Interstitial oxygen imaging from thermal donor growth—A fastphotoluminescence based method

T. Niewelt a,n, S. Lim b, J. Holtkamp a, J. Schon̈ a, W. Warta a, D. Macdonald b, M.C. Schubert a

a Fraunhofer Institut für Solare Energiesysteme, Heidenhofstr. 2, 79110 Freiburg, Germanyb Research School of Engineering, College of Engineering and Computer Science, The Australian National University, Canberra ACT 0200, Australia

a r t i c l e i n f o

Article history:Received 21 March 2014Received in revised form30 April 2014Accepted 5 May 2014Available online 27 May 2014

Keywords:Interstitial oxygenThermal donorsMobility correctionPhotoluminescence imaging

a b s t r a c t

We present a fast method to create interstitial oxygen concentration maps from resistivity calibratedphotoluminescence images prior to and after a heat treatment at 450 1C. The method utilizes theinfluence of thermal donors on the effective doping concentration of a sample. Although thedetermination of thermal donor concentrations from conductivity measurements is customary inliterature, we found that implementation of a mobility model is necessary to determine accurateconcentrations of thermal donors. Therefore an iterative correction algorithm is presented, which allowsprecise determination of thermal donor concentrations from resistivity measurements. The determina-tion of interstitial oxygen concentrations from thermal donor concentrations is based on an updatedparameterization based on a model of Wada et al. (Phys. Rev. B: Condens. Matter 30 (1984) 5884–5895)that is also presented in this paper. The method is demonstrated on a 1.3 Ω cm p-type Czochralski grownsilicon sample with an interstitial oxygen concentration in the range of 7.5�1017 cm�3 and yields goodagreement with FTIR measurements.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Oxygen is usually introduced into the silicon crystal duringcrystal growth and can be present in concentrations up to therange of 1018 cm�3 in silicon grown with the Czochralski method.High interstitial oxygen concentrations ([Oi]) can give rise to thegrowth of oxygen complexes called thermal donors (TD) [1] ornew donors [2,3] and recombination active oxide precipitates [4]during high temperature treatments. In the presence of boron, e.g.in standard p-type silicon, interstitial oxygen forms complexesthat are responsible for light induced degradation [5,6]. Thus, thedetermination of the oxygen content of silicon wafers is crucial forquality control and process design in photovoltaic production aswell as for many investigations on crystal defects.

The most widespread and well established way to determine[Oi] is to evaluate characteristic infrared absorption measured withFourier transform infrared spectroscopy (FTIR). Veirman et al. [7]have presented an alternative measurement technique that isbased on monitoring the change of the conductivity of wafersdue to TD growth after a 450 1C tempering step. This method isalso capable of performing lateral scans of [Oi] with scanning

4-point-probe measurements. Both methods are limited in resolu-tion and are time consuming on relevant sample sizes.

In this paper, we utilize resistivity calibrated photolumines-cence (PL) images [8] to perform high resolution [Oi] images in astrongly reduced time. Also, a necessary correction for the influ-ence of TDs on carrier mobilities in silicon is introduced utilizing arecent model by Schindler et al. [9].

2. Method

2.1. Working principle

The method is applied to as-cut wafers after a temperaturestep at or above 850 1C to dissolve all TDs already present inthe material from crystal growth. In this temperature range, theformation of new donors is not expected [3] and thereforethe electrical properties of the wafer should be determined bythe sample doping. Afterwards, the sample undergoes hot DIwater etching to achieve a high surface recombination velocity[10]. For very high surface recombination velocities, the excesscarrier density Δn is determined by the time necessary to reachthe surface (transit time) instead of bulk charge carrier lifetime. Inthis case (surface limitation of Δn), PL intensity is proportional tothe effective doping concentration [8]. Without compensation

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Solar Energy Materials & Solar Cells

http://dx.doi.org/10.1016/j.solmat.2014.05.0110927-0248/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author. Tel.: þ49 761 4588 5461.E-mail address: tim.niewelt@ise.fraunhofer.de (T. Niewelt).

