www.sciencemag.org/cgi/content/full/334/6062/1530/DC1

Supporting Online Material for

Peak External Photocurrent Quantum Efficiency Exceeding 100% via MEG in a Quantum Dot Solar Cell

Octavi E. Semonin, Joseph M. Luther, Sukgeun Choi, Hsiang-Yu Chen, Jianbo Gao, Arthur J. Nozik,* Matthew C. Beard*

*To whom correspondence should be addressed. E-mail: arthur.nozik@nrel.gov (A.J.N.), matt.beard@nrel.gov (M.C.B.)

Published 16 December 2011, Science 334, 1530 (2011) DOI: 10.1126/science.1209845

This PDF file includes:

Materials and Methods SOM Text Figs. S1 to S10 Table S1 References

Materials and Methods

Synthesis of PbSe Quantum Dots

All chemicals unless otherwise noted are purchased from Sigma Aldrich and were anhydrous ifavailable. Synthesis follows previous work (18, 21). Lead oxide (1 g, 99.9995%, Alfa Aesar),oleic acid (3-5 g, 90%), and 1-octadecene (10 mL, 90%) are added to a 100 mL round bottom3-neck flask and are heated to 120C under vacuum on a Schlenk line to complex lead oleate.Under N2, the flask is heated to the desired injection temperature (normally 150-180C) and15 mL of 1 M Se (99.99%) dissolved in tri-n-octylphosphine (97%, Strem) is injected alongwith 0.15 g diphenylphosphine (98%). Size is controlled mainly by reaction time and injectiontemperature. The reaction is cooled by placing the flask in room-temperature water after 2-4minutes of growth and 10 mL of hexane (95%) is injected. The flask is then transferred to ahelium-filled glovebox where ethanol (99.5%) is added to the reaction solution to extract theQDs via centrifugation. Hexane and ethanol are used for two additional cleaning steps. Thefinal product is weighed and suspended in hexane at 20 mg/mL for dip-coating.

Substrates

Glass substrates with patterned indium tin oxide (ITO, 150 nm thick, 20 Ω/square) are purchasedfrom Thin Film Devices in Anaheim, CA. The substrates are cleaned by ultrasonication inorganic solvents and 100 nm Ag bus bars are evaporated just outside the edge of the deviceto lower the series resistance due to the extended ITO cathode. A 40-60 nm ZnO film is thendeposited via a sol-gel process described in ref. (35); a modified procedure developed by Beeket al. (36). This recipe uses one part diluted diethylzinc in toluene (15% by weight, caution:diethylzinc is pyrophoric), dissolved into 1-4 parts anhydrous tetrahydrofuran prepared underN2. The solution is spun-cast in air at 4000 rpm for 30 seconds, rested at room temperature for15 minutes and then annealed at 130C for 5 minutes.

Device Assembly

PbSe QD films are assembled in a helium filled glovebox using the layer-by-layer dip-coatingdeposition as described previously (15), with modifications for the secondary treatment withhydrazine. Normally, we perform 10-20 cycles of PbSe QDs (concentration 20 mg/mL) inhexane with 0.005M 1,2-ethanedithiol (98%) in acetonitrile (99.8%) using a NIMA Technology(Coventry, England) dip coater, followed by 5 more cycles with 1M hydrazine (98%, caution:explosive) in acetonitrile using the same PbSe solution. While the EDT layer is 50-250 nmthick, the hydrazine layer is only 30-50 nm in thickness, as determined by surface profilometry.For this deposition we use slower withdrawal speeds (100 mm/min) and an added film soak of5 seconds during the hydrazine cycles. Gold electrodes are deposited via thermal evaporationof 99.999% Au at a pressure of 10−7 Torr and a rate of 0.2 A/s for the first 10 nm, ramping to2 A/s for the final 90 nm.

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Characterization

External quantum efficiency and current-voltage measurements are both taken in an oxygen-and water-free nitrogen glovebox with a custom-built EQE apparatus and a custom-built solarsimulator, both described in (21). External quantum efficiency is measured by illuminatingwith monochromatic light and comparing the current generated by the test solar cell to thatgenerated by calibrated photodiodes (which have a known EQE). The incident light comesfrom white light passed through a monochromator, where typically a 75W Xe arc lamp is usedas the source, except for the UV-optimized arrangement, which uses a 100W Hg arc lamp. Weuse a Si photodiode for the 300-1060 nm range and a Ge photodiode for 1060-1750 nm. For theUV-optimized arrangement, we use a Newport UV-818-L with a calibration uncertainty of 1%(one standard deviation = 0.5%). The photodiodes all have NIST traceable calibration, and areall larger in area than the test solar cells. Additionally, the EQE measured on our apparatus hasbeen compared against a Thorlabs FDS-100-CAL Si calibrated photodiode (see fig. S5), whichis also traceable to NIST certification. The full-spectrum arrangement has more significant error(3-5%) in the UV-spectrum due to low light, so we use the UV-optimized arrangement for thisregion, reducing our measurement uncertainty to below 1% (see Error Analysis, below).

