Electronic structure simulation of thin silicon layers: Impact of orientation, confinement, and strain
Graphical abstract
Introduction
Microelectronic industry is driven by the need for faster and smaller devices [1], [2], [3]. For a long time, geometric scaling theory has served this purpose [4]. As device dimensions enter the deep-submicrometer regime, many parasitic effects like drain-induced barrier lowering, velocity saturation, hot carrier generation, and subthreshold leakage limits the geometrical scaling [5]. Therefore, the microelectronic community has come up with novel concepts for further scaling. One approach is the use of the Fully Depleted Silicon On Insulator (FDSOI) architecture [6].
FDSOI transistors feature a fully depleted body, which is isolated by an insulator box. This introduces better electrostatics leading to lower leakage current and better channel control in comparison to bulk planar transistors [1], [5], [6], [7]. The device performance is heavily influenced by the properties of the ultra-thin body [8]. The conventional body thickness of a FDSOI transistor is in the range of 4 nm to 6 nm. For such small body thicknesses, silicon loses its translational symmetry in the confinement direction, and the lattice becomes two-dimensional [3].
Understanding the material at the atomistic level is essential, especially when size quantization plays a role. This has been demonstrated for quantum dots [9], [10] and nanowires [11], [12], [13]. Despite the high relevance in technology, there exists only a limited number of studies on the electronic structure of quasi-two-dimensional silicon [12], [14], [15]. In this work, Density Functional Theory (DFT) is employed to study the impact of orientation, confinement, and strain on thin silicon slabs. Most previous work deals with {100} cleaved slabs [2], [16], [17], [18]. Our study includes other low-index orientations like {110} and {111}. Moreover, the impact of uniaxial and biaxial strain on the confined structures is investigated. Band structure properties are presented for various combinations of strain, thickness of the silicon layer, and orientation. The band gap values, for example, can be used for multi-scale modelling of the electronic transport properties of FDSOI transistors, because device models require suitable band structure properties as input parameters. Moreover, changes of band gap type (i.e. indirect or direct) are evaluated. Under specific confinement and strain conditions, the ultra-thin silicon exhibits a direct band gap, which makes the material interesting for optical applications.
The publication is organized as follows:
Model system: This section introduces the slab structures and the associated technology parameters for which the study is employed.
Simulation details: A brief description of the simulation parameters for the structures under study is given.
Results and discussion: The impact of orientation, confinement, and strain on the band gap is presented and discussed.
Summary and conclusion: This section summarizes and concludes the present work.
Section snippets
Model system
Fig. 1 depicts the system under study. In this work, {100}, {110}, and {111} are the three silicon orientations under investigation. Surface reconstructions of silicon surfaces are well-known [19]. Considering surface reconstructions, however, requires much larger simulation cells in the in-plane direction, leading to a drastic increase in computational time. Since our focus is on the intrinsic properties of the silicon slab instead of the surface properties, we limit the present study on
Simulation details
Fig. 2 shows the schematic of the simulation procedure. The initial step involves relaxing bulk silicon with an unconstrained unit cell. This is followed by the optimization of the cleaved structures, whose unit cell has been constrained in the periodic direction while it remains unconstrained in the confinement direction. Next, the optimized cleaved structures are strained and re-optimized using the same cell constraints as in the previous step. The final step involves a band structure
Impact of confinement
Silicon is an indirect band gap material with the valence band maxima at [000] () and six equivalent conduction band minima located along (at around 85% of the distance between and ). The ellipsoids shown in Fig. 3 represent the constant energy surfaces for the conduction band subband. Shrinking of bulk silicon to thin silicon slabs leads to a strong size quantization resulting in two-dimensional subband ladders, which will be discussed in the following paragraph. The parabolic band
Summary and conclusion
The effect of orientation, confinement, and strain on the electronic structure of quasi-two-dimensional silicon was investigated systematically by using DFT. From the simulation of free standing silicon slabs, it has been observed that confinement can change the band gap type of silicon. With confinement of bulk silicon in the {100} direction, the band gap type can transform from indirect to direct. For the {110} and {111} cleaved slabs the band gap type is always indirect, except for the 1 nm
CRediT authorship contribution statement
Thomas Joseph: Investigation, Visualization, Writing – original draft. Florian Fuchs: Supervision, Writing – review & editing. Jörg Schuster: Funding acquisition, Project administration, Writing – review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (28)
- et al.
Radially resolved electronic structure and charge carrier transport in silicon nanowires
Physica E
(2019) - et al.
Appearance of direct gap in silicon and germanium nanosize slabs
Opt. Mater.
(2001) Strain-induced effects in advanced MOSFETs
- et al.
Atomistic study on electronic properties of nanoscale SOI channels
J. Phys. Conf. Ser.
(2008) - et al.
Impact of body-thickness-dependent band structure on scaling of double-gate MOSFETs: a DFT/NEGF study
IEEE Trans. Nanotechnol.
(2009) - et al.
Design of ion-implanted MOSFET’s with very small physical dimensions
IEEE J. Solid-State Circuits
(1974) - et al.
Strain: a solution for higher carrier mobility in nanoscale MOSFETs
Annu. Rev. Mater. Res.
(2009) - et al.
Frontiers of silicon-on-insulator
J. Appl. Phys.
(2003) - et al.
Impact of channel thickness variation on bandstructure and source-to-drain tunneling in ultra-thin body III-V MOSFETs
IEEE J. Electron Dev. Soc.
(2016) - et al.
Validity of the parabolic effective mass approximation in silicon and germanium n-MOSFETs with different crystal orientations
IEEE Trans. Electron Devices
(2007)
First-principle study of quantum confinement effect on small sized silicon quantum dots using density-functional theory
Optical properties of doped silicon quantum dots with crystalline and amorphous structures
J. Phys. Chem. C
Strain-driven electronic band structure modulation of si nanowires
Nano Lett.
Size dependence of band gaps in silicon nanostructures
Appl. Phys. Lett.
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