Solar Energy Materials & Solar Cells 131 (2014) 117–123

effects, e.g. from TDs in p-type silicon, this corresponds to thedopant concentration and the PL image can be calibrated withlocal conductivity data from e.g. four-point-probe measurementsto a doping image [8]. In order to create TDs, the sample issubjected to an annealing step at 450 1C for several hours, whichgives rise to TD formation [1].

After the annealing step the aforementioned surface treatmentis repeated and a second PL image is taken. This image andresistivity measurement to calibrate it will be influenced by thecreated TDs due to their electronic structure. A detailed insightinto these influences and an algorithm to account for them will begiven in Section 2.2. Taking these influences into account, thesecond PL image can be calibrated to an effective doping image. Asthe difference between the doping image (before annealing) andthe effective doping image (after annealing) results solely from thepresence of TDs, an image of their concentration NTD can becalculated by considering their charge state, which can be assessedwith the algorithm as well.

The formation kinetics of TDs is highly dependent on the initial[Oi]. We have combined features of parameterizations by Wadaet al. [11] and Wijaranakula [12] into a new model that ispresented in Section 2.3. Utilizing this new parameterization, wecalculate high resolution [Oi] images for a given annealing treat-ment defined by temperature T and duration t from the previouslycalculated NTD images. Fig. 1 briefly illustrates the process steps ofthe presented method.

2.2. Precise determination of thermal donor concentration

As the method is based on the evolution of TD concentration,its precise determination is crucial. TDs act as donors and thus itappears convenient to determine NTD from conductivity measuredin a TD-free state (i.e. after a high temperature step) of the sample,swithoutTD, and after intentional formation, smeas. Because theelectronic properties of TDs differ from common dopants, suchas boron or phosphorus, special care has to be taken, in order todetermine their actual concentration.

TDs introduce two energy states in the bandgap of silicon closeto the conduction band [13]. The exact position of these states isdetermined by the number of oxygen atoms included in the TD,but the most common sizes of TDs create levels in a narrow energyrange [14]. Therefore their charge state (TDcharge) is dependent onthe position of the Fermi energy EF following Fermi–Dirac-Statis-tics. In p-type silicon TDs will always act as double donors andthus compensate the sample doping. In n-type samples, the chargestate of TDs will depend on the position of EF relative to the energystates of TDs and therefore on the doping concentration (Ndop) andalso on NTD. Furthermore, multiply charged defects and donorcompensation have a strong impact on charge carrier mobilities ofminority and majority charge carriers mmin and mmaj. As Schindleret al. [9] pointed out, the influence of compensation effects canreduce the mobilities by up to 50% compared to widely usedmodels. To account for these influences, we have developed analgorithm, that utilizes Klaassen’s model for charge carrier mobi-lities [15,16] with additions for compensation effects by Schindler[9] and an iterative method to determine NTD and TDcharge.

The necessary input parameters for the algorithm are the actualdoping concentration Ndop (NA in p-type, ND in n-type) and themeasured conductivity smeas of the sample including TDs. In thecase of compensated silicon, both dopant concentrations have tobe known. The first step is to determine an apparent dopingconcentration Ndop

n from smeas by neglecting the additional influencesof TDs on carrier mobilities, similar to a common resistivity-to-dopingcalibration. The difference between Ndop and Ndop

n divided by twoserves as a first estimate of NTD and as starting value for theiterative algorithm. It should be mentioned that most research onTD evolution in the past neglected the difference between thisestimate and the actual NTD.

The algorithm calculates charge carrier mobilities mmin,i andmmaj,i from NTD,i and TDchargei according to Schindler’s model. Thenit determines the charge carrier concentrations p0,i and n0,i, toreproduce smeas. The carrier concentrations lead to NTD,iþ1 andTDchargeiþ1 using common charge carrier statistics. Fig. 2 shows aschematic illustration of the computational steps. We found insimulations that few iterations of this process lead to precise

Fig. 1. Schematic illustration of the measurement and evaluation.

