Efficiency dip observed with InGaN-based
multiple quantum well solar cells
K. Y. Lai,1 G. J. Lin,2 Yuh-Renn Wu,2 Meng-Lun Tsai3 and Jr-Hau He2,4,*
1
Department of Optics and Photonics, National Central University, Chung-Li 320, Taiwan
Institute of Photonics and Optoelectronics, National Taiwan University, Taipei, 10617, Taiwan
3
Epistar Corporation, Hsinchu 300, Taiwan
4
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, King Abdullah University of
Science & Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
*
jrhau.he@kaust.edu.sa
2
Abstract The dip of external quantum efficiency (EQE) is observed on
In0.15Ga0.85N/GaN multiple quantum well (MQW) solar cells upon the
increase of incident optical power density. With indium composition
increased to 25%, the EQE dip becomes much less noticeable. The
composition dependence of EQE dip is ascribed to the competition between
radiative recombination and photocurrent generation in the active region,
which are dictated by quantum-confined Stark effect (QCSE) and
composition fluctuation in the MQWs.
©2014 Optical Society of America
OCIS codes: (350.6050) Solar energy; (040.5350) Photovoltaic; (250.5590) Quantum-well, wire and -dot devices; (160.2100) Electro-optical materials.
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1. Introduction
The wide span of III-nitrides’ band gap (Eg), covering nearly the entire solar spectrum, has
made the compound a promising material candidate for the next-generation photovoltaic
devices [1]. The potential of nitride solar cells not only roots in the ideal values of Eg, but also
the very high absorption coefficients (> 104 cm−1) in light of the compound’s direct Eg [2,3].
In addition to these merits, nitride semiconductors exhibit many other favorable photovoltaic
properties. For instance, their strong interatomic bonds and high thermal conductivities make
the alloys suitable for high temperature operation [4], which is highly desired by concentrator
solar cells. Moreover, the electrical and optical properties of InxGa1-xN exhibit very low
sensitivity to high-energy proton irradiation, as compared with other well-developed solar
materials (such as Si, GaAs and GaInP) [5]. The superior radiation resistance makes InxGa1xN attractive for the applications in space photovoltaics.
In the design of device structure for nitride solar cells, MQWs are among the most
adopted for the active region [6–14]. The popularity of MQW structure comes from two
important considerations: i) the critical thickness of InxGa1-xN on GaN is less than 100 nm for
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x > 0.1 [15], but high indium contents are usually inevitable for a cell to absorb longwavelength (λ > 450 nm) light. To avoid the trade-off between crystal quality and solar
absorption, the MQW containing InGaN layers thinner than 10 nm is regarded as a feasible
method for the active region. ii) Since the energy levels in a MQW structure is quantized, the
absorption energy of the active region, being determinant to short-circuit current (Jsc), can be
engineered not only by Eg of the wells, but also by the well widths. This extra manipulating
dimension is further expanded by the notion that the open-circuit voltage (Voc) of a MQW
solar cell can be independently optimized by Eg (or the width) of the barriers, without
changing the parameters of the wells [16]. Such decoupled control over Jsc and Voc is not
possible for conventional single-junction cells.
However, it cannot be over emphasized that the high radiative recombination efficiencies
in a MQW structure could counter affect the generation of photocurrents. In a MQW solar
cell, although the alternate wells and barriers offer additional freedoms in tuning Jsc and Voc,
the potential barriers of the MQW prevent electrons and holes from escaping the active region
and thus lower the carrier collection efficiency. As a result, the loss of photocarriers through
recombination, either radiative or nonradiative, is a vital factor in energy conversion
efficiency, and should be taken into account when optimizing the device structure. The
recombination dynamics is even more complicated in InGaN-based MQWs considering
QCSE and indium segregation [17,18], both of which are the characteristics peculiar to
InGaN thin layers because of the polarization-induced internal fields and the low miscibility
of InN in GaN [19,20]. Yet, the correlation between carrier recombination and photocurrent
generation in InGaN-based MQW solar cells is not well clarified to date.
