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Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Temperature-Dependent 

Measurements of an Inverted 

Metamorphic Multijunction 

(IMM) Solar Cell

Preprint

Myles A. Steiner, John F. Geisz, 

Daniel J. Friedman, Waldo J. Olavarria, 

Anna Duda, and Tom E. Moriarty

Presented at the 37th IEEE Photovoltaic Specialists Conference 

(PVSC 37)

Seattle, Washington

June 19-24, 2011

Conference Paper

NREL/CP-5200-50736

July 2011
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1 

TEMPERATURE-DEPENDENT MEASUREMENTS OF AN INVERTED METAMORPHIC 

MULTIJUNCTION (IMM) SOLAR CELL

Myles A. Steiner, John F. Geisz, Daniel J. Friedman, Waldo J. Olavarria, Anna Duda, and Tom E. Moriarty

National Renewable Energy Laboratory, Golden, CO 80401, USA

ABSTRACT

The inverted metamorphic multijunction (IMM) solar cell 

has demonstrated efficiencies as high as 40.8% at 25°C 

and 326 suns concentration. The actual operating 

temperature in a commercial module, however, is likely to 

be as much as 50-70°C hotter, reaching as high as 

100°C. In order to be able to evaluate the cell 

performance under these real-world operating conditions, 

we have measured the open-circuit voltage, short-circuit 

current density and efficiency at temperatures up to 

125°C and concentrations up to 1000 suns, as well as the 

temperature coefficients of these parameters. Spectral 

response and one-sun current-voltage characteristics 

were measured by carefully adjusting the incident 

spectrum to selectively current-limit the different subcells. 

Concentrator measurements were taken on a pulsed solar 

simulator to minimize any additional heating due to the 

high intensity illumination. We compare our measured 

values to predictions based on detailed models of various 

triple junction solar cells. By choosing the optimum 

bandgaps for high temperature operation, the IMM can 

potentially result in greater energy production and lower 

temperature sensitivity under real operating conditions 

than a Ge-based solar cell.

INTRODUCTION

The operating temperature of a solar cell is an important 

parameter for determining the conversion efficiency. 

Multijunction concentrator solar cells are typically 

evaluated under flash illumination at 25°C, but this 

standard measurement condition significantly 

underestimates the thermal load on the cell in an actual 

real-world module, where the steady-state concentrated 

illumination can raise the operating temperature to as high 

as 100°C. At elevated temperatures, the bandgaps of the 

subcells decrease which generally increases the 

photocurrent. At the same time, the open-circuit voltage 

(Voc) and the efficiency generally decrease. To maximize 

the efficiency under realistic temperatures, the bandgaps 

of the subcells should ideally be chosen based on 

modeling at those temperatures. The inverted 

metamorphic multijunction (IMM) solar cell has allowed 

designers to fabricate high-efficiency solar cells with 

bandgaps that approach the ideal combination, and 

laboratory prototypes have demonstrated efficiencies as 

high as 40.8% at 25°C and 326X [1,2]. Several 

companies are presently developing commercial versions 

of the IMM. Because of the freedom to choose the bottom 

subcell bandgap, the IMM has the capability, in principle,

of increasing the energy production under real operating 

conditions compared to Ge-based cells. Outdoor 

temperature measurements on lattice-matched Ge-based 

cells have been reported at both the cell level [3] and 

module level [4], and initial temperature-dependent results 

on aspects of epitaxial liftoff IMM cells were reported 

recently [5], but the efficiency of an IMM cell under

controlled conditions at elevated temperature and 

concentration has not been fully investigated. In this 

paper, we report on measurements of the conversion 

efficiency of a triple junction IMM solar cell at 

temperatures up to 125 °C and concentrations up to 1000 

suns. The cell studied here has bandgaps of {1.81, 1.40, 

1.00} eV and was described in detail in reference [1]. This 

combination is close to ideal at 25°C under the G173 

direct spectrum when the top two junctions are 

constrained to be lattice-matched Ga.51In.49P and GaAs.