Fig. 2. Schematic illustration of the mobility correction tool. Starting from conductivity measurements before and after annealing (swithoutTD and smeas) a set of parameters iscalculated for an iterative algorithm resulting in the true TD concentration and their charge state.

T. Niewelt et al. / Solar Energy Materials & Solar Cells 131 (2014) 117–123118

values for the actual NTD even if strong compensational effects inp-type or recharging of TDs occur.

2.3. Parameterization of thermal donor growth

The method presented by Veirman et al. [7] utilizes a para-meterization by Wijaranakula [12] to determine [Oi] from the NTD

calculated from resistivity measurements. While this parameter-ization works well with the weakly doped n-type material used byVeirman, we encountered serious deviations when applying it tothe NTD data of p-type material we had calculated with thealgorithm presented in Section 2.2. Although these deviationswere reduced after correcting the NTD data analysed by Wijaranakulawith our algorithm and refitting Wijaranakula’s equation to thecorrected data, there was a systematic error with increasingannealing time. We associate this error to an influence of theelectron concentration during the annealing process. As TDsintroduce additional electrons into the crystal, their equilibriumconcentration and thus also their formation kinetics depends onthe doping concentration of the sample. This influence wasneglected in Wijaranakula’s parameterization and is not discussedin the parameterization on TD growth kinetics by Voronkov et al.[17], which to our knowledge is most up to date. Therefore wechose to use the model of Wada et al. [11], which includes thisinfluence based on theoretical considerations. As Wijaranakulapointed out, this model does not account for the capture ofinterstitial oxygen atoms in complexes during annealing at ele-vated temperatures and is therefore not capable of describing thedecrease in NTD after prolonged annealing found in variousexperiments, i.e. [18,19]. We modified the model suggested byWada and added a time dependent term for the remainingavailable interstitial oxygen concentration. This parameterizationwas realized by a simple fit of a convenient function to [Oi](t) data forannealing temperature of 450 1C presented by McQuaid et al. [19].Furthermore, we included the influences of the TDs charge and bandgap narrowing into the Wada model. With these changes, wedetermined the fit parameters a and b by Wada utilizing NTD datafor annealing at 450 1C presented by Kamiura et al. [18]. It should bementioned that we corrected this data with our algorithm presentedabove and that the parameterization was done for tanneal o200 h forsimplicity reasons. The new parameterization including the fitparameters for the oxygen loss is given in Table 1. It should benoted, that the model byWada does not account for the influences ofcrystal defects like silicon interstitials or vacancies on the formationkinetics of TDs that were found by various authors, e.g. [20,21].Therefore, extreme concentration levels or strong lateral concentra-tion variations of these defects are not covered by the presentedparameterization.

3. Setup and samples

In the used PL imaging setup a 790 nm fibre coupled laserdiode is used to illuminate the samples. We utilize a beam shapingoptic to provide a good homogeneity of illumination intensityacross the sample. The imaging system consists of a cooled silicon

CCD-camera and a stack of optical filters to suppress the detectionof reflected laser light. The setup is capable of providing imageswith resolutions down to 25 mm.

To develop the presented method, we investigated Czochralskigrown boron doped silicon wafers of representative resistivitiesand oxygen concentrations typical for PV application. We foundthat the surface preparation of the samples is crucial, as it has tofeature sufficiently high surface recombination velocities to effi-ciently limit the excess charge carrier density. Experiments con-ducted on wafers after removal of the saw damage resulted inreduced image quality. Therefore, an as-cut wafer with a resistivityof �1.3 Ω cmwas processed for this paper in order to demonstratethe method. It underwent standard cleaning followed by anannealing process at 870 1C in a diffusion furnace without processgas flows. In order to allow a variation of annealing durations andto simplify sample handling, the 156�156 mm² wafer was lasercut to samples of 5�5 cm². Due to the high temperature step thesamples were free of TDs. They were measured and processedaccording to the sequence introduced in Section 2.1. The necessarycalibration of PL images to doping maps was conducted utilizingfour point probe measurements with a Napson RG100/RT3000measurement tool. The annealing was done on a hotplate fordurations ranging from 3 to 64 h. To confirm the results of thepresented method the oxygen concentration of the samples wasdetermined with FTIR measurements in a Bruker IFS-113v systemaccording to DIN 50438-1 after a KOH etch to receive a shinysurface.

