Study of Radiative and Heat-Generating Recombination in GaAs
Ryan Crum and Tim Gfroerer, Davidson College, Davidson, NC
Mark Wanlass, National Renewable Energy Lab, Golden, CO
Motivation
Abstract
Conduction Band
Conduction Band
ENERGY
-
Defect Level
HEAT
HEAT
LIGHT
+
+
Valence Band
Light- and heat-generating recombination decrease the efficiency of GaAs-based solar cells. In this investigation, we couple
results from recent radiative studies with new measurements of heat generation. This coupling of results is important because
heat-generating recombination dominates at low excitation while radiative recombination (luminescence) dominates at higher
laser intensities. In past studies of diffusion in semiconductors, images of luminescence were used to examine the diffusion of
carriers away from the excitation position. But with complementary heating profiles, we are able to ascertain the underlying
carrier density more accurately. Since heat-generating recombination scales linearly with the density, while radiative
recombination is proportional to the density squared, we show that the heating profile is comparable to the square root of the
luminescence profile. We have also studied the diffusion of heat (i.e. thermal diffusion) in GaAs, but we will need to account for
heat loss in order to compare our results with theoretical predictions.
Valence Band
Analyzing the Outward Diffusion of Carriers
Light- and heat-generating recombination decrease the efficiency of
GaAs-based solar cells because the release of light/heat reduces the
energy available for generating electricity.
Heat-generating
recombination tends to occur in the presence of defects (and their
associated energy levels) while light-generating recombination is more
likely when defect levels are not present.
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slope = - ( * freq / D)
2
D = .038 cm /sec
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-4
0
10
Experimental Setup
Laser Profile
Luminescence
Sqrt of Luminescence
Temperature Diff
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Normalized Signal
10
-5
0.00
-2
10
*
-3
10
Temperature Difference (K)
10
10
100 μm
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10
Time Window:
0-33 ms
67-100 ms
133-167 ms
200-233 ms
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10
-4
0
100
200
300
Distance (m)
When we analyze a sequence of thermal images where the laser
alternates between on and off in consecutive frames, we observe a
relatively rapid diffusion of heat radially outward over time. Hence, we
study the frame coincident with the first laser pulse to obtain the most
accurate representation of the position-dependent heat generation.
Salazar, Agustin, Arantza Mendioroz, Raquel Fuente, and Ricardo Celorrio,
J. Appl. Phys. 107, 043508 (2010).
10
-5
10
0
100
200
300
400
Distance (m)
Conclusions
10
0.08
0
In past studies, images of luminescence (radiative recombination) have been used to monitor the diffusion of electrons and holes
away from the excitation position. In our study, we measure the luminescence profile along with the temperature gradient due
to heat generation. We obtain temperature profiles that are broader than the profiles of luminescence. This observation is
consistent with how these mechanisms depend on carrier density: heat-generating recombination should be directly
proportional to the density of carriers while radiative-recombination is proportional to the density of carriers squared. Since the
carrier density decreases with distance from the excitation position, radiative recombination dominates at short distances while
heat-generating recombination becomes more important with increasing distance. We test this hypothesis by plotting the square
root of the luminescence, which matches the temperature profile surprisingly well.
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0.06
Single Pulse Evolution
• We found that the diffusion of carriers is best represented by the temperature difference rather than the luminescence.
• When analyzing luminescence, the square root of the signal should be used to obtain an accurate measurement of the
carrier density.
• Our measurement of the thermal diffusivity constant in GaAs differs from the accepted value by an order of magnitude.
We believe that the error in our measurement may be due to local heat loss.
Temperature Difference (K)
0
0.04
The steady-state thermal profile for a laser that is chopped at frequency f
can be used to determine the thermal diffusivity of the material. The
natural logarithm of the temperature difference plotted verses the radial
distance should be linear with a slope equal to –(π*f/D)-1/2 .* We obtain an
experimental value of 0.038 cm2/sec for the thermal diffusivity (D), while
the accepted value for D in GaAs is 0.3 cm2/sec. We suspect that the error
may be due to heat loss (as shown below).
10
Diffusion of Heat in GaAs
0.02
Distance (cm)
-4
The 18mm focal length aspheric lens focuses the 0.34W (only 0.17W is
absorbed) Gaussian laser beam to a 4 m FWHM spot on the sample. In
order to optimize the speed of the thermal imaging, a shutter was used
to synchronize the laser excitation with individual frames from the FLIR
T300 thermal camera (30 Hz).
1/2
Ln(T)
Heat-Generating Recombination Light-Generating Recombination
Thermal Diffusivity of GaAs
Time Window:
0-33 ms
33-67 ms
67-100 ms
100-133 ms
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10
-2
10
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10
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10
0
100
200
300
400
Distance (m)
When we study the evolution of the temperature profile following a single
pulse (rather than a sequence of pulses), local heat loss appears to
dominate over thermal diffusion.
Acknowledgements
We thank Jeff Carapella for growing the test structures and we
acknowledge the Donors of the American Chemical Society – Petroleum
Research Fund for supporting this work.