EXPERIMENT 

The inverted structures were grown at NREL in an 

atmospheric pressure OMVPE reactor, and processed 

using standard cleanroom lithographic techniques applied 

to an inverted device [1,2]. The structure is grown with the 

top two subcells lattice-matched to the GaAs substrate, 

and with the top subcell thinned to 1 μm to try to match 

the photocurrent of the middle subcell. A transparent 

GaInP graded buffer then reduces the in-plane lattice 

constant to create a virtual substrate for the GaInAs 

bottom subcell. During processing, the structure was

bonded to a silicon wafer handle and the original GaAs 

substrate removed. A bilayer ZnS/MgF2 anti-reflection 

coating was deposited after fabrication. Cells were 

processed with a mesa area of 0.12 cm2 and an 

illuminated area of 0.10 cm2

. Numerous such cells have 

been fabricated at NREL and were screened at one-sun 

to find high-performing devices. Single junction isotype 

cells corresponding to the three subcells were also 

fabricated and measured. The isotype cell for a given 

subcell has the same structure in the active layer as the 

subcell and nominally the same filtering layers above but 

without p-n junctions.

To control the temperature during all measurements, a

gold-plated copper sample stage was mounted on a 

thermoelectric heater, powered by a Wavelength 

Electronics LFI-3751 controller. Temperature was 

monitored with a 10 kΩ thermistor that was embedded in 

the copper block, and the surface temperature was 

measured with a calibrated platinum-RTD surface probe. 

Data were collected at nominal ambient temperatures of 

25, 53, 85, 105 and 126 °C as determined by the surface 

probe. Temperatures were adjusted to within 0.5° on the 

various instruments.

Cells were carefully measured at different temperatures 

as follows: the spectral response of each subcell (and
2 

isotype) was measured at each temperature and then 

used in conjunction with calibrated reference cells to 

appropriately adjust the spectrum on a solar simulator. 

The simulator spectrum had to be re-adjusted for each 

temperature before the one-sun IV curves could be 

measured, and care was taken to regain the same 

temperature under the simulator as during the QE 

measurement. Note that the reference cells remained at 

25°C. Cells were then measured at high concentration 

under a flash simulator with the spectrum adjusted as 

much as possible for each temperature, and the 

concentrations were calculated using the one-sun shortcircuit current density for the appropriate temperature. We 

assume that the subcell photocurrent ratios at any 

particular temperature remain constant with concentration.

The experimental procedure outlined here ensures (as 

much as possible) that the observed temperature 

dependences of the Voc, Jsc, FF and efficiency reflect the 

interaction of the cell with the features of the reference 

spectrum rather than with the particular characteristics 

and idiosyncrasies of the simulator spectrum. This is 

especially true for Xenon-lamp-based simulators with 

strong emission peaks, though it also remains true for 

newer metal-halide-based simulators, for example [5].

Outdoor on-sun measurements can obviously come quite 

close to achieving the correct spectrum, though the air 

mass can vary widely over the course of the day, and 

taking measurements at high concentration requires 

special attention to the spectral effects and uniformity of 

the particular optics.

External quantum efficiency (EQE) measurements were 

taken with a combination of light-biasing and voltagebiasing, to properly measure the individual subcell QEs; 

LEDs at 465, 850 and 940 nm were used for the lightbiasing. One-sun current-voltage (JV) measurements 

were taken on a Spectrolab X25 multisource simulator. 

The single junction isotype cells were measured on a 

single source simulator.

The one-sun JV curves for the IMM were also measured 

separately on a single-source simulator with additional 

high-power collimated LED biasing lights, to selectively 

current-limit each of the junctions and measure the 

subcell JV curves. The limiting subcell was always

illuminated at nominally one-sun as determined by a 

matched set of calibrated reference cells, and the two 

other junctions were over-illuminated with LED light. 

Three separate curves are required at each temperature, 

limiting each of the top, middle and bottom junctions, and 

the total spectrum was determined for each illumination 

condition. The analysis of the data follows the general 

method of Kurtz et al. [6], with additional corrections for 

spectral mismatch between the temperature-dependent

EQE of the device and the 25°C EQE of the reference 

cells.

Concentrator measurements were taken on a Spectrolab 

pulsed solar simulator (HIPSS), where the lamp voltage 

was adjusted at each temperature to obtain the correct 

photocurrent ratio between the GaInP and GaAs subcells, 

based on the EQE. Raising the lamp voltage increases 

the spectral content in the UV range and damps out the 

spikes observed in the spectrum in the near-IR region. 

