Enhanced optical absorption in nanopatterned silicon thin films with a nano-cone-hole structure for photovoltaic applications
In this paper, the optical properties of the silicon nano-cone-hole (NCH) structure array are studied. The ultimate efficiency of the optimized NCH array is enhanced by 23.11% compared to an optimized nanohole array of the same thickness. The absorptance enhancement of the NCH arrays is attributed to its lowered reflectance, more supported resonant modes, and enhanced mode interaction. The angular dependence of ultimate efficiency is also investigated.
Enhanced optical absorption in nanopatterned silicon
thin films with a nano-cone-hole
structure for photovoltaic applications
Qing Guo Du,
Chan Hin Kam,
Hilmi Volkan Demir,
Hong Yu Yu,
and Xiao Wei Sun
School of Electrical and Electronic Engineering, Nanyang Technological University,
Nanyang Avenue, Singapore 639798, Singapore
*Corresponding author: email@example.com
Received March 14, 2011; accepted April 6, 2011;
posted April 11, 2011 (Doc. ID 144085); published April 29, 2011
In this paper, the optical properties of the silicon nano-cone-hole (NCH) structure array are studied. The ultimate
efficiency of the optimized NCH array is enhanced by 23.11% compared to an optimized nanohole array of the
same thickness. The absorptance enhancement of the NCH arrays is attributed to its lowered reflectance, more sup-
ported resonant modes, and enhanced mode interaction. The angular dependence of ultimate efficiency is also
investigated. © 2011 Optical Society of America
OCIS codes: 310.6628, 310.6845, 040.5350.
The silicon solar cell is presently dominating the solar
cell market, owing to its abundant supply, nearly ideal
band gap, and matu re fabrication process. Most commer-
cial silicon solar cells are made from bulk silicon with the
thickness of a few hundred micrometers, i.e., a large
amount of silicon is consumed, leading to a higher cost
for the final product . The thin film silicon solar cell
with thicknesses in the range of a few micrometers is
a promising way to reduce costs. However, weak absorp-
tion, especially in the long wavelength side near the
bandgap edge of the silicon, remains a challenge. To ad-
dress this problem, light trapping techniques, including
randomly textured structures [2,3], periodic gratings
, photonic crystals [5–7], and plasmonic structures
[1,8,9], have recently been developed.
Instead of texturing the front and back surface of
the solar cells, it is possible to texture the active layer
into nanostructured arrays such as with nanowire
(NW) [10–14] nanocone (NC) , and nanohole (NH)
 arrays. Theoretical studies [16–20] show that there
is a large enhancement of the optical absorption due
to efficient antireflection of the incident light and effec-
tive optical coupling between nanoarrays and the inci-
dent light. It is further demonstrated that NH arrays
 exhibit stronger optical absorption compared to
NW arrays [17,18] with the same filling ratio and thick-
ness. In this Letter, to further increase the optical absorp-
tion, we proposed and numerically demonstrated a new
nanostructured architecture of nano-cone-hole (NCH)
array that enables significantly enhanced absorption,
surpassing those of the previously reported arrays.
Figure 1(a) shows the schematic of the proposed NCH
array. It can be seen that the NCH array is arranged in a
square lattice in the x–y plane and surrounded by air.
Sunlight is directly incident on top of the structure along
the z direction. The two-dimensional (2D) side and top
views are shown in Figs. 1(b) and 1(c), respectively. Con-
sidering the fabrication tolerance, the tip of the NCH
is not exactly at the bottom surface; instead, a small
hole with radius of 20 nm is left on the bottom surface
[Fig. 1(b)]. The lattice constant (period) of the square lat-
tice is indicated as a. The radius of the air hole at the top
surface is r, and the thickness is h. The air filling ratio
) is defined as the ratio of the top-surface air hole
area to the unit cell surface area, given by f
Here the NH array has the same lattice constant a as NCH
array and the air filling ratio f of the NH array is defined
as in . In our analysis, the thickness h of the NCH and
NH arrays is fixed at 2:33 μm, the same as in [17,19], for
easy comparison. The silicon dielectric function used is
taken from . The finite-difference time-domain
(FDTD) method was employed for all simulations using
Lumerical FDTD Solutions, a commercial FDTD software
package. Periodic boundary conditions were adopted in
the x and y directions, and a perfectly matched layer
boundary condition was used in the z direction. The
reflectance (R) and transmittance (T) were calculated
first, and the absorptance (A) was determined by
A ¼ 1 − R − T.
In Fig. 2, the absorptance and reflectance of the
optimized NCH and NH arrays are presented. The ab-
sorptance nonpatterned thin film with an optimized anti-
reflective (AR) coating is also presented for reference.
From Fig. 2(a), the absorptance of the NCH array is sig-
nificantly enhanced across the whole wavelength range
investigated, except for a narrow range around 0: 8 μm.
This implies that the NCH array exhibits a better light
trapping property compared to the NH array. In addi-
tion to the enhancement of absorpta nce in the short
Fig. 1. (Color online) (a) Schematic of the NCH array. (b) 2D
side view and (c) top view of the NCH array.
