Supplemental Material
Evidence of significant down-conversion in a Si-based
solar cell using CuInS2/ZnS core shell quantum dots.
Spiros Gardelis and Androula G. Nassiopoulou
IMEL/NCSR Demokritos, Terma Patriarchou Grigoriou, Aghia Paraskevi, 15310
Athens, Greece
A different approach to calculate the enhancement of conversion efficiency due
to the down-conversion effect of the CuInS2/ZnS quantum dots.
In order to estimate the percentage of the conversion efficiency due to downconversion, we follow a different approach.1-3
For the Si solar cell without the dots the short circuit current density, JSC, Si is given
by:
𝑒
1100𝑛𝑚
𝐽𝑆𝐶,𝑆𝑖 = ℎ𝑐 × ∫350𝑛𝑚 𝜆 × 𝐸𝑄𝐸𝑆𝑖 (𝜆) × 𝐼𝐴𝑀1.5𝐺 (𝜆) 𝑑𝜆,
(s1)
e is the electron charge, h is Plank’s constant, c is the speed of light, λ is the
wavelength and IAM1.5G is the intensity of the AM1.5G solar spectrum in W/cm2 shown
in Figure S1.4 The integral is over the whole spectral range for our measurements (i.e.,
350-1100 nm).
For the cell with the dots we have to take into account down-conversion, thus the
short-circuit current density, JSC,A,B is given by:
𝐽𝑆𝐶,𝐴,𝐵 =
800
𝑒
× {∫
(1 − 𝛢(𝜆)) × 𝜆 × 𝐸𝑄𝐸𝐴,𝐵 (𝜆) × 𝐼𝐴𝑀1.5𝐺 (𝜆)𝑑𝜆}
ℎ𝑐
350𝑛𝑚
800𝑛𝑚
𝑒
+ × {∫
𝐴(𝜆) × 𝜆 × 𝐸𝑄𝐸𝐴,𝐵 (𝜆) × 𝑄𝑌 × 𝐼𝐴𝑀1.5𝐺 (𝜆)𝑑𝜆}
ℎ𝑐
350𝑛𝑚
1100𝑛𝑚
𝑒
+ ℎ𝑐 × {∫800𝑛𝑚 𝜆 × 𝐸𝑄𝐸𝑆𝑖 (𝜆) × 𝐼𝐴𝑀1.5𝐺 (𝜆)𝑑𝜆},
(s2)
Α(λ) is the absorption from the dots. From our results we can observe that the dots
absorb only below 800 nm. The first term corresponds to the photocurrent which is
generated in the cell by the light which is transmitted through the layer of the dots
reaching the cell underneath. The second term is exactly the photocurrent which is
due to down-conversion, that is due to the red photons which are emitted by the dots
when these are excited by the high energy photons. QY is the quantum yield of the
dots and is 30%.5 The third term is the photocurrent which is generated by the photons
above 800 nm, which are not absorbed by the dots. The term of interest is the downconversion term. We will now calculate the percentage of the photocurrent which is
due to down-conversion. In our calculations, we consider that reflection from the dots
is very small, thus 𝐴(𝜆) = 1 − 𝛵(𝜆) . This percentage, called (DC)A,B in the article, is
given by:
800𝑛𝑚
(𝐷𝐶)𝐴,𝐵 (%) =
∫350𝑛𝑚 𝐴(𝜆)×𝜆×𝐸𝑄𝐸𝐴,𝐵 (𝜆)×𝑄𝑌×𝐼𝐴𝑀1.5𝐺 (𝜆)𝑑𝜆
800𝑛𝑚
∫350𝑛𝑚 𝜆×𝐸𝑄𝐸𝑆𝑖 (𝜆)×𝐼𝐴𝑀1.5𝐺 (𝜆)𝑑𝜆
,
(s3)
Figure S2 shows the spectral dependence of the short-circuit photocurrent density for
the bare cell.
Figures S3 and S4 show the spectral dependence of the down-conversion term for the
short-circuit photocurrent density for samples A and B, respectively.
The spectral dependence of EQESi and EQEA,B have been measured and shown in the
article (Figure 5).
Figure S1.4
Figure S3.
Figure S2.
Figure S4.
Calculating the enhancement of conversion efficiency due to down-conversion from
equation(s3), we find 4% and 11% for sample A and B, respectively. These values are
very close to the ones in the article. In conclusion, we verified the contribution of
down-conversion enhancement due to the presence of the dots with two different
ways and we got similar results.
(1) H. –C. Chen, C. –C. Lin, H. –W. Han, Y. –L. Tsai, C. –H. Chang, H. –W.
Wang, M. –A. Tsai, H. –C. Kuo, P. Yu, Optics Express 19, No. S5, A1142
(2011)
(2) C. –C. Lin, H. –C. Chen, H. –V. Han, Y. –L. Tsai, C. –H. Chang, M. –A. Tsai,
H. –C. Kuo, P. Yu, Proc. SPIE 8256, Physics, Simulation, and Photonic
Engineering of Photovoltaic Devices, 825609 (2012)
(3) C. –C. Lin, H. –C. Chen, Y.L. Tsai, H. –V. Han, H. –S. Shih, Y. –A. Chang,
H. –C. Kuo, P. Yu, Optics Express 20 Issue S2, A319 (2012)
(4) Solar spectrum taken from:
http://pveducation.org/pvcdrom/appendices/standard-solar-spectra
(5) www.oceannanotech.com