Stretched exponential transport transients in

GaP alloys for high efficiency solar cellsDan Hampton and Tim Gfroerer, Davidson College, Davidson, NC

Mark Wanlass, National Renewable Energy Lab, Golden, CO

AbstractThe efficiency of solar cells can be increased by using larger bandgap materials inmulti-junction devices. However, due to challenges in constructing the lattice-mismatched 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.

Motivation: Multi-junction solar cells

If higher energy photons are absorbed in higher bandgap alloys, the heat loss caused by excess photon energy relative to the gap is reduced.

400 800 1200 1600 2000 2400

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1.502 eV GaInP

1.75 eV GaAsP

Sol

ar S

pect

ral I

rrad

ianc

e (W

m-2

nm-1

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Wavelength (nm)

GaAs bandgap

Visible

Proposed Transport Method

N+ P+

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Depletion Layer

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-

-+

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Depletion with bias

+

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Conventional vs. Stretched Modeling of

Capacitance Transients

DLTS: Trapping During a Bias Pulse

Arrhenius Plot

Discussion

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.

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.

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.

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.

• 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).

DLTS Experimental Setup

The Stretched Exponential Function: Ae-(kt)d

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100

101

102

103

104

Rate

(S-1

)

1/KT (eV-1)

Capture

Escape

Ea=.370eV

Ea=.394eV

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.

GaInPGaAsP

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101

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Rat

e (S

-1)

1/KT (eV-1)

Capture

Escape

Ea=.322eV

Ea=.208eV

Ene

rgy

Distance

Holes

Slow Response Fast Response

Conduction Band

Valence Band

Defect Levels

++

Conduction Band

Valence BandIncr

easi

ng E

nerg

y

+Hole

Cap

ture

Esc

ape

+

Rate ~ e -Ea/KT

Tra

p D

epth

Hopping Transport

Temperature Dependent Exponential

While stacking materials of different bandgaps will increase theefficiency of solar cells, it will also create defects within the device because of lattice-mismatching.

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.

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.

AcknowledgementsWe 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.

Defect Levels

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.

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1

10 Stretched Exponential Conventional Exponential

Ca

pa

cita

nce

(p

F)

Time (seconds)

Escape

Capture

1E-3 0.01 0.1

1

10

400ms time window

40ms time window

Stretched Exponential Conventional Exponential

Ca

pa

cita

nce

(p

F)

Time (seconds)

Escape

Capture