Tricks and traps in the latest
record-efficiency solar cells
Tim Gfroerer
Davidson College, Davidson, NC
with Mark Wanlass
National Renewable Energy Lab, Golden, CO
~ Supported by the American Chemical Society –
Petroleum Research Fund ~
Experiments and Analysis by . . .
Malu Fairley (Spelman ’03)
Brant West (’08)
Patten Priestley (’03)
Peter Simov (’08)
Adam Topaz (’08)
Outline
• Semiconductors, solar cells, and defects
• Radiative efficiency and dependence on
defect level distributions
• Diode capacitance and the DLTS experiment
• Non-exponential behavior and a new model
for carrier transport 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
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.
Silicon
bandgap
1.50
-2
-1
Solar Spetral Irradiance (Wm nm )
The Solar Spectrum at the Surface
of the Earth
1.25
1.00
0.75
0.50
Visible
0.25
0.00
400
800
1200
1600
Wavelength (nm)
2000
2400
A Trick: Multi-Junction Solar Cells
High bandgap
Medium bandgap
Low bandgap
Higher energy photons are absorbed in higher bandgap alloys, reducing the heat loss
caused by excess photon energy relative to the gap.
A Trap: Lattice Matching
Growing a stack of defect-free alloys usually requires lattice matching.
The dashed vertical line is a common triple-junction lattice target.
GaInP
bandgap
1.50
-2
-1
Solar Spetral Irradiance (Wm nm )
The Solar Spectrum with TripleJunction Bandgaps
1.25
GaAs
bandgap
1.00
0.75
0.50
Ge
bandgap
Visible
0.25
0.00
400
800
1200
1600
Wavelength (nm)
2000
2400
GaInP
bandgap
1.50
-2
-1
Solar Spetral Irradiance (Wm nm )
A Trick: Lattice-Mismatched InGaAs
1.25
GaAs
bandgap
1.00
InGaAs
bandgap
0.75
0.50
Visible
0.25
0.00
400
800
1200
1600
Wavelength (nm)
2000
2400
Semiconductor Defects
Lattice-Mismatch Applet
Defect Level Physlet
~ from Physlet Quantum Physics: An Interactive Introduction
by Mario Belloni et al. (2006).
Defect-Related Trapping
and Recombination
Conduction Band
ENERGY
-
Defect Level
HEAT
HEAT
+
Valence Band
Electrons can recombine with holes by hopping through defect levels and releasing
more heat. This loss mechanism also reduces the efficiency of a solar cell.
One More Trick: Step-Grading
GaInP window
GaAsxP(1-x) active layer
Lattice-matched GaInP barrier
GaAsP buffer
GaAsP Lattice-mismatch step grade
GaAs Substrate
Typical sample structure (not to scale).
{
Ga0.86As0.15P
Ga0.89As0.12P
Ga0.91As0.09P
Ga0.94As0.06P
Ga0.97As0.03P
Equilibrium Occupation in a Low
Temperature Semiconductor
Holes
Electron Trap
Hole Trap
Electrons
Photoexcitation
Photoexcitation
Photoexcitation
Photoexcitation
Band-to-Band Radiative Recombination
Band-to-Band Radiative Recombination
Band-to-Band Radiative Recombination
Electron Trapping
Electron Trapping
Defect-Related Recombination
Defect-Related Recombination
Note:
Sub-bandgap
photons may
also be emitted
Defect-Related Recombination
Note:
Sub-bandgap
photons may
also be emitted
Luminescence Spectra
8
10
7
Luminescence (a.u.)
10
B-to-B
Defect-related
GaAsxP1-x
T = 77K
6
10
x = 0.844
5
10
Shifted
Vertically
For clarity
4
10
x = 0.927
3
10
B-to-B
Defect-related
2
10
x = 1.00
1
10
1.2
1.4
1.6
1.8
2.0
Energy (eV)
Radiative recombination can reveal defect-related transitions that lie
below the usual band-to-band (B-to-B) emission.
Thermally Activated Escape
E
 Escape 

  e  E / kT
 Rate 
Thermally Activated Escape
E
 Escape 

  e  E / kT
 Rate 
Radiative Efficiency
Conduction Band
-
light in
heat
PHOTON
+
Valence Band
light out
light in = heat + light out
radiative efficiency = light out / light in
Photoluminescence Experimental Setup
Doubled-YAG laser
0.2 W @ 532 nm
Variable Temp
Cryostat
Photodiode
Lowpass
Filter
Sample
Spectrometer
ND Filters
Beamsplitter
: Laser Light
: Luminescence
Some data with conventional
theoretical fits
1.0
Assumptions:
2.
Defect levels clustered near the
middle of the gap –
no thermal excitation out of traps
(# of electrons) = (# of holes) = n
Theoretical Efficiency:
Efficiency 
2
77K
120K
165K
207K
250K
290K
0.8
Radiative Efficiency
1.
Temperature:
band-band
dominates
0.6
0.4
defects
dominate
0.2
RadiativeRate
Bn

