2016 - APL - Monroy - Dependence of the photovoltaic performance of pseudomorphic InGaN MQWs

Dependence of the photovoltaic performance of pseudomorphic InGaN/GaN multiple-
quantum-well solar cells on the active region thickness

Anna Mukhtarova, Sirona Valdueza-Felip, Luca Redaelli, Christophe Durand, Catherine Bougerol, Eva Monroy,
and Joël Eymery
Citation: Applied Physics Letters 108, 161907 (2016); doi: 10.1063/1.4947445
View online: http://dx.doi.org/10.1063/1.4947445
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/108/16?ver=pdfcov
Published by the AIP Publishing
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APPLIED PHYSICS LETTERS 108, 161907 (2016)

Dependence of the photovoltaic performance of pseudomorphic InGaN/GaN
multiple-quantum-well solar cells on the active region thickness

Anna Mukhtarova,1,2,a) Sirona Valdueza-Felip,1,2,a) Luca Redaelli,1,2 Christophe Durand,1,2
Catherine Bougerol,1,3 Eva Monroy,1,2 and Joe€l Eymery1,2,b)

1Universite Grenoble Alpes, 38000 Grenoble, France
2CEA-CNRS group “Nanophysique et semiconducteurs”, CEA-INAC-PHELIQS, 17 av. des Martyrs,
38054 Grenoble, France
3CEA-CNRS group “Nanophysique et semiconducteurs”, Institut Neel-CNRS, 25 av. des Martyrs,
38042 Grenoble, France

(Received 22 February 2016; accepted 12 April 2016; published online 22 April 2016)

We investigate the photovoltaic performance of pseudomorphic In0.1Ga0.9N/GaN multiple-
quantum well (MQW) solar cells as a function of the total active region thickness. An increase in
the number of wells from 5 to 40 improves the short-circuit current and the open-circuit voltage,
resulting in a 10-fold enhancement of the overall conversion efficiency. Further increasing the
number of wells leads to carrier collection losses due to an incomplete depletion of the active
region. Capacitance-voltage measurements point to a hole diffusion length of 48 nm in the MQW
region. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4947445]

InGaN alloys exhibit many favorable features for photo- to continue improving the efficiency of InGaN-based devi-
ces, Young et al.6 investigated the influence of a front-side
voltaic applications such as a direct bandgap tunable in all
anti-reflective coating and a back-side dichroic mirror on
the visible spectrum range, large absorption coefficient, and
superior radiation resistance.1 In spite of these advantages, structures containing a 30 period In0.2Ga0.8N/GaN (3/4 nm)
MQW grown on bulk (0001) GaN substrates. The applica-
some challenges have to be overcome to develop efficient
tion of these optical coatings increased the initial peak exter-
InGaN-based photovoltaic devices. One of the most impor-
nal quantum efficiency (EQE) by 56% and conversion
tant is the structural degradation of InGaN layers with high
In content due to alloy inhomogeneity and misfit relaxation.2 efficiency by 37.5% under 1 sun AM0 equivalent illumina-

To circumvent this problem, the use of multiple quantum tion. Regarding the design of the active region, many groups

wells (MQWs) instead of thick InGaN layers can delay have focused on the optimization of the photovoltaic per-
the strain relaxation related to dislocation formation.3
Furthermore, the MQW architecture enables independent formance of the InGaN/GaN MQW solar cells by changing
control of the short-circuit current Jsc and the open-circuit the quantum well thickness,11 the barrier thickness,12–14 the
voltage Voc in a solar cell structure:4 the barrier material with In mole fraction of the wells,8 and the number of quantum
larger bandgap determines Voc, while the optimization of the wells,7,15,16 but mainly up to 50 MQWs.
width and depth of the quantum wells (QWs) allows tuning
the absorption, hence the short-circuit current Jsc. In this letter, we study the influence of active region