4. Comparison to scanning methods

Fig. 3 presents the NTD-distributions of the samples calculatedfrom the resistivity calibrated PL images before and after theannealing. Due to the range of annealing durations from 3 to 64 hwe find a broad range of NTD in the different samples. All samplesthat underwent more than 3 h of annealing exhibit a radialstructure of grown TDs. Note that this structure was not visiblein PL images or resistivity measurements prior to annealing. Theslight variation of the determined NTD levels for samples that wereannealed for the same time indicates scattering in the PL-to-resistivity calibration due to the finite number of calibration pointsand image noise. The resulting [Oi] images of the calculations areshown in Fig. 4. While the overall level of determined [Oi] variesslightly due to the aforementioned calibration scattering, thelateral variation in the circular structure is consistent in allsamples with tanneal exceeding 3 h. Due to the increasing contrastwith annealing time the 24 and 64 h samples are capable ofdetecting a very fine structure of lateral [Oi] variation. This effect isfurther discussed in Section 5. We found optical artefacts affectingthe determined oxygen concentrations near the sample edges.These can be reduced by usage of further optical filters in the PLsystem and usage of image processing algorithms, e.g. point-spread-functions [22].

The PL based method features two significant advantages overFour-Point-Probe scans: higher resolution and short acquisitiontimes. While the resolution of Four-Point-Probe is limited to 1 mm

Table 1Modified Wada model (for T¼450 1C and tr200 h).

Wada model for NTD (t) (from [11]) NTD ðtÞ ¼ ab � Oi½ �3ðtÞ � 1

n2 � 1�exp �b� Di � Oi½ �ðtÞ � t� �� �

with the oxygen diffusion constant Di and the electron concentration during growth nOxygen concentration (empiricalmodel)

Oi½ �ðtÞ ¼ Oi½ �t ¼ 0 � 1�P1 � exp � tP2

� ��1

� �þt � P3

� �

Fit parameters P1¼0.237, P2¼1.092�106, P3¼1.186�10�8 (fit to data from [19]) a¼5.229�10�10 cm�4, b¼3.008�10�9 cm�4 (fit to datafrom [13])

T. Niewelt et al. / Solar Energy Materials & Solar Cells 131 (2014) 117–123 119

in our setup, the luminescence based thermal donor concentrationimage in Fig. 5 features a resolution of about 100 mm. Althoughhigh resolution conductivity scanning tools might be available, theresolution is limited due to drastically increasing measurementtimes. The acquisition of PL images of strongly compensated as-cutwafers in the used measurement setup takes less than 10 minindependent of the sample size, also allowing multiple samples tobe measured at once.

A comparison of a linescan along the calculated [Oi] image andan FTIR linescan along an equivalent sample is shown in Fig. 6. Wefind good qualitative and quantitative agreement for measure-ments more than 5 mm from the sample edges, where the result isinfluenced by an optical artefact. Although the radial [Oi] varia-tions observed in the image are too small to be detected with FTIRand vanish also in the image linescan, the prominent dip at around

32 mm distance from the edge is clearly detected in both methods.The absolute level of [Oi] determined with the PL based methodscattered between the samples between 5 and 15% below thevalue determined from FTIR measurements on the same samples.This can be accounted to the small set of data included in theparameterization presented in Section 2.3 so far. Considering thatwe did not include any of our measurements in the parameteriza-tion, the deviation of less than 10% is excellent. The decreasedlateral contrast compared to the FTIR results was found to besystematical across the samples. It might originate from opticalblurring and could then be reduced with appropriate imageprocessing.

