Structures and electronic properties of si nanowires grown along the [1 1 0] direction role of surface reconstruction

Đây là một bài báo khoa học về dây nano silic trong lĩnh vực nghiên cứu công nghệ nano dành cho những người nghiên cứu sâu về vật lý và khoa học vật liệu.Tài liệu có thể dùng tham khảo cho sinh viên các nghành vật lý và công nghệ có đam mê về khoa học

Structures and electronic properties of Si nanowires grown along the [1 1 0]

direction: Role of surface reconstruction

Department of Physics Engineering, Mie University, 1577 Kurima-Machiya, Tsu 514-8507, Japan

a r t i c l e i n f o

Article history:

Received 30 May 2008

Accepted for publication 4 August 2008

Available online 9 August 2008

Keywords:

Density functional calculation

Surface energy

Silicon

Nanostructures

a b s t r a c t

The atomic and electronic structures of silicon nanowires grown along the [1 1 0] direction are systemat-ically investigated using first-principles pseudopotential method For nanowires whose diameters are

4 nm, the calculations taking account of various surface reconstructions both with and without hydro-gen atoms on nanowire facets demonstrate that the reconstruction on nanowire facets is strongly depen-dent on hydrogen chemical potentiallH The nanowire terminated by H atoms is stabilized for highlH

whereas the pristine nanowire is favorable for lowlH The nanowires with partially hydrogenated facets also appear within a certainlHrange Peculiar features in the electronic structure caused by facet edges are found in both pristine and partially hydrogenated nanowires

Ó 2008 Elsevier B.V All rights reserved

1 Introduction

Semiconductor nanowires (NWs) are recently paid much

atten-tion as potential building blocks for nanoelectronic and photonic

devices Silicon NWs (Si NWs) are in particular attracting great

interest due to their compatibility with conventional Si-based

technology Furthermore, they are scientifically of interest and

importance for a prototype of nanoscale materials to study effects

of quantum confinement, dimensionality, and orientation So far, Si

NWs of diameters below 10 nm have been synthesized by solution

More recently, Si NWs fabricated by means of Au

nanocluster-catalyzed VLS method using the chemical vapor deposition (CVD)

have been shown to be the controlled growth of molecular-scale

(HRTEM) has shown that Si NWs are single crystal with little or

no visible amorphous oxide down to diameters as small as 4 nm

Furthermore, it have been shown that, importantly, the

smallest-diameter NWs are grown primarily along the [1 1 0] direction while

the NWs with large diameter are grown along the [1 1 1] direction

The HRTEM has also observed the hexagonal nanowire shape

which consists of {0 0 1} and {1 1 1} facets On the other hand,

re-cent theoretical investigations have investigated the effect of the

nanowire size on the electronic properties for Si NWs terminated

on the structural, electronic, and optical properties of

hydrogen-passivated Si NWs with diameter up to 4.2 nm and found that quantum confinement becomes significant for diameter less than

2 nm, where the dielectric function exhibits strong anisotropy and new low-energy absorption peaks start to appear in the imag-inary part of the dielectric function for polarization along the wire

on the opto-electronic properties for dihydride and monohydride

remain matters to debate about effects of surface reconstruction both on {0 0 1} and {1 1 1} facets of Si NWs: since the reconstruction could depends on temperature and pressure of hydrogen ambient during and after the fabrication process in the CVD, it is expected that various surface reconstructions including those in clean sur-faces exhibit on the nanowire facets Due to higher surface–volume ratio in thin NWs compared to those in thick or bulk phase, effect

of surface reconstruction could be crucial on the electronic proper-ties of thin NWs

In this paper, effects of surface reconstruction on structural and electronic properties of Si NWs grown along the [1 1 0] direction are systematically investigated based on total energy electronic structure calculations In particular, we focus on the surface recon-struction of nanowire facets in Si NWs with diameter of 4 nm, which have been successfully fabricated by the CVD The relative stability among NWs with various surface reconstructions is deter-mined based on the calculated formation energy depending on hydrogen chemical potential which represents temperature and pressure effects of hydrogen ambient Furthermore, effects of sur-face reconstruction of nanowire sur-facets on the electronic structures are examined from the calculated band structures and wave func-tion characters We find that the reconstrucfunc-tion on nanowire facets

0039-6028/$ - see front matter Ó 2008 Elsevier B.V All rights reserved.

* Corresponding author Tel.: +81 59 232 1211x3978; fax: +81 59 231 9726.

E-mail address: akiyama@phen.mie-u.ac.jp (T Akiyama).

