Journal of Luminescence 181 (2017) 223–229

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Journal of Luminescence

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Full Length Article

On the composition of luminescence spectra from heavily dopedp-type silicon under low and high excitation

Hieu T. Nguyen n, Daniel MacdonaldResearch School of Engineering, College of Engineering and Computer Science, The Australian National University, Canberra, ACT 2601, Australia

a r t i c l e i n f o

Article history:Received 6 May 2016Received in revised form2 August 2016Accepted 17 August 2016Available online 17 September 2016

Keywords:LuminescenceHeavily-doped siliconBand gapFermi energyDensity of statesHot carriers

x.doi.org/10.1016/j.jlumin.2016.08.03613/& 2016 Elsevier B.V. All rights reserved.

esponding author.ail address: hieu.nguyen@anu.edu.au (H.T. Ng

a b s t r a c t

We present a systematic investigation of the effects of doping on the luminescence spectra from p-typecrystalline silicon wafers. First, we explain the difference in the approaches between the line shapeanalysis and the generalized Planck’s law in modeling the spectral shape, and connect the two methodstogether. After that, we elucidate the separate impacts of individual phenomena including band gapnarrowing, band tails and dopant bands, Fermi level shifting, and hot carriers on the luminescencespectra in heavily-doped silicon. Finally, employing appropriate excitation levels, we can unambiguouslyre-examine the growing of the band tails and the broadening of the shallow dopant band, as well as themerging of the valence and shallow dopant bands together, on measured luminescence spectra.

& 2016 Elsevier B.V. All rights reserved.

1. Introduction

Due to rich features contained in photoluminescence (PL)spectra from crystalline silicon (c-Si) wafers, photoluminescencespectroscopy (PLS) has been employed to study many fundamentalproperties of c-Si, such as the band gap at different temperatures[1] and doping levels [2,3], absorption coefficients [4–7], dopingconcentrations [8], or radiative recombination rates [6,9,10].Recently, with the advent of micro-PLS tools equipped with con-focal optics, it is feasible to pinpoint to micron-scale features in c-Si wafers and solar cells to study the luminescence properties ofthe material and defects [11–15], or to characterize devices[16–19]. Recently, we have employed micro-PLS to qualitativelyassess doping levels of localized heavily-doped regions in c-Siwafers and solar cells [20], since these regions emit a distinctluminescence peak courtesy of the band-gap narrowing effects inheavily-doped silicon at temperatures around 80 K [2,3]. In prin-ciple, such distinct peaks could allow quantitative micron-scale PLmethods for measuring doping concentrations and junctiondepths. However, the detailed analysis of such spectra is compli-cated by the fact that there are numerous physical phenomenaoccurring in parallel inside the heavily-doped c-Si, rather than justa simple narrowing of the band gap caused by a single effect.

uyen).

These phenomena can be understood by a systematic investigationof the PL spectra.

When the doping density increases, there are at least fourphenomena occurring simultaneously which impact PL spectrafrom c-Si. Firstly, the conduction band and valence band rigidlyshift towards one another due to increasing interactions amongfree carriers, and between free carriers and dopant atoms, causinga reduction in the band gap [21–23]. Secondly, the two band edgesare perturbed and band tails are formed, yielding not only aneffectively-smaller band gap but also a wider distribution of freecarriers at the two band edges [24–27]. Thirdly, the shallowdopant band, located slightly above the valence band (for p-typesilicon), broadens due to an increasing interaction among thedopant atoms. When the doping density approaches the Motttransition (�3�1018 cm�3), this dopant band slowly overlaps thevalence band tail, and eventually the two bands (dopant andvalence) merge together at a doping density higher than the Motttransition, forming a deeper and continuous band tail [26,28].Fourthly, the Fermi level shifts towards the valence band (forp-type silicon) and eventually moves into the valence band(i.e. the semiconductor becomes degenerate) at a doping densitymuch higher than the Mott transition [29]. The effects of thesephenomena on the band diagram of c-Si are illustrated in Fig. 1.

In fact, many authors presented intensive experimental resultson the PL spectra from heavily-doped c-Si [2,3,30–34]. Moreover,based on the experimental PL spectra, Dumke [33], Wagner [2],and Wagner and Alamo [34] extracted the apparent band-gap shift

dopant band andband tail are merged

Ener

gy

Ener

gy

Density of States

shallow dopantEF

EC

EV

band tail

EF

EC

EV

Density of StatesFig. 1. Illustration of the band diagram of (a) slightly-doped and (b) heavily-dopedp-type c-Si. EC, EV, and EF are the conduction and valence band edges, and the Fermilevel, respectively.

