Solar+cells+with+porous+siliconmodification+of+surface-recombination+velocity

Appl.Phys.A73,495–501(2001)/Digital Object Identifier(DOI)10.1007/s003390100799Applied Physics AMaterialsScience&ProcessingSolar cells with porous silicon:modification of surface-recombination velocityG.Kopitkovas1,I.Mikulskas1,K.Grigoras2,I.ˇSimkien˙e2,R.Tomasiunas1,∗1Institute of Materials Science and Applied Research,Vilnius University,Sauletekio10,2054Vilnius,Lithuania2Semiconductor Physics Institute,Gostauto11,2600Vilnius,LithuaniaReceived:26June2000/Accepted:4December2000/Published online:26April2001– Springer-Verlag2001ser-induced transient-grating measurements were performed to monitor the influence of porous silicon on the surface recombination of a highly doped n+-silicon emitter of solar cells.With this technique,photocarrier dif-fusion and recombination with a time resolution of some tens of picoseconds can be ing pulses of the second-and third-harmonic radiation from an Nd3+:Y AG laser(quantum energy2.34and3.51eV,respectively),two different-depth regions of the emitter were ing a kinetic model,which includes carrier diffusion and re-combination at the surface and in the bulk of the emit-ter,surface-recombination velocities in a series of samples typical for each successive operation of solar-cell technol-ogy with different surface-doping level and surface prepar-ation were evaluated.From the analysis,we conclude that porous silicon formed on the emitter passivates the surface of the silicon layer,i.e.reduces the rate of surface recom-bination at the porous silicon–crystalline silicon interface. Ytterbium as a co-dopant of the emitter increases the surface-recombination velocity.PACS:73.25.+i;73.50Gr;78.47.+pOptical properties of porous silicon have been intensively examined because of the strong room-temperature lumines-cence,stimulating hopes for introducing all-silicon-based optoelectronics in the near future[1].Beside luminescence, porous silicon became quite attractive for solar-cell re-searchers,mainly because of its high total area and low light reflection[2].Solar cells usually incorporate a shallow and highly doped emitter,which causes some additional defects and increases carrier recombination at the surface.A porous-silicon layer formed on the emitter also improves the device performance due to passivation of the surface[3].Therefore, both carrier surface-recombination and diffusion processes influenced by porous silicon need to be studied.The study ∗Corresponding author.(Fax:+370-2/767-313,E-mail:rolandas.tomasiunas@ff.vu.lt)of fast relaxation and recombination dynamics in the emit-ter is also of importance with respect to the initial physical processes which take place in solar cells immediately after photogeneration of carriers by short laser pulses.In this paper,investigations of p−n+junctions,obtained by phosphorus doping from silicon oxidefilms deposited by a spin-on technique,are presented.This technique seems to be suitable in solar-cell preparation,as no protection for the rear side of the wafer is necessary and even simultaneous doping of both sides of the wafer with different impurities is possible[4].In some samples the emitter was prepared by adding ytterbium oxide(YbO2)to the doping solution.The impact of this rare-earth metal on the lifetime and surface-recombination parameters is also demonstrated.Bulk and surface-recombination parameters were monitored by a laser-induced transient-grating technique.Transient laser-induced-grating(LIG)experiments are known to provide a good insight into these processes[5]. We have reported our experimental observations of the tran-sient LIG experiments performed on self-supporting porous-silicon membranes with intense picosecond laser pulses[6], where we have shown how the level of porosity influences carrier recombination and diffusion in the porous silicon itself.The aim of the present work is to complete our previ-ous report[7]and to discuss new experimental results within a framework of a kinetic model,which enables us to extract more precise values of the recombination rate at the porous silicon–crystalline silicon interface.The paper is organized as follows.Section1describes sample-preparation technology,experimental