Surface Science

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / s u s c

NWs with partially hydrogenated facets appear within a certainlH

range We further propose that peculiar features in the electronic

structure caused by facet edges could be realized in both pristine

and partially hydrogenated nanowires

2 Calculation procedure

All calculations have been performed within the generalized

calculation and for the geometry optimization In the optimized

geometries the remaining forces acting on the atoms are less than

plane-wave basis set with a cutoff energy of 10 Ry which gives

an enough convergence of total energy to discuss the relative

sta-bility We employ a supercell in which a nanowire is placed with

Two atomic-layers are employed to simulate the periodicity along

one-dimensional Brillouin zone

We construct hexagonal nanowire models whose diameters are

3.7 nm according to the following procedure: First, we have

which the ratio of surface energy to the distance from the centre

of crystal to the surface is constant Assuming that nanowire facets

during the growth consist of clean surface, we have obtained that

the ratio of the distance for {0 0 1} facet to that for {1 1 1} facet is

considered in this study Next, we have determined the nanowire

The diameter of nanowire model is 3.7 nm, which is comparable

to the experimental value of 4 nm Therefore, it is expected that

clean surface will appear on the nanowire facets during the growth

condition However, surface Si atoms can be terminated with H

atoms after the growth by changing hydrogenation conditions

Considering such situations, we here consider both pristine and

hydrogen terminated NWs We adopt asymmetric dimers with

p(2  1)-type structure for pristine {0 0 1} facets, and monohydride

For pristine {1 1 1} facets, we take account of two types of (2  1)

configurations, because recent calculations for flat Si(1 1 1) surfaces

the buckling structure when the width of dangling bonds is less

calcu-lated results indicate a plausibility of the buckling structure as a

relevant surface reconstruction on {1 1 1} facets with finite flat

sur-face area The dimers, adatoms, and stacking faults (DAS) model

be-cause such reconstruction requires more surface areas For

H-ter-minated {1 1 1} facets, the (1  1) structure is considered

The relative stability of Si NWs is determined using the

to be the chemical potential at which the formation energy of

the standard partition function, within the harmonic approxima-tion, including both rotational and zero-point vibrational energies

[23]

3 Results and discussion

Fig 1a shows the calculated formation energy per Si–H unit as a function of H-chemical potential for various structures The calcu-lated formation energy indicates that the energetically lowest

struc-ture This structure is found to be stable compared to the pristine nanowire with buckling structure (pristine: {1 1 1}-(2  1) buckling

inFig 1) by 0.12 eV/Si–H pair, which is comparable to the energy

-bonded chain implies that the stability of {1 1 1} facets is similar

0.75 eV, H-terminated nanowire on both {0 0 1} and {1 1 1} facets

nanowire consists of monohydride configuration on {0 0 1} facets and (1  1) H-terminated surfaces on {1 1 1} facets: the NWs with dihydride facets are not found as stable configurations over entire

shown that Si NWs with canted dihydride NWs could appear for high

stable over wide H-chemical potential range and dihydride structure

dihydride {0 0 1} facets might appear in the limited condition

In addition to these structures, we found that partially

pris-tine and completely H-terminated NWs are stabilized, respectively

(Fig 2b) and {1 1 1} facets are hydrogenated for 0.78 <lH<

in the former structure (12 atoms in the unit cell) is smaller than the number in that in the latter one (24 atoms in the unit cell), these partially hydrogenated structures can be interpreted as inter-mediate structures between pristine and completely hydrogenated structures The estimated temperature range for partially hydroge-nated NWs is 530–570 K, implying that partially hydrogehydroge-nated NWs can be formed in such narrow temperature range However, due to the very small energy difference, it can be expected that these NWs coexist in this temperature range

The analysis of the electronic structure for stable NWs clarifies that the surface reconstruction on nanowire facets crucially affects

struc-ture of stable NWs In the case of NWs which possess nanowire

1

For the flat Si(1 1 1) surfaces, the validity of surface separation has been checked

by using slab geometry with 7–12 Å thick vacuum region We found that the surface

energy and positions of surface atoms of Si(1 1 1)-(2  1)p-bonded chain surface are

identical within 0.01 eV and 0.01 Å, respectively.

2

Although the size of unit cell along the [1 1 0] direction is insufficient to obtain the

most stable c(4  2) reconstruction on Si(0 0 1) surfaces, the energy difference

between p(2  1) and c(4  2) is found to be negligible compared with the energy

differences discussed in the paper (the calculated energy difference is within 0.01 eV/

1  1 cell) Therefore, the relative stability depending on hydrogen chemical potential

3 The result is different from the relative stability between the buckling and p-bonded chain structures in Ref [21] This is because the geometry of top-layer Si atoms on nanowire facets are different from that in Ref [21] There are boundaries between the (2  1) withp-bonded chain and (1  1) structure along the ½1 1 0 direction in the nanometer-scale Si(1 1 1) surface while no boundary exists on

top-electronic states appear around the band gap In the pristine

formed In addition, the electronic states originating from the

nanowire edges between adjacent {1 1 1} facets are formed near

Due to these electronic states, it is expected that pristine and

{0 0 1} facets hydrogenated NWs exhibit semimetallic character

This is quite different from the metallic and semimetallic

Si(0 0 1), respectively, exhibit semiconductor behaviour, such elec-tronic structures are typical for NWs containing pristine facets edges

