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

3

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

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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

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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

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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

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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: