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0.7-eV GaInAs Junction for a 

GaInP/GaAs/GaInAs(1-eV)/ 

GaInAs(0.7-eV) Four-Junction 

Solar Cell 

Preprint 

D.J. Friedman, J.F. Geisz, A.G. Norman, 

M.W. Wanlass, and S.R. Kurtz 

Presented at the 2006 IEEE 4th World Conference on 

Photovoltaic Energy Conversion (WCPEC-4) 

Waikoloa, Hawaii 

May 7–12, 2006 

Conference Paper 

NREL/CP-520-39913 

May 2006 
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0.7-eV GaInAs JUNCTION FOR A GaInP/GaAs/GaInAs(1eV)/GaInAs(0.7eV) 

FOUR-JUNCTION SOLAR CELL* 

D.J. Friedman, J.F. Geisz, A.G. Norman, M.W. Wanlass, and S.R. Kurtz 

National Renewable Energy Laboratory, Golden, CO 80401 USA 

ABSTRACT 

We discuss recent developments in III-V multijunction 

solar cells, focusing on adding a fourth junction to the 

Ga0.5In0.5P/GaAs/Ga0.75In0.25As inverted three-junction cell. 

This cell, grown inverted on GaAs so that the latticemismatched Ga0.75In0.25As third junction is the last one 

grown, has demonstrated 38% efficiency, and 40% is 

likely in the near future. To achieve still further gains, a 

lower-bandgap GaxIn1-xAs fourth junction could be added 

to the three-junction structure for a four-junction cell 

whose efficiency could exceed 45% under concentration. 

Here, we present the initial development of the GaxIn1-xAs 

fourth junction. Junctions of various bandgaps ranging 

from 0.88 to 0.73 eV were grown, in order to study the 

effect of the different amounts of lattice mismatch. At a 

bandgap of 0.88 eV, junctions were obtained with very 

encouraging ~80% quantum efficiency, 57% fill factor, and 

0.36 eV open-circuit voltage. The device performance 

degrades with decreasing bandgap (i.e., increasing lattice 

mismatch). We model the four-junction device efficiency 

vs. fourth junction bandgap to show that an 0.7-eV fourthjunction bandgap, while optimal if it could be achieved in 

practice, is not necessary; an 0.9-eV bandgap would still 

permit significant gains in multijunction cell efficiency while 

being easier to achieve than the lower-bandgap junction. 

INTRODUCTION 

The past few years have seen the introduction 

(sometimes reintroduction) of a variety of III-V 

multijunction solar cell structures with the potential for very 

high efficiencies. These approaches include monolithic [1-

7], mechanical [8-10], and wafer-bonding schemes [11] for 

stacking the junctions, which may be grown latticematched [1-5] or lattice-mismatched [4,6,7] to their 

substrates. One such new device is the 

Ga0.5In0.5P/GaAs/Ga0.75In0.25As three-junction cell [12], 

grown inverted so that the 1-eV Ga0.75In0.25As junction, 

which is lattice-mismatched to the GaAs substrate, is 

grown last. This cell has demonstrated an efficiency of 

37.9% at 10 suns concentration. The device that 

demonstrated this efficiency had room for further 

optimization of current-matching and series resistance, 

with further incremental improvements expected to bring 

the efficiency above 40%. This device structure is 

illustrated in Fig. 1(a) as grown. A key part of the structure 

is the GaxIn1-xP grade, whose transparency to the light 

intended for the GaxIn1-xAs junction is necessary for the 

operation of the cell. After growth of the structure, the 

Ga0.75In0.25As-junction back side of the structure is bonded 

to a foreign substrate, and the original GaAs substrate is 

removed. 

junction

(1.0 eV)

Ga In As 0.75 0.25

Ga In P x 1-x

grade

GaAs

junction

(1.42 eV)

Ga In P 0.5 0.5

junction

(1.85 eV)

GaAs

substrate

lattice-mismatched

to GaAs

GaAs

substrate

(a) 3J structure (b) 4J structure (c) 4th junction test structure

GaAs

junction

(1.42 eV)

