Electronic growth and stratification in Electronic growth and stratification in Pb nanoislands: experiment and Pb nanoislands: experiment and

modelingmodeling

Institute of Solid State Physics, Russian Academy of Sciences, Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, RussiaChernogolovka, Russia

Moscow State UniversityMoscow State University

A.Ionov, S.Bozhko, A.Ksyonz A.Ionov, S.Bozhko, A.Ksyonz

OutlineOutline

Pb island on Si(111)

Pb island as an abrikosov’s vortex trap

Basics of Electronic growth

• thin Pb islands on Si(111): STM experiments

• Quantum size effect and models of Electronic growth

• QWS in Pb/Si(111) film by ARPES and STS

Pb islands structure grown on Si(7 7 10)

• Experimental

• STM Results

• DFT simulations

Conclusions

Does quantum confinement effect on the crystal structure of a bulk of the Pb islands?

Status Quo Pb films on the Si(111)Status Quo Pb films on the Si(111)

STM images and corresponding histograms obtained after deposition 3ML of Pb at 192K (left, 200×200nm2) and at 200K (right, 300×300nm2).

-Wetting layer 1-3ML depending on the deposition temperature

- The islands grow up in a bi-layer growth mode - the island height changes by 2ML during the growth

- Island thickness of 7ML is preferable

- Islands possess a steep edges and flat tops

Surface Science 493 (2001) 526-538M.Hupalo, S.Kremmer, V.Yer, L.Berbil-

Bautista, E.Abram, M.C.Tringides

Phys.Rev.Lett., 86, (2001) 5116-5119 W. B. Su, S. H. Chang et.al,

Pb islands growth follows the Stransky-Krastanov scenario

Quantum size effectQuantum size effect

2

λsNt F

N,s – integers, λF-electron wave length, t-thickness of

Pb(111) monolayer

The thickness Nt of confining well has to satisfy the requirement of energy quantization that is the electron wavefunction has to form standing waves:

Pb island

The island height is stable only when the requirement is met

N 3 4 5 6 7 8 9 10 11

S=2Nt/λF4.3 5.8 7.2 8.7 10.1 11.6 13.0 14.5 15.9

Possible stable heights for Pb(111) crystal determined by the requirement of energy quantization. The islands can be stable only when

both N and s are integers (marked by red)

out of energy quantization requirementsN=8, S=11.6

energy quantization

requirements are fulfilled

N=7, S=5, Nt=5λF

Electron standing wave resulted in non homogeneous distribution of electron charge density. Oscillations of charge density cause open of energy gap at k=kF .

1-d model of electronic growth1-d model of electronic growth

Confinement of the electrons to a quantum well causes the Fermi sphere of allowed states to be reduced to a discrete set of subbands. Electrons are free

to move in X-Y plane

3-d model of electronic growth3-d model of electronic growth

0 2

z2F

n

1n

kk

0 II2z

2IIII

2tot )dkk(kk

m2π

AE

totb

totS nElayerfilm)(nEE

2m

kkd

8π

2VE

22

kk

32b

F

Nt

πnkZ

- total energy per atom of bulk Pb

layerfilm)(nE tot

totbE

SE -surface or electron confinement energy

– total energy of the film

α

bulkF

s N

Nt2ksinE

77

The essential physics of the surface energy of a metal film can be captured with a model of a free-electron gas confined to a quantum well. The surface energy for a Pb(111) film was calculated in a frame of a free-electron gas confined to a quantum well. When the Pb thickness is 7 ML, electron energy is minimal.

N – number of Pb layersNt – thickness of the filmα =1.77±0.09 is a fitting parameter

3-d model of electronic growth3-d model of electronic growth

Phys.Rev.B 72 075402 (2005) P. Czoschke, Hawoong Hong, L. Basile, and T.-C. Chiang

The relative surface energy is well described by the sinusoidal form

φ - a phase shift factor that is dependent on the interface properties of the film

What is the situation in a What is the situation in a thickthick film?film?

Growth of the Pb islands on the Si(7710Growth of the Pb islands on the Si(7710))

•STM 3D image of the Pb nanoislands on Si(7710)STM 3D image of the Pb nanoislands on Si(7710)

Pb on Si(Pb on Si(557557))

Growth of Pb islands on Si(557): On the terrace (111)On the triple steps and terraces

Pb/Si(557) : LEED pattern, energy Ep=101eV. , substrate temperature 78К, 2ML Pb deposited.

Surface Science 515 (2006) 312E, Hoque, A. Petkova, M. Henzler

LAS-3000 equipped by LAS-3000 equipped by RT STM GPI-300RT STM GPI-300

STM UHV 300mK « M3 »

Base pressure 10-10mbarTemperature 300KMagnetic field No

Base pressure 10-11mbarTemperature 300mKMagnetic field up to 10T

ExperimentExperiment

Pb islands deposited on Si(7 7 10)Pb islands deposited on Si(7 7 10)

STM images obtained after deposition 16 ML of Pb at room temperature.

