Computational Studies of
Silicon Nanostructure Surfaces
R. Q. Zhang
City University of Hong Kong
“International Workshop on High-volume Experimental Data,
Computational Modeling and Visualization”
October 17th - 19th, 2011, Fragrant Mountain, Beijing, China
Outline

Why nanosurface

Surface effect on band structures

Surface doping

Surface induced thermal conductivity
attenuation

Summary
Outline

Why nanosurface

Surface effect on band structures

Surface doping

Surface induced thermal conductivity
attenuation

Summary
Si Crystal
Si (100) Surface
Band structure of silicon
10
5
Energy (eV)
0
-5
-10
-15

X
U
L
K point

K
Intel's roadmap
Surface of SiNWs
R.Q. Zhang, et al., JCP 123, 144703 (2005); October 24, 2005 issue of VJNST
Analysis + DFT
<112> wire
Remarkable effects of surface
dihydride configurations
Symmetric
Canted
HOMO
C. S. Guo, X. B. Yang, and R. Q. Zhang, Solid State Commun., 149, 1666(2009).
(111) surfaces terminated with SiH3:
Symmetric, rotated, and tilted
rhombus
rhombus
symmetric
rotated
tilted
nanowire
DDD Ma, et al, Science
For both bulk and
NW surface, the
tilted one is the most
stable.
The surface states are
not at the band edge.
Hu Xu, R.Q. Zhang et al., Phys. Rev. B 79, 073402 (2009)
SA/V ratio of nanowires:  1/a
Area
Volume
SA/V ratio
4aL
a2L
4/a
2aL
a2L
L
a
a
a
L
2/a
SA/V ratio increase will enhance
• structure change
• charge transfer
• boundary effect
• confinement
• ……
 stability
 excited-state property
 band structure
 doping effect
 thermal transport
Methodologies

Surface effect on band structures
=> DFT, DFT/MD

Surface doping
=> DFT

Surface induced thermal conductivity
attenuation
=> Tersoff potential based MD
Outline

Why surface

Surface effect on band structures

Surface doping

Surface induced thermal conductivity
attenuation

Summary
Band structure tuning of SiNWs
Indirect <==>direct?
Band structure of silicon
2
10
5
1
Energy(eV)
Energy (eV)
0
-5
-10
0
-1
-15

X
U
L
K point

K
-2
T
Si crystal
X
<112> SiNW
Indirect band structure of <112> SiNWs
=> quasidirect bandgap
A.J. Lu, R.Q. Zhang, et al., Nanotechnology, 19, 035708 (2008)
Tuning energy band of <112> SiNWs by
varying cross-section shape
(111)
-0.2
(111)
Direct
0.0
(110)
 (eV)
0.2
(110)
0.4
Indirect
0.6
-0.4
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Aspect Ratio
(111) To (110) side facet ratio
A.J. Lu, R.Q. Zhang, et al., Appl. Phys. Lett., 92, 203109 (2008).
Tuning energy band of <112> SiNWs by
varying cross-section shape
(110)
(110)
(111)
(111)
2
Energy(eV)
1
LDOS distribution determines the
band gap characteristic.
0
-1
-2
T
X
Tuning energy band of <112> SiNWs by
atomic phosphorus adsorption
Why phosphorus?
- a similar atomic radius to silicon
- the higher electronegativity
Tuning energy band of <110> SiNWs by
atomic nitrogen adsorption – metallization
X. B. Yang and R. Q. Zhang, Appl. Phys. Lett., 94, 113101 (2009).
Outline