Ga In P 0.5 0.5

junction

(1.85 eV)

GaAs

substrate

Ga In P x 1-x

grade

junction

(1.0 eV)

Ga In As 0.44 0.56

junction

(1.0 eV)

Ga In As 0.75 0.25

Ga In P x 1-x

grade

Ga In P x 1-x

grade

junction

(0.73-0.88eV)

Ga In As x 1Šx

simul. junction

(1.0 eV)

Ga In As 0.75 0.25

Ga In P x 1-x

grade

Fig. 1. Schematics of the device structures. The drawings are not 

to scale, and elements such as tunnel junctions and contact 

layers are not shown. Cross-hatching indicates substrate 

removed after growth. (a) Three-junction structure. (b) Proposed 

extension to four junctions. (c) Test structure, omitting the three 

higher-bandgap junctions while accounting for the mechanical 

effect of the Ga0.75In0.25As third junction. As discussed below in 

the text, we will later consider a variant of the (a) and (b) 

structures in which the bandgaps of the junctions below the 

GaInP junction are allowed to vary. 

Once this device is fully optimized, one option for 

further efficiency improvement in a future generation of 

devices based on this structure is to add a fourth junction 

of GaxIn1-xAs with a bandgap of approximately 0.7 eV, as 

illustrated in Fig. 1(b). (Indeed, a very general device 

structure incorporating an arbitrary number of latticemismatched junctions has been described by Wanlass 

[patent pending].) At a concentration of 500 suns, such a 

junction would contribute an additional 5% (absolute) 

*This work has been authored by employees of the Midwest 

Research Institute under Contract No. DE-AC36-99GO10337 with 

the U.S. Department of Energy. The United States Government 

retains and the publisher, by accepting the article for publication, 

acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do 

so, for United States Government purposes.

1
efficiency for an overall real-world efficiency that could 

exceed 45%. 

The challenge in adding an 0.7-eV fourth junction is its 

large lattice mismatch with the original GaAs substrate, 

which at 4% is twice the 2% lattice mismatch of the 1-eV 

third junction. It is likely that increasing lattice mismatch 

will be accompanied by increasing difficulty of making 

epilayers of the high quality required for a solar cell; note 

however that very good InP/GaAs cells, having the same 

4% degree of mismatch, have been obtained using 

GaInAs grades [13]. Here, we present the initial 

development of the fourth junction. We study its device 

properties experimentally as a function of its bandgap (and 

therefore as a function of lattice mismatch). We also 

model the four-junction structure as a function of the 

fourth-junction bandgap, showing that high efficiencies are 

possible even with a fourth junction bandgap of 0.9 eV 

rather than 0.7 eV. 

DEVICE FABRICATION 

Device structures were grown by organometallic 

vapor-phase epitaxy. For this initial stage of development, 

a GaxIn1-xP grading-layer sequence including a terminating 

1-μm-thick buffer layer [12], and then a 2-μm-thick 1-eV 

isotype Ga0.75In0.25As layer, were first grown on a GaAs 

wafer. The isotype Ga0.75In0.25As layer simulates the 

presence of the 1-eV third junction. Then a second 

GaxIn1-xP grading sequence (followed, in one case 

discussed below, by an InxAs1-xP grade) was grown to 

grade from the lattice constant of the 1-eV Ga0.75In0.25As to 

the lattice constant of the (nominally) 0.7-eV GaxIn1-xAs 

junction. Finally the GaxIn1-xAs junction of interest was 

grown, with a 2-μm-thick p-type base and an 0.1-μm ntype emitter. While the junction will eventually be used in 

the inverted configuration, for simplicity these test 

structures were grown in upright configuration. The 

resulting structure, shown in Fig. 1(c), accounts for the 

effect of the lattice-mismatched growth on the properties 

of the low-bandgap GaxIn1-xAs junction, while bypassing 

the complexities of growth and measurement of the other 

three junctions, and the added steps of processing an 

inverted cell. 

