National Chung Hsing University, Taichung 40227, Taiwan
³Department of Electrophysics, National Chiao Tung University, Hsinchu 30010, Taiwan
⁴Institute of Electronics Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan
⁵School of Electronic and Optical Engineering, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, 210023, China

^*C.-H. Chen and W.-W. Li contributed equally to this work.
^†chchen0428@gmail.com
^‡xuyong.hn@gmail.com
^§yenfulin@nchu.edu.tw

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Vol. 10, Iss. 4 — October 2018

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Images

Figure 1
Silicene superlattice structure, potential profile, and band structure. (a) The structure of a silicene superlattice, a silicene monolayer connected to source (S) and drain (D) electrodes, with four strips of ferromagnetic insulators on top. (b) Side view of silicene showing that the two sublattice atomic planes have a vertical separation distance of 0.46 Å, forming a buckled structure. (c) The potential profiles $U (x)$ for spin-up electrons (solid red line) and spin-down electrons (dashed black line). $Δ_{ex}$ is the exchange-splitting energy induced by the ferromagnetic insulator. Schematic band structure of silicene around $K$ and $K^{'}$ points for three different staggered sublattice potentials, (d) $Δ_{Z} = 0$ , (e) $Δ_{Z} = Δ_{Z, C}$ , and (f) $Δ_{Z} > Δ_{Z, C}$ , which can be induced by application of an out-of-plane electric field. $Δ_{Z, C} = Δ_{S O} = 3.9$ meV denotes the critical staggered sublattice potential where silicene becomes semimetallic for $K ↑$ and $K^{'} ↓$ .
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Figure 2
Band structure and transmission spectra of the silicene superlattice with a ferromagnetic insulator. (a) Energy band structure of silicene superlattice as a function of wave vector $k_{y}$ for four combinations of spin and valley flavors. Filled areas indicate the allowed bands. (b) Energy band structure of the silicene superlattice as a function of the Bloch-wave vector for normal incidence $k_{y} = 0 {nm}^{- 1}$ . (c) The unbiased transmission spectrum for eight-barrier silicene superlattices with lateral widths $a = b = 50$ nm and staggered sublattice potential $Δ_{Z} = 40$ meV. (d) Transmission spectrum as a function of bias voltage $V_{S D}$ for spin-up electrons in the $K^{'}$ valley. The potential barrier and exchange-splitting energy are $U = 175$ meV and $Δ_{ex} = 36$ meV, respectively.
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Figure 3
Bias-dependent transmission spectra. (a) Bias-dependent transmission spectra for spin-up electrons in the $K^{'}$ valley with larger bias and energy range than that in Fig. 2. The lateral width, number of barriers, and staggered sublattice potential are $a = b = 50$ nm, $N = 8$ , and $Δ_{Z} = 40$ meV, respectively. The transmission spectra for (b) narrower width $a = b = 10$ nm, (c) lower number of barriers $N = 4$ , and (d) smaller staggered sublattice potential $Δ_{Z, C} = Δ_{S O} = 3.9$ meV. The transport windows are denoted by the regions between two white lines.
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Figure 4
Spin-resolved current $I_{S}$ vs bias voltage $V_{S D}$ [upper panels in (a)–(d)] and valley-resolved current $I_{V}$ vs bias voltage $V_{S D}$ [lower panels in (a)–(d)]. The parameters used in (a)–(d) are the same as those used in Figs. 3–3, respectively.
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Figure 5
Total current vs bias voltage $V_{S D}$ at room temperature. Trend of the change of total current as a function of bias voltage $V_{S D}$ for variation of (a) the number of barriers, (b) lateral widths, and (c) staggered sublattice potential. (d) Comparison of the PVCR in this work with other recently reported results at room temperature.
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