Pb film was deposited using electron bombardment-assisted Pb film was deposited using electron bombardment-assisted evaporation in a preparation chamber. The substrate temperature evaporation in a preparation chamber. The substrate temperature was 300K, the pressure was in the range of 2×10was 300K, the pressure was in the range of 2×10-10-10 Torr. Torr.

STM image of the Pb film on SiSTM image of the Pb film on Sithe drawing plane coincides with the Pb(111) island top surfacethe drawing plane coincides with the Pb(111) island top surface

b) Plot of the cross section

b The red dashed line corresponds to the (7710 ) substrate. The cross-section c reveals the layered structure of the island

c) Cross-section c demonstrates the top layer of the island which does not contacted the substrate surfaced) Histograms of the heights in the areas 1 and 2 reveal the existence of steps 2nm in height.

c)

Some islands cross-sections demonstrates that the top layer of 7ML in thick of the island grows without any contact with the substrate, i.e. the island grows in the homoepitaxial regime: Pb on Pb. In this case there is no any influence of the lattice mismatch on interface and elastic stresses. The reason of relaxation in this case could be the electronic growth mechanism. Possible origin for the 2nm pancake growth could lie in the electron energy term of the total energy of the island.

Growth of Growth of PbPb islands on islands on Si(Si(77107710))homoepitaxial regime:homoepitaxial regime:

The layer thickness statistics obtained from 12 different Pb-islands.

7 ML7 ML

Pb/Si(Pb/Si(77710)- balance of energy710)- balance of energy

-The total energy of a Pb nanoisland non-divided into layers exceeds the total energy of a lamellar island of the same size. - Defect generation is due to energy gain of both elastic stress Em and electron confinement energy ES.

The thickness of 7 monolayers Pb is the most energetically favorable, even with respect to the bulk material.

ConclusionsConclusions

Candidates for quantum wellsCandidates for quantum wells

Twinning is a predominant mechanism of energy Twinning is a predominant mechanism of energy relaxation in face-centered cubic metals with low relaxation in face-centered cubic metals with low stacking-fault energy in (111) planes. stacking-fault energy in (111) planes.

Twin boundaries seems to be the most favorable Twin boundaries seems to be the most favorable candidate to realize the island stratification because of candidate to realize the island stratification because of the low formation energy.the low formation energy.

Twin Twin boundariesboundaries in Pb nanoparticles in Pb nanoparticles

Configuration transition, involving vanishing of a twin on the left side, Configuration transition, involving vanishing of a twin on the left side, leaving a stalking fault, and appearance of twin on the right side. (The first leaving a stalking fault, and appearance of twin on the right side. (The first configuration was stable for 1.5 sec, the second configuration was stable for configuration was stable for 1.5 sec, the second configuration was stable for 6.5 sec, the transition time is less than 0.04 sec.)6.5 sec, the transition time is less than 0.04 sec.)

Phys.Rev.Lett. 78 (1997) 2585, T. Ben-David, Y. Lereah, G.Deutscher, J. M. Penisson, A. Bourret, R. Kofman, and P. Cheyssac

DFT calculations of Pb cluster DFT calculations of Pb cluster

The ab initio calculations were performed with The ab initio calculations were performed with the the CASTEPCASTEP program program from from Material Studio Material Studio ((Accelrys Software Inc.Accelrys Software Inc.)) using using Research Research computing Centrecomputing Centre of Moscow State University of Moscow State University

Crystal Pb slab within range 3-41 layers was Crystal Pb slab within range 3-41 layers was modellingmodelling

Film was simulated as a Pb slab with a perfect crystal structure. Left panel

represents a sequence of close-packed hexagonal planes forming FCC Pb

crystal structure.

DFT calculations of Pb cluster DFT calculations of Pb cluster

CBA

A

A

A

B

B

B

C

C

Primitive unit

Z

0.93

bulkF

s N

Nt2ksinE

The thickness of 7 monolayers Pb is the most energetically favorable

Calculated surface energy is fitted by

Perfect crystal structure

The ab initio calculations were performed with the CASTEP program from Accelrys Software Inc. using 'Lomonosov' supercomputer of Moscow State University

DFT calculations of Pb cluster DFT calculations of Pb cluster

AB

A

A

A

B

B

BC

C

C

Primitive unitZ

Bottom part of a slab is a mirror reflection of a top one

Crystal contains twinning boundary

The thickness of 14 monolayers that is 2 slabs with a perfect crystal structure 7 ML in thick separated by a twinning boundary possesses a negative surface energy of 9mV

per atom. System of conductive electrons generates twinning boundaries in a

bulk of Pb crystal !

perftot

tbtottb EEE

DFT simulation of difference in total energy per DFT simulation of difference in total energy per single atom located in hcp and fcc positions on single atom located in hcp and fcc positions on

the surface of slabs N monolayers in thick.the surface of slabs N monolayers in thick.

Difference in atom energy in hcp and fcc position as

a function of a slab thickness

Atom in hcp position Atom in fcc position

ConclusionsConclusions

The growth of Pb-nanoislands on the vicinal Si(7710) stepped surface The growth of Pb-nanoislands on the vicinal Si(7710) stepped surface follows Stransky-Krastanov scenario. The growth of tilted Pb bulk follows Stransky-Krastanov scenario. The growth of tilted Pb bulk islands is accompanied by theirs stratification into layers.islands is accompanied by theirs stratification into layers.

The formation of stable blocks of equal thickness (single layer The formation of stable blocks of equal thickness (single layer thickness 2nm, 7ML of Pb) during the growth of Pb on Si(7710) was thickness 2nm, 7ML of Pb) during the growth of Pb on Si(7710) was detected – pancake structure.detected – pancake structure.

DFT simulations prove that the size of the blocks corresponds to DFT simulations prove that the size of the blocks corresponds to energy minimum of the electrons confined in the quantum well. The energy minimum of the electrons confined in the quantum well. The layers are separated by a twinning boundaries.layers are separated by a twinning boundaries.

Such growth mode is realized due to the minimization of the electron Such growth mode is realized due to the minimization of the electron energy owing to the quantum confinement effect and is in a good energy owing to the quantum confinement effect and is in a good agreement with the agreement with the electronic growth model..

D.RoditchevD.Roditchev

D.FokinD.Fokin

A.ChaikaA.Chaika A.Ksyonz A.Ksyonz

A.Ionov A.Ionov

S.BozhkoS.Bozhko

T.CrenT.Cren

V.DubostV.Dubost

F.DebontridderF.Debontridder

CollaboratorsCollaborators

I.SvekloI.Sveklo

Thank you for your Thank you for your attention!attention!

Pb/Si(Pb/Si(77710)- balance of energy710)- balance of energy

Young module

×109 N/m2

LiLi 0.50.5

TlTl 0.80.8

PbPb 1.71.7

YbYb 1.81.8

SnSn 4.1-5.54.1-5.5

AlAl 6.86.8

NiNi 20-2220-22

WW 35-4035-40

The film-substrate interface and elastic energy due to a Pb-Si lattice mismatch

2.02

nm

1.89

nm

One Pb(111) atomic layer is 2,86Å in thick, one Si atomic step height is 3,13Å .If Pb layers are parallel to the Si(111) surface plane than the maximum lattice mismatch of 1,3Å is achieved at Pb layer thickness of 7ML. Thus, for a 2nm thick Pb slab the stress achieves its maximum. The value of elastic stress can be partially reduced by 1° tilt of Pb layers. Wetting layer also reduces elastic energy. Nevertheless the elastic stress can assist in a crystal defects generation.

Pb/Si(Pb/Si(77710)- balance of energy710)- balance of energy

2nm Pb

Si

Island stratificates if energy gain due to quantum confinement effect exceeds energy loss due to creation of interlayer defect

Stratificated (pancake like) island

Pb

Si DDPerfect crystal structure of the

island

– proportional to the number of

atoms in the island

– energy due to a stress at the film – substrate interface

– energy of interlayer defects,

stress at the film – substrate interface can be reduced by interlayer defects

perfm

perfb

perftot EEE

perfbE

perfmE

stratd

stratS

stratm

perfb

strattot EEEEE

stratdE

perfm

stratm EE

0E stratd

stratSE – energy of layers due to quantum

confinement effect , when requirements of formation of electron standing wave met in the layers

0E stratS

77

The essential physics of the surface energy of a metal film can be captured with a model of a free-electron gas confined to a quantum well. The surface energy for a Pb(111) film calculated using a model based on a free-electron gas confined to a quantum well. When the Pb thickness is 7 ML, electron energy is minimal.

N – number of Pb layersNt – thickness of the filmα =1.77±0.09 is a fitting parameter

3-d model of electronic growth3-d model of electronic growth

Phys.Rev.B 72 075402 (2005) P. Czoschke, Hawoong Hong, L. Basile, and T.-C. Chiang

The relative surface energy is well described by the sinusoidal form

φ - a phase shift factor that is dependent on the interface properties of the film

α

bulkF

s N

Nt2ksinE

Si(111) Si(7 7 10)

STM images of the clean initially Si(7 7 10) surface showing the triple step structure with (7×7)-reconstruction on Si(111) terraces. The directions of steps edges are (-110). The height of the triple step is known to be 3,13Å×3=9,39Å

ExperimentExperiment

11210 inmiscut o

slow cool down to RT

flash at 1250ºC

quench to 850ºC

cooling to 1050ºC in 1 min

postanneal at 850ºC for 20 minutesLEED, Ep=60eV

STM images of vicinal surfaceSTM images of vicinal surface

STM images of the clean initially Si(557) surface showing in (a): large areas covered with Si(7 7 10) stepped structure; in (b): the triple step structure with (7x7)-reconstruction on Si(111) terraces. Inset : Fast

Fourier Transformation of (a) reveals two characteristic peaks corresponding to the (7 7 10) stepped structure.

