Solar Cells, Sluggish Capacitance,
and a Puzzling Observation
Tim Gfroerer
Davidson College, Davidson, NC
with Mark Wanlass
National Renewable Energy Lab, CO
~ Supported by Bechtel Bettis, Inc. and the American
Chemical Society – Petroleum Research Fund ~
Experiments by . . .
Kiril Simov (Davidson ’05)
Patten Priestley (Davidson ’03)
and Malu Fairley (Spelman ’03)
Outline
• Semiconductors, defects, and solar cells
• Diode capacitance and the DLTS
experiment
• Our measurements and an unusual result
• A new model for minority carrier
trapping/escape during DLTS
Semiconductors
a
free atoms
V(r)
r
atomic crystal
Energy levels
Spacing decreasing
n=3
n=2
n=1
-
a
Periodic
Potential
Physlet
InGaAs Bandgap vs. Alloy Composition
1.6
1.4
GaAs
InP
Bandgap (eV)
1.2
Substrate
1.0
Bandgap
vs. Lattice
Physlet
Severe
Mismatch
0.8
0.6
0.4
0.2
5.6
InAs
5.7
5.8
5.9
6.0
Lattice parameter (Angstroms)
6.1
Semiconductor Defects
Lattice-Mismatch Applet
Defect Level Physlet
(from the forthcoming Physlet Quantum Physics:
An Interactive Introduction to Quantum Theory
by Mario Belloni et al., due out this Fall
Solar Cell Operation
Conduction Band
-
E-Field
-
ELECTRON
ABSORPTION
CURRENT
PHOTON
-
Valence Band
HOLE
+
E-Field
+
+
+
When a photon is absorbed, an electron is excited into the conduction band, leaving a
hole behind in the valence band. An internal electric field sweeps the electrons and
holes away, creating electricity.
Defect-Related Trapping
and Recombination
Conduction Band
ENERGY
-
Defect Level
PHONONS
PHONONS
+
Valence Band
But electrons can recombine with holes by hopping through defect levels and
releasing phonons (heat). This loss mechanism reduces the efficiency of a solar cell.
Defect-Related Transition
Probabilities
-
P ~ (0.5)10 ~ 10-3
P ~ 10-1
P ~ (0.5)16 ~ 10-5
P ~ 10-5
P ~ 10-3
P ~ (0.5)4 ~ 10-1
+
+
+
The probability P of transitions involving phonon emission depends on the number of
phonons required, which is determined by the position of the defect level in the gap.
p/n Junction Formation
+
+
+
+ + +
+
+
+
+ +
+ + P+ + +
+ + + +
+ + + + +
+
+
+
+
+
-
Depletion Layer
-
-
N -
Bias-Dependent Depletion
+
+
+
+ + +
+ + + +
+ + P+ +
+ + + +
+ + + +
+
+
-
+
-
+
+
+
Depletion Layer
-
+
-
N+ -
With
Bias
-
+
Diode Capacitance
d1
No
bias
Vbuilt-in
d2
Reverse
bias
C = DQ/DV
~ e0A/d
Vbuilt-in+Vapplied
Reverse bias increases the separation between the layers where free
charge is added or taken away.
Defect characterization via DLTS
+
+
+
+ + + + + + + +
+ + P+ + + + + +
+
+
+ + +
+
+ -
+
+
+
-
+
-
-
+
-
N+ -
Depletion
Temporary
Layer With Bias
Reduced Bias
+
Typical DLTS Measurements
0
e
T = 200K
T = 180K
T = 160K
T = 140K
-1
Capacitance Change (a.u.)
