Carrier lifetime measurements from transient electrical

photoresponses

D.M. Bielle-Daspet, A.M. Johan, F. Espioussas

To cite this version:

D.M. Bielle-Daspet, A.M. Johan, F. Espioussas. Carrier lifetime measurements from tran-sient electrical photoresponses. Revue de Physique Appliquee, 1980, 15 (2), pp.219-227.<10.1051/rphysap:01980001502021900>. <jpa-00244718>

HAL Id: jpa-00244718

https://hal.archives-ouvertes.fr/jpa-00244718

Submitted on 1 Jan 1980

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

219

Carrier lifetime measurements from transient electrical photoresponses

D. M. Bielle-Daspet, A. M. Johan and F. Espioussas

Centre d’Etude Spatiale des Rayonnements, B.P. 4346, 31029 Toulouse Cedex, France

Résumé. 2014 Les durées de vie mesurées à partir des photoréponses de conductivité (sous courant ou tension cons-tants de polarisation), de courant de diffusion et de tension de circuit ouvert, créées par excitation transitoire deporteurs, sont considérées. Partant des expressions analytiques, la discussion porte sur les expressions clef, lesconditions de validité et les applications de chacune des méthodes discutées, en supposant une excitation uni-forme de porteurs dans un échantillon unidimensionnel et homogène; la discussion tient compte des caracté-ristiques de l’échantillon (épaisseur W, durée de vie volumique 03C4v, vitesses de recombinaison aux surfaces s1,2,coefficient de diffusion D des porteurs minoritaires et densité d’équilibre en porteurs majoritaires p0), de la densitéde porteurs en excès 0394p, de la durée T de l’impulsion lumineuse et des temps t auxquels la réponse est considérée.L’étude expérimentale porte surtout sur des échantillons de silicium d’épaisseur jusqu’à 1 mm, éclairés par desimpulsions laser de durée T = 2 à 30 ns. Les réponses à une lumière pénétrante (03BB = 1,06 03BCm, 03B1 = 40 cm-1dans le silicium usuel; 0394p = 10-4 à 102 p0) et à une lumière fortement absorbée (03BB = 0,69 ou 0,53 03BCm, 03B1 = 2 x 103et 104 cm-1 ; intensité du faisceau E0 = 10-4 à 103 mJ/cm2) sont utilisées pour montrer sous quelles conditionsles photoréponses observées conduisent aux mêmes valeurs mesurées de la durée de vie des porteurs, et donnentune mesure de leur durée de vie volumique.

Abstract. 2014 Carrier lifetime measurements from photoconductivity (with constant current and constant voltagepolarizations of the sample), diffusion photocurrent and open circuit photovoltage responses to transient carrierexcitation are compared. Using analytical expressions, the key expressions, conditions of validity and applica-tions of each method are discussed, assuming uniform carrier injection in an unidimensional sample of homo-geneous material; the discussion is done taking into account the sample characteristics (width W, bulk lifetime 03C4v,surface recombination velocities s1,2, minority carrier diffusion coefficient D, equilibrium majority carrier den-sity p0), excess carrier density 0394p, light pulse duration T and times t of the response considered. The experimentalstudy especially deals with silicon samples up to W = 1 mm thick, illuminated by T = 2 ns to 30 ns laser beams.The responses to penetrating light (03BB = 1.06 03BCm, 03B1 = 40 cm-1 in ordinary silicon, 0394p = 10-4 to 102 p0) andstrongly absorbed light (03BB = 0.69 or 0.53 03BCm, 03B1 = 2 x 103 and 104 cm-1, beam intensity E0 = 10-4 to103 mJ/cm2) are used to show the conditions under which the photoresponses observed lead to the same measuredvalues of carrier lifetime and give bulk lifetime measurement.

Revue Phys. Appl. 15 (1980) 219-227 FÉVRIER 1980, PAGE

Classification

Physics Abstracts07.50 - 72.40

1. Introduction. - The minority carrier lifetimeand mobility are the most important factors affectingthe conversion efficiency and spectral response ofsolar cells. And, among them, the minority carrierlifetime is the most sensitive to the cristal defects ofthe component. This is the reason why special attentionis devoted to this electrical parameter in variousworks applying to solar cells. With this view, weundertook studies on the possibilities of directcarrier lifetime measurements that the transientelectrical photoresponses can give, taking into accountboth the low carrier injection range (where usualmeasurement methods generally apply) and the higherinjection one which is involved in solar cells usedunder concentrated sunlight.

In a previous paper [1] we already discussed themeasurement possibilities which are given by thetransient short-circuit current and open-circuit voltage

RIVED 1 1)1 PH’" SIQU APPTIQI l 1 5, N° 2, Il VRIER 1980

responses to caracterize the minority carrier lifetimein the base and emitter regions of a device. Thepurpose of the present paper is larger : the studydeals with the various transient electrical responses,which are viewed as a whole and with the aim of mea-

suring carrier lifetime in material as well as in devicesamples. In the following, the conditions of validityand the respective advantages of the photoresponseswill thus be compared taking into account (i) thesamples caracteristics (resistivity, dimensions, ...)(ii) the carrier excitation level used and (iii) the

excitating light wavelength employed for the experi-ment.

Indeed, the transient electrical photoresponsesgive a group of methods for measuring the carrierlifetime, in which the carrier lifetime is found directlyfrom the decay (or increase) of voltage or currentsignals [2]. These photoresponses and associated

15

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:01980001502021900

220

methods are based on either the variation in conduc-tivity produced by both electrons and holes inducedin excess in the sample [3, 4] - photoconductivitymethods using voltage (1) 0394V03C3(t) or current AI,(t)signals depending on whether the sample studied isunder constant polarization current or voltage -, oron the diffusion of only the minority carriers inducedin excess in the sample - diffusion current

method [5, 6] or even open-circuit voltage methods [7,8]. Viewed as a whole, the above methods (’) thenmay have the advantages of covering various samplestructures, including devices at their successive manu-facturing stages, and of being utilizable with a singleexperimental set up.

But, although transient electrical photoresponsestend to be commonly used today for measurementsof carrier lifetimes, they are generally used indivi-dually, on samples differing in type and/or struoture,and under low carrier injection level conditions.

Moreover, only for method using the variation in

conductivity has the theory been well establishedfor a long time ; method using the minority carrierdiffusion has been used more recently [1] and is lessknown especially from the point of view of its condi-tions of validity for measuring carrier lifetimes.The following study will thus attempt first of all to

compare the key expressions and conditions of

validity of each of the above methods, starting withthe existing analytical studies of transient photo-responses for uniform carrier injection in an homo-geneous sample [3, 6, 7, 8] (Section 2.1). This makes itpossible to compare the characteristics of eachmethod considered and to estimate its possibility ofapplication under weak and strong carrier injectionconditions (Section 2.2).

In Section 3, the above synthesis is compared withexperimental results, in particular results obtained

by applying the various methods to the same sample.The experimental study will also attempt to find thelimits within which these methods remain applicablein practice, particularly towards high carrier injectionconditions and as a function of the coefficient of

absorption of the photon pulse. Using the laser pulseexcitation technique, the possibilities and limitationsof the above methods are illustrated especially in thecase of bulk samples of silicon, considering the

photoresponses induced by penetrating 1.06 ym lightpulses and the photoresponses induced by pulses ofstrongly absorbed 0.53 pm or 0.69 gm light.

(1) The photoconductivity method using the L1 Va(t) signals,or photoconductivity decay technique, is the standard method for

measuring carrier lifetime in bulk semiconductors such as ger-manium and silicon. This standard method is described in the 1971Annual Book of A.S.T.M. Standard n° 8, p. 476.

(2) In this paper, we will not consider (i) the possibility of carrierlifetime measurement by means of transient secondary photocurrent,which may be used for measuring carrier lifetime in the base of abipolar transistor structure [7] ; (ii) the high injection effects on theelectrical properties [10].

2. Expressions for transient electrical photoresponsesand conditions of validity of the associated carrierlifetime measurement methods. - The electrical pho-toresponse expressions are obtained by solving thecontinuity and transport equations of the carriersand by taking into account the sample boundaryconditions. The detailed calculations for uniform

photoexcitation at weak carrier injection levels aregiven in references [3, 6] and [8] for the transientphotoconductivity, diffusion photocurrent and opencircuit photovoltage, respectively.The purpose of the following analysis is to sum-

marize the assumptions on which the electrical

photoresponse expressions are based, and to showunder what conditions these expressions, which areof the form of a sum of harmonics of order k due tothe sample boundary conditions, can be reduced to arather simple form which can be used as a carrierlifetime method. The key expressions, conditions ofvalidity and applications of the methods are thendiscussed from a comparative point of view.