methods and the relevant experimental arrangement.Section2deals with the kinetic model proposed for analyzing carrier dynamics at the cell surface and Sect.3is devoted to a discussion of the results.1Experimental procedureStarting material of the prepared cells was(100)-oriented p-type(1Ω×cm,CZ)silicon wafers of480µm thickness496with polished surfaces (sample no.1).They were sliced into 2×3cm 2cells.The samples were rinsed for 10min in boiling dimethylformamide and in acetone and then cleaned by ethanol.The native SiO 2layer was removed by pure HF.For doping,tetraethoxysilane solution mixed with H 3PO 4at volume ratio 1:1was applied by the spin-on technique (sample no.2).The diffusion was performed by annealing for 30min at 950◦C in an argon environment followed by a slow cooling down.Simultaneously,this process facilitates the gettering of defects.The phosphorus concentration of 2×1020cm −3at the surface was measured using Auger elec-tron spectroscopy combined with Ar +-ion milling [4].Additionally,the emitter in several samples was formed using a modified doping solution,when YbO 2was added to the mixture (sample no.4).The possible influence of rare-earth elements on the diffusion procedures in silicon is still not completely investigated.The action of ytterbium could be twofold.First of all,the atomic radius of phosphorus is smaller than the atomic radius of silicon (P /Si =0.932),whereas the atomic radius of ytterbium is larger (Yb /Si =1.44).So,the rare-earth element moving into a vacant pos-ition can reduce the lattice stress and exclude formation of dislocations that occur during incorporation of phosphorus into silicon.This effect occurs when the concentration of phosphorus exceeds 5×1015cm −3;therefore a great amount of dislocations is created when the phosphorus concentration is higher,i.e.close to the solubility limit.Secondly,ytter-bium creates in silicon two donor levels (E c −0.23eV and E c −0.31eV);thus,it does not act as a compensating im-purity during the phosphorus doping,and therefore a highly doped n +layer can be prepared.After emitter formation,the top surface was passivated with a 0.1µm thick porous-silicon layer (sample nos.3,4).The porous silicon was formed by electrochemical etching of the samples in HF :H 2O (1:1)solution for some tens of sec-onds at 30mA /cm 2.The etching technique is described in more detail elsewhere [8].Just for comparison,samples with an extremely highly doped emitter (n ++),prepared by a convenient phosphorus-diffusion technique (doping from gaseous sources in a diffu-sion furnace),were also included in the measurements (sam-ple no.5).Phosphorus concentration at the surface was about 1021cm −3for those samples.The basic parameters of the five samples investigated throughout this work are given in Table 1.The principal struc-ture of the samples is presented in Fig.1a.The emitter thick-ness was measured using scanning electron microscope cross-sectional pictures of the stained p −n +junction.In the LIG technique,two coherent laser pulses inter-fere in the sample,creating a transient photocarrier grating and the diffraction of a third time-delayed pulse on it mon-itors the washing out of the grating in time,which can beSample Emitter thickness Emitter doped,co-dopedPorous silicon formedNo.1p -type silicon wafer–No.20.5µm ∼2×1020cm −3n -type (P)–No.30.4µm ∼2×1020cm −3n -type (P)+No.40.4µm ∼2×1020cm −3n -type (P,Yb)+No.50.5µm∼1×1021cm −3n -type (P)–Table 1.Basic parameters of thesamplesFig.1.a A schematic sketch of the samples.b A scheme of light penetration for excitation with different wavelengths.PS,porous silicondue to both carrier recombination and carrier lateral diffu-sion.Single pulses of τL ∼40ps duration (FWHM)with a wavelength of 1.06µm were selected from a train of pulses produced by a mode-locked Y AG:Nd 3+laser.Frequency-doubled (0.532µm)or -tripled (0.355µm)pulses were split into two intense pump pulses of the same intensity I p .These two coherent pump beams impinge with an angle Θon the surface of the sample,writing a LIG in the direction parallel to the sample surface with a grating period Λ=λp /2sin (Θ/2),where λp is the wavelength of the pump beam.The grating period Λranged from 2.37µm to 20µm (Θ∼8.5◦and ∼1◦,respectively).Excitation intensities up to I p =6MW /cm 2were achieved using a pump spot diam-eter of 300µm.The short-wavelength excitation,which is497 more strongly absorbed in silicon,was employed in order tocreate the charge carriers just at the surface area(Fig.1b).In order to measure the decay of the LIG after excitation,a probe pulse of1.06µm wavelength(at which the samplesare transparent enough)and of sufficiently low intensity wasdelayed up to1000ps using an optical delay line.The inten-sity of the delayed diffracted probe pulse I pr was monitoredby a silicon photodiode.The LIG diffraction efficiencyη,defined asη=I pr/I p0,where I p0is the probe-pulse inten-sity,was evaluated.All experiments were performed at roomtemperature.It should be added that the approximation of a thin phasegrating for both cases of excitation is supposed to be valid,i.e.2π×λp×d/(Λ2×n) 1(d is the sample thicknessand n is the real part of the refractive index)and,in add-ition,the change of the complex index of refraction is suchthat|∆n| λp/(2π×d)(i.e.the phase modulation is small,Φ=2π×∆n×d/λp 1).In such a case a relationη(t)∼(Φ(t)/2)2∼∆n2(t)∼N2(t)(1)holds,which links the measured quantityη(t)with the solu-tion of the theoretical calculation.2Kinetic modelWe suppose that within the duration of the pump pulses,free electron–hole pairs with spatially modulated densityN(x,y,t)are created in the core of the n+layer(x-axis is per-pendicular to the sample surface and y-axis is parallel to thesample surface and corresponds to the grating alteration di-rection).Carriers may recombine or they can diffuse along thex and y coordinates.The temporal and spatial evolution of thephotoexcited carrier densities is described by following rateequation∂N(x,y,t)∂t =G+D ax×∂2N(x,y,t)∂x2+D ay×∂2N(x,y,t)∂y2−N(x,y,t)τd−B×N(x,y,t)2−C×N(x,y,t)3(2a)with boundary conditions as follows∂N(0,y,t)∂x =SD ax×N(0,y,t)(2b)N(x,y,0)=0(2c)∂N(x=d,y,t)∂x=0(2d)where G means the generation rate and D ax and D ay are the ambipolar diffusion coefficients of photocarriers for the direc-tions x and y,respectively.B and C are the coefficients of bimolecular and Auger recombination,respectively.τd stands for the corresponding linear recombination time and S is the surface-recombination velocity.We suppose that the diffu-sion coefficient is spatially invariant;thus,we use one value for all directions(D a=D ax=D ay).In order to reveal cor-rectly the surface-recombination velocity,we had to simplify the situation and to analyze two different cases:(i)relative ‘large-period grating’Λ L;and(ii)relative‘small-period grating’Λ<L(L is the diffusion length).In the case of the‘large-period grating’,the erasure of the grating is de-termined by carrier diffusion perpendicular to the surface with simultaneous recombination at the surface and in the bulk.Thus,the surface-recombination velocity as an import-ant parameter can be revealed from solving numerically(2a)–(2d).In this case,after separating the variables x and y,we obtain∂N(x,t)∂t=N0×(1−R)τL×exp(−α×x)×exp−t−t0τL×b2+D a×∂2N(x,t)∂x2−N(x,t)τd−C×N(x,t)3(3a)∂N(0,t)∂x=SD a×N(0,t)(3b) N(x,0)=0(3c)∂N(x=d,t)∂x=0(3d) where b=12√ln2andαand R are the absorption and reflectivity coefficients,respectively.Thefirst term in(3a)describes the generation rate in terms of the pump-ing pulse with Gaussian temporal widthτL and N0is the excess carrier concentration at time t0,i.e.the center of the Gaussian temporal profile.Because of an indirect band gap semiconductor case where Auger recombination pre-vails over the bimolecular one,we have neglected the bi-molecular recombination term in(3a).Thus,two free pa-rameters enter(3a)–(3d):D a and S.To solve this equation,first we have to get the diffusion coefficient.For that we have used the second case,i.e.the‘small-period grating’, where the grating erasure is defined by carrier diffusion (along the surface).According to that,(2a)–(2d)was modified as∂N(y,t)∂t=G+D a×∂2N(y,t)∂y2−N(y,t)τd−C×N(y,t)3.