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Diffusion lengths of silicon solar cells from luminescence images

Diffusion lengths of silicon solar cells from luminescence images
Diffusion lengths of silicon solar cells from luminescence images

Diffusion lengths of silicon solar cells from luminescence images P.Würfel,a?T.Trupke,b?and T.Puzzer

Centre of Excellence for Advanced Silicon Photovoltaics and Photonics,University of New South Wales,

Sydney,NSW2052,Australia

E.Sch?ffer,W.Warta,and S.W.Glunz

Fraunhofer Institut für Solare Energiesysteme,Heidenhofstrasse2,Freiburg79110,Germany

?Received2May2007;accepted8May2007;published online27June2007?

A method for spatially resolved measurement of the minority carrier diffusion length in silicon

wafers and in silicon solar cells is introduced.The method,which is based on measuring the ratio of two luminescence images taken with two different spectral?lters,is applicable,in principle,to both photoluminescence and electroluminescence measurements and is demonstrated experimentally by electroluminescence measurements on a multicrystalline silicon solar cell.Good agreement is observed with the diffusion length distribution obtained from a spectrally resolved light beam induced current map.In contrast to the determination of diffusion lengths from one single luminescence image,the method proposed here gives absolute values of the diffusion length and,in comparison,it is much less sensitive to lateral voltage variations across the cell area as caused by local variations of the series resistance.It is also shown that measuring the ratio of two luminescence images allows distinguishing shunts or surface defects from bulk defects.?2007 American Institute of Physics.?DOI:10.1063/1.2749201?

INTRODUCTION

Current methods for determining spatial variations of the

diffusion length include spectral response or spectrally re-

solved light beam induced current1?LBIC?and electrolumi-nescence imaging.2Spatially resolved spectral LBIC is a

mapping system and,while very accurate,it is relatively

slow.A scan on an industrial sized solar cell?e.g.,10?10cm2?with200?200pixels takes several hours.Elec-troluminescence imaging has been proposed by Fuyuki et al. as a much faster alternative technique.2,3Typical data acqui-sition times for electroluminescence images taken with a sili-con charge coupled device?CCD?camera with1024?1024pixels are on the order of only1s.4–6However,the approach proposed by Fuyuki et al.of using a single elec-troluminescence image as a reliable and quantitative mea-surement of the diffusion length can be highly inaccurate for various reasons that will be discussed in this paper.

The determination of the diffusion length from spectral

response or from spectrally resolved LBIC is based on the

fact that the contribution to the measured photocurrent of

electron-hole pairs generated at variable distance from the

p-n junction depends on the minority carrier diffusion length. Carriers do not effectively contribute to the photocurrent if the penetration depth of the incident photons is much larger than the diffusion length.In a different method for the deter-mination of the diffusion length to be discussed here,this situation is reversed.It measures luminescence signals and is based on the fact that photons generated inside the bulk of a solar cell at a point further away from the surface than their own penetration depth will be reabsorbed before reaching the surface and will therefore not contribute to the measured emission intensity.The rate of spontaneous emission of crys-talline silicon at room temperature and thus the emitted lu-minescence intensity is considerable in the wavelength range from850to1250nm,corresponding to photon penetration depths ranging from20?m to several centimeters,i.e.,from much smaller than the thickness of a silicon solar cell?typi-cally200–300?m?to much larger than that thickness.Re-stricting the measured luminescence signal to speci?c wave-length ranges by using suitable?lters,thus,allows information to be gained about either the total carrier density across the entire sample thickness?long wavelength lumines-cence with long penetration depth?or about the carrier den-sity near the front surface?short wavelength luminescence with short penetration depth?.The knowledge about the total carrier density and about the carrier density near the front, respectively,allows the carrier density pro?le and,thereby, the diffusion length to be determined,as will be shown theo-retically and experimentally below.

Importantly,this method can,in principle,either be ap-plied to photoluminescence?PL?imaging7measurements on silicon wafers at an early stage of solar cell fabrication or to electroluminescence?EL?measurements carried out on fully processed solar cells.It may also be applied to other materi-als suited for solar cell fabrication.

THEORY

The quantitative description of the dependence of the emission spectrum on the minority carrier diffusion length is carried out in two steps.Firstly,we describe analytically how the diffusion length affects the depth distribution of minority carriers that are injected into the base of a solar cell via an applied voltage.In a second step,we then describe how that minority carrier distribution affects the emission spectrum.

a?On leave from University of Karlsruhe.

b?Electronic mail:thorsten@trupke.de

JOURNAL OF APPLIED PHYSICS101,123110?2007?

0021-8979/2007/101?12?/123110/10/$23.00?2007American Institute of Physics

101,123110-1

The resulting relationship between the diffusion length and the emission spectrum is then used to derive a quantitative relationship between the diffusion length and the ratio of luminescence signals in two different spectral ranges.These spectral ranges are speci?ed experimentally by the transmis-sion of?lters being used for the two luminescence measure-ments.

Carrier distribution

We consider the injection of electrons from the p-n junc-tion into the p-type base of a solar cell.With an applied voltage V appl,the electron concentration n e?0?on the p side of an abrupt p-n junction that is located at x=0is given as

n e?0?=n i2

N A

exp?eV appl kT

?,?1?

where n i is the intrinsic carrier concentration and N A is the doping concentration in the base.The rear surface at x=d is characterized by a surface recombination velocity S such that the electron diffusion current at the rear j e?d?is given by

j e?d?=?D e dn e

dx

?d?=Sn e?d?,?2?

with D e the electron diffusion coef?cient.Note that j e?d?in Eq.?2?is a particle current,not an electrical current.

With these two boundary conditions,the electron distri-bution n e?x?follows from the continuity equation for elec-trons in steady state,

d2n e dx2?

n e

L e2

=0,?3?

and is

n e?x?=A exp?x L e?+B exp??x L e?,?4?with

A=n e?0?

1?r

1?r+?1+r?exp?2d/L e?

?5?

and

B=n e?0?

1+r

1+r+?1?r?exp??2d/L e?

,

where L e=?D e?e is the diffusion length and r=SL e/D e.

Equations?1?–?5?allow the calculation of the minority carrier density pro?le as a function of the applied voltage,of the diffusion length,and of the rear surface recombination velocity.