Junctions of various bandgaps ranging, from 0.88 to 

0.73 eV, were grown in order to study the effect of the 

different amounts of lattice mismatch. For the lower end of 

the bandgap range, where it was necessary to grade to a 

larger lattice constant than InP, an In1-xAsxP grading layer 

was used for that final stage of the grade. 

RESULTS 

Figure 2 shows the internal quantum efficiencies (QE) 

for three variants of the device structure illustrated in Fig. 

1(c). For each device, the GaxIn1-xP composition was 

changed by the same amount in each grade step, but 

different numbers of grade steps were used in the different 

devices. As the number of grade steps is increased, the 

lattice mismatch to GaAs correspondingly increases, and 

the bandgap of the GaxIn1-xAs junction grown on the 

GaxIn1-xP grade structure decreases. The device with the 

lowest lattice mismatch, and a corresponding bandgap of 

0.88 eV, has a peak QE of about 80% as shown in curve 

(a). The base of this device is doped to 1017/cm3

 with a 

corresponding depletion width of only 0.1 μm, so the high 

QE is due to collection of carriers by diffusion and not 

field-aided collection. Fitting the QE to a standard QE 

model yields a diffusion length longer than the base 

thickness of 2 μm. 

1.0

0.8

0.6

0.4

0.2

0.0

Internal quantum efficiency

0.7 0.8 0.9 1.0 1.1

Energy (eV)

 MF943n4

 MG155n5

 MG244n8

0.77 eV 0.88 eV

band

gap

(eV):

0.73 eV

Fig. 2. Quantum efficiencies for GaxIn1-xAs junctions with 

bandgaps of (a) 0.88 eV, (b) 0.77 eV, and (c) 0.73 eV. The device 

IDs are indicated in the legend. 

This QE, while it is less than the ~95% QE needed to 

obtain the full efficiency boost desired in the four-junction 

structure, is a promising result. However, the 0.88-eV 

bandgap of this device needs to be lowered in order to 

produce the current needed for application under the 

1.85eV/1.4eV/1.0eV junctions above it. Curve (b) shows 

the QE for a device with more grade steps added to the 

graded layer, extending the grade all the way to the 

composition InP (i.e., GaxIn1-xP with the last step having 

x=0) for a resulting Ga0.5In0.5As-junction bandgap of 0.77 

eV. Compared to the higher-bandgap device, the QE for 

the 0.77-eV device is degraded, especially in its “red” 

response near the band edge. The degraded red 

response suggests a degraded base diffusion length; 

fitting to the QE model yields a base diffusion length of 1 

μm. 

The next step in characterizing the device performance 

of these junctions is the measurement of the currentvoltage (IV) curves under illumination. However, the 

choice of appropriate filtering of the incident illumination is 

not straightforward. We could test these devices under 1-

eV lowpass filter, which would quantify their performance 

under the overlying 1.85eV/1.4eV/1.0-eV junctions. These 

conditions give the lowest JSC for the device with the 

highest, 0.88 eV, bandgap. This tells us what we already 

knew, that a 0.88 eV bandgap is too high for use under a 

1-eV junction. Of greater interest, we want to quantify what 

the performance of the devices would be if they had the 

desired bandgap. For this purpose, it is more meaningful 

to pass to the junction all of the light in the spectrum with 

photon energies up to about 0.3 eV above the bandgap of 

the junction under test, as discussed further below. 

2
To see a full picture of the performance of these fourth 

junctions, we need to test them under both of these 

spectral filtering conditions. The most important effect of 

the spectral filtering on the IV curve is the light level. We 

therefore simulate the desired filtering conditions by 

computing the JSC for each device from its measured QE, 

numerically cutting off the spectrum at a photon energy 

about 0.3 eV above the device’s bandgap. More precisely, 

for a given fourth-junction bandgap, we calculate the 

corresponding bandgaps of the second and third junctions 

which would optimize the cell efficiency, as discussed 

below. These bandgaps are given in Table I as Opt. Eg2

and Opt. Eg3, respectively. We use the Eg3 energy as the 

cutoff for the numerical filter on the spectrum. 