We use large 1 in2 companion films to extract the reflectance of our patterned device stacks,as in Law et al. (18). The large area companion films are made alongside the patterned sub-strates used for devices in a dip coater arm equipped to hold multiple substrates, ensuring thatthe device stacks were identical. Reflectance measurements of these films were performed inair with an integrating sphere in a Shimadzu UV-Vis-NIR-3600 spectrophotometer.

Ellipsometry

The complex refractive index N(hν) = n(hν) + ik(hν) spectra for the PbSe QD films, ITO,ZnO, and gold were determined by spectroscopic ellipsometry: in air for ITO, ZnO, and goldand both in air and under vacuum for the PbSe QD layers. In air, the ellipsometric data wereobtained by a rotating compensator-type variable-angle spectroscopic ellipsometer (M-2000DI model, J.A. Woollam Co., Inc.) at various incident angles ranging from 55 to 75 withan increment of 5. Transmittance measurements were also performed in a normal-incidenceconfiguration, whose results were combined with ellipsometric data in the modeling proceduresto improve the accuracy of analysis. We note that in this configuration some oxidation of thePbSe QD layers does occur, although the complex index of refraction and the reflectance areboth stable for at least several minutes, longer than the measurement time (see fig. S9). Also,the effects of this oxidation on the absorption into the active layer are generally limited to thesub-1.5 eV region of the spectrum, chiefly near the lowest energy exciton.

In order to address the oxidation effects of the PbSe QD films, which can lead to problems inthe optical modeling below 1 eV, we also obtain ellipsometric data under vacuum such that wecan reduce air exposure effects. This approach uses a fixed-angle spectroscopic ellipsometerat 70. The ellipsometric measurement in this mode shows less oxidation (as evidenced byimproved optical modeling results), although there is some brief air-exposure during loading ofthe sample into the vacuum chamber.

A multilayer model was employed to analyze the ellipsometric data, which consists of glasssubstrate/film of interest/surface roughness/ambient. The N(hν) of QD films was constructed

3

by a set of oscillators such as Gaussian, Lorentzian, and Tauc-Lorentzian. The surface rough-ness (represented by Bruggeman effective medium approximation) and the film thickness es-timated by ellipsometric measurements are in an excellent agreement with the results fromsurface profiling measurements. The complete ellipsometric modeling process is detailed inref. (37). The resulting n(hν) and k(hν) are then used to parameterize the optical model of thedevice, plotted in Fig. S2 for the layers modeled in fig. 2.

Optical Modeling

Both the reflectance and EQE spectra exhibit significant interference fringes indicating thebuildup of optical modes within the dielectric stack. These fringes depend upon the thick-ness of each layer so an optical model using the ellipsometric measurements described aboveis employed to extract the IQE. This model is detailed in ref. (18). The thickness of each layerwas determined by cross-sectional SEM and then allowed to vary by ∼ 10% in the model by aleast-squares fit to the measured reflectance.

SOM Text

Error Analysis

The quoted peak EQE values incorporate a number of sources of error, which are relativelystraightforward to summarize by looking at the EQE calculation itself:

EQET =ITIR

EQER, (1)

where IT is the current generated by the test cell, IR is the current generated by the referencecell, and EQER is the known EQE of the reference cell (calculated from the calibration inA/W). From this equation we can see that there are only three possible sources of error (IT ,IR and EQER). There are fluctuations in the intensity of the lamp source, electrical noise,and drift by the chopper wheel, all of which will lead to fluctuations in the output current(IT , IR). We obtain an estimate of all these by measuring the output current 5-30 times andcalculating a standard deviation of the mean. The third source of error, EQER, has a calibrationuncertainty of ±3% for the full-spectrum EQE measurements presented in Fig. 2, while for theUV-optimized arrangement it is ±0.5%. Since the output current errors are typically < 0.1%,this mostly determines our uncertainty (one standard deviation):

σEQET = EQET

σIT

IT

+

σIR

IR

+

σEQER

EQER

. (2)

Multiplication Model

The fits used in Fig. 3C implement the same general function derived by Beard et al. (7)and is defined below. This model uses two degrees of freedom: the MEG efficiency, ηMEG,