Photon emission

Photons with energy??in the energy interval d??are generated by spontaneous radiative recombination of elec-trons and holes at a rate g??x,???per energy.For nondegen-erate electron and hole concentrations,the generation rate of photons by radiative recombination via band-band transitions is given by8,9

g??x,???=?????

????2

4?2?3c2

1

exp????????x??/kT??1

,

?6?where?????is the absorption coef?cient for band to band transitions and???x?is the local separation of the quasi-Fermi-energies.In most practical cases,the?1in the de-nominator of Eq.?6?can be neglected.Under the assumption of low injection conditions within the base,Eq.?6?can then be rewritten as

g??x,???=?????

????2

4?2?3c2

exp????kT

??n e?x?N A n i2?.?7?

Equation?7?predicts the local spectral distribution of spon-taneously emitted photons inside the sample.The same spec-tral distribution of photons would also be measured outside the sample if no reabsorption on the way to the surface oc-curred.

The emitted photon current dj?,em????in the energy in-terval d??that is measured outside the sample follows from integrating the contributions from the photon generation rate g??x,???over the thickness of the solar cell.Accounting for reabsorption with absorption coef?cient?and taking into account one re?ection at the front?R f?and one re?ection at the rear?R r?yields

dj?,em

d????

????=?1?R f??????0d?g??x,????exp???????x?

+R r????exp????????2d?x????dx?8?for the emitted photon current.Multiple re?ections and, thereby,the in?uence of light trapping on the spectrum are neglected in Eq.?8?,an assumption that is justi?ed by the selection of short pass?lters used in our experiments,as discussed below.In the above treatment,it is assumed that nonradiative recombination is the dominant recombination mechanism.The generation of electron-hole pairs by the re-absorption of spontaneously emitted photons?photon recy-cling?is therefore neglected in the continuity equation for the electrons in Eq.?3?.By the same reasoning,photons emitted into directions where they are totally re?ected are left out of the analysis,considering that their reabsorption will not give rise to newly emitted photons.If radiative recombination were dominant,as in many direct semiconductor materials, the electron concentration would become homogeneous through photon recycling and no information on the electron diffusion length could be gained from the shape of the emis-sion spectrum.

With the electron distribution in Eq.?4?,the emitted pho-ton spectrum is found from Eqs.?7?and?8?by numerical integration.The resulting spectrum thus contains the infor-mation on the distribution of the electrons.

Detection of emitted photons

In previous work on luminescence imaging of silicon solar cells and silicon wafers,a silicon CCD camera has been used,providing excellent spatial resolution of1024?1024pixels.On the other hand,a silicon sensor is not

particularly sensitive to the long wavelength radiation emit-ted by silicon samples.Since long wavelength radiation is poorly absorbed,it may be scattered laterally within the CCD array and may eventually be absorbed in the wrong pixel,thereby causing a smearing of the contrast.In addition,long wavelength light is also subject to light trapping within the silicon sample itself,which can lead to long wavelength photons escaping the sample far away from the point where they were generated,an effect that also leads to a smearing of the contrast.Measurements with an InGaAs camera,which is strongly absorbing across the entire spectral range in which signi?cant luminescence from silicon occurs ?850–1250nm ?,would avoid the contrast smearing within the CCD itself but would still be affected by light scattering within the measured sample.In fact,that latter effect would be even more pronounced than with a silicon CCD camera,because an InGaAs sensor measures the entire long wave-length tail of the luminescence,which is most strongly af-fected by light trapping and to which a silicon CCD camera is insensitive.

To reduce these problems,we restrict the detection of photons to wavelength ???cutoff by using a short pass ?lter,which blocks photons that have a penetration depth larger than the thickness of the sample.This cutoff ?lter will elimi-nate all long wavelength emitted light,which is enhanced by light trapping in the solar cell,which also justi?es the above approach of neglecting multiple re?ections within the sample in the derivation of Eq.?8?.The absorption length 1/?of emitted photons as a function of the wavelength ?is shown for silicon at T =300K in Fig.1using absorption coef?cient data determined by Weakliem and Red?eld.10This depen-dence suggests a cutoff wavelength for the short pass ?lter ?cutoff between 1000and 1050nm.By using 1000and 900nm ?lters in the luminescence images presented in this study,the in?uence of lateral smearing within the sample is completely eliminated.

To properly model the intensity detected by the CCD camera,its sensitivity ?camera ?????including the transmis-sion of its lens ?and the transmission of the short pass ?lter T filter must be included

dj ?,detect d ????????=T filter ?????camera ????dj ?,em

d ????

????.?9?

Figure 2shows the photon generation rate g ?????calculated according to Eq.?6?using the absorption coef?cient data from Weakliem and Red?eld 10multiplied by ?camera ????.The peak of the rate of spontaneous emission itself ?prior to multiplication by the sensitivity of the camera ?is at ?=1140nm.However,the sensitivity of the camera decreases strongly with increasing wavelength,shifting the peak in the detected photon current to ?1020nm.Numerical integration of the total and of the detectable photon currents,respec-tively,shows that,depending on the exact values for ?camera ????,only on the order of 5%of the total lumines-cence signal that is emitted by silicon solar cells can be cap-tured with a silicon CCD camera,which suggests that a sig-ni?cant improvement in the sensitivity could be achieved by using,e.g.,an InGaAs camera.

In?uence of the diffusion length on the detected spectrum

Figure 2demonstrates the principle of how the carrier distribution in?uences the emitted spectrum.The two curves represent the photon ?uxes that would be detected by the CCD camera for the same carrier density located either near the front or at the rear surface of a 200?m thick wafer.While no difference is observed at long wavelengths,the detected photon ?ux at shorter wavelength is strongly re-duced for the emission from the rear surface due to reabsorp-tion of photons on their way to the front surface.The ratio of the luminescence intensities at long and short wavelengths,respectively,thus contains information about the optical path the photons have traveled within the sample and,thereby,about the carrier distribution.