DefectRate  RadiativeRate An  Bn 2
0.0
19
10
20
10
21
10
22
10
-3 -1
Recombination Rate (cm s )
23
10
A Better Model and a Different Plot
Theoretical Efficiency:
Bn p
Efficiency 
TotalRate
23
DOS
10
22
10
-3 -1
Total Rate (cm s )
Improvements:
1. Defect level distribution can be
tailored to achieve the best fit
2. Theory accounts for thermal
excitation out of traps
3. (# of e-s in conduction band) = n
can differ from
(# of holes in valence band) = p
EV
21
10
Energy
EC
77K
120K
165K
207K
250K
290K
20
10
19
10
25
10
27
10
29
10
31
10
-6
p x n (cm )
33
10
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.
The Defect-Related Density of
States (DOS) Function
Conduction Band
1.2
1
Energy
0.8
Defect States
0.6
0.4
0.2
0
-0.5
Ev
Valence Band
-0.3
-0.1
Energy
0.1
0.3
0.5
Ec
New Theoretical Fit With Improved
Defect Level Distribution Analysis
Improvements in fit:
References: (students in red)
T. H. Gfroerer, L. P. Priestley,
F. E. Weindruch, and M.W. Wanlass,
Appl. Phys. Lett. 80, 4570 (2002).
A. Topaz, B. A. West, T. H. Gfroerer,
and M. W. Wanlass, Appl. Phys. Lett.
90, 092110-1 (2007).
DOS
22
10
-3 -1
2.
Asymmetric DOS produces shallow
slope at low carrier concentration
Thermal activation out of traps gives
comparable temperature dependence
Total Rate (cm s )
1.
23
10
EV
21
10
Energy
EC
77K
120K
165K
207K
250K
290K
20
10
19
10
25
10
27
10
29
10
31
10
-6
n x p (cm )
33
10
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
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
~ eA/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
Device Structure and Band Diagram
Ga0.65In0.35P (S)
Barrier
GaAs0.72P0.28 (S+)
N+
P
GaAs0.72P0.28 (Zn)
Ga0.65In0.35P (Zn)
Barrier
GaAsP step-grading
GaAs Substrate
{
N+ P Junction
Conduction band
Energy
Quasi EF,p
Quasi EF,n
+ + +
Valence band
---Position
Depletion
region
W
Exponential transient analysis
Steady-state Bias = -2V
Pulse height = +1V
400ms RF
400ms RS
 Escape 

  e  E / kT
 Rate 
5
10
Ea = 93meV
40ms RF
40ms RS
2
Ea = 91meV
-1
Rate (s )
Capacitance Change (pF) on a log scale
10
1
155K
160K
165K
170K
175K
180K
0.5
0.0
0.1
Ea = 81meV
10
0.2
Time (s)
0.3
0.4
1
Ea = 91meV
60
65
70
75
-1
1/kT (eV )
Reciprocal Analysis
Steady-state Bias = -2V
Pulse height = +1V
5
10
Slope of 1/C(t) (a.u.)
Capacitance Change (pF) on a reciprocal scale
10
155K
160K
165K
170K
175K
180K
1
0.0
0.1
3
Ea = 0.38eV
10
2
10
1
40 ms response
400 ms response
0.2
Time (s)
0.3
0.4
60
65
70
-1
1/kT (eV )
75
80
Hopping between traps
+
+
+
+
+ +
+
+
+
+
+
+
+
+
+ +
+
++
-
Depletion Layer With Bias
-
-
N+ -
+
Hopping between traps
+
-
+
+
+
+ +
++ N+ +
+
+
+
+
++ + +
+ +
+
Temporary Reduced
Bias
Hopping between traps
+
-
+
+
+
+ +
++ N+ +
+
+
+
+
++ + +
+ +
+
Depletion Layer With Bias
Hopping between traps
+
+
+
+ +
++ +
N+ +
+
+
+
++ + +
+ +
+
+
Depletion Layer With Bias
Hopping between traps
+
+
+
+ +
++ +
N+ +
+
+
+
++ + + +
+
+
+
Depletion Layer With Bias
Hopping between traps
+
+
+
+
+ +
+
+
+
+
+
+
+
+
+ +
+
++
-
Depletion Layer With Bias
-
-
N+ -
+
Discussion of DLTS Results
• Non-exponential transient rates are incompatible with
conventional thermal activation analysis
• Reciprocal of the capacitance varies linearly with time,
and the slope yields a single thermal activation energy
• Hopping? (thermally-activated reciprocal behavior is a
characteristic of hopping transport).
• Test dependence on transport distance by varying
magnitude of pulse. (in progress!)
DLTS Reference
• T.H. Gfroerer, P.R. Simov ('08), B.A. West ('08), and
M.W. Wanlass, 33rd IEEE Photovoltaics Specialists
Conference (to be presented in May, 2008).
Conclusions
• Further improvements in solar cell
efficiency will depend on better latticemismatched designs
• Lattice-mismatch introduces defects which
can degrade solar cell performance
• Understanding the impact of defects will
facilitate better designs
• Photoluminescence and DLTS are powerful
tools for characterizing defect properties
in semiconductors