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1
Test Methods for Contactless Carrier Recombination Lifetime in Silicon
Wafers, Blocks, and Ingots
Ronald A. SintonSinton Instruments, Inc. Boulder, Colorado USA
SEMI Standards MeetingHamburg, 21 September, 2009
2
Explore, evaluate, discuss, and create consensus-based standard measurement methods, specifications, guidelines,
and practices that, through voluntary compliance, will promote mutual understanding and improved communication between users and suppliers of photovoltaic manufacturing
equipment, materials and services to enhance the manufacturing efficiency and capability so as to reduce manufacturing cost of the photovoltaic (PV) industry. “
Charter of Global Photovoltaic Committee
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Carrier Recombination Lifetime
e ee
e
e e e
Carrier-recombination lifetime: The central parameter to the device design, production, and process control for silicon solar cells.
4
Why measure lifetime?-After crystal growth: Process monitoring of feedstock contamination, contamination from crucible, bad growth conditions.
-After wafering: Qualify wafers for sale or purchase.
-After dopant diffusion: Monitor the quality of the dopant diffusion, check for chemical contamination, verify bulk lifetime, estimate final solar cell efficiency.
-After nitride deposition: Monitor nitride quality, optimize firing parameters for bulk and surface passivation quality.
-R&D: For use in characterizing bulk lifetimes and surface passivations. Input data for cell design and process optimization.
5
What determines bulk lifetime?
Metallic Impurities: Fe, Cr, Al, Au, Cu, others.
Can be from feedstock, crucible, gas contamination, chemical contamination.
Other defects: In boron CZ, B:O pairs, oxygen precipitates
Crystalline defects: dislocations, grain boundaries
6
What determines measured lifetime?
-Bulk lifetime
-Surface Recombination
-Wafer thickness
-Dopant-diffused region recombination
-Diffusion of excess carriers in the wafer or block
7
What are the excess carrier recombination lifetime and excess-carrier density ranges that are important
for solar cells?
Lifetime: 0.1 to 10,000 μs Carrier Density: 1x1013 to 5x1016 cm-3
Scope of the measurement:
8
Carrier Recombination Lifetime: 0.1 to 10,000 μs
0.01 0.1 1 10 100 1000 10000 100000Carrier Recombination Lifetime (μs)
Bulk material
Cells and Passivated wafers
as-cutwafers
9
Silicon Solar Cell I-V Curves
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Solar Cell Voltage
Cur
rent
Den
sity
(A/c
m2 )
Industrial Solar Cell
High-efficiency Commercial cell
0
6
12
1.00E+12 1.00E+13 1.00E+14 1.00E+15 1.00E+16 1.00E+17
Excess Carrier Density (cm-3)
10
Fig. 1. The modeled recombination lifetime of a 3-ohm-cm B-doped CZ sample after degradation of the B:O defect[1]. This curve is based on recombination parameters from the studies of Bothe [1].
Injection level dependence of the Effective Excess-Carrier Recombination Lifetime
0.0E+002.0E-054.0E-056.0E-058.0E-05
1.0E-041.2E-041.4E-041.6E-041.8E-04
1.E+13 1.E+14 1.E+15 1.E+16 1.E+17
Excess carrier density (cm-3)
Effe
ctiv
e Li
fetim
e (s
econ
ds)
11
How To Write a “Lifetime” Test Method?
1) Develop a consensus: How should lifetime be measured so that the results are physically relevant for silicon solar cells and can be compared between laboratories, institutes, and industrial companies using different measurement methods?
2) Submit a document to become a test method.
12
Consensus: White Paper
1) General framework for a lifetime measurement and interpretation (sensor-type independent).
13
Contributors (white paper comments)K. Bothe ISFH, Germany: μ-pcd, PhotoLuminescence, RF- pcd, RF-QSSPC, Infra-red Lifetime Mapping.T. Roth, Fraunhofer ISE, Germany: μ-pcd, PL, RF-pcd, CDI, RF-QSSPC, QSSPL.W. Warta: Fraunhofer ISE (same tool experience).R. M. Swanson, SunPower Corp, USA.R. Falster: MEMC.S. Johnston: NREL USA: μ-pcd, RF-pcd, RF-QSSPC, PL.K. Lauer, CiS Mikrosensorik, Germany: μ-pcd, QSSPC.J. Nyhus, REC, Norway: μ-pcd, luminescence, QSSPC.T. Trupke, BT Imaging, Australia: PL, QSSPC, QSSPL, Imaging PL.L. Janssen, Solland, Netherlands: QSSPC, μ-pcd.N. Stoddard, BP SolarA. Cuevas, Australian National University, QSSPC.
