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Understanding quantum confinement in nanowires: basics, applications and possible laws
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 423202 (http://iopscience.iop.org/0953-8984/26/42/423202) View the table of contents for this issue, or go to the journal homepage for more
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 423202 (28pp)
doi:10.1088/0953-8984/26/42/423202
Topical Review
Understanding quantum confinement in nanowires: basics, applications and possible laws S Noor Mohammad Sciencotech, 780 Girard St. NW, Washington, DC 20001, USA E-mail:
[email protected] Received 2 June 2014, revised 9 August 2014 Accepted for publication 12 August 2014 Published 23 September 2014 Abstract
A comprehensive investigation of quantum confinement in nanowires has been carried out. Though applied to silicon nanowires (SiNWs), it is general and applicable to all nanowires. Fundamentals and applications of quantum confinement in nanowires and possible laws obeyed by these nanowires, have been investigated. These laws may serve as backbones of nanowire science and technology. The relationship between energy band gap and nanowire diameter has been studied. This relationship appears to be universal. A thorough review indicates that the first principles results for quantum confinement vary widely. The possible cause of this variation has been examined. Surface passivation and surface reconstruction of nanowires have been elucidated. It has been found that quantum confinement owes its origin to surface strain resulting from surface passivation and surface reconstruction and hence thin nanowires may actually be crystalline-core/amorphous-shell (c-Si/a-Si) nanowires. Experimental data available in the literature corroborate with the suggestion. The study also reveals an intrinsic relationship between quantum confinement and the surface amorphicity of nanowires. It demonstrates that surface amorphicity may be an important tool to investigate the electronic, optoelectronic and sensorial properties of quantum-confined nanowires. Keywords: nanowires, silicon nanowires, quantum confinement, fundamentals, application, possible laws (Some figures may appear in colour only in the online journal)
1. Introduction
is known as the quantum confinement effect. The salient feature of this effect is that the electrons in the nanocrystal are confined in a region smaller than the typical carrier de Broglie wavelength. If kB is the Boltzmann constant, h is the Planck’s constant ℏ = h / 2π , me* is the effective electronic mass and T is the temperature, then this de Broglie wavelength is
If the dimension of a nanocrystal (e.g. nanowire, nanotube, nanodot, etc) is large compared to the wavelength of electrons inside it, these electrons behave as free particles. However, if the nanocrystal size is comparable to the wavelength of the electrons, the electronic and optical properties of this nanocrystal deviate significantly from their corresponding bulk values. With the nanocrystal dimension decreasing and reaching a certain optimal limit, called the exciton Bohr radius, the energy spectrum of this nanocrystal turns out to be discrete. Its energy band gap EG also becomes dependent on its dimension. This effect 0953-8984/14/423202+28$33.00
λDB =
ℏ . 2me*kBT
(1)
Due to quantum confinement, the nanocrystal band structure is modified, as is the density of states due to shifts and degeneracy 1
© 2014 IOP Publishing Ltd Printed in the UK
Topical Review
J. Phys.: Condens. Matter 26 (2014) 423202
splitting in the band structure. If the nanocrystal is a semiconductor, the changes in the density of states in the conduction band and the valence band(s) of this nanocrystal affect the level occupancy, interband transitions, density and carrier mobility. The energy band gap EG consequently becomes larger than its bulk band gap EGB. Its electrical and optical properties also become different from those in the corresponding bulk. The first experimental evidence of quantum confinement was observed in CuCl clusters grown on silicate glasses [1]. Spectroscopic studies of these clusters indicated a blueshift as large as 0.1 eV of the absorption spectrum as compared to that in the corresponding bulk. The blueshift of the absorption threshold in CdS clusters due to decrease in cluster size measured subsequently was much larger—more than 1 eV [2]. The shift in the first absorption peak closer to the blue was attributed to an increase in the energy band gap EG, which resulted from decrease in the cluster size. It had genesis in quantum confinement. Among various nanocrystals, silicon nanowires (SiNWs) are technologically very important. Significant advances in the structures, electronic properties and transport properties of these SiNWs were reviewed by Rurali [3]. However, the quantum confinement in SiNWs was not articulated well. It appears still to be poorly understood. Our goal in this investigation is to address it in some detail. For this, we focus mainly on quantum confinement in the 100 , 111 , 112 and 110 SiNWs. We resort primarily to the first principles theoretical simulations and the experiments available in the literature. Although dedicated to SiNWs, the discussions herein are applicable also to other semiconducting nanowires, such as those from elements (e.g. Ge) and compounds (e.g. GaAs, InP, GaP, GaN, ZnSe, etc).