The spectral dependence of the detectable photon current for realistic carrier distributions was calculated according to Eqs.?7?–?9?for variable diffusion lengths.We assumed a solar cell with 300?m thickness and an applied voltage of V appl =0.6V.Front and rear re?ectances were assumed to be constant over the wavelength range considered.The resulting spectra were then multiplied with transmission curves of

dif-

FIG.1.?Color online ?Absorption length of photons as a function of wave-length according to literature data for the absorption coef?cient of crystal-line silicon at room temperature ?Ref.10?

.

FIG.2.?Color online ?Calculated emission rate multiplied by the sensitivity of a silicon CCD detector without reabsorption ?front ?and with reabsorption on a 200?m optical path ?rear ?.

ferent short pass ?lters;the latter modeled as a step function according to T filter =1for ???cutoff and T filter =0for ???cutoff .

Figure 3shows the numerically integrated detectable photon currents for short pass ?lters with cutoff wavelengths ranging from 900to 1050nm ?a curve calculated for a mea-surement with no ?lter is also included ?.These data are nor-malized at large diffusion length,i.e.,they represent the sig-nals relative to what would be measured with a completely homogeneous carrier concentration;the latter pinned to n e ?0?by the applied voltage according to Eq.?1?.Importantly,the variation as a function of the diffusion length of that relative luminescence signal is different for different short pass ?lters being used.For the 900nm short pass ?lter,a strong depen-dence of the normalized luminescence signal on the diffusion length is predicted for L e ?50?m,and relatively little addi-tional variation for L e ?100?m.This is expected because the additional carriers that diffuse deeper into the cell for longer diffusion lengths do not affect the measured signal at short wavelengths due to reabsorption.In contrast,without a short pass ?lter,some photons with penetration depths on the order of 300?m or larger are being measured ?see Fig.2?and,in that case,the variation of the normalized lumines-cence signal is relatively stronger for long wavelength ?bot-tom curve in Fig.3?.Figure 3thus shows that the short wavelength part of the luminescence spectrum that is mea-sured with a 900nm short pass ?lter selectively gives infor-mation about the carrier density near the front surface ?i.e.,near the junction ?,while measurements without ?lter or with a longer wavelength ?e.g.,1000nm ?short pass ?lter are more strongly affected by the carrier density pro?le through-out the entire device.

Diffusion length from a single luminescence image

The results from Fig.3predict a direct relationship be-tween the measured luminescence intensity and the diffusion length,which suggest that,in principle,the diffusion length distribution in a solar cell can be determined by measuring a single EL image,as was proposed and demonstrated experi-mentally by Fuyuki et al.2The graph,however,also shows

that the assumption of Fuyuki et al.of the intensity varying linearly with the diffusion length is only valid for small dif-fusion lengths.In addition,to obtain values for the diffusion length from the luminescence intensity,it is necessary to calibrate the intensity curve in Fig.3,e.g.,by comparison with the intensity of a solar cell,for which the diffusion length is known ?e.g.,much larger than the cell thickness ?and which is in exactly the same geometry ?thickness,sur-face morphology,antire?ection coating,voltage,etc.?.

Another,far more severe problem with the approach of Fuyuki et al.is the effect of lateral voltage variations across the cell.Due to the exponential relationship between the lo-cal excess minority carrier density and the voltage ?Eq.?1??,a small variation of the voltage of ?60mV results in a very large variation of the measured luminescence intensity by a factor 10.In EL images taken with a current density equiva-lent to 1sun illumination,lateral variations in the voltage on that order can be caused,e.g.,by local variations of the series resistance or by broken metal grid ?ngers.11

As an example,Fig.4shows an EL image of a 12.2?12.2cm 2multicrystalline silicon solar cell measured with a 1000nm short pass ?lter mounted in front of the CCD camera.The cell was processed on industrial directionally solidi?ed multicrystalline material using a standard industrial screen-printing process including isotexturing of the surface.A prominent feature in that image is the dark region in the bottom left section of the cell ?dashed rectangle ?,in which the luminescence intensity is up to a factor of 5lower than the average intensity from that cell.In a PL image taken on the same cell but with the cell operated near the maximum power point ?image not shown here ?,this area appears brighter than the rest of the cell,demonstrating that a locally enhanced series resistance is responsible for the reduced EL intensity from that area 11and not a reduced diffusion length.This example emphasizes the signi?cant in?uence of

lateral

FIG.3.?Color online ?Normalized luminescence emission intensities ex-pected to be registered by a silicon CCD camera equipped with short pass ?lters with variable cutoff wavelengths of 900nm ?dashed ?,1000nm ?dot-ted ?,and 1050nm ?dash dotted ?as a function of the electron diffusion length in a 300?m thick silicon solar cell.The bottom curve shows that dependence for a measurement without a short pass

?lter.

FIG.4.?Color online ?Electroluminescence image of a multicrystalline sili-con solar cell with an area of 12.2?12.2cm 2.The image is taken with a 1000nm short pass ?lter and with a data acquisition time of 1s ?see text for details ?.

voltage variations on the luminescence intensity,which is completely ignored in the simpli?ed analysis of a single lu-minescence image in terms of the diffusion length.2

Diffusion length determined from the ratio of two luminescence images

In order to avoid the necessity of a calibration and to eliminate the effect of a laterally inhomogeneous voltage dis-tribution,we propose to measure at least two luminescence images in different wavelength ranges.The latter may be de?ned by two different short pass ?lters mounted in front of the camera objective.According to Eqs.?6?and ?7?,the lu-minescence signals in different spectral ranges will be af-fected by variations of the voltage by the same exponential factor.By dividing two luminescence signals,the effect of an inhomogeneous voltage distribution,therefore,cancels out.

Figure 5shows the theoretical results for the ratio of the expected luminescence signals for various pairs of short pass ?lters as a function of the diffusion length L e .The division of two relative luminescence signals measured with two differ-ent short pass ?lters gives a number which is indicative of the absolute diffusion length and which is free from all ex-ternal effects that affect the measured intensity,such as the voltage.In Fig.5,three curves are shown for each combina-tion of ?lters for rear surface recombination velocities of S =0,100,and 104cm/s.It is seen that the observed ratios of luminescence intensities are little affected for S ?100cm/s.In contrast,for S =104cm/s,the carrier distribution no longer varies signi?cantly with the diffusion length L e for L e ?100?m,but is governed by surface recombination.In this case,the analysis of luminescence intensity ratios yields an effective diffusion length instead of the bulk diffusion length,a problem that is known for other methods as well.At least a reasonably accurate estimate of the rear surface re-combination velocity is,thus,required to analyze absolute diffusion lengths from intensity ratios.The combinations of ?lters used for the calculations shown in Fig.5are only some possible examples which show a strong enough depen-dence on the diffusion length.Other combinations would give similar results.

