Hindawi Publishing Corporation
Journal of Solid State Physics
Volume 2014, Article ID 291469, 19 pages
http://dx.doi.org/10.1155/2014/291469
Review Article
Optical Measurement Techniques of Recombination Lifetime
Based on the Free Carriers Absorption Effect
Martina De Laurentis and Andrea Irace
Dipartimento di Ingegneria Elettrica e delle Tecnologie dell’Informazione, Università degli Studi di Napoli “Federico II”,
Via Claudio, 21, 80125 Napoli, Italy
Correspondence should be addressed to Andrea Irace; andrea.irace@unina.it
Received 15 November 2013; Revised 21 February 2014; Accepted 3 April 2014; Published 24 June 2014
Academic Editor: George Cirlin
Copyright © 2014 M. De Laurentis and A. Irace. his is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We review successful measurement techniques for the evaluation of the recombination properties in semiconductor materials
based on the optically induced free carrier absorption. All the methodologies presented share the common feature of exploiting a
laser beam to excite electron-hole pairs within the volume of the sample under investigation, while the probing methods can vary
according to the diferent methodology analyzed. As recombination properties are of paramount importance in determining the
properties of semiconductor devices (i.e, bipolar transistor gain, power devices switching features, and solar cells eiciency), their
knowledge allows for better understanding of experimental results and robust TCAD simulator calibration. Being contactless and
applicable without any particular preparation of the sample under investigation, they have been considered attractive to monitor
these parameters inline or just ater production of many diferent semiconductor devices.
1. Introduction
he minority carriers recombination lifetime is one of the
most important parameters as it both characterizes the
semiconductor materials and it strongly inluences devices
properties. As more than 95% of all the produced electronic
devices are fabricated through CMOS process, nowadays the
majority of the studies on recombination lifetime concerns
power electronics, diodes, IGBTs—where lifetime killing
methodologies are mostly employed—or solar cells, where
recombination parameters are directly related to the conversion capability of these devices.
Solar cells, without doubt, occupy an important role
in the energy worldwide scenario, so the industry and
research interest in their production and characterization
are increasing. As said, their eiciency in converting the
energy from solar to electrical critically depends on the
recombination process by means of two parameters: the bulk
recombination lifetime �� , which accounts for the recombination of electrons and holes inside the silicon crystal, and
the surface recombination velocity ��� which is strongly
dependent on the interface between the material and its
boundaries: the former accounts for material quality, while
the latter usually depends on the fabrication process. hese
parameters are strongly related to the presence of defects
within the semiconductor forbidden gap (which directly
afects devices performance) and to the surface quality. hey
also depend on the semiconductor growth technique, on the
doping, on the surface condition, and on the free carrier
density injected in the material under operating conditions.
In the last decades the researchers eforts were addressed
to develop contactless and totally compatible methods that
allow for monitoring these quantities during the production
process without interfering with other fabrication steps. It is
thus obvious that methods based on optical or microwave
radiations have been preferred.
In this paper we present a review of two important
contactless techniques used to determine the semiconductor
materials lifetime: the Pump and Probe method (PP) [1]
and the Infrared Lifetime Mapping method (ILM), otherwise
known as Carriers Density Imaging (CDI) [2, 3]. hese
techniques are based on the free carriers absorption that
occurs in the semiconductor materials. As the name suggests,
this is the contribution to the absorption of the free carriers
present in the material that involves photons with wavelength
belonging to the NIR/middle infrared region, corresponding,
2
in terms of energy, to the energy lower than the material
band-gap. In fact, the free carriers concentration (and its
variation) inside the material determines a variation of the
material optical absorption coeicient. his implies that a
variation of transmittance can be detected and observed
when a sub-band-gap radiation is transmitted by the material.
he generation of the excess free carriers can be optically
induced by illuminating the sample with a laser pulse, whose
photons energy is higher than the sample band gap.
he PP technique belongs to the class of transient methods. hese methods are attractive because they give a result
directly related to the velocity of the recombination process.
In fact, the signal detected is the time dependent signal
transmitted by the sample. he PP allows for characterizing
materials with very low lifetime too and usually it does
not require any calibration procedure. Moreover the actual
advantage of the method is the possibility to separate the bulk
from surface efect, which means to simultaneously measure
the bulk lifetime and the surface recombination velocity.
he ILM/CDI belongs to the steady-state methods class.
hese methods measure a physical quantity related to the
carrier density. It allows for a fast and high spatially resolved
measurement of the lifetime in each point of the wafer
without performing a scanning of it, since an infrared CCD
camera is used to detect the transmitted infrared radiation.
Its greater attractive feature is the capability to perform the
lifetime mapping in few minutes, which could provide, in
calibrated condition, an online monitoring feature.
he paper is organized as follows: in the irst two sections we briely recall the concept of recombination lifetime
together with the main recombination mechanisms in semiconductor materials; in the subsequent sections we describe
in detail of the selected techniques, having previously recalled
the analytical tools necessary to their understanding.
2. The Concept of Recombination Lifetime
he term “lifetime” is used in physics in a totally intuitive
manner to indicate the temporal interval between the generation and the death of a particle. Nevertheless oten the
“death” is only a change of the particle state, like in the case
of the recombination process in the semiconductors theory.
In fact the recombination lifetime refers to the time in which
the electron returns from an excited state to the equilibrium
state. he excitation can be obtained, for example, by a
photon absorption or an electrical injection process in the
forward-biased p-n junction. he electron comes back in
the equilibrium state, occupying the vacancy let by the
excitation. In the semiconductors theory this vacancy is
described like a particle, named hole, with the same electron
charge but diferent mass [4, 5]. In this way the electron decay
to the equilibrium state is described as its recombination
with the hole. his recombination process destroys the charge
constituted by the pair and the recombination lifetime then
refers to the electron-hole pair: what ceases to exist is this
charged pair and it ceases to exist because the electron of the
pair recombines with the hole of the pair. In other words,
the recombination process is the destruction (or decay)
Journal of Solid State Physics
of the excess carriers (the electron-hole pairs) generated in
the semiconductors as consequence of an excitation. he
temporal interval during which the excess carriers decay is
deined as recombination lifetime, �rec .
Mathematically, in a irst order approximation, �rec is
deined as the ratio
�rec =
Δ�
R
(1)
between the excess carriers density Δ� [cm−3 ] and the recombination rate R = −�(Δ�)/�� [s−1 ] of the excess carriers
itself.
From (1), named Δ�(0), the excess carriers concentration
at the instant � = 0 when the excitation source is turned of, it
is derived that � characterizes the excess carriers decay:
Δ� (�) = Δ� (0) exp (−
1
).
�rec
(2)
In steady-state conditions the excitation source is at all
times turned on, constant or with assigned time dependence,
and an equilibrium condition between the generation rate
and recombination rate is reached, G = R, so that it is
possible to deine the recombination lifetime as
�rec =
Δ�
.
G
(3)
In general it must be clearly remarked that the recombination phenomenon can be comprehensively treated only by
means of quantum mechanical calculations. Since it involves
transitions between energetic states, it is implicit that the
recombination rate depends on occupation probability of the
energy levels, and, thus, on the energy as well as on the
temperature, on the electrons, and holes concentration, and
it is in general a nonlinear function of Δ�. Consequently the
recombination lifetime depends on them and thus it must be
considered that in general it is �rec = �rec (�, �, �, �, Δ�, Δ�)
(where � and � are the concentration of the electrons and
holes, resp.); that means, among other things, that �rec is a
function of the injection level Δ�/� (Δ�/�).
2.1. Recombination Process. he total recombination rate is
a superposition of several recombination mechanisms. As
summarized in (4), among these the main are the ShockleyRead-Hall, the radiative, and the Auger recombination (the
irst one linearly dependent on the excess carrier generation
only at lower injection level, the second one and the third,
resp., proportional to the square and to the cube of the excess
free carriers concentration):
R = RSRH + RRad + RAug .
(4)
he sketch in Figure 1 gives an intuitive � − � picture
of these processes, while in the following we give a short
description of them. We invite the readers to refer to [6, 7] and
especially to [8] for all the analytical and theoretical details.
Journal of Solid State Physics
3
Conduction band
Conduction band
E
E
Ec
Ec
Et
E
Phonon
Eg
E
Photon
⟨111⟩
⟨100⟩
k
Photon
⟨100⟩
⟨111⟩
k
Valence band
Valence band
(a)
(b)
C. band
E
Ec
E
⟨100⟩
⟨111⟩
k
Valence band
(c)
Figure 1: Main Recombination Mechanisms in semiconductors: (a) Trap-assisted recombination. (b) Direct Recombination. (c) Auger
Recombination.
2.1.1. Shockley-Read-Hall Recombination. Shockley, Read,
and Hall in 1952 were the irst to note that, in the indirect
band-gap semiconductors, like silicon and germanium, the
recombination lifetime is sensitive to the material property
and that the recombination rate varies linearly with the
carriers concentration on a wide range of concentrations
and temperatures [9, 10]. Since this cannot be explained
with a two-bodies collision mechanism, adopted to explain
the interaction between the electrons and which implies a
quadratic dependence, they supposed and demonstrated that
the process takes place by means of the material impurities
that introduce some intermediate energy levels in the forbidden gap. hese levels act as recombination centers (or traps,
from which the process is otherwise depicted as trap assisted
recombination) and an intermediate step is introduced in the
recombination process.
herefore the electron in a irst step falls down to the
intermediate levels; then it falls down to the valence band
in the same way. Nevertheless, since the process is observed
in the materials called indirect semiconductors, because of
noncorrespondence in the momentum-space (�-�����) [4, 5]
between the maximum of the valence band and the minimum
of the conduction band, an electron in the conduction band
cannot simply decay to the valence band releasing its energy,
but it must also change its momentum. his can happen with
the assistance of the crystal lattice: the electron gives the
lattice its energy in the form of heat, and, simultaneously, this
interaction allows it to change its momentum �, producing
lattice vibration. In the quantum model this is described as
the interaction of the electron with the lattice vibrational
quanta, the phonons. his ictitious particles are deined with
an own momentum [4], so that when the electron interacts
with them, it can change its momentum to preserve the total
momentum of the whole particle.
he second step can be equivalently described as an
hole that ascends to the intermediate level (equivalently
described as an “hole capture” of the trap), recombining with
an electron. Really, depending on the nature of the trapping
4
Journal of Solid State Physics
process, one of the two steps can be a radiative process, so that
the electron losses its energy emitting a photon. his process
does not imply a momentum change.
It must be noted that the trap assisted recombination is a
very complex phenomenon that can be properly described
by means of the quantum mechanics and, we remark, it
can be assumed linearly dependent on the excess carriers
concentration only on a limited, even if wide, range of
concentrations and temperatures. he readers can ind a
complete and exhaustive treatment in [8, 11].
2.1.2. Radiative Recombination. In direct band-gap semiconductors, where the minimum of the conduction band
coincides with the maximum of the valence band, the electron
band to band transition can happen without involving the
crystal lattice, but only with the emission or absorption of
a photon, depending on the kind of process (if it is an
absorption or a decay). his is possible because the change
of momentum is not required and thus only the energy
conservation must be preserved.
Since the process simultaneously involves both the
charges, electrons and holes, the probability that it occurs
is proportional to the square of the population of the two
involved levels and, likewise, the recombination rate too.
2.1.3. Auger Recombination. In 1955 Pincherle published a
brief letter on the Proceeding of Physical Society [12] in
which the inverse proportionality of the minority carriers
density lifetime to the square of the majority carriers density,
experimentally observed by Moss in impure lead sulide
(PbS) [13] in 1953 and by Hornbeck and Haynes in silicon
(Si) in 1955 [14], was justiied and predicted by means of the
Auger efect [15]. In the subsequent years between 1956 and
1958 Landsberg et al. [16–18] developed the irst theory on the
Auger recombination.
he Auger recombination in semiconductors involves
three carriers: when an electron recombines with a hole, the
energy and the momentum variation are transferred to a
third carrier, either an electron or a hole. he conduction
band Auger recombination (case “c” of the igure), which
involves two electrons in the conduction band and a hole in
the valence band, is sketched in Figure 1. In a similar way,
the valence band Auger recombination involves one electron
in the conduction band and two holes in valence band. he
Auger recombination can involve trap levels too [8, 19–21].
he process is strongly dependent on the carriers injection
level and it becomes dominant at high carriers concentration.
From this short summary on the recombination mechanism and recalling (1) and (4), it is possible to derive that that
the recombination lifetime can be expressed as
1
1
1
1
=
+
+
.
�rec �SRH �rad �Auger
(5)
In indirect band-gap semiconductors, like Si, the SRH
is dominant at moderate carrier densities (up to 1018 cm−3 ),
while the Auger recombination dominates under high doping
and high injection condition (see, e.g., [22]). his implies that
�rad is enough higher than �SRH and �Auger and thus in (5) the
second term is usually negligible. Radiative recombination
dominates in direct band-gap materials, like GaAs and InP.
2.2. Surface Recombination Lifetime and Surface Recombination Velocity. he materials’ samples and the devices
(or the active region of them) are space limited by their
surfaces, which constitute an interface between two diferent
media, like the silicon-air surface or the silicon-oxide surface.
Likewise to the impurities and to the defects, these surfaces—
which are discontinuities of the periodical crystal structure—
introduce allowed energy states within the forbidden band.
hese states afect the recombination process in a way that
is very similar to the Shockley-Read-Hall model for the
bulk recombination. his kind of recombination is known
as surface recombination and it is characterized by an own
recombination lifetime �� .
Usually all the experimental techniques determine a
parameter that is a combination of the bulk contribute �� and
of the surface one, called efective lifetime:
1
1
1
=
+ .
�ef �� ��
(6)
Nevertheless to characterize the recombination at the
surface, rather than �� another parameter is usually used,
the so-called surface recombination velocity or SRV. Anyway,
without entering in detail, for which we refer to [8, 23–27],
to deine SRV we have to consider that, since the carriers that
recombine at the surfaces of the sample can be described as a
current-like low outside the latest, it is much easier to model
the presence of the recombination centers on the surface
by means of appropriate boundary conditions that bind the
values of the carriers concentration and its gradient at the
boundaries. his leads to the following SRV deinition:
SRV = �[
��/��
,
]
�(�) boundary
(7)
if � is the space coordinate and a 1-� problem is under
consideration, being � the carriers ambipolar or monopolar
difusion coeicient, as determined by the carriers injection
level.
Even if the majority of the experimental cases are well
explained with a constant SRV, a more complicated theory
can be taken into account when a nonnegligible bandbending is present at the surface [26].
3. Free Carriers Absorption
In semiconductor materials the injected or generated free
carriers contribute to the absorption process by means of
intraband transitions. It is known that three absorption
mechanisms happen in these kinds of materials. We briely
remember them.
(i) Intrinsic or Band-gap Absorption occurs in the intrinsic semiconductors when photons with energy �ph ≥
�� (�� is the material band gap) irradiate the material. his absorption determines a transition from the
Journal of Solid State Physics
5
valence band to the conduction one. he conventional
visible and NIR photodetectors are based on this
efect.
(ii) Impurity Level to Band Absorption occurs in extrinsic
materials, like in the extrinsic infrared photodetectors, when photons with energy �� ≤ �ph ≤ ��
impinges on the material. he photons absorption
determines transition from the impurity intraband
energy level to the band, as the name suggests.
his phenomenon is used, for example, to tune the
wavelength response of the IR detectors, by choosing
impurities with diferent energy level belonging to the
material band-gap.
(iii) Free Carriers Absorption. he free carriers present
in the semiconductor materials contribute to the
absorption process, absorbing photons with energy
�ph ≤ �� (that corresponds to the middle or far
infrared region) and determining intraband transition. his phenomenon can degrade the detectors
response, since the absorption increases as power
function of the wavelength. Nevertheless, it is useful
to measure the carriers concentration, with this efect
being proportional to them.
he FCA has been widely studied in the middle of the
20th century, by means of both classical Drude model and
quantum one (see, e.g., [28–39]).
he absorption of a photon with energy smaller than
the energy band-gap of the semiconductor material allows
the free carrier to have a transition from a lower energetic
state of the band to a higher energetic state of the same
band. Nevertheless, since the two involved states belong to the
same band, the transition can occur only with a momentum
change. his change is possible by means of interactions of
the free carriers with the material lattice (lattice vibration
described by means of phonons) or by means of scattering
from ionized impurities. he classical theory, based on the
Drude model, describes the free carriers in the solid like a
gas of particles with a density �, subjected to collisions with
the relatively ixed ions of the lattice in which it is moving.
It leads to a dependence of the free carriers absorption
coeicient on the carriers concentration and on the square
of the wavelength of the absorbed photons:
�fc =
��2 �2 1
,
�� �0 �4��3 �
(8)
where � is the electron charge, �� is the carrier efective mass,
�0 is the vacuum permittivity, � is the material refractive
index, � is the light speed, � is the wavelength of the absorbed
photons, and � is the relaxation time, which represent the
average time between two subsequent collisions, or, in other
words, the free motion time of the gas particle before another
collision with the lattice ions happens.
In the previous expression the relaxation constant is
assumed independent of the energy, but really it is a complicated function of the energy and contains the details of
the collision mechanism. hese details have been investigated
by means of the quantum theory, studying the interaction
mechanisms between the carriers and the semiconductors
lattice which are described as interaction between the carriers
and the vibrational modes of the lattice. Moreover the
quantum theory of the free carriers absorption justiies the
oten observed deviation from the experimentally observed
�2 dependence in some materials and compounds. In general,
without entering the details of the calculation and of the
phenomenon description, we can synthesize—like in [40]—
that the main scattering process involving the free carriers
in the semiconductors materials contributes with a resultant
dependence of the absorption coeicient on the wavelength.
he latest can thus be expressed by a weighted sum of few
terms, like
�� = � � ��� ,
(9)
where the label � refers to a particular kind of scattering
process and each � � is constants dependent on the carriers
concentration and on the temperature as well on other
parameters, like the carriers efective mass. he impurities
concentration in the material determines the dominant mode
of scattering and the relative value of the exponent � of
the wavelength. Moreover the value should increase with
the doping. Typical values are between 1.5 and 3.5. Some
examples are given in literature by studying the diferent
kind of scattering and considering diferent materials and
compounds. For example, Fan and Becker [29] reported a
value � = 1.5 for the scattering by the acoustic phonons in
silicon and germanium, while in [35] the quantum mechanical calculation of the free carriers absorption, considering the
scattering by the optical phonons in the III–V compounds, is
presented and experimentally veriied, inding a value � =
2.5. Furthermore [33] shows that the scattering by ionized
impurities can lead to � = 3 or � = 3.5.
he details of the calculations are reported in the cited
papers and also in many books, like in [41], where it is
remembered that a tabulation of the expression for �fc for the
several scattering mechanisms is given in [42].
An experimental determination of the free carrier
absorption coeicient for the silicon, at ixed temperature
of 350 K, was given by Schroder et al. in 1978 [39]. In
accordance with the theoretical classical model, the following
dependence on the free electrons and holes densities � and �
in the n-type and p-type material, respectively, was found at
�� ≃ 1 × 10−18 �2 �,
�� ≃ 2.7 × 10−18 �2 �,
(10)
where the wavelength � is measured in cm.
he experimental dependence on the wavelength at different doping levels in the n-type silicon and p-type at 300 K
can be found in [34] and [37], respectively, while the free
carrier absorption versus wavelength for high purity Si at
diferent temperatures was reported in [38].
6
4. Free Carriers Absorption Methods to
Measure and Map the Recombination
Lifetime in Semiconductors Materials
he intrinsic bond between the free carriers concentration
and the optical absorption change, as previously seen, had
ofered the possibility to directly monitor the former, measuring the latter. Moreover the great appeal in the use of
this efect was and is the possibility to measure the quantities related to the carriers density (like the recombination
lifetime) and to measure them in an absolutely not invasive
and contactless way, so that the sample integrity is totally
preserved.
On this principle many of techniques that allow for
measuring the recombination lifetime in semiconductors
materials are based. In practice these techniques operate
with a common principle that makes use of a sub-band-gap
radiation to monitor the absorption variation in the sample
due to the excitation of an ultra-band-gap radiation. So that
the sub-band-gap radiation constitutes the sensitive element
in the measurement, that is, the probe, while, adopting the
habitual nomenclature used in optics to name an exciting
source, the ultra-band-gap radiation constitutes the pump. In
this way all the techniques based on FCA can be classiied
as Pump and Probe. We can refer to them as the FCA PP
techniques. One of the irst applications can be seen in two
works published in 1966 by Chiarotti and Grassano [43, 44].