H.T. Nguyen, D. Macdonald / Journal of Luminescence 181 (2017) 223–229224

and the position of Fermi level as a function of doping densities.However, although changes in luminescence spectra at heavydoping reflect complex combinations of the four phenomenadescribed above, these phenomena are often lumped into twosimple properties of the spectra: the energy shift of the peak, andthe broadening of the width; and thus the individual effects ofeach phenomenon on the spectral shape are likely to be con-founded [2,3,30–34].

In addition, although Schmid et al. [32] and Wagner [2]reported the PL spectra at different doping densities for pþ silicon,the effects of the band tails and shallow dopant band, as well astheir evolutions with doping densities, could not be observed inthe spectra from these works. These features were either maskedby the deep-level emission at low excitation levels due to unin-tended impurities [32], or smeared out due to the broadening ofthe band-to-band spectra and the relative suppression of theshallow dopant peak under high excitation levels [2,32]. Therefore,there is still a lack of empirical luminescence data, in which theeffects of these phenomena are unambiguously revealed. Fur-thermore, although the so-called line shape analysis is commonlyused to study the properties of luminescence spectra at differentdoping densities [2,3,31,33], the formula describing the spectralshape in this method is very different from that of the generalizedPlanck's law [35,36], which has also beenwidely used to model thePL spectra [4–7,9,37–40].

In this study, we systematically re-examine the experimentaldata and model the PL spectra in order to separate the impacts ofindividual parameters on the spectral shape at both low and highexcitation levels, obtained from heavily-doped p-type c-Si wafers.Moreover, in our experiments, when the shallow dopant andvalence bands have not merged together, the use of a low excita-tion level (in this case around 4 W/cm2) helps avoid the over-lapping of the shallow dopant and band-to-band luminescencepeaks. Once the two bands merge into one, the use of a highexcitation level (250 kW/cm2) can suppress the influence ofunintentional deep-level centers on the PL spectra, which areevident in the low excitation spectra and greatly affect the inter-pretation of the PL spectral shape. First, we resolve the differencesin the formulas between the line shape analysis and the general-ized Planck's law, and connect the two methods together. We thenelucidate the separate impacts of individual parameters, includingthe band gap, Fermi level, hot carriers, and band tails on the PLspectra from heavily-doped p-type c-Si wafers using both

modeling and empirical results. The results show that, when sili-con becomes degenerate, these parameters have complementaryimpacts on the spectral shape, and thus the energy shift of theluminescence peak cannot be simply explained by a single quan-tity of band-gap narrowing. Finally, we show the impacts of theband tails as well as the shallow dopant band on the PL spectra,and clarify the difference in the spectra between the high excita-tion (HE) and low excitation (LE) measurements. These under-standings of the luminescence spectra in heavily-doped c-Si, atboth low and high excitation levels, are likely to aid the furtherdevelopment of powerful new techniques for silicon photovoltaicsbased on spectral luminescence.

2. Experimental details

The samples investigated are float-zone boron-doped crystal-line silicon (c-Si) wafers having different doping concentrationsfrom 5.7�1016 to 1.1�1020 cm�3. Their doping densities weremeasured using the electrochemical capacitance–voltage (ECV)technique. In preparation for PL measurements, the wafers werechemically etched in an HF/HNO3 solution to remove residual sawdamage. After that, they were passivated with an 18-nm layer ofAl2O3 deposited on both surfaces by plasma assisted atomic layerdeposition (PA-ALD). They were then annealed at 450 °C informing gas consisting of argon and hydrogen for thirty minutes toactivate the surface passivation [41]. The presence of the surfacepassivation layers increases the excess carrier density under illu-mination, leading to a stronger PL signal, even for the highexcitation cases.

The experimental setups of our low excitation (LE) and highexcitation (HE) systems are described in detail in Ref. [7] and Ref.[15], respectively. Both systems utilize an excitation wavelength of785 nm in this work. In the LE experiments, the on-sample laserspot size, on-sample excitation power, and spectral resolution are2.2 mm in diameter, 150 mW (corresponding to an excitationintensity of �4 W/cm2), and 5 nm, respectively. These parametersin the HE experiments, in which the laser is coupled through aconfocal microscope, are 1.7 mm in diameter, 6 mW (correspondingto an excitation intensity of �250 kW/cm2), and 0.25 nm,respectively. The injection level is estimated to be in the range of1�1016 and 1�1018 cm�3 in the LE and HE experiments,respectively. The spectral responses of both systems were deter-mined with the same calibrated tungsten-halogen light source.The sample temperature was controlled by a liquid-nitrogen-cooled cryostat.