EXPERIMENTS

Two dielectric short pass ?lters with cutoff wavelengths of 900and 1000nm,respectively,were used for this study.Our experiments revealed small nonhomogeneities across the area of both short pass ?lters being used,resulting in relative lateral signal variations of luminescence images of about 5%upon rotation of the ?lter by 90°.To reduce the in?uence of these ?lter nonhomogeneities,each luminescence image was measured by averaging four otherwise identical exposures,with the ?lter being rotated by 90°after each exposure.This averaging procedure was employed here in order to avoid the nonideal ?lter properties limiting the accuracy of the method.While causing longer total data acquisition time,this com-plication is purely a result of the nonideal ?lters being used here and does not represent a fundamental requirement or limitation of the method.Further work will focus on identi-fying more homogeneous dielectric ?lters.

Figure 4shows an EL image taken with a silicon CCD camera that was cooled to ?30K and with the 1000nm short pass ?lter.A current of 30mA/cm 2?similar to the short cir-cuit current of the cell at 1sun illumination ?was fed into the bus bars of the cell via two arrays of ten spring loaded con-tact pins.The contacting stage available for this study is not ideal,as the spring loaded pins and the rail they are mounted in are partially visible in the luminescence images in the vicinity of the bus bars,thereby shading part of the cell.This is only a practical and temporary limitation of our speci?c setup.

As discussed above,the dark area on the bottom left hand side of the EL image shown in Fig.4?dashed vertical rectangle ?is caused by a locally enhanced series resistance.A variety of localized brighter spots are observed within that area near the grid ?ngers,which indicates relatively lower localized series resistance.Similar observations were re-cently reported 11and interpreted as local spots where the front grid makes better contact to the silicon than in the surrounding area of enhanced series resistance.In addition,the image shows the in?uence of several broken metal grid ?ngers ?e.g.,black arrow in Fig.4?which,as reported previously,4,12are characterized by dark lines along the grid ?nger in EL images.Two cracks on the left side of the right hand bus bar ?dotted white arrows ?and a large horizontal crack ?two white arrows ?were introduced during manual cell handling at UNSW.Neither the large horizontal crack nor the two smaller cracks were present during the spectrally re-solved LBIC measurement shown below,which was carried out at Fraunhofer ISE,Germany,prior to shipping the cell to UNSW.The three solid white arrows in the top right corner indicate two lengthy and one pointlike area of reduced EL intensity.The blurring of the EL intensity indicates a strong lateral current ?ow into those areas.However,from this single EL image,it is not possible to determine whether these regions correspond to local shunts or to very active recom-bination sites.

The features highlighted in the EL image shown in Fig.4provide information about various fault mechanisms and electronic defects present in that solar cell.However,these features lead to strong relative variations of the EL

intensity

FIG.5.?Color online ?Calculated ratio of electroluminescence intensities,each measured with a different short pass ?lter.The cutoff wavelengths for the ?lters are indicated.Results for each signal ratio are shown for three different rear surface recombination velocities S r =1cm/s ?solid line ?,100cm/s ?dotted ?,and 104cm/s ?dashed ?,respectively.

by up to a factor of 5,as seen in the cross sections shown on the left hand side and at the bottom of Fig.4.The cross sections represent the counts per pixel along the vertical and horizontal lines in Fig.4,respectively,on a scale from zero to 6000counts/s.These variations,which are not related to diffusion length variations,make an analysis of this indi-vidual image in terms of variations of the diffusion length impossible.

A second luminescence image was measured under iden-tical operating conditions of the solar cell,but with a 900nm short pass ?lter replacing the 1000nm short pass ?lter.That second image,which is not shown here,exhibits the same features as the image shown in Fig.4.Figure 6shows the pixel by pixel ratio of the two EL images taken with the 1000nm short pass ?lter and with the 900nm short pass ?lter,respectively.The ratio was corrected for the ratio in data acquisition times for the two measurements.The com-parison of that ratio image with Fig.4shows that most of the voltage related intensity variation observed in the individual images cancels out in the ratio,as predicted theoretically.Even the quite substantial intensity variations in the indi-vidual images that are caused by high series resistance,by broken ?ngers,by cracks,or by signi?cantly higher current ?ow into the regions near the bus bars are not visible in the intensity ratio image.

The remaining intensity variations in the ratio image from Fig.6reveal the variation of the diffusion length L e .

The theoretical curves shown in Fig.5were calculated for perfect short pass ?lters,assuming a step function for their transmission.For the conversion of the experimental lumi-nescence intensity ratio from Fig.6into a diffusion length,that theoretical relationship was calculated taking into ac-count the experimentally measured wavelength dependent transmittance of the 900and 1000nm short pass ?lters,re-spectively,and the wavelength dependent re?ectance of the solar cell.Both the transmittance of the ?lters and the re?ec-tance of the solar cell were measured with a Cary 500spec-trophotometer.The resulting theoretical curve is very similar to the curve in Fig.5.Because it is speci?c to the ?lters used in our experiments,the curve is not shown here.

The diffusion length distribution calculated from the ra-tio of the two luminescence images ?Fig.6?using this theo-retical relationship is shown in Fig.7.The theoretical rela-tionships between the intensity ratio and the diffusion length ?Fig.5?converge towards constant values for large diffusion length.The white regions that are observed in the ratio image shown in Fig.6correspond to intensity ratios that are larger than this saturation value and are,thus,not physically mean-ingful within the above theoretical model for the carrier dis-tribution.Possible origins for these deviations will be dis-cussed further below.In the conversion of intensity ratios into diffusion length,all areas with intensity ratios greater than 37.5were converted into a diffusion length greater than 330?m,which means that in Fig.7they are mapped

with

FIG.6.Intensity ratio of two electroluminescence images taken under identical operating conditions of the solar cell but using two different short pass ?lters with cutoff wavelengths of 900and 1000nm,respectively.The large voltage related intensity variations observed in the individual images ?see Fig.4?are eliminated.

the same color.Small diffusion lengths that are observed in

the bottom left corner of Fig.7result from the very high

series resistance effects in that area,which appear to be not

perfectly eliminated in the intensity ratio.

