Recombination and lifetime
26.10.2015
Main question
Will this wafer make a good solar cell?
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Where are we?
dV
Jn(x)
Gn(x)
Un(x)
dx
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Jn(x+dx)
Continuity equation
• Assuming uniform generation and no net charge transport
(disregarding surface recombination) within the semiconductor:
• Solving for τeff yields:
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More generally, see:
Nagel et al, “Generalized
analysis of quasi-steadystate…”, JAP, 1999
Continuity equation – steady state
•
The photoluminescence intensity is detected with constant excitation over a
long time, so we can assume steady state
•
In steady state (dΔn/dt=0), the generation rate G and recombination rate U are
balanced:
•
Need to know Δn and G to determine the effective lifetime
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Recombination processes
Un(x)
RADIATIVE
(BAND-TO-BAND)
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SHOCKLEY-REEDHALL
AUGER
Bulk recombination – simplified equations
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Urad
UAug
USRH
Up,rad = Δn/τp,rad
Up,Aug = Δn/τp,Aug
Up,SRH = Δn/τp,SRH
τp,rad = 1/(Brad · Na)
τp,Aug = 1/(Ap · Na2)
τp,SRH = 1/(Bp,SRH · Nt)
Effective lifetime
• Several recombination mechanisms will occur simultaneously in
any given material
• The total effective lifetime is given by the inverse sum of the
separate lifetime contributions
(τeff)-1 = (τmech1)-1 + (τmech2)-1 + (τmech3)-1 + …
• Mostly, one or a few recombination processes with low
associated lifetimes will dominate
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Bulk lifetime in silicon
Bentzen: PhD thesis
26.10.2015
Surface recombination
•
A surface is an extended defect
• Introduces states in the band gap
• Dangling bonds
• Impurities
•
•
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Most often described using a
surface recombination velocity (S)
and a recombination flux
Formalism analogous to SRH
Surface recombination
Usurf
nsurfpsurf – ni2
Usurf · δx =
(1/Sn)(psurf + pt) + (1/Sp)(nsurf + nt)
δx
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Surface recombination
Usurf
Nt
Up,surf · δx = Sp · Δn
Sp = Bn · Nt
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δx
x
Surface recombination current
•
Surface recombination will contribute to the current densities at the surface
Jp,surf = q · ∫ Up,surf · dx = q · Sp · Δn
Jn,surf = -q · ∫ Un,surf · dx = q · Sn · Δn
δx
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Surface recombination and lifetime
• Surface recombination must be considered when measuring
lifetime
(1/τeff) = (1/τbulk) + (1/τsurf)
• If S is too high compared with τbulk, τeff will be determined only
by the surface recombination
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Surface recombination and lifetime
S
Dn
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Surface recombination and lifetime
•
For high values of S (S · d/Dn > 100)
S
(1/τeff) = (1/τbulk) + Dn(π/d)2
•
All charge reaching the surface recombines
•
Validity of equation:
Dn
•
•
Exact value of S no longer important
Diffusion towards surface becomes limiting factor
•
•
•
Diffusion constant (Dn)
≈ 30 cm2/s
Wafer thickness (d)
≈ 300 µm
Equation valid within ~ 5% as long as S > 100 000 cm/s
Rein: “Lifetime spectroscopy”
26.10.2015
Surface recombination and lifetime
• For low values of S (S · d/Dn < ¼)
(1/τeff) = (1/τbulk) + (2 · S/d)
S
Dn
• Limited by recombination at surface
• Validity of equation:
• Diffusion constant (Dn)
≈ 30 cm2/s
• Wafer thickness (d)
≈ 300 µm
• Equation valid within ~ 5% as long as S < 250 cm/s
Rein: “Lifetime spectroscopy”
26.10.2015
Surface passivation
•
•
Abrupt semiconductor surfaces: large S
For lifetime measurements, low S is required
•
•
High quality bulk material
Recipe
• Remove surface damage
• Clean surface thoroughly
• Apply a suitable passivating film
SiO2, a-SiNx:H, a-Si:H, a-AlxO:H…
• Measure the lifetime
IFE
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Diffusion length and lifetime
• The diffusion length (L) is defined as follows:
L = (D · τ)1/2
• L is a measure of the average distance a minority charge carrier
is able to move without recombining
• L is important in determining which solar cell structures can be
realized from a given material
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Diffusion length and solar cell performance
Ln ≥ W
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Ln < W
Ln << W
The Einstein relation
• The Einstein relation relates minority carrier mobilities and
diffusitivities
kT/q = D/µ
• Electrons
• µ = 1450 cm2/V · s
• D = 37,7 cm2/s
• Holes
• µ = 500 cm2/V · s
• D = 13,0 cm2/s
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Diffusion length and lifetime
Diffusion length versus lifetime
Diffusion length [um]
1,00E+04
1,00E+03
Measured Dn
Measured Dp
Calculated Dn
Calculated Dp
1,00E+02
1,00E+01
1,00E+00
1,00E+01
1,00E+02
1,00E+03
Lifetime [us]
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1,00E+04
1,00E+05
Measured data from Wacker Siltronics
Lifetime measurements
• How do we measure the lifetime?