3. Connections between line shape formula and generalizedPlanck's law

The so-called line shape analysis has been used to describe theband-to-band luminescence spectra from a semiconductor bymany authors [2,3,31,33]. In n-type semiconductors, the line shapeformula is given by:Z 1

0f e Eeð ÞDe Eeð Þf h Ehð ÞDh Ehð ÞdEe; ð1Þ

where fe, De, and Ee (fh, Dh, and Eh), respectively, are the distribu-tion function, density of states DOS, and amount of energy abovethe conduction band edge EC (below the valence band edge EV) offree electrons (holes).

There are several assumptions need to be noted in thisapproach. First, the above formula only describes the ability of thematerial to generate photons. The emitted photon flux is alsodetermined by the energy distribution of photons, which is a

Fig. 2. Illustration of the energy relationship among emitted photons ћω, phononsEP (‘þ ’ denotes a phonon emission event, whereas ‘� ’ denotes a phonon absorp-tion event), free holes Eh, and free electrons Ee in p-type silicon under illumination.See the text for descriptions of the symbols.

Fig. 3. Comparison between measured and modeled (band-to-band, withoutbroadening effects) PL spectra at 79 K under (a) LE and (b) HE levels.NA¼5.7�1016 cm�3.

H.T. Nguyen, D. Macdonald / Journal of Luminescence 181 (2017) 223–229 225

product of the distribution function (fγ) and DOS (Dγ) of photons,and is given by [42]:

f γ ℏωð Þ � Dγ ℏωð Þp ℏωð Þ2exp ℏω

kT

� ��1� ℏωð Þ2 � exp �ℏω

kT

� �: ð2Þ

where ћω and kT are the energy of emitted photons and thermalenergy, respectively. Therefore, the spontaneous spectral shape ofthe thermal radiation from n-type semiconductors (i.e. withoutillumination) should be determined by the following relationship:

I ℏωð ÞpZ 1

0f e Eeð ÞDe Eeð Þf h Ehð ÞDh Ehð ÞdEe

� �

� ℏωð Þ2 � exp �ℏωkT

� �� �: ð3Þ

However, under illumination, the Fermi level EF is split into twoseparate levels EFC¼EFþΔEFC and EFV¼EF-ΔEFV for electrons andholes, respectively. Therefore, the distribution functions of elec-trons and holes under illumination (fe,illum and fh,illum) should bewritten as:

f e;illum Eeð Þ ¼ 11þexp

Ee � EF þΔEFCð ÞkT

� � and f h;illum Ehð Þ ¼ 11þexp

EF �ΔEFVð Þ � EhkT

� �:In non-degenerate semiconductors, under low excitation levels

in which the quasi-Fermi levels are far enough from the bandedges, i.e. Ee-(EFþΔEFC) and (EF-ΔEFV)-Eh are several times largerthan kT, we can rewrite fe,illum and fh,illum as:

f e;illum Eeð Þ � f e Eeð Þ � exp ΔEFCkT

� and f h;illum Ehð Þ � f h Ehð Þ � exp ΔEFV

kT

� :

Therefore, under illumination, Eq. (3) should become:

I ℏωð ÞpZ 1

0f e Eeð ÞDe Eeð Þf h Ehð ÞDh Ehð ÞdEe

� �

� ℏωð Þ2 � exp �ℏω� ΔEFCþΔEFV� �

kT

� �� �: ð4Þ

Eq. (4) is of similar form to the generalized Planck's law fornon-degenerate semiconductors [35,36]. The first square bracketin Eq. (4) is, in principle, related to the band-to-band absorptioncoefficient, which is solely determined by the distribution func-tions and DOS of electrons and holes in the material. Some studiesdid not consider the energy distribution of photons fγ�Dγ, and didnot account for the separation of the Fermi level under illumina-tion, and as such their line shape formulas were different from thegeneralized Planck's law [2,3,31,33]. This difference has beennoticed by Daub and Würfel [5].

However, at low temperatures, there is negligible reabsorptionof the generated photons, and thus the carrier distributions do notaffect the spectral shape and we can neglect the term ΔEFCþΔEFVin Eq. (4). Also, when the silicon wafers become degenerate, theexcitation levels have little impact on the band-to-band PL spectralshapes, as empirically verified in Section 5 (see Fig. 7e and f).Therefore, in principle, we can use Eq. (3) to describe the spectralshape of the band-to-band luminescence from both non-degenerate and degenerate silicon at low temperatures. Forp-type silicon in this study, we simply swap the roles of electronsand holes in Eq. (3) together, and thus the Fermi level EF will benegative if it is higher than the valence band edge EV, and positiveif it moves into the valence band.

4. Effects of different parameters on the band-to-band PLspectra

In this section, we elucidate the separate impacts of individualparameters, including the band gap, Fermi level, and band tails onthe band-to-band PL spectra from heavily-doped silicon wafers. Atrelatively low doping densities, for which the dopant band has anegligible impact on the PL spectra, and the DOS in both

conduction and valence bands is still a parabolic function, thespectral shape at 79 K from silicon can be determined by Eq. (3). Inaddition, from Fig. 2, we also have the relationship:

ℏω7EP ¼ EeþEhþEG; ð5Þ

where EP and EG are the phonon energy and silicon band gap,respectively. ‘þ/� ’ denotes the emission/absorption of phonons.

Fig. 3a compares the modeled spectrum including three com-ponents - Transverse-Acoustic (TA) phonons, Transverse-Optical(TO) phonons, and both TO and zone-center optical (OΓ) phonons -with the measured LE spectrum from a lightly-doped c-Si waferhaving a doping density NA of 5.7�1016 cm�3 at 79 K. The generalshape of the modeled spectrum, in particular the TO component,follows the empirical spectrum closely, except for a mismatcharound 1.07 eV. The peak around 1.07 eV occurs due to free car-riers recombining through neutral shallow dopant atoms, and wasreported and denoted as BTO

3 by Dean et al. [43]. However, inFig. 3b, the high energy side of the HE spectrum remarkablydeviates from the modeling although their low energy sides matchvery well. The difference can be explained by the incompletethermalization of hot carriers in the HE measurements. Under veryhigh injection levels, more free carriers are distributed furtherfrom the band edges, and the energy distribution of the lumi-nescence is broadened [28]. Meanwhile, this incomplete therma-lization of free carriers does not change the band gap, and thus thelower energy side of the PL spectrum does not change.

Fig. 4. Modeling of individual effects of EG, EF, and ES on band-to-band PL spectra at 79 K.

Fig. 5. Measured (under HE levels) and modeled (band-to-band) PL spectra fordifferent combinations of EG, EF, and ES at 79 K in a degenerate silicon wafer.NA¼2.7�1019 cm�3.

H.T. Nguyen, D. Macdonald / Journal of Luminescence 181 (2017) 223–229226

Near the Mott transition, there is a significant overlap betweenthe shallow dopant and the TO components, and thus Eq. (3) doesnot reproduce the spectral shape well any more. When the dopingdensity increases further, the shallow dopant band merges withthe valence band and Eq. (3) becomes valid again. However, since anew deep and continuous band tail is formed due to the mergingof the two bands, the spectrum is broadened significantly which isnot accounted for in Eq. (3). To account for the band tails, themerging of shallow dopant band, and the incomplete ionization offree carriers, a broadening term ES is introduced into Eq. (3) via therelationship [2,3,33]:

IBroadening ℏωð ÞpZ 1

0I ℏω0ð Þexp � ℏω0 �ℏωð Þ2

E2S

" #d ℏω0ð Þ; ð6Þ

In fact, the broadening model employed in Eq. (6) is a simpleway to account for the band tailing effects. Above the Mott tran-sition, the DOS in the valence band is no longer a parabolic func-tion, but has a complex structure due to the combination of theshallow dopant band and valence band tail [26]. However, wefound that Eqs. (3) and (6) are sufficient to qualitatively explainthe effects of the band gap, Fermi level, and band tails on ourmeasured PL spectra, as discussed below.

Now, we investigate the separate effects of individual para-meters (EG, EF, and ES) on the PL spectra when the doping densityincreases. Fig. 4a–c plot the modeled PL spectra when one para-meter is changed while the other two are kept the same. In Fig. 4a,the narrowing of EG only shifts the spectra towards lower energieswithout altering their shapes. In Fig. 4b, EF does not affect thespectral shape until it reaches EV and moves beyond EV. Theincreasing EF (when situated in the valence band) not only shiftsthe spectra to higher energies, but also broadens all their com-ponents due to the band filling effects. Nevertheless, the lowenergy thresholds of all components (marked by broken arrows in

Fig. 4b) are still the same since the EF shifting does not change theband edge positions. In Fig. 4c, the broadening factor ES simplybroadens the spectra, causing different components to overlaptogether. As a result, EG and EF have opposing effects on thespectral peak location, whereas EF and ES have similar effects onthe broadening width of the PL spectra.