May 1, 2011 / Vol. 36, No. 9 / OPTICS LETTERS 1713
0146-9592/11/091713-03$15.00/0 © 2011 Optical Society of America
wavelength range, it is worth noting that the absorptance
curve of the NCH array shows a large redshift towards
the long wavelength, which means that the inefficient ab-
sorption in the long wavelength range (>0:8 μm) suffered
by thin film solar cells has been alleviated greatly. In the
long wavelength range, each peak in the absorptance
spectra corresponds to a quasiguided resonant mode
, and these modes supported by nanostructures help
to enhance absorption [7,18,19]. From Fig. 2(a), both
the NCH and NH arrays sup port resonant modes that re-
sult in stronger absorptance compared to nonpatterned
thin film layers. The NCH array supports more modes
compared to the NH array. For the sake of easy visuali-
zation, the inset in Fig. 2(a) shows the magnified absorp-
tance spectra of the NCH and NH arrays in the
wavelength range from 0.90 to 0:95 μm (indicated by
the purple dashed curve). It is clear that more modes
(peaks) are supported by the NCH array compared to
the NH array, contributing to the further enhancement
of the absorptance in the case of the NCH arrays. Be-
sides, the overall absorptance of NCH arrays is also im-
proved compared to the NH arrays, which resulted
mainly from a stronger coupling between the incoming
light and the supported modes in the NCH structure.
The reflectance spectra of the NCH and NH arrays are
compared in Fig. 2(b). Thanks to the better gradual chan-
ging of the effective refractive index of the NCH arrays
, it is clear that the reflectance of the NCH array is
much lower than that of the NH array in the whole
wavelength range, especially for short wavelengths.
Assuming that each photon absorbed by the active
layer can generate an electron–hole pair, the ultimate
efficiency, η, can be written as 
where IðλÞ is the solar intensity of the Air Mass 1.5
(AM1.5) direct normal and circumsolar spectrum ,
AðλÞ is the absorptance, λ is the wavelength, and λ
the wavelength corresponding to the bandgap. The effi-
ciency of the NCH array (NH array) is calculated for var-
ious a and f
ðf Þ, while keeping h ¼ 2:33 μm for easy
The ultimate efficiency of the NCH array is shown in
Fig. 3(a). For comparison, instead of using the data of
 directly, we optimized the efficiency of the NH arrays
using the FDTD method [Fig. 3(b)]. Our results are very
close to those reported in . In Fig. 3(a), we observe
that a larger f
promises a higher efficiency, regardless
of the lattice constant for all NCH arrays. With the in-
, the change of the effective refractive index
across the thickness of the NCH arrays in the z direction
is more gradual, w hich results in a better antireflection
characteristic, further enhancing the absorption. This
can be verified by the absorptance and reflectance
spectra for different f
with a ¼ 800 nm in Figs. 4(a)
and 4(b). With the larger f
, the absorptance is higher
and the reflectance is lower. The influence is more pro-
nounced in the short wavelength range. For all f
transmittance (which is not shown here) is close to zero
in the short wavelength range, which additionally verifies
that the antireflection characteristic is more effective in
this range. The efficiency increa ses with the increasing of
the lattice constant up to a ¼ 800 nm, after which the
efficiency begins to drop with the further increase of
a. More modes are supported for a larger a [18,19],
and simultaneously, the reflectance in the short wave-
length range increases . The absorptance and reflec-
tance spectra of different a with f
¼ 0:7 are depicted
in Figs. 4(c) and 4(d), respectively. With the increased a,
the absorptance decreases in the short wavelength range
and then increases in the long wavelength range. The re-
sonant modes are mainly contributing to the absorption
in the long wavelength range, and the antireflection prop-
erty dominates in the short wavelength range. There is a
trade-off between these two, especially for a larger lattice
constant. When a is smaller than 800 nm, more supported
Fig. 2. (Color online) (a) Absorptance of the optimized NCH
array and NH array. Inset, enlarged spectra from 0.9 to 0:95 μm.
(b) Reflectance of the same NCH array and NH array.
Fig. 3. (Color online) (a) Ultimate efficiency of the NCH array
for different lattice constants, a, and maximum filling ratios,
. (b) Ultimate efficiency of the NH array for different lattice
constants, a, and filling ratios, f .
Fig. 4. (Color online) (a) Absorptance and (b) reflectance of
the NCH array of different f
with a ¼ 800 nm and
h ¼ 2:33 μm. (c) Absorptance and (d) reflectance of the NCH
array of different a with f
¼ 0:7 and h ¼ 2:33 μm.