For comparison,Fig.8shows a map of the diffusion

length distribution of the same cell measured with spectrally

resolved LBIC.Given that the results from Fig.7are ob-

tained from two relative luminescence measurements with

very strong lateral features resulting from various fault

mechanisms,good quantitative agreement between the two

images is observed.The LBIC data span a larger dynamic

range with diffusion lengths ranging from?60?m in the low quality areas to greater than300?m in the good areas. For comparison,the lowest quality areas in the luminescence

image are on the order of100?m,with similar values ??300?m?as in the LBIC data for the good areas.In the cell investigated in this study,the areas of low diffusion

length are grain boundaries or dislocation networks with

fairly small feature https://www.doczj.com/doc/48203202.html,teral carrier diffusion from adja-

cent areas of higher minority carrier diffusion lengths can

affect the carrier distribution within these low quality areas,

which is currently thought to reduce the contrast between

good and bad areas in the luminescence results.For cells

with larger areas?e.g.,grains?of high and low minority car-

rier lifetimes,respectively,this smearing effect will be less of

a problem.

Transient features

After turning on the forward current through the cell for

the EL measurements,we observe an initial gradual increase of the luminescence signal with time,which is not related to temperature effects and not correlated to electrical current variations.With a forward current density equivalent to 1sun operating conditions,the luminescence signal reached a stable value after1min in our experiments.Such observa-tions can be related, e.g.,to the breaking of iron-boron pairs13,14or to the formation/dissociation of boron-oxygen complexes15in the bulk of the cell.A discussion of bias induced degradation in silicon solar cells can be found in Ref.16.Importantly,such transient effects can strongly im-pact on the accuracy of our method,which relies on both luminescence measurements being taken under identical op-erating conditions.Signi?cant changes within the solar cell material during or between the two luminescence measure-ments in?uence the intensity ratio and,thereby,the measured diffusion length.A stable luminescence signal must,there-fore,be reached?rst before the two luminescence images are measured.As discussed above,this can mean,in practice, that certain types of cells must be forward biased for some time before the measurements are carried out or that both measurements must be made within a short time interval. The diffusion length that is subsequently calculated from our measurements corresponds to the diffusion length in the satu-rated state and,as such,is relevant to the solar cell operation, because the solar cell will also normally be operated in that state.As a convenient way to check that transient features have no signi?cant in?uence on the accuracy of the method, a third luminescence image could be measured that repeats the?rst measurement with the same?lter?the1000nm

short FIG.7.?Color online?Diffusion length distribution calculated from the intensity ratios from Fig.6.The color bar gives the diffusion length in micrometers.

pass?lter in the above example?.No signi?cant variation between the?rst and third images taken should be detect-able.

Another unexpected transient feature was observed within the high series resistance area.The white regions with intensity ratios greater than37,seen on the left hand side of Fig.6,are caused by blinking of the luminescence intensity in these areas.We observe that,in repetitive measurements of the intensity ratio,these features sometimes appeared as bright spots,sometimes as dark spots,and sometimes they completely disappeared.Our explanation for this effect is an intermittent mechanical and,thus,electrical contact between the metal grid and the silicon,which could be caused,e.g., by thermal expansion upon application of the forward bias. Injection level dependent diffusion length

In the luminescence based method described here,the two luminescence measurements are carried out under oper-ating conditions that are close to the operating conditions present under1sun illumination,i.e.,at a well de?ned injec-tion level.This is of some relevance because the minority carrier lifetime and,thus,the diffusion length can vary by orders of magnitude as a function of the injection level,es-pecially in multicrystalline silicon.In spectral LBIC mea-surements,the solar cell is operated under external short cir-cuit conditions and under fairly intense local illumination by various modulated laser diodes with different wavelengths. The estimation of the injection level under such experimental conditions is not trivial and depends strongly on the experi-mental setup and the exact device properties.In LBIC ex-periments,the minority carrier diffusion length is,thus,de-termined at an injection level that may not be de?ned as precisely as in the luminescence method discussed here. Given these considerations,the agreement between the lumi-nescence results and the LBIC map?Figs.7and8,respec-tively?is surprisingly good.

Sharpening of images

Some features appear signi?cantly sharper in the inten-sity ratio image from Fig.6than in the single EL image from Fig.4.The features marked with white arrows in the top right corner are a good example.In individual images,the sharpness and,therefore,the ability to localize the defected or shunted region is limited by smearing of the local voltage, which in turn is a series resistance effect caused by lateral currents?owing through the emitter from good quality re-gions into low quality regions.6,17,18As discussed above,the intensity ratio removes any effects caused by lateral voltage variations and,thereby,results in a sharper image allowing a more accurate localization,e.g.,of shunted areas.

Shunt detection

The areas indicated by white arrows in Fig.4appear as white regions in the intensity ratio shown in Fig.6.Indeed, the ratio is greater than38in those areas and,thus,larger than theoretically predicted for an in?nite diffusion length.In order to explain this observation,we note that in the

above FIG.8.?Color online?Diffusion length of the solar cell from Fig.7,determined from a spectral LBIC map.

theoretical model the carrier concentration always decays with increasing distance from the junction.There are,how-ever,cases where the distribution of carriers from the surface into the interior of a solar cell does not follow Eq.?4?.Spe-ci?cally,there are cases where the carrier density near the junction is lower than in the bulk.One example is the pres-ence of a localized shunt in the p -n junction,which causes the voltage and,thereby,the minority carrier concentration at the junction to be reduced.The shunted region will,there-fore,emit less luminescence and appear as a dark spot in a single CCD image ?white arrows in Fig.4?,particularly at short wavelengths at which the carrier concentration close to the p -n junction is probed.If the shunt has a small lateral extension and if it is not going through the whole thickness,lateral bulk minority carrier diffusion will result in a rela-tively higher carrier concentration further away from the junction and,thereby,in a relatively higher long wavelength emission.In the ratio of two images taken at long and short wavelengths,respectively,the shunt will,therefore,appear particularly bright,with intensity ratios even exceeding the ratios expected for an in?nitely large diffusion length ?homo-geneous pro?le ?.Thus,a dark spot in a single image which turns bright in the ratio image may be identi?ed as a shunt.Dark lock-in thermography 19?DLIT ?measurements with 0.5V applied voltage in forward and reverse directions were carried out and revealed no shunt type behavior in the areas indicated by white arrows in Fig.6.We,therefore,conclude that the high luminescence intensity ratios in those areas are caused by recombination active defects at the surface,caused,e.g.,by scratches,which have a similar in?uence on the relative carrier pro?le as shunts.

