Defect-related recombination and free-carrier diffusion near an isolated defect in GaAs
Mac Read and Tim Gfroerer, Davidson College, Davidson, NC
Mark Wanlass, National Renewable Energy Lab, Golden, CO
Radiative Recombination
Defect-related Recombination
Conduction Band
Conduction Band
ENERGY
-
Defect Level
HEAT
HEAT
LIGHT
+
+
Valence Band
Valence Band
Electrons can recombine with holes in semiconductors by hopping through
localized defect states and releasing heat. This defect-related trapping and
recombination process is a loss mechanism that reduces the efficiency of
many semiconductor devices.
Diffusion
Low-excitation
High-excitation
+
d
-
y
D
y
+
- +
-
D
Defect
-
d
x
D
+
+
x
-
Electron
+
Hole
The carrier lifetime is determined by how long it takes an electron to find a
suitable hole for recombination. At low excitation density, electrons are
more likely to encounter a defect before a hole, allowing for defect-related
trapping and recombination. At high excitation, the electrons and holes
don’t live as long, reducing the diffusion length d and the probability of
reaching a defect before radiative recombination occurs.
Abstract
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 lifetime-limited 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.
Time Step Algorithm
The algorithm to find steady state carrier densities (n) in each pixel
follows a simple rate equation including generation, recombination,
and Laplacian diffusion:
Simple Recombination Model
Simple Model Assumptions:
dP  dN  n
Total




2
 recombination   An  Bn


rate




Defect
Radiative 


Generation 

n(t )  
  recombination  recombination   Diffusion   (t )
rate




rate
rate


Total




 recombination   A (dP * dDN  dN * dDP )  B * dP * dN


rate


Defective Pixel DOS vs Energy
1E17
1E16
-0.4
-0.2
0.0
0.2
0.4
Energy (% of band gap)
* All defect states are located near the middle of the bandgap
so we neglect thermal excitation of carriers into bands.
Where:
Where: Aτ = 1 / defect capture time (1/τ )
Where: dN = number of electrons in the conduction band
dDn = number of trapped electrons
2
dP = number of holes in the valence band
d (n)
dDp = number of trapped holes
n = total number of excited carriers
Diffusion  Dn 
2
dx
A = defect constant
The new defect-related DOS function shown above fits our
Re combination
B = radiative constant
radiative efficiency measurements by generating asymmetric band
(Depend
on
the
model)


Rates
filling. When the electron traps are saturated, the concentration
Method: We determine the 2 A coefficients (one for the defect pixel of electrons in the conduction band dN rises sharply with
•We use Laplacian diffusion to determine the flux between adjacent and one for the non-defective pixels) that minimizes the error
excitation. Since a high concentration of holes dP is already
pixels during each time step and then calculate new carrier densities. between the measured and simulated efficiencies.
present in the valence band, a rapid increase in the radiative rate
•We allow the diffusion process to continue until the average
BdPdN occurs.
lifetime of the generated carriers is reached.
Experimental Images
Simple Model Results
100 µm
100 µm
100 µm
100 µm
100 µm
Photoluminescence images are obtained from an undoped
GaAs/GaInP heterostructure. The excitation intensity-dependent
images shown above center on an isolated defect in the thin,
passivated GaAs layer.
Complex Recombination Model
DOS (#/cm3)
Motivation
Complex Model Results
100 µm
100 µm
100 µm
We model the defect as an isolated pixel with an augmented rate
of defect-related recombination An. Diffusion to this pixel
reduces the carrier density n near the defect, and since
brightness is proportional to the radiative rate Bn2, the adjacent
region appears darker. This model yields poor agreement
between experiment and theory.
If we allow the defect rate coefficient A to vary with excitation,
we can reproduce our experimental results. However, variation
of A with excitation is non-physical. We need a better model for
defect-related recombination.
Conclusions
• Even for high-quality semiconductor materials with few defects, diffusion can lead to significant defect
recombination at low excitation intensity.
• At low density, carriers diffuse more readily to defective regions rather than recombining radiatively, producing
larger effective “dead” areas.
• Assigning a single defect coefficient to each pixel and allowing for diffusion does not yield good agreement, but
by allowing the coefficient to change with laser intensity, we can reproduce the experimental 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.
Acknowledgments
We thank Jeff Carapella for growing the test structures, and Caroline
Vaughan and Adam Topaz for their work on finding the DOS functions.
We also thank the Davidson Research Initiative and the Donors of the
American Chemical Society – Petroleum Research Fund for supporting
this work.