In 1970 Gauster and Bushnell [45] used the technique to
derive the silicon absorption cross section and suggested that
the method can be useful to investigate a variety of processes
such as the multiphonon absorption, the recombination of
the carriers, and the measurement of the carriers lifetime.
Interesting in their work is the use of a pulsed pump beam.
FCA PP techniques can be either steady-state methods or
dynamic (we will refer to the former with Steady-State PP or
easily SS PP methods, while to the latter with Transient PP,
or TPP). In the SS PP case the measurement is performed
with the pump on or with a modulated pump (so that the
lock-in detection can be used to increase the signal to noise
ratio) and what is directly observed in the measurement is
the distribution of the free carriers when the steady state has
been established. he recombination lifetime is deined by
the relation (3), where the generation rate G is proportional
to the pump intensity. his requires a calibration performed
comparing the distribution without the pump excitation and
with the pump excitation, so that the variation of the carriers
density can be evaluated and then the related quantities, like
the actual recombination lifetime. ILM and the Modulated
Free Carriers Absorption [46–50] belong to the Steady-State
PP methods. In the case of the TPP, to infer the value of
the recombination lifetime in the sample, a pulsed pump
is used. In fact, by recording the signal of the detected
probe beam just in the transient time ater the turn of
of the pumb beam, the sample recombination lifetime can
be estimated. We will describe it in detail in the following
sections together with the ILM. hey are, in our opinion and
in accordance with our experience, the most consolidate and
eicient, being also perfectly complementary regarding their
range of application.
Journal of Solid State Physics
We will see that the major advantage of the TPP technique is the possibility to discriminate the bulk contribution
from the surface contribution with only one measurement,
whereas, on the other hand, as the name said, the ILM can
give in one measurement the mapping of the actual lifetime
mapping of the whole sample (the use of the adjective “actual”
will be clear in the Section 7). Both techniques can operate in
low injection regime.
5. Transient Pump and Probe
Technique to Measure the Recombination
Lifetime in Semiconductors
he experimental Transient Pump and Probe scheme to
measure the recombination lifetime was well settled by Ling
et al. in 1987 [1], but only with subsequent works [51–54],
based on the analytical analysis of the interaction of a pulse
laser beam with a semiconductor wafer performed by Luke
and Cheng [55], the potentialities of the technique were
clear. hese consist in the capability to discriminate between
the surface contribution to the recombination and the bulk
one with only one measurement, or, in other words, to
measure simultaneously the bulk recombination lifetime and
the surface recombination velocity. Moreover, performing
more than one measurement with little changes in some
parameters, other characteristic electrical parameters of the
materials can be retrieved.
Two schemes of Pump and Probe setup have been
proposed, depending on the angle between the pump and
probe beams: the transverse coniguration and the parallel
coniguration. he parallel coniguration is more suitable for
wafer lifetime mapping, obtained by scanning the sample
along the plane orthogonal to the beams incidence plane
[56, 57]. In this case the difusion length of the free carriers
in the sample, � = √��, limits the resolution of the system.
In fact, in order to have a right interpretation of the signal
the spot size of the probe beam must be more than or
equal to the expected difusion length. Otherwise, if the spot
size is smaller, the observed signal is more inluenced by
the difusion than by the recombination. Nevertheless if the
probe beam is highly focused on the sample, the desired
experimental condition can be easily obtained.
In the perpendicular coniguration the sensitivity of the
measurement is substantially increased by making a long path
of interaction between pump and probe beam. his path is,
in principle, only limited by the spot size of the pump beam
[58]. Since there are no stringent requirements concerning
the state of wafer surface, the use of a transverse probe is also
attractive, if the conditions of the sample do not allow for an
eicient coupling of the probe radiation with the crystal, as
in the case of a sandblasted wafer surface, or if special surface
treatments are present and need to be characterized or cannot
be removed for any reason. In both cases, as previously said,
the pump photons energy is higher than the wafer band-gap
(� � > � gap ), but its intensity is not so high to determine a high
injection level (Figure 2). In this condition all parameters
involved in the recombination process can be assumed to be
constant during the time decay.
Journal of Solid State Physics
7
Conduction band
Ec
Eph = h
Ec
Photon
Conduction band
phonon
Conduction band
Ec
Photon
Eg
Eph = h
E
Valence band
Eg
Eg
Ei
Eph = h
E
E
Valence band
Valence band
(a) �ph > ��
(b) �� < �ph < ��
(c) �ph < ��
Figure 2: (a) Intrinsic or band-to-band absorption occurs when the energy of the absorbed photon is greater than the material band-gap. (b)
Extrinsic or impurity level to band absorption occurs in extrinsic materials when the photon energy is greater than the impurities energy but
smaller than the energy band-gap. In the igure the process is sketched in the case of a p-type semiconductors. (c) Intraband or free carriers
absorption can occur when the photon energy is smaller than the energy band-gap.
Sample
�
y
Oscilloscope
Lens
Probe beam
� > �gap
Diode laser
with driver
Optical iber
InGaAs
photodiode
Lens
x
Sample holder:
xy stage
Pump pulse
�p < �gap
Trigger signal
Nd:YAG pulsed laser
Figure 3: Pump and Probe setup in the parallel coniguration. he pump pulsed beam and the probe beam impinge on the sample surface.
he probe beam is focused on the sample surface, attenuated by the sample, and then detected by the InGaAs photodiode. he difusion
length determines the lateral resolution for the lifetime mapping, so that the probe spot size must be chosen to be more than or, at least, equal
to it [56].
A sketch of the parallel and transverse coniguration of
TPP setup is shown in Figures 3 and 4, respectively. he
continuous probe laser beam (usually a laser diode beam
@1550 nm) is detected by a photodiode ater the propagation
inside the sample (parallel to sample surface in the case of
transverse coniguration and orthogonal to it in the other
case). Triggered on the pulse pump, the decay curve acquired
by the InGaAs detector,
� (�) = �0 �−�0 (�)� (1 − �−�fc (�,�)� ) ,
(11)
is composed of two contributions: the initial material absorption coeicient, �0 (�), and the time dependent free carriers
absorption coeicients at the probe wavelength, �fc (�, �).
In Figure 5 a typical signal of the transmitted probe radiation in which the temporal dependence of the absorption can
be observed once the pump is turned of is shown.
To clarify how the Transient PP method works, it is useful
to recall the analysis of the interaction of a laser pulse with
a semiconductors sample. We report in the following the
analysis as presented in [52], where the study of Luke and
Cheng [55] is extended to the case of diferent SRV on the
two surfaces of the wafer.
5.1. Modeling of the Analysis of the Interaction of a Laser
Pulse with a Silicon Wafer. Let us consider a semiconductor
wafer with a thickness �, and a laser pulse impinging on its
surface 1, as shown in Figure 6. Let � be the minority carriers
difusion coeicient in the material, �1 and �2 the surface
recombination velocity on the surfaces 1 and 2, respectively,
and let us consider the same coordinate system as reported in
the cited igure.
8
Journal of Solid State Physics
Trigger signal
Oscilloscope
Lens
InGaAs
photodiode
Sample
x
Probe beam
� > �gap
Diode laser
with driver
Pump pulse
�p < �gap
Optical iber
xyz stage
Pulsed laser
Figure 4: Pump and Probe setup in the transverse coniguration. he pump pulsed beam impinges on the sample surface, while the probe
beam is orthogonal and propagates inside the sample.
5
V − V0 (mV)
0
−5
−10
−15
−20
0
0.5
1
1.5
2
2.5
3
3.5
t (�s)
Figure 5: A typical signal of TPP. he attenuation of the probe beam
can be observed just ater the turn of of the pump pulse (the signal
is normalized to the continuous level).
y
If the duration of the pump pulse is much shorter than
the expected recombination lifetime, the analysis can be
carried out for an ideal delta-pulse �(�) = �0 �(�) (�0 is the
number of photons and �(�) the unitary Dirac distribution)
and then it can be easily extended to the other cases [52, 55].
Moreover, let us consider a pulse beam with a uniform spot
size impinging on the sample surface along the propagation
direction of the probe beam and similarly a probe spot size
on the sample thickness. In this condition the interaction
volume between the pump and the probe is extended to
the whole thickness (we are approximating the interaction
volume to a parallelogram) and the distribution of the excess
free carriers inside it can be considered changing only along
the propagation direction of the pump, denoted with �. he
distribution of the excess free carriers generated along the
wafer thickness for time � > 0, in low injection regime and
neglecting the electric ield, can be considered governed by
the 1-� difusion equation
�2 � (�, �) � (�, �)
�� (�, �)
−
=�
��
��2
��
z
(12)
with the boundary conditions
Pump pulse
−d/2
0 d/2
x
�[
�
��(�, �)
= �1 � (− , �) ,
]
��
2
�=−�/2
−�[
Probe beam
S1
S2
Figure 6: Coordinate system and wafer position adopted for the
analysis of the interaction of a laser pulse with a silicon wafer.
�
��(�, �)
= �2 � ( , �)
]
��
2
�=�/2
(13)
(14)
and initial condition given by the multiple relections of the
pulse along the sample thickness, like in the Fabry-Perot
cavity,
� (�, 0) = �0 (1 − �) �
�−�(�+�/2) + ��−�� ��(−�+�/2)
,
(1 − �2 �−2�� )
(15)
Journal of Solid State Physics
9
with � and � being the relection coeicient on the wafer
surfaces and the silicon absorption coeicient at the pump
wavelength, respectively.
he most general solution of (12) can be expressed as
∞
� (�, �) = ∑ �−(1/�� +�� �)� (� � cos �� � + �� sin �� �) ,
2
the sample cross section is assured, the interaction volume
is extended to the whole sample thickness, so that, since the
excess free carriers distribution depends only by the spatial
coordinate � along which the pump pulse is propagating, the
expression (20) becomes
(16)
�av (�) ∝ ∫
�=1
−�/2
where the coeicients �� , �� , and �� can be found using
boundary conditions (13) and initial condition (15), respectively. In particular the coeicients �� are the solutions of the
characteristic equation
�� � = arctan
�1
�
+ arctan 2 + ��,
�� �
�� �
�/2
� (�, �) ��
� �
= ∑�� �� �� (− , ) �� (�)
2 2
�
= ∑�� ��
�
(17)
(21)
sin ��
� (�) ,
�� �
where we have deined
�� (�) = �−(1/�� +�� �)� ,
2
while, if
�� = �� �,
(1 − �) �
,
�0 =
1 − ��−2��
�� (�) = �� cos �� � + sin �� �,
� (�� , �� ) = ∫ � (�) ��.
