Optical properties of latticemismatched semiconductors for
thermo-photovoltaic cells
TIM GFROERER, Davidson College
Davidson, NC USA
in collaboration with the National
Renewable Energy Laboratory, USA
- Supported by Research Corporation
and the Petroleum Research Fund
Outline
Motivation
Sample Structure and
Experimental technique
Results and Analysis
Conclusions and Future Work
Motivation: Thermophotovoltaic
(TPV) Power
Heat
Heat Source
Blackbody Radiation
Blackbody Radiator
Semiconductor TPV
Converter Cells
TPV Cells are designed to convert infrared
blackbody radiation into electricity.
Motivation (continued)
Blackbody Radiation Absorbed
Bandgap vs. Alloy Composition
1.6
1.0
GaAs
o
1.4
Normalized intensity
T = 1300 C
Bandgap (eV)
1.2
Substrate
1.0
Severe
Mismatch
0.8
0.6
0.8
0.6
0.4
0.2
0.4
0.0
InAs
0.2
5.6
5.7
5.8
5.9
6.0
Lattice parameter (Angstroms)
6.1
0.0
0.5
1.0
1.5
Energy (eV)
Increasing the Indium concentration in the InGaAs lowers the bandgap and
increases the fraction of blackbody radiation that is absorbed in the cell.
Sample Structure
Nominal Epistructure
Parameters
Eg(x)
Active
Active Layer
Layer
x
y
m
n
0.73 eV
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
m = Total Mismatch (%)
InAsP grading layers above the substrate are used to reduce the density of
misfit dislocations at the interfaces of the active layer.
Experimental Setup
Laser Diode
1 Watt @ 980 nm
Cryostat @ 77K
Photodiode
Lowpass
Filter
Sample
ND Filters
: Laser Light
: Luminescence
Experimental Data
Absolute Radiative Efficiency
100
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
20
10
22
10
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.
Results: Data Calibration
Data from Eg = 0.73 eV Sample
Derivatives of Best-Fit Curve
40
30
Derivative (arbitrary units)
Relative Radiative Efficiency (a.u.)
2.0
1.5
1.0
0.5
20
10
Inflection
Point
0
-10
-20
Eg= 0.73 eV
0.0
rd
3 Order Polynomial Fit
18
10
20
10
22
10
24
10
-3 -1
e-h Pair Generation and Recombination (cm s )
First Derivative of Fit
Second Derivative
-30
-40
18
20
22
24
-3 -1
Log[Generation and Recombination (cm s )]
The derivatives show where the curvature of the relative efficiency inflects. We
scale the relative efficiency to 50% absolute efficiency at the infection point.
A Simple Theoretical Model
Efficiency =
Where A = SRH Coefficient,
B = Radiative Coefficient
and n = Carrier Density
Absolute Radiative Efficiency
Radiative Rate
Bn 2

Total Rate
An  Bn 2
100
80
60
40
20
Eg= 0.73 eV
Theoretical Fit
0
18
10
20
10
22
10
24
10
-3 -1
e-h Pair Generation and Recombination (cm s )
Total Rate @ 50%
Efficiency =
An + Bn2 = 2A2/B
-3 -1
Threshold
21
10
2
@ 50% Radiative
Efficiency, n = A/B
________________
A /B (cm s )
Defect-related vs. Radiative Rate
Increasing
Lattice
Mismatch
20
10
0.50
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.
Shape of the Efficiency Curve
Lattice-mismatched case
100
100
80
80
Absolute Radiative Efficiency
Absolute Radiative Efficiency
Lattice-matched case
60
40
20
Eg= 0.73 eV
Theoretical Fit
60
40
20
Eg= 0.60 eV
Theoretical Fit
0
0
18
10
20
10
22
10
24
10
-3 -1
e-h Pair Generation and Recombination (cm s )
10
18
10
20
10
22
10
24
-3 -1
e-h Pair Generation and Recombination (cm s )
While the simple theory fits well in the lattice-matched case, the model does
not fit the shape of the efficiency curve in the mismatched samples.
Defect-related Density of States
-3
-1
Density of states (cm eV )
Distribution of defect
levels in simple theory
Distribution of defect
levels in better theory
14
14
10
1 x 10
10
14
13
3 x 10
11
11
10
10
8
10
8
10
10
5
10
10
2
10
5
2
-1
-1
10
10
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0
0.1
0.2
0.4
0.5
Energy (eV)
Energy (eV)
valence
band edge
0.3
conduction
band edge
valence
band edge
conduction
band edge
0.6
A Better Theoretical Fit
100
80
Absolute Radiative Efficiency
Absolute Radiative Efficiency
100
DOS
60
40
20
Eg= 0.60 eV
Theoretical Fit
18
10
20
10
22
10
DOS
60
40
20
Eg= 0.60 eV
Theoretical Fit
0
0
10
80
24
-3 -1
e-h Pair Generation and Recombination (cm s )
18
10
20
10
22
10
24
10
-3 -1
e-h Pair Generation and Recombination (cm s )
The addition of band-edge exponential tails to the density of defect states
gives a much better fit.
Conclusions
 Moderate mismatch does not increase defect-
related recombination relative to the radiative
rate in these structures. Large mismatch has
an appreciable effect on this ratio.
 The threshold that distinguishes these two
regimes is approximately 1% lattice mismatch.
 The shape of the efficiency curve in all
mismatched samples differs from the latticematched case.
 The change is attributed to a re-distribution of
defect levels within the gap.
Future Work
 Continue fitting low temperature efficiency
curves to more detailed theory accounting for
the distribution of energy levels at defects.
 Compare results with complementary transport
measurements including photoconductivity
and DLTS.
 Connect defect-related density of states with
the microscopic structure of defects.
 Measure efficiency curves at higher
temperatures to further characterize defectrelated, radiative, and Auger recombination.