Several groups have investigated the photovoltaic per- thickness on the photovoltaic performance of In0.1Ga0.9N/GaN
(1.3/8.7 nm) MQW solar cells. The well thickness (1.3 nm)
formance of InGaN/GaN MQW solar cells during the last
decade.5–10 Yamamoto et al. investigated the photovoltaic and In composition (10%) are specifically chosen to avoid the
characteristics of InGaN-MQW-based solar cells under con-
centration conditions, showing a Voc ¼ 1.9 V, Jsc ¼ 510 mA/ degradation of the photovoltaic properties associated with
cm2, and fill factor FF ¼ 70%, leading to an overall power lattice-mismatch strain relaxation.11,16 The evolution of the
conversion efficiency of g ¼ 3.4% under 200 suns of AM1.5
illumination at room temperature.9 More recently, Liu et al.5 conversion efficiency is measured as a function of the number
demonstrated devices with record efficiencies under 1 of quantum wells in the active region (Nw ¼ 5, 15, 30, 40, 60,
and 100). Efficiency saturation for samples with more than 40
sun (AM1.5) based on 20 periods of In0.23Ga0.77N/GaN
(3/10 nm) quantum wells grown on patterned sapphire sub- wells is explained by an incomplete depletion and an increase

strates without top antireflection coating. They reported pho- in carrier recombination in the active region. Calculations
tovoltaic characteristics of Voc ¼ 1.89 V, Jsc ¼ 3.92 mA/cm2,
fill factor FF ¼ 50.96%, and efficiency of g ¼ 3.77%. based on capacitance-voltage measurements allow the estima-
However, in this work, the authors show neither evidence
tion of the hole diffusion length in the MQW region.
explaining why the most efficient device has a much lower
reverse dark current than its counterparts, nor they show the Junctions containing an InGaN/GaN MQW active

spectral photoresponse of the solar cells. On the other hand, region with different number of wells were grown by metal-

a)A. Mukhtarova and S. Valdueza-Felip contributed equally to this work. organic vapor phase epitaxy on 2-inch c-plane sapphire sub-
b)Email: [email protected] strates (0.25 off-cut) with a closed coupled showerhead

reactor. The sample structure, depicted in Fig. 1(a), consists
of a 1.8 lm unintentionally doped GaN buffer layer with re-
sidual doping of about 3 Â 1016 cmÀ3 and dislocation density
of about 2 Â 108 cmÀ2, followed by a 3.6 lm-thick Si-doped
n-GaN layer (n ffi 6 Â 1018 cmÀ3) and a highly doped 10 nm-
thick nþ-GaN layer (n ffi 1 Â 1019 cmÀ3). The active region
includes 5–100 non-intentionally doped In0.1Ga0.9N/GaN

0003-6951/2016/108(16)/161907/5/$30.00 108, 161907-1 Published by AIP Publishing.

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161907-2 Mukhtarova et al. Appl. Phys. Lett. 108, 161907 (2016)

FIG. 1. (a) Schematic diagram of the p-i-n InGaN/GaN solar cell structure.
(b) HR-TEM image of a few In0.1Ga0.9N/GaN quantum wells in sample S100.

(1.3/8.7 nm) MQWs, as summarized in Table I (samples FIG. 2. X-ray reciprocal space map around the (1 À1 0 5) Bragg peak for
the samples containing (a) a 30-period In0.1Ga0.9N/GaN MQW (S30), and
S5-S100). Nominal growth temperatures of the wells and (b) a 100-period In0.1Ga0.9N/GaN MQW (S100). Qx and Qz are the recipro-
barriers were set to 750 and 900 C, respectively, and the cal space vectors in A˚ À1.