(18)
(4�� �0 �) �−��/2
��� = 2
,
[�� (�� � + sin �� �) + (�� � − sin �� �)] (�2 + ��2 )
��
In the more general case of Gaussian pump pulse centered
at instant �0 and with width �,
�� (�) =
it results in
� � cos �� + �1 sin ��
�
�� ≡ � = − �
,
��
�� � sin �� − �1 cos ��
�� = ��� [�� (cos �� sinh
+ ��� [(
0
� �
= ∑�� �� �� (− , ) �� (�) ,
2 2
�
(19)
(24)
where
�
× (1 − ��−�� ) ] .
�� (�) = ∫ �� (�) �� (� − �) ��
0
= �� (�) ��� ((� /2)�� +�0 )
2
Since the measurement determines the absorption due to all
the free carriers generated along the excited volume of the
sample by the pump pulse, we have to consider the average
of the free carriers in that volume (at the beginning of the
section we have called it interaction volume �int ):
1
∫ � (�, �) ��
�int �int
(23)
�
�gav = ∫ �av (�) �� (� − �) ��
��
��
��
cos �� sinh
− sin �� cosh
)
�
2
2
�av (�) =
�0 −(�−�0 )/2�2
;
�
√2��
�av can be derived from the convolution of �av given by (20)
with the pulse
�� ��
��
+ sin �� cosh
)
2
�
2
× (1 + ��−�� ) ]
(22)
��
(20)
with � int being the section of the interaction volume in the
horizontal plane. he latest approximation in (20), as pointed
out at the beginning of the section, subsists considering a
pump pulse that uniformly illuminates the sample along the
propagation direction of the probe beam. his condition can
be easily obtained experimentally by means of suitable optics,
like a cylindrical lens.
If the diameter of the probe beam is larger than the
sample thickness, in a way that the uniform illumination of
× [erf (
�
� − �0
�
�
� + 0 ) − erf ( �� −
)]
√2 � √2�
√2
√2�
(25)
with
�� =
1
+ ��2 �.
��
(26)
he semilog plot of �gav (�) allows for deining an instantaneous observed lifetime �0 given by
1
1
�
= − ln [�gav (�)] =
+ �� (�) ,
�0
��
��
(27)
where, from (20), (24), and (25) it is clear that �� is a
time dependent ratio between two series and it depends on
10
Journal of Solid State Physics
the physical wafer parameters, �, �� , �, �1 , and �2 (see also
(17)). Nevertheless it can be demonstrated [52, 55] that its
asymptotic value is a constant:
�� (�) �→ ��� = �1 �.
�→∞
(28)
he previous expression shows that the asymptotic value of
the inverse of the instantaneous observed lifetime can be
expressed as the sum of two independent terms:
1
1
1
1
=
+ ��� =
+
,
�0� ��
�� ��1
(29)
the irst of which is equal to the inverse of the bulk lifetime
and the second one is independent of latest and dependent
on the surface efects, as �1 depends on �1 , �2 , and � (the
subscript � refers to this dependence of the asymptotic value
of �).
so that
(��� − ��� )anal = (
can be used to evaluate � and
�� =
1
1
−
)
�0� �0� exper
(�0� )anal
1 − (��� )exper (�0� )anal
(32)
(33)
gives �� . he subscripts “anal” and “exper” indicate that
the quantities are analytically computed or experimentally
determined. Luke and Cheng wisely suggest that to derive ��
it is better to use �0� , since it can be better determined and that
the error computed to neglect the dependence of �� on �� is
about 0.1 per cent over the range of � = 1 to 106 cm/s, or rather
for 40 ≤ �� ≤ 106 cm2 /s. his shows the complementary of
the single slope and dual slop methods.
6. TPP Parameter Extraction
he relation (29) is the core of the TPP method. In accordance
with the sample properties and the set-up coniguration,
diferent information can be extracted by the measurement.
In this way the TPP presents several versions.
6.1. Single Slope Method. When the surface efects can be
neglected or when ��1 is known, from (29) the bulk lifetime
can be directly derived. Luke and Cheng [55] plotted ��1
versus the wafer thickness � for diferent values of the surface
recombination velocity (from 10 to 106 cm/s), supposing �2 =
�1 , and showed that, for � > 105 , when � increases, the value
of ��1 does not change. Really the product �� is determinant,
since when it increases, the root �1 � of the transcendental
equation (17) approaches a limit value. his suggests that for
�� → ∞ the surface efects can be neglected and the bulk
lifetime can be easily derived as
� �
�� = 0� �1 ,
(30)
��1 − �0�
with ��1 = 1/�1 � being analytically computed and �0� derived
from the experimental data. he simulations reported in [55]
show that in practice the inluence of � can be neglected for
�� > 120 cm2 /s.
6.2. Dual Slope Method. If the surface efects cannot be
neglected, two values of the instantaneous observed lifetime
can be used to derive from the experimental data the bulk lifetime and the surface recombination velocities: the asymptotic
value (deined in (29)), and the maximum value (deined in
the same manner, where obviously �� (�) is replaced with its
maximum value max[�� (�)] ≡ ��� ).
In this way, if �2 = �1 = �, to determine the two unknown
quantities �� and �, we have a system with two equations:
1
1
=
+ ��� ,
�0� ��
1
1
=
+ ��
�0� ��
(31)
6.3. Two Wafer Method. In the region not covered by the
previous two methods, Luke and Cheng proposed to utilize
the �� dependence on the wafer thickness. In fact using two
wafers which difer only in thickness, �1 and �2 , the former
system (33) can be replaced with
(
1
1
) =
+ (��� (�1 , �, �))1 ,
�0� 1 ��
1
1
+ (��� (�1 , �, �))1 .
( ) =
�0� 2 ��
(34)
Really the method works well even for large value of
��, so that more than complementary to the previous ones,
can substitute them. Nevertheless Irace et al. [59] observed
that since the two measurements of �0 are done on the same
material and, at most, averaged on an area of about 1 cm2 ,
equal to the probe beam spot, it can be safely assumed
that the bulk recombination lifetime remains unchanged.
On the other hand, since the separation and calculation of
the surface efects rely on the hypothesis that also SRV has
to remain unchanged, there is the problem of assessing a
surface treatment procedure that is well reproducible and
sets equal surface recombination velocities on both sides of
each sample and in both samples. hese considerations led
them to perform an analysis of the error sources of this
procedure and of the uncertainties that they can lead to.
hey showed the efect of diferent values of SRVs on the
two measurements using a graphical approach. herefore,
for each measured value of the instantaneous lifetime, it is
possible to draw a line on the �� − �-plane that, of course, will
span all the allowed values of �� and �. On the other hand,
because two measurements are available, the two solutions
intersect in a single point, corresponding to the looked for
(�� , �) pair. If there are uncertainties �� (� = 1, 2) on the
quantities, a region can be identiied in the plane, bounded by
the lines �01 ± Δ�1 and �02 ± Δ�2 , respectively, for each sample.
Intersecting these two regions, the area where the solution
of the (34) lies can be identiied. It contains the information
about the uncertainty on the surface recombination velocity
Journal of Solid State Physics
11
the hypothesis of equal surface recombination velocities. he
technique uses the relection or absorption of a microwave
radiation on wafer surface as probe signal.
From 2002 to 2005 Irace and coworkers [63–68] transposed and tested the idea with a pump and probe setup, using
a laser diode @1550 nm as probe beam and the fundamental
and the second harmonic of a 7 ns pulsed Nd-YAG laser (� 1 =
1064 nm and � 2 = 532 nm resp.) to pump the sample.
Deining
10−3
�eff = 12 �s
�eff = 5 �s
�eff = 6 �s
10−4
�b (s)
�eff = 15 �s
10−5
10−6
d1 = 500 �m
d2 = 200 �m
�eff 1 = 5.5 �s
�eff 2 = 11.5 �s
�� = lim � (�, �) = ln (
�→∞
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
S (cm/s)
Figure 7: �� − SRV plane as reported in [59].
or can take into account the efects of the experimental
uncertainties on the measured �0 value. An example of the
above procedure is given in Figure 7.
6.4. Dual Slope Method on Both Surface. If �0 ≠ �1 a further
equation is needed to determine all the three parameters. Kousik et al. in 1991 [52] proposed to perform the
measurement lipping the wafer, to have one measurement
with the pump beam impinging on the wafer surface with
recombination surface velocity �1 and one complementary
measurement with the pump impinging on the other surface.
he available equations are thus
1
1
=
+ ��
�0� ��
for (�1 , �2 )
1
1
=
+ ���
�0� ��
1
1
=
+ ���
�0� ��
or
(�2 , �1 ) ,
for
(�1 , �2 ) ,
for
(�2 , �1 ) ,
(35)
where the notation (�� , �� ) (� ≠ �) means that the pump
impinges on the surface �� .
6.5. Multiwavelength Method. he bulk lifetime and the
surface recombination velocity do not depend on the pump
wavelength but from (27) we can see that the instantaneous
observed lifetime �0 depends on it. In particular, the dependence is all included in the initial part, while the asymptotic
part is unafected. his means that, for � → ∞, ln(�av (�, �))
has the same slope 1/�0� (see (24)–(29)). In other words,
the asymptotic separation, between two decay curves relative
to two diferent pump wavelengths �av (� 1 , �) − �av (� 2 , �),
approaches a constant value. his observation suggested to
Buczkowski and coworkers [62] in 1991 (when the dual slope
method was not proposed yet) that the surface efects can
be extracted from this value. hey veriied the idea with a
diferent technique, called two-laser microwave relection, in
�rel (� 1 , �)
)
�rel (� 2 , �)
(36)
with �rel = �av (�, �)/�av (�, 0), and Δ� = � 1 − �, it is clear that
(36) is a function of Δ�, �, �, �1 , �2 .
If �1 = �2 = �, the experimental determination of ��
for a ixed pair of wavelength, is enough to determine �.
Successively, �� can be determined by means of (29).
For any pair of wavelengths, � is an increasing function of
�. For small value of �, where the surface efects are negligible
with respect to the bulk ones, it is diicult to distinguish
between two cases with diferent absorption; therefore, the
values assumed by � are small. When � increases, the
separation between the decay curves increases, reaching a
saturation value for high �. his limits the applicability of the
method to � < 105 , while the lower limit is determined by the
signal-to-noise ratio.