4

and s, which determines the increase in the multiplication rate with excess energy. The MEGefficiency defines the threshold energy Eth as

Eth = Eg +Eg

ηMEG, (3)

where Eg is the bandgap of the QD. The model then has the functional form

QE = 1 +Pxs(1 + 2Pzs)

(1 + Pxs)(1 + Pzs), (4)

where P describes the competition between the multiplication and cooling rates. We relateηMEG to P by ηMEG = P/(1 + P ), and x and z are defined as

x =

(hν − Eth) /Eth if hν ≥ Eth

0 otherwise , (5)

and

z =

(hν − 2Eth) /Eth if hν ≥ 2Eth

0 otherwise , (6)

where hν is the photon energy. When fitted to spectroscopic data (7), this model yields ηMEG =0.60 and s = 2.2, and the black curve in Fig. 3C is the calculated quantum yield from these fittingparameters. In this work we modify the model by multiplying the calculated quantum yield inEq. 4 by the mean of the peak IQE values for the two below-threshold devices, yielding thedashed black curves in Figs. 2a and 2b (they are identical). This normalization value is 0.86,and is the same value we divide by to convert the measured peak IQE values (blue circles in Fig.2b) into the normalized peak IQE values (purple circles). Finally, by allowing the normalizationfactor, N , to float, we apply a least-squares linear fit of eq. 4 multiplied by N to the IQEof the 0.72 eV solar cell, allowing N , ηMEG, and s to float, and find N = 0.848 ± 0.007,ηMEG = 0.62 ± 0.01, and s = 2.8 ± 0.3, showing reasonable agreement with the fit to thespectroscopic data.

Figures

0.08

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0.00

Abso

rbed

Pho

tons

(nm

-3)

5004003002001000distance (nm)

3.35 eV

1.55 eV

5

Fig. S1: Depth-dependent optical generation profile at 3.35 eV and 1.55 eV photon energiesfor the same 0.72 eV device in Fig. 2E and 2F. These curves are produced by the optical modeldiscussed above and detailed in ref. (18) — integrating along the depth (z axis) gives the totallight absorbed by that section of the stack at a given wavelength, yielding the curves shown inFig. S3.

2.8

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Real Index, n 0.98 eV 0.83 eV 0.72 eV

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Extinction Coefficient, k 0.98 eV 0.83 eV 0.72 eV

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0.0

n or

k

654321

Photon Energy (eV)

n (above): Glass ITO ZnO

k (below): Glass ITO ZnO

Fig. S2: Typical complex refractive index spectra of the Glass, ITO, ZnO, PbSe QD, and Aulayers measured and used in this work. The first two panels show the n and k values used formodeling of the devices in Figs. 2 and 3B.

1.0

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tion

of L

ight

3.53.02.52.01.51.0Photon Energy (eV)

Reflectance Transmittance

Absorptance:

ITO ZnO 0.74 eV PbSe Gold

Fig. S3: Sample output from the optical model for the 0.72 eV device from Figs. 2 and 3. Notethat the ITO has significant absorption above 3 eV and below 1.5 eV (absorbing even morethan the PbSe QD layer in the latter range). The complex refractive index spectra used in thismodeling is shown in Fig. S2.

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140120100

80604020

0

Modeled Re!ectanceRe!ectanceIQE Variations in modeled IQE

Variations in modeled re!ectance

A B CEg = 0.98 eV Eg = 0.83 eV Eg = 0.72 eV

Photon Energy (eV) Photon Energy (eV) Photon Energy (eV)1.0 1.5 2.0 2.5 3.0 3.5 1.0 1.5 2.0 2.5 3.0 3.5 1.0 1.5 2.0 2.5 3.0 3.5

Fig. S4: Effect of varying the thickness of the PbSe QD layer in the optical model on modeledreflectance and calculated IQE. We allow the thickness to vary in increments of 1 nm and plotthe resulting IQE curves. We find that below 2 eV, and especially near the first optical transition,the variation is much greater, while above 2.5 eV there is virtually no change.

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(%)

3.43.2Photon Energy (eV)

UV Optimized

Thorlabs Calibration Measured

EQE Peaks

Fig. S5: Measurement of the Thorlabs FDS-100-CAL Si photodiode (calibrated by ThorlabsNov 24, 2010) with our EQE system in an oxygen-free nitrogen glovebox atmosphere. Herewe compare the given EQE for the device with serial #10112425 against our measurement,showing excellent agreement for photon energies greater than 1.3 eV. Both the full-spectrummeasurement and the UV-optimized arrangement (inset) are within 3% of the FDS-100-CALcalibration, less than the quoted calibration uncertainty of ±5%. Much of the disagreement hereis likely due to the Thorlabs calibration uncertainty rather than a measurement error. Our great-est disagreement (about 5%) with the Thorlabs calibration is at a much lower photon energythan the regime in which we report an EQE > 100%. This occurs near the band edge, where weexpect temperature fluctuations to affect the bandgap, and therefore the EQE. It is also possiblethat the spectral width of our monochromatic light could affect the EQE in this region.

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140

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60

40

20

0

IQE

(%)

3.53.02.52.01.51.0

Photon Energy (eV)

PbSe QD Bandgap: 0.72 eV 0.83 eV 0.98 eV

Fig. S6: IQE plotted against photon energy, hν, for all of the devices shown in Fig. 3B. Notethe increasing heights and red-shift of the MEG onset with decreasing band-gap.

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%)

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(a.u

.)

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cm-2eV

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3.53.02.52.0Photon Energy

Extra Current(mA cm-2eV-1)

EQE EQE/A MEG Region

(~1 mA/cm2)

Solar Intensity Photons s-1m-2eV-1

Fig. S7: Contribution of MEG to photocurrent. In order to make an estimate of the impactof MEG on the solar cell PCE, we multiply the IQE in excess of the baseline 85% (shadedregion) by the AM1.5G solar spectrum. This gives a rough estimate of the spectral “bonus”photocurrent MEG could provide to a properly optimized solar cell (blue curve). This curve,when integrated for the smallest bandgap device, yields a bonus current of about 1 mA/cm2, or4%. This is a small contribution, and for larger bandgap QDs, it is even smaller, in agreementwith previous estimates (7).

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1.00.90.80.70.0

0.1

0.2

0.3

0.4

V oc(V

)

Bandgap (eV)

EDTEDT+Hy

Fig. S8: Comparison of EDT-only versus EDT+hydrazine treatment on open circuit voltage(Voc) for a range of QD bandgaps. Previous work (38) on ZnO/PbSe heterojunctions has shownthat the valence band maximum is pinned to sub-bandgap-states in the ZnO, regardless of QDsize, and that electron injection into the ZnO should be blocked for PbSe QDs with bandgapsless than approximately 0.7 eV. This finding agrees with our work — solar cells made from abatch of QDs with a smaller bandgap show a much lower Voc, which limits our ability to exploresmaller bandgaps.

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Initial 2 minutes 4 minutes

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3020100Time (min)

Initial 2 minutes 4 minutes

Evolution @ 3 eV

Photon Energy (eV)

Fig. S9: Effect of brief air exposure on the n and k of a film of 0.98 eV PbSe QDs depositedwith 25 cycles of EDT and 5 cycles of hydrazine. We plot n on the left and k on the right at zerominutes (black), two minutes (red), and four minutes (blue). We also show in the inset the timeevolution of k at 3 eV over a longer period of time, indicating that there is virtually no changein the first five minutes, followed by larger shifts from 10-30 minutes.

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20

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(%)

EQE: PbSe 0.72 eV: M = 1.12 PbSe 0.98 eV: M = 1.156 Reference Cell

Spectral Intensity: Simulator Lamp AM1.5G

Fig. S10: Spectral mismatch correction factor for the power conversion efficiency characteri-zation of the two devices shown in Fig. 3. The mismatch factor, M , is calculated by

M =

λ2λ1

ERef (λ)SR dλ λ2λ1

ES(λ)ST dλ λ2λ1

ERef (λ)ST dλ λ2λ1

ES(λ)SR dλ(7)

where ERef is the spectral intensity of the sun, ES is the spectral intensity of the solar simulatorlamp, SR is the spectral responsivity of the reference photodiode used to control for intensity,and ST is the spectral responsivity of the test cell. The uncorrected power conversion efficiency(η(0)) and short circuit current (J (0)

sc ) can be corrected to their true 1-sun values (η(1) and J (1)sc )

by dividing by M :η(1) = η(0)/M, J (1)

sc = J (0)sc /M. (8)

See ref. (39) for a complete discussion of mismatch factors and their calculation. The integratedphotocurrents (which agree with the 1-sun Jsc values to within 7%) and mismatch factors forthe devices are shown below in Table S1.

Table S1: Compiled mismatch calculation values.

QD Bandgap Lamp Jsc (mA cm−2) AM1.5G Jsc (mA cm−2) Mismatch, M0.72 eV 28.5 25.8 1.120.98 eV 30.3 26.6 1.16

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