To measure the IV curve of the device, we put a GaAs 

filter (i.e., a 1.4-eV low-pass filter) above the device as a 

first approximation to the desired filtering. We then put the 

device into short circuit, adjust the light level to the desired 

light level deduced from the QE, and then measure the IV 

curve. The fact that the actual spectral content of the 

illumination differs somewhat from what it would be under 

the filter is not expected to change the shape of the IV 

curve significantly. 

Table 1. Parameters characterizing the GaxIn1-xAs junctions 

studied. VOC, JSC, and FF are for the IV curves of Fig. 3. For a 

given fourth-junction bandgap Eg and a first junction with Eg=1.85 

eV, there are optimal bandgaps for the second and third 

junctions. These are taken from Fig. 7 and given in the table as 

Opt. Eg2 and Opt. Eg3, respectively. 

Device ID x Eg

(eV) 

VOC

(V) 

JSC

(mA/cm2

) 

FF 

(%) 

Opt.Eg2

(eV) 

Opt.Eg3

(eV) 

MF943n4 0.40 0.88 0.361 10.5 57 1.56 1.21

MG155n5 0.51 0.77 0.214 9.0 48 1.51 1.15

MG244n8 0.53 0.73 0.088 8.2 30 1.48 1.12

The dark and illuminated IV curves for the devices of 

Fig. 1, measured as described above, are shown in Fig. 3. 

The device with the lowest bandgap is badly shunted, but 

the two higher-bandgap devices are not. The device 

parameters for these devices from the IV curves of Fig. 

3(b) are summarized in Table I. Figure 4 shows 

graphically the dependence of VOC on bandgap. Also 

shown for comparison are data points for higher-bandgap 

devices with near-ideal GaAs-like behavior. The VOCs of 

the 0.88- and 0.77-eV fourth junctions fall below the line 

extrapolated from the GaAs-like near-ideal junctions by 

~100 mV, indicating an enhanced rate of minority-carrier 

recombination in the junction. The 0.73-eV device has a 

much more significantly degraded VOC. Because the 

difference in composition and strain between the 0.77- and 

0.73-eV devices is small, the significantly degraded 

behavior of the 0.73-eV device suggests that the In1-xAsxP 

grade step used in this device, at its present state of 

development, is not of the same quality as the GaxIn1-xP 

grade. 

10

5

0

-5Current (mA/cm2

)

-0.1 0.0 0.1 0.2 0.3 0.4

Voltage (V)

(a) 1-eV filter

 (simulated)

-10

-5

0

5

10Current (mA/cm2

)

-0.1 0.0 0.1 0.2 0.3 0.4

Voltage (V)

(b) optimal

 filter

 (simulated)

 device ID Eg(eV)

 MF943n4 0.88

 MG155n5 0.77

 MG244n8 0.73

Fig. 3. IV curves for the devices whose QEs are shown in Fig. 2. 

As described in the text, these curves were measured illuminating 

the devices with as much light as would be transmitted by a lowpass filter. For panel (a) the filter was set at 1 eV; for (b) the filter 

was set at the value tabulated as Opt. Eg3 in Table 1. 

1.5

1.0

0.5

0.0

VOC (V)

0.8 1.0 1.2 1.4 1.6 1.8

Eg (eV)

VOC

 measured

 extrapolated

GaInP

GaInAs

(for 4th junc)

GaInAs

GaAs

Fig. 4. VOC vs. bandgap for the GaInAs fourth junctions of Table I, 

compared to higher-bandgap devices that are closer to ideal. The 

dashed line is a fit to the higher-bandgap-device data. 

The composition and strain of the epilayers were 

studied by x-ray diffraction. Figure 5 shows the x-ray 

reciprocal space map for the 0.77-eV device. The 

compositions of the 1-eV simulated third junction and the 

0.77-eV fourth-junction GaxIn1-xAs layers as deduced from 

the reciprocal-space map are indicated, along with their 

strains as compared with the strain-free condition 

indicated by the diagonal line. These reciprocal-space 

maps are a powerful tool for optimizing the compositions 

and strain of the various mismatched layers of the 

structure. 