If �1 ≠ �2 , having only two pump wavelengths, � 1 and � 2 ,
it is possible to determine both the surface recombination
velocities by means of measurements with the pump impinging one time on one of the wafer surface and another time
with the pump impinging on the other wafer surface, like
in the dual slope method. In this manner �1 and �2 can be
determined from the experimental decay curve solving the
system
(��12 )exper = � (�; �1 , �2 ) for pump on surface 1
(��21 )exper = � (�; �2 , �1 ) for pump on surface 2
(37)
(with obvious meaning of the subscripts 12 and 21). hen ��
is computed using (33), with �� � relative to one of the two
measurements.
he main advantage of the technique is that it gives the
values of �1 , �2 , and �� even when the sample thickness
is comparable to the minority carriers difusion length, for
which the efects of recombination at the two interfaces are
coupled.
6.6. Cross-Sectional Proiling Technique. he previously
exposed methods are based on the assumption that the other
parameters of the sample are well known (see, e.g., (17) and
(28), (29), depending on �) but it could not be the real case
and, moreover, some other experimental variables could not
be exactly controlled. Mathematically this means that the
used equation systems require additional equations to be
solved.
Moreover they work in conditions such that the interaction volume between the pump and probe is wide as the whole
12
sample thickness. In this condition, depending on the sample
thickness and on the difusion length, the bulk contribution
to the recombination lifetime could be dominant respect to
the surface contribution or vice versa. To overcome these
diiculties Gaubas et al. [69, 70] proposed an alternative
method based on the simultaneous analysis of the time and
amplitude characteristics of the excess free carriers decay by
scanning the sample thickness with a probe beam spot size
smaller than the wafer thickness. In this way the interaction
volume between the pump (illuminating the whole sample
along the propagation direction of the probe) and the probe
is limited to a narrow portion along the sample thickness.
hey showed (with simulation and experimental results) that
the transient decay shape changes with the depth along the
sample thickness, with that meaning, as the distance of the
probe beam from the pump incident surface on the sample
increases. In particular they observed that the decay shows
concavity change, which passes to concave to convex when
the depth approaches the middle of the sample. his happens
because the surface efects decrease and the observed fraction
of the excess free carriers in that region is more governed by
the bulk recombination. he same behavior is observed without the scanning but changing only the probe beam spot size.
Recently an improved version of the technique has been
reproposed, where a detailed analysis of diferent probe beam
shapes has been evidenced (i.e., both the case of collimated
and divergent probe beam) [71, 72]. he improvement is the
combination of it with the multiwavelength method. In the
particular case the pump is a tunable source in the range
500–1150 nm, constituted by an Optical Parametric Oscillator
(OPO) pumped with a third harmonic of a ND:YAG laser. In
this way the method results more robust and accurate since
it has both the advantages of of the cross-sectional proiling
technique and of the multiwavelength one.
About the latest it must be observed that a tunable source
allows for having more than two wavelengths to perform the
measurements, so that instead of the system (37), relations
like (36) are used for each pair of wavelengths. his avoids
the measurements with the pump impinging one time on one
surface and one time on the other surface, which can lead
to some errors. Moreover the desired quantities are better
and more accurately retrieved by itting simultaneously a set
of equations similar to (27), obtained, nevertheless, with a
more accurate theoretical model of the best it curve. he
measurement is then performed from the a-priori knowledge
of the other sample parameters involved, and allows for a
better the determination of them.
At the beginning of this section, we stated that the parallel
coniguration is more suitable for wafer lifetime mapping
(see, e.g., [56]); nevertheless, it must be observed that the
lifetime mapping cannot be done with a unique acquisition.
he sample must be scanned, so that, depending on the pump
pulse frequency, on the probe beam spot size and sample
dimension the measurement requires an amount of time that
typically is at least of order of minutes. For a more eicient
and advantageous lifetime mapping an array of detectors can
be used to photograph the whole sample in one time. he
technique that we present in the next sections allows exactly
for this.
Journal of Solid State Physics
Moreover, it must be noted that in the transient lifetime
measurements could happen that the efective measured
lifetime can difer from the actual lifetime by a factor equal
to 2 or 3 [61]. his inconvenience is not present in the steadystate techniques. We will understand this in the next section,
before presenting the ILM technique.
7. Differential and Actual Lifetime
In the paper we have several times mentioned that the
recombination parameters in general depend on the excess
carriers concentration, thus on the injection level. When the
injection level is high, that is, when the generated excess
carriers concentration Δ� is higher than the majority carriers
concentration, really the observed transient decay is not a
single-exponential and should require, for data extraction, a
more complicated treatment. Nevertheless Aberle et al. [73–
76] acutely noted that the situation can be treated in small
signal regime. hey suggested that it can be actuated adding
a constant bias of suitable intensity to the pulse pump to
generate a constant background carriers concentration, �� ,
a lot higher than the excess carriers concentration induced
by the pump pulse, �� (�). So that the excess carriers can be
written as
� (�, �) = �� (�) + �� (�, �) .
(38)
In this way they showed that the measured lifetime is not
the actual but a diferential lifetime related to the former by
the relation
� (�� ) =
1 ��
∫ � �Δ�
�� 0 dif
(39)
with a similar expression for the surface recombination
velocity. he diferential and the actual lifetime are equal
only in the particular case of a constant bulk lifetime.
his situation is oten veriied in the case of low-injection
condition. At high-injection conditions, when for example
the Auger recombination becomes dominant, it can be easily
demonstrated that the small signal approach predicts a value
of the diferential lifetime three times smaller than the actual
one. For the radiative recombination the reduction factor is 2
[76].
he steady-state methods, where the generation rate and
the excess carriers density are controlled simultaneously,
present the advantage to measure directly the actual lifetime.
In fact, in the steady-state conditions, since the generation
rate and the recombination rate are equal and proportional to
the power density of the bias light, on the approximation that
the excess carriers concentration is approximately constant
throughout the sample, the result is [75]
� (�� ) =
1 �
∫ � (�) ��.
� 0 dif
(40)
Consequently, as the integration is performed by the detector,
the actual lifetime is directly measured. his is a further
advantage of the ILM method, which is detailed in the next
sections.
Journal of Solid State Physics
13
8. Infrared Camera Lifetime Mapping/Carrier
Density Imaging
he Infrared Lifetime Mapping (ILM) method was presented
the irst time in 2000 by Bail et al. [2]. Subsequently in 2001
Riepe and coworkers [3] presented a variation on the theme
called Carrier Density Imaging (CDI), improved with the
lock-in detection technique [77].
he method is also based on the free carriers absorption. Like in the pump and probe method, the sub-bandgap radiation is used as a probe propagating through the
sample, to monitor the absorption variation (or rather, the
transmittance variation) due to the free carriers generated by
the above band gap pump photons. Nevertheless, a black body
radiation is used as probe instead of a laser. his radiation,
belonging to the 5–25 �m range of the IR spectrum, is
partially transmitted by the silicon wafer and can be detected
by an infrared CCD (charge coupled device) camera, like the
ones used in IR thermography setups [77, 78]. So that, when
the sample is not excited by the laser pump beam (pump of ),
the CCD camera returns an image with a reference intensity
level, �of . his image corresponds to the currents intensities
produced by each pixel sensor illuminated by the black body
infrared radiation that had passed through the silicon wafer.
In others words, it is a matrix of � × � elements, ��� , as many
as the number of CCD pixels. When the pump impinges on
the sample (pump on), the absorption of photons with energy
greater than the energy band gap generates an excess of free
carriers (hole-electron pairs) that modiies the absorption
coeicient and consequently causes an intensity variation of
the transmitted black body radiation. he camera snapshot
relects this variation with a diferent intensity currents map
�on .
he authors showed that it is easy to derive the excess
carriers density variation per unit area, �� (where � is the
free carriers density and � is the sample thickness) from the
camera contrast
� = �of − �on ,
(41)
once it is calibrated, and, successively, the efective, actual
lifetime. his is the reason of the adopted name for the
technique, CDI, given by [3]. he efective, actual lifetime is
derived by means of the steady-state solution of the difusion
equation
�ef =
��
,
�
(42)
where � is the generation rate, equal to the pump density
photons low per unit time (which has the dimension of
[lenght−3 × time−1 ]) reduced by the relative quantity relected
by the wafer incident surface
� = Φ (1 − �� ) ,
(43)
with �� being the silicon wafer front side relectance at pump
wavelength.
he ILM schematic setup is shown in Figure 8.
Black body radiation
� < �gap
CCD camera
Wafer
Tw
Pump beam
� > �gap
Lens
Diode laser
Optical iber
Black body
Tb
Figure 8: In the ILM/CDI schematic setup.
8.1. he Detected Black Body Radiation. he camera signal is
proportional to the black body radiation transmitted through
the wafer (of thickness � and relectance on the incident
surface �) and integrated on the camera spectral range
[� min , � max ]:
� = Γ∫
� max
≈ Γ∫
� max
� min
� min
(1 − �)2 �−�fc (�)�� (�, �� ) ��
(1 − �) �fc (�) �� (�, �� ) ��,
(44)
2
where Γ is a proportionality constant that takes into account
the CCD response and the sample geometry;
� (� det , �� ) =
�
1
2�ℎ�2
≈ �−Ψ/���
�5 �(ℎ�/��� �� )−1 �5
(45)
(with � = 2�ℎ�2 and Ψ = ℎ�/�� ) is the black body spectral
density, given by Planck’s Law approximated in the case of
black body temperature �� greater than hundreds kelvin (ℎ
is the Planck constant, � is the vacuum light velocity, and ��
is the Boltzmann constant); � is the silicon wafer relectance
at the black body wavelength and, we remember, �fc is the free
carriers absorption coeicient (cm−1 ) [2, 34, 37–39].
8.2. Emission Mode. Since each body which is heated behaves
like a black body, the emitted infrared radiation can be
detected increasing the wafer temperature �� and, like in the
absorption mode, the optical pumping determines a variation
of the carriers intensity that leads to a variation of the emitted
radiation. From the Kirchhof Law at thermal equilibrium
the emission coeicient � must be equal to the absorption
coeicient �.
In the emission mode the wafer is heated above the black
body temperature, so that the black body radiation of the
wafer on the background is dominant. In fact, as made explicit
in [79], the camera detects a signal that is the superposition
14
Journal of Solid State Physics
100
200
180
80
160
120
100
80
40
�app (�s)
y (mm)
140
60
60
40
20
20
0
0
0
20
40
60
x (mm)
80
100
Figure 9: Typical ILM image as reported in [60].
of the black body radiation given by (44) and of a black
body radiation emitted just by the sample, since at thermal
equilibrium the free carriers also emit infrared radiation.