(4) Taking into account that our experiment gives information on the temporal evolution of the diffraction efficiency,i.e.the photocarrier density,the variables y and t can be separated and(4)can be rewritten in the formd N(t)d t=N0×(1−R)τL×exp−t−t0τL×b2−N(t)τl−C×N(t)3(5) with a linear grating decay timeτ−1l=τ−1d+D a×4π2/Λ2, which includes the diffusive decay timeΛ2/(4π2×D a).The498solution of(5),convoluted with the probe-beam temporal profile,is used for simulating the LIG decay curves meas-ured for differentΛ.Plotting in the usual wayτ−1l against4π2/Λ2,from the slope we extract the value of the am-bipolar diffusion coefficient D a.Finally,while returning to the‘large-period grating’case,from the bestfit of meas-ured dynamic grating kinetics using(3a)–(3d)and the ob-tained value of D a,the surface-recombination velocity can be extracted.3Experimental results and discussionThe diffraction of the probe beam on the LIG can be de-scribed in the framework of third-order non-linear opti-cal phenomena[4],entailing the proportionalityη∼I2p. Therefore,first of all we have studied the diffraction efficiencyηas a function of I p in order to check the ex-pected quadratic law.For all measured samples,a quadratic dependence was observed over more than one order of mag-nitude of I p.The excitation intensity we have used for pumping the sample was I p=6MW/cm2.We have used as low as possible excitation intensity in order to be sure of avoiding Auger-recombination domination,but at the same time,keeping a sufficient signal/noise ratio.Nevertheless, in bulk Si,at high carrier concentration the Auger colli-sion process dominates the recombination event through intermediate recombination centers(Shockley–Read–Hall mechanism)and the radiative recombination,which is less efficient in indirect semiconductors.Therefore,in order not to lose the whole competition of the processes involved, we have kept the Auger-recombination term in our calcu-lation.In the case of Auger domination,no differences in the kinetics of samples with different surface quality should be observed.We exclude Auger collisions with localized carriers.However,we would like to make a remark concerning light absorption in porous silicon itself.Of course,there was some absorption.But it is not included in our calculation, taking into account the relative small thickness and absorp-tion coefficient of the porous-silicon layer(smallα·d)and considering that it gives negligible input into the diffracted signal compared to the light absorbed by single crystalline silicon.(The absorption coefficient at355nm wavelength is more than ten times higher for crystalline silicon as for porous silicon[9].)First,we start with the‘small-period grating’case.The re-sults of grating dynamics of all samples excited by355nm wavelength and measured for several values ofΛ=2.37,3.1, 5.34and9.01µm are displayed in Fig.2.Values ofτl were obtained from the linear part of the grating decay in time-resolved diffraction efficiency measurements.Thus,from the slope we extract the value of the ambipolar diffusion coef-ficient D a.Independently,linear grating decays in different samples reveal an average value of ambipolar diffusion coef-ficient of7cm2/s,except for some deviation for sample no.3 with a compromised value of4cm2/s.These values are in good agreement with the generally anticipated diffusion coef-ficients of crystalline Si[10].The second and most important‘large-period grating’case(Λ=20µm),when studying photocarrier diffusion in the x direction with consequent evaluation of thesurface-Fig.2.The linear grating decay-time dependence on the grating period.Plot ofτl against4π2/Λ2for the three samples with different emitters.Excita-tion quantum energy is3.51eV.The slope yields the value of the diffusion constant D arecombination velocity,was performed at two different exci-tation wavelengths,i.e.LIGs penetration depths.The second and third laser harmonics used for pumping,with correspond-ing absorption coefficientαvalues of approximately104and 105cm−1for silicon[9],formed gratings of1and0.1µm thickness,respectively.For brevity,in the text below we will use‘bulk LIGs’and‘surface LIGs’for gratings having the two penetration depths,respectively.The decays of diffraction efficiencyηmeasured for all samples at two different excitation wavelengths,together with the numerically calculated decay curves obtained on the basis of(1)and(3),are displayed in Fig.3a–e.Parame-ters entering(3)are N0,R,τL,τd,t0,α,D a,C and S.The only free parameter