In order to demonstrate the possibility of distinguishing shunted regions from bulk defects,we investigated a shunted industrial multicrystalline silicon solar cell with an ef?ciency of 14.0%?compared to around 15%typical for nonshunted cells from the same batch ?and with an area of 15?15cm 2.A shunt resistance of 1.33?was determined for that cell from the reverse current at a reverse bias of ?3V.A DLIT measurement on that cell revealed localized shunts within a 3.2?3.2cm 2area near one of the bus bars ?Fig.9?c ??.Figure 9?a ?shows an EL image of that section taken with a 1050nm short pass ?lter,and Fig.9?b ?shows the intensity ratio of two EL images taken with a 1050nm short pass ?lter and with a 900nm short pass ?lter,respectively.The intensity ratio in the shunted region takes on values up to ?300,which is more than three times more than the ratio in the nonshunted region,where it varies between 70and 100.The comparison of Figs.9?a ?–9?c ?shows that,in cells with moderate to strong local shunts,the intensity ratio image allows identify-

ing shunted regions and clearly distinguishing them from bulk recombination active regions in the vicinity.CONCLUSIONS

A quantitative determination of the spatially resolved diffusion length from the ratio of two luminescence images measured with two different spectral ?lters has been dis-cussed theoretically and demonstrated experimentally on a screen printed multicrystalline silicon solar cell.Good agree-ment is observed between the absolute diffusion length from that method and the results from a spectrally resolved LBIC map.

In this study,we used a silicon CCD camera with a reso-lution of 1024?1024pixels.Although a silicon CCD is much less sensitive to the long wavelength luminescence emission of a silicon solar cell than to visible radiation ?only picking up about 3%–5%of the total emitted luminescence even without a ?lter ?,taking an image with short pass ?lter-ing requires only about 1s for ?cutoff =1000nm and about 100s for ?cutoff =900nm.Allowing for 1min of forward bi-asing of the cell prior to the luminescence measurements,a high resolution map of the diffusion length can,thus,be obtained in under 3min,much faster than the measurement time for a LBIC map with lower spatial resolution.The data acquisition time can be further reduced by binning of pixels,thereby sacri?cing spatial resolution.Binning 5?5pixels still yields a diffusion length image with 204?204pixels and can be achieved with a total exposure time of only 4s.In cases where no transient effects are observed,a diffusion length image can,thus,be taken in a matter of a few seconds.

The variation of the luminescence intensity ratio with diffusion length ?Fig.5?is weak and also depends more strongly on the surface recombination velocity for large dif-fusion lengths.As a result,the luminescence technique dis-cussed here becomes less quantitative for diffusion lengths that are comparable to or larger than the thickness of the cell,similar to LBIC measurements.Our results indicate that in small areas of reduced minority carrier diffusion length that have a lateral extension on the order of the diffusion length,a quantitative analysis of the luminescence intensity ratio can overestimate the diffusion length.In contrast,our method gives reliable values for larger regions of constant diffusion length.Surface texturing leads to comparable errors in the luminescence technique and in LBIC,because the texture affects the angle between the solar cell surface and the inter-nal light path ?for incident light in LBIC and for emitted light in luminescence ?.For geometrical surface textures like in-verted pyramids,the angle of the internal light path is

pre-

FIG.9.?Color online ??a ?Electroluminescence inten-sity from a 3.2?3.2cm 2section of a shunted multic-rystalline silicon cell measured with a 1050nm short pass ?lter.?b ?Ratio of EL intensities measured with a 1050nm short pass ?lter and with a 900nm short pass ?lter,respectively.?c ?Dark lock-in thermography ?Ref.19?measurement carried out with 0.5V reverse bias.

dictable and can be accounted for analytically.For random textures,it may be necessary to empirically determine cor-rection factors to determine absolute diffusion lengths.The latter statement again holds equally for both the lumines-cence technique and for LBIC.

The method that has been presented here is not limited to electroluminescence,but with some modi?cations,it can also be applied to photoluminescence.Photoluminescence imaging7has the great advantage that it can be applied to silicon wafers at all stages of solar cell production,from raw wafers through to?nished solar cells.The methods described here could,thus,become a useful tool in calibrating photo-luminescence images on silicon wafers;the latter generally not a trivial task due to the dependence of the luminescence signal on the minority carrier lifetime,the doping concentra-tion,the sensitivity of the detector,and the optical properties of the sample and the incident intensity.In previous work on PL imaging,a powerful infrared laser was used for excita-tion,leading to a depth dependent generation pro?le that extends into the cell and is dif?cult to describe by the theo-retical model above.In that case,in order to determine the theoretical relationship between the luminescence intensity ratio and the diffusion length,carrier density pro?les for dif-ferent diffusion lengths may be calculated numerically,e.g., using PC1D simulations.20

A quantitative analysis of a single electroluminescence image in terms of absolute local diffusion length variations as proposed by Fuyuki et al.2is possible in principle,but is, however,limited in practice to very speci?c cases where lat-eral variations of the voltage can be neglected.Even small voltage variations of10mV will lead to large relative errors in the resulting diffusion length of?50%.As has been shown here,such errors resulting from lateral voltage varia-tions are eliminated by calculating the ratio of two lumines-cence images measured in different spectral ranges but with identical operating condition of the solar cell.As further ad-vantages of the method proposed here,photon reabsorption within the silicon sample is accounted for quantitatively and images of the absolute diffusion length are obtained without the need for calibration.

