Exploring Free Carrier Diffusion
with Light- and Heat-Generating
Recombination
Ryan Crum and Tim Gfroerer
Davidson College
Mark Wanlass
National Renewable Energy Lab
Funded by the American Chemical
Society – Petroleum Research Fund
E-Field
Conduction Band
-
-
-
-
-
Energy
Photon
Band Gap
+
Valence Band
+
+
E-Field
+
+
Heat-Generating
Recombination
Light-Generating
Recombination
electron
electron
-
Energy
heat
photon
Defect
Level
heat
+
hole
Rate ≈ A*n (n = carrier density)
+
hole
Rate ≈ B*n2 (n = carrier density)
+
+
+
-
+-
+-
-
+
+ - + -
+
-
Thermal Camera
+-
+-
+Light Camera
-
+-
+
Temperature Difference (K)
10
Time Window:
0
10
-1
10
-2
10
-3
10
-4
10
-5
Laser Profile
0-33 ms (open)
33-67 ms (closed)
67-100 ms (open)
100-133 ms (closed)
133-167 ms (open)
167-200 ms (closed)
200-233 ms (open)
0
100
200
Distance (m)
300
0
Temperature Difference (K)
10
Heat Loss
-1
10
Time Window:
0-33 ms (open)
33-67 ms (closed)
67-100 ms (closed)
100-133 ms (closed)
-2
10
Heat Diffusion
-3
10
-4
10
0
100
200
Distance (m)
300
400
0
10
Laser Profile
Temperature Profile
Light Profile
-1
Normalized Signal
10
-2
10
-3
10
-4
10
-5
10
0
100
200
Distance (m)
300
400
0
10
-1
Normalized Signal
10
Laser Profile
Light Profile
Sqrt of Light Profile
Temperature Profile
~ An
~ Bn
-2
10
-3
10
~ Bn
2
2

-4
10

-5
10
0
100
200
Distance (m)
300
400
• We found that the diffusion of carriers is best
represented by the temperature difference rather
than the light signal.
• When analyzing light profiles, the square root of the
signal should be used to obtain an accurate
measurement of the carrier density.