2. 1 ELECTRICAL PHOTORESPONSE EXPRESSIONS. -

The electrical photoresponse expressions given beloware based on the usual hypotheses concerning semi-conductor N or P regions : (i) unidimensional,(ii) homogeneous, with negligible electric field,(iii) subjected to a uniform and weak enough carrierinjection so as not to alter appreciably the equilibriummajority carrier density, i.e. electric field and averagefilling rate of the band-gap energy levels, and (iv) cha-racterized by constant values of the N or P regionparemeters W (thickness), 03BCn,p or Dn,p (electronand hole mobilities or diffusion coefficient), r, (bulkcarrier lifetime) and boundary conditions SI,2 (surfacecarrier recombination velocities at x = 0 and W).

Because of the transient carrier excitation condi-tions dealt with in this paper, the photoresponseexpressions also assume (v) that the excitation pulseduration T is small [6] compared to the effectivecarrier lifetime t (carrier lifetime taking into accountthe material bulk carrier lifetime T, as well as the

parameters W, ,un,p, S1,2 of the N or P region), (vi) car-rier trapping phenomena (3) [11, 12] are negligible inthe sample under study, and (vii), if carrier recombi-nation occurs via recombination centers, the recombi-nation center density is small enough (3) so that theneutral and negatively charged recombination centerdensities remain negligible compared to the totalcarrier quantities (no + nl) and (po + pi) respectivelyin the sample, where the symbols no, po, n1, p 1 havetheir usual meaning [11].

(3) In all the carrier lifetime measurement methods, injection ofexcess carries must be accomplished. In all cases, thèse excesscarriers consist of electron-hole pairs produced, in addition tothose present at equilibrium, either directly by means of band-to-band excitation or due to over-all electrical neutrality following acarrier contact injection. For the transient injection case [11],

221

2.1.1 Expressions for conductivity photoresponses. - Let us

assume a P type sample and equilibrium conductivity a. Thephotoconductivity responses â Va(t) and MJ:(t) which refer toconstant current and constant voltage conditions (Fig. la), res-

pectively, are based on the variation in conductivity àa(t) in theilluminated volume under the effect of àn(t) = àp(t) excess elec-trons and holes created. The detailed study of àa(t) is done inref. [3] and gives the following full and simplified expressions :

with [1] :

F ig. 1. - Principle of the transient electrical responses of photo-conductivity (a), diffusion photocurrent and open circuit photo-voltage (b) (equipotential surfaces normal to carrier current flow).

a readjustment time -rl of the charges at the recombination centersis necessary before the conditions of equal capture rate of electronsand holes are satisfied. At times t &#x3E; re, the lifetimes of electronsand holes are identical under transient conditions. But only whenthe hypothesis (vii) is satisfied is Tch negligible compared withelectron-hole transient lifetime and is the transient carrier lifetimeidentical to the minority carrier steady-state lifetime, especiallyunder weak carrier injection.When trap centers exist in the sample, and if the injected carrier

density is not large compared with the trap density, the time thatthe trapped carriers spend in the traps induces an apparently longdecay constant of the excess carriers [11, 12].

where D = D. is the minority carrier diffusion coefficient and (kis the solution of :

cotg (çn/2) - (çnD/sW) = 0. (4)

If s « 2 DI W, expression (4) admits the solution 03BEk = 2(k - 1),k = 1, 2, 3, ..., so that :

The harmonics of order k &#x3E; 1 therefore have an amplitude Rkand time constant ’Cak very small compared to R1 and 03C403C3, and decreas-ing as k increases. The same is true if s » 2 D/W, a conditionwhich includes Çk = 2 k - 1, with R21R, and 03C403C32/03C403C31 # 1/9.

Expression (1) for àa(t) can therefore be written in the form :

and

2.1.2 Expressions for diffusion photocurrent iD(t). - Only theminority carriers àn(t) from illuminated neutral regions are concem-ed in this photoresponse due to the carriers’ability to reach andcross a collection zone (a zone which is equivalent to a large recombi-nation velocity s, boundary (4)), such as an n+ p junction (Fig. lb).

Unlike the previous photoresponses based on the conductivityvariation, the iD(t) response involves a major contribution from thek &#x3E; 1 harmonics [6] (1). Because of this contribution, the expressionfor ip(t) may, for large enough sl, be written as :

Xk depends on the recombination velocity S2 on the back side :

Depending on whether the values of the product txf= are large orsmall with respect to one, expression (10) is reduced to either ofthe two following simplified forms [6] :

or

(1) With respect to reference [6], s, = wD, d = TG and

Xf = Zf /Tv.From the study of référence [6], the given expressions for iD(t)

appear valid as soon as fi is large compared with unity, i.e., SI largecompared with the minority carrier diffusion velocity vn inside thesample.