Based on the modeling results above, one would expect that, indegenerate p-type silicon (i.e. when EF moves into the valenceband), there is more than one single combination of {EG, EF, ES}giving a good fit with the measured spectra. Indeed, Fig. 5 com-pares the HE spectra to the modeled PL spectra with variouscombinations of {EG, EF, ES}. The fitted spectra, excluding thebroadening parameter ES, are also included for comparisons. Theresults from Fig. 5a and b clearly show that the choice of {EG, EF, ES}is arbitrary due to the complementary effects of these parameterstogether. These results are consistent with the results reported byDaub andWürfel [5]. By comparing the absorption curves betweenheavily-doped and lightly-doped silicon wafers, these authorsfound various amounts of apparent band-gap narrowing in theheavily-doped silicon wafers, depending on which energy rangethey chose to compare. Note that, the excitation level has littleimpact on the band-to-band spectral shape in degenerate silicon,as demonstrated in Section 5.

However, although determining the exact values of EG and EF indegenerate silicon using Eq. (3) and (6) has a large uncertainty, themodeling is still useful to explain the properties of the PL spectraat high doping densities. Combining the effects of EG and EF, onewould expect that the shifting of the spectrum peak location issmaller than the amount of band-gap narrowing in heavily-dopedsilicon. In addition, the spectral width should be broadened morequickly when the doping level is above the Mott transition thanbelow the Mott transition, since both EF and the band tails con-tribute to the broadening in the former case, whereas only theband tails contribute to the broadening in the latter case. In orderto fortify these predictions, we plot the HE spectra with increasingdoping densities at 79 K in Fig. 6. When the doping densityincreases from 1.4�1019 cm�3 to 1.1�1020 cm�3, the spectrumpeak energy is reduced only about 10 meV, whereas the amount ofband-gap narrowing was reported to be between 40 and 60 meV

Fig. 6. Evolution of measured PL spectra with doping density, under HE level at 79 K.

H.T. Nguyen, D. Macdonald / Journal of Luminescence 181 (2017) 223–229 227

by different authors [44–46]. In addition, the full-width at half-maximum (FWHM) of the spectra increases 24 meV when thedoping density increases from 1.4�1019 cm�3 (FWHM¼42 meV)to 1.1�1020 cm�3 (FWHM¼66 meV), but increases only 12 meVfrom 5.7�1016 cm�3 (FWHM¼27 meV) to 1.2�1018 cm�3

(FWHM¼39 meV).In fact, the much smaller shifting of the peak energy (compared

to the amount of band-gap narrowing), and the rapid increment ofthe FWHM of the PL spectra above the Mott transition can also beobserved in the experimental results reported by Wagner (see, forexample, Figs. 3 and 4 in Ref. [2]). In our work, by modeling theseparate impacts of individual parameters on the PL spectra, wecan show that this modest peak energy shift is due to the opposingimpacts of the band gap and the Fermi level rather than a singlequantity of band-gap narrowing itself, whereas the rapidincreasing FWHM is due to the combined effects of both the Fermilevel and the band tails.

Fig. 7. Comparison of normalized measured PL spectra between LE and HE mea-surements with different doping densities at 79 K.

5. Evolution of PL spectra with doping densities under low andhigh excitations

In this section, we examine the evolution of the PL spectra withincreasing doping densities, and elucidate the difference in thespectra between the LE and HE measurements. Fig. 7 shows thenormalized PL spectra, under LE and HE levels at 79 K, at differentdoping densities. At LE level, in Fig. 7a we can observe unam-biguously four peaks. Respectively, the three peaks located at 1.14,1.1, and 1.04 eV are the band-to-band luminescence assisted by theemissions of Transverse-Acoustic (TA) phonons, Transverse-Optical (TO) phonons, and both TO and zone-center optical (OΓ)phonons [2,43]. The peak located at �1.07 eV is attributed to thefree carriers recombining through neutral shallow dopant atoms[4,43,47]. When the dopant density increases, both the shallowdopant (1.07 eV) and main TO (1.1 eV) peaks broaden due to thebroadening of the shallow dopant band and the extension of theband tails, and the shallow dopant peak also becomes more andmore pronounced (Fig. 7b-d). Above the Mott transition (Fig. 7eand f), the shallow dopant and original TO peaks merge togetherand form a new TO peak due to the merging of the shallow dopantand valence bands. Nevertheless, the new main peak still con-tinues broadening and moves towards lower energies withincreasing doping densities. Note that, in Fig. 7b, there is anothersmall shoulder marked by a broken arrow at �1.09 eV. Thisshoulder was reported and denoted as BTO by Dean et al. [43] at

lower temperatures, and was attributed to the recombination ofexcitons bound to the neutral shallow dopant atoms.

