Imaging and modeling diffusion to isolated defects in a GaAs/GaInP heterostructure
Tim Gfroerer, Mac Read, and Caroline Vaughan, Davidson College, Davidson, NC
Mark Wanlass, National Renewable Energy Lab, Golden, CO
Motivation
Defect Level
ENERGY
HEAT
LIGHT
HEAT
+
+
Valence Band
Valence Band
Nonequilibrium 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.
Experimental Images
Conduction Band
Ec
Ev
Valence Band
Better Recombination Model?
High-excitation
y
D
y
-
+
Defect
100 µm
100 µm
100 µm
x
-
Electron
+
Hole
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.
Experimental Setup
Energy
Ec
6
-
x
D
100 µm
+
d
0.4
0
D
+
0.2
New Fit
10
-1 -1
-
0.0
10
-3
d
- +
-0.2
New Density of States (DOS) Function
DOS / cm eV s )
+
-0.4
Ev
If we assume that all defect levels are concentrated near the center of the bandgap as shown
above, then the concentration of non-equilibrium electrons in the conduction band n will equal
that of holes in the valence band, and thermal excitation out of the traps can be neglected. These
assumptions lead to the defect-related recombination rate An that is used in the panels to the left.
Diffusion
Low-excitation
Defect DOS
No Defect DOS
-1
Radiative Efficiency
-
Defect-related electron-hole pair recombination impairs the performance of many semiconductor devices.
In photoluminescence images, defective regions appear dark because carriers are more likely to
recombine nonradiatively.
We use photoluminescence imaging to observe isolated defects in a
GaAs/GaInP heterostructure. We find that the area of the defect-darkened region depends strongly on the
photoexcitation intensity. With increasing excitation, the density of electrons and holes increases, so they
are more likely to encounter each other and recombine radiatively before reaching the defect. We model
the behavior with a computer simulation that allows for lifetime-limited Laplacian diffusion of carriers, and
we report good qualitative agreement between the experimental and simulated images. We are currently
developing a more sophisticated model in hopes of achieving better quantitative agreement.
A-type Density of States (DOS) Function
-1 -1
Conduction Band
-3
Conduction Band
Abstract
DOS / cm eV s )
Radiative Recombination
Energy
Defect-related Recombination
Yes! A Better Recombination Model
5
10
4
Defect DOS
No Defect DOS
10
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.
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.
Raditative Efficiency
Simple Recombination Model
On Defect
Off Defect
-3
10
10
10
100 µm
-2
10
-4
3
Ev
10
-0.4
-0.2
0.0
0.2
0.4
-1
0
10
Ec
1
10
2
10
3
10
10
2
Power/Area (W/cm )
Energy
The new defect-related DOS function shown above fits our radiative efficiency measurements by
generating asymmetric band filling. When the electron traps are saturated, the concentration of
electrons in the conduction band ne rises sharply with excitation. Since a high concentration of holes
np is already present in the valence band, a rapid increase in the radiative rate Bne np occurs.
Conclusions and Future Work
•Even for high-quality semiconductor materials
with few defects, diffusion can lead to significant
defect recombination at low excitation intensity.
Changing Laser Focus
0
100 µm
100 µm
100 μm
0
10
Measurements of radiative
efficiency (emitted / absorbed
light) as a function of
photoexcitation. The solid lines
are theoretical fits assuming
that the rate of defect-related
recombination is simply a
constant A times the
photoexcited carrier density n.
We use a high-sensitivity camera to obtain photoluminescence images
over a broad range of laser powers. We can also measure the integrated
photoluminescence intensity as a function of photoexcitation.
100 µm
100 µm
Radiative Efficiency
-1
10
-2
10
-3
On Defect
Off Defect
Unfocused
10
-4
10
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.
-2
10
-1
10
0
10
1
10
2
10
3
10
2
Power/Area (W/cm )
Radiative efficiency measurements cannot be explained if we assume that the
defect-related recombination rate equals An. We need a better model.
•A defect-related recombination model that
allows for an asymmetric distribution of defect
levels within the bandgap is needed to account
for our experimental results.
•To incorporate the new recombination model
into our diffusion simulation, we need to
understand why/how our radiative efficiency
measurements depend on the laser spot size.
Radiative Efficiency
•At low density, carriers diffuse more readily to
defective regions rather than recombining
radiatively, producing larger effective “dead”
areas.
10
-1
10
-2
10
Excitation Area:
-3
2
8 x 10 cm
-4
2
5 x 10 cm
-5
2
9 x 10 cm
-3
10
-2
10
-1
0
1
2
10
10
10
10
2
Power/Area (W/cm )
3
10
?
Acknowledgments
We thank Jeff Carapella for growing the test structures and Adam Topaz for writing the code that
identifies good defect-related DOS functions. We also thank the Davidson Research Initiative and
the Donors of the American Chemical Society – Petroleum Research Fund for supporting this work.