Contactless Determination of Minority-Carrier Lifetimes ... - LSI - USP

Contactless Determination of Minority-CarrierLifetimes by Photoconductance MeasurementsCarlos A. S. Ramos a) and Manuel Cid SánchezLaboratório de Microeletrônica - Departamento de Engenharia de Sistemas Eletrônicos - PSIEscola Politécnica da Universidade de São Paulo. P.O. Box. 61548Zip Code 05424-970, São Paulo/SP, Brazil.a)cramos@lme.usp.br, mcid@lme.usp.br.AbstractLifetime measurements of minority carriers in siliconwafers are extremely useful for process control anddevice optimization as well as for the study of physicalproperties of the material. The use of the WCT-100lifetime tester apparatus, described here, allows a fastand easy to use method to determine the sampleparameters, without the need of complex electronics andlight sources, being capable to measure lifetimes in thenanosecond to millisecond range.Also, it is possible to investigate the injection leveldependence of the lifetime over a wide range of lightintensities, from 0 to 1000 suns, simply varying theposition of the source relative to sample. This allowstheoretical fittings of the obtained results, in order toextract parameters such as energy and density of defectsin the gap.1. IntroductionContactless measurements of minority carrier lifetimes, anon destructive method obtained by means of quasisteady-statephotoconductance (QSSPC) data [1] [2] [3],has been widely used in investigations of materialproperties and process control.The WCT-100 uses a coil to inductively couple thesample signal to an digital oscilloscope and amicrocomputer for data analyses and storage (figure 1).The QSSPC technique measures the photoconductanceof a sample subjected to a relatively long (~2ms – steadyor quasi-steady-state illumination) light pulse, generatedby a flash lamp, an array of light-emitting diodes (LEDs)or another source.Under this condition, the photogenerated excess carrierdensity, ∆n=∆p, results in an increase in waferconductance given by:∆ σL= ( µ n ∆n+ µ p ∆p)qW= q∆n(µ n + µ p )W (1)where W is the wafer width, µ n and µ p are the carriersmobilities.Also, the generation and the recombination rates must bebalanced, leading us to:Jphotogeneration=Jrecombination (2)In terms of effective minority carrier lifetime we have:J ph =q∆nW/τ eff (3)Combining equations (2) and (3), we can obtain anexpression for determining the effective lifetime of theminority carriers:τ eff =σ L /[J ph (µ n +µ p )] (4)In the WCT-100 the conductance is measured through acalibrated RF bridge, after zeroing the signal of thewafer over the inductive coil, and the light intensity bymeans of a reference solar cell, located near the sample.Inductive CouplingRFFlash LampSample WaferCRMicrocomputerOsciloscopeFig. 1: WCT-100 sample signal acquisition scheme.Since the RF bridge circuit, operating in a frequency of8-10Mz, is well designed, the output voltage and thewafer sheet conductance follow a linear relationship, in arange that depends on the circuit topology (in our casefrom 0.02S to 0.3S). The variable resistor/capacitor areused to balance the bridge to zero, prior to themeasurements.The value of J ph measured by the reference solar cellshould also be modified, taking in mind the conditions ofour particular sample like thickness, reflectivity or lighttrapping features. Even considering all these cases, thephotogeneration in the sample should lie in a thigh rangebetween 0.8-1.1 of that measured by the reference [4].In this way, the effective lifetime is measured at everylight intensity, following the procedures and equationsoutlined above.In order to obtain a more accurate value of the minoritycarrier lifetime it is necessary to separate the bulkcontribution from the surface effects, by means of a