Below the Mott transition (Fig. 7a–d), the spectra capturedunder the HE level are significantly different from those capturedunder the LE level. Compared to the LE spectra, the TO componentof the HE spectra is broader, and their shallow dopant peak is lesspronounced. The broader TO peak of the HE spectra is due to themuch higher excess carrier density in the band edges, wideningthe energy distribution of the free carriers [28]. Meanwhile, thecompression of the shallow dopant component in the HE spectra,compared to the TO component, can be explained by the weakerdependence on the excitation intensity of the shallow dopantpeak. Since the shallow dopant band is located inside the for-bidden gap, it can be considered as a defect band. Therefore, this

Fig. 8. Normalized PL spectra, measured with the HE system at 79 K, at differentexcitation powers.

Fig. 9. Comparison of normalized PL spectra between LE and HE measurements atdifferent temperatures. NA¼1.2�1018 cm�3.

Fig. 10. Temperature dependence of PL spectra, measured with both LE (a and b)and HE (c) systems. The two arrows in Figure 10c show the shifting of the peaklocation.

H.T. Nguyen, D. Macdonald / Journal of Luminescence 181 (2017) 223–229228

shallow dopant peak does not increase with the excitation level asquickly as the TO peak [19]. However, when the valence andshallow dopant bands merge together, the main TO peaks of thespectra between the LE and HE measurements are similar (Fig. 7eand f). Here, we did not try to model the PL spectra because, nearthe Mott transition, the band-to-band spectrum is significantlyaffected by the shallow dopant peak (Fig. 7b–d), and as such theband-to-band spectral shape cannot be reproduced well usingEq. (3). When silicon becomes degenerate (Fig. 7e and f), as

discussed in Section 4, there is no unique solution of {EG, EF, ES} todescribe the band-to-band spectral shape.

Surprisingly, there is another very broad peak located at �1 eVon the LE spectra in Fig. 7c–f. This peak is not present in Fig. 7b(boron concentration NA ¼ 3.4�1017 cm�3), but then appears inFig. 7c (NA¼6�1017 cm�3) even though the doping densityincreases only slightly. Therefore, this broad peak is unlikely to berelated to the boron dopants themselves. In addition, since theshape and intensity of this peak are consistent among differentlocations within the same wafer, it cannot be due to extendeddefects such as dislocations or oxygen/metal precipitates. There-fore, it is likely to be related to deep-level impurities introducedunintentionally but homogeneously in the wafers. Therefore, wedenoted it as “deep-level” peak in Fig. 7c-f. However, this “deep-level” peak completely disappears in all HE spectra. In order toverify that this “deep-level” peak is not an artifact from the LEmeasurements, we performed the HE measurements on the c-Siwafer having NA¼1.2�1018 cm�3 with different excitation inten-sities. When the excitation intensity is reduced more than oneorder of magnitude, we start observing the “deep-level” peak onthe normalized spectra (Fig. 8). The results demonstrate that the“deep-level” peak is, in fact, still present on the HE spectra, but ismasked by the strong luminescence signals from both the shallowdopant band and the two band edges. Furthermore, Fig. 9 con-tinues by showing the evolution of PL spectra of this silicon wafer(NA¼1.2�1018 cm�3) when the temperature increases. The“deep-level” peak is completely suppressed at 150 K whereas theshallow dopant peak is still present, although the intensity of theformer is stronger than the latter at 79 K.

In fact, the properties of this “deep-level” peak are similar tothe findings reported by Parsons [31] and Schmid et al. [32]. Theseauthors found a deep-level luminescence peak which was presentin their lightly-excited heavily-doped silicon wafers at low tem-peratures, but disappeared at either higher temperatures or highexcitation levels. They attributed the observed deep-level peak tothe recombination of the majority carriers in the shallow dopantband with the minority carriers, trapped by the compensatingimpurities introduced unintentionally into the wafers during theingot growth. Employing the HE system, we can avoid the influ-ence of this unexpected peak on the luminescence spectra, whichotherwise greatly affects our modeling and interpretation of the PLspectra from heavily-doped c-Si.

