Supplemental Material
Transparent SiO2-Ag Core-satellite Nanoparticle Assembled Layer for
Plasmonic-based Chemical Sensors
Tsung-Han Chena#, Ren-Der Jeana#, Kuo-Chuang Chiub, Chun-Hua Chen*a, Dean-Mo Liu*a
a
Department of Materials Science and Engineering, National Chiao Tung University, Hsinchu,
Taiwan 300, ROC
b
Material and Chemical Research Laboratories, Industrial Technology Research Institute,
Hsinchu, Taiwan 310, ROC
*Corresponding authors: Dean-Mo Liu, deanmo_liu@yahoo.ca
Chun-Hua Chen, chunhuachen@mail.nctu.edu.tw
#
Equal contribution as first author
Classical Mie theory
The extinction cross section, σ, for small spherical nanoparticles can be simply
expressed as below 1:
 ( ) 
24 2 R 3 m3 2


2
( 1  2 m ) 2   22
(1)
where the complex dielectric constant for bulk Ag is  = 1+ i2 and the dielectric constant of
surrounding environment is m. When the particle size is much smaller than the wavelength
incident (R <<), the complex dielectric constant of bulk Ag used for Mie calculation have to
be modified with the Drude model. The size-dependent dielectric functions can be computed
with25:
 ' ( , r )   'bulk 
 p2
 p2

,
( 2  d2 ) ( 2  r2 )
 " ( , r )   "bulk 
i p2r
[ ( 2  r2 )]

(2)
i p2d
(3)
[ ( 2  d2 )]
1
where the ω, ωp, ωd, and ωr are the light frequency, the bulk plasmon frequency, the bulk
damping constant, and the particle damping constant, respectively. Parameters of
ωp=1.371016 s-1 and ωd=Vf/L =2.671013 s-1 were taken from (Ref. 2). The ωr can be
expressed by:
r  d  A
Vf
r ,
(4)
where Vf is the Fermi velocity (1.391015 nm/s), L is the mean free path of the electrons in
the bulk material (52 nm for Ag), and A is the theory-dependent quantity of order 1.
Effective medium model (EMT)
The effective dielectric function, eff, given by EMT is expressed as3:
 eff   SiO
 Ag   SiO
 f
 eff  2 SiO
 Ag  2 SiO
2
(5)
2
2
2
where Ag is the Drude-modified dielectric constant of Ag in the SiO2@Ag nanoparticle
colloids, SiO2 is the dielectric constant of SiO2 matrix. The filling factor f of the SiO2@Ag
nanoparticles is the volume fraction of Ag in the SiO2 matrix, which is a variable for fitting.
The calculated eff is taken into the classic Mie theory to calculate the absorption spectra of
SiO2@Ag nanoparticle films.
Core-effective medium layer (EML)
The core has a radius R1 with a dielectric constant of c. The EML, SiO2/air or Ag/air,
has a thickness R2-R1 and an effective dielectric constant of s. In the present calculation, the
size of the core and the thickness of EML were open for fitting. Calculation of the absorption
spectra of this particular core-shell configuration, for the extinction cross-section, is given as
follow4,5:
2
 ( ) 
8 2 R23  m

 (   m )( c  2 s )  (1  g )( c   s )( m  2 s ) 
Im  s

 ( s  2 m )( c  2 s )  (1  g )( 2 s  2 m )( c   s ) 
(6)
where m is the dielectric constant of medium and g=1-(R1-R2)3 is the volume fraction of the
EML. We treat a given dielectric constant of medium, air (m=1.0) and SiO2 (m=2.13). The
default setting of SiO2 core radius is 10 nm from the HRTEM image and Ag is 0.98 nm from
the Drude modified size.
3
References
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2
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Castillón-Barraza, and A. Posada-Amarillas, Physica E 27, 104 (2005).
3
G. A. Niklasson, C. G. Granqvist, and O. Hunderi, Appl. Optics. 20, 26 (1981).
4
J. Zhu, Physica E 27, 296 (2005).
5
S. Bruzzone, G. P. Arrighini, C. Guidotti, Mater. Sci. Eng. C 23, 965 (2003).
4