The intensity was controlled with a pair of apertures near 

the flash bulbs. With only one adjustable control on the

flash spectrum, precise matching of the photocurrent 

ratios between all three subcells is impossible, but we 

estimate the illumination of the bottom subcell to be ≤ 5% 

high, and the one-sun data indicate that the bottom 

subcell was never current-limiting.

RESULTS

Figure 1 shows the EQE measured at five temperatures. 

Each subcell plateaus at approximately 85% which 

includes a 6.7% shadow loss from the grid coverage and 

a ~3-5% reflection loss. The plateaus remain 

approximately constant as temperature increases, but the 

bandgap of each subcell decreases linearly with 

temperature, consistent with the Varshni model in this 

temperature range. The coefficients are listed in Table 1. 

The short-wavelength tails on the middle subcell EQEs 

appear to be real rather than measurement artifacts, and 

do not decrease in magnitude with changes in lightbiasing or voltage-biasing. We speculate that these tails 

result from photon coupling between the top and middle 

subcells [7]. We would expect the same effects to be 

present at short-circuit under a solar simulator, so the tails 

cannot be ignored when using the spectral response to 

adjust the simulator, as discussed below.

The short-circuit current densities (Jsc) at 1000 W/m2

, as 

measured on the single-source simulator with LED 

Figure 1 External quantum efficiency as a function 

of ambient temperature. The bandgaps at 25°C are 

1.81, 1.40 and 1.00 eV. The yellow curve is the G173 

direct spectrum at 1000 W/m2

. 

subcell d(Eg)/dT 

(meV/°C) 

d(Jsc)/dT 

(μA/cm2

/°C)

d(Voc)/dT 

(mV/°C) 

GaInP -0.43 7.1 ± 0.5 -2.21 ± 0.04

GaAs -0.47 -2.8 ± 0.9 -2.27 ± 0.04

GaInAs -0.40 -- -2.06 ± 0.04

IMM N/A 5.3 ± 0.6 -6.44 ± 0.07

Table 1 One-sun temperature coefficients of Eg, 

Jsc and Voc for the IMM subcells. The Voc

coefficients are derived from matched isotypes.

Uncertainties on the Eg coefficients are ± 0.02. 

The bottom row lists the coefficients of the full 

triple junction as derived from the X25 

multisource measurements.
3 

biasing, are shown in Figure 2 (solid triangles). Jsc for the 

GaInP subcell increases linearly with temperature at a 

rate of (7.1 ± 0.5) μA/cm2

/°C. The Jsc(T) dependences for 

the GaAs and GaInAs subcells are more complicated, as 

they depend on the bandgaps of both the subcell in 

question and of the subcell above, which filters the shorter 

wavelength light. They may also depend on the degree of 

photon coupling from the subcell above [7]. The GaAs Jsc

decreases slightly with temperature while the GaInAs Jsc

is approximately constant to within the noise in the data.

The actual Jsc(T) for the multijunction follows the minimum 

of the subcell curves. As noted above, the shortwavelength tails on the GaAs subcell EQE likely represent 

the effect of photon coupling from the top subcell, and 

close inspection of Figure 1 shows that the tails decrease 

in magnitude with temperature. Given the significant 

spectral content in the 500-650 nm wavelength range, this 

represents a loss in Jsc(T) and helps explain why the 

overall GaAs subcell Jsc decreases. Indeed a GaAs 

isotype cell deliberately grown without the shortwavelength tail and measured in the same way shows a 

slight increase in Jsc with temperature. 

Jsc(T) data from the one-sun X25 multisource 

measurement are also shown in Figure 2 as open circles. 

The data from the two simulators follow each other 

reasonably well, with a small offset. The X25 data 

correspond to a temperature coefficient for the IMM Jsc of 

d(Jsc)/dT = (5.3 ± 0.6) μA/cm2/°C at one sun. 