pressure is set to 400 mbar (see experimental conditions in probe signal. An Agilent 4155C semiconductor parametri-
cal analyzer recorded the current density vs. voltage (J–V)
Ref. 17). The MQW region is capped with 60 nm of characteristics.
Mg-doped p-GaN with NA ffi 4 Â 1018 cmÀ3 acceptor density
estimated from capacitance-voltage measurements.18 The Figure 1(b) presents a high-resolution transmission elec-
tron microscopy (HR-TEM) image of the MQW structure in
root-mean-square roughness measured by atomic force mi- the active region of the sample with 100 quantum wells
croscopy on a 5 Â 5 lm2 surface is below 1.5 nm for all sam- (S100), showing well-defined wells with sharp interfaces.
ples.18 The MQW period thickness, strain state, and In For all samples, the MQW period was extracted from the
inter-satellite distance in the x-2h X-ray scan along the
content were analyzed by high-resolution X-ray diffraction (0002) symmetric reflection of the MQW (see results in
Table I). Figure 2 shows the reciprocal space maps around
using a Seifert XRD 3003 PTS-HR system with a beam con- the (1–105) asymmetric reflection for the samples with 30
(S30) and 100 (S100) quantum wells. For all samples, the
centrator before a Ge(220) four-bounce monochromator, and GaN and MQW asymmetric reflection peaks are aligned
along Qz, which confirms the pseudomorphic growth within
a Ge(220) two-bounce analyzer in front of the detector. the experimental error bars (the maximum error of the relax-
ation parameter defined in Ref. 11 is estimated to be 640%).
All samples were processed into solar cells with two Assuming a pseudomorphic growth of the MQWs on the
device sizes (1 Â 1 and 0.5 Â 0.5 mm2) [see the schematic GaN buffer layer (biaxial strain) and the values of the well
design in Fig. 1(a)]. Ohmic contacts to n-GaN were formed and barrier thicknesses deduced from HR-TEM measure-
ments, the In content in the quantum wells is estimated to be
around the perimeter of the mesa by electron-beam evapo- 10 6 2%.19,20

ration of Ti/Al/Ni/Au (30/70/20/100 nm). The p-GaN con- Figure 3 presents the spectral dependence of the external
quantum efficiency (EQE) of these solar cells. The EQE was
tacts consist of a semitransparent layer of Ni/Au (5/5 nm) evaluated as: EQE ¼ (Jop/Pop)Á(ht/q), where Jop is the photo-
annealed in O2 and a 130 nm-thick Ni/Au grid with 5 lm current density, Pop is the optical power density, q is the
wide fingers spaced by 150 lm. The devices do not incor- elementary charge, h is the Planck’s constant, and t is the
frequency of the incident light. The peak of MQW EQE
porate any metal back reflector or antireflection coating.

External quantum efficiency measurements were per-

formed at room temperature exciting with a 450 W Xe-arc

lamp coupled to a Gemini-180 double monochromator for
the ultraviolet spectral range (250À400 nm), and with a
1000 W halogen lamp coupled with an Omni Lambda 300
monochromator for the visible range (360À700 nm). A
He-Cd laser (k ¼ 325 nm) was used to calibrate the photo-
current versus the optical power. Capacitance-voltage
(CÀV) measurements were performed with an Agilent
4284A LCR meter, using a 1 kHz, 100 mV (peak-to-peak)

TABLE I. Experimental values of the structural properties and photovoltaic performance of In0.1Ga0.9N/GaN multiple-quantum well solar cells: number of
quantum wells (Nw), superlattice period (TSL), total thickness of the quantum well region (HSL), external quantum efficiency (EQE), open-circuit voltage
(Voc), short-circuit current (Jsc), fill factor (FF), and overall conversion efficiency (g) under 1 sun AM1.5 G equivalent illumination.

Sample QW number (NW) TSL (nm) HSL (nm) EQE at 380 nm (%) Voc (V) Jsc (mA/cm2) FF (%) g (%)

S5 5 10.0 50 4 1.6 0.11 54 0.09
S15 15 9.6 144 16 1.8 0.24 56 0.24
S30 30 9.7 291 38 2.1 0.42 54 0.48
S40 40 10.3 412 36 2.4 0.63 56 0.85
S60 60 10.6 636 31 2.3 0.68 56 0.88
S100 100 10.7 1070 24 1.9 0.68 60 0.78

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161907-3 Mukhtarova et al. Appl. Phys. Lett. 108, 161907 (2016)

FIG. 3. Spectral response and reverse dark current Jd (inset) of the InGaN/
GaN MQW solar cells with different number of quantum wells (Nw). The
growth and device realization of (S5, S15, and S30) and (S40, S60, and

