Defect-related recombination and free-carrier diffusion near an isolated defect in GaAs

1
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
Better Recombination Model
Motivation
Abstract
Defect-related Recombination
Radiative Recombination
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 modeled the
behavior with a simulation that allows for
lifetime-limited diffusion and defect-related
recombination only through mid-bandgap energy
levels, we did not obtain good agreement between
the experimental and simulated images. We are
now testing a more sophisticated model which
allows for an arbitrary distribution of defect
levels within the bandgap.
Conduction Band
Conduction Band
-
-
Defect Level
ENERGY
HEAT
HEAT
LIGHT


Time Step Algorithm
Simple Recombination Model
Valence Band
Valence Band
The algorithm to find steady state carrier
densities (n) in each pixel follows a simple rate
equation including generation, recombination, and
Laplacian diffusion
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.
Assumptions
All defect states are located
near the middle of the bandgap
so we neglect thermal excitation of
carriers into bands. Method We determine
the 2 A coefficients (one for the defect pixel
and one for the non-defective pixels) that
minimizes the error between the measured and
simulated efficiencies.
Where At 1 / defect capture time (1/t )
dDp number of trapped electrons
dDn number of trapped holes The
density of states (DOS) function now allows for
thermal excitation and asymmetric band filling,
affecting dP, dN, dDp, and dDn. In our
computation, we also adjust the amplitude of the
DOS functions to correct for changes with laser
focusing (see Caroline Vaughans poster!).
Diffusion
Where
Where dP number of electrons in the
conduction band dN number of
holes in the valence band n
total number of excited carriers
A defect constant B
radiative constant
Low-excitation
High-excitation

-

d
-
Complex Model Motivation
-
y
D
D
y



(Depend on the model)
In our experimental images, radiative efficiency
increases more rapidly with carrier density than
the simple model predicts. By allowing the
defect and nondefect A values to change with
laser intensity in the simple model, we find that
a larger defect A is needed for lower carrier
densities (see below). The defect-related
recombination model described above can produce a
similar effect. At low carrier density,
electrons are trapped and defect-related
recombination dominates, but when the traps are
filled, the radiative efficiency increases
rapidly as all new electrons enter the conduction
band.
-
-
d

• We use Laplacian diffusion to determine the flux
  between adjacent pixels during each time step and
  then calculate new carrier densities.
• We allow the diffusion process to continue until
  the average lifetime of the generated carriers is
  reached.

x
x
D
-

Defect
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 dont live as long,
reducing the diffusion length d and the
probability of reaching a defect before radiative
recombination occurs.
Experimental Images
Simple Model Results
Density Depletion Region
-
BigA 4.2107 SmA 8.1104
-
-
Using the time step algorithm and the simple
recombination model described above , we obtain
these theoretical images. The simulated images,
with A4.2107 cm3/s (defect pixel) and A8.2104
cm3/s (non-defect pixels), produced the lowest
error in the context of this model.
By allowing the A values to change for each laser
power, we are able to reproduce the experimental
results. These images, using defect A values
ranging from 4.2107 cm3/s to 2108 cm3/s and
non-defect A values from 8.2104 cm3/s to 1.6105
cm3/s, show that we need a more sophisticated
model for defect-related recombination.
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.
Low density High density
A4.2107 cm3/s A8.2104 cm3/s
Conclusions
Acknowledgments

• 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 defect-related
  recombination model that allows for an arbitrary
  distribution of defect levels within the bandgap
  is needed to account for our experimental
  results. We are now testing such a model.

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.
We model the defect as an isolated pixel with
augmented defect-related recombination.
Diffusion to this pixel reduces the carrier
density n near the defect, and since the
brightness is proportional to the radiative rate
Bn2, the adjacent region appears darker.