Supporting Information
Surface plasmon modes guided by Ga-doped ZnO layers bounded by
different dielectrics
Wasanthamala Badalawa 1, Hiroaki Matsui 1, Akifumi Ikehata2 and Hitoshi Tabata 1, 3
1
Department of Electrical Engineering and Information Systems, University of Tokyo,
Bunkyo-ku, Tokyo 113-8656, Japan.
2
Analytical Science Division Nondestructive Evaluation Laboratory, National Food Research
Institute, Tsukuba, Ibaraki 305-8642, Japan.
3
Department of Bioengineering, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan.
1) Lattice parameters and crystallinity of ZnO: Ga layers
ZnO: Ga (7%) layers were grown on glass substrates (BK-7) using a pulsed layer ablation at 260oC
in an O2 atmosphere at 10-4 Pa. Lattice parameters and crystallinity were evaluated by x-ray
diffraction (XRD). Figures S1 show the 2/ patterns of the (0002) plane of 218-nm, 107-nm and
41-nm-thick layers, revealing that all layers were polycrystalline with a preferential orientation along
the c-axis direction. c-axis lattice length slightly increased with decreasing layer thickness.
Full-width half-maximum (FWHM) values of 218-nm, 107-nm, and 41-nm-thick layers were 0.31o,
0.30o and 0.37o, respectively. Lattice parameters and crystallinity of 218 nm-thick layer were similar
to those of 107-nm and 41-nm-thick layers.
1000000
(0002)
100000
100000
10000
k
WL
c = 5.221Å
10000
(0002)
t = 218nm
100
100
35
35
2 (degree)
40
40
(c)
100000
c = 5.227Å
k
(0002)
c = 5.233Å
10000
WL
1000
1000
30
30
1000000
(b)
Intensity (a.u.)
(a)
Intensity (a.u.)
Intensity (a.u.)
1000000
k WL
1000
t = 107nm
30
30
35
2 (degree)
35
40
40
100
t = 41nm
30
30
35
35
2 (degree)
4040
Figure S1. 2 diffraction patterns of the (0002) plane for the ZnO: Ga layers with different
layer thicknesses (t): (a) 218 nm, (b) 107 nm, and (c) 41 nm.
2) The complex dielectric functions of ZnO: Ga layers
Figure S2 (a) shows the complex dielectric functions ( = 1 +i2) of ZnO: Ga layer (218-nm
thickness) calculated using “Lorentz oscillator and Drude model” from experimental results of
absolute transmission and reflection measurements, as measured in frequency range from 4,000
to 10,000cm-1. On the other hand, the complex dielectric functions of 107-nm-thick and
42-nm-thick layers were obtained by angle-dependent Ellipsometers (M-2000UI) in frequency
range from 5,882 to 40,816 cm-1. The dielectric functions of all layers showed same behavior.
The plasma frequency, (p), defined by 1(p) = 0 were ( 7776 cm-1 ), ( 7501 cm-1 ), and ( 7639
cm-1 ) at 218-nm, 107-nm and 41-nm-thick layers, respectively.
These p values are dependent on electron density (ne) on the
66

(a) t = 218nm
-12
-126
6
4000
are the permittivity of free space and the high-frequency
represents the screened plasma frequency. The energy-loss
00
10000 20000 30000 40000
100
1 (0) =7502cm-1 33
50
50
-12
-12
6
64000
6000
00
100006
6
8000
= 41nm
(c) t 10000
20000
0
100
30000
0
10000 20000 30000 40000
40000
100
00
1 (0) =7639cm-1 33
1
-6-6
50
50
00
10000
-12
-12
4000
10 1
Energy loss
0
2
-6
-6
0
function of Au is comparably small in NIR frequencies.
00
6
100006
8000
100
NIR frequencies. As shown in Fig. S2(d), ZnO:Ga has its
maximum energy-loss position in NIR and this peak
(b) t = 107nm
50
2
functions (-Im -1) of Au and ZnO:Ga are also compared in
6000
1
dielectric constant, respectively. Furthermore, the energy-loss

2
1 (0) =7776cm-1 3
-6
-6
bulk dielectric function and  is the effective mass. 0 and ∞
100
00
1
basis of the Drude model;  p  ne /  0  , where () is the
2
66
6000
0
-1
100.1
(d)10000
8000
20000
30000
0
40000
ZnO: Ga
-2
100.01
Au
-3
10
0.001
4000
4
6
Wave number
8000
8
10
(103 cm-1)
Figure S2. Complex dielectric functions ( = 1+i2) of ZnO: Ga layers having different layer
thicknesses: (a) 218 nm, (b) 107 nm, and (c) 41 nm. Black and red lines indicate 1 and 2,
respectively. (d) Comparison of energy loss function (-Im ) of Au and Ga doped ZnO in NIR,
red and black lines represent ZnO:Ga and Au respectively .
3) SPR spectra and Dispersion relation
Figures S3 (a, c) show angle- and frequency-dependent SPR reflectivity spectra at room
temperature for 180-nm, 162-nm, and 141-nm-thick layers as a function of the incident angle
() from 45o (black line) to 75o (pink line) in 5o increments, respectively. A frequency position
of SPR reflectivity shifted to higher frequencies with increasing ., as expected SPR behavior.
10000 20000 30000 40000
These results were similar to the SPR reflectivity of 218 nm-thick layers [Fig. 1(a) in the text],
relating to a symmetric SP mode (s-mode) excited on the air-ZnO interface. Figure S3 (d) shows
the dispersion relation (-kx curve) of the 180-nm, 162-nm and 141-nm-thick layers, as obtained
from the SPR reflectivity in Figs. S3 (a, c). These results support a cutoff thickness of the
s-mode (135 nm).
ZnO:Ga 180nm
Rp/Rs ratio
1
(b) t = 162nm
0.5
0
1
1
(a) t = 180 nm
(c) t = 141nm
0.5
0.5
 = 45o
 = 75o
4
6
kx (104 cm-1)
8
0
4000
4
kx
6000
6
(104 cm-1)
0
8000
4
8 4000
6000
6
kx (104 cm-1)
8000
8
Frequency (103 cm-1)
7000
7
6
6000
5
5000
4
4000
(d)
c
c/nglass
ZNO_180NM2
ZNO_141NM2
ZNO_162NM2
180nm
162nm
141nm
2.5300003.5 40000 4.550000 6.5 60000 7.5
kx (104 cm-1)
Figure S3. Angle- and frequency-dependent SPR reflectivity (Rp/Rs) of ZnO: Ga layers with
different thicknesses (t): (a) 180 nm, (b) 162 nm, and (c) 141 nm. Incident angle ()
varies from 45o (black line) to 75o (pink line) in 5o increments. (d) Dispersion
relation (-kx curve) of ZnO: Ga layers of different thicknesses; 180 nm (black dots),
162 nm (blue dots) and 141 nm (red dots). c and c/nglass represent light lines of air
and glass, respectively. nglass is the refractive index of glass.