應力於結晶與奈米級矽固體之作用 Strain Effect on Crystalline and Nano-scale Silicon Solids

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應力於結晶與奈米級矽固體之作用Strain Effect on Crystalline and Nano-scale

Silicon Solids

指導教授 : 劉致為博士學生 : 黃筱鈞國立臺灣大學電子工程學研究所

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Outline

□ Thesis organization□ Chapter 2： Strain-induced Raman Shift□ Chapter 3： Carrier Mobility in Orthorhombically Strained Silicon□ Chapter 4： 2-D Electrons in Strained Silicon Inversion Layers□ Chapter 5： Surface Effect on Strained Silicon Clusters□ Chapter 6： Strain Effect on Silicon Atomic Wires□ Summary and Future Work

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Thesis organization

Strain Type

Phonon-limited Mobility

Silicon Structure

Hooke’s Law

Modeling/

Simulation

Chap 2 Biaxial & tensile on Si1-xGex

Bulk

(diamond)

Spring Equation

MATLAB

Chap 3 Orthorhombic

Bulk Mobility

Bulk

(diamond)

MATLAB


Channel Mobility

(2DEG)

Bulk

(diamond)

MATLAB

Chap 5 Biaxial & tensile on Ge

Cluster (diamond)

Generalized form

Gaussian

(DFT)

Chap 6 Distorted Cluster

(relax Si3)

TranSIESTA-C

(DFT+NEGF)

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Thesis organization： Strain Type

Strain Type


Silicon Structure

Hooke’s Law

Modeling/

Simulation


Bulk

(diamond)

Spring Equation

MATLAB

Chap 3 Orthorhombic

Bulk Mobility

Bulk

(diamond)

MATLAB


Channel Mobility

(2DEG)

Bulk

(diamond)

MATLAB

Chap 5 Biaxial & tensile on Ge

Cluster (diamond)

Generalized form

Gaussian

(DFT)

Chap 6 Distorted Cluster

(relax Si3)

TranSIESTA-C

(DFT+NEGF)

Si1-xGex

TS-Si

Bulk Si

CS-Si1-xGex OS-Si

Si3 atomic wire

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Strain-induced Raman Shift

□ Raman spectra of a typical thin Si epilayer grown above a thick Si

1-xGex buffer layer on Si (001) substrate

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□ Qualitative and quantitative prediction of Raman shift□ Simplified unit cell in Si epi-layer (instead of diamond structure)□ Backscattering geometry (only singlet is observed)

[D. J. Lockwood, PRB, 1992]□ Forced to vibrate at a different force constant when strain is applied

Singlet

Dou

blet

Deformation under tensile strain

Triply degenerate

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□ Spring equation form of Hooke’s Law□ Frequency is related to the square root of U’s second derivative

2

2

d xF ma m kx

dt

2

20

d x kx

dt m

0

kw

m

21

2U kxdx kx

Restoring force

Potential energy

DE describing motion

Angular frequency of SHO

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□ U from Harrison’s total/cohesive energy (1972, 1981)□ U’s second derivative

0coh pro bondE E V r E

1.5 2 2.5 3 3.5 4-5

-4

-3

-2

-1

0

1

2

3

4

5

interatomic distance(A)

-Eco

h/bo

nd(e

V)

2 4-10

-5

0

5

10

15

20

Der

ivat

ives

interatomic distance(A)

B' B''

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□ Sqrt(k) vs. bond length

□ Region of interest: 2.35 ~ 2.4 A (Si1-xGex, 0<x<0.5)

□ Compare with Raman data from published empirical equation□ a~200, a good prediction

2.35 2.36 2.37 2.38 2.39 2.40

2.46

2.48

2.50

2.52

2.54

2.56

2.58

2.60

2.62

2.64

sqrt

(k)

bond length(A)2.35 2.36 2.37 2.38 2.39 2.40

502

504

506

508

510

512

514

516

518

520

522

Ram

an P

eak(

cm-1

)

bond length(A)

Si Siw a k

~ 200a

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Carrier Mobility in Orthorhombically Strained Silicon

□ Vertical MOSFET□ Unstrained Si substrate□ Compressively strained SiGe pillar□ Orthorhombically strained Si sidewall layer

Bulk Si

CS-Si1-xGex OS-Si

[001]

[010]

[100]

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LCAO 16x16 Hamiltonian

(spin-orbit, 2nd nearest neighbor)

