Electronic structure simulation of thin silicon layers: Impact of orientation, confinement, and strain

Highlights

• Systematic study of strained silicon slabs with varying thicknesses has been performed.

• The strain dependence of the band gap of thin silicon slabs deviates strongly from bulk silicon.

• A suitable combination of strain and thickness enables opto-electronic applications.

Abstract

Silicon-on-insulator is a key technology to support the continuation of Moore’s law. This publication investigates the impact of orientation, confinement, and strain on the electronic structure of thin silicon slabs using density functional theory. The comparative study of low-index orientations demonstrates that confinement not only widens the band gap but also transforms the band gap type. For thin silicon layers, strain can alter band gap and band gap type, too. By comparing our findings for different crystal orientations, we demonstrate that the consideration of the electronic structure of strained and confined silicon is of high relevance for modelling actual devices.

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.