Excitation-dependent transition between defect-related and radiative
recombination in lattice-mismatched InGaAs/InAsP heterostructures
F.E. Weindruch and T.H. Gfroerer, Davidson College
M.W. Wanlass, National Renewable Energy Laboratory
Abstract
Calibration to Obtain the Absolute Efficiency
Data from Eg = 0.73 eV Sample
Lattice-mismatched (Indium-rich) InGaAs heterostructures grown on InP substrates are
strong candidates for thermophotovoltaic cells, devices that convert thermal radiation into
electricity. We are studying a set of incrementally lattice-mismatched InGaAs/InAsP double
heterostructures by measuring the radiative efficiency as a function of excitation power at
77K and comparing the rates of defect-related (nonradiative) and radiative recombination in
these structures. We present preliminary results on how the transition between defectdominated and radiative recombination depends on lattice-mismatch.
Derivatives of Best-Fit Curve
40
Motivation: Thermophotovoltaic (TPV) Power
Blackbody Radiation
Heat
30
Derivative (arbitrary units)
Relative Radiative Efficiency (a.u.)
2.0
1.5
1.0
0.5
Eg= 0.73 eV
0.0
3 Order Polynomial Fit
10
10
19
10
20
10
21
10
22
10
Inflection
Point
0
-10
-20
First Derivative of Fit
Second Derivative of Fit
-30
rd
18
20
23
-40
24
1x10
10
18
-3 -1
24
Log[e-h Pair Generation and Recombination (cm s )]
The derivatives of the polynomial fit show where the curvature of the relative efficiency inflects.
We scale the relative efficiency curves to obtain 50% absolute efficiency at the infection point.
Semiconductor TPV
Converter Cells
Blackbody Radiator
22
-3 -1
e-h Pair Generation and Recombination (cm s )
Heat Source
20
TPV Cells are designed to convert infrared blackbody radiation into electricity.
A Theoretical Model
100
Bandgap vs. Alloy Composition
Blackbody Radiation Absorbed
1.6
1.0
T = 1300 C
0.8
1.2
Substrate
Substrate (InP)
Severe
Severe Mismatch
Mismatch
1.0
Normalized Intensity
0.8
0.6
0.6
80
60
40
20
0.4
Eg= 0.73 eV
Theoretical Fit
0
0.2
10
18
19
20
10
10
10
21
10
22
23
24
1x10
10
-3 -1
0.4
InAs
5.7
5.8
5.9
6.0
e-h Pair Generation and Recombination (cm s )
0.0
InAs
0.2
5.6
DefectRelated
6.1
0.0
0.5
1.0
1.5
2.0
Energy (eV)
spacing
(Angstroms)
AtomAtom
Spacing
(Angstroms)
2
Bn
2
An  Bn
Radiative Rate
Efficiency =
=
Total Rate
2.5
Where A = SRH Coefficient, B = Radiative Coefficient and n = Carrier Density
Increasing the Indium concentration in the InGaAs lowers the bandgap and increases the fraction
of blackbody radiation that is absorbed in the cell.
Comparing the Defect-Related and Radiative Rates
@ 50% Radiative Efficiency, n = A/B
Total Rate at 50% Efficiency = An + Bn2 = 2A2/B
Sample Structure
0.73 eV
y
m
n
0.47
0
0
0
0.65 eV
0.40
0.14
-0.46
2
0.60 eV
0.34
0.27
-0.87
4
0.55 eV
0.28
0.40
-1.28
6
0.50 eV
0.22
0.53
-1.69
8
-3 -1
x
21
10
Threshold
2
Active Layer
Eg(x)
A /B (cm s )
Nominal Epistructure
Parameters
Increasing
Lattice
Mismatch
20
10
0.50
m = Total Mismatch (%)
0.55
0.60
0.65
0.70
0.75
Nominal Bandgap Energy(eV)
Exceeding a threshold mismatch of ~1% increases the defect-related rate relative to the radiative rate.
Experimental Setup
A Change in the Shape of the Efficiency Curve
Lattice-Matched Case
Laser Diode (980 nm)
100
100
Cryostat @ 77K
Absolute Radiative Efficiency
Photodiode
Lowpass
Filter
Sample
ND Filters
80
60
40
20
Eg= 0.73 eV
Theoretical Fit
0
: Laser Light
Lattice-Mismatched Case
10
: Luminescence
Absolute Radiative Efficiency
Bandgap
energy
(eV)
(eV)
Energy
Bandgap
1.4
GaAs
GaAs
Radiative
Absolute Radiative Efficiency
Lattice-mismatched In-rich InGaAs on InP
18
19
10
20
10
10
21
10
22
23
1x10
80
60
40
20
Eg= 0.60 eV
Theoretical Fit
0
24
10
18
10
-3 -1
e-h Pair Generation and Recombination (cm s )
19
10
20
10
21
10
22
10
1x10
23
10
24
-3 -1
e-h Pair Generation and Recombination (cm s )
While the theory fits well in the lattice-matched case, the model does not fit the shape of the efficiency curve in the mismatched
samples. This phenomenon is attributed to a change in the distribution of energy levels at defect sites.* (See reference below)
Experimental Data
Absolute Radiative Efficiency
120
Conclusions
100
•Moderate mismatch does not affect the rate of defect-related recombination relative to the radiative rate.
•Large mismatch has an appreciable effect on this ratio.
•The threshold that distinguishes these two regimes is approximately 1% lattice mismatch.
•A change in the shape of the efficiency curve is observed for all mismatched samples relative to the lattice-matched case.
The phenomenon is attributed to a change in the distribution of energy levels at defect sites. Further work is needed to test
this hypothesis.
80
60
40
Eg= 0.73 eV
Eg= 0.65 eV
Eg= 0.60 eV
Eg= 0.55 eV
Eg= 0.50 eV
20
0
18
10
19
10
20
10
21
10
22
10
23
1x10
Acknowledgements and References
24
10
-3 -1
e-h Pair Generation and Recombination (cm s )
Photoluminescence intensity (normalized by the excitation power) vs. the
rate of electron-hole pair generation and recombination in steady state.
This project is supported by the Research Corporation and the Petroleum Research Fund.
* T. Saitoh, H. Iwadate and H. Hasegawa, Jpn. J. Appl. Phys. 30, 3750 (1991).
Corresponding Author: Tim Gfroerer
Physics Department, Davidson College
Davidson, NC 28036 (tigfroerer@davidson.edu)