The 1 μm top subcell thickness was chosen to match 

photocurrents with the GaAs subcell, but the calculation 

does not include the effects of photon coupling. Therefore 

the middle subcell produces extra photocurrent and the 

photocurrents are not matched at 25°C. Most significantly, 

the cell crosses over from top-cell limited at low 

temperature to middle-cell limited at high temperature. If 

the temperature were increased much above 126°C, the 

bandgap of the current-limiting GaAs subcell would cross 

into the prominent water absorption band at ~930 nm in 

the terrestrial spectrum, shown in Figure 1, and the total 

Jsc would decrease significantly.

Figure 2 also shows as dashed lines the Jscs as 

calculated directly from the subcell EQEs of Figure 1, by 

integrating the product of (EQE x spectrum). It would 

appear from these latter data that Jsc for all three subcells 

increases linearly with temperature, and that the top and 

middle subcells remain closely current-matched until over 

100°C. However, these curves are substantially offset 

from the purple X25 curve. Calculating Jsc in this way 

requires an absolute EQE measurement, often difficult to 

achieve and especially so for small cells and for cells 

where there is any significant shunt conductance on any 

of the subcells, as in the case of the GaAs subcell in the 

IMM measured here. The EQE for a multijunction cell is 

also difficult to measure under one-sun illumination and 

was measured here at much lower intensities, which may 

introduce errors if Jsc is not strictly linear with intensity at 

low intensities. The calculated Jscs are therefore directly 

affected by any error in the EQE. By contrast, measuring 

the subcell Jscs by selectively light-biasing the various 

subcells under the solar simulator as described here is a 

technique that is based on using primary-calibration 

reference cells to accurately set the intensity. Spectral 

effects are subsumed into a spectral mismatch correction 

factor that is immune from absolute errors in the EQE [8], 

and any spectral errors in the EQE (ie. shape) are shifted 

to a higher-order correction. 

One-sun JV curves for the three single junction isotypes 

were also measured as a function of temperature to find 

the temperature coefficients of Voc, listed in Table 1. The 

values are consistent with those reported in the literature 

[5,9]. One expects the voltage coefficient of the 

multijunction cell to be the sum of the voltage coefficients 

of the individual subcells. Here the individual coefficients 

sum to (-6.54 ± 0.07) mV/°C which agrees with the value 

of (-6.44 ± 0.07) derived from the X25 multisource 

measurement.

High concentration JV curves were measured on the 

HIPSS and normalized by the one-sun Jsc values from the 

X25 measurement. The characteristics of these data are 

plotted in Figure 3 as a function of concentration. The top 

panel shows the expected logarithmic dependence of Voc

on concentration over the full temperature range. There is 

some roll-off observed above ~700 suns which we 

tentatively attribute to heating, because the cell is secured 

to a silicon wafer with a 10 μm thin, thermally insulating 

epoxy; further investigation is underway to confirm this.

Since commercial production versions of the IMM are 

generally designed to be well-heat-sunk using thermally 

conductive epoxies or solders, or wafer-bonding 

processes, the roll-off observed here is not expected to be 

reproduced in production cells. 

For a given concentration, the Voc decreases linearly with 

temperature, and calculating dVoc/dT at each 

concentration gives the thermal coefficient of Voc at 

various concentrations, shown in Figure 4. The general 

trend of dVoc/dT with concentration is consistent with 

modeling. dVoc/dT decreases from -6.4 mV/°C at one sun 

to -4.0 mV/°C at 1000 suns, as expected [10].

Figure 2 Jsc(T) for the IMM subcells. Solid lines were 

measured on a single source simulator using LED 

bias lights to over-illuminate the non-limiting 

junction. Dotted lines are based on the EQE. The 

purple curve (open circles) shows the Jsc values for 

the full IMM cell as measured on the X25 multisource

simulator.
4 

The middle panel of Figure 3 shows the fill factor as a 

function of concentration; the one-sun values are from the 

X25 measurement. The FF rises nearly linearly from one 

sun to ~100 suns before beginning to roll over. This nearlinearity in FF with Log(concentration) at all temperatures 

indicates that the spectrum was accurately adjusted: for 

high quality solar cells under a fixed spectrum, the FF is 

expected to increase linearly with Log(Concentration), 

before resistive effects begin to dominate. At the same 

time, for multijunction solar cells the fill factor is always 

minimized when the subcell photocurrents are matched

[11]. Assuming the one-sun FF is correct for a particular 

temperature, large misadjustments in the HIPSS spectrum 

would therefore tend to inflate the FF of the concentrated 

IV curves, and one would expect to see a large jump in FF 

from one-sun to several suns rather than a smooth 

increase.

