Released Plasmonic Electric Field of Ultrathin
Tetrahedral-Amorphous-Carbon Films Coated Ag
Nanoparticles for SERS
Fanxin Liu2,1*, Chaojun Tang2, Peng Zhan1, Zhuo Chen1, Hongtao Ma3 & Zhenlin
Wang1*
1 National Laboratory of Solid State Microstructures and School of Physics, Nanjing
University, Nanjing 210093, PR China
2 Department of Applied Physics, Zhejiang University of Technology, Xiaoheshan,
Hangzhou 310023, PR China
3 SAE Magnetics (HK) Ltd (TDK), Dongguan 523087, PR China
*Address correspondence to [email protected], [email protected]
Supporting Information
I. Explains for the junction of electric field in the ta-C for the calculated field
enhancement of ta-C coated Ag nanosphere.
Air
ε3
E0
ta-C
ε2
r
Ag
ε1
θ
x(nm)
r1
z(nm)
Figure S1. Schematic of an Ag/ta-C core/shell spherical nanoparticle.
 1 ,  2 ,  3 are the relative
permittivities of Ag core, ta-C shell, and surrounding medium (air), respectively. r1 is core radius,
r2 is shell radius, and E0 is electric field of incident light. θ is the angle between position vector r
and x axis.
We can well understand the distribution properties of electric fields in the Ag core, the ta-C
shell and the surrounding medium, by analyzing the following boundary conditions:




n̂  ( E1  E2 )r  r1  0 , n̂  (  1 E1   2 E2 )r  r1  0 ,




n̂  ( E2  E3 )r  r2  0 , n̂  (  2 E2   3 E3 )r  r2  0 ,


(1)

where E1 , E 2 , and E3 are the electric fields in the Ag core, the ta-C shell and the surrounding
medium, respectively;
 1 ,  2 , and  3 are the relative permittivities of the three corresponding
regions, respectively; n̂ is the unit vector along the normal direction of the geometrical
boundaries of the ta-C-coated Ag sphere.
For simplicity, but without loss of generality, we will apply the above boundary conditions to a
special case in which n̂ is along the x-axis direction. In this case, the above boundary conditions
become into the follow expressions:
E1 z  E 2 z , 1 E1 x   2 E 2 x ,
E 2 z  E 3 z , 2 E 2 x   3 E 3 x ,
(2)
where the subscripts of x and z represent the components of electric fields along the directions of
the x- and z axes, respectively. In fact, for this case corresponding to
  0 , the z components of
electric fields E1 z  E2 z  E3 z  0 , and the total fields are determined only by the x components
of E1 x , E2 x , and E3 x . Obviously, there is always a discontinuity in the electric field intensity
(E/Ein)2 at the two boundaries of x=15 and 16 nm in Fig. 2(b), because the x components of E1 x ,
E2 x , and E3 x are unequal. Here we should mention that such a discontinuity is a general
property of metal spheres coated by a dielectric layer, except that the relative permittivities  1 ,  2 ,
and  3 become equal at certain resonance frequencies.
Very interesting, if the relative permittivity  1 of a metal sphere is larger than the relative
permittivity  2 of a coated dielectric shell, the electric field intensity (E/Ein)2 in the dielectric shell
will be larger than that in the metal sphere near the boundary. This conclusion can be easily got
from the boundary condition of
 1 E1 x   2 E 2 x . In contrast, if  1 is smaller than  2 , (E/Ein)2
in the dielectric shell will be smaller than that in the metal sphere near the boundary. This is the
case in our work. In fact, (E/Ein)2 is not completely zero in a ta-C film, and this can be seen in our
numerical results. However, the electric fields in the ta-C film are much weaker than those in the
Ag sphere and near the surface of the whole particle. Our numerical results show that the smallest
value of (E/Ein)2 in the ta-C film is about 18, and the largest value is about 45.
In addition, within the quasi-static approximation, the electric fields in the Ag sphere should be
uniform, so the value of (E/Ein)2 is almost unchanged in the Ag sphere.
II. Electric Field Distribution of big Ag nanosphere coated with 1 nm ta-C
Figure S2. Plasmonic electric field intensity (E/Ein)2 along the X axis in Fig. S1, for the
170nm-Ag/10-Å-ta-C core-shell sphere at the surface plasmon resonance of 514 nm (black line),
non-resonances of 600 nm (red line) and 480 nm (green line). The dotted circle indicates the
position of the ta-C shell. This figure shows clearly that for both resonance and non-resonance
wavelength, the electric field intensity at the ta-C/air interface is always higher than that at the
Ag/ta-C interface.
III. Typical electric field distribution of the ta-C coated Ag nanosphere
Figure S3. The (E/Ein)2 distribution of 30 nm Ag sphere coated with different ta-C films thickness
from 1 to 10 nm at their respective resonances.
IV. Wavelength-dependent relative permittivity (ε) imaginary part of Ag.
Figure S4. The imaginary part of Ag relative permittivity (ε) as a function of photon energy. Black
line represents experiment data by Johnson et al., and red line represents the results from Drude
model.
V. Experimental evidence to for ta-C films pinhole-free.
We have performed oxalic acid corrosion test for the ultrathin ta-C films. It is noted here that
the test is based on the industrial standard. In oxalic acid corrosion experiments, three batches
rowbars with different sample sizes were maintained in oxalic acid solution (0.05 M) for 4 min.
And then the pole areas of FeCo alloy deposited with 5 Å and 10 Å ta-C films were monitored by
optical microscopy and scanning-electron microscopy (SEM) for corrosion checking. Figure S5
showed that there were no pinholes for a 10 Å ta-C film, while the 5 Å ta-C film was not
pinhole-free. According to the criteria of industrial standard, the 10 Å ta-C film is pinhole-free.
Figure S5. (a) Oxalic acid corrosion test for the ta-C films thickness with 10 Å and 5 Å. (b) SEM
image of typical pinhole corrosion.
VI. The electric field of 30nm-Ag/10Å-ta-C and .uncoated 30 nm Ag.
Figure S6. The (E/Ein)4 for a uncoated 30 nm Ag nanosphere (a) and a 30nm-Ag/10Å-ta-C
core/shell sphere (b) at the same excitation wavelength of 514 nm. (c) The (E/Ein)4 distribution as a
function of X-axis.
VII. Raman spectrum of only milk on SERS substrate.
We have also performed Raman measurements of only milk on SERS substrate, shown in
Figure S7. The result shows that the milk solution on SERS substrate has no any Raman signals.
Figure S7. Raman spectrum of milk on the 10Å ta-C coated Ag nanoparticle SERS substrate.