H.T. Nguyen, D. Macdonald / Journal of Luminescence 181 (2017) 223–229 229

Next, we examine the impacts of temperatures on the PLspectra of the heavily-doped silicon wafers. The LE (Fig. 10a and b)and HE (Fig. 10c) spectra show a remarkably different trend fromeach other. In Fig. 10a, the band-to-band PL intensity increaseswith temperatures, contradicting the thermal quenching propertyof the luminescence from c-Si [6]. At low temperatures and lowexcitation levels, excess carriers are trapped at the “deep-level”centers, and thus the band-to-band luminescence is suppressed.However, when the temperature increases, the “deep-level”luminescence is quenched as the trapped carriers are thermallyexcited back to their corresponding band edges. Therefore, theexcess carriers in the band edges effectively increase, leading tothe increment of the band-to-band PL intensity. This increment ismore than the expected thermal quenching rate of the band-to-band luminescence up to a certain temperature. However, whenthe temperature is high enough (400 K in this case), the thermalquenching becomes more dominant again, causing a reduction inthe PL intensity as depicted in Fig. 10b.

In the HE measurements (Fig. 10c), since the “deep-level”luminescence has little impact on the total spectra, the PL signaldisplays the expected thermal quenching property due to theknown temperature dependence of the radiative recombinationcoefficient [6,10]. However, one can observe two distinct trends inthe peak location of the spectra. The peak energy increases whenthe temperature increases from 79 to 120 K, contradicting theexpected temperature-induced band-gap narrowing in c-Si [1].Nevertheless, with further increasing temperatures, the peakenergy displays the expected reduction due to the band-gap nar-rowing effects. This property is observed in all heavily-dopedwafers investigated in this study. One possible explanation of thisbehavior is that, the excess carriers in the band tails are thermallyexcited to higher energy levels, and thus the luminescence peak isfirst shifted to higher energies with increasing temperatures.Another reason could be due to the thermal broadening of thespectra, which may effectively shift the spectral peak position intoslightly higher energies in a similar manner to Fig. 4c. However,the HE spectra from slightly-doped silicon (not shown here) showa consistent peak shift towards low energies with increasingtemperatures, thus suggest that the latter reason is unlikely to bethe case. Up to a certain temperature, the amount of band-gapnarrowing due to the rising temperature dominates the spectraagain, and thus the PL peak shifts back to lower energies.

6. Conclusion

We have investigated the effects of doping on the photo-luminescence spectra from boron-doped crystalline silicon wafers.Utilizing a low excitation level, we can avoid the overlapping ofthe dopant and band-to-band luminescence components. Utilizinga high excitation level from the micro-photoluminescence spec-troscopy system, we can suppress the influence of the unexpectedimpurities on the spectra. Therefore, we can perform a systematicstudy on the effects of different phenomena on the luminescencespectra. We have also explained the difference between the twocommon approaches in studying the luminescence spectra,including the line shape analysis and generalized Planck's law.

Acknowledgment

This work has been supported by the Australian Research Council(ARC) and the Australian Renewable Energy Agency (ARENA) through

research grant RND009. The Australian National Fabrication Facility isacknowledged for providing access to some of the facilities used inthis work. The authors are in debt to Prof. H. Tan for providing accessto the spectroscopic equipment, and Dr. S. Mokkapati for assistingwith some of the experimental setups.

References

[1] W. Bludau, A. Onton, W. Heinke, J. Appl. Phys. 5 (1974) 1846.[2] J. Wagner, Phys. Rev. B 29 (1984) 2002.[3] J. Wagner, Phys. Rev. B 32 (1985) 1323.[4] E. Daub, P. Würfel, Phys. Rev. Lett. 74 (1995) 1020.[5] E. Daub, P. Würfel, J. Appl. Phys. 80 (1996) 5325.[6] T. Trupke, M.A. Green, P. Würfel, P.P. Altermatt, A. Wang, J. Zhao, R. Corkish,

J. Appl. Phys. 94 (2003) 4930.[7] H.T. Nguyen, F.E. Rougieux, B. Mitchell, D. Macdonald, J. Appl. Phys. 115 (2014)

043710-1.[8] M. Tajima, Appl. Phys. Lett. 32 (1978) 719.[9] P.P. Altermatt, F. Geelhaar, T. Trupke, X. Dai, A. Neisser, E. Daub, Appl. Phys.

Lett. 88 (2006) 261901-1.[10] H.T. Nguyen, S.C. Baker-Finch, D. Macdonald, Appl. Phys. Lett. 104 (2014)

112105-1.[11] M. Tajima, Y. Iwata, F. Okayama, H. Toyota, H. Onodera, T. Sekiguchi, J. Appl.