222

2.1.3 Expressions for open-circuit photovoltage v.(t). - Theopen-circuit photovoltage responses veo(t) developed across thecollecting zone obey the collecting zone current equation :

where

and

Here, Ih,(t) is the total induced photocurrent, due to the excesscarriers which can be created both in the neutral regions (i.e. dif-fusion current) and in the collecting zone itself. VAo and VI. are theequilibrium applied voltage and collecting zone voltage, respectively,and C is the collecting zone capacity C(VI). In the case where thecollecting zone is a pn junction, I(VA) is given exactly by :

where Io is a constant.The analytical expressions of the transient photoresponse vco(t)

are discussed in ref. [8]. This study shows that in this type of photo-response the collection zone time constant and the minority carriersof the two regions bordering this zone play an important part.However, for just this reason, the analytical expressions for vco(t)remain cumbersome. As the purpose of the present study is to

compare the conditions under which the photoresponses may bereduced to simpler forms to provide a method for measuringcarrier lifetime, the following study will consider the photoresponsesin those cases which lend themselves to a simplified formulation [1].2.1.3.1 Under the effect of Ihv(t). - Expression (16) shows

that the induced response vcoCt) increases and is only described bya simple expression if, at the times t considered, the conditions beloware satisfied :

and

where K is a constant.At times t &#x3E; t’ where the diffusion of a single type of carrier

dominates, the vco(t) responses then obey :

where iD(y &#x3E; t’) = Ihv(y &#x3E; t’) is given by (14) or (15).From (22), the increase in v co(t) is then, under the conditions

in expression (14) i.e, if long enough times tare considered :

When iD(y &#x3E; t’) is given by (15), only the variation with t of thederivative of the expression (22) may be reduced to a simple form,if short enough times t are considered :

2.1.3.2 When /hv is zero. - The simplest way of studying thephenomena which may e i-nvolved in the decay of UcoM is to usethe charge controlled model. This model gives a quasistatic approxi-mation valid in first order. Expression (16) then becomes

with

where QN+ and Qp represent the charges stored on either side of thecollection zone.

Such a study is done in detail in reference [5] for the case wherea collection zone can be assimilated with an ideal p-n junction.This implies in particular that (i) the carrier recombination is

negligible both inside the collecting zone and on its surface channelsand (ii) the collecting zone behavior is dominated by carrier diffusionprocesses such as I(VA) is described by expression (19) with

QN+o and Qp. are the reference charges of the N+ and P regions oneither side of the collection zone. The lifetimes iN+ and 03C4P inexpression (27) are the operative lifetimes of the minority carriersof the N+ and P regions, and may take into account the variousphenomena which can intervene in this minority carrier transport,e.g., the high doping and doping profile effects in a diffused N+region.For VA » kT/q = UT, expressions (19), (27), and (28) then lead

to a linear vco(t) decay of the form :

where

However, when VA # vco(t) UT, the vco(t) response decreasesexponentially according to :

2.2 COMPARED ASPECTS OF THE CARRIER LIFETIMEMEASUREMENT METHODS USING TRANSIENT PHOTORES-

PONSES. - The above analysis makes it possible to seethe conditions of validity and key expressions onwhich the carrier lifetime measurement methods

using the transient photoresponses are based. Assum-ing hypotheses (i) through (vii) are satisfied :

a) Expressions (7), (8) and (9) indicate that thedecrease in conductivity responses (Fig. la) is

governed by a time constant r,. This lifetime La is

essentially a function ofparameters Ty, W, s1,2 of thesample, and last r, if W/2 s r, when s, # s2 = S.

b) The diffusion photocurrents lend themselves tothe measurement of the carrier lifetime when theycan be describeg by expressions (14) or (15) : depend-ing on the time t of the decrease of the responsesconsidered, and depending on the parameters D, W,ïy, si, s2 of the diffusion region studied, expressions(14) and (15) therefore show that the lifetimes 03C4i or T,are given by the time constant of the response

iD(t &#x3E; tl) or the time constant of the productiD(3 T t t 1). Jt, respectively [6]. In addition,it should be noted that the use of expressions (14)and (15) above assume that the total current Ihv(t)given by the collection zone is, at the times t &#x3E; t’

studied, dominated by the diffusion of excess minoritycarriers from a single edge region

223

in the example in figure lb, if carrier lifetime of the Pregion is considered, for example) as discussed in

ref. [1].

