First principles investigation of the structural, electronic, and optical properties of new c-Si₁₂ silicon allotrope with a cubic structure

Highlights

• The obtained optimal lattice constant and Si-Si bond length for c-Si₁₂ structure are larger than diamond-Si one.

• The bulk modulus for c-Si₁₂ structure is smaller than diamond-Si and all other Si allotropes.

• The band gap of c-Si₁₂ is smaller than diamond-Si and other Si allotropes and silicon c-Si₁₂ allotrope is a semiconductor with an indirect band gap equal to 0.996 eV.

• There is a distance about 0.187 eV between an indirect and direct band gaps.

• The static dielectric constant of c-Si₁₂ is smaller than Diamond-Si and other Si allotropes.

Abstract

In this paper, some structural, electronic, and optical properties of c-Si₁₂ silicon allotrope was investigated based on the density functional theory approach. The results were compared to some of silicon allotropes. The structural results show that both the optimal cubic lattice constant and Si–Si bond length in the c-Si₁₂ structure are larger than the diamond-Si one, although the bulk modulus for the c-Si₁₂ structure is smaller than the diamond-Si and other Si allotrope structures. The electronic results indicate that c-Si₁₂ structure is a semiconductor with an indirect band gap having an energy distance about 0.187 eV between its indirect and direct band gaps. In the optical properties section, the dielectric function, energy loss function, refractive index, and reflectivity of the c-Si₁₂ structure were investigated and compared to the experimental data for the diamond silicon allotrope. Our results indicate that in the visible range, the optical absorption of the c-Si₁₂ structure is larger than the diamond-Si which implies the promising optical properties of the c-Si₁₂ structure and its advantage with respect to the diamond-Si one.

Introduction

The tremendous advances in the semiconductor technology are indeed indebted to the silicon. The metal-oxide-silicon field-effect transistor (MOSFET) which is one of the most fundamental blocks of the novel electronic industry and revolutionizing the world economy, relies on the silicon technology that is pivotal to the digital age. The synergy combination of the two leading factors, i.e., the silicon high abundance and miniaturization of the MOSFETs, caused the mass-product of silicon devices, having a wide range of applications in the computers, smartphones [[1], [2], [3]], as well as the sensors and optoelectronic devices [[4], [5], [6]].

Silicon is widely used in the monocrystalline diamond-Si or large-grained polycrystalline form in the solar cells and photovoltaic applications [[7], [8], [9]]. The conventional form of the silicon (diamond-Si) is an indirect semiconductor with a band gap equal to 1.1eV. Diamond-Si, also has a direct band gap which is larger than 3eV [7]. The indirect band gap is a disadvantage since it needs to utilize the phonons for absorbing the photons [7,9]. Due to the silicon's indirect band gap, the Si absorber layer should be thick enough to absorb all the low energy photons. Despite this disadvantage, 90% of the commercial photovoltaic market is used by the Si solar cells [[10], [11], [12], [13]]. Due to the industrial applications, it seems that the investigation of direct or quasi-direct band gap in different allotropes of silicon is needed. The direct band gap silicon allotropes can be important for the next generations of silicon-based electronics.

There are several allotropes for silicon which can be stable or metastable at the ambient or high-pressure conditions. The diamond-Si structure is stable at the ambient conditions. By increasing the pressure, the diamond-Si structure can be transformed into other phases. For example, when the pressure increase to 10–11 GPa, the diamond-Si undergoes a transition to the metallic β-Sn phase [14,15]. Upon more increasing of the pressure, the β-Sn phase converts into an orthorhombic (Imma) phase and then into a simple hexagonal phase [14,15]. At the estimated pressure equal to 38 GPa, the simple hexagonal phase transforms to an orthorhombic phase (Cmca) [14,16] and at the pressure equal to 42 GPa, a transition to the hexagonal-close-packed (hcp) structure occurs [14,16]. With decreasing the pressure, several metastable phases are formed, beginning from the high-pressure phases of Si: Slow decompression from the β-Sn phase of Si leads first to the rhombohedral R8 phase at about 10 GPa (which remains as a metastable phase under normal conditions) and then to the cubic BC8 phase at about 2 GPa [14,17,18]. Numerous allotropes for silicon were theoretically reported in some papers [7,[19], [20], [21], [22], [23], [24], [25], [26], [27], [28]]. Recently, a new allotrope of silicon was synthesized through synthesizing the Na₄Si₂₄ precursor at high pressure, utilizing a thermal ‘degassing’ process [29] to remove the sodium atoms. Moreover, Wenjing Li et al. reported the structural determination of the high-pressure phases of CsSi₆ using an unbiased swarm structure [30]. They showed that by the removal of Cs atoms from Im3m phase of CsSi₆, the Si clathrate structure (c-Si₁₂) is dynamically and mechanically stable at the ambient conditions [30]. In the present work, in addition to the structural (e.g., the optimal lattice constant, Si–Si bond length, and bulk modulus) and electronic (e.g., the density of states and energy band structure) properties, the optical properties of c-Si12 silicon allotrope are investigated.