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1 Introduction2 Measurement of carrier recombination lifetime in a sample.3 The interpretation of lifetime data on wafers4 Interpretation of Lifetime Data Taken on Ingots or Blocks
Table 1. List of contactless sensors in relatively widespread use in 2009 for determining lifetime in silicon using the described measurement methodology.
Table 2. Parameters that should be reported from a lifetime measurement to make it unique and reproducible between labs and different measurement techniques.
Contactless Carrier-Lifetime Measurement in Silicon Wafers, Ingots, and Blocks
15
5 Specific Example, Description of RF-photoconductance test method. (Very brief description).
6 References:
Contactless Carrier-Lifetime Measurement in Silicon Wafers, Ingots, and Blocks
16
Steady-State Excess Carrier Lifetime
Gnneff
Δ=Δ )(τ
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100 120Time (μs)
Ligh
t
0
2E+14
4E+14
6E+14
8E+14
1E+15
1.2E+15
1.4E+15
Car
rier d
ensi
ty
Excess Carrier density
Light
17
Transient Excess Carrier Lifetime
dttndtnneff /)()()(
ΔΔ
−=Δτ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10 20 30 40 50 60Time (μs)
Ligh
t
0
2
4
6
8
10
12
Car
rier d
ensi
ty
Excess Carrier density
Light
18
Generalized Quasi-Steady-State Excess Carrier Lifetime
dttndtGtnneff /)()()()(
Δ−Δ
=Δτ
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 50 100 150 200 250 300 350Time (μs)
Ligh
t
0.0E+00
5.0E+13
1.0E+14
1.5E+14
2.0E+14
2.5E+14
3.0E+14
3.5E+14
4.0E+14
4.5E+14
5.0E+14
Car
rier D
ensi
tyLight
Excess Carrier density
19
Fig. 1. The modeled recombination lifetime of a 3-ohm-cm B-doped CZ sample after degradation of the B:O defect[1]. This curve is based on recombination parameters from the studies of Bothe [1].
Injection level dependence of the Effective Excess-Carrier Recombination Lifetime
0.0E+002.0E-054.0E-056.0E-058.0E-05
1.0E-041.2E-041.4E-041.6E-041.8E-04
1.E+13 1.E+14 1.E+15 1.E+16 1.E+17
Excess carrier density (cm-3)
Effe
ctiv
e Li
fetim
e (s
econ
ds)
20
Method How is excess carrier density sensed?
Issues: Pros / Cons
RF-QSSPC Eddy current sensing of Photoconductance
Conversion to Δn using known mobility function
Simple calibration that is valid for a wide range of samples. Requires mobility and photogeneration
calculation or measurement. Non mapping or coarse mapping only. Trapping and Depletion
Region Modulation artifacts at low carrier density.
RF Transient Eddy current sensing of Photoconductance
Conversion to Δn using known mobility function
Simple calibration. Can be subject to trapping and DRM artifacts at low carrier density.
ILM/CDI IR free-carrier absorption or emission. High-resolution imaging capability. Surface texture complicates interpretation, subject to
trapping and DRM artifacts.
μ-PCD Microwave reflectance sensing of photoconductance. Carrier density
can be set by bias light, or by injecting known number of photons in
a very short pulse.
High-resolution mapping capability. Non-linear detection of photoconductance in some injection- level or dopant ranges, skin-depth comparable to
sample thickness in some cases. DRM and trapping artifacts at low carrier density.
Photoluminescence Band-gap light emission, model for coefficient of radiative emission.
Model for re-absorption.
Artifact-free data available even below the intrinsic carrier density. Used in both non-imaging and high-resolution imaging applications. Strong
doping dependence, photon reabsorption depends on surface texture, detector EQE, and wafer
thickness.
Table 1. List of contactless sensors in relatively widespread use in 2009 for determining lifetime in silicon
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Wafers
Interpretation of lifetime data
22
Carrier Recombination Lifetime: Surface Recombination
Front Surface passivation
substrate
Rear surface passivation
WnSnS
nnbackfront
bulkeff
)()()(
1)(
1 Δ+Δ+
Δ=
Δ ττ
[ ]nNWqn
JJnn A
i
backoefrontoe
bulkeff
Δ++
+Δ
=Δ 2)(
1)(
1ττ
Surface and bulk
Emitter and bulk
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Carrier Recombination Lifetime: Surface Recombination
Front Surface passivation
substrate
Rear surface passivation
Transit time D
Wneff 2)(
2
>Δτ
pn
pn
pDnDDDpn
D+
+=
)(Diffusion coefficient
6 μs for 180 μm p-type 1 ohm-cm
24
Silicon Solar Cell I-V Curves
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Solar Cell Voltage
Cur
rent
Den
sity
(A/c
m2 )
Industrial Solar Cell
High-efficiency Commercial cell
0
6
12
1.00E+12 1.00E+13 1.00E+14 1.00E+15 1.00E+16 1.00E+17
Excess Carrier Density (cm-3) Jo measurement
25
Ingots and Blocks
Interpretation of lifetime data
26
Lifetime ~ bulk lifetime if absorption depth >> L
Lifetime < a few μs
S = ∞
1000 nm
530 nm
Electrons photogenerated near the surface recombine instantly, electrons created deep in the silicon live longer.