•
•
•
•
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Photoconductance
Photoconductance decay
Radiative recombination
IR-absorption by excited charge
(σ ~ Δn)
(dσ/dt ~ d(Δn)/dt)
(IPL ~ Δn)
(Ifca ~ Δn)
Lifetime measurements
• Which methods do we use to measure the lifetime?
•
•
•
•
Quasi-steady state photoconductance (QSSPC/«Sinton»)
Microwave detected photoconductance decay (μ-PCD)
Photoluminescence imaging (PL)
Carrier density imaging (CDI)
• Artifacts of lifetime measurements
• Trapping
• Applications of lifetime measurements
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Quasi-Steady State PhotoConductance
d∆n(t )
∆n
= G (t ) − U eff = G (t ) −
=0
dt
τ eff
τ eff = G (t ) / ∆n
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QSSPC
•
Quasi-steady state: flash decay
slow compared to lifetime
•
Lifetime determined from excess
carrier density in quasi-steady state
Flash lamp
Reference cell
Sample
Inductive coil
τeff,QSSPC = Δn/gE
•
Excess carrier density linked to
conductivity
Δn = Δσ(t)/q(µn + µp)W
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Computer
RF bridge
QSSPC
Bentzen: PhD thesis
26.10.2015
QSSPC
• Advantage
• Measures lifetime as a function
of injection level
• Robust physical models
• True lifetimes can be extracted
• Disadvantage
• Usually measures across large
area
Bentzen: PhD thesis
26.10.2015
Microwave photoconducance decay
∆n
d∆n(t )
= G (t ) − U eff = G (t ) −
τ eff
dt
τ eff =
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∆n
∆n
=
d∆n(t )
d∆n(t )
− G (t )) (
(
)
dt
dt
μ-PCD
•
Very short pulse applied to sample
• Measures dΔn(t) /dt, not the
steady state generation rate gE
τeff,u-PCD = Δn/(dΔn(t)/dt)
•
Change in photoconductivity
measured as microwave reflection
Δn/(dΔn(t)/dt)
=
Δσ(t) /(q(µn + µp)WdΔn(t)/dt)
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Microwave antenna
Electronics
Laser diode
Sample
u-PCD – measurement examples
•
•
•
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When measuring thick samples,
such as blocks, a long wavelength
can be used
Photogeneration far from surface
Surface passivation not critical
•
•
•
On wafers, surfaces are always
close at hand
A surface passivation is required
Without passivation, the maximal
measured lifetime only is a few µs
u-PCD
• Advantage
• High spatial resolution obtainable
• Disadvantages
• No implicit knowledge of injection level
• Lifetime versus injection level requires adjustments of bias light
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PhotoLuminescence imaging
d∆n(t )
∆n
= G (t ) − U eff = G (t ) −
=0
dt
τ eff
τ eff = G (t ) / ∆n
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PL imaging
• Method
• Relate measured luminescence
signal from radiative
recombination to ∆𝑛
• Extract effective lifetime from
ratio of ∆𝑛 to generation rate G
U𝑟𝑟𝑟 = 𝐵𝐵𝐵𝐵(𝑛𝑛 − 𝑛𝑛2)
~
𝐵𝑟𝑟𝑟 ∆𝑛(∆𝑛 + 𝑁𝑁)
26.10.2015
τeff = ∆𝑛/G
Angelskår
Generation rate
• Simple!