In this letter, we report a direct observation of efficiency dip exhibited by InGaN/GaN
MQW solar cells upon the increase of incident optical power densities. The efficiency dip is
revealed by the MQW structure emitting blue light. However, for the MQW with green
emission (by increasing indium contents), the dip effect is almost unnoticeable. The
discrepancy is attributed to the different carrier dynamics in the well regions, dictated by
QCSE and indium segregation. Detailed mechanisms responsible for the observed results will
be explained.
2. Experiment
The MQW solar cells were grown by metalorganic chemical vapor deposition on c-plane
sapphire substrates. Indium compositions of 15% and 25% were employed in the active
regions. Both types of the MQWs are sandwiched by a 2.5-μm n-type (Si: 2 × 1018 cm−3) GaN
layer and a 0.2-μm p-type (Mg: 5 × 1017 cm−3) GaN layer. The repeat of intentionally
undoped InxGa1−xN/GaN MQWs are 12 for x = 0.15 and 9 for x = 0.25 in consideration of
lattice strain. In device fabrication, indium tin oxide (ITO) was deposited by electron beam
evaporation on p-GaN to form transparent ohmic contacts. 1 × 1 mm2 diode mesas were then
defined by chlorine-based plasma etching. Ti/Al/Ni/Au metal grids were deposited on the
ITO and n-GaN to serve as the electrodes.
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Fig. 1. (a) PL spectra of the MQWs with 15% and 25% indium at the incident power density of
5 W/m2. (b) PL peak wavelengths as a function of driving current for the MQWs with 15% and
25% indium.
3. Results and discussion
Figure 1 presents the photoluminescence (PL) spectra at the incident power density of 5 W/m2
for the two InxGa1-xN/GaN MQW solar cells. It can be seen that the peak intensity from the
MQW with 15% indium is around 1.6 times stronger than that from the MQW with 25%
indium. Moreover, the full width at half maximum (FWHM) of the blue peak (15% indium) is
only 60% of the other one. The stronger and narrower PL peak given by the 15%-indium
MQW indicates a superior quality in carrier confinement. Increasing the indium content to
25% makes stronger the compressive strain exerted on the InxGa1-xN wells, which tends to
create misfit dislocations in order to release the accumulated lattice tension [15]. The
dislocations not only act as non-radiative recombination centers [21], but also smear out the
well/barrier boundaries, making electrons and holes more likely to escape from the wells
and/or recombine with deviated emission energies. Consequently, the PL performances
deteriorate with increased indium contents.
QCSE can also affect carrier recombination in the MQW [17]. Figure 1(b) shows the PL
peak wavelengths of the two solar cells with incident power density increasing from 5 W/m2
to 25 W/m2. The normalized full spectra can be seen in Figs. 2. The peak wavelength of the
blue-emitting MQW is retained at 457.0 ~455.5 nm for all power densities, while that of the
green-emitting MQW shifts from 537.0 nm at 5 W/m2 to 533.0 nm at 25 W/m2. The larger
blue-shift of the green-emitting MQW is caused by the screening of QCSE [22]. The
increased lattice strain with 25% indium leads to stronger piezoelectric polarization along the
c-axis, and thus induces a larger internal electric field. The large internal field pushes
electrons and holes towards the opposite sides in the wells, resulting in the lower radiative
recombination efficiency and reduced recombination energies [22,23]. As more carriers are
injected into the wells, the increased Coulombic force counterbalances the polarizationinduced fields, restoring the flat-band condition, hence the blue-shift. The degree of QCSE
and the aforementioned carrier-confinement qualities will be shown to play decisive roles in
the quantum efficiencies of the MQW solar cells.
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Fig. 2. Normalized PL spectra at the power densities from 5 W/m2 to 25 W/m2 for the MQW
solar cells with the indium compositions of (a) 15%; (b) 25%.
EQEs of the MQW solar cells with different indium compositions are presented in Fig. 3(a).
The EQE shown here is defined as: EQE = (Jop/q)/(Pop/hv), where Jop is the photocurrent
density, q the electronic charge, Pop the optical power density, h Planck’s constant, and v the
frequency of incident light [24]. In the figure, both of the solar cells exhibit the maximum
efficiencies at λ = 380 nm. Similar observation was also reported by other groups [25–27].