ACKNOWLEDGMENTS

The authors would like to thank Martin A.Green from UNSW for valuable discussions and also Martin Kasemann from Fraunhofer Institute for Solar Energy Systems, Freiburg,Germany,and Jan Bauer from Max Planck Institute for Microstructure Physics,Halle,Germany,for carrying out lock-in thermography measurements.The supply of a shunted screen-printed solar cell by Hans-Peter Hartmann, Deutsche Cell GmbH,Freiberg,Germany,is also gratefully acknowledged.The Centre of Excellence for Advanced Sili-con Photovoltaics and Photonics is supported under the Aus-tralian Research Council’s Centres of Excellence Scheme. 1W.Warta,J.Sutter,B.Wagner,and R.Schindler,Proceedings of the Second World Conference on Photovoltaic Energy Conversion,Vienna, Austria,1998,p.1650.

2T.Fuyuki,H.Kondo,T.Yamazaki,Y.Takahashi,and Y.Uraoka,Appl. Phys.Lett.86,262108?2005?.

3T.Fuyuki,H.Kondo,Y.Kaji,T.Yamazaki,Y.Takahashi,and Y.Uraoka, Proceedings of the31st IEEE Photovoltaic Specialists Conference,Or-lando,2005,p.1343.

4T.Trupke,R.A.Bardos,M.D.Abbott,F.W.Chen,J.E.Cotter,and A. Lorenz,Proceedings of the WCPEC-4,Waikoloa,2006,p.928.

5K.Bothe,P.Pohl,J.Schmidt,T.Weber,P.P.Altermatt,B.Fischer,and R. Brendel,Proceedings of the21st European Photovoltaic Solar Energy Conference,Dresden,Germany,2006,p.597.

6M.Kasemann,M.C.Schubert,M.The,M.K?ber,M.Hermle,and W. Warta,Appl.Phys.Lett.89,224102?2006?.

7T.Trupke,R.A.Bardos,M.C.Schubert,and W.Warta,Appl.Phys.Lett. 89,044107?2006?.

8P.Würfel,S.Finkbeiner,and E.Daub,Appl.Phys.A:Mater.Sci.Process. A60,67?1995?.

9P.Würfel,Physics of Solar Cells?Wiley-VCH,Weinheim,2005?.

10H.A.Weakliem and D.Red?eld,J.Appl.Phys.50,1491?1979?.

11T.Trupke,E.Pink,R.A.Bardos,and M.D.Abbott,Appl.Phys.Lett.90, 093506?2007?.

12Y.Takahashi,Y.Kaji,O.Ogane,Y.Uruoka,and T.Fuyuki,Proceedings of the WCPEC-4,Hawaii,2006,p.924.

13G.Zoth and V.Bergholz,J.Appl.Phys.67,6764?1990?.

14J.Schmidt,Prog.Photovoltaics13,325?2005?.

15J.Schmidt and K.Bothe,Phys.Rev.B69,024107?2004?.

16S.W.Glunz,E.Sch?ffer,S.Rein,K.Bothe,and J.Schmidt,Proceedings of the WCPEC-3,Osaka,Japan,2003,p.919.

17J.C.Goldschmidt,O.Schultz,and S.W.Glunz,Proceedings of the20th EPVSC,Barcelona,Spain,2005,p.663.

18T.Trupke,R.A.Bardos,M.D.Abbott,K.Fisher,J.Bauer,and O. Breitenstein,Proceedings of the International Workshop on Science and Technology of Crystalline Silicon Solar Cells,Sendai,Japan,2–3October 2006?unpublished?.

19O.Breitenstein and https://www.doczj.com/doc/48203202.html,ngenkamp,Lock-In Thermography:Basics and Use for Functional Diagnostics of Electronic Components?Springer, Heidelberg,2003?.

20P.A.Basore and D.A.Clugston,Proceedings of the25th IEEE Photovol-taic Specialists Conference1996,p.377.

铝矿石成分对氧化铝生产的影响

铝矿石成分对氧化铝生产的影响 1.山西分公司铝土矿资源概况 我国铝土矿资源较为丰富,主要集中在山西、河南、贵州、广西四省,总储量23.4亿吨,其中山西省储量为9.89亿吨,占总储量的42%。截至2005年上半年,山西分公司已取得采矿权的铝土矿区10个,保有资源量7029万吨,其中:A/S 8以上高品位矿1248万吨(占17.76%);A/S 6.5-8的中等品位矿石2253万吨(占32.05%);A/S 6.5以下低品位矿3528万吨(占50.19%),高品位铝矿石较少,主要为中低品位的铝土矿,山西分公司2007年计划供矿:老系统拜耳法 A/S≥9.0,AO≥67%,烧结法A/S6.5±0.3,AO≥62%,新系统A/S7.0±0.3 ,AO≥65%。 近年来,我国氧化铝企业为提高产量,降低成本,尽量提高供矿品位,而我国80%以上的铝土矿为中低品位,平均铝硅比仅为5.56,随着高品位铝土矿储量日渐减少,供矿品位不得不下降,结果引起产量减少,碱耗和矿耗指标明显升高,导致成本升高。因此,需要合理选择供矿品位,深入研究不同铝土矿的性质特点及杂质对氧化铝生产的影响,最大程度地发挥不同品位铝土矿生产氧化铝的效益,有效利用有限的铝土矿资源,成为山西分公司氧化铝生产企业的迫切任务。 2.山西铝土矿化学成分及矿物组成 铝土矿是一种组成复杂,化学成分变化很大的矿石。铝土矿的化

