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
Abstract
Defect-related Recombination
Radiative 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
+
-
d
x
D
+
x
-
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 don’t live as long, reducing the diffusion length d
and the probability of reaching a defect before radiative
recombination occurs.
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 lightemitting 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.
Time Step Algorithm
Simple Recombination Model
The algorithm to find steady state carrier densities (n) in each pixel follows a
simple rate equation including generation, recombination, and Laplacian diffusion:


Defect
Radiative 


Generation 

n(t )  
  recombination  recombination   Diffusion   (t )
rate




rate
rate


Where: Generation
ExcitationIntensity

Rate
PhotonEnergy * SampleThickness
d (n)
Diffusion  Dn 
2
dx
2
Re combination

 (Depend on the model)
Rates
•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.
Assumptions:
dP  dN  n
Total




2
recombinat
ion

An

Bn




rate


* All defect states are located near the middle of the bandgap
so we neglect thermal excitation of carriers into bands.
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
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.
Experimental Images
Simple Model Results
Total




 recombination   A (dP * dDN  dN * dDP )  B * dP * dN


rate


DOS/τ vs Energy
DOS/τ (#/cm3*eV*s)
Motivation
Better Recombination Model
Defect Pixel
Non-Defect
Pixels
Ev
Ec
Where: Aτ = 1 / defect capture time (1/τ )
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 Vaughan’s poster!).
Complex Model Motivation
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.
Iex= 60 W/cm
2
Temp = 165K
7
BigA = 4.2*10
4
SmA = 8.1*10
Density Depletion Region
1.0
0.95
Iex= 6 W/cm
2
Temp = 165K
7
BigA = 5.0*10
5
SmA = 6.0*10
0.80
0.76
0.89
0.70
0.82
0.65
0.76
0.59
0.69
0.54
Iex= 0.6 W/cm
-
-
Temp = 165K
BigA = 4.2*107
SmA = 8.1*104
Carrier density is reduced
by diffusion to the defect
-
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
Iex= 0.06 W/cm
2
A=4.2*107 cm3/s
A=8.2*104 cm3/s
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.
Using the time step algorithm and the simple recombination model described
above , we obtain these theoretical images. The simulated images, with
A=4.2*107 cm3/s (defect pixel) and A=8.2*104 cm3/s (non-defect pixels),
produced the lowest error in the context of this model.
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 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.
0.76
2
Temp = 165K
8
BigA = 2.0*10
5
SmA = 1.6*10
0.20
0.72
0.19
0.67
0.17
0.62
0.16
0.56
0.14
0.51
0.13
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 4.2*107 cm3/s to 2*108 cm3/s and non-defect A values from
8.2*104 cm3/s to 1.6*105 cm3/s, show that we need a more sophisticated
model for defect-related recombination.
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.