is,however,S,because D a=7cm2/s as we have already obtained,the value of N0is propor-tional to the total number of photocarriers created during the pump-pulse excitation and corresponds to the average non-equilibrium concentration1.5×1019cm−3,τd=1µs as a fastest lifetime limit for crystalline silicon[11],the value ofτL=40ps is given by our pumping laser,t0= 50ps and the value of the Auger-recombination coefficient C=4×10−31cm6/s[11]and reflectivities R=0.58(at 0.355µm),R=0.35(at0.532µm)are known for crys-talline silicon.Crucial messages from these measurements are:(i)the curvesfit satisfactorily the experimental points be-longing to the“surface LIGs”,but they fail to follow the experimental points of the“bulk LIGs”;(ii)in the case of“bulk LIGs”,the kinetics are relatively slow with almost single-exponential decays;(iii)in the case of“surface LIGs”,the experimental points proceed in a non-exponential decay for all measured samples.“Surface LIGs”are more efficient for interpreting the re-sults than“bulk LIGs”,when taking into account the shal-low emitter.In the latter case,the excitation depth exceeds the p−n+junction and,consequently,gives rise to an ad-ditional photocarrier-redistribution process just at the deple-499 Fig.3a–e.The grating dynamics measured at two different excitation quantum energies(open circles,2.34eV;filled circles,3.51eV).The points areexperimental values,the lines are theoretical modeling according to(3a)–(3d).Eachfilled area corresponds to a series of kinetics calculated withD a=7cm2/s intermediate values of the surface-recombination value S(also presented in eachfigure).Dashed curve in c calculated using D a=4cm2/s and S=1.3×105cm/stion region of the junction.An internal electricfield in the junction created by photocarriers(a function,typical for so-lar cells)would diminish the resultantflow from surface to junction.Slow kinetics of“bulk LIGs”are governed by recombina-tion at the junction,including the depletion region.The slow-est one,measured for sample no.1(sample without junction), supports this interpretation.In this case,the LIGs penetra-500tion factor does not influence the kinetics and gives a rather good coincidence of experimental and calculation data for both excitation wavelengths.This differs for the samples with junction.The non-exponential decay of “surface LIGs”indicates domination of surface-recombination with carrier diffusion from the ually,in picosecond “surface LIGs”,the surface-recombination influences washing out of the LIGs till ∼400÷500ps after excitation.Further decay is mainly governed by carrier recombination in the bulk.Moreover,from the simulation of photocarrier-concentration dynamics we have obtained that after ∼400ps the first carriers reach the junction region.Then,the boundary conditions used for solving (3)are no longer valid.This is quite well expressed in our figures,where starting ∼400ps after excitation,the theoretical curves deviate distinctly from the experimental points.The values of surface-recombination velocity S obtained from theoretical simulation are summarized in Fig.4.Low-est values of 0.7÷1×105cm /s were obtained for sample no.1,the starting material of solar cells (p -type silicon wafer with polished surfaces).After forming the emitter and changing the type from p to n ,higher S values with in-creasing phosphorus-doping concentration were obtained.The highest values obtained in our experiments ranged up to 3.2×105cm /s for a doping concentration of 1021cm −3.These values correspond very well with the results presented by King and co-workers for both n -type [12]and p -type [13]highly doped silicon,and also with the very recent results ob-tained by Cuevas et al.