Stretched exponential transport transients in
GaP alloys for high efficiency solar cells
Dan Hampton and Tim Gfroerer, Davidson College, Davidson, NC
Mark Wanlass, National Renewable Energy Lab, Golden, CO
Abstract
10
Escape
Capacitance (pF)
Motivation: Multi-junction solar cells
The efficiency of solar cells can be increased by using larger bandgap materials in
multi-junction devices. However, due to challenges in constructing the latticemismatched system with semiconductors having the desired bandgaps, defects are
formed throughout these devices. Defects trap charge carriers and provide a
recombination mechanism for electrons and holes, acting as one of the key
inhibitors of solar cell efficiency. Using Deep Level Transient Spectroscopy
(DLTS), we find that the transport of some charge carriers in the high-bandgap
GaP alloys cannot be modeled with conventional thermal activation and ballistic
transport in the bands. Rather, our capture and escape transients require a
stretched exponential function to obtain good fits. Our analysis indicates that a
hopping-type transport mechanism may be operating in these alloys.
Stretched Exponential
Conventional Exponential
Capture
1
40ms time window
DLTS: Trapping During a Bias Pulse
400ms time window
Depletion Layer
1E-3
+
+
+
+
+
-
+
+-
-
The same data shown below, but with a logarithmic time scale. Transients
were recorded with 40 ms and 400 ms time windows (plotted together
above) to test the compatibility of the fit over different time scales.
+
P
+
+-
Arrhenius Plot
+
GaInP
GaAsP
2 eV GaInP
1.50
4
10
Depletion with bias
1.75 eV GaAsP
1.25
5
10
Capture
Escape
3
0.25
DLTS Experimental Setup
0.00
800
1200
1600
2000
3
10
-1
-1
Visible
Ea=.208eV
10
2
Rate (S )
0.50
10
Ea=.394eV
Deep level transient spectroscopy (DLTS) employs transient capacitance
measurements on diodes during and after the application of a bias pulse to
monitor the capture/emission of carriers into/out of defect-related traps.
0.75
400
4
10
GaAs bandgap
1.00
0.1
Time (seconds)
Rate (S )
-2
-1
Solar Spectral Irradiance (Wm nm )
When a photon is absorbed, an electron is excited into the conduction
band, leaving a hole behind in the valence band. Some heat is lost,
reducing efficiency. Then an internal electric field sweeps the electrons
and holes away, creating electricity.
- - - - - - - N+ - - -
0.01
Capture
1
10
2
10
Escape
1
Ea=.370eV
10
Ea=.322eV
0
10
0
10
2400
Wavelength (nm)
60
65
70
75
70
80
80
85
90
95
-1
-1
If higher energy photons are absorbed in higher bandgap alloys, the heat
loss caused by excess photon energy relative to the gap is reduced.
75
1/KT (eV )
1/KT (eV )
In our analysis, we fix the stretching parameter (d) and amplitude (A), sometimes
allowing A to change linearly with temperature. We then obtain stretched capture
and escape rates at each temperature. Arrhenius plots of the rates are linear and
yield comparable capture and escape activation energies.
Proposed Transport Method
Conduction Band
Energy
While stacking materials of different bandgaps will increase the
efficiency of solar cells, it will also create defects within the
device because of lattice-mismatching.
Slow Response
The computer operates the temperature controller and retrieves
data from the digital oscilloscope at incremental temperatures.
The pulse generator applies the reverse and pulse biases to the
sample while the capacitance meter reads the resulting change in
capacitance as a function of time.
Conventional vs. Stretched Modeling of
Capacitance Transients
The Stretched Exponential Function:
d
-(kt)
Ae
Conduction Band
10
+
Hole
Defect Levels
Rate ~ e -Ea/KT
Temperature Dependent
Exponential
Capture
0.1
Holes
Defect Levels
Valence Band
Distance
• Non-exponential capacitance transients are evident in 2
technologically important GaP alloys.
• The capacitance transients require thermally-activated
stretched exponential analysis to obtain good fits.
• The comparable activation energies for the capture and
escape suggests a transport-limited mechanism (rather than
thermal activation into and out of traps).
1
0.0
+
Discussion
Escape
Valence Band
Defects provide energy levels that restrict the movement of
charge carriers. This inhibits the production of electricity. The
conventional model of capture and escape into and out of these
levels suggest that the capture should be rapid while escape
transients should be exponential with a thermally activated rate.
+
The transient response of GaP alloys may be due to charge carriers
hopping from one defect level to the next. The varying distance in
real-space between defects, or clusters of defects, influences the
transport rate, yielding non-exponential behavior.
Stretched Exponential
Conventional Exponential
Capacitance (pF)
Escape
Capture
+
Trap Depth
Increasing Energy
Hopping Transport
Fast Response
0.2
0.3
0.4
Time (seconds)
Representative fits of conventional and stretched exponentials to GaAsP
transients measured at 162.5 K (the escape results are shifted vertically for
clarity.) The superiority of the stretched exponential fitting is clearly evident.
A fixed stretching parameter of d = 0.33 was used for all GaAsP transients.
Acknowledgements
We thank Jeff Carapella for growing and processing the test
structures and the Donors of the American Chemical Society –
Petroleum Research Fund for supporting this work.