Supplementary Information for
Woojun Yoon,
† 
,*
Janice E. Boercker,
†
Matthew P. Lumb,
† ‡
Diogenes Placencia,
†
Edward E.
Foos,
†
and Joseph G. Tischler
†
†
U.S. Naval Research Laboratory, 4555 Overlook Avenue SW, Washington, DC 20375 United
States
‡
The George Washington University, 2121 I Street NW, Washington, DC 20037 United States
*E-mail: woojun.yoon@ieee.org
1

Table S1
|
Reactant concentrations, solvent volumes, and OA to Pb ratios used for each nanocrystal QD diameter. The number in parentheses next to the solvent volume is the total reaction volume.
QD diameter
(nm)
2.9
3.1
3.3
3.5
3.8
4.0
4.1
78
78
77
77
[Pb] mM
76
78
77
[TMS] mM
36
35
36
36
36
36
36
[OA] mM
164
230
228
229
760
228
962
ODE
(mL)
19.9 (21.1)
19.8 (21.6)
19.2 (20.9)
19.9 (21.7)
15.6 (20.9)
10 (10.9)
14.4 (20.9)
OA/Pb
2.1
2.9
3
2.9
9.8
3
12.5
Table S2
|
Injection temperatures, reaction temperatures, reaction times, and weight loss at
600 o C (for as-synthesis PbS QDs) for each PbS QD diameter. The reaction temperature increased/decreased throughout the reaction, the lowest and highest temperatures are noted.
QD diameter
(nm)
2.9
3.1
3.3
3.5
3.8
4.0
4.1
Injection
Temperature
(°C)
110
130
129
150
130
130
130
Reaction
Temperature
(°C)
92-96
115-114
114-111
~144
108-112
114-120
117
Time
(seconds)
90
154
94
90
120
60
130
Weight loss at
600 o C
(%)
56.3
63.2
64.4
72.5
66.4
69.9
73.6
2

Figure S1
|
X-ray powder diffraction (XRD) pattern of PbS nanocrystal QDs (red) with the first exciton peak at (a) 1009 nm and (b) 1059 nm, respectively. XRD data obtained for PbS QDs was indexed to bulk PbS (green) by comparison to JCPDS card#1-880.
3

Figure S2
|
Transmission electron microscope (TEM) image and size distribution statistics from the analysis of TEM images of PbS nanocrystal QDs with the first exciton peak at 1.2 eV. The
QD size was estimated according to Moreels et al .
1
and it is in a good agreement with the result obtained from size distribution statistics of the TEM images.
4

Figure S3
|
X-ray photoelectron spectroscopy of BDT-PbS nanocrystal QD films
5

Figure S4
|
Attenuance spectra of PbS QD films before and after 1, 3-benzenedithiol (BDT) treatment.
6

Quantum confinement
Even with small variation in size, the quantization energy varied in a pronounced manner from
1.0 eV to 1.4 eV because the energy dependence of the absorbance varies as d -1.0
, 1 where d is the
QD diameter in nm (Fig. S5). The PL emission exhibited a Stokes shift in the first exciton energy with respect to the first exciton attenuance energy that decreased from ~162 meV for 2.9 nm
QDs to 54 meV for 4.1 nm QDs (the inset of Fig.S5). The Stokes shift increased with
confinement, which has been reported previously for QD systems, 2,3 due to the energy splitting
of the ground exciton state increasing with decreasing diameters.
4
Figure S5 | Quantum confinement effect on the first exciton attenuance and the PL peak energies as a function of d -1 , where d is the QD diameter in nm. Both solid lines are linear fits.
The inset shows the Stokes shift as a function of first exciton attenuance energy for PbS QDs.
7

Interfacial LiF thickness dependence of J-V characteristics
Prior to fabrication, we carefully optimized the LiF layer thickness.
The devices were fabricated using 4.1 nm PbS QDs ( E g
=1.04 eV) with varying LiF thicknesses of 6 Å, 10 Å and
14 Å (between the PbS QD layers and Al), respectively. Following the fitting procedure described previously, the diode parameters were extracted from the measured J V in the dark
(Figure S6a). The optimum LiF thickness was found to be 10 Å. The series resistance of devices with the thicker 14 Å LiF layer increased to 8.1 Ω
 cm
2 due to the increased bulk resistance of the thicker LiF. The shunt resistance also increased as the thickness of LiF increased due to reduced leakage current by increased coverage of thicker LiF layer. For the device with 6 Å thick LiF, the
J
0
decreased by one order of magnitude with thicker LiF layer at the expense of the increased series resistance . Table S3 summarizes the effect of varying LiF thickness on the diode parameters in the dark.
Table S3
|
Diode parameters obtained from current density-voltage (J-V) characteristics in the dark of the metal-PbS QD (E g
=1.04 eV) Schottky junction solar cells (ITO/PbS
QDs/LiF/Al).
QD size
(nm)
4.1
LiF thickness
(Å)
6
10
14
R s

A
(Ω  cm 2 )
R sh

A
(Ω  cm 2 )
J
0
(A/cm
2
) n
1.8

0.1 (9.8

6.1)

10 3 (6.1

2.2)

10 -7 2.1

0.1
1.0

0.1 (1.6

0.4)

10
4
(5.1

0.8)

10
-8
1.8

0.1
8.1

0.8 (1.0

0.6)