5. Sensitivity study

The lateral [Oi] inhomogeneities of the wafer in Fig. 4 are onlyobserved in samples with annealing times greater than 3 h. Thesensitivity to detect lateral contrasts is increased with prolongedannealing duration due to the TD formation kinetics. As themethod is based on the measurement of changes in conductivitydue to the dopant behaviour of TDs, the sensitivity of the methodalso depends on the total oxygen content and the base dopingconcentration NA in p-type or ND in n-type silicon, respectively. Toillustrate these dependencies and give an impression of therequired annealing time for a given material we have conducteda numerical study of the minimal detectable lateral concentrationcontrast in dependence of the annealing duration tanneal, theoxygen content [Oi], the base doping and the signal-to-noise-ratio (SNR) of the used imaging system.

5.1. Simulation method

We have performed simulations of the expected remainingfraction of PL intensity fPL after annealing relative to the intensitybefore assuming comparable surface properties. fPL is calculatedbased on the considerations in [8] taking minority carrier mobilitychange due to TD formation Δm into account as follows:

For p� type silicon : f PL;p�type ¼IPL;annealedIPL;start

¼ 1�2 NTD

NA

� �1

1þΔμð1aÞ

For n� type silicon : f PL;n�type ¼ 1þTDcharge NTD

ND

� �1

1þΔμð1bÞ

As the criterion for a determinable intensity contrast betweentwo regions of interest (ROI) of an image, we chose a contrast-to-noise-ratio (CNR) exceeding unity. Thus, the difference in PLintensity ΔS between two ROIs must exceed the noise level N ofthe considered image fraction: ΔS/NZ1. For simplicity reasons, wehave chosen a fixed SNR of 100 for the simulations of the influenceof annealing time, oxygen content and doping concentration. Thislevel of SNR should be achievable on most imaging setups bychoosing appropriate exposure times and image resolutions. Thesimulation first calculates the expected resulting PL intensityfraction IPL,A as a function of annealing time for a given set ofoxygen concentration [Oi]A and doping concentration Ndop,A in ROIA and then calculates the intensity in ROI B, IPL,B, that could bedistinguished from it with an image processing algorithm. Then aniterative algorithm calculates the respective TD concentration NTD,

B, from which it is possible to calculate [Oi]B for a given time tutilizing a parameterization as presented in Section 2.3. Theprocess scheme is given in Fig. 7. All simulations were done for[Oi]B4[Oi]A and therefore IPL,Bo IPL,A for p-type and IPL,B4 IPL,A forn-type.

Fig. 3. Thermal donor concentrations in the wafer calculated from resistivitycalibrated photoluminescence images. The eight samples were annealed at 450 1Cfor four different durations, as indicated in the picture. A magnification of the lowerleft sample is shown in Fig. 5.

Fig. 4. Interstitial oxygen concentrations in the wafer calculated from resistivitycalibrated photoluminescence images of eight samples. The apparent variation of[Oi] towards the sample edges results from optical artefacts. The medians of thedetermined [Oi] of all samples are in the range of 770.5�1017 cm�3. Note that theapparent variation of [Oi] towards the sample edges results from optical artefactsand the apparent decrease in some of the former wafer edges can be attributed toan uncorrected thickness variation.

T. Niewelt et al. / Solar Energy Materials & Solar Cells 131 (2014) 117–123120

5.2. Simulation results

In order to demonstrate the influence of the sample dopingon the methods ability to detect a given contrast, we varied dop-ing concentration and type for a given [Oi] of 7�1017 cm�3

resembling a common concentration in industrial Czochralskigrown silicon. We chose doping concentrations resembling 1 and

10 Ω cm resistivity to cover common doping levels. The results arepresented in Fig. 8 and illustrate the increasing sensitivity with theannealing time tanneal. As the method is based on detectingchanges in PL intensity, the concentration of thermal donors hasto reach the range of two orders of magnitude below the sampledoping to achieve significant signals. In order to detect concentra-tion variations, even the difference between two ROI has to reachthis extent. This corresponds well with the observed effect inSection 4 that short annealing times can reveal the overall [Oi]level but lateral contrast is increased with prolonged annealing:The most prominent circular variation in the wafer of about 6%could not be detected after 3 h of annealing while dependant onimage scaling it is clearly visible after 12 h. The improved sensi-tivity for short annealing times on n-type material originates fromthe fact, that TDs increase the net doping and therefore PLintensity in n-type, while the occurring compensation effects inp-type decrease it. The enhanced formation of TD in p-typematerial can compensate this effect, but the increased precisioncompared to n-type in Fig. 8 is likely to vanish for non-fixed SNR.