Why surface

Surface effect on band structures

Surface doping

Surface induced thermal conductivity
attenuation

Summary
Conventional n- and p-type Si doping
Si
B
P
h+
e-
E
E
Ec
Ev
Donor
level
Ec
Ev
Acceptor
level
Temperature dependence of carry
concentration
  Ndeee
Nanodevices using doped SiNWs
- CMOS
- Solar cells
- Thermoelectrics
- Sensors
-…
Attempted volume doping in SiNWs
Experimental observation:
Less controllable and also less effective
due to the donor deactivation
•
•
M. Diarra, et al., Phys. Rev. B 75, 045301 (2007).
M. T. Bjork, et a., Nat. Nanotechnol. 4, 103 (2009).
Theoretical:
Impurities favor the surface position and
such doping reduces the density of carriers
•
M. V. Fernandez-Serra, et al., PRL 96, 166805(2006).
Charge transfer due to surface passivation
Nanodot
Si35H36
H(SiH)
-0.0550
H(SiH2)
-0.0670
Si(SiH)
0.0548
Si(SiH2)
0.1733
M.X. He, R.Q. Zhang, et al., J. Theor. Comput. Chem., 8, 299–316 (2009).
Surface Passivation Doping of Silicon Nanowires
Qp  8q /(a D)
2
q is the partial charge on a surface hydrogen atom = -0.06 |e| ,
a is the silicon lattice constant 5.43 Å, and
D is the diameter = 100 nm .
p= 1.61019 cm-3
Hole concentration due to surface doping: 1019 cm-3
C.S. Guo, R.Q. Zhang, et al., Angew. Chem. Int. Ed, 48/52, 9896(2009).
IDS (A)
Experimental verification 1: FET
at Vds = - 2 V
in vacuum
Original Si wafer
H-SiNWs (in vacuum)
H-SiNWs (in air)

p

p
1×109 (intrinsic）
0.235
9.6×1017
0.508
1.25×1018
3.3×106 (n-）
1.83
4.1×1017
4.67
7.3×1017
Carrier
Concentration
Experimental verification 2:
A p-n junction arry by surface passivation doping
C.S. Guo, L.B. Luo, R.Q. Zhang, S.T. Lee, et al., Angew. Chem. Int. Ed, 48/52, 9896 (2009)
Outline

Why surface

Surface effect on band structures

Surface doping

Surface induced thermal conductivity
attenuation

Summary
Theory
Green-Kubo expression
1

VkBT 2

m
0
z component of heat current
J z (0) J z (t ) dt
J (t ) 
d
(ri Ei )

dt i
<autocorrelation function>
Double exponential approximation
1
 m  a
 m  o
)]
 ( m ) 
[ Ao o (1  e
)  Aa a (1  e
2
VkBT
(small MD simulation time + reduced cut-off artifacts)
Fitting
For bulk silicon with 512 atoms:
100
20
15
60
 (W/mK)
(W/mK)
80
40
10
5
20
(b) 1000K
(a) 300K
0
0
20
40
60 80 100
m (ps)
0
0
10
20 30 40
m (ps)
50
The fitting parameters Ao, o, Aa and a are then used to calculate
the thermal conductivity (red curve) at m.
Test
For bulk silicon with 512 atoms,
The predicted the thermal conductivity:
At 300K: ~ 82 W/mK
At 1000K: ~ 15.5 W/mK
Reported results:
At 300K: ~85 W/mK [*] with Tersoff potential;
At 1000K: 17.78 2.61W/mK [**] with Stillinger-Weber
potential
[*] Li X., Maute K., Dunn M. L., and Yang R., Phys. Rev. B, 81 (2010) 245318
[**] Chen J., Zhang G., and Li B., Phys. Lett. A, 374 (2010) 2392
Models
Surface nitrogenation induced
thermal conductivity attenuation
Phonon spectra along the
longitude direction
Si-Si vibrational characteristic
Si-N vibrational modes
Summary

SA/V ratio – 1/a

Surface effect on band structures

Surface doping – passivation & transfer

Thermal conductivity attenuation
Acknowledgements
Co-authors:

Surface effect on band structures: H. Xu, C.S. Guo, A.J. Lu

Surface doping: C.S. Guo, X.B. Yang

Surface induced thermal conductivity attenuation: H.P. Li
Grants:
RGC, CityU
Thank You！