S100) have been done in two different batches.

increases from 4% to 38% with the number of periods (from FIG. 4. (a) Current density–voltage characteristics of the InGaN/GaN solar
5 to 30), in agreement with literature values.15,16 The EQE cells with different number of wells (Nw) under 1 sun of AM1.5G equivalent
increase is attributed to the enhancement of the absorption in illumination. Dependence of the (b) open-circuit voltage, (c) fill factor, (d)
thicker active regions. Further enlargement of the active short-circuit current density, and (e) conversion efficiency on thickness of
region results in a saturation of the EQE, falling down to the MQW-region. Dotted lines are guidelines for the eye.
24% for the sample with Nw ¼ 100 (S100), which points out
losses in collection efficiency in spite of the enhanced In order to investigate the reason of the saturation of the
absorption. short-circuit current Jsc for a number of quantum wells larger
than 40, we estimate the depletion width in our samples by
A slight red shift of the spectral response is observed measuring the capacitance C of large cells (1 Â 1 mm2) at
when increasing the number of wells. This result cannot be 0 V. In a simple p-i-n junction, the depletion width is inver-
justified by a change of the electric field distribution in the sely proportional to the capacitance, following the equation
structure with the number of MQWs. The most probable
explanation would be a slight enhancement of the In incorpo- w ¼ eoerA=C;
ration and/or barrier thickness along the growth axis (within
the X-ray diffraction measurement error bars) that might be where w is the width of the depletion region, A is the area of
related to a temperature gradient or to the onset of relaxation the solar cell, eo is the vacuum permittivity, and er is the rela-
for very long growth times. tive permittivity of the semiconductor (here erGaN ¼ 8.9). For a
number of up 30 quantum wells, the calculated depletion width
The dependence of the reverse dark current density Jd shown in Figure 5(a) is proportional to the MQW thickness,
on the reverse bias is presented in the inset of Fig. 3. The and we can suppose that all the MQWs are fully depleted. The
drop of the leakage current for samples with more QWs sug- maximum width of the depletion region is reached for 40 wells,
gests that the dislocation density does not significantly and it is estimated to be w ¼ 300 6 10 nm. For higher number
increase even for the thickest active region sample, since the of quantum wells, the depletion width saturates, indicating that
presence of dislocations generally results in an enhancement an increasingly large part of the MQW is not depleted. This
of the leakage current.21 leads to an enhanced recombination of the carriers in the non-
depleted part of the MQW region, decreasing the carrier collec-
The J-V characteristic of the samples under 1-sun illumi- tion for active regions with thicknesses above $300 nm, in
nation using an AM1.5G solar simulator (1 sun ¼ 1 kW/m2) is accordance with EQE measurements.
presented in Fig. 4(a). The open-circuit voltage Voc increases
monotonously from 1.4 to 2.4 V with the number of quantum
wells (Fig. 4(b)), whereas the fill factor does not present a
clear trend, remaining around 54%–56% (Fig. 4(c)). On the
other hand, the short-circuit current Jsc (Fig. 4(d)) increases
with the number of wells in agreement with the EQE results
shown in Figure 3, saturating at about 0.68 mA/cm2 for 40–60
MQWs. This variation has a direct impact on the conversion
efficiency (Fig. 4(e)), calculated as g ¼ (VocJscFF)/Pin, which
is improved by one order of magnitude when increasing the
number of quantum wells from 5 to 60 (gmax ¼ 0.88%).

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161907-4 Mukhtarova et al. Appl. Phys. Lett. 108, 161907 (2016)

similar to S100. However, further increasing the bias the
slope decreases, indicating that the depletion region starts
extending into the doped layers. The absence of a sharp
change in the slope might point to a gradient in the MQW
doping in the vicinity of the intentionally doped layers, pos-
sibly due to Si diffusion into the MQW.