The FF decreases with increasing temperature, but more 

slowly at higher concentrations, as indicated in Figure 4. 

The FF peaks at higher concentrations as the temperature 

increases. This latter trend is also clearly visible in the 

bottom panel of Figure 3, showing the efficiency as a 

function of concentration: the efficiency peak increases 

from 290 suns at 25°C to 460 suns at 126°C; the peak 

efficiency correspondingly drops from 39.5% to 33.8%.

The increase in peak concentration is possibly the result, 

in part, of enhanced thermionic emission over one or 

more of the various heterojunction interfaces between 

junction layers and confinement layers within the device, 

effectively lowering the resistive barrier to majority carrier 

transport [12]. In addition to the emitter sheet resistance, 

these internal resistances all contribute to efficiency 

rollovers at several hundred suns rather than several 

thousand. These internal resistances are the subject of 

ongoing experimental and theoretical investigations. 

The efficiency data show a linear decrease in efficiency 

with increasing temperature. The temperature coefficients 

at various concentrations are also shown in Figure 4. The 

IMM is less sensitive to temperature variations at higher 

concentrations, varying by -0.052 %/°C at 1000 suns 

compared to -0.077 %/°C at one-sun. Taking 500X and 

75°C as representative of a typical concentrator module, 

and comparing the performance to 500X and 25°C, the

conversion efficiency of this particular IMM cell decreases 

from 39.6% to 36.8%, a relative change of about eight 

percent.

DISCUSSION

The IMM design need not have only one latticemismatched junction. The triple-junction cell in reference 

[2] that demonstrated 40.8% efficiency had mismatched 

bottom and middle cells. The IMM presents a platform for 

exploring various bandgap combinations, some of which 

may be more appropriate for a cell that is meant to 

operate at elevated temperatures rather than at 25°C.

Figure 5 shows the modeled dependence of cell efficiency 

on temperature for several different combinations of 

junction bandgaps, at 500 suns. The calculation uses a 

dark current model which aims to more realistically match 

the magnitudes of the dark currents to what is 

experimentally achievable than does the detailed-balance 

approach [13], while maintaining the proper temperature 

dependence [14]; in the detailed-balance approach, the 

efficiencies of Figure 5 would be several points higher

Figure 3 Solar cell parameters extracted from the 

HIPSS data. The one-sun values were measured 

separately and used to normalize the concentration 

axis. The illuminated cell area was 0.1 cm2

. 

Figure 4 Temperature coefficients of Voc, FF and 

efficiency as a function of concentration. The 

green curves in the bottom frame show results for 

a Ge-based triple junction, from ref [3]. Open 

symbols show modeled results for the IMM and the 

Ge-based cell.
5 

because the calculation does not account for as many 

loss mechanisms, but the overall trends would be the 

same as shown. 

The {1.81, 1.40, 1.00} eV bandgap combination 

corresponding to the cell studied here is represented by 

the red dotted line in Figure 5. Modeling by Kurtz et al. 

[15] showed that a ~1.0 eV third junction would maximize 

the 25°C, 500X efficiency of a triple junction with fixed 

Ga.51In.49P and GaAs upper subcells. This represents the 

simplest IMM design, with only one mismatched junction, 

but Figure 5 clearly shows other bandgap combinations 

that realize increased conversion efficiencies. The {1.85, 

1.34, 0.93} eV combination is optimal for a 25°C (~300K) 

operating temperature, while for a 75°C (~350K) operating 

temperature, higher bandgaps of {1.88, 1.37, 0.95} eV are 

optimal. For both cases there is also a second local 

maximum in efficiency corresponding to bandgap 

combinations with bottom junction bandgaps of around 

0.7 eV which give comparable efficiencies [14]; here we 

focus on the designs with the higher ~0.93-0.95 eV 

bottom junction bandgap, which in the InGaAs materials 

system is more closely lattice-matched to GaAs. The 

design which is optimized for 75°C is only slightly suboptimal at 25°C, while being significantly better than the 

25°C design at 75°C and above. For comparison, the 

figure also shows the efficiency curve for the {1.85, 1.39, 

0.67} eV bandgap combination of the industry-standard 

GaInP/Ga(In)As/Ge cell, which was designed to be latticematched to a Ge substrate for ease and costeffectiveness of production.