As the extent of TD formation is closely related to the oxygenconcentration it is trivial that their effect on resistivity for a givenNdop and tanneal depends on the oxygen concentration level. Toillustrate this dependency we simulated the expected sensitivityfor a 1 Ω cm p-type wafer with [Oi] of 10�1017, 7�1017 and4�1017 cm�3, respectively (see Fig. 9). This resembles the typicalrange of oxygen incorporation in Czochralski grown silicon today.

Fig. 5. Comparison of the determined thermal donor distributions on a sample after 64 h of annealing. Left: from resistivity calibrated PL images, right: from scanning Four-Point-Probe measurements with 1 mm resolution. The superior resolution of PL images (here: �100 mm) reveals the circular structure in more detail.

Fig. 6. Comparison of a FTIR linescan along the sample after 3 h of annealing withthe result of the PL based method after 24 h of annealing. The FTIR measurementwas not conducted on the same sample due to the oxygen loss related to theannealing. For tanneal¼3 h this loss is below detection precision of the FTIRmeasurement. The deviation between both measurements is below 10% and thequalitative agreement due to radial symmetry of the wafer is sufficient to comparethe results.

Fig. 7. Process scheme of the simulation used to estimate the sensitivity of themethod.

Fig. 8. Simulation of the detectable lateral variation in oxygen concentration from7�1017 cm�3 on wafers with different doping type and level in dependence ofannealing time.

T. Niewelt et al. / Solar Energy Materials & Solar Cells 131 (2014) 117–123 121

For the simulations presented above, the SNR was kept fixed to100. While this boundary condition is well satisfied or exceeded withour imaging setup for measurements on unpassivated wafers withnormal doping concentrations, we have encountered SNR of below 70for strongly TD-compensated p-type samples and for short exposuretimes. To assess the impact of this decreased ratio we have simulatedthe case of measuring a 1Ω cm p-type wafer with fixed absolute noiselevel. This resembles measurements that are dominated by amplitudeindependent noise phenomena e.g. for short exposure time on acamera with a high read-out-noise level. The result of this variation isshown in Fig. 10. Due to the decreasing PL signal intensity of p-typematerial with increasing TD concentration the detection probability fora given concentration contrast is decreased. N-type samples areunaffected by this effect as their SNR would even increase overannealing time due to the increasing PL signal. As the differencebetween fixed noise level and fixed SNR is negligible in the simula-tions, Fig. 10 also indicates the impact of increased or decreased SNRon detection limits for concentration contrasts.

6. Conclusion

We have presented a new method to determine the spatialdistribution of the interstitial oxygen concentration [Oi] in siliconwafers. The [Oi] measured with this method are in good agreementwith FTIR measurements. After sufficiently long annealing at450 1C a fine ring structure with high TD concentrations was

detected which we attribute to variations of [Oi]. It was shown,that the sensitivity of the method to lateral contrasts stronglydepends on the annealing time tanneal and is also affected by theoxygen concentration level and sample doping type andconcentration.

The method provides significantly higher lateral resolution andreduced measurement time compared to scanning methods todetermine [Oi].

Due to the optical excitation and image detection, the methodis subject to optical artefacts as for example optical blurring at thesample’s edges. These effects could be minimized with furthereffort in images processing, which should allow detection oflateral [Oi] inhomogeneities on the sub mm scale.

As the presented method, in contrast to FTIR measurements,does not suffer from inherent limitations concerning samplethickness, it might be an option to determine [Oi] in very thinsilicon wafers. Further work on that issue appears sensible.

Acknowledgements

This work was supported by the German Federal Ministry forthe Environment, Nature Conservation and Nuclear Safety withinBORNEO project (Grant no. 0325450B).

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