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硅烷偶联剂kh

硅烷偶联剂kh570 一、概述: 偶联剂kh570是一类具有两不同性质官能团的物质,它们分子中的一部分官能团可与有机分子反应,另一部分官能团可与无机物表面的吸附水反应,形成牢固的粘合。偶联剂在复合材料中的作用在于它既能与增强材料表面的某些基团反应,又能与基体树脂反应,在增强材料与树脂基体之间形成一个界面层,界面层能传递应力,从而增强了增强材料与树脂之间粘合强度,提高了复合材料的性能,同时还可以防止不与其它介质向界面渗透,改善了界面状态,有利于制品的耐老化、耐应力及电绝缘性能。 化学名称:γ―甲基丙烯酰氧基丙基三甲氧基硅烷 化学结构式:CH3CCH2COO(CH2)3Si(OCH3)3 对应牌号:中科院KH-570、美国联碳公司A-174、美国道康宁公司Z-603、日本信越公司KBM-503 典型特征:偶联剂570为甲基丙烯酰氧基官能团硅烷,外观为无色或微黄透明液体,溶于丙酮、苯、乙醚、四氯化碳,与水反应。沸点为255℃,密度P25'g/m1:1.040,折光率ND:1.429,闪点:88℃,含量为≥97% 二、应用领域: 1、用于玻璃纤维的表面处理,能改善玻璃纤维和树脂的粘合性能,大大提高玻璃纤维增强复合材料的强度、电气、抗水、抗气候等性能,即使在湿态时,它对复合材料机械性能的提高,效果也十分显着。目前,

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效方法。 中国铝业中州分公司采用的就是烧结法生产氧化铝。脱硅器是湿法系统的关键设备之一,属于密闭性的压力容器。中州分公司氧化铝年产量从最初的20万t逐年递增,提升到现在年产80万t的生产能力,而脱硅器则仅在最初的4组直接加热脱硅器的基础上,增加了2组间接加热脱硅器,产量大幅度提高,清理作业也日渐频繁。时间紧,工作量大,脱硅系统面临的压力愈来愈大。如何采用行之有效的方法安全清理脱硅器,中州分公司在十几年的生产实践中,进行了积极的探索。 中州分公司目前运用的直接加热脱硅器和间接加热脱硅器规格分别为2.6m×9.5m和2.8m×12m,平均2个月就要清理一组,一般是5-7个脱硅罐,其结垢具有质密、厚度均匀等显著特点。常用的脱硅器清理方法有以下3种。

选用硅烷偶联剂的一般原则

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玻璃钢套管与传统套管相比的优点

玻璃钢增强干式电容型套管与传统套管相比的优点玻璃钢增强干式电容型套管的主绝缘为电容芯子,电容芯子是用高绝缘性能玻璃纤维浸以超低粘度耐高温环氧树脂,用微机缠绕设备按测地线缠绕交叉叠加构成绝缘层,采用半导体适形材料制成电容屏,绝缘层与电容屏交替缠绕间隔设置经高温固化制成纯固体电容芯子,联结法兰由高强度铝合金制成,与电容芯子胶装成一体;增爬伞裙采用硅橡胶一次注射成型在电容芯子表面,与电容芯子形成有机整体。与传统的瓷外套套管对比如下: 1、产品属无油,无气纯固体主绝缘结构产品,无任何填充物,无需专门的维护保养; 2、设计绝缘裕度大,以半导体材料电容屏,最大限度提高了起晕电压,运行中无局放; 3、耐高温、阻燃绝缘材料,无分解;电气性能稳定,无燃烧及爆炸危险; 4、结构紧凑,体积小,重量轻,便于运输,可任意角度安装; 5、玻璃纤维增强缠绕,优化力学铺层设计,抗弯强度高,机械性能优异,适用于重震地区; 6、具有极佳的耐高温性能,最高耐温+155℃,最低温-200℃; 7、硅橡胶复合外套防污性能优异,自洁而无需清扫,可用于重污秽区; 8、使用寿命长,交货期短、长期运行成本低。 9、产品生产周期短,可根据用户要求进行特殊设计;

10、除可以安装复合外套也可以提供高强瓷增爬伞裙; 11、可以满足智能电网要求,套管可以加智能装置,可以实现对套管的在线监测; 12、内部不用填充SF6气体,杜绝了爆炸和泄漏的隐患; 13、内部局放不存在逐渐放大而引起绝缘油老化问题。 针对国外环氧树脂浸纸高压套管盛行的今天,玻璃钢增强干式电容型套管为国内乃至国际上提供了一种新的选择,中国创造带来了一种新的革新。 于此同时,复合材料也存在着老化问题,制造设备成本昂贵。但相信前景还是很广阔的。

氧化铝生产工艺流程图

氧化铝生产工艺流程图 流程仿真技术原理 根据工艺过程所涉及到的基础物性数据,引用或创建特定的物性包,建立生产过程中的单元设备的数学模型和单元设备之间的模型,从而完成完整描述实际生产过程系统的数学模型[6,7]。通过一定的数学方法对过程中所涉及到的模型进行联列求解。通过装置的稳态和动态模型,进行不同方案和工艺条件的分析,为新工艺的规划、研究开发和技术可靠性进行分析,为生产实际提供优化操作指导。在动态模拟中,还可以通过不同控制策 略的比较,对生产过程进行优化控制[5]。 生产过程的数学模型通常为一大型非线性代数方程组,过程模拟实质就是通过求解该非线性方程组来预测在一定工艺条件下生产过程的性能。常用 的求解方法主要有序贯模块法、联立方程法和联立模块法[3]。 氧化铝生产工艺 氧化铝的生产方法有酸法、碱法和热法。目前氧化铝工业生产实际应用的是碱法。碱法又包括拜耳法、烧结法及各种形式的联合法。因拜耳法生产成本低,经济效益好,流程相对简单,应用最广,所以主要介绍一下拜耳法的生产工艺。 所谓拜耳法是因为它是由K.J.bayer在1889-1892年提出而得名的。拜耳法主要包括两个主要过程,一是Na2O与Al2O3摩尔比为1.8的铝酸钠在常温下,只要添加氢氧化铝作为晶种,不断搅拌,溶液种的Al2O3就可以呈氢氧化铝析出,直到其中Na2O:Al2O3的摩尔比提高到6为止,此即为铝酸钠溶液的晶种分解过程。另一过程是已经析出了大部分氢氧化铝的溶液。在加热时,又可以溶出铝土矿中的氧化铝水合物。此即利用种分母液溶出铝土矿的过程。交替使用这两个过程处理铝土矿,得到氢氧化铝产品,构成所谓拜耳法循环[8]。拜耳法的生产工艺流程图如图1 所示。

硅烷偶联剂的使用方法

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关于耐高温玻纤管和硅树脂玻纤管的区别

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