3
0.70

0.69

0.68

Qz (A o-1)

-0.495 -0.490 -0.485 -0.480

Qx (A o-1)

Ga0.76In0.24As (1 eV)

0.12% tensile strain

Ga0.49In0.51As (0.77 eV)

0.23% tensile strain

MG155

GaInP buffer

InP buffer

Fig. 5. X-ray reciprocal space maps for the Eg= 0.77 eV device. 

The compositions and strains for the GaxIn1-xAs layers are 

indicated. 

Figure 6 shows cross-sectional transmission electron 

microscopy (XTEM) images of the 0.88-eV GaInAs 

junction and the 1.0-eV GaInAs simulated junction for 

device MF943. The images show that the dislocations are 

largely confined to the GaInP grading layers. In these 

particular images, no dislocations are seen in the GaInAs 

layers, due to the extremely high magnification of the 

images compared to the threading dislocation density. 

GaxIn1-xAs (0.88 eV)

GaxIn1-xP grade

2 μm

-220DF

MF943

GaxIn1-xP buffer

(a)

Ga0.75In0.25As (1.0 eV)

GaxIn1-xP grade

2 μm

-220DF

MF943

GaxIn1-xP buffer

(b)

Fig. 6. XTEM images of (a) the 0.88-eV junction and (b) the 1.0-

eV simulated junction for device MF943. 

DISCUSSION 

The next steps in the development of this latticemismatched fourth junction will involve manipulation of the 

grading layer to improve the device performance by 

minimizing strain-generated structural defects. Such 

manipulation could include the number of steps used in 

the grade, but could also involve moving from GaxIn1-xP to 

alternative alloys for the grade material. 

Because the device data shown here indicate that it is 

increasingly difficult to get good device quality in the fourth 

junction with decreasing bandgap, it is worth asking 

whether a 0.7-eV bandgap is really necessary, or if a 

higher bandgap might suffice. A 0.7-eV fourth junction is 

called for if the bandgaps of the top three junctions are 

fixed at 1.85/1.42/1.0 eV. However, in practice it is 

possible to have the second-junction bandgap be higher 

than 1.42 eV while maintaining the desired latticematching to GaAs, by going to a GaInAsP composition. 

Likewise, the bandgap of the lattice-mismatched GaInAs 

third junction could easily be raised simply by not grading 

the lattice constant so far from that of GaAs.Ideally, the 

top-junction bandgap should also be raised, but this has 

proven challenging (although see [14]). For this reason 

and for simplicity, we compute for idealized junctions the 

optimal second- and third-junction bandgaps as a function 

of the fourth-junction bandgap, for a top-junction bandgap 

fixed at 1.85 eV. The junctions are optically thinned as 

necessary. The resulting optimal second- and thirdjunction bandgaps, and the corresponding four-junction 

device efficiency, are shown in Fig. 7 for illumination 

conditions of 500 suns under the low-AOD spectrum. 

1.6

1.4

1.2

1.0

junction bandgaps (eV)

0.7 0.8 0.9 1.0

4th junction band gap (eV)

55

54

53

52

51

50

efficiency (%)

2nd junction

3rd junction

Idealized 4-junction cell

500 suns, low-AOD spectrum

Top junction Eg=1.85 eV

2nd- and 

bandgaps

 efficiency (a)

(b)

3rd- junction

Fig. 7. (a) Four-junction device efficiency at 500 suns 

concentration, and (b) the corresponding optimal 2nd and 3rd 

junction bandgaps, for an idealized four-junction device with topjunction bandgap fixed at 1.85 eV. A finite reflectivity 

representative of a two-layer antireflective coat is assumed. 

The figure shows that raising the fourth-junction 

bandgap from 0.7 eV to 0.93 eV, while adjusting the 

second and third junction bandgaps to 1.56 and 1.21 eV 

respectively, results in an efficiency loss of only 1.5%. The 

reason for this is that there is very little light in the 

terrestrial spectrum between 0.8 and 0.9 eV due an to 

atmospheric absorption band that removes most of the 

light in that spectral range. Calculating the efficiency of the 

1.85/1.42/1.0-eV three-junction device in the same 

manner as for Fig. 7 gives an efficiency of 49%. Thus, 

there is 4% (absolute) efficiency to be gained by going 

from the three-junction to the four-junction structure with a 

fourth-junction bandgap of 0.9 eV, but only an additional 

1.5% (absolute) may be further gained by going to a 

fourth-junction bandgap of 0.7 eV. 