1714 OPTICS LETTERS / Vol. 36, No. 9 / May 1, 2011
modes help to bring up the efficiency . When a is larger
than 800 nm, the mode enhancement will be suppressed
by the energy loss in the short wavelength range resulting
from an increased reflection. The optimized ultimate ef-
ficiency is achieved at 32.65% when a ¼ 800 nm and
¼ 0:7 [Fig. 3(a)]. It is worth noticing that for wave-
lengths ranging from 600 to 800 nm, the absorptance and
reflectance exhibit a nonmonotonic dependence on the
lattice constant. For a ¼ 600 nm, a better AR perfor-
mance can be obtained in this wavelength range, but
not the ultimate efficiency, which is larger for
a ¼ 800 nm. This is mainly caused by the contribution
in the long wavelength range. The optimized ultimate ef-
ficiency of the NH arrays is shown in Fig. 3(b). The re-
lationship between the ultimate efficiency and the
design parameters a and f for the NH has been clearly
explained . The highest efficiency is 26.52% with a ¼
600 nm and f ¼ 0:5 for the NH array (indicated by the
black arrows) in Fig. 3(a). Compared to NH arrays,
the ultimate efficiency of the NCH arrays is enhanced
by 23.11%, surpassing the feasible enhancement using
the NH structure.
For the thin film structure, the efficiency can be signif-
icantly improved by an AR coating. For example, with an
optimized 70 nm Si
, the ultimate efficiency of the AR
thin film solar cell is increased to 21.21%, which has been
enhanced by 36.84 % compared to that of the thin film
without the AR coating (15.50%). Here, we also investi-
gate the influence of the AR coating for the optimized
NCH and NH arrays. The dielectric function of Si
taken from . The efficiency of the NCH and NH arrays
is increased to 34.23% and 28.83%, respectively, with op-
timized AR coating thicknesses of 73 and 63 nm, respec-
tively. The efficiency of the NCH array is enhanced by
18.73% compared to the NH array, which is still signifi-
cant. The AR coating mainly contributes to the improve-
ment of absorptance in the short wavelength range. The
modes supported by the NCH and NH arrays are not in-
fluenced by the AR coating.
In Figs. 5(a) and 5(b), we show the angular depen-
dence of the ulti mate efficiency for the optimized NCH
and NH arrays, respectively. For both the NCH and
NH arrays, TM polarization has higher ultimate efficiency
than TE polarization. For the incident angles up to 60°
that we simulated, the NCH array always showed better
efficiency than the NH array.
In conclusion, we presented a new NCH array struc-
ture with the highest ultimate efficiency of 32.65%, which
is much larger than that can be obtained by the NH array.
The optical properties of the NCH array are analyzed in
detail. Lower surface reflectance, more supported reso-
nant mod es, and enhanced modes interaction are the
main reasons for the significantly enhanced absorption
of the NCH array. The NCH array has better ultimate ef-
ficiency than the NH array, even for large incident angles
up to 60°.
1. K. R. Catchpole and A. Polman, Opt. Express 16,
2. E. Yablonovitch and G. D. Cody, IEEE Trans. Electron
Devices 29, 300 (1982).
3. Z. Yu, A. Raman, and S. Fan, Proc. Natl. Acad. Sci. USA 107,
4. Z. Yu, A. Raman, and S. Fan, Opt. Express 18, A366 (2010).
5. L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C.
Kimerling, and B. A. Alamariu, Appl. Phys. Lett. 89
6. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D.
Joannopoulos, Opt. Express 15, 16986 (2007).
7. S. B. Mallick, M. Agrawal, and P. Peumans, Opt. Express 18 ,
8. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater,
Nano Lett. 8, 4391 (2008).
9. H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
10. N. S. Lewis, Science 315, 798 (2007).
11. B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J.
Huang, and C. M. Lieber, Nature 449, 885 (2007).
12. M. D. Kelzenberg, D. B. Turner-Evans, B. M. Kayes, M. A.
Filler, M. C. Putnam, N. S. Lewis, and H. A. Atwater, Nano
Lett. 8, 710 (2008).
13. J. Zhu, Z. F. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor,
Y. Q. Xu, Q. Wang, M. McGehee, S. H. Fan, and Y. Cui, Nano
Lett. 9, 279 (2009).
14. M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B.
Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon,
R. M. Briggs, N. S. Lewis, and H. A. Atwater, Nat. Mater. 9,
15. K.-Q. Peng, X. Wang, L. Li, X.-L. Wu, and S.-T. Lee, J. Am.
Chem. Soc. 132, 6872 (2010).
16. B. M. Kayes, H. A. Atwater, and N. S. Lewis, J. Appl. Phys.
97, 114302 (2005).
17. L. Hu and G. Chen, Nano Lett. 7, 3249 (2007).
18. C. X. Lin and M. L. Povinelli, Opt. Express 17, 19371 (2009).
19. S. E. Han and G. Chen, Nano Lett. 10, 1012 (2010).
20. F. Wang, H. Yu, J. Li, X. Sun, X. Wang, and H. Zheng, Opt.
Lett. 35, 40 (2010).
21. E. D. Palik, Handbook of Optical Constants of Solids, Vol. 1
22. M. J. Minot, J. Opt. Soc. Am. 66, 515 (1976).
23. W. Shockley and H. J. Queisser, J. Appl. Phys. 32,
24. American Society for Testing and Materials, “Air Mass 1.5
Spectra,” retrieved from http://rredc.nrel.gov/solar/spectra/
Fig. 5. (Color online) Angular dependence of the ultimate ef-
ficiency of the (a) TE and (b) TM modes of the optimized NCH
and NH arrays, respectively.
May 1, 2011 / Vol. 36, No. 9 / OPTICS LETTERS 1715