Very thick
Wavelength dependence for QSS lifetime measurements on blocks
1+=
Lbulk
eff αττ
27
Monochromatic Light
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.00E-07 1.00E-06 1.00E-05 1.00E-04 1.00E-03
Measured Lifetime (seconds)
Bul
k Li
fetim
e (s
econ
ds)
Tau eff (510nm)Tau eff (660nm)Tau eff (900nm)Tau eff (1045nm)1 : 1
Analytical calculation
28
Broadband Light (filtered Xenon)
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.00E-07 1.00E-06 1.00E-05 1.00E-04 1.00E-03
Measured Lifetime (seconds)
Bul
k Li
fetim
e (s
econ
ds)
1 : 1RG1000RG850BG38
PC1D simulation
29
What Carrier Density to Report (QSSPC)?
0.0E+00
5.0E+13
1.0E+14
1.5E+14
2.0E+14
2.5E+14
3.0E+14
3.5E+14
4.0E+14
0 0.05 0.1 0.15 0.2
width (cm)
Elec
tron
Con
cent
ratio
n (c
m-3
) Weighted electron density
Mean electron density
∫
∫∞
∞
=
0
0
2
dxn
dxnnav
∫∫∞
∞
Δ
⎟⎠⎞⎜
⎝⎛ Δ
=
0
2
2
0
dxn
dxnWeff
Sinton et al. ECPVSEC Paris 2004, Bowden et al. JAP 2007.
30
High-lifetime silicon CZ or FZ boules
31
Transient PCD on blocks or boules
Light
In Steady-state with light on
0.0E+001.0E+152.0E+153.0E+154.0E+155.0E+156.0E+157.0E+158.0E+159.0E+151.0E+16
0 0.005 0.01 0.015 0.02
Distance into Si (m)
Car
rier D
ensi
ty
Carrier Density
At 500 microseconds
0.0E+00
2.0E+14
4.0E+14
6.0E+14
8.0E+14
1.0E+15
1.2E+15
1.4E+15
1.6E+15
0 0.005 0.01 0.015 0.02
Distance into Si (m)C
arrie
r Den
sity
Carrier Density
PC1D simulations
32
Transient PCD on blocks or boules
1.0E+12
1.0E+13
1.0E+14
1.0E+15
1.0E+16
0 0.005 0.01 0.015 0.02 0.025
Distance into Si (m)
Carr
ier D
ensi
ty
Carrier Density illuminated
After 0.5 ms
After1.0 ms
After 2.0 ms
After 4.0 ms
3 mm
30 msPC1D simulations
33
Data: Taking Measurements
34
How to actually do a lifetime measurement: 4 steps.
1) Illuminate a sample, and measure the resulting signal with the sensor, (Raw data).
2) Use a calibration curve to convert the signal into physical units.
3) Convert the physical units into carrier density vs. time, illumination.
4) Evaluate the excess-carrier recombination lifetime by applying the equations for the transient, QSS, or steady- state case.
35
Table 2. Parameters to Report (sufficient for comparison between labs and methods)
Results:Measured lifetime, τeff
Carrier density (or range) to report lifetime
Interpretation (if any): S, τbulk , Joe
Sample parameters:
Thickness
Doping (cm-3)
p- or n-type
Surface passivation (front and back)
Analysis type:Transient, QSS, or Generalized
Excitation Wavelengths
Trapping or DRM correction (if required)
Instrument parameters:
Light time profile
Sensor type and calibration to Δn
Sense depth (ingot or block only unless sensitivity varies over a wafer thickness)
Photogeneration calibration
Detection area, number of points, method of averaging points (if any).
36
Table 2. Parameters to Report (sufficient for comparison between labs and methods)
Results:Measured lifetime, τeff
Carrier density (or range) to report lifetime
Interpretation (if any): S, τbulk , Joe
Sample parameters:
Thickness
Doping (cm-3)
p- or n-type
Surface passivation (front and back)
Analysis type:Transient, QSS, or Generalized
Excitation Wavelengths
Trapping or DRM correction (if required)
Instrument parameters:
Light time profile
Sensor type and calibration to Δn
Sense depth (ingot or block only unless sensitivity varies over a wafer thickness)
Photogeneration calibration
Detection area, number of points, method of averaging points (if any).