10
5
(1.6

0.4)

10
-8
1.7

0.1
The J V characteristics under 1 sun illumination are shown in Figure S6b. The photovoltaic performance was optimized with the device incorporating a 10 Å thick LiF layer in terms of reduced R s
and J
0
and increased R sh
, exhibiting the power conversion efficiency of 2.5

0.3%
8

with a high fill factor (FF) of 59.7

1.3%, the V oc
of 483

3 mV, and the J sc
of 8.4

0.7 mA/cm 2 .
(Figure S6c and d).
Figure S6
| Interfacial LiF thickness dependence of J V characteristics. a,
J V characteristics of the QD solar cells (ITO/PbS QDs/LiF/Al) with varying the LiF thickness in the dark. The open symbols are experimental data, while the solid lines are fits according to a one diode model including series and shunt resistances. b, J V characteristics of the devices with varying the LiF thickness under AM 1.5G filtered spectral illumination (100 mW/cm
2
). c, Short-circuit current density ( J sc
), and d, open-circuit voltage (V oc
) and fill factor (FF) as a function of the thickness of LiF layer.
9

PbS QD absorber thickness dependence of J-V characteristics
The absorber layer thickness was linear with the number of spin-coating (Figure S7a).
Following the fitting procedure described previously, the diode parameters were extracted from the measured J V in the dark (Figure S7b). Figure S7c shows the effect of the PbS QD absorber layer thickness on the diode parameters of the devices with a fixed LiF layer thickness of a 1.0 nm in the dark. As the thickness increased, both R s
and R sh
increased, while J
0
was not affected significantly. This is consistent with the decreased FF and almost invariant V oc
of the diode under illumination. Although the PV performances were maximized for the thickness of about 130 nm~150 nm (Table S4) , the J sc
decreased as the absorber layer thickness increased. In general the J sc
values obtained in this study are lower than those reported elsewhere.
10

Figure S7 | PbS QD absorber thickness dependence of J-V characteristics. a. The dependence of PbS QD film thickness on the number of spin coating cycles for two different size of PbS QDs. b J V characteristics of the QD solar cells (ITO/PbS QDs/1 nm LiF/Al) with varying the PbS QD layer thickness in the dark. The open symbols are experimental data, while the solid lines are fits according to a one diode model including series and shunt resistances. c,
The dependence of diode parameters obtained from J V characteristics in the dark of Schottky junction solar cells (ITO/PbS QDs/LiF/Al).
Table S4
|
Solar cell parameters obtained from current density-voltage (J-V) characteristics of the devices (ITO/PbS QDs/LiF/Al) under AM 1.5G filtered spectral illumination (100 mW/cm 2 ).
QD size Thickness # of spin-coating
(nm) (nm)
3.8
4.1
136
204
286
96
148
266
350
6
8
10
5
7
9
11
J sc
(mA/cm 2 )
V oc
(mV)
FF
(%)
Eff.
(%)
8.6

0.3 545

9 61.5

0.4 2.8

0.1
6.7

0.8 542

10 55.4

0.9 2.0

0.3
3.1

1.3 542

8 50.1

1.2 1.1

0.3
6.5

1.0 450

30 52.6

2.3 1.6

0.2
8.4

0.7 483

3 59.7

1.3 2.5

0.3
4.3

1.1 430

20 49.4

2.1 0.9

0.4
2.9

0.9 450

20 46.5

3.5 0.6

0.2
Lig htinte nsit y dependence of J-V characteristics
The J V characteristics of the diodes under different illumination intensity ( P
0
) are shown in
Fig. S8a. The cell performance parameters, J sc and V oc
extracted from the J V characteristics under different illumination intensity as a function of P
0
, are shown as symbols in Fig. S8b and
S8c. The dependence of J sc
follows J sc
=   P
0
 , where  =0.07 A/W and  =1.01, indicating the linear dependence of J sc
on P
0
. Since J sc
is dependent on P
0
, it follows from equation 2 that V oc should exhibit a slope of nkT / q , when it is plotted as a function of the logarithm of P
0
. The experimental V oc
data are fitted with a linear function of slope of n=1.37 (Fig. S8b). In
11

comparison, ideality factors of 1.25 and 1.38 have been reported for Schottky-barrier solar cell under illumination fabricated using 1.1 eV (~3.8 nm) and 1.3 eV (~3.1 nm) PbS QDs, respectively.
6 The ideality factor greater than unity indicates that the trap-assisted recombination process is dominant in PbS QD Schottky-barrier solar cells under illumination.
6
Note that the ideality factor extracted from dark J V measurement is larger than that measured from the light intensity dependence of the V oc
. This can be due to the deep traps contributing to larger ideality factor, while those traps are inactivated under illumination.
7 We also observed that the superposition of light and dark J V curves does not hold (Fig. 2b and S6b).
12

Figure S8
|
Light-intensity dependence of J-V characteristics. a, J V characteristics under various intensities of simulated AM 1.5G filtered illumination (The inset shows the same J V curves in a linear scale). b, Short-circuit current density ( J sc
), and c, open-circuit voltage ( V oc
) as a function of the optical power density ( P
0
) for the device. The symbols are experimental data determined from the J
–
V characteristics, while all solid lines are fits as discussed in text.
13

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2
3
4
5
6
7
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