The decreased EQE at the wavelengths below 370 nm indicates that the incident photons are
absorbed in the MQW structure, instead of the p-type capping layer [27]. One can see that the
EQE peak with 25% indium is lower, but wider than the one with 15% indium. The result is
ascribed to composition fluctuation [7], crystal imperfections [28], and the hole-blocking
band discontinuity in the active region of high indium contents [29], which have been
thoroughly discussed in the cited references. Compared to those obtained with 15% indium,
the lower EQEs with increased indium indicate lower Jsc, which is shown by the J-V curves
under air-mass (AM) 1.5G solar spectrum in Fig. 3(b). Table 1 lists the device characteristics
determined from the figure.
Fig. 3. (a) EQE spectra of the two MQW solar cells with the incident power density at λ = 380
nm fixed at 5 W/m2. (b) J-V curves under AM 1.5G for the solar cells with 15% and 25%
indium compositions.
Table 1.
The device characteristics determined from Fig. 3(b).
In (%)
15%
25%
Jsc (mA/cm2)
1.05
0.85
Voc (V)
2.30
1.86
FF (%)
63
28
η (%)
1.52
0.44
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Figure 4 presents the peak EQE at 380 nm of the two solar cells with the incident power
densities (at 380 nm) increasing from 5.0 W/m2 to 6.1 W/m2. The two solar cells exhibit very
different photoelectric characteristics: the device with 25% indium shows increased EQE
from 5.0 W/m2 to 5.2 W/m2 and remains fairly unchanged for higher power densities, whereas
the one with 15% indium gains a little EQE initially, but loses noticeable efficiencies from
5.2 W/m2 to 5.7 W/m2 and picks up the EQE again afterwards. The distinctive EQE dip
observed on the 15%-indium device can be analyzed with the rate equation in the MQW:
dn
= G − An − Bn 2 − Cn3 − E
dt
(1)
where n is carrier concentration; G is the generation rate being proportional to the incident
power densities; A, B, and C are the coefficients of Shockley-Read-Hall (SRH) nonradiative
recombination, spontaneous radiative recombination, and Auger nonradiative recombination,
respectively; E is the rate of carrier flow out of the quantum wells through thermionic
excitation or insufficient quantum confinement, being contributive to the photocurrents (and
thus EQE) of the solar cell. Equation (1) suggests that the rise and sink of EQE seen in Fig. 4
is dictated by the competition between E and the recombination terms (A, B, C). Since the
excitation power densities during the measurement are very low, Auger recombinations
within the MQW should be insignificant according to the studies by Shen et al. [30]. Further,
it is believed that the SRH recombination, compared with radiative recombination, is less
likely to cause the EQE sag seen in the figure. The premise is based on two considerations: i)
as n is increased by the higher excitation power density, the n2 dependence of radiative
recombination should make the term Bn2 dominates over An in Eq. (1). ii) If the defectinduced SRH recombination is the reason for the sink of EQE, the efficiency dip should take
place in the MQW with higher indium content, i.e. 25%, whose A coefficient is larger than
that of the MQW with 15% indium because of the larger lattice mismatch between the well
(InGaN) and the barrier (GaN). However, the EQE dip occurs in the MQW with 15% indium
(fewer defect density), indicating that crystal defects are not the main culprit for the sagging
efficiency.
Fig. 4. The measured EQEs at λ = 380 nm as a function of incident power density for the two
MQW solar cells.
Summarily, the meandering of EQE with increased incident power can be explained with
the simplified equation:
dn
≈ G − Bn 2 − E
dt
(2)
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A detailed mechanism can be visualized as follows: upon photo-illumination, electrons/holes
are generated and confined in the quantum wells. The confined carriers can be further excited
out of the wells, swept by the junction field, and collected by the electrodes, making
contribution to EQE. Alternatively, the carriers can also be lost through radiative
recombination, producing photons and thus resulting in the decreased EQE. Whether EQE is
dominated by radiative recombination or photocurrent excitation is closely related to the
dependence of B and E on indium composition of the MQW. In the quantum wells with 15%
indium, carrier concentration rises when the incident power density increases, and the much
more efficient radiative recombination [compared to the other device, as depicted in Fig. 1(a)]
quickly consumes the confined carriers, giving rise to the EQE dip seen at 5.7 W/m2. As the
incident power density increases further, electron-hole pairs are continuously pumped into the
wells and fill up the discrete energy levels, making it easier for the carriers to be excited out
of the wells and thus adds more photocurrents, leading to the increased EQE.