• Assume all photons entering the wafer are absorbed, and create
an electron-hole-pair:
Photon flux
1017cm-2s-1
Reflectance at
excitation wavelength
Thickness of wafer,
assumed uniform distribution
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Relation to excess charge carrier density
•
Radiative recombination in (p-type) silicon:
Silicon wafer
•
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Including Brad, the effect of camera, filters, surface
morphology in a calibration factor C:
Luminescence spectrum of silicon
•
•
•
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Band to band luminescence around 10001100nm
Radiative (and non-radiative) defects yield
dark signal since luminescence is outside
detection limit (long-wavelength IR)
High band-to-band luminescence signal means
defects do not dominate
Camera filters designed to filter out reflected
laser light (~800 nm), and detect only band-toband luminescence
Quasi-steady-state photoconductance
pvcdrom.pveducation.org
Bentzen: PhD thesis
26.10.2015
Calibration of luminescence intensity to
excess carrier density
•
•
•
QSSPC measures conductivity and yields free
carrier density given a mobility model
Intensity vs. free carrier density
Determines calibration constant C
Low injection, high doping
•
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Now we can measure the PL intensity to get a
map of Δn!
Herlufsen et al., 24th EUPVSEC, 2009
Complications
•
Need to know doping – preferably have uniform doping…
•
•
Inhomogeneously doped wafers can show large variations in luminescence intensity
Minor effect on the conversion from conductivity to excess carrier density, due to mobility
model
•
QSSPC calibration over large area
• Mobility models – compensated silicon
• Need to take care for mc-silicon, averaged intensity
•
Compensated silicon
• Mobility model (as far as I know…) for QSSPC measurements still under
discussion
• Net doping variations will dominate the image
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Complications
•
•
Luminescence from emitters is usually neglected
Reabsorption of luminescence photons
•
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Uniformity of reflectance
•
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Lifetime scales with reflectance
Blurring if diffusion length is much longer than a pixel size (160
um)
•
•
weak effect in the detected spectral range
Small effect in solar grade silicon, limited to a few pixels
Radiative recombination coefficient decreases at high injection
level, screening effect
Diffuse surfaces cause blurring
Effect of reflectance
120 us
5 us
Lifetime map
•
•
•
26.10.2015
28
38%
%Reflectance map
The generation rate G is not constant over the wafer
Misinterpreted as lower lifetime, but also an actual decrease in passivation quality?
Thickness?
Partly corrected by having a laterally varying generation rate G
High-resolution PL of multicrystalline
silicon
20 mm
Intensity
As-cut wafer
•
•
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Intensity
Passivated wafer
Same surface treatment (except for a-Si deposition)
Blurring due to longer diffusion length?
Electrons:
D = 37,7 cm2/s
τ~15 us
L~ 200 um
Slip lines in monocrystalline silicon
• Slip lines
• Crystal defects during growth
• Can lead to breakage during
wafering
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Compensated silicon
•
•
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UMG material
See large effects of doping, also an
issue for QSSPC calibration
Research ongoing to adapt technique
for compensated material
Haunschild et al., 35th PVSEC, 20
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The effect of non-recombinative traps
• Charge neutrality requires that
Δn = Δp
• Certain traps only store charge carriers for some time before rereleasing them to the nearest energy band
• With a number of electron traps (nt), the conductivity becomes
Δσ(t) = q(µnΔn + µpΔp)W + qntµnW
• This effect will lead to an apparent increase in lifetime
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Trapping – calculated example
Auger
Fei
Totalmeasured
FeB
Emitter
Totalno trappning
Bentzen: PhD thesis
26.10.2015
Case 1: Counting dissolved impurities
• A lifetime determined by dissolved impurities can be described
as follows:
1/τ = σtvthNt
• Scattering cross section (σt)
• Thermal velocity of electrons (vth)
• Concentration of defects (Nt)
• If the lifetime is dominated by one defect with a known σt, the
defect concentration can be estimated
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Case 2: Counting precipitates
• A lifetime determined by precipitates can be described by the
following empirical equation:
L = 0.7 · (Np) -1/3
• Precipitate density (Np)
• Hard in principle, lifetime usually limited by other factors
Luque & Hegedus: “PV Handbook”
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Case 3:
Determining Fei concentration in Si
• Fe is an important defect in mc-Si technology
• The concentration of Fe in B-doped Si can be determined by
lifetime measurements
• Interstitially dissolved Fe (Fei+) is a common “lifetime killer” in Si
• In p-Si, Fei+ tends to pair up with B acceptors (Bs-) forming socalled Fe-B pairs (FeB)
• FeB pairs can be split up by illumination into Bs- and Fei+
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Case 3:
Determining Fei concentration in Si
• Before illumination
(τbefore) -1 = (τsurf) -1 + (τFeB) -1
• After illumination and pair separation
(τafter) -1 = (τsurf) -1 + (τFe_i) -1
• Difference
(τafter) -1 - (τbefore) -1 = (τFe_i) -1 - (τFeB) -1
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