TB parametersStrain

εxx, εyy, εzz

Bond length, bond angle (direction cosines)

Bandstructure

Density of states per spin

for each band n

Square of group velocity for each band n

Scattering rates (acoustic, optical phonon) for each

band n


(diagonal components)

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□ Band splitting of orthorhombically strained silicon

0.0 0.2 0.4 0.6 0.8

0

1

2

valence band edge

conduction band edge

SOHH

LH

x [100]

y [010]

z [001]

En

erg

y (e

V)

Ge mole fraction x

[010][100][001]

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□ Electron and hole mobility of orthorhombically strained silicon□ Two-fold electron mobility enhancement at 20% Ge□ Two-fold hole mobility enhancement at 30% Ge

0.0 0.1 0.2 0.3 0.4 0.5 0.6

750

1000

1250

1500

1750

2000

2250

Ele

ctro

n M

ob

ility

(cm

2 /Vs)

Pilar Ge mole fraction x

xx

(growth direction)

zz(channel direction)

yy

0.0 0.1 0.2 0.3 0.40

500

1000

1500

2000

Ho

le m

ob

ility

(cm

2 /(V

s))

Pilar Ge mole fraction x

xx

(growth direction)

yy

zz

(channel direction)

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2-D Electrons in Strained Silicon Inversion Layers

□ Planar MOSFET□ Channel mobility modeled as 2DEG

Ev

Ec

EF

subbands

N+ poly gateP substrate

Ec

Ev

2 2

232 i i i

dz e z z E z

m dz

2

22

0

1depl i i

Si

d zz e N z

dz

Self-consistently

Airy function approximation

1/32 3 3/ 2 , 0,1,2,...

2 4i z sE m qF i i

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□ Constant-energy ellipses (6 equivalent valleys) of Si conduction band

□ Energy lineups of Si conduction band w. and w/o tensile strain

Δ2 Δ4

E0

E1E2

E6

E0'

E1'E2'

Δ2

Δ4

E0

E1E2

E6

E0'

E1'E2'

ΔE=Δstrain+(ΔE0'-ΔE0)

Δ2Δ4

[001]

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μi

Subband mobility

ΔEstrain= 0.67xinto step function

Momentum relaxation rate (intra, inter)

1/τ=Σ U(E-ΔEstrain)/τfor each subband

μi

Subband mobility

μi

Subband mobility

……

Mobility (averaged over

subband occupation)

Airy function approximation (w/o iteration)

Subband levels Wavefunctions

Iteration with Airy function approximation

UCB’ s SC calculation(w. iteration)Vg Fs

20 subbands/WFs

NiInversion charge

per subband

Effective field(Inversion +

depletion charge)

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0 20 40 60 80 100

0.00E+000

5.00E+007

1.00E+008

1.50E+008

2.00E+008

2.50E+008

3.00E+008

Delta4;Subband1

Distance from surface (A)

SC Airy

0 20 40 60 80 100-5.00E+007

0.00E+000

5.00E+007

1.00E+008

1.50E+008

2.00E+008

2.50E+008

3.00E+008

3.50E+008

4.00E+008

Delta2;Subband2


SC Airy

0 20 40 60 80 100

0.00E+000

1.00E+008

2.00E+008

3.00E+008

4.00E+008

5.00E+008

Delta2;Subband1


SC Airy

0 20 40 60 80 100

0.00E+000

5.00E+007

1.00E+008

1.50E+008

2.00E+008

2.50E+008Delta4;Subband2


SC Airy

0 20 40 60 80 100

0.00E+000

5.00E+007

1.00E+008

1.50E+008

2.00E+008

2.50E+008

3.00E+008

Delta2;Subband3


SC Airy

0 20 40 60 80 100

0.00E+000

5.00E+007

1.00E+008

1.50E+008

2.00E+008

2.50E+008

3.00E+008

Delta4;Subband3


SC Airy

□ Airy function vs. SC wavefunctions for delta 2 and delta 4 valleys

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0 2 4 6 8 100.0

0.5

1.0

Delta 2

En

erg

y(e

V)

Subband level

Airy SC

0 2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Delta 4E

ne

rgy(

eV

)

Subband level

Airy SC

□ Airy function vs. SC subband levels for delta 2 and delta 4 valleys

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0.1 1

1000

Ph

on

on

-lim

ited

Mo

bili

ty (

cm2

/Vse

c)

Effective Field (MV/cm)

Unstrained Si MOS Strained Si MOS on Si0.7Ge0.3

0.0 0.1 0.2 0.3 0.40.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Mo

bili

ty E

nh

an

cem

en

t Fa

cto

r

Substrate Ge Content (%)

□ Phonon-limited mobility vs. effective field□ Mobility enhancement factor vs. substrate Ge content

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Surface Effect on Strained Silicon Clusters

□ Generalized Hooke’s Law

* *(i, j=1-6, sum over j)i ij jC

1 111 12 12

2 212 11 12

3 312 12 11

4 444

5 544

6 644

0 0 0

0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

ec c c

ec c c

ec c c

ec

ec

ec

x ye e f 123

11

2ce e f f

c

?

-0.77

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□ Horizontal fixed (5.65A); vertical tuned various α□ Searching for min E(α)□ Simulation building block: single silicon unit cell (diamond structure)

1x1y1z□ 2x1y1z, 1x2y1z, 1x1y2z represent two unit cells stacking up in x, y,

z direction, respectively□ From 1x1y1z (18 atoms) to 3x3y1z (110 atoms)

2x1y1z 1x2y1z 1x1y2zx

yz

(a) (b) (c)

1x1y1z

a┴=5.43+0.22α

a||=5.65

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□ Gaussian 03 and GaussView□ Model Chemistry [theoretical method/basis set]: BLY3P/6-31G(d)□ No min E(α) on the plot of total E versus α candidates for 1x1y1z, 2x

2y1z, etc□ Squeezed (more negative α), total energy goes down

-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1-5209.906

-5209.904

-5209.902

-5209.900

-5209.898

-5209.896

-5209.894

-5209.892

-5209.890

tota

l en

erg

y (h

art

ree

s)

alpha

1x1y1z w/o H

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□ Clusters w. bare silicon (w. dangling bonds)□ Clusters w. silicon and valence hydrogen atoms (instead of dangling

bonds)□ Min E(α) on the plot of total E versus α candidates for 1x1y1z□ Min E(α) by (1) squeezed (more negative α), total energy goes up

(2) a energy step (4.8 eV) for all α> -0.77

-0.90 -0.85 -0.80 -0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45

-5234.85

-5234.80

-5234.75

-5234.70

-5234.65

tota

l en

erg

y (h

art

ree

s)

alpha

1x1y1z w H

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x

yz

1x1y1z 2x2y1z 3x3y1z x

yz

-0.80 -0.75 -0.70 -0.65 -0.60-15685.8

-15685.6

-15685.4

-15685.2

-15685.0

-15684.8

tota

l en

erg

y (h

art

ree

s)

alpha

2x2y1z w H

-0.80 -0.78 -0.76 -0.74 -0.72 -0.70-31936.5

-31936.0

-31935.5

-31935.0

-31934.5

-31934.0

tota

l en

erg

y (h

art

ree

s)

alpha

3x3y1z w H

□ Valence hydrogen pair with angle of 54.7 degree (instead of 109.8)□ 1x1y1z (1), 2x2y1z (5), 3x3y1z (13): yes

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0 -0.1 -0.11 -0.12 -0.15 -0.22 -0.24 -0.26 -0.28 -0.4

V V V V V V V V V V

-0.5 -0.6 -0.7 -0.75 -0.76 -0.77 -0.78 -0.8 -0.85 -0.88

V V V V V

-0.9 -0.95 -1.0 -1.1 -1.5 -1.6 -1.7 -1.8 -2.0

Antenna check for 2x2y1z

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□ Only 1x1y2z has antenna (same with 1x1y3z, 1x1y4z, etc)□ 3x2y1z no, 2x2y2z yes□ Square symmetry on x-y plane required?

2x1y1z 1x2y1z 1x1y2zx

yz

(a) (b) (c)

-0.80 -0.75 -0.70 -0.65 -0.60

-9010.34

-9010.32

-9010.30

-9010.28

-9010.26

-9010.24

-9010.22

-9010.20

-9010.18

-9010.16

-9010.14

tota

l ene

rgy

(har

tree

s)alpha

1x1y2z w H

2x2y2z3x2y1zx

yz

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□ 2x2y1z minus one (3), 3x3y1z minus one (11): yes□ 3x3y1z minus two, 2x1y2z, 3x1y3z: no

2x2y1z minus one

3x3y1z minus one 3x3y1z minus two

3x1y3z2x1y2zx

yz

Near square symmetry, x-y plane

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□ Simulation of up to 9 unit cells□ Bare silicon clusters: unstable with dangling bonds□ With surface hydrogen: obey the same rule with bulk silicon- deform

ation of shorten heights with α = -0.77 by (1) squeezed, total energy goes up (2) energy step starting at α = -0.77

□ Bond angle effect under deformation□ Near-square symmetry on one of the surface of the x-y plane

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Strain Effect on Silicon Atomic Wires

□ Molecule systems (equilibrium) coupled to electrodes and bias voltage is applied (non-equilibrium)

□ TranSIESTA-C: Density Functional Theory (DFT) and Non-equilibrium Greens Function (NEGF) solving self-consistently

□ Several approximation is adopted

SIESTA: Electronic StructureDensity Functional TheoryLCAO, numerical orbitals w. finite rangePseudo-potentials

TransportFull description of electrodes using ab initio self-energiesNon-equilibrium electron distribution using NEGFCalculation of electron current

D H

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□ Molecular system: Si3 cluster (Si3 atomic wire in zigzag fashion)

□ Electrode: Li [He]2s1 closely resembles Au [Xe]4f145d106s1

□ Two-probe system: Si3 cluster coupled to lithium electrode

2.28Å 2.28Å

2.73Å2.23Å 2.23Å

Lithium electrodeLithium electrode

Si3 atomic wire

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□ Isolated Si3 cluster (van der Waals radii; HOMO; LUMO)

□ Relaxed Si3 atomic wire (new MPSH LUMO as a channel)

□ MPSH: Molecular Projected Self-Consistent Hamiltonian

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□ I-V characteristic of relaxed Si3 atomic wire

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-300

-200

-100

0

100

200

300C

urr

en

t(u

A)

Voltage(V)

relaxed Si3 atomic wire

,R

Lb bI V T E V dE

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Strain Effect on Silicon Atomic Wires□ Transmission spectrum vs. MPSH eigenstates (red dot)

□ T(E, Vb) at Vb= 0, 1, 2V; LUMO closely associate with the peak

-1.1 -0.1 0.9 1.90.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

Vb=0V

LUMOHOMO

T(E

)

E(eV)

-1.1 -0.1 0.9 1.90.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

Vb=1V

LUMOHOMO

T(E

)

E(eV)

-1.1 -0.1 0.9 1.90.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

Vb=2V

LUMOHOMO

T(E

)

E(eV)

-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

0.5

1.0

1.5

2.0

Vb(V)

E(eV)

T(E

,V)

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□ Three strain type

CASE I n=1~4(a1, a2, a3, a4)

CASE II n=1~4(m1, m2, m3, m4)

CASE III n=1~2(d1, d2)

2.28Å 2.28Å

2.73Å2.23Å 2.23Å

an=0.1*n Å

2.28Å 2.28Å

2.73Å2.23Å 2.23Å

mn=0.1*n Å

2.28Å 2.28Å

2.73Å2.23Å 2.23Å

dn=0.2*n Å

CASE I

CASE II

CASE III

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Strain Effect on Silicon Atomic Wires□ I-V characteristic of strained Si3 atomic wire (CASE I)

□ 0V ~ 1.2V: a4 < a3 < a2 < a1 < relax□ 1.2V ~ 2V: relax < a1 < a2 < a3 < a4

0.0 0.5 1.0 1.5 2.0

0

50

100

150

200

250

300

Cu

rre

nt(

uA

)

Voltage(V)

relax a1 a2 a3 a4

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Strain Effect on Silicon Atomic Wires□ I-V characteristic of strained Si3 atomic wire (CASE II)

□ 0V and 2V: m4 ~ m3 ~ m2 ~ m1 ~ relax□ Between 0V and 2V (esp. 1V): relax < m1 < m2 < m4 < m3

0.0 0.5 1.0 1.5 2.0

0

50

100

150

200

250

Cu

rren

t(u

A)

Voltage(V)

relax m1 m2 m3 m4

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Strain Effect on Silicon Atomic Wires□ I-V characteristic of strained Si3 atomic wire (CASE III)

□ 0V ~ 2V: d2 < d1 < relax

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-300

-200

-100

0

100

200

300

Cu

rre

nt(

uA

)

Voltage(V)

relax d1 d2

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-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

2.5

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2

sa2

T(E

,V)

Vb(V)

E(eV)


□ T(E, Vb) for CASE I, n=1~4

□ T(E, Vb) for CASE II, n=1~4

□ T(E, Vb) for CASE III, n=1~2

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

2.5

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2

sa1

Vb(V)

E(eV)

T(E

,V)

-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

2.5

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2

T(E

,V)

Vb(V)

sa3E(eV)

-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

2.5

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2

T(E

,V)

Vb(V)

sa4E(eV)

-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

2.5

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2

T(E

,V)

Vb(V)

sm1E(eV)-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

2.5

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2T

(E,V

)

Vb(V)

sm2E(eV)

-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

2.5

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2

T(E

,V)

Vb(V)

sm3E(eV)-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

2.5

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2

T(E

,V)

Vb(V)

sm4E(eV)

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2

T(E

,V)

Vb(V)

d1E(eV)-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

0.20.4

0.60.8

1.01.2

1.41.6

1.82.0

2.2

T(E

,V)

Vb(V)

d2E(eV)

-2 -1 0 1 2

0.0

0.5

1.0

1.5

2.0

0.5

1.0

1.5

2.0

Vb(V)

E(eV)

T(E

,V)

Relax

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□ Current is obtained by Landauer-Buttiker formula□ Bias window: the energy region which contributes to the current inte

gral (only positive part is shown)

0 1 2

1

0.5

0

-0.5

-1

Bias voltage (V)

Ene

rgy

(eV

) ,R

Lb bI V T E V dE

0 / 2L b L bV eV

0 / 2R b R bV eV

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Strain Effect on Silicon Atomic Wires□ Transmission spectrum within bias window at Vb= 1 and 2 V

□ LUMO peak (1) bottom (2) move to center (3) bottom

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.50.0

0.5

1.0

1.5

2.0

2.5

T(E

)

E(eV)

relax a1 a2 a3 a4

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

3.0

T(E

)

E(eV)

relax a1 a2 a3 a4

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

T(E

)

E(eV)

relax m1 m2 m3 m4

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

3.0

T(E

)

E(eV)

relax m1 m2 m3 m4

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.50.0

0.5

1.0

1.5

2.0

2.5

T(E

)

E(eV)

relax d1 d2

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

3.0

T(E

)

E(eV)

relax d1 d2

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Strain Effect on Silicon Atomic Wires□ MPSH eigenstates at Vb= 1 and 2 V

□ LUMO with (1) HOMO/HOMO+1 (2) LUMO+1; HOMO/HOMO-1 (3) LUMO+2; HOMO

0 1 2 3 4-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Vb=1V

E(e

V)

an(=n*0.1A)

HOMO-1(4) HOMO(5) LUMO(6) LUMO+1(7) LUMO+2(8)

0 1 2 3 4-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Vb=2V

an(=n*0.1A)


E(e

V)

0 1 2 3 4-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Vb=1V

mn(=n*0.1A)


E(e

V)

0 1 2 3 4-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Vb=2V

mn(=n*0.1A)


E(e

V)

0 1 2-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Vb=1V

dn(=n*0.2A)


E(e

V)

0 1 2-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Vb=2V

dn(=n*0.2A)


E(e

V)

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Summary and Future Work： Summary

□ A simple spring model is developed to make qualitative and quantitative predictions of Raman peak red-shift in tensile strain silicon epi-layer.

□ Phonon-limited bulk mobility under orthorhombic strain is calculated. Strong electron and hole mobility enhancement is observed.

□ Phonon-limited electron channel mobility under tensile strain is calculated. Airy function is a fair approximation. Enhancement factor saturates at 20% Ge content.

□ Surface hydrogen atoms is necessary to stabilize silicon clusters up to 9 unit cells in a morphology of shorten heights (α = -0.77) under tensile strain. Near square symmetry is required for above observation.

□ I-V characteristic of relaxed and strained Si3 atomic wire is investigated. Bias window and MPSH eigenstates are helpful in understanding the changes in I-V characteristic in three strain conditions.

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Summary and Future Work： Future Work

□ Experimental confirmation□ More sophisticated molecular electronics with realistic metal

electrodes

Documents

應力於結晶與奈米級矽固體之作用 Strain Effect on Crystalline and Nano-scale Silicon Solids