A Comprehensive Ab Initio Study of Electronic, Optical and Cohesive Properties of Silicon Quantum Dots of Various Morphologies and Sizes up to Infinity

TL;DR

This study uses ab initio density functional theory to analyze and model the electronic, optical, and cohesive properties of silicon quantum dots across various sizes and shapes, successfully extrapolating to bulk silicon.

Contribution

It provides a comprehensive, model-independent ab initio analysis and accurate extrapolation formulas for silicon nanocrystals' properties up to infinite size.

Findings

Accurately reproduces experimental and theoretical results for small nanocrystals.

Successfully extrapolates properties to bulk silicon with high accuracy.

Provides formulas for properties like band gap and cohesive energy across sizes.

Abstract

We present a comprehensive and integrated model-independent ab initio study of the structural, cohesive, electronic, and optical properties of silicon quantum dots of various morphologies and sizes in the framework of all-electron static and time-dependent density functional theory (DFT, TDFT), using the well-tested B3LYP and other properly chosen functional(s). Our raw ab initio results for all these properties for hydrogen passivated nanocrystals of various growth models and sizes from 1 to 32 Angstroms, are subsequently fitted, using power-law dependence with judicially selected exponents, based on dimensional and other plausibility arguments. As a result, we can reproduce with excellent accuracy not only known experimental and well-tested theoretical results in the regions of overlap, but we can also extrapolate successfully all the way to infinity, reproducing the band gap of crystalline silicon with almost chemical accuracy as well as the cohesive energy of the infinite crystal with very good accuracy. Thus, our results could be safely used, among others, as interpolation and extrapolation formulas not only for cohesive energy and band gap, but also for interrelated properties, such as dielectric constant and index of refraction of silicon nanocrystals of various sizes all the way up to infinity.