These calculations, motivated by the relative ease in 

fabricating a high-quality 0.9-eV junction compared to an 

0.7-eV junction, suggest that in practice the former may be 

the preferred realization of the four-junction structure. 

Furthermore, 0.9-eV GaInAs is much less mismatched to 

GaAs (mismatch ∆a/a0=2.8%) than is 0.7-eV GaInAs 

(mismatch ∆a/a0=3.9%). The larger lattice mismatch of the 

0.7-eV GaInAs would require a thicker grading layer, 

which would require more time to grow. The larger lattice 

4
mismatch would also increase the difficulty of mitigating 

bowing of the wafer due to residual strain in the epilayer. 

As an alternative to the four-junction structure, one 

may reexamine the three-junction structure, now 

considering the second- and third-junction bandgaps to be 

variable. As in the calculation in Fig. 7, we calculate the 

efficiency of this structure as a function of the third 

(bottom) junction bandgap, optimizing the second-junction 

bandgap while keeping the top junction fixed at 1.85 eV. 

The resulting efficiency and optimal second-junction 

bandgap are shown in Fig. 8. The results may be directly 

compared to Fig. 7, and for convenience the four-junction 

efficiency from Fig. 7 is shown in Fig. 8 as the dashed 

curve. The crosses on the efficiency and bandgap curves 

in Fig. 8 shows the 1.85/1.42/1.0-eV configuration. The 

figure shows that if the second-junction bandgap is 

lowered slightly to 1.34 eV, the efficiency increases by 

almost 2%. This is only half the efficiency gained by going 

to the four-junction structure with a 0.9-eV fourth junction; 

the total amount of lattice mismatch is no less; and the 

second junction would no longer be lattice-matched to 

GaAs. However, the three-junction structure is simpler and 

would require one less tunnel junction, so it may well be 

worth considering as an alternative or an intermediate step 

to the four-junction structure. 

1.5

1.4

1.3

junction band gaps (eV)

0.8 0.9 1.0 1.1

3rd junction band gap (eV)

52

50

efficiency (%)

48

X

X

Idealized 3-junction cell

500 suns, low-AOD spectrum

Top junction Eg=1.85 eV

2nd junction band gap

 efficiency (a)

(b)

3 junction

4 junction

Fig. 8. (a) Three-junction device efficiency at 500 suns 

concentration, and (b) the corresponding optimal second junction 

bandgap, for an idealized three-junction device with top junction 

bandgap fixed at 1.85 eV. A finite reflectivity representative of a 

two-layer AR coat is assumed. Also shown for comparison in (a) 

as the dashed curve is the four-junction efficiency from Fig. 7 (a). 

The crosses mark the 1.85/1.42/1.0-eV configuration. 

CONCLUSIONS 

We have grown GaxIn1-xAs junctions with bandgaps 

from 0.88 to 0.73 eV lattice-mismatched to GaAs, intended 

for use as the bottom junction of the four-junction 

extension of the GaInP/GaAs/ GaxIn1-xAs inverted solar 

cell. The 0.88-eV junction showed a QE of 80% without 

the use of field-aided carrier collection, a promising initial 

result. Making high-quality junctions becomes increasingly 

challenging with decreasing bandgap, suggesting that 

1.85/1.56/1.21/0.93 eV may be the preferred bandgap 

configuration. Real-world efficiency for such a device is 

projected to be near 45% under concentration. 

ACKNOWLEDGMENTS 

We thank C. Kramer, M. Young, and A. Kibbler for 

growth and processing support, and J. Kiehl for 

concentrator measurements. This work is supported or 

funded under DOE Contract No. DE-AC36-99GO10337. 

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