Clean SiClean Si(557)(557) surface surface

Si(7710) triple steps and terraces Si(111)(7x7). Period -5.33nm (16 atomic rows)

Teys et al.Surf. Sci. 600 (2006) 4878–4882

Si(557) staircase:

triple steps and terraces Si(111) (7x7). Period - 5.7nm (17 atomic rows)

A.Kirakosian et al.,Appl. Phys. Letters 79 (2001) 1608

Surface consists of Si(111)7x7 terraces separated by triple steps

Atomic structure of a triple steps is not clear

Triple step structure Si(557)

5,5×5,5nm2 STM image. a) Vb=-2.1V, I=80 pА, b) Vb=0,4V, I=90pА

Triple step can be considered as a set of a single and double steps Si(223)

triple steps and terraces Si(111)(7x7). Period – 4.8нм

(141/3 atomic rows)A.Chaika et.al.

Surf.Sci.603 (2009) 752J.Appl.Phys. 105 (2009) 034304

[223][223][111][111]

FCC and HCP structuresFCC and HCP structures

Spheres may be arranged in a single closest-packed layer by placing each sphere in a contact with 6 others. A second similar layer may be packed on top of this by placing each sphere in contact with 3 spheres of the bottom layer. In FCC the spheres in a third layer are placed over the holes in the first layer not occupied by the second layer.

Pb island superconductivity

STM image of Pb film grown on Si(111)

STM image of Pb island lateral dimension about 110nm, height 5.5nm

nm4507.19K T Pb C Magnetic field always penetrate into island

Wedge-shaped layered Pb islands grown on Wedge-shaped layered Pb islands grown on vicinal Sivicinal Si

b) STM image of the wetting layer obtained on an island-free

area

c) The height modulation of the clean vicinal Si(7710) triple step

structure (bottom curve) compared to that of the wetting layer covered

surface

d) The flat top of Pb-islands is tilted by 9.1°±0.4° with respect to

the substrate (7710) plane;

e) The periodicity of the wetting layer at Si(111) terraces matches

the size of the (7x7) unit cell;

f) At first stages, wire-like Pb-islands grow separately on Si(111)

terraces.

STM/STS of superconductive Pb island

STS image of Pb island 1.7×1.7um2

T=0.3K, H= 0.09T

Pb island on Si(111)

Pb island as an abrikosov’s vortex trap

Growth of Growth of PbPb islands on islands on Si(Si(77107710))homoepitaxial regime:homoepitaxial regime:

Some islands cross-sections demonstrates that the top layer of 7ML thick of the island grows without any contact with the substrate.

The top 7 ML layer of the island grows in the homoepitaxial regime: Pb on Pb. In this case there is no any influence of the lattice mismatch on interface and elastic stresses. The reason of relaxation in this case could be the electronic growth mechanism.

Possible origin for the 2nm pancake growth could lie in the electron energy term of the total energy of the island.

E=Eb+ES+Ed+Em , Em=0if ES+Ed <0 stratification

×

7 ML7 ML

Pb/Si(Pb/Si(77710)- balance of energy710)- balance of energy

The total energy of a Pb nanoisland non-divided into layers exceeds the total energy of a

lamellar island of the same size.Defect generation is due to energy gain of both

elastic stress Em and electron confinement energy ES.

The thickness of 7 monolayers Pb is the most energetically favorable, even with

respect to the bulk material. 2nm Pb

Si

Quantum confinement energy ES<0

stratification

potential barrier between neighbor layers

layers separated by defects

Nano Res. 2010, 3, 800, Yu Jie Sun, S. Souma, Wen Juan Li, T. Sato, Xie Gang Zhu, Guang Wang, Xi Chen, Xu Cun Ma, Qi Kun Xue, Jin Feng Jia, T. Takahashi, and T. Sakurai

ARPES and STS experiment on 24 ML Pb film grown on Si(111) by

QWS in QWS in Pb grown onPb grown on Si(111)Si(111)

Calculated DOS of the first QWS below EF(a, d), ARPES(b, e) and STS(c, f) spectra (measured at 4.2 K) of a 24 and 23 ML Pb films respectively

Band dispersion for a 24 ML Pb film along the Γ K direction. The red and blue lines correspond to calculated pz and pxy QWSs, respectively

Pb brillouin zone