In order to clarify the origin of semimetallic character, we ana-lyze the character of wave functions in the {0 0 1} facets

plots of wave functions for symmetrically equivalent two highest occupied (HO) and four lowest unoccupied (LU) states,

the wave functions of the doubly-degenerate HO states and four

Fig 1 Calculated formation energies of NWs grown along the [1 1 0] direction for various surface reconstructions as a function of hydrogen chemical potential (a) Formation energy over wide temperature range and (b) that for narrow range where partially hydrogenated structures are stabilized (represented by vertical dotted lines) Dashed lines denote metastable structures The temperature of H 2 -gas temperature at 1 atom is also shown.

Fig 2 Cross-sectional views of (a) pristine, (b) {1 1 1} facets hydrogenated, (c) {0 0 1} facets hydrogenated, and (d) completely H-terminated NWs Open and filled circles represent Si and H atoms, respectively The six-membered rings which constitute nanowire edges between adjacent {1 1 1} facets are represented by grey areas in (a) and (b).

p*-like bands on {1 1 1} facets, respectively This is because

nano-wire edges between adjacent {1 1 1} facets consist of six-membered

-bonded chain on {1 1 1} facets belong to seven-membered ring:

the difference in atomic configuration causes the suppression of

the edge atoms, implying that the suppression of lattice relaxation

results in the weakness of surface bound states As a result, the

bands on {1 1 1} facets We note, however, that more elaborate

cal-culations beyond DFT calcal-culations, such as GW approximation

semi-metallic behaviour comes from the limitation of DFT calculation

surface related electronic states are completely eliminated around

the band gap More importantly, the gap energy (0.94 eV) is large

compared to that in bulk Si (0.74 eV) and the direct band gap

char-acter is found The band structure of monohydride nanowire is

qualitatively consistent with the calculated results for Si NWs with

terms of the projection of energy band in bulk Si and confinement

effect: the confinement decreases the energy of HO states and

in-creases the energy of the LU states, but the magnitude of the

en-ergy shift depends on their effective masses Due to the large

effective mass along the longitudinal direction of the LU states

-point for NWs grown along the [1 1 0] direction, the energy shift of the projected LU states becomes small, resulting in the direct band gap character

4 Summary

We have investigated atomic and electronic structures of silicon NWs along the [1 1 0] direction based on first-principles pseudopo-tential calculations For atomic structure, we found that partially hydrogenated NWs as well as H-terminated and pristine NWs can be formed depending on hydrogen chemical potential The existence of the nanowire edges between different nanowire facets

-bonded chain configuration We have also confirmed the direct band gap character with larger gap energy than bulk value for com-pletely hydrogenate nanowire, consistent with previous theoreti-cal studies Surface related electronic states caused by nanowire facets appear for pristine and partially hydrogenated NWs result

in semimetallic nature different from flat surfaces This semimetal-lic nature originates from the suppression of lattice relaxation for edge atoms which results in the weakness of surface bound states Although the size dependence on the structural and electronic properties have been left in the present study, the calculated re-sults imply that over wide range of the nanowire diameter the reconstruction on nanowire edge crucially affects the structural

-1 0 1

X -1 0 1

X -1 0 1

X -1

0 1

X Γ

Fig 3 Energy bands of (a) pristine, (b) {1 1 1} facets hydrogenated, (c) {0 0 1} facets hydrogenated, and (d) completely H-terminated NWs The zero of energy is set to the Fermi level Arrows in (b) and (c) represent the surface related electronic states due top-bonded chain on {1 1 1} facets and dangling bonds on p(2  1) surface of {0 0 1} facets, respectively Arrowheads in (b) indicate the electronic states related top-bonded chain of nanowire edges between adjacent {1 1 1} facets The calculated gap energy in bulk Si

is 0.73 eV.

Fig 4 Cross-sectional views of the wave functions at zone boundary of (a) two highest occupied and (b) four lowest unoccupied states in the {0 0 1} facets hydrogenated nanowire The density of isosurfaces is 1.5  10 3 e/Å 3 The wave functions ofp- andp*

-like bands on Si(1 1 1)-(2  1) surfaces are also shown on the inset of (a) and (b), respectively.

and electronic properties of Si NWs grown along the [1 1 0]

direction

Acknowledgements

This work was supported in part by Grant-in-Aid for Scientific

Research from JSPS under Contract No 18560020 Codes used in

this work are based on Tokyo Ab-initio Program Package (TAPP)

Computations were performed at RCCS (National Institutes of

Nat-ural Sciences) and ISSP (University of Tokyo)

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