confinement in InAs nanowires covered with an InP shell. So, what are the basic differences in quantum confinement in nanowires with and without a shell? Fifth, recent experiments [8–10] on silicon nanowire with crystalline silicon (c-Si) core and amorphous silicon oxide shell demonstrated dramatic improvement in effective diffusion length of carriers. Does it mean the nanowire surface leads simultaneously to quantum confinement and enhancement in surface recombination? Does it mean there is a relationship between surface amorphicity and quantum confinement in nanowires? If it is true, then how do stress and strain contribute to it? Sixth, quantum confinement has experimentally been found to lead to dramatic enhancement in current–voltage characteristics of SiNW transistors [11]. A functional form of this quantum confinement suitable for theoretically developing relationships for current–voltage characteristics of nanowire transistors could not, however, be realized. Seventh, to our knowledge, basics of quantum confinement in nanowires and the broad appeal of quantum confinement in nanowires taking all possible elements of it into account, have never been systematically examined. These are all vital, but not thoroughly studied. Probably a very comprehensive review-oriented study may satisfy this goal. Our objective is to try it in the present investigation. For this, the details of the theoretical methods employed to realize quantum confinement will not been described. We consider them beyond the scope of the present study. Nevertheless, for the convenience of non-experts, the salient features of these methods are presented in appendix A. 3. Salient features of silicon nanowire synthesis Nanowires, including SiNWs, are produced on a nanoparticle surface by a variety of mechanisms [12, 13] with or without employing a foreign element catalytic agent (FECA). The well-known growth mechanisms for nanowire growths are the vapor–liquid–solid (VLS) mechanism [14], the vapor– quasiliquid–solid (VQS) mechanism [15], the self-catalytic growth mechanism [16] and the solution growth mechanism [17]. If the growth is not mediated by a FECA, the precursors of the nanowire growth species called, for the sake of convenience, the RS species, land on the nanoparticle surface for nanowire growth. If it is mediated, on the other hand, by FECA formed on a nanoparticle, the precursors of the RS species land on FECA for nanowire growth. The RS species released from their precursor undergo diffusion through the nanopores in nanoparticle or FECA before supersaturation and nucleation into nanowire at the liquid/solid (L/S) interface. The liquid of this L/S interface is the network of molten (semimolten) nanopores or even the molten alloy material (e.g. droplet). The solid of this interface is the substrate at the initiation of growth, but the tip of the nanowire during the subsequent stages of the growth. This tip has the network of molten (semimolten) nanopores; it is otherwise just molten. SiNWs appear almost always to have a cylindrical structure of radius rD and diameter DNW (DNW = 2rD). They may also be very thin. Li et al [18] and Ma et al [19] produced ultrathin single-crystal SiNWs of average diameter DNW = 2 nm and yet without using any FECA. Wu et al [20] made
2. Existing problems and goals of the present study Before setting our goals, we describe the problems that hinder the advances in the basic understanding of quantum confinement. First, as noted by Rurali [3], the first principles results for energy band gap EG as a function of SiNW diameter, are extensive, though very scattered. They have all been fitted to an empirical relation for band gap. Even experimental data have been fitted to this relation. But no attempt has yet been put forth to examine if this relation has any theoretical foundation. The goal of the basic science is best served with this relation being established as a universal relation. Second, no attempts have been made to determine why the first principles data are so scattered and not in good agreement with the available experiments. Third, surface passivation has been extensively treated by the first principles methods. But the role of this passivation in the dramatic enhancement of carrier mobility in nanowires has not been addressed. Lin et al [4] found that such enhancement does take place due to surface passivation. We found that it has genesis in quantum confinement [5]. Fourth, quantum confinement in nanowires has been observed with and without a shell covering their cores. Tian et al [6] observed quantum confinement in InAs nanowires not covered with a shell. But Zanolli et al [7] observed quantum 2
Topical Review
J. Phys.: Condens. Matter 26 (2014) 423202
a systematic study of orientation dependence of SiNW properties. Structural stability of these SiNWs is determined by a rule by Wulff [21]. Using a simple electrochemical etching process to create crystalline Si nanocrystals, Canham [22] was the first to demonstrate the experimental proofs of quantum confinement in Si nanocrystals. He was followed by Lehmann and Gösele [23]. They found luminescence visible at room temperature. Transmission electron microscopy (TEM) images by Cullis and Canham [24] revealed that the etched structures were actually made of bundles of disordered nanowires. This is a crucial observation. We do argue that this very disordered (amorphous-like) structure of nanowires was probably responsible for the very origin of quantum confinement. Note that, among various semiconductors, amorphous silicon (a-Si) has two important advantages over bulk crystalline silicon. First, due to structural disorder [25, 26], the luminescence efficiency is much higher in a-Si than in c-Si. Second, the band gap energy of the bulk a-Si (EG ≈ 1.6 eV) is larger than that of the bulk c-Si (EGB ≈ 1.1 eV). Over the years, numerous first principles ab initio calculations have been performed on the electronic and transport properties of SiNWs, considering their structures to be cylindrical. If atomic scale details are taken into account, SiNWs may though be found to have both cylindrical and non-cylindrical structures of surface-to-volume ratio δSVR. Zhao and Yakobson [27] studied the faceting of SiNWs grown along the 111 axis. They found that the ground-state cross section of δSVR up to 5 nm is not really cylindrical, it’s pentagonal. Such a pentagonal cross section may be created by putting together five prisms cut out of a {1 1 0} Si plane. For the bulk (core) of the 110 SiNWs, the cross section is however hexagonal with four {1 1 1} and two {1 0 0} facets; and it is in agreement with the experiments by Ma et al [19]. Wu et al [20] and Cao et al [28] showed that the faceting of the 100 SiNWs predicted by Ismail–Beigi and Arias [29], Lee and Rudd [30], Kim and Fischetti [31], Rurali [32], Rurali and Lorente [33] and Vo et al [34] is true mainly for SiNWs of diameters DNW > 1.7 nm. Nanowires of diameters DNW EG111 ~ EG112 > EG110 .
the 111 SiNW band gap may be slightly larger or smaller than the 112 SiNW band gap. Quantum confinement in SiNW [36] becomes significant for DNW