Carrier dynamics in the MQW with 25% indium can be dramatically different. The
increased indium composition results in severer QCSE, which greatly lowers the radiative
recombination rate by spatially separating electrons and holes, making the Bn2 term less
competitive than E in Eq. (2). Moreover, it has been found that increasing indium content in
the MQW tends to induce compositon fluctuations in the InxGa1-xN alloy [18,20]. The indium
fluctuation gives rise to the shallow quantum wells with the band gap energies close to that of
the barriers. Carriers trapped in these shallow wells can be easily excited, either thermally or
optically, over the barrier height, and generate additional photocurrents. Our studies with
scanning transmission electron microscopy has revealed that the 25%-indium MQW contains
much more shallow wells than the one with 15% indium [28]. The strong QCSE and inferior
carrier confinement are believed to be the main factors leading to the less apparent EQE dip
seen with the high-indium-content MQW.
In order to theoretically compare the EQE of the MQW solar cells, the output
photocurrents from the two devices were calculated by solving self-consistent 1D Poisson and
drift-diffusion equations [31]. In the calculation, an ideal MQW structure is assumed and
QCSE is considered by setting the polarization-induced charges at the GaN/InxGa1-xN
interfaces to be 1.6 × 1013 and 2.2 × 1013 cm−2 for x = 0.15 and 0.25, respectively [31]. SRH
nonradiative carrier lifetime (τnr) in the MQW is 150 ns for x = 0.15 and 110 ns for x = 0.25
[31]. Figure 5 presents the simulated EQE values at λ = 380 nm as a function of power
density for the two solar cells. One can see the simulated EQEs for the MQW with 25%
indium are higher than the measured values, which can be due to the unideal carrier collection
of the real device. More importantly, the EQE curves of the two devices exhibit opposite
trends as the power density increases. For the MQW with 25% indium, the EQE gradually
increases with more incident photons, telling that carrier consumption in the quantum wells is
dominated by photocurrent generation. On the other hand, the EQE with 15% indium
decreases at higher power densities, indicating that the carrier loss due to radiative
recombination outweighs photocurrent generation. Nevertheless, the EQE dip observed in
Fig. 4 is not seen in the calculated results. One of the main reasons is the inhomogeneous
distribution of indium composition in the MQW, which is not considered in the simulation
and can significantly change the carrier densities in the MQW. As mentioned earlier, the
immiscibility of InN and GaN usually leads to localized regions with the indium composition
considerably higher or lower than the nominal value, and this can greatly influence the
measured EQE values through the photocurrents generated from the localized regions. The
randomly distributed indium fluctuation has been shown to play vital roles in carrier
transportation in InGaN-based MQWs and should be treated with sophisticated methods [32].
Although the measurement results are not fully repeated by the simulation, the presented
theoretical analysis shows that the radiative recombination in the active region can adversely
affect the EQE of InGaN/GaN MQW solar cells.
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Received 18 Aug 2014; revised 27 Sep 2014; accepted 4 Oct 2014; published 29 Oct 2014
(C) 2014 OSA
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Fig. 5. Simulated EQE curves at λ = 380 nm as a function of incident power density for the
MQW solar cells with 15% and 25% indium.
4. Conclusion
The dipping behavior of EQE exhibited by InGaN-based MQW solar cells is observed and
theoretically analyzed. It is found the dip effect is apparent with the MQW containing 15%
indium, and become less obvious when the indium percentage goes up to 25%. The result is
attributed to two competing terms in the rate equation describing carrier dynamics in the
MQW, i.e. radiative recombination and photocurrent excitation. The investigation presented
here is an important step toward unfolding the photovoltaic behaviors of MQW structures.
Acknowledgments
The research was supported in part by National Science Council (102-2221-E-008-074, 1022628-M-002-006-MY3 and 101-2221-E-002-115-MY2), National Taiwan University
(103R7823), the Aim for the Top University Project of National Central University
(103G903-2), and Energy Technology Program for Academia, Bureau of Energy, Ministry of
Economic Affairs (102-E0606).
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(C) 2014 OSA
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