e
-2
e
Pulse
toward
zero
bias
free carriers
-3
e
Return to steady-state reverse bias
-4
e
-5
e
trapped carriers
-6
e
0.0
0.1
0.2
0.3
Time (ms)
0.4
0.5
DLTS Experimental Setup
Computer with LabVIEW
(5)
Digital Scope
(Tektronix)
Capacitance
meter (Boonton)
(4)
Cryostat with sample
(1)
(2)
77K
(3)
Oxford
Agilent
Temp Controller
Pulse Generator
Device Structure and Band
Diagram
0.05m (Zn) In0.53Ga 0.47As
19
-3
NA = 1x10 cm
0.05m (Zn) InP
18
-3
N A = 2x10 cm
0.05m (Zn) In0.53Ga 0.47As
19
-3
NA = 1x10 cm
0.5m (S) In 0.53Ga0.47As
16
-3
ND = 3x10 cm
0.1m (S) InP
19
-3
ND = 1x10 cm
W
Energy
Depletion
region
Quasi EF,p
++++
-----
Quasi E F,n
Position
p+/n Junction
m (S) InP
18
-3
ND = 3x10 cm
Conduction band
Valence band
Transient Capacitance: Escape
-2
T = 130K
T = 140K
T = 145K
T = 150K
T = 160K
10
e
-4
Steady-State Bias = -1.1V
Pulse = +0.1V
-6
e
esc = 110 s
-1
e
Average Ea = 0.29 eV
12
e
Escape Rate (s )
Capacitance Change (a.u.)
e
8
e
6
e
4
e
-8
e
Pulse = +0.1V relative to SS
and
and
and
SS Bias = -0.1V
SS Bias = -1.1V
SS Bias = -2.1V
2
e
0.0
0.1
0.2
0.3
0.4
0.5
70
80
90
-1
Time (ms)
1 / kT (eV )
100
Filling Pulse Dependence: Capture
-2
e
-1
e
e
-3
-3
e
DC0 - DCtraps (a.u.)
-2
Capacitance Change (a.u.)
T = 77K
Pulse Length:
10 s
30 s
100 s
200 s
e
T = 77K
-4
e
-5
e
cap = 113 +/- 2 s
-4
e
-5
e
-6
e
-6
e
-7
e
Steady-State bias = -0.3V
Pulse: +0.2V (relative to SS)
-7
e
-8
-200
0
200
400
Time (s)
600
800
e
0
200
400
Pulse Length (s)
600
Proposed Model
W
Energy
Depletion
region
Quasi EF,p
++++
Conduction band
-----
Traps
d
Quasi E F,n
Position
p+/n Junction
Valence band
Testing the Model
3
e
Bias = -0.1V
Bias = -1.1V
Bias = -2.1V
Bias = -3.1V
-2
2
e
Pulse = +0.1V
T = 77K
-4
e
Thickness (nm)
Capacitance change DC0 (a.u.)
e
-6
e
1
e
0
e
-8
e
Dd
DW
D C0 (a.u.)
-1
e
-10
e
0.0
0.2
Time (ms)
0.4
0.6
0
1
2
Reverse Bias (V)
3
Variable-Bandgap Lattice-Mismatched Stuctures
Undoped InAsyP1-y, 30 nm
Undoped InxGa1-xAs, 1.5 μm
Undoped InAsyP1-y buffer, 1 μm
Undoped InAsyP1-y step-grade region:
0.3 μm/step (~ -0.2% LMM/step), n steps
Undoped InP substrate
Radiative Recombination
Conduction Band
-
light in
heat
PHOTON
+
Valence Band
light out
light in = heat + light out
radiative efficiency = light out / light in
10
16
10
12
-3
-1
Density of States (cm eV )
Defect-Related Density of States
10
8
10
4
10
0
0.0
0.1
Valence
Band
0.2
0.3
0.4
Energy (eV)
0.5
0.6
Conduction
Band
The distribution of defect levels within the bandgap can be represented by
a density of states (DOS) function as shown above.
Radiative Efficiency Measurements
100
Eg = 0.80 eV
Log(DOS)
100
light
80
40
20
heat
0
10
19
10
21
EV
Energy
EV Energy EC
60
Log(DOS)
Radiative Efficiency (%)
60
Log(DOS)
Radiative Efficiency (%)
80
40
EV Energy EC
20
EC
Eg = 0.68 eV
0
10
23
10
25
-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 )
Four Conclusions
• 0.29eV hole trap is observed in n-type
InGaAs under reverse bias
• Temperature-dependent capture and escape
rates are symmetrical
• Rates level off at cold temperatures due to
tunneling
• Device modeling points to defect states near
the p+/n junction
Two References
• T.H. Gfroerer et al., APL 80, 4570 (2003).
• T.H. Gfroerer et al., IPRM (2005).