The photoresponse of the cells for wavelengths below
the GaN bandgap (>360 nm) is due to photogeneration and
carrier collection in the MQW region. In solar cells with
fully depleted MQW (S5–S30), the photogenerated carriers
are collected due to the electric field. The drift current, Jdrift,
can be expressed as

Jdrif t ¼ q TkU0ð1 À eÀaxd Þ; (1)

where Tk is the optical transmission towards the MQW
(including losses due to the semitransparent contact and the

topmost p-type layer), U0 the incident flux density, a the
absorption coefficient (ffi105 cmÀ1), and xd the absorption
thickness of the depletion region. Assuming that Jsc ¼ Jdrift
and taking into account the values of Jsc from Table I, the
value of the q TkU0 ¼ 14.7 6 1.7 A cmÀ2 factor can be

extracted (the error bar corresponds to the different estima-

tions based on the samples S5, S15, and S30).

For samples with thicker active regions (S60 to S100),

the MQW region is only partially depleted, as schematically

described in the inset of Fig. 5(a). However, carriers photo-

generated beyond the depletion region can still diffuse and be

collected, generating a diffusion current Jdiff ¼ qTkU0eÀaxd

½aLp=ð1 þ aLpފ that must be taken into account to calculate
the total generated photocurrent22

Jsc ¼ Jdrif t þ Jdif f ¼ qTk U0 À 1 eÀaxd (2)
1 þ aLp ;

FIG. 5. (a) Depletion region width as a function of the thickness of the where Lp is the minority carrier (hole) diffusion length in
MQW-region in the InGaN/GaN solar cells. Inset: Schematic of the electric the MQWs. Using the values of Jsc from Table I for S60 and
field distribution in partially depleted p-MQW-n diode, where the MQW is S100 and taking into account the estimated factor q TkU0
weakly (non-intentionally) n-doped. (b) 1/C2 as a function of the applied (14.7 6 1.7 A/m2), we can deduce the Lp $ 48 6 6 nm. As
bias, V. S5 is measured only until À5 V because of the very high electrical expected, this value is significantly lower (by at least a factor of
field across the junction, which is close to the GaN breakdown field.
4) than the minority carrier diffusion length parallel to the c-axis
In a p-i-n junction, applying a negative bias should measured by electron beam induced current in doped GaN.23
result in an increase of the depletion region width w and
hence in a decrease of the capacitance C of the cell. In Fig. In summary, we have investigated the dependence of the
5(b), the squared inverse capacitance (1/C2), of samples S5,
S60, and S100 is plotted as a function of bias. From the slope photovoltaic performance of In0.1Ga0.9 N/GaN (1.3/8.7 nm)
of these curves, we can extract the net dopant concentration MQW solar cells as a function of the number of wells
of the layer into which the depletion region is extending.12 (5À100, active region thickness of $50À1000 nm) for pseu-
For S5, since the MQW is already fully depleted at 0 V, domorphic structures grown on GaN-on-sapphire specifically
increasing the negative bias causes the depletion region to
gradually extend into the p- or n-doped layers. Consistently, designed to limit strain relaxation and structural defect forma-
the net dopant concentration obtained from the slope of the
curve in Fig. 5(b) is 3.3 Â 10À18 cmÀ3. For S100, the MQW tion. Increasing the number of wells from 5 to 40 significantly
region is thicker than the depletion region at zero bias; as a
consequence, the 1/C2 curve is much steeper, and its slope improves the photovoltaic characteristics (Voc, Jsc), resulting
corresponds to a dopant concentration of 2.6 Â 10À16 cmÀ3, in an enhancement of the conversion efficiency by a factor of
comparable to the expected residual doping in the MQW. 10 (gmax $ 0.9). In spite of the absence of strain relaxation in
For S60, the MQW region is thicker than the depletion these samples, a saturation of Jsc (and hence of g) is measured
region at zero bias; thus, at low bias, the slope of the curve is for cells with active regions above 40 MQWs. This feature

is attributed to carrier collection losses and increased recombi-

nation in the MQW region associated with its incomplete

depletion. A hole diffusion length inside the MQW region of
about 48 6 6 nm is estimated from diffusion and drift current

equations taking into account the depletion width value

extracted from cell capacitance measurements.

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161907-5 Mukhtarova et al. Appl. Phys. Lett. 108, 161907 (2016)

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