Effect of Thickness on the Surface and Electronic Properties of Bi Film

doi:10.11900/0412.1961.2017.00422

Acta Metall Sin

2018, Vol. 54

Issue (6): 935-942 DOI: 10.11900/0412.1961.2017.00422

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Effect of Thickness on the Surface and Electronic Properties of Bi Film

Caihong DONG¹, Yongli LIU², Yang QI²(

)

1 College of Science, Northeastern University, Shenyang 110819, China
2 School of Materials Science and Engineering, Northeastern University, Shenyang 110819, China

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Caihong DONG, Yongli LIU, Yang QI. Effect of Thickness on the Surface and Electronic Properties of Bi Film. Acta Metall Sin, 2018, 54(6): 935-942.

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Abstract

Bismuth and its alloys exhibit a number of peculiarities and mysterious features due to its three-dimensional (3D) hexagonal crystal, and have attracted the interest of many researchers for many years. Currently, the trivial-to-topological and semimetal-semiconductor transitions have been focused, as the result of its semi-metallic and large spin-orbit coupling. The binary compounds of Bi₂M₃ and binary alloys Bi_xM_1-_x (M=Se, Sb and Te) are found to be 3D topological insulators, as the result of small band gap and large spin-orbit coupling in Bi crystals and Bi compounds, which make these crystals topologically important. In the case of Bi films, strong spin-orbit (SO) coupling interaction is also a fundamental mechanism to induce the Z₂ topology. Recently, ultrathin Bi films have also been theoretically predicted to be an elemental two-dimensional topological insulator. And, all the ultrathin Bi(111) films are characterized by a nontrivial Z₂ number independent of the film thickness. In the past few years, ultrathin films of Bi with a thickness down to several BLs (bilayers) on Si substrate have been prepared in experiments, finding that thicknesses have an effect on the properties of Bi films. However, the effect of thickness on films had not be studied for microscopic mechanism experimentally in detail. In this work, the effects of thickness on the surface and electronic properties of (00Ɩ) and (012) oriented films of Bi using the first-principles method were studied. With the increase of thickness, (00Ɩ) oriented Bi films became more stable, and the film of the even-numbered layers was more stable than that of the odd-numbered layer. However, the (012) oriented Bi films presented totally different behavior comparing with the (00Ɩ) oriented Bi film. The stabilities of (012) oriented film became less stable as the thickness increased, and possessed the approximated surface energy of even-numbered layers (00Ɩ) oriented Bi films when their layer numbers were closed to four. Further analysis of the cohesive energy, geometry structure and electronic band structures showed that, all the thin films presented the transition from semi-conductors to semi-metal or metal as the thickness increases.

Key words: Bi film thickness stability transition electrical conductivity first-principles calculation

Received: 10 October 2017

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https://www.ams.org.cn/EN/10.11900/0412.1961.2017.00422 OR https://www.ams.org.cn/EN/Y2018/V54/I6/935

Table 1 Calculated lattice parameters a, b and c of Bi crystal in this work, together with the results of calculated and experimental work^[20,27]

Fig.1 Hexagonal crystal structure (a), Brillouin zone using a rhombic hexahedral cell (b), direct band gap

E g, d

and indirect band gap

E g, i

calculated by PBE method (c) and band structure of bulk Bi along high-symmetry (d) (E_F—Fermi energy)

Fig.2 The comparison of the surface energies of Bi thin films oriented in (00Ɩ) and (012) directions along with different thickness

Fig.3 Atomic configuration of Bi(00Ɩ) direction (The numbers (green color on line) represent the bonding length)
(a) top view, the green dotted lines show the (1×1) surface unit cell
(b, c) side views with the odd- and even-layers, respectively.d₁ and d₂ denote the layer distance internal and between the bilayer (BL) structure respectively, two layers connected by a short interlayer spacing (d₁) form the stable bilayer

Distance / nm	1 BL	2 BL	3 BL	4 BL	5 BL	6 BL
$Δ d 1,2$	0	-0.00250	-0.00330	-0.00320	-0.00223	-0.00325
$Δ d 2,3$		0.0165	0.0177	0.0174	0.0160	0.0175
$Δ d 3,4$		-0.00270	-0.00308	-0.00272	-0.00283	-0.00263
$Δ d 4,5$			0.0177	0.0169	0.01406	0.0159
$Δ d 5,6$			-0.00330	-0.00272	-0.00259	-0.00237
$Δ d 6,7$				0.0174	0.0141	0.0150
$Δ d 7,8$				-0.00320	-0.00283	-0.00237
$Δ d 8,9$					0.0160	0.0159
$Δ d 9,10$					-0.00336	-0.00259
$Δ d 10,11$						0.0175
$Δ d 11,12$						-0.00328
Distance / nm	1 SL	3 SL	5 SL	7 SL	9 SL	11 SL
$Δ d 1,2$		0.0273	0.0146	0.00668	0.00223	-0.000152
$Δ d 2,3$		-0.0394	-0.0214	-0.0105	0.00777	0.00177
$Δ d 3,4$			0.0460	0.0320	0.0178	0.00934
$Δ d 4,5$			-0.0532	-0.0357	-0.0234	-0.0112
$Δ d 5,6$				0.0573	0.0453	0.0291
$Δ d 6,7$				-0.0610	-0.0502	-0.039
$Δ d 7,8$					0.0703	0.0573
$Δ d 8,9$					-0.0656	-0.05867
$Δ d 9,10$						0.0758
$Δ d 10,11$						-0.115

Table 2 Optimized results of structural parameters for Bi(00Ɩ) even- and odd-numbered layer films with thickness of 1~6 BL and 1~11 SL (single-layer), the variation of interlayer distance

Δ d i, j = d i, j 1 - d i, j 0

(

d i, j 1

is the relaxed interlayer distance, while

d i, j 0

is ideal interlayer distance, i and j are atomic layers), ideal interlayer distance of bulk structure

d i, i + 1

=0.1651 nm and 0.2328 nm for odd and even i, respectively

Fig.4 Atomic structures of Bi film
(a) top view of Bi(012) direction, the mirror planes of structure are shown as dashed lines
(b) side view perpendicular to the mirror plane
(c) side view parallel to the mirror plane
(d, e) side views of four atomic layers Bi(012) direction with unrelaxed bulk structure and after structural optimization, respectively
(f) side view of (00Ɩ) direction with relaxed structure, which is analogous to the structure of (012) direction after structural optimization while their stacking sequence is different

Fig.5 The comparison of cohesive energy of Bi thin films oriented in (00Ɩ) even-numbered layers and (012) direction with different thicknesses, the stable areas are indicated by solid curves and the unstable areas in dash curves

Fig.6 Band structures of Bi(00Ɩ) films with 1~6 BL thickness

Fig.7 Band structures of Bi(00Ɩ) films with 1~11 SL thickness

Fig.8 Band structures of Bi(012) films with 1~6 BL thickness

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