Depending on the wafer temperature with respect to the black
body temperature (and vice versa), the emission component
can dominate on the transmitted one. Denoted with �fc (�),
the emissivity of the wafer due to the free carriers, the
emission component of the signal can be written like in (44)
using Planck’s law (45) for nonideal black bodies (�(�) < 1):
�em = Γ ∫
� max
� min
�fc (�)
� −Ψ/���
�
��.
�5
(46)
he total signal detected by the camera is thus
� = �em − ��� ,
(47)
where �em and ��� are given by (44) and (52), respectively. It
is clear now that if �� ≪ �� the emission signal dominates
(in the experiments �� > 350 K [2, 79, 80]).
8.3. ILM/CDI Calibration. he calibration can be performed
comparing camera image of well-characterized wafer (usually
a p-type) that difers from a reference one only in dopant
concentrations � and, at the most, in the thickness �
(Figure 9). In fact, the plot of the camera contrast relative to
each pixel individuated by the coordinates in the �-� plane,
��(�, �) = ��� �� (�, �) − ��1 �1 (�, �), obtained subtracting
the image of the �th wafer to that one of the reference
wafer, labeled 1, as function of the free carriers density per
unit area relative to the same wafers and to the same pixel,
Δ(��)(�, �) = �� (�, �)�� − �1 (�, �)�1 , gives the following
experimental relation:
�� (�, �) = �Δ (��) (�, �) ,
(48)
that, suitably corrected, gives the inal conversion rule
between the free carriers density per unit area variation and
camera contrast:
Δ (��) (�, �) =
� (�, �)
� (�, �) .
��
(49)
he correction factor � takes in account the fact that only
wafers with one type of dopant are used in the calibration [2],
while the absorbed pump photons generate excess electrons
and holes that bring about a variation in the absorbed black
body radiation. his correction factor in the case of p-type
calibration wafers must be
� = (1 +
��
),
��
(50)
where �� and �� are the absorption coeicients of the free
electrons and holes, respectively, at the absorbed radiation
wavelength � (the black body detected radiation) [2, 34, 37–
39]. Obviously the absorption coeicients must be inverted
in (50) if the calibration is performed with n-type wafers.
he factor �(�, �), suggested by [81], takes into account both
the individual pixel sensor responsivity (the variation of the
sensor response to the variation of the incident radiation)
and the CCD sensor geometrical coniguration. It must be
considered that the central pixels of the CCD array see the
sample under a larger steradian than the pixels near the array
edge [81], so that the incident IR power low is diferent. he
�(�, �) factor is speciic to each CCD array comparing the
pixels response respect to the response of a reference pixel.
8.4. ILM/CDI Sensitivity. To quantify the ILM/CDI sensitivity a noise equivalent lifetime (NEL) is deined [2, 81] as
the efective minority carrier lifetime that the sample must
have to generate an infrared camera contrast that equals the
camera noise. his quantity is related to camera detection
limit (or minimum resolvable contrast), that is, the minimum
variation of the incident radiation that the camera can
distinguish. For the infrared camera it is expressed in terms
of the minimum appreciable variation of temperature, the socalled NETD (noise equivalent temperature diference), since
they are usually used to detect the temperature dependent
black body radiation, like in the ILM/CDI and thermography
applications. Nevertheless, as observed in [82], the nominal
value of the NEDT cannot be considered, since it is deined
by measuring a black body at room temperature and using
speciic camera settings and speciic f -number of the optics,
while the experimental condition is usually diferent. It must
be measured for the speciic setup and its results are usually
higher than the nominal one.
Using the (45), the minimum contrast can be written as
��� = Γ (� (� det , �� + NETD) − � (� det , �� ))
≈Γ
≈Γ
�
(�−Ψ/(�� +NETD) − �−Ψ/�� )
�5det
� ΨNEDT −Ψ/��
,
�
�5det ��2
(51)
where, we remember, � = 2�ℎ�2 and we have redeined
Ψ = ℎ�/�� � det . he latest approximation derives from the
consideration that is NETD ≪ �� (for state-of-art cameras
NEDT ∼ 10 mK).
When the camera ILM/CDI signal equals the minimum
camera contrast, then �ef = NEL. Neglecting the relectance
Journal of Solid State Physics
15
(in the experiment it is possible using an antirelection
coating on the back of the wafer), supposing that the radiation
is optically iltered at wavelength � det (as oten it is in
practice), we can approximate (44) as
�
� ≈ Γ�Δ�� 3 �−Ψ/�� ,
(52)
� ���
so that from (42), (43), (52), and (51), we obtain
ℎ�
NETD
1
NEL =
,
�� ��2 �2det �Φ (1 − �� ) √�
(53)
where � is the number of averaged images [2, 81, 82].
he sensitivity of the ILM/CDI in the emission mode
can be derived in the same manner, obtaining at the end
an expression similar to the previous one where �� appears
instead of �� .
Equation (53) shows that the setup sensitivity increases
(i) when the black body temperature in the absorption
mode and the wafer temperature in the emission mode
increase. his suggests that the latest mode results
are more sensitive. In fact in accordance with the
Kirkof Law, at thermal equilibrium the absorbed
infrared radiation is equal to the emitted infrared
radiation, but, in spite of the smaller emissivity of
the wafer with respect to the quasi-ideal black body
used, the dependence of the black body radiation
on temperature must be considered. herefore, while
relatively intense signals are reached in emission mode
heating the wafer, in the other coniguration the black
body must be cooled, determining a reduction of the
emitted infrared intensity;
(ii) when a detection wavelength around 8 �m is used.
his wavelength corresponds to the maximum of
the black body spectral emission. Cameras with the
maximum response in the MIR must be chosen;
(iii) with the increasing of the camera sensitivity (decreasing of the NEDT) and camera speed (the camera
frame rate increases and thus the number of averaged
images, or rather the averaging time). he introduction of the lock-in technique [77], already suggested
in [2] and tested the irst time in the CDI apparatus
by Riepe et al. [3], allows for reducing the NEL by 2
orders of magnitude.
8.5. Lateral Resolution. he lateral resolution of the ILM
depends on the optical set up and on the camera resolution.
With a 384×288 pixel array detector and an optics that allows
for focusing on an area varying between 15×15 100×100 mm,
the lateral resolution (given by the ratio between the focused
area and the number of lateral pixels) of about 50 and 350 �m,
respectively, can be reached [81]. With the modern camera,
increasing the number of pixel, and with diferent optics, the
resolution can be increased to few tens of microns.
9. Dynamic Carrier Lifetime Imaging
We have noted that, being the ILM a steady-state technique,
one of its disadvantages is the necessity of an accurate
calibration. Ramspeck and coworkers recently developed a
dynamic version of the technique (dynamic-ILM) [61] that
presents the advantages of the transient technique to avoid
the calibration and the advantages of the ILM to yield a very
fast and high spatially resolved data acquisition.
he setup is similar to the common ILM technique
but the applied excitation source is a square-wave-shaped
illumination and it implements a lock-in technique for the
data processing (this not only to improve the signal-to-noiseratio, as we will see). he pump period is chosen such that the
sample reaches a stationary condition in the semiperiod when
the pump is on. In this way four images are recorded: the
irst one immediately ater switching on the pump; the second
when the steady-state condition is achieved; the third immediately ater switching of of the pump; and the fourth when
the new steady state is achieved with the pump of. he latest
image records the background illumination that must be used
to correct the other images. If the camera integration time is
chosen suiciently short, that means of the order of the sample expected efective lifetime, �int ≈ �ef , the irst and the third
images record the transient rise and decay of the excess free
carriers and, in this condition, a suicient contrast between
the signals relative to the the images of the transients respect
the signal relative to the image of the steady-state is achieved.
In Figure 10 the illustration of the images acquisition
timing with respect to the pump illumination is reported, as
shown in the original work [61].
he authors observe that the ratio between the background corrected images relative to the steady-state and
to the rise transient, respectively, (the irst image and the
second one) depends only on �int and �ef , so that, known the
former, the second one can be evaluated without requiring
further calibration. Nevertheless, using the lock-in detection
the correction of the background results are automatic. In
fact, the acquisition is composed by two subsequent steps: in
the irst one the four images recorded during one excitation
period are multiplied with coeicient of a sine and a cosine
function, in phase with the excitation; in the second one
the four images are summed up. he results are the cosinecorrelation function, �cos , and the sine-correlation function,
�sin , that give, respectively, the diference between the irst
and the third images, and between the second and the fourth
images:
�int
�cos = ∫
0
Δ� (�) �� − ∫
�/2+int
�/2
� (�) ��
= �st-st {�int − 2���� [1 − exp (−
�/4+�int
�sin = ∫
�/4
= �st-st
Δ� (�) �� − ∫
3�/4+int
3�/4
× {�int − 2�ef [exp (−
�int
)]}
�ef
� (�) ��
� + 4�int
�
) − exp (−
)]} ,
4�ef
4�ef
(54)
Journal of Solid State Physics
1st image
1.0
2nd image
3rd image
4th image
tint = 300 �s
120
Excess carrier
density Δn(t)
0.8
105
tint = 1100 �s
Image
acquisition
time tint
0.6
Phase Φ (∘ )
Normalized carrier density Δn(t) and generation rate �
16
75
0.4
0.2
0.0
tint = 2000 �s
90
60
Generation
rate �
45
0
T
Time t (�s)
0
1000
Lifetime �eff (�s)
(a)
(b)
Figure 10: (a) Schematic of the generation rate G, excess carriers density Δ�(�), and image acquisition during one measurement period of
length �, as reported in the original work of Ramspeck et al. [61]. (b) Relationship between lifetime �ef and phase lock-in phase Φ for several
image acquisition times as reported in the original work of Ramspeck et al. [61].
where �st-st = G�ef represents the steady-state signal that
would be recorded if any background would be present, while
� is the lock-in period. he authors observe that the lockin phase, deined as Φ = arctan(�sin /�cos ), is an increasing
function of �ef , depending on the parameters �int and �,
that for small value of �int is enough linear for low lifetime.
