Transcript Slide 1

Defect-related recombination and free-carrier diffusion near an isolated defect in GaAs
Mark Crowley and Tim Gfroerer, Davidson College, Davidson, NC
Mark Wanlass, National Renewable Energy Lab, Golden, CO
Motivation
Abstract
Radiative Recombination
Defect-related Recombination
Conduction Band
Conduction Band
-
Defect Level
ENERGY
HEAT
Simple Recombination Model
HEAT
LIGHT
+
+
Valence Band
Valence Band
When defects are present in a semiconductor, intermediate
energy levels are formed allowing carriers to “step” down to
lower energy levels and recombine by releasing heat. This
energy is lost so defect related recombination reduces the
efficiency of photovoltaic cells.
When defects are present in semiconductors, localized energy levels appear within the bandgap. These new electronic states
accommodate heat-generating recombination – a problematic energy loss mechanism in many semiconductor devices. But at
high excitation, the density of electrons and holes is higher, so they encounter each other more frequently. Early encounters
augment light-emitting recombination, reducing the average lifetime and diffusion distance so the carriers are less likely to
reach defects. In images of the light emitted by GaAs, we observe isolated dark regions (defects) where the darkened area
decreases substantially with increasing excitation. When we model the behavior with a simulation that allows for lifetimelimited diffusion and defect-related recombination only through mid-bandgap energy levels, we do not obtain good
agreement between the experimental and simulated images. A more sophisticated model which allows for an arbitrary
distribution of defect levels within the bandgap produces results that are more consistent with experimental images.
Experimental Images
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1.0
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d
-
y
D
y
+
- +
-
.9
-
Defect
-
d
x
D
100 μm
100 μm
Complex Recombination Model
.6
D
+
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.001W
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In the complex model we allow for differing defect and band
occupation densities and calculate the recombination as
.3
Total




 Recom bination   A (dP  dDN  dN  dDP)  B  dP  dN


rate


x
-
Electron
+
Total




2
Recom
binat
ion

An

Bn




Rate


This model does not seem to produce very good results
with constant A values (which must be the case in a real
physical system).
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+
Where:
dN = number of electrons in the conduction band
dP = number of holes in the valence band
n = total number of excited electrons or holes
We calculated the recombination rate as follows
Where:
A = defect-related constant
B = radiative constant
High-excitation
+
dP  dN  n
Simple Model Images
Diffusion
Low-excitation
In the simple model we assume that all defect states are
located near the middle of the bandgap so we can neglect
thermal excitation of carriers into bands. In this case:
Hole
Electrons and holes (carriers) can diffuse before recombining.
At lower excitation, fewer carriers are present and therefore
it takes longer for them to pair up and recombine. This
extended lifetime allows more time for a carrier to encounter
a defect. At higher excitation, more carriers are present and
individual carriers are more likely to find a partner for
radiative recombination before reaching the defect.
Depletion in Solar Cells
100 μm
100 μm
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.2
Complex Model Images
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Time Evolution Algorithm
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We model the defect as an isolated central pixel with a
greater defect-related recombination rate. In each time step,
we compute the change in the carrier density in each pixel in
the following way:


 Defect
  Radiative

 

n(t )  Generation 

   Recom binat
 
ion   Recom binat
ion  Diffusion
Rate
t
  Rate
  Rate




 

100 μm
~ 2 nm
100 μm
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Absorption
Layer ~ 2 mm
Carrier diffusion creates depleted (or dead) regions near
defects in solar cells. At high excitation (above), the
depletion region is small and many carriers can be extracted
for electricity. At lower excitation (below) the depletion
region of the defect grows and carriers close to the defect
will be lost to defect-related recombination.
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.001W
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.3
Where:
 Generation

LaserIntensity 

 
 Rate
 PhotonEnergy SampleThickness
d 2n
Diffusion  D  2
dx
ion
 Recom binat

  (Depend on the model)
 Rates

100 μm
100 μm
.5
.2
• We use Laplacian diffusion to determine the
flux between adjacent pixel.
• We end the simulation when a steady-state
carrier distribution is obtained.
Where: Aτ = 1 / defect capture time (1/τ )
B = radiative constant
dN = number of electrons in the conduction band
dP = number of holes in the valence band
dDn = number of trapped electrons
dDp= number of trapped holes
Occupation densities and recombination rates depend on the
defect-related density of states function, which is generated using
Adam Topaz’s fitter program.* This recombination model does a
much better job of modeling the experimental data as shown left.
* A. Topaz (Davidson '08), B.A. West (Davidson '08), T.H. Gfroerer,
and M.W. Wanlass, Applied Physics Letters 90, 092110 (2007).
New Images To Reduce Error
In order to try to reduce error further, we have obtained new, more
carefully taken images of a defect in the same material. Although the
modeling process has not been completed, the figures below show
how the complex recombination model fits the radiative efficiency
measurements better than the simple model.
Defect Pixel
Non-Defect Pixels
Conclusions
Absorption
Layer ~ 2 mm
Defect-related
dead volume
• Even in high quality solar cells, defects produce “dead spots” where defect-related recombination is high.
• These defects act as sinks, drawing in nearby charge carriers by diffusion.
• Due to the low population and long lifetime of carriers at lower laser intensities, more distant carriers diffuse
to the defect, producing a larger dead volume relative to higher laser intensities.
• When modeling these defects, if we use a simple model that does not account for the occupation of defect
and band states separately, we are unable to reproduce the experimental images.
• When state occupations are computed independently, the model produces much better images.
Acknowledgement: We thank Jeff Carapella for growing the test structures and the Donors of
the American Chemical Society – Petroleum Research Fund for supporting this work.