[14]on phosphorus-diffused n -type silicon with values in a range around 2×105cm /s.Never-theless,our main attention was focused on the modification of surface-recombination velocity in the emitter with porous silicon.We found that porous silicon diminishes the recom-bination velocity from 1.6÷2.2×105cm /s (before porous-silicon formation –sample no.2)to 1.3÷1.7×105cm /s (after porous-silicon formation –sample no.3).In order to remove the uncertainty while evaluating the precise value of the diffusion coefficient for sample no.3,in Fig.3c we have depicted additionally a curve calculated using D a =4cm 2/s and S =1.3×105cm /s.Then,when trying to get the best fit,we had to lower the range of S values to 1÷1.4×105cm /s1x102x103x104x10SamplesS ,c m /sFig.4.The extracted surface-recombination velocities for all samples meas-ured.Bold values calculated using D a =4cm 2/sin the calculation.This tendency is in line with our previ-ous expectations made on similar samples [7].Differently from our former results,some increase in S was obtained when comparing the phosphorus /ytterbium-doped sample (sample no.4)to those only phosphorus-doped (sample no.3)(Fig.4).But in both cases the surface-recombination velocity value becomes lower after porous-silicon-layer formation.We consider porous silicon as a partially interconnected network of Si nanocrystallites with typical dimensions of 3÷5nm.It is well known that the interior of the nanocrystal-lites preserves the silicon crystalline structure,but there is a lot of localized states (tail states)near the band edge of porous silicon,originating probably from perturbed bonds near to the surface.So,the interpretation of reduction of the surface-recombination in the emitter covered by porous sili-con could be threefold.First,a part of the natural defects at the surface can be removed while etching.Second,surface passivation by hydrogen coverage of the surface bonds can take place.Third,a lot of localized states formed in porous silicon are efficient at capturing carriers [15–17],thus,af-terwards acting as a repulsion barrier for the photoexcited carriers.4ConclusionsLIG experiments performed at room temperature with a pi-cosecond time resolution on a series of samples typical for several successive operations of solar-cell technology,i.e.different doping and surface preparation of the emitter,revealed a tendency of surface-recombination velocity in-crease with doping concentration.Porous silicon formed on the emitter surface has modified the trap distribution bal-ance while influencing the surface-recombination velocity decrease.This result confirms the fundamental prediction of surface passivation by the porous phase of the material.It is important for solar-cell technologists,who will use this quality of porous silicon as a tool for improving the solar-cell efficiency.Our observations are based on an analysis made by a model involving carrier diffusion from the sur-face and recombination at the surface /in the bulk of the emitter.Acknowledgements.This work was supported in part by NATO Linkage Grant no.HTECH.LG972051and by a grant from the Lithuanian State Science and Studies Foundation.References1.L.Canham:Appl.Phys.Lett.57,1046(1990)2.L.Stalmanis,ureys,K.Said,M.Caymax,J.Poortmans,J.Nijs,R.Mertens,S.Strelke,C.Levy-Clement,L.Ventura,A.Slaoui,G.Bre-mond,A.Daami,ugier:Proc.14th Eur.Photovoltaic Solar En-ergy Conf.,Barcelona,Spain,June 30–July 4,1997(Stephens,Bed-ford,UK 1997)pp.2484–24873.V .Paˇc ebutas,K.Grigoras, A.Krotkus:Phys.Scr.,T.69,255(1997)4.H.J.Eichler,P.Günter,D.W.Pohl:Laser-Induced Dynamics Gratings (Springer,Berlin 1986)5.R.Tomasiunas,I.Pelant,J.Kocka,P.Knapek,R.Levy,P.Gilliot,J.B.Grun,B.Hönerlage:J.Appl.Phys.79(5),2481(1996)6.K.Grigoras,V .Paˇc ebutas,J.Sabataityt˙e ,I.ˇSimkien˙e ,ardauskas,E.Gaubas,J.Härkönen:Phys.Scr.,T.79,236(1999)5017.K.Grigoras,A.Major,I.ˇSimkien˙e,E.Gaubas:Semicond.Sci.Tech-nol.13,517(1998)8.K.Grigoras,V.Paˇc ebutas:Rev.Sci.Instrum.67,2337(1996)9.See, e.g.,V.Grivickas,P.Basmaji:Thin Solid Films235,234(1993)10.See,e.g.,J.Linnros,V.Grivickas:Phys.Rev.B50,16943(1994)11.See,e.g.,V.Grivickas,M.Willander:Properties of Crystalline Sili-con,ed.by R.Hull(EMIS Datareviews20)(INSPEC,London1999) Chapt.13.5,pp.710–71712.R.R.King,R.A.Sinton,R.M.Swanson:IEEE Trans.Electron Devices37,365(1990)13.R.R.King,R.M.Swanson:IEEE Trans.Electron Devices38,1399(1991)14.A.Cuevas,P.A.Basore,G.Giroult-Matlakowski,C.Dubois:J.Appl.Phys.80,3370(1996)15.P.M.Fauchet,Y.Kostoulas,J.V.Vandyshev,V.Petrova-Koch:Ultra-fast Phenomena IX,ed.by P.F.Barbara,W.H.Knox,G.A.Mourou,A.H.Zewail(Springer,New York1994)16.J.von Behren,K.B.Ucer,L.Tsybeskov,J.V.Vandyshev,P.M.Fauchet:J.Vac.Sci.Technol.B13,1225(1995)17.R.Tomasiunas,J.Moniatte,I.Pelant,P.Gilliot,B.Hönerlage:Appl.Phys.Lett.68(23),3296(1996)。