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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
Total
Motivation Abstract
recombination A (dP * dDN dN * dDP) B * dP * dN
Defect-related Recombination Radiative Recombination
When defects are present in semiconductors, localized energy levels appear within the bandgap. These new electronic states rate
Conduction Band Conduction Band accommodate heat-generating recombination – a problematic energy loss mechanism in many semiconductor devices. But at high DOS/τ vs Energy
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
DOS/τ (#/cm3*eV*s)
Defect Level of the light emitted by GaAs, we observe isolated dark regions (defects) where the darkened area decreases substantially with
ENERGY
HEAT
HEAT increasing excitation. When we modeled the behavior with a simulation that allows for lifetime-limited diffusion and defect-related Defect Pixel
LIGHT
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. Non-Defect
Pixels
Valence Band Valence Band Time Step Algorithm Simple Recombination Model
Electrons can recombine with holes in semiconductors by hopping The algorithm to find steady state carrier densities (n) in each pixel follows a Assumptions:
through localized defect states and releasing heat. This defect-related simple rate equation including generation, recombination, and Laplacian diffusion: dP dN n Ev Ec
trapping and recombination process is a loss mechanism that reduces Total Where: Aτ = 1 / defect capture time (1/τ )
the efficiency of many semiconductor devices. Defect Radiative
Generation recombination An Bn
2
dDp = number of trapped electrons
n(t ) recombination recombination Diffusion (t )
rate dDn = number of trapped holes
Diffusion rate
rate rate * All defect states are located near the middle of the bandgap
The density of states (DOS) function now allows for thermal excitation and
Where: Generation ExcitationIntensity so we neglect thermal excitation of carriers into bands.
asymmetric band filling, affecting dP, dN, dDp, and dDn. In our computation,
Low-excitation High-excitation
Rate PhotonEnergy * SampleThickness Where: dP = number of electrons in the conduction band we also adjust the amplitude of the DOS functions to correct for changes
+ - + dN = number of holes in the valence band with laser focusing (see Caroline Vaughan’s poster!).
d
d (n)2
n = total number of excited carriers
Diffusion Dn
-
- Complex Model Motivation
dx 2 A = defect constant
y D y D
B = radiative constant
+ + + Re combination
(Depend on the model)
Method: We determine the 2 A coefficients (one for the defect pixel and one for
In our experimental images, radiative efficiency increases more rapidly with
- d - Rates the non-defective pixels) that minimizes the error between the measured and
carrier density than the simple model predicts. By allowing the defect and
simulated efficiencies.
x x •We use Laplacian diffusion to determine the flux between adjacent pixels during nondefect A values to change with laser intensity in the simple model, we find
each time step and then calculate new carrier densities. that a larger defect A is needed for lower carrier densities (see below). The
D Defect - Electron + Hole •We allow the diffusion process to continue until the average lifetime of the defect-related recombination model described above can produce a similar
generated carriers is reached. effect. At low carrier density, electrons are trapped and defect-related
The carrier lifetime is determined by how long it takes an electron to recombination dominates, but when the traps are filled, the radiative efficiency
Experimental Images Simple Model Results
find a suitable hole for recombination. At low excitation density, increases rapidly as all new electrons enter the conduction band.
electrons are more likely to encounter a defect before a hole, allowing
for defect-related trapping and recombination. At high excitation, the 2 2
Iex= 60 W/cm Iex= 6 W/cm
electrons and holes don’t live as long, reducing the diffusion length d Temp = 165K 1.0 Temp = 165K
and the probability of reaching a defect before radiative BigA = 4.2*10
7
4 0.95
BigA = 5.0*10
7 0.80
SmA = 8.1*10 SmA = 6.0*10
5
recombination occurs. 0.76
Density Depletion Region
0.89
0.70
0.82
0.65
0.76
0.59
0.69
0.54
2
2 Iex= 0.06 W/cm
Iex= 0.6 W/cm
- Temp = 165K
0.76
Temp = 165K
BigA = 2.0*10
8
0.20
- BigA = 4.2*107
SmA = 8.1*104
SmA = 1.6*10
5
0.19
Carrier density is reduced 0.72
by diffusion to the defect 0.67 0.17
- 0.62 0.16
0.56 0.14
0.51 0.13
Using the time step algorithm and the simple recombination model described
By allowing the A values to change for each laser power, we are able to
Photoluminescence images are obtained from an undoped GaAs/GaInP above , we obtain these theoretical images. The simulated images, with
reproduce the experimental results. These images, using defect A values
heterostructure. The excitation intensity-dependent images shown A=4.2*107 cm3/s (defect pixel) and A=8.2*104 cm3/s (non-defect pixels),
ranging from 4.2*107 cm3/s to 2*108 cm3/s and non-defect A values from
above center on an isolated defect in the thin, passivated GaAs layer. produced the lowest error in the context of this model.
8.2*104 cm3/s to 1.6*105 cm3/s, show that we need a more sophisticated
Low density model for defect-related recombination.
Conclusions
A=4.2*107 cm3/s
High density
A=8.2*104 cm3/s • 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.
Acknowledgments
• Assigning a single defect coefficient to each pixel and allowing for diffusion does not yield good agreement, but by allowing the coefficient to We thank Jeff Carapella for growing the test structures, and Caroline Vaughan and
We model the defect as an isolated pixel with augmented defect-related
change with laser intensity, we can reproduce the experimental images. Adam Topaz for their work on finding the DOS functions. We also thank the
recombination. Diffusion to this pixel reduces the carrier density n near
Davidson Research Initiative and the Donors of the American Chemical Society –
the defect, and since the brightness is proportional to the radiative rate • A more sophisticated defect-related recombination model that allows for an arbitrary distribution of defect levels within the bandgap is needed to Petroleum Research Fund for supporting this work.
Bn2, the adjacent region appears darker. account for our experimental results. We are now testing such a model.