For measurements performed with �int = 300 �s and � =
25 ms the function results are linear for lifetime smaller than
200 �s, with a sensitivity of 0.25∘ × �s−1 (see the right side of
Figure 10(a)). hey conclude that if a shorter integration time
is chosen, the sensitivity increases, and the linear range shits
toward the lower lifetime values.
10. Conclusion
In this paper we have examined all two optical techniques
to measure the recombination lifetime in the semiconductor
materials: the Transient Pump and Probe and the Infrared
Lifetime Mapping. Both techniques are based on the Free
Carriers Absorption and can be classiied as Pump and Probe
methods, since they make use of the common operation
principle that uses a sub-band-gap radiation as probe to
monitor the absorption variation in a sample induced by
the generation of excess free carriers by means of a pump
radiation.
In the TPP method the signal, where the interesting
quantities are retrieved, is the transient evolution of the
excess carrier density. his is generated by the pump pulse
just ater the turn of of the latter. Its main merit is the
possibility to directly determine from the measurement a
simultaneous evaluation of the bulk recombination lifetime
and of the surface recombination velocity. Moreover, we have
shown that little variations in the setup coniguration give the
method the lexibility to measure other electrical parameters
of the sample. Furthermore, it allows for measuring very short
lifetime, of the order of few nanosecond (depending on the
pump pulse width).
he ILM, on the other hand, allows a very fast mapping
of the actual recombination lifetime on the sample. In fact
this method uses an infrared camera sensor to detect the
free carriers absorption, so that the local information on the
carrier density can be derived in a single acquisition without
scanning the sample. Having additional knowledge about
the carrier generation rate �, the efective carrier lifetime,
�ef = Δ�/�, of the sample is calculated. In spite of being
a steady-state method, based on the measurement of the
frequency response of the semiconductor when excited by
a modulated laser beam, it presents the disadvantages that
the correct determination of the lifetime critically depends
on the accuracy of the calibration procedure applied and
on the accurate accounting of the lateral inhomogeneities in
the optical properties of the sample. We have illustrated as
this disadvantage is surmounted by the its dynamic version,
which releases the measurements from the calibration, so that
the methods results are to be perfectly complementary with
respect to the TPP.
Conflict of Interests
he authors declare that there is no conlict of interests
regarding the publication of this paper.
Journal of Solid State Physics
References
[1] Z. G. Ling, P. K. Ajmera, M. Anselment, and L. F. Dimauro,
“Lifetime measurements in semiconductors by infrared absorption due to pulsed optical excitation,” Applied Physics Letters,
vol. 51, no. 18, pp. 1445–1447, 1987.
[2] M. Bail, J. Kentsch, R. Brendel, and M. Schulz, “Lifetime
mapping of Si wafers by an infrared camera [for solar cellproduction],” in Proceedings of the 28th Photovoltaic Specialists
Conference, pp. 99–103, IEEE, Anchorage, Alaska, USA, 2000.
[3] S. Riepe, J. Isenberg, C. Ballif, S. Glunz, and W. Warta, “Carrier
density and lifetime imaging of silicon wafers by infrared
lock-in thermography,” in Proceedings of the 17th European
Photovoltaic Solar Energy Conference, pp. 1597–1599, 2001.
[4] N. Ashcrot and N. Mermin, Solid State Physics, Cengage
Learning, Singapore, 1976.
[5] C. Kittel and P. McEuen, Introduction to Solid State Physics,
Wiley, New York, NY, USA, 1996.
[6] J. Nelson, he Physics of Solar Cells, Imperial College Press, 2003.
[7] V. K. Khanna, “Physical understanding and technological control of carrier lifetimes in semiconductor materials and devices:
a critique of conceptual development, state of the art and
applications,” Progress in Quantum Electronics, vol. 29, no. 2, pp.
59–163, 2005.
[8] P. Landsberg, Recombination in Semiconductors, Cambridge
University Press, 1991.
[9] R. N. Hall, “Electron-hole recombination in germanium,” Physical Review, vol. 87, no. 2, p. 387, 1952.
[10] W. Shockley and W. T. Read, “Statistics of the recombinations of
holes and electrons,” Physical Review, vol. 87, no. 5, pp. 835–842,
1952.
[11] V. K. Khanna, “Carrier lifetimes and recombination-generation
mechanisms in semiconductor device physics,” European Journal of Physics, vol. 25, no. 2, pp. 221–237, 2004.
[12] L. Pincherle, “Auger efect in semiconductors,” Proceedings of the
Physical Society B, vol. 68, no. 5, article 108, pp. 319–320, 1955.
[13] T. S. Moss, “Photoelectromagnetic and photoconductive efects
in lead sulphide single crystals,” Proceedings of the Physical
Society B, vol. 66, no. 12, article 301, pp. 993–1002, 1953.
[14] J. A. Hornbeck and J. R. Haynes, “Trapping of minority carriers
in silicon. I. P-type silicon,” Physical Review, vol. 97, no. 2, pp.
311–321, 1955.
[15] P. Auger, “he compound photoelectric efect,” Journal de
Physique et le Radium, vol. 6, no. 6, article 205, 1925.
[16] P. T. Landsberg and T. S. Moss, “Recombination theory for
indium antimonide,” Proceedings of the Physical Society B, vol.
69, no. 6, article 310, pp. 661–669, 1956.
[17] P. T. Landsberg, “Lifetimes of excess carriers in InSb,” Proceedings of the Physical Society B, vol. 70, no. 12, article 109, pp. 1175–
1176, 1957.
[18] A. Beattie and P. Landsberg, “Auger efect in semiconductors,”
Proceedings of the Royal Society of London A: Mathematical and
Physical Sciences, vol. 249, no. 1256, pp. 16–29, 1959.
[19] A. B. Grebene, “Comments on auger recombination in semiconductors,” Journal of Applied Physics, vol. 39, no. 10, pp. 4866–
4868, 1968.
[20] P. Lal, C. Rhys-Roberts, and P. Landsberg, Auger Recombination
Into Traps, Ft. Belvoir Defense Technical Information Center,
1964.
[21] P. T. Landsberg, “Trap-Auger recombination in silicon of low
carrier densities,” Applied Physics Letters, vol. 50, no. 12, pp. 745–
747, 1987.
17
[22] J. Dziewior and W. Schmid, “Auger coeicients for highly doped
and highly excited silicon,” Applied Physics Letters, vol. 31, no. 5,
pp. 346–348, 1977.
[23] D. J. Fitzgerald and A. S. Grove, “Surface recombination in
semiconductors,” Surface Science, vol. 9, no. 2, pp. 347–369, 1968.
[24] P. T. Landsberg, “Some general recombination statistics
for semiconductor surfaces,” IEEE Transactions on Electron
Devices, vol. ED-29, no. 8, pp. 1284–1286, 1982.
[25] D. E. Aspnes, “Recombination at semiconductor surfaces and
interfaces,” Surface Science, vol. 132, no. 1–3, pp. 406–421, 1983.
[26] G. J. Rees, “Surface recombination velocity: a useful concept?”
Solid State Electronics, vol. 28, no. 5, pp. 517–519, 1985.
[27] D. K. Schröder, “Carrier lifetimes in silicon,” IEEE Transactions
on Electron Devices, vol. 44, no. 1, pp. 160–170, 1997.
[28] H. B. Briggs, “Infra-red absorption in silicon,” Physical Review,
vol. 77, no. 5, pp. 727–728, 1950.
[29] H. Fan and M. Becker, “Infra-red optical properties of silicon
and germanium,” in Semi-Conducting Materials: Proceedings
of a Conference Held at the University of Reading under the
Auspices of the International Union of Pure and Applied Physics,
in cooperation with the Royal Society, p. 132, Butterworths
Scientiic Publications, 1951.
[30] H. B. Briggs and R. C. Fletcher, “New infrared absorption bands
in p-type germanium,” Physical Review, vol. 87, no. 6, pp. 1130–
1131, 1952.
[31] H. B. Briggs and R. C. Fletcher, “Absorption of infrared light by
free carriers in germanium,” Physical Review, vol. 91, no. 6, pp.
1342–1346, 1953.
[32] A. H. Kahn, “heory of the infrared absorption of carriers in
germanium and silicon,” Physical Review, vol. 97, no. 6, pp. 1647–
1652, 1955.
[33] H. Y. Fan, W. Spitzer, and R. J. Collins, “Infrared absorption in
n-type germanium,” Physical Review, vol. 101, no. 2, pp. 566–572,
1956.
[34] W. Spitzer and H. Y. Fan, “Infrared absorption in n-type silicon,”
Physical Review, vol. 108, no. 2, pp. 268–271, 1957.
[35] S. Visvanathan, “Free carrier absorption due to polar modes in
the III-V compound semiconductors,” Physical Review, vol. 120,
no. 2, pp. 376–378, 1960.
[36] W. P. Dumke, “Quantum theory of free carrier absorption,”
Physical Review, vol. 124, no. 6, pp. 1813–1817, 1961.
[37] H. Hara and Y. Nishi, “Free carrier absorption in p-type silicon,”
Journal of the Physical Society of Japan, vol. 21, no. 6, p. 1222,
1966.
[38] W. Runyan, Technology Semiconductor Silicon, 1966.
[39] D. Schroder, R. homas, and J. Swartz, “Free carrier absorption
in silicon,” IEEE Transactions on Electron Devices, vol. 25, pp.
254–261, 1978.
[40] J. I. Pankove, Optical Processes in Semi-Conductors, Dover
Publications, 1971.
[41] P. Basu, heory of Optical Processes in Semiconductors: Bulk and
Microstructures, Oxford University Press, New York, NY, USA,
1997.
[42] B. Nag, Electron Transport in Compound Semiconductors,
Springer, 1980.
[43] G. Chiarotti and U. M. Grassano, “he excited states of the F
center investigated by means of modulated optical absorption,”
Il Nuovo Cimento B Series 10, vol. 46, no. 1, pp. 78–92, 1966.
[44] G. Chiarotti and U. M. Grassano, “Modulated F-center absorption in KCl,” Physical Review Letters, vol. 16, no. 4, pp. 124–127,
1966.
18
[45] W. B. Gauster and J. C. Bushnell, “Laser-induced infrared
absorption in silicon,” Journal of Applied Physics, vol. 41, no. 9,
pp. 3850–3853, 1970.
[46] E. J. Conway, “Light-induced modulation of broad-band optical
absorption in CdS,” Journal of Applied Physics, vol. 41, no. 4, pp.
1689–1693, 1970.
[47] F. Sanii, R. J. Schwartz, R. F. Pierret, and W. M. Au, “Measurement of bulk and surface recombination by means of modulated
free carrier absorption,” in Proceedings of the 20th IEEE Photovoltaic Specialists Conference, pp. 575–580, September 1988.
[48] F. P. Giles, F. Sanii, R. J. Schwartz, and J. L. Gray, “Nondestructive
contactless measurement of bulk lifetime and surface recombination using single pass infrared free carrier absorption,” in
Proceedings of the 22nd IEEE Photovoltaic Specialists Conference,
pp. 223–228, October 1991.
[49] S. W. Glunz, A. B. Sproul, W. Warta, and W. Wettling, “Injectionlevel-dependent recombination velocities at the Si-SiO2 interface for various dopant concentrations,” Journal of Applied
Physics, vol. 75, no. 3, pp. 1611–1615, 1994.
[50] S. W. Glunz and W. Warta, “High-resolution lifetime mapping
using modulated free-carrier absorption,” Journal of Applied
Physics, vol. 77, no. 7, pp. 3243–3247, 1995.
[51] Z. G. Ling and P. K. Ajmera, “Measurement of bulk lifetime and
surface recombination velocity by infrared absorption due to
pulsed optical excitation,” Journal of Applied Physics, vol. 69, no.
1, pp. 519–521, 1991.
[52] G. S. Kousik, Z. G. Ling, and P. K. Ajmera, “Nondestructive
technique to measure bulk lifetime and surface recombination
velocities at the two surfaces by infrared absorption due to
pulsed optical excitation,” Journal of Applied Physics, vol. 72, no.
1, pp. 141–146, 1992.
[53] T. Otaredian, “Separate contactless measurement of the bulk
lifetime and the surface recombination velocity by the harmonic
optical generation of the excess carriers,” Solid-State Electronics,
vol. 36, no. 2, pp. 153–162, 1993.
[54] Z. G. Ling, P. K. Ajmera, and G. S. Kousik, “Simultaneous
extraction of bulk lifetime and surface recombination velocities
from free carrier absorption transients,” Journal of Applied
Physics, vol. 75, no. 5, pp. 2718–2720, 1994.
[55] K. L. Luke and L.-J. Cheng, “Analysis of the interaction of a laser
pulse with a silicon wafer: determination of bulk lifetime and
surface recombination velocity,” Journal of Applied Physics, vol.
61, no. 6, pp. 2282–2293, 1987.
[56] J. Linnros, “Carrier lifetime measurements using free carrier
absorption transients. I: principle and injection dependence,”
Journal of Applied Physics, vol. 84, no. 1, pp. 275–283, 1998.
[57] J. Linnros, “Carrier lifetime measurements using free carrier
absorption transients. II. Lifetime mapping and efects of
surface recombination,” Journal of Applied Physics, vol. 84, no.
1, pp. 284–291, 1998.
[58] R. Bernini, A. Cutolo, A. Irace, P. Spirito, and L. Zeni, “Contactless characterization of the recombination process in silicon
wafers: separation between bulk and surface contribution,”
Solid-State Electronics, vol. 39, no. 8, pp. 1165–1172, 1996.
[59] A. Irace, L. Sirleto, G. F. Vitale et al., “Transverse probe optical
lifetime measurement as a tool for in-line characterization of the
fabrication process of a silicon solar cell,” Solid-State Electronics,
vol. 43, no. 12, pp. 2235–2242, 1999.
[60] M. C. Schubert, S. Riepe, S. Bermejo, and W. Warta, “Determination of spatially resolved trapping parameters in silicon with
injection dependent carrier density imaging,” Journal of Applied
Physics, vol. 99, no. 11, Article ID 114908, 2006.
Journal of Solid State Physics
[61] K. Ramspeck, S. Reissenweber, J. Schmidt, K. Bothe, and R.
Brendel, “Dynamic carrier lifetime imaging of silicon wafers
using an infrared-camera-based approach,” Applied Physics
Letters, vol. 93, no. 10, Article ID 102104, 2008.
[62] A. Buczkowski, Z. J. Radzimski, G. A. Rozgonyi, and F. Shimura,
“Bulk and surface components of recombination lifetime based
on a two-laser microwave relection technique,” Journal of
Applied Physics, vol. 69, no. 9, pp. 6495–6499, 1991.
[63] L. Sirleto, A. Irace, G. F. Vitale, L. Zeni, and A. Cutolo,
“Separation of bulk lifetime and surface recombination velocity
by multiwavelength technique,” Electronics Letters, vol. 38, no.
25, pp. 1742–1743, 2002.
[64] L. Sirleto, A. Irace, G. F. Vitale, L. Zeni, and A. Cutolo,
“Separation of bulk lifetime and surface recombination velocity
obtained by transverse optical probing and multi-wavelength
technique,” Optics and Lasers in Engineering, vol. 38, no. 6, pp.
461–472, 2002.
[65] L. Sirleto, A. Irace, G. Vitale, L. Zeni, and A. Cutolo, “All-optical
multiwavelength technique for the simultaneous measurement
of bulk recombination lifetimes and front/rear surface recombination velocity in single crystal silicon samples,” Journal of
Applied Physics, vol. 93, no. 6, pp. 3407–3413, 2003.
[66] A. Irace, L. Sirleto, P. Spirito et al., “Optical characterization
of the recombination process in silicon wafers, epilayers and
devices,” Optics and Lasers in Engineering, vol. 39, no. 2, pp. 219–
232, 2003.
[67] A. Irace, F. Sorrentino, and G. F. Vitale, “Multi-wavelength
transverse probe lifetime measurement for the characterization
of recombination lifetime in thin mc-Si samples for photovoltaic industry use,” Solar Energy Materials and Solar Cells, vol.
84, no. 1–4, pp. 83–92, 2004.
[68] A. Irace, F. Sorrentino, and G. F. Vitale, “Multi-wavelength all
optical measurement for the characterization of recombination
process in thin mc-Si samples,” Solar Energy, vol. 78, no. 2, pp.
251–256, 2005.
[69] E. Gaubas and J. Vanhellemont, “A simple technique for the
separation of bulk and surface recombination parameters in
silicon,” Journal of Applied Physics, vol. 80, no. 11, pp. 6293–6297,
1996.
[70] E. Gaubas, J. Vaitkus, E. Simoen, C. Claeys, and J. Vanhellemont,
“Excess carrier cross-sectional proiling technique for determination of the surface recombination velocity,” Materials Science
in Semiconductor Processing, vol. 4, no. 1–3, pp. 125–131, 2001.
[71] M. De Laurentis, A. Irace, and G. Breglio, “Accurate modelling
of the pump-probe spatial interaction in an all-optical recombination lifetime measurement setup,” in Proceedings of the 1st
Mediterranean Photonics Conference, p. 40, Ischia, Italy, 2008.
[72] M. De Laurentis, A. Irace, and G. Breglio, “Determination of the
surface electrical activity in silicon wafers with a laser pumpprobe measurement,” in Proceedings of the 6th International
Conference on Photo-Excited Processes and Applications, p. 121,
2008.
[73] A. G. Aberle, J. Schmidt, and R. Brendel, “On the data analysis of
light-biased photoconductance decay measurements,” Journal
of Applied Physics, vol. 79, no. 3, pp. 1491–1496, 1996.
[74] J. Schmidt and A. G. Aberle, “Accurate method for the determination of bulk minority-carrier lifetimes of mono- and
multicrystalline silicon wafers,” Journal of Applied Physics, vol.
81, no. 9, pp. 6186–6199, 1997.
[75] F. M. Schuurmans, A. Schönecker, A. R. Burgers, and W. C.
Sinke, “Simpliied evaluation method for light-biased efective
Journal of Solid State Physics
[76]
[77]
[78]
[79]
[80]
[81]
[82]
lifetime measurements,” Applied Physics Letters, vol. 71, no. 13,
pp. 1795–1797, 1997.
J. Schmidt, “Measurement of diferential and actual recombination parameters on crystalline silicon wafers,” IEEE Transactions on Electron Devices, vol. 46, no. 10, pp. 2018–2025, 1999.
O. Breitenstein and M. Langenkamp, Lock-in hermography:
Basics and Use for Functional Diagnostics of Electronic Components, Springer, 2003.
W. Warta, “Advanced defect and impurity diagnostics in silicon
based on carrier lifetime measurements,” Physica Status Solidi
(A) Applications and Materials Science, vol. 203, no. 4, pp. 732–
746, 2006.
M. C. Schubert, J. Isenberg, and W. Warta, “Spatially resolved
lifetime imaging of silicon wafers by measurement of infrared
emission,” Journal of Applied Physics, vol. 94, no. 6, pp. 4139–
4143, 2003.
J. Isenberg, S. Riepe, S. W. Glunz, and W. Warta, “Carrier density
imaging (CDI): a spatially resolved lifetime measurement suitable for in-line process-control,” in Proceedings of the 29th IEEE
Photovoltaic Specialists Conference, pp. 266–269, May 2002.
J. Isenberg, S. Riepe, S. W. Glunz, and W. Warta, “Imaging
method for laterally resolved measurement of minority carrier
densities and lifetimes: measurement principle and irst applications,” Journal of Applied Physics, vol. 93, no. 7, pp. 4268–4275,
2003.
P. Pohl and R. Brendel, “Temperature dependent infrared camera lifetime mapping (ILM),” in Proceedings of the 19th European
Photovoltaic Solar Energy Conference, pp. 46–49, Paris, France,
2004.
19
Journal of
Journal of
Gravity
Photonics
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
The Scientiic
World Journal
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Journal of
Advances in
Condensed Matter Physics
Soft Matter
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Journal of
Aerodynamics
Journal of
Fluids
Hindawi Publishing Corporation
http://www.hindawi.com
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Volume 2014
International Journal of
Optics
Submit your manuscripts at
http://www.hindawi.com
International Journal of
Statistical Mechanics
Hindawi Publishing Corporation
http://www.hindawi.com
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Volume 2014
Journal of
Thermodynamics
Journal of
Computational
Methods in Physics
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Solid State Physics
View publication stats
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Advances in
Astronomy
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Journal of
Journal of
Hindawi Publishing Corporation
http://www.hindawi.com
Physics
Research International
Advances in
High Energy Physics
Volume 2014
Astrophysics
Biophysics
Hindawi Publishing Corporation
http://www.hindawi.com
Atomic and
Molecular Physics
Journal of
Journal of
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
International Journal of
Superconductivity
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014