Mapping free carrier diffusion in
GaAs with radiative and heatgenerating recombination
Tim Gfroerer and Ryan Crum
Davidson College, Davidson, NC
with Mark Wanlass
National Renewable Energy Lab, Golden, CO
~ Supported by the American Chemical Society –
Petroleum Research Fund ~
Solar Cell Operation
Conduction Band
-
E-Field
-
HEAT
ELECTRON
ABSORPTION
PHOTON
CURRENT
HOLE
-
Valence Band
+
E-Field
+
+
+
When a photon is absorbed, an electron is excited into the conduction band, leaving a
hole behind in the valence band. Some heat is lost, reducing efficiency. Then an
internal electric field sweeps the electrons and holes away, creating electricity.
Light- and Heat-Generating Recombination
Conduction Band
ENERGY
-
Photon
Conduction Band
-
Defect
Level
HEAT
HEAT
+
+
Valence Band
Valence Band
Rate ≈ B x n 2 (n = carrier density)
Rate ≈ A x n (n = carrier density)
Electrons can recombine with holes by releasing light or heat.
This loss mechanism also reduces the efficiency of a solar cell.
Experimental Setup
Laser spot ~
4 mm diameter
-
+
+
+
+
-
-
+
-
+
+-+ -
-
+
Luminescence
Camera
+
GaAs sample (plan view)
-
Thermal
Camera
-
-
+
Time evolution of thermal profile
0
Temperature Difference (K)
10
Time Window:
Laser on!
Heat loss
-1
10
0-33 ms
33-67 ms
67-100 ms
100-133 ms
Thermal diffusion
-2
10
-3
10
0
100
200
Distance (mm)
300
400
Luminescence and Thermal Profiles
0
Normalized Light or Heat Signal
10
Laser Excitation
Light Emission
T (Heat)
-1
10
-2
10
-3
10
-4
10
-5
10
0
100
200
300
Distance From Excitation Position (mm)
400
Square-root of the Luminescence
0
Normalized Light or Heat Signal
10
Laser Excitation
Light Emission
1/2
(Light Emission)
T (Heat)
Rate ≈ A x n
-1
10
-2
10
-3
10
Rate ≈ B x n 2
-4
10
-5
10
0
100
200
300
Distance From Excitation Position (mm)
400
Free-Carrier or Thermal Diffusion?!
0
Normalized Light or Heat Signal
10
Laser Excitation
Light Emission
1/2
(Light Emission)
T (Heat)
Thermal Diffusion
-1
10
-2
10
-3
10
-4
10
-5
10
0
100
200
300
Distance From Excitation Position (mm)
400
Conclusions
• We use optical and thermal imaging to
map the free-carrier density near a
localized photo-excitation source.
• The density profiles agree when we
account for the bimolecular nature of
radiative recombination.
• BUT: a thermal diffusion calculation also
mimics the temperature profile …
• So what have we measured?!
We’ll figure it out!