The 75°C optimal cell design is similar to the IMM cell in 

reference [2] with two mismatched junctions, at 1.34 eV 

and 0.89 eV, but the optimal design requires less-severe 

graded buffers for both the middle and bottom junctions, 

and a slightly elevated top subcell bandgap.

The modeled temperature dependences can be compared 

with experimental data where available. We calculated 

d(Eff)/dT for the {1.81, 1.40, 1.00} eV cell at 500X from 

Figure 5 and repeated the modeling at 50, 100 and 

1000X. The calculated coefficients are plotted in the 

bottom frame of Figure 4 (open diamonds). The values 

are slightly greater than the experimental data but the 

dependence on concentration is approximately the same. 

Figure 4 also includes experimental data from Kinsey et 

al. [3] on the Ge-based triple junctions, as well as 

modeled results for that bandgap combination. Both the 

experimental data and the simulated results show a lower 

sensitivity to temperature, at all concentrations, for the 

IMM cell studied here as compared to the Ge-based 

device.

It is worth commenting briefly on the effect on Eff(T) of the 

prominent water absorption band at 0.90 eV (~1377 nm) 

in the terrestrial spectrum, shown in yellow in Figure 1.

Highest efficiency at 75°C is achieved by having optically 

thick junctions with a bottom subcell bandgap energy just 

above the absorption band, so that the photon collection 

is maximized. In an unfiltered single junction cell, the 

photocurrent would simply plateau as the bandgap 

decreases into the absorption band at elevated 

temperatures, but in a multijunction cell the bandgap of 

the filtering middle junction also decreases with 

temperature, and therefore the photocurrent generated by 

the bottom subcell will drop sharply with temperature. The 

bottom subcell may even become current-limiting at some 

temperature, with a corresponding decrease in efficiency. 

It is therefore deleterious to design a cell such that the 

bottom subcell bandgap is situated in the water absorption 

band at the expected operating temperature. One may 

note that the bandgap combination designed for 25°C

operation has a 0.93 eV bottom subcell, just above the 

water absorption band, whereas the cell designed for 

75°C has a 0.95 eV bottom subcell as measured at room 

temperature. We observed in Figure 1 that the bandgap of 

the GaInAs bottom subcell shifts to longer wavelengths, 

changing by -0.40 meV/°C. Based on this shift, we predict 

that at 75°C the 0.95 eV cell will have a bottom subcell 

bandgap shifted to 0.95 eV – 0.40 meV/°C x 50°C = 0.93 

eV, again optimally positioned just above the water 

absorption band.

In summary, we have conducted a careful measurement 

of the performance of a {1.81, 1.40, 1.00} eV IMM solar 

cell as a function of temperature and concentration. The 

measurement involves a complete data set of spectral 

response, one-sun JV and concentrator JV for each 

temperature. The peak efficiency decreases from 39.5% 

at 290 suns and 25°C to 33.8% at 460 suns and 126°C.

Jsc(T) of the individual subcells can also be measured and 

indicate a crossover from top-cell-limited to middle-celllimited behavior at ~100°C.

Figure 5 Three-junction cell efficiencies calculated 

for several different combinations of junction 

bandgaps, as a function of cell operating 

temperature. The cells are illuminated by the G173 

AM1.5 direct spectrum at 500 suns. In cases where 

the bandgap combination has been optimized for a 

given cell operating temperature, that temperature is 

indicated in the figure legend. The indicated 

bandgaps are all at 25°C; for cell operating 

temperatures other than 25°C, the model accounts 

for the change of bandgaps with cell temperature.
6 

ACKNOWLEDGEMENTS 

The authors thank M. Young for dedicated work 

fabricating the cells, and J. Olson, R. France, P. Ciszek

and C. Osterwald for useful conversations. Work was 

supported by the U.S. Department of Energy under 

Contract No. DE-AC36-08GO28308 with the National 

Renewable Energy Laboratory. This work is subject to 

government rights.

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