Phys. 111 (2012) 113523-1.[12] M. Tajima, IEEE J. Photovoltatics 4 (2014) 1452.[13] P. Gundel, M.C. Schubert, W. Kwapil, J. Schön, M. Reiche, H. Savin, M. Yli-Koski,

J.A. Sans, G. Martinez-Criado, W. Seifert, W. Warta, E.R. Weber, Physica StatusSolidi RRL 3 (2009) 230.

[14] P. Gundel, M.C. Schubert, W. Warta, Physica Status Solidi A 207 (2010) 436.[15] H.T. Nguyen, F.E. Rougieux, F. Wang, H. Tan, D. Macdonald, IEEE J. Photovoltaics

5 (2015) 799.[16] R. Woehl, P. Gundel, J. Krause, K. Rühle, F.D. Heinz, M. Rauer, C. Schmiga,

M.C. Schubert, W. Warta, D. Biro, IEEE Trans. Elec. Devices 58 (2011) 441.[17] P. Gundel, D. Suwito, U. Jäger, F.D. Heinz, W. Warta, M.C. Schubert, IEEE Trans.

Elec. Devices 58 (2011) 2874.[18] A. Roigé, J. Alvarez, J.-P. Kleider, I. Martin, R. Alcubilla, L.F. Vega, IEEE J. Pho-

tovoltaics 5 (2015) 545.[19] H.T. Nguyen, Y. Han, M. Ernst, A. Fell, E. Franklin, D. Macdonald, Appl. Phys.

Lett. 107 (2015) 022101-1.[20] H.T. Nguyen, D. Yan, F. Wang, P. Zheng, Y. Han, D. Macdonald, Physica Status

Solidi RRL 9 (2015) 230.[21] J.C. Inkson, J. Phys. C: Solid State Phys. 9 (1976) 1177.[22] G.D. Mahan, J. Appl. Phys. 51 (1980) 2634.[23] K.-F. Berggren, B.E. Sernelius, Phys. Rev. B 24 (1981) 1971.[24] M. Eswaran, B. Bergersen, J.A. Rostworowski, R.R. Parsons, Solid State Com-

mun. 20 (1976) 811.[25] R.R. Parsons, Can. J. Phys. 56 (1978) 814.[26] J.R. Lowney, J. Appl. Phys. 59 (1986) 2048.[27] P.V. Mieghem, Rev. Mod. Phys. 64 (1992) 755.[28] P.P. Altermatt, A. Schenk, G. Heiser, J. Appl. Phys. 100 (2006) 113714-1.[29] K. Morigaki, F. Yonezawa, Suppl. Prog. Theor. Phys. 57 (1975) 146.[30] R.E. Halliwell, R.R. Parsons, Solid State Commun. 13 (1973) 1245.[31] R.R. Parsons, Solid State Commun. 29 (1979) 763.[32] P.E. Schmid, M.L.W. Thewalt, W.P. Dumke, Solid State Communications, 38,

(1981) 1091.[33] W.P. Dumke, Appl. Phys. Lett. 42 (1983) 196.[34] J. Wagner, J.A. del Alamo, J. Appl. Phys. 63 (1988) 425.[35] P. Würfel, J. Phys. C: Solid State Phys. 15 (1982) 3967.[36] P. Würfel, S. Finkbeiner, E. Daub, Appl. Phys. A 60 (1995) 67.[37] T. Trupke, E. Daub, P. Würfel, Sol. Energy Mater. Sol. Cells 53 (1998) 103.[38] T. Trupke, J. Appl. Phys. 100 (2006) 063531-1.[39] M.A. Green, Appl. Phys. Lett. vol. 99 (2011) 131112-1.[40] C. Schinke, D. Hinken, J. Schmidt, K. Bothe, R. Brendel, IEEE J. Photovoltatics

3 (2013) 1038.[41] W. Liang, K.J. Weber, D. Suh, S.P. Phang, J. Yu, A.K. McAuley, B.R. Legg, IEEE

J. Photovoltaics 3 (2013) 678.[42] P. Würfel, Physics of Solar Cells: From Basic Principles to Advanced Concepts,

Wiley-VCH (2009), p. 14.[43] P.J. Dean, J.R. Haynes, W.F. Flood, Phys. Rev. 161 (1967) 711.[44] W.P. Dumke, J. Appl. Phys. 54 (1983) 3200.[45] J. Wagner, J.A. del Alamo, J. Appl. Phys. 63 (1988) 425.[46] D. Yan, A. Cuevas, J. Appl. Phys. 116 (2014) 194505-1.[47] B. Bergersen, J.A. Rostworowski, M. Eswaran, R.R. Parsons, Phys. Rev. B 14

(1976) 1633.