Sample ρ bulk(Ωcm)Thickness(µm)τ eff(µs)FZ50-B 50.0 300 3672FZ 0.47 350 99FZ 0.90 402 275CZ 1.40 345 255Table 2: Effective lifetime for samples subjected to a lightphosphorous diffusion step at ∆n=10 14 cm -3 .Roughly, we can use the direct measurement of theeffective lifetime at a specified carrier density todetermine the degradation of a wafer after eachfabrication process. From the data of table 1 and 2 it canbe observed, that the effective lifetime measured forwafers subjected to a different processes, does not showa significant dispersion.As explained above, the value of J 0 , obtained from thefitting in the graph of figure 4, imposes some limits inthe measurable lifetime depending on the resistivity ofthe wafer, with the higher doping densities placing amore stringent limit.This limit (τ eff→lim =qni 2 W/J 0 N A ) is showed in the table 3,with the experimental lifetimes measured from the figuregraph of the figure 3.Using qni 2 =11.75C/cm 6 and J 0 =3.6x10 -14 A/cm 2 , wehave:Sample ρ bulk(Ωcm)τ eff →∆n=10 14 cm -3(µs)τ eff →J 0 lim.(µs)FZ50-B 50.0 3672 18268FZ 0.47 99 164FZ 0.90 275 338CZ 1.40 255 548Table 3: Experimental measurements and expected limitsto the measurable lifetime imposed by emitterrecombination.By the results presented, we see that the effectivelifetime measured for the high resistivity sample can beinterpreted as a true reflection of τ bulk . The surface is nota limiting factor for determining his value.In the other way, since the contribution due to J 0 is in thesame order as the measured τ eff for the other samples, theevaluation of τ bulk becomes impossible. A betterpassivation (J 0 bellow 10 -14 A/cm 2 ) would be required fora direct measurement on these samples [8] [10].3. ConclusionsIt was presented a powerful method to examine the bulkand surface conditions of samples subjected to adifferent processes.By means of photoconductance measurements, it ispossible to study various mechanisms present in asemiconductor and their characteristic parameters, suchas bulk lifetime, surface recombination and emitterrecombination current in a wide range of injection levelconditions.Specific experiments can be prepared in order toinvestigate any phenomena of interest, and the results arefast and easily handled or fitted by any modelinvestigated.The QSSPC has also a numerous applications forprocess monitoring during solar cell fabrication, sincethe substrate and passivation quality can be evaluated forindividual fabrication steps, beginning with the initialmaterial quality, without the necessity of metalliccontacts.This method is simple and the data have a clear physicalinterpretation, being capable to measure high to very lowlifetimes with the same apparatus.Not presented here, but of great interest, is the possibilityof predicting the open circuit voltage (V oc ) of solar cellsprecursors, for each step of processing.As additional advantages we can say:- The light source is inexpensive, since has no specialrequirements for short duration or sharp cut-off;- Even measuring lifetimes less than 1µs, the dataacquired is from a 2.3ms decaying waveform,eliminating the fast electronics required for a transientdecay measurement;- The result depends upon the absolute value of a smallsignal, rather than its derivative;- Ranging the applicability, it is effectively a steady-statemeasurement, similar to the cell in actual operation.3. AcknowledgmentsThis work was supported by FAPESP, under contract n o95/09435-0 and by Rhae/CNPq under contract n o610157/94.References:[1] Ronald A. Sinton, Andrés Cuevas; Appl. Phys. Lett. 69(17), 21 October 1996, p. 2510.[2] Andrés Cuevas, Ronald A. Sinton; Prog. in Photovoltaics:Research and Applications, Vol. 5, (1997).[3] Jan Schmidt, Andrés Cuevas; Journal of Applied Physics,Vol. 86, n o 6, September 1999, p. 3175.[4] User Manual - WCT-100 Photoconductance Tool – revisedversion 1998 – Sinton Consulting 1132, Green CircleBoulder , CO 80303.[5] E. Yablanovitch, et. al.; Physical Review Letters, Vol. 57,n o 2 – July 1986, p. 249.[6] Richard R. King et. al.; 22 nd IEEE Photovoltaic SpecialistsConference, Las Vegas, NV, October, 1991.[7] Andrés Cuevas; Solar Energy Materials and Solar Cells,Vol. 57 (1999), p. 277.[8] D. E. Kane, R. M. Swanson; 18 th IEEE PhotovoltaicSpecialists Conference, Las Vegas, NV, October, 1985.[9] D. Macdonald, Andrés Cuevas; Applied Physics Letters,Vol. 74, n o 12, March 1999, p. 1710.[10] Andrés Cuevas et. al.; IEEE Transactions on ElectronDevices, vol. 46, n o 10, October 1999, p. 2026.[11] Dieter K. Schroder; Semiconductor Material and DeviceCharacterization, “A Wiley-Interscience publication” ,ISBN 0-471-51104-8, 1990, pp.359-447.