37
Parameters to Report (sufficient for comparison between labs and methods)Results:
Result description Symbolic Value Units Measured effective lifetime τeff seconds,ms,µsCarrier density range Δn cm‐3 Interpretation parameters [if any]
Surface recombination S cm2/s Bulk lifetime τbulk seconds,ms,µsEmitter saturation current Joe A/cm2 Other
Interpretation Notes:
Sample Parameters:
Parameter description Symbolic Value Units Sample thickness w cm,µm Doping concentration NA (ND) cm‐3 Doping type n / p Surface passivation, front and back ‐ Defect state [if applicable] ‐
Fe dissociation level ‐ B:O degradation level ‐ Other
Analysis type:
Transient
Quasi‐steady‐state (QSS) Generalized
Instrument Parameters:
Parameter description Value Units Light time profile
Calibration of photogeneration Sensor type
Calibration to Δn Sense depth cm,µm Detection area
Area Number of points Method of averaging points [if any]
Excitation wavelengths/frequencies Transfer function τeff to τbulk Trapping or DRM correction [if any]
38
Table 1. Parameters to Report (sufficient for comparison between labs and methods)
Results:
Result description Symbolic Value Units Measured effective lifetime τeff seconds,ms,µsCarrier density range Δn cm‐3 Interpretation parameters [if any]
Surface recombination S cm2/s Bulk lifetime τbulk seconds,ms,µsEmitter saturation current Joe A/cm2 Other
Interpretation Notes:
Sample Parameters:
Parameter description Symbolic Value Units Sample thickness w cm,µm Doping concentration NA (ND) cm‐3 Doping type n / p Surface passivation, front and back ‐ Defect state [if applicable] ‐
Fe dissociation level ‐ B:O degradation level ‐ Other
39
Table 1. Parameters to Report (sufficient for comparison between labs and methods)
Analysis type:
Transient
Quasi‐steady‐state (QSS) Generalized
Instrument Parameters:
Parameter description Value Units Light time profile
Calibration of photogeneration Sensor type
Calibration to Δn Sense depth cm,µm Detection area
Area Number of points Method of averaging points [if any]
Excitation wavelengths/frequencies Transfer function τeff to τbulk Trapping or DRM correction [if any]
40
Carrier recombination measurements using an RF-eddy-current conductance sensor
(RF-QSSPC, RF Transient PCD)
One specific example:
41
Xenon Flashlamp
IR-pass filter
intensity measurement reference cell
Transparent eddy-current sensor (13.56 MHz)Sense depth 2.5 mm into the silicon
Silicon wafer or ingot
Light source, reference intensity sensor, and photoconductance sensor.
Transparent eddy-current sensor
42
Step 1: Take data.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 50 100 150 200 250 300 350Time (μs)
Ligh
t
0.0E+00
5.0E+13
1.0E+14
1.5E+14
2.0E+14
2.5E+14
3.0E+14
3.5E+14
4.0E+14
4.5E+14
5.0E+14
Sign
al
Light
Instrument Signal
43
Step 2: Conductance Calibration: Traceable to 4-point-probe
Lifetime Tester Calibration
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 1 2 3 4 5 6 7 8 9 10
Voltage minus offset
Sie
men
s (1
/ohm
/sq)
Measured voltage - offsetfit
Siemens =0.00026(V--0.69052)^2+0.03109(V--0.69052)
44
Step 3: Photoconductance & Carrier Density
• The mobility equation converts the conductivity to an average carrier density.
)( ),(),( ApAn NnNnqWn
Δ+ΔΔ
=Δμμ
σ
45
Step 4: Carrier density vs. time & light.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 50 100 150 200 250 300 350Time (μs)
Ligh
t
0.0E+00
5.0E+13
1.0E+14
1.5E+14
2.0E+14
2.5E+14
3.0E+14
3.5E+14
4.0E+14
4.5E+14
5.0E+14
Car
rier D
ensi
tyLight
Excess Carrier density
46
0.0E+00
2.0E-05
4.0E-05
6.0E-05
8.0E-05
1.0E-04
1.2E-04
1E+13 1E+14 1E+15 1E+16 1E+17
Excess Carrier Density (cm-3)
Car
rier R
ecom
bina
tion
Life
time
(sec
)
Fig. 1. The recombination lifetime of a 3-ohm-cm B-doped CZ sample after degradation of the B:O defect[1]. This data was obtained by the QSSPC method[2] and has uncertainties less than 10% in both the lifetime and carrier-density axis.
47
White Paper: A consensus on a fundamental framework for silicon PV carrier recombination lifetime testing.
The analysis applies to any sensor, facilitating comparisons between labs and methods.
Results based on this framework are physically rigorous and suitable for use in solar-cell modeling, optimization, and process control.
Conclusions: