7Photoluminescence Analysis of Thin-Film Solar CellsThomas Unold and Levent G€utay

7.1Introduction

Luminescence describes the emission of light from a solid arising from deviationsfrom thermal equilibrium, as distinct from black-body radiation which is observedin thermal equilibrium [1, 2]. The thermal equilibrium state can be disturbed byvarious forms of excitation, such as the application of an external voltage (electro-luminescence, see Chapter 3), an incident electron beam (cathodoluminescence,see Section 12.2.5), mechanical stress (mechanoluminescence), a heating rampreleasing carriers from deeply trapped states (thermoluminescence), and also by theabsorption of light of sufficient energy, which is commonly called photolumines-cence (PL). The emission of PL radiation is caused by the transition of electrons fromhigher occupied electronic states into lower unoccupied states, under the emissionof photons if the transition is dipole-allowed. According to the laws of quantummechanics, the transition rate can be calculated by first-order perturbation theoryusing Fermi�s golden rule. Using this formalism, optical transitions from anoccupied density of initial states to an unoccupied density of final states can beexpressed by [2, 3]

RspðEÞ /ðMifj j2f ðEiÞ 1�f ðEi þEÞð ÞgðEiÞgðEi þEÞdEi ð7:1Þ

where Mif represents the matrix element coupling the wavefunctions of the initialandfinal state, f(E) represents theFermi–Dirac occupation function, and g(E) denotesthe density of electronic states. Usually the optical transition matrix element iscalculated in the semiclassical approximation, where the exciting light is treated byclassical electrodynamics. Using the fact that the same transitionmatrix element anddensity of states govern absorption and emission events, a relationship between theabsorption coefficient a(E) and the spontaneous emission rate was derived based ondetailed balance arguments in thermal equilibrium [4]

R0sp ¼

8pn2rh3c2

aðEÞE2

expðE=kBTÞ�1ð7:2Þ

Advanced Characterization Techniques for Thin Film Solar Cells,Edited by Daniel Abou-Ras, Thomas Kirchartz and Uwe Rau.� 2011 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2011 by Wiley-VCH Verlag GmbH & Co. KGaA.

j151

where nr is the refractive index of thematerial, h is Planck�s constant, c is the speed oflight, and kB is the Boltzmann constant. Equation (7.2) is very useful in the sense thatit directly relates the absorption coefficient of amaterial to its emission spectrum andin principle allows for calculating one quantity if the other quantity is known. Since inPLmeasurementswe are interested indeviations from thermal equilibrium,wewritethe net spontaneous emission rate as

Rsp ¼ R0sp

npn0p0

�R0sp ¼ Bðnp�n0p0Þ ¼ Bn2i ðexpðDm=kBTÞ�1Þ ð7:3Þ

where n and p are the total carrier densities, n0 and p0 are the equilibrium carrierdensities related to the intrinsic carrier density by n2i ¼ n0 p0;Dm ¼ EFn�EFp repre-sents the quasi-Fermi level splitting between the quasi-Fermi level for electronsEFn and for holes EFp, and B defines the material-specific radiative recombinationcoefficient [1]

B ¼ 1n2i

8ph3c2

ð1

0

n2raðEÞexpð�E=kBTÞE2dE ð7:4Þ

It is useful to distinguish the following experimental conditions: (i) n� n0 andp� p0. In this case, the PL photon flux is given by YPL/Bnp. This situation isreferred to as the high-injection condition, where the radiative lifetime trad¼ 1/(Bn)depends on the injection ratio. (ii) When p� p0 for p-type material (n� n0 for n-typematerial), then YPL/Bnp0 and the PL flux depends on the majority carrier densitywith a radiative lifetime trad¼ 1/(Bp0) independent of the injection ratio. Thissituation is referred to as the low-injection condition. Typical values for the radiativecoefficient and radiative lifetime assuming a doping level of 1016 cm�3 are BSi¼2� 10�15 cm�3 s�1 and tSi¼ 0.025 s for silicon and BCuInSe2 � 6� 10�11 cm�3 s�1

and tCuInSe2 � 1 ms for CuInSe2 [1, 5].In most materials, nonradiative recombination occurs via deep defects in the

energy band gap, limiting the recombination lifetime to significantly smaller valuesthan the radiative lifetime since the total recombination rate comprises all individualrecombination rates

t�1tot ¼ t�1

rad þ t�1nonrad ð7:5Þ

From the ratio of measured lifetime to radiative lifetime, the PL efficiency of amaterial can be defined as gPL ¼ ttot=trad.

So far, we have been mostly concerned with radiative transitions taking placewithin the sample. However, the correct calculation of the number of photonsemitted from a sample in a PL experiment is much more complicated since detailsof the absorption profile, diffusion and drift and recombination of carriers with thesample, and the propagation of the emitted photons through the sample surface haveto be taken into account. In most PL experiments, the information depth is givenby the absorption length 1/a of the exciting light or by the diffusion length ofminoritycarriers, which ever of these two quantities is larger [2]. For an exact treatment,

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closed-form solutions are difficult to obtain and numerical simulation has to beemployed. However, assuming homogenous material properties and flat quasi-Fermi levels and taking into account that light is emitted through the sample surfacewithin a narrow emission cone 1/4n2r , the photon flux detected outside the samplecan be expressed by [6]

YPLðEÞ ¼ 1

4p2�h3c2aðEÞE2

expððE�DmÞ=kBTÞ�1ð7:6Þ

where the absorptivity is given by a(E)¼ (1�Rf) (1� exp(�a(E)d)) with the frontsurface reflectivity Rf and the sample thickness d. Equation (7.6) has been referred toas the generalized Kirchhoff�s or generalized Planck�s law because of its resemblanceto these well-known relations valid for thermal equilibrium conditions. Note thatEq. (7.6) is only valid if equilibration between the electronic states involved (e.g.,carriers in the conduction band and carriers in the valence band) can occur on thetime scale of the radiative recombination time. For most materials, this is true atroom temperature for thermal-emission depths smaller than about Egap� 0.3 V.However, it is certainly not true for carriers in deep band tail states at temperaturesin the range of 10 K. Since the quasi-Fermi level splittingDm contained in Eq. (7.6) isrelated to themaximumopen-circuit voltage,Voc, achievable for a photovoltaic device,this relation can be used for predicting this device property using luminescencemeasurements at room temperature [6–9].

If measurements of the absolute magnitude of the luminescent photon fluxemitted from a sample under photoexcitation are available, the quasi-Fermi levelsplitting can be derived from the magnitude and spectral shape of the luminescencesignal. This method in particular allows for the investigation of the influence ofsubsequent processing steps on the quality of an absorber material. If the opticalconstants are known for the material, the data may be evaluated using Eq. (7.6) andthe correct values for the spectral absorptivity. However, for thin-film compoundsemiconductor materials, the absorption coefficient very often is not exactly known,and one has to make simplifying assumptions. In this case, the high-energy wingof the PL signal may be evaluated at photon energies sufficiently larger than the bandgap, where the absorptivity can be approximated to be constant and a(E)� 1 is areasonable assumption. Then, Eq. (7.6) can be rewritten as

lnYPL Eð Þ

1023 E2=cm2 eV s

� �¼ �E�Dm

kTð7:7Þ

allowing for an extraction of the quasi-Fermi level splitting Dm from a fit to the high-energy wing of the PL spectrum. Note that the equation assumes an absorber layerwith homogeneous phase composition and constant quasi-Fermi levels throughoutthe material. For extracting the local optical threshold energy from a PL spectrum,the determined value Dm is reinserted in Eq. (7.6) which allows for the extractionof the spectral absorptivity a(E) for the lower energetic region of the luminescencespectrum.

7.1 Introduction j153

7.2Experimental Issues

7.2.1Design of the Optical System

A schematic of a typical PL setup is shown in Figure 7.1. The sample can bemountedin ambient conditions for fast room-temperature measurements or in a cryostat forlow-temperature measurements in vacuum or, as is the case in dynamic cryostats, inhelium or nitrogen atmosphere. As an excitation source, any light source of suitableluminance and appropriate wavelength range can be used. The most general lightsource would be a white light from a halogen or xenon lamp filtered by a mono-chromator, which allows for a wide range of excitation wavelengths, however, at thecost of very low excitation power. Because of the widespread availability and highmonochromatic power, inmost setups laser excitation sources are used, for example,gas lasers such as helium–neon (633 nm) or argon (514 nm) lasers, or solid-state laserdiodes. The excitation source is guided or focused onto the sample by a flat mirror orfocusing device (lens or parabolic mirror). The luminescence radiation emitted fromthe sample is then collected by a light collection device, which again can be given bya lens or also by a parabolic or off-axis parabolic mirror. The collimated light passesan order-sorting filter system which prevents the detection of unwanted higherorders. For most applications, colored glass long-pass filters are chosen with cutoffwavelengths slightly larger than half the measurement wavelength. The lumines-cence light is then focused into themonochromator system through an entrance slit.As a general comment regarding the focusing assemblies in the whole luminescencesetup, we point out that off-axis parabolic mirrors are considered first because theyare dispersion free. The luminescence light exits themonochromator through an exitslit and reaching the radiation detector, which can be a photodiode, photomultiplier,or avalanche photodiode, or a one- or two-dimensional detection device such asa photodiode array or CCD array.

Figure 7.1 Experimental setup for room- and low-temperature PL measurements.

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In the case of a single-area detector, the spectral resolution of the system isdetermined by the dispersion of the grating (nm/mm) times the entrance/exit slitwidth. Note that the focusing unit directing the light into the monochromator has tobe designed to match the aperture of the monochromator specified by the f-numberf/#¼ f/D, where f is the focal length and D collimated beam diameter, to achieve anoptimal illumination of the dispersion grating and mirrors inside the monochro-mator. If the focusing f/# is too small, then light is scattered inside the monochro-mator, and if the focusing f/# is too large then the spectral resolution is decreased.In the case of a diode array, the exit slit is omitted, and the spectral resolution isdetermined by the dispersion times the diodewidth,which is typically 10–30 mm.Theadvantage of using a detector array is the possibility to record a single spectrum in oneshot, without the need for scanning the grating. The advantage of using single-areadetectors is the higher signal-noise ratio achievable by using low-noise amplificationby avalanche diodes or photomultiplier tubes in combination with lock-in-detection.The excitation signal can be modulated by an optical chopper wheel or by directelectrical modulation of a laser diode.

If measurements with high spatial resolution are of interest, a microscope setupcan be used [10]. In Figure 7.2, a PL setup utilizing a confocal microscope isoutlined. In this configuration, the excitation source is focused onto the samplesurface through a microscope lens. The luminescence light is collected through thesame lens, separated from the exciting light beam by means of a beam splitter,and focused onto a fiber connected to the detecting system. This system exhibitsdiffraction-limited resolution of approximately 0.6l/NA, where NA is the numerical

Figure 7.2 Setup for spatially resolved measurements using a confocal microscope.

7.2 Experimental Issues j155

aperture of the microscope objective and l is the wavelength of the detectedluminescence signal. A spatial resolution of down to about 500 nm can be obtainedin an optimized system investigating luminescence light of approximately 1000 nm.The sample is mounted on a xy-positioning table, which allows for a two-dimen-sional scan of the emitted luminescence radiation. As the excitation area in a micro-PL is in the range of 1mm2, very high excitation intensities can be achieved, whichmay lead to local heating and high-injection effects. This has to be kept in mindwhen analyzing the data. Efforts should be made to keep the excitation level as lowas possible.

7.2.2Calibration

The two most important calibrations to be performed are wavelength calibration ofthe monochromator and the determination of the transfer function of the completeoptical system. The wavelength calibration is commonly performed using an argonor mercury–argon lamp, which is placed at the sample position. The atomic linesrecorded by the detection system are then fitted to the known line spectrum of thelamp type which, for example, may be downloaded from the NISTWebsite [11]. Thetransfer function contains the wavelength-dependent attenuation of the propagatingluminescence signal after passing all optical components of the collection anddetection system, that is, all lenses, mirrors, windows, filters, gratings, and thequantum efficiency of the detector. Tomeasure this function, a radiation source withknownemission spectrum is placed at the sample position and its emission spectrumis recordedwith all optical components in place. If variousfilters or gratings are used,each one of these optical elements has to be considered. For absolute calibrationof the luminescence photon flux, a black-body calibration source with knownemissivity and temperature is used. Calibrated tungsten-band lamps have beenuseful to perform this task.

In order to obtain the proper luminescence signal, the measured signal has to bemultiplied by the transfer function and subsequently converted into energy space bytaking into account the change from constant wavelength intervals to constantenergy intervals, which requires a multiplication of the luminescence signal by afactor of l2.

7.2.3Cryostat

If low-temperature measurements are of interest, a cryostat has to be used. Com-monly used cryostats are either liquid helium or nitrogen flow or closed-cycle heliumcryostats. The advantage of a closed-cycle cryostat is that no liquid helium isnecessary, at the expense of mechanical vibrations of about�10 mmwhen comparedwith continuous-flow cryostats. Helium-flow cryostats allow for lower minimumtemperatures of 1.5 K when compared to closed-cycle cryostat with which only 4Kcan be reached. When performing low-temperature measurements on thin-film

156j 7 Photoluminescence Analysis of Thin-Film Solar Cells

materials, special care has to be taken to correctly determine the sample temperatureduring the measurement. Because the thin materials are commonly grown on glasssubstrates which are considerably bad thermal conductors, the temperature of thethin-film sample can differ considerably from the temperature of the cold fingerof the cryostat. To properly calibrate the temperature, a second sensor mountedon a glass substrate identical to the sample glass substrate should be employed inthe system.

7.3Basic Transitions

A number of different transitions can occur in a PL measurement depending on themeasurement conditions and thematerial properties. In the following, we give a verybrief description of the most important radiative transitions occurring in semicon-ductor materials. In general, the different transitions can be distinguished by theirtransition energy and by the change of the transition energy and luminescence yieldwith varying excitation intensity and temperature. Therefore, it is useful to define thefollowing two dependencies. The luminescence yield of a transition line in generalis found to obey the expression [1, 2]

YPLðwÞ ¼ wk ð7:8Þwherew is the excitation intensity and k is a characteristic parameter usually rangingbetween 0.5 and 2. The luminescence yield of transitions involving localized statesgenerally decreases with increasing temperature owing to the thermal emission ofthe trapped carriers to the conduction or valence band. This dependence ontemperature can be described by

YPLðTÞ ¼ 11þC exp �Ea=kTð Þ ð7:9Þ

where Ea represents a characteristic activation energy and C is a constant which isproportional to T3/2 if the thermal quenching involves thermal emission to theconduction or valence band [12, 13]. Bear in mind that the activation energies candiffer significantly if or if not a T 3/2 dependence is included in the model.

The shift of transition energy with increasing temperature may be influenced by ashift in the optical gap with temperature [1]. Because this applies to all of thetransitions discussed in the following section, this will not be discussed individuallybut only stated here. Typically, a decrease in the bandgapwith increasing temperatureof the order of 10�4 eV/K is observed that may compensate positive peak shifts of theorder of kBT in the experiment. Radiative transitions can occur with or withoutthe emission of phonons, depending on the electron–phonon coupling strength andthe measurement temperature, thereby often leading to so-called phonon replica ofthe transitions. Because of limitation in space, these phonon replicas will not bediscussed in the present section, and the interested reader is referred to theliterature [1, 2].

7.3 Basic Transitions j157

7.3.1Excitons

The classical PL experiment is performed at low temperatures in the vicinity of 10K.At this temperature, the luminescence efficiency can be considerably higher than atroom temperatures as the ratio of radiative to nonradiative recombination rate isgreatly increased and recombination events arising from electron–hole pairs boundto each other by theirCoulomb interaction, so-called free excitons,may be observable.The transition energy of free excitons can be calculated using a simple hydrogenicmodel yielding

EFX ¼ Eg�Ex; Ex ¼ mre4

2ð4pe0er�hÞ2n2ð7:10Þ

where Ex is the exciton binding energy and mr is the reduced electron–hole mass1=m�

r ¼ 1=m�e þ 1=m�

p [1]. The quantum number n specifies the possible excitedstates of the exciton. It is obvious from Eq. (7.10) that the binding energy of excitonsmostly depends on the dielectric constant er and the reduced effective mass. ForCuGaSe2 thin films with a dielectric constant of about 13 and effective masses ofm�

e � 0:14 and m�p � 1, a free exciton-binding energy of 10meV is expected, which

agrees reasonably well with the experimentally determined value EFE¼ 13meV [14].Exciton-binding energies increase for large band-gap materials such as ZnO due totheir smaller dielectric constants [15]. Optical transitions related to free excitons areonly detectable at sufficiently low temperatures when kBT<Ex and will dissociateat higher temperatures. The thermal quenching of the free exciton luminescence canbe described by Eq. (7.9), where the activation energy corresponds to the exciton-binding energy if the quenching process corresponds to the dissociation of theexcitons into free carriers. However, if many transitions are present, the activation

High temperatureLow temperature

BBFX BX

DA

e-A0

p-D 0

E D

EA

conduction band

valence band

DA

e-A0

Figure 7.3 Optical transitions observable in luminescence measurements.

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energy in Eq. (7.9) may not be unambiguously identified with the free-excitontransition. A more unambiguous determination of the binding energy is possibleif excited states of the exciton can be detected [14, 16].

For the change of the PLyieldwith excitation intensity for free excitons, one expectsk¼ 1 for resonant excitation and k¼ 2 for excitation above the band gap [17]. Schmidtet al. showed that if several transitions concur, the exciton k value can take valuesranging from1 to 2 depending on thematerial and experimental conditions. Excitonsdo not exhibit a shift in their transition energy, if the excitation intensity is increased.

Free excitons get easily bound to impurities, which leads to a modification of theirtransition energy by the interaction with the impurity. The transition energy forbound exciton emission is given by

EBX ¼ Eg�EBE ð7:11Þwhere the term EBE represents the binding energy of the complex [2]. This term istypically a fraction of the ionization energy of the isolated impurity in the case ofcharged impurities and the sumof the free-exciton binding energy added to a fractionof the impurity binding energy in the case of neutral defects, as described byHayne�srule [18, 19]

EBE ¼ cnEA=D þ EFE for neutral defectsciEA=D for charged defects

�ð7:12Þ

The proportionality factors cn and ci depend on the effective mass ratiom�e =m

�h and

were estimated for donors in CuGaSe2 to be of the order of cn� 0.3 and ci� 1 [14].Considering the binding energy of 13meV of free excitons in CuGaSe2, bindingenergies of about 17meV for excitons bound to shallow donors were obtained [14].Excitons can also be bound to deeper impurities in which case their binding energymay be much larger than the binding energy of free excitons. The ratio between freeand bound exciton emission present in a photoluminescence experiment dependson the number of impurities present in the material and on the measurementtemperature. According to Lightowlers [20], for impurity concentrations of N> 1015

cm�3 in silicon, essentially all free excitons get captured by donors or acceptors andlead to bound-exciton luminescence.

Bound excitons do not have kinetic energy causing their linewidth to be muchsmaller than the linewidths of order of kBT found for free excitons. Excitontransitions can also be broadened by inhomogeneities in the material propertiessuch as composition variations and material strain. Since radiative emissions fromfree and bound excitons can occur with the additional emission of phonons, phononreplica of the exciton emission lines are frequently detected and have to bedistinguished from transitions arising from excitons bound at different impurities.

7.3.2Free-Bound Transitions

In nonideal semiconductormaterials, there are always localized states present due todonor or acceptor impurities which can give rise to carrier recombination by

7.3 Basic Transitions j159

transitions between the free carriers in the bands and the localized states in the bandgap, so-called free-to-bound (FB) transitions [1]. It is possible to detect both con-duction-band-to-acceptor (e-A0) and/or valence-band-to-donor state (p-D0) transi-tions. Shallow transitions from the conduction band to donors or from the valenceband to acceptors are unlikely, because in these cases, the probability for phonon-related transitions is much higher than the probability of transitions involving therelease of a photon [21].

Free-bound transitions can be identified by their spectral signature and specifictemperature-dependent und intensity-dependent behavior. The transition lineshapecan be described by a modification of Eq. (7.2) in which the square-root dependenceof the density of states of parabolic conduction or valence bands in direct-gapsemiconductors is considered [2, 22]

YPLðEÞ / E2ðE�ðEg�EA=DÞÞ0:5 expððEg�EA=D�EÞ=kTÞ ð7:13Þ

where EA/D is the donor or acceptor ionization energy. The peak position of thetransition as obtained from setting the derivative of Eq. (7.13) equal to zero is relatedto the optical gap by

YPLðEÞmax / Eg�EA=D þ kBT=2 ð7:14Þ

Note that both these expressions strictly only apply to direct-gap semiconductorswith ideal parabolic bands. The thermal quenching of the luminescence yield FBtransitions is again described byEq. (7.9), where now the activation energy representsthe ionization energy of the impurity state. For the excitation intensity dependence ofFB processes k¼ 1 is expected in the ideal case since the transition rate dependson one free carrier type, which depends linearly on the excitation intensity, and on thedonor or acceptor density, which is independent of the excitation intensity. Note thatwhen impurities are present in large densities, they begin to form impurity bands,which merge with the nearest intrinsic band, making the distinction betweenfree-bound and band–band transitions difficult [1].

7.3.3Donor–Acceptor Pair Recombination

If both donors and acceptors are present in significant concentrations and thetemperature is low enough, it is possible to observe donor–acceptor pair (DAP)recombination processes, which involve transitions between two localized electronicstates. These transitions originate from neutral donors and neutral acceptors(having previously captured a free carrier) which recombine to leave two oppositelycharged defects [1]. The Coulomb energy between the ionized donor and acceptoris transferred to the emitted photon resulting in an emission energy of

EDA ¼ Egap�EA�ED þ ECoul ð7:15aÞ

ECoul ¼ e2

4pe0er rDAð7:15bÞ

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where EA and ED are the ionization energies of the donor and acceptor, respectively,and ECoul describes the Coulomb interaction between the ionized donor and acceptorwhere rDA is the distance between the donor and the acceptor involved in theemission, which depends on the impurity density and the excitation density, ander denotes the static dielectric constant. Since the effective distance between donorsand acceptors decreases with the injection level, the effect of theCoulomb interactionis smallest for low excitation intensities and gets largest for high excitation inten-sities. The dependence of the luminescence peak energy EDA on the excitationintensity, wexc, can be empirically described by [23]

EDAðwexcÞ / EDAðw0Þþ b logwexc

w0

� �ð7:16Þ

where typical values of b are found to be around 1–5meV per decade of excitationintensity. The maximum possible Coulomb-energy related shift of DAP transitionscan be estimated from the binding energy of the spatially more extended defect,usually the donor level, in the hydrogenic impurity model given by [24]

EMax ¼ e4m�e

2ð4pere0�hÞ2ð7:17Þ

For typical values of er¼ 13.6 and m�e ¼ 0:09 for CuInSe2, a maximum shift of

Emax¼ 6.6meV is estimated [25, 26]. Thermal quenching of DAP-transitions isdescribed by an equation similar to Eq. (7.9), now containing two activation energies

IPL ¼ 11þC1 expð�Ea1=kTÞþC2 expð�Ea2=kTÞ ð7:18Þ

where again the constants C1 andC2 are proportional to T3/2 if the quenching occurs

by thermal emission of charges to the valence band and conduction band, respec-tively [12]. Under the assumption that the constants C1 and C2 are of similarmagnitude, the activation energy observed at lower temperature is related to theionization energy of the shallower impurity state and the activation energy observedat higher temperatures is related to the ionization energy of the deeper level.However, in some cases it is not possible to get meaningful fits using Eq. (7.18)and the analysis of the data using the single activation energy contained in Eq. (7.9)should be considered [13].

The change of the DAP-lineshape with increasing temperature is complicated,because the recombination process involves a tunneling step which depends on thedistance of the recombination pairs. Briefly, for increasing temperatures moredistant pairs get thermally re-emitted to the bands before they recombine, increasingthe number of close pairs in the radiative recombination. Due to the larger Coulombterm for the close pairs this leads to a blue shift of the order of kBT of the emissionspectrumwith increasing temperature [1, 2]. For the luminescence yield as a functionof excitation intensity k¼ 1 is expected in the ideal case but as was already discussedabove, significantly smaller values than that may be observed in the case of differentcompeting transition types. Schmidt et al. show that for certain experimental

7.3 Basic Transitions j161

conditions the k values of the exciton and DAP transition are related to each otherby kexc¼ 2 kDAP [17].

7.3.4Potential Fluctuations

For high concentrations of donors and acceptors when NA=Da3B > 1, the Bohr-radiia�B ¼ 4pe0e�h

2=m�e2 of the impurity wavefunctions start to overlap, leading toimpurity-related band formation [27]. If the donors� and acceptors� concentrationsare of similar magnitude, the semiconductor becomes compensated, with a netdoping density much lower than the dopant concentration. Since the distribution ofdopants in the lattice is statistical, the band structure becomes distorted by potentialfluctuations due to local variations in the fixed space charge, which cannot bescreened by the low free-carrier density. Such potential fluctuations which areindicated in a schematic band diagram in Figure 7.4 strongly influence the opticaland electrical properties as now transitions with significantly smaller transitionenergy than the standard DAP or FB transition energy become possible [26–30].

The average depth of the fluctuations, c, can be estimated from the average chargefluctuations occurring within a certain volume defined by the screening radius rscontaining an impurity concentration Nt ¼ N þ

A þN�D screened by a free-carrier

density p by [27]

c ¼ e2

4pere0Ntrsð Þ0:5 ¼ e2

4pere0

N2=3t

p1=3ð7:19Þ

where rs given by rs ¼ N1=3t p�2=3 for p-type material. Typical values for CuInSe2 thin

films can be estimated assumingNA¼ND¼ 1018 cm�3, p¼ 1016 cm�3, and er¼ 13.6to yield c¼ 78meV with a screening length of rs� 270 nm. Because DAP recom-bination involves tunneling between the two impurity sites, the transition energy

Figure 7.4 Effect of potential fluctuations on the band edges and the radiative transitions betweentrapped electrons and holes. j(x) denotes the spatial varying electrostatic potential arising fromthe potential fluctuations and the dashed line represents an acceptor/donor level or band.

162j 7 Photoluminescence Analysis of Thin-Film Solar Cells

can be significantly reduced in the presence of band fluctuations, which experimen-tally leads to a low-energy tail and broadening of the luminescence transitions. Theemission energy of DAP recombination in highly compensated material can beestimated with

EPF�DA ¼ EDA�2c ð7:20Þwhere EDA is given by Eq. (7.15a) [23]. It is obvious fromEqs. (7.19) and (7.20) that theemission energy for highly compensated DAP transitions depends on the number ofimpurities, the compensation ratio, and the free-carrier density which in turndepends on the excitation level in the experiment.

Therefore for increasing excitation level, a strong blue shift of the emission line isexpected which can greatly exceed the b¼ 1–2meV expected for the DAP Coulombterm given in Eq. (7.15b). Experimentally peak shifts as large as b¼ 10–30meV areobserved [26, 28, 29].

If the temperature is increased, the emission peak in strongly compensatedsemiconductors is found to red shift at low temperatures and low excitationintensities. This can be explained with a lack of complete thermalization of thecarriers trapped in different potential wells, which leads to an incompletefilling of thelowest energetic wells. If temperature is increased, the carriers becomemoremobileand also populate the deepest wells, leading to a red shift of the emission line withincreasing temperature. If the temperature is further increased, the more distantpairs are increasingly thermally emitted to the bands leaving the closer pairs and thusproducing a blue shift, in accordance with the effect observed for DAP transitions.A detailed discussion of the effect of potential fluctuations in compensated semi-conductors can be found in the literature [26, 27, 29–31].

7.3.5Band–Band Transitions

With increasing temperature excitons and impurities become ionized and theconduction and valence bands become increasingly occupied with photoexcitedcarriers such that band–band transitions become more probable. The lineshape ofband–band transitions can be described by Eq. (7.2) using the appropriate absorptioncoefficient for band–band transitions. For a direct-gap semiconductor with parabolicbands, the following expression is obtained [2]

YPLðEÞ / E2ðE�EgÞ0:5expð�ðE�EgÞ=kTÞ ð7:21Þ

where Eg ist the band gap of the material. This equation is very similar to theexpression obtained for the free-bound emission stated above, which means that inorder to distinguish between band–band transitions and free-bound transitions,knowledge of the value of the band gap determined by independent means is veryhelpful. As for free-bound transitions, the peak position increases with temperatureas kBT/2. In band–band transitions, both free-carrier types are involved, both dependon the excitation intensity, and thus k values>1 can be observed. Note that in the case

7.3 Basic Transitions j163

of high injectionwith band–band transitions dominating recombination k¼ 1will beobserved, because in this case the lifetime is inversely proportional to the injectionlevel as discussed in the introduction.

7.4Case Studies

In this section,we discuss some typical PLmeasurement results for chalcopyrite-typeCu(In,Ga)Se2 thin films and also completed solar cells. The defect physics andtherefore also the nature of the dominant PL transitions in this material is found tostrongly depend on the film composition, most prominently on the [Cu]/[In] þ [Ga]ratio. Sharp transitions are observed for material grown under copper-rich condi-tions, whereas broad, mostly featureless transitions are observed in the case ofcopper-poor growth conditions [12, 25, 28, 29, 32]. We will also distinguish betweenlow-temperature and room-temperature luminescence analysis. Both techniqueshave advantages and disadvantages depending on the material and the investigatedmaterial properties.

7.4.1Low-Temperature Photoluminescence Analysis

In Figure 7.5, low-temperature PL spectra of a Cu-rich grown epitaxial CuGaSe2sample are shown. The sample was grown on GaAs(100) by metal organic vaporphase epitaxy (MOVPE). The Cu/Ga-ratio of the sample was determined as[Cu]/[Ga]� 1.1 by energy dispersive X-ray analysis (EDX, see Section 12.2.3). Themeasurement was performed at 10 K and the sample was illuminated by the

Figure 7.5 PL spectra for a Cu-rich grown epitaxial CuGaSe2 thin film measured at variousexcitation fluxes and 10K.

164j 7 Photoluminescence Analysis of Thin-Film Solar Cells

514.5 nm line of anArþ laser using different excitationfluxes. The PL spectra exhibitdistinct transition peaks at 1.72, 1.66, and 1.63 eV, and a further peak occurring asa shoulder at 1.60 eV with full-widths-at-half-maximum (FWHM) of approximately10, 19, 27, and 55meV. These four peaks have been identified in the literature asan exciton-related transition (EXC), and three different donor–acceptor transitions(DA1, DA2, DA3) [14, 29].

This assignment can be justified by evaluating the peak energies and their shiftwith excitation intensity, and also the corresponding k values describing the depen-dence of the PL yield on excitation intensity. In Figure 7.6a, the intensity of the DA1,DA2, and EXC transitions are plotted as a function of the excitation intensity usinglogarithmic scaling of the axes. A fit using Eq. (7.8) yields k values of k¼ 0.6 forthe DA1 and DA2 transition and k¼ 1.2 for the EXC transition. Values of k� 1 areexpected for donor–acceptor or free-bound transitions, whereas k values �1 are

Figure 7.6 (a) Intensity dependence of the PL yield of transitions DA1, DA2, and EXC. (b) Shiftof PL peaks as a function of excitation intensity.

7.4 Case Studies j165

expected for exciton or band–band transitions. Considering the known value forthe band gap Egap¼ 1.73 eV of CuGaSe2 at 10K, the EXC transition energy is located10meV below the band gap, which agrees well with experimentally determinedsingle-crystal free exciton-binding energies of 13meV [14].

The shift of the peak energies with excitation intensity shown in Figure 7.6bindicates values ofbEXC¼ 0meV,bDA1¼ 1.5meV, andbDA2¼ 4meV. The fact that theEXC transition does not shift with excitation intensity confirms the assignment to anexciton transition. In fact, a more detailed analysis of this transition shows that it canbe deconvolved into two closely spaced transitions located at 1.7139 and 1.7105 eV,which have been identified with a free-exciton and a bound-exciton transition.A detailed discussion of this assignment can be found in the literature and is beyondthe scope of this article [14]. Peak shifts of b 1–4meVare values typically observedfor DAP recombination processes, andmay arise from the increasing contribution ofthe Coulomb interaction as the distance between the participating donors andacceptors is decreased when the density of photoexcited carriers increases withexcitation intensity. This confirms an assignment of the transitions DA1 and DA2 toa DAP recombination. The fourth transition line (DA3) located at 1.6 eV could berelated to a phonon replica of DA2 since its energetic distance between DA2–DA3� 30meV is comparable to typical LO-phonon energies Eph� 34meV inCuGaSe2 [29]. However, it is also possible that DA3 is a separate DAP transitionas has been suggested from cathodoluminescence measurements showing thespatial location of the DA3 transitions to be distinct from the spatial locations ofthe DA2 transition [33].

We note that although the observed k values are significantly smaller than thevalues of k¼ 1 and k¼ 2 expected for donor–acceptor and exciton transitions in theideal case, these values agree well with the theory of Schmidt et al. [17] who predictedkexc � 2kDAP for the situation of different concurring radiative and nonraditativetransition.

Cu-poor prepared Cu(In,Ga)Se2 films that generally lead to much higher solarconversion efficiencies than Cu-rich prepared films show a very different lumines-cence behavior at low temperature. In Figure 7.7, the PL spectrum of a coevaporatedCu(In,Ga)Se2 thin-film solar cell with [Cu]/([InþGa] )¼ 0.9 and [Ga]/([InþGa])¼0.3 in a glass/Mo/Cu(In,Ga)Se2/CdS/ZnO stacking structure is measured at 15 Kusing a 660-nm laser diode as an excitation source.

Now a single but much broader transition is observed. The peak energy of thistransition is 1.11 eV with a FWHMof 60meV. Aplot of the peak energy and intensityversus excitation intensity (not shown here) yields b¼ 10meV and k¼ 0.96 at 15Kmeasurement temperature. Although this k value is compatible with the valuesobserved for the DAP transitions of the Cu-rich sample, the b value is much largerthan the 1–4meVobserved above and also much larger than the total shifts expectedfor DAP transitions in chalcopyrite materials. Such large b values are a clearindication of potential fluctuations due to strong compensation in the material asalready discussed in the Section 7.3.4. This assignment is corroborated by temper-ature-dependent measurements as shown in Figure 7.8a where the shift of the peakenergy of the transition is plotted as a function of temperature.

166j 7 Photoluminescence Analysis of Thin-Film Solar Cells

Figure 7.7 PL spectrum of Cu-poor Cu(In,Ga)Se2 with [Cu]/([In] þ [Ga])¼ 0.9 and[Cu]/([In] þ [Ga])¼ 0.3 measured at 15 K.

Figure 7.8 (a) PL-peak shift with temperature for Cu-poor Cu(In,Ga)Se2. (b) Dependence of PLyield on temperature.

7.4 Case Studies j167

It can be seen that the peak energy first shifts to smaller energies (redshift) at lowtemperatures and then to larger energies for temperatures above 50K (blueshift).This behavior is a characteristic signature of potential fluctuations [25, 26, 29–31] asdiscussed above. An analysis of the PL yield in Figure 7.8b using Eq. (7.18) yieldsactivation energies of 6 and 82meV assuming a T3/2 dependence of the emissionprefactors. Although the errors are relatively large, it can be concluded that a veryshallow level atE1¼ 6meVand a deep level atE2¼ 82meVparticipate in the observedtransition. However, we have to caution that the interpretation of transition energiesand their temperature dependence is difficult in the presence of potential fluctua-tions, because thermal redistribution processes within the potential well landscapetake place.

7.4.2Room-Temperature Measurements: Estimation of Voc from PL Yield

When the temperature is raised to room temperature, band–band transitions becomevery likely, as the bands are now sufficiently populated by photoexcited carriers.A room temperature PL spectrummeasured for the sample of Figure 7.7 is shown inFigure 7.9 exhibiting an even broader transition with a peak energy of 1.13 eV anda FWHM� 100meV (solid line, left scale).

An evaluation of the PL yield with excitation intensity gives a k¼ 1.4 andb¼ 0meV, which allows to identify the recombination process as band–bandtransitions. Note that the exciton-binding energy is of the order of tens of millivoltsin this material leaving excitons fully ionized at 300 K.

Also included in thefigure is a PL-spectrumof a coevaporated Cu(In,Ga)Se2 solarcell processed with similar but not identical preparation conditions and a [Ga]/([InþGa]) ratio of 0.27 [9]. The device structure is glass/Mo/Cu(In,Ga)Se2/CdS/

Figure 7.9 Room-temperature PL spectrum of the Cu-poor Cu(In,Ga)Se2 device of Figure 7.7(left scale, solid line) and a Cu-poor Cu(In,Ga)Se2 device from a different coevaporation processmeasured in a setup with absolute calibration (right scale, open circles).

168j 7 Photoluminescence Analysis of Thin-Film Solar Cells

ZnOwith an active area of 0.5 cm2. It can be seen that the spectral shape agrees wellfor these two samples, with a slight shift in the peak energy by 20meV. For themeasurement, the device was fully illuminated with light from a 780-nm laserdiode. In order to allow a prediction of the open circuit voltage corresponding toAM1.5 illumination conditions, the monochromatic excitation photon flux in theexperiment was adjusted to correspond to the number of photons that would beabsorbed for broad-band AM1.5 excitation, which for a 1.1-eV band-gap material isapproximately 2�1017 cm2/s or 60mW/cm2. The luminescence radiation wasmeasured by a liquid nitrogen cooled germanium detector in a setup calibratedto yield absolute photon numbers. According to themethod outlined in Section 7.1,the absolute quasi-Fermi level splitting is estimated by plotting the quantity ln(YPL(E)/10

23/E2) versus energy and fitting the high-energy wing using Eq. (7.7) asshown in Figure 7.10a. From the slope, m, the temperature of the photoexcitedelectron–hole ensemble T¼ (1/kB/m)¼ 320 K and from the y-axis intercept atE¼ 0 eVa quasi-Fermi level splitting ofDm¼ 0.58 eV is obtained. This value agrees

Figure 7.10 (a) Determination of thequasi-Fermi level splitting from calibratedroom-temperature PL measurement.(b) Absorptivity (triangles, right scale) andabsorption coefficient (open circles, left scale)

determined from the calibrated PLmeasurement. Also included is a direct gapabsorption coefficient with square-rootdependence on energy (dashed line).

7.4 Case Studies j169

very well with the experimentally determined open-circuit voltage for whichVoc¼ 0.56 V was obtained, using exactly the same illumination conditions [9]. Thededuced temperature of T¼ 320 K is higher than the measurement temperatureT¼ 300 K, most likely due to sample heating from the large-area illuminationduring the experiment. The good agreement betweenVoc andDm demonstrates thefeasibility of themethod to judge the electronic quality of thematerial without needof electrical contacts or electrical measurements. On the other hand, it also showsthat for this particular example very little losses occur in the functional layers and atthe contacts, leading to ameasuredVoc almost as high as the bulk value of the quasi-Fermi level splitting.

As described in Section 7.1, the energy-dependent absorptivity function can bedetermined by plugging the values for the temperature and Dm back into Eq. (7.6).The resulting absorptivity function a(E) is shown in Figure 7.10b (triangles, rightscale). Using the approximation a(E)� 1� exp(�a(E)d) and assuming a homo-geneous sample thickness of 1 mm, the absorption coefficient can then be derivedfrom the absorptivity. The result is shown in Figure 7.10b (open circles. left scale).The absorption coefficient derived from the PL measurement may be compared toan absorption coefficient expected for a direct-gap semiconductor with idealparabolic bands [1] a(E)¼A (E�Egap)

0.5, which is included in Figure 7.10b usinga dashed line (A¼ 105 cm�1 and band-gap value Egap¼ 1.19 eV). It can be seen thatthe theoretical curve agrees well with the experimental curve in the region aboveEgap. For energies below Egap, the experimental curve does not vanish rapidly butshows an exponentially decaying band tail with a characteristic energy of E0¼ 15meV. Figure 7.10b shows that a defined value of the absorptivity, for example, a(E)¼ 1/e, may be used to derive an optical threshold from the PL measurement,which is related to the optical band gap of the material. This result will be used inthe next section to map spatial inhomogeneities in the optical properties of asample by PL.

7.4.3Spatially Resolved Photoluminescence: Absorber Inhomogeneities

Thin semiconductor materials often show significant nonuniformities in theirmorphology, grain orientation, composition, and their electronic and optoelectronicproperties [34–39]. Although the knowledge of the impact of these inhomogeneitieson cell performance is still limited, generally, spatial inhomogeneities of the absorberlayer are considered to be disadvantageous for the cell efficiency, which was recentlyshown in several modeling approaches [40–42]. PL performed with microscopicspatial resolution can be used for investigating spatial inhomogeneities of absorberlayers and for quantifying the variation of material properties on microscopiclength scales [36, 43]. The experimental setup used in a PL-scanning experimentwas described in the experimental section.

In the following, micro-PL scans for a Cu(In,Ga)Se2 thin-film sample with[Ga]/([InþGa])¼ 0.3 and [Cu]/([InþGa])� 0.8measured at room temperature

170j 7 Photoluminescence Analysis of Thin-Film Solar Cells

are shown. The sample configuration was glass/Mo/Cu(In,Ga)Se2/CdS. Thesample was excited by a 532-nm laser at an excitation flux corresponding to104 � AM 1:5. The detector system of the micro-PL setup was a spectrograph witha photodiode array, which allowed for straightforward measurements of a data setcontaining a complete PL spectrum for each point of the scan. An image of thespectrally integrated luminescence intensity, which is related to the local recom-bination lifetime, is shown in Figure 7.11. It can be seen that the integratedluminescence signal varies by a factor of 3 with typical structure sizes on themicrometer scale. To analyze the spatial variation of the quasi-Fermi level splittingand of the optical threshold, themicro-PL spectra in Figure 7.11 are analyzed usingthe approach outlined above, extracting the quasi-Fermi level splitting from a fit tothe high-energy tail of the data. Since in this experiment no absolute calibratedphoton counts were recorded, only relative changes of the quasi-Fermi levelsplitting can be extracted. The results for this quantity for the measured area areshown in Figure 7.12a. It can be seen from the images that the spatial variationclosely resembles the variations seen for the integrated PL yield. In Figure 7.12b, ahistogramof the distribution ofDm is displayed showing amaximumvariation of 40meV and a distribution width of FWHM� 13meV. From each recorded PLspectrum, an absorptivity function a(E) and an optical threshold Eth related toa(Eth)¼ 1/e is derived by using the method described in the previous section,which we associate with the local optical band gap [43]. The resulting map ofoptical threshold values and the distribution histogram are shown in Figure 7.13aand b.

It can be seen that the maximum lateral variation of the band gap amounts toapproximately 15meV with a FWHM� 6meV, which is just less than half the valueobtained for the distribution width of the quasi-Fermi level splitting. In this example,we have considered the variation of the optical threshold energy to be equal to a localvariation of the band gap, which is expected from alloying inhomogeneities in

Figure 7.11 Two-dimensional scan of the spectrally integrated PL intensity for a Cu(In,Ga)Se2thin film at room temperature.

7.4 Case Studies j171

Cu(In,Ga)Se2, that is, a locally varying Ga content. Generally, the extracted localvariation of the optical threshold energy can be caused by further effects than onlya shift of the optical gap, such as large local variations of the absorber thickness orchange in the characteristic band-tail energy. To strictly exclude thickness variationsfrom the analysis, it would be necessary to monitor the local thickness, for example,by atomic force microscopy and include this information in the evaluation proce-dure [44].We note that in general the variation of the quasi-Fermi level splitting tendsto decrease with increasing excitation level [45]. Although an excitation flux com-parable toAM1.5 conditionswould be desirable, it is generally very difficult to achieveformicro-PLmeasurements at room temperature because of the too small number ofphotons involved. In summary, the results shown here indicate that the absorberlayer contains spatial variations of the quasi-Fermi levels splitting and of the localband gap. As the spatial variation of the optical threshold does not seem to correlatewith the spatial variation in the quasi-Fermi level splitting, and the distribution of theoptical threshold values is significantly smaller than the distribution of Dm, we

Figure 7.12 (a) Two-dimensional maps of the lateral variation of the quasi-Fermi level splitting.(b) Corresponding statistical distributions of the 2D data.

172j 7 Photoluminescence Analysis of Thin-Film Solar Cells

conclude that a local variation in recombination lifetime is the main cause of theobserved variation in PL yield and Dm.

Figure 7.13 (a) Two-dimensionalmaps of the lateral variations of the optical threshold (local bandgap). (b) Corresponding statistical distributions of the 2D data.

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