c) Except in some cases, and thus unlike the casesof the previous photoresponses, the open-circuitphotovoltage responses can lead to unreliable measure-ments of the carrier lifetime in a given sample neutralregion, especially when they are used alone. However,the transient photovoltage may present specific appli-cations, particularly for N+-P structure samples [1],either because the photovoltage response decaypermits measurements which are complementary(see also [7]) to those obtained using diffusion photo-currents (for example, evaluation of ’rN’ using ’tc,if rp is given by idp(t) or vice versa), or because, forthe light pulse used, the increase and the decay of asingle photovoltage response are each dominated by adifferent region, i.e., ’tN+ and sp # 03C4c for example [1].Concerning the conductivity AV,(t) or AIz(t) and

diffusion current iD(t) photoresponses, their addi-tional major properties, from the point of view oftheir experimental use, can be summarized as follows :

d) All these responses show a linear increase withthe injected carrier level d insofar as the carriermobilities ,un,p are independent of 4. The responsemaximum corresponds to times tmax = T when theexcitation pulse G(t) is rectangular G(t T) = G,Li = GT ; it corresponds to times tmax = 2 T andT tmax 2 T in the case of a triangular pulse ofhalf-width duration T for the 0394V03C3(t) or AI,(t) andiD(t) responses [6], respectively.

e) Depending on the sample studied, they can leadto various measurement sensitivities in the lowestLi range (Fig. la) : the responses 0394V03C3(t) and AIz(t)vary as Q-2 and [03C3(1 + r/Re)]-1 respectively, i.e.,çither strongly depend on the sample conductivityCi or depend on both u and the sample contactresistances in r. The iD(t) response sensitivity onlyvaries with the sample minority carrier mobility /ln;it can therefore be better than the sensitivity of theresponses 0394V03C3(t) and 0394I03A3(t) in strong conductivitysamples. The same is true for the response sensiti-vity vco(t).

f ) The time constants 03C403C3 and Ti are not identical.For thin neutral regions, the conductivity responsesthen usually afford better possibilities than the iDresponses do (cf. expressions (7), (8), (9) and (14),(15), (12), (13)).

g) Moreover, it should be noted that, when theexcess carrier density Li is increased up to Li valuesaround the equilibrium majority carrier density po,the expressions (7), (14) and (15) can again be usedto describe the photoresponses around a given time t,provided the variations of the sample parameters,un,p or Dn,p, r, and s1,2 with Li and the time t aretaken into account [4, 6]. In this Li range however,the photocurrent iD(t) decay method given by (14) or

(15) may appear more precise than those for the pho-toconductivity decay : the expressions for 0394V03C3(t) and0394I03A3(t), as given in figure la, are then more complicatedfunctions of T,, than (7). But, as d increases above po,the expression (7) is again likely to describe the

photoconductivity response decay. In this A &#x3E; pocase, it can be noted that the responses iD(t) lendthemselves even better to measuring the carrierlifetime as this measurement can be made near thestart of the decay (cf. (15)) and thus lowers the effectsof the variations D(x, t), 03C4v(x, t) with the induceddensity n, p(x, t) of carriers present in x at the time t.

3. Expérimental results. - The purpose of the

following experimental data is to compare the resultsobtained from the methods analyzed in section 2,and to study the hypotheses (i) to (vii) involved inthe analysis of section 2. For this reason, the reportedresults deal particularly with P-type silicon mono-crystalline samples, of - 1 and 10 03A9.cm, even thoughthis type of sample does not lend itself to illustratingthe various possibilities that diffusion current ip(t)and voltage vco(t) photoresponses can have in a

device [1]. The first part of the results is then devotedto the comparison of the photoresponses of conducti-vity 0394V03C3(t) and 0394I03A3(t), diffusion current and open-circuit voltage induced, with the aid of a 1.06 gmpenetrating light pulse, over a wide range of carrierinjection level d . The second part of the resultsaims to illustrate the effects that the light absorptioncoefficient have on the transient electrical photo-responses and on their associated possibilities in

measuring carrier lifetime. This deals especially withthe shape and decay of bulk sample photoresponsesmeasured, depending on the sample illuminated

face, when using a smoothly and a strongly absorbedlight pulse. The corresponding studies and resultsare illustrated in figures 2 to 4.

The surfaces of the monocrystalline samples studied (Fig. 2)are carefully cleaned (s small), and the sample length and widthare chosen large enough compared to the sample thickness so thatthe samples studied can be considered as unidimensional (cf. hyp. (i)).For the photoconductivity measurements, the polarisation valuesV and 7 are also chosen so that the transit time of the excited carriers,from their site of excitation to one of the sample contacts, remainslarge compared to the decay of the measured signal, i.e., signaldecay independent of V or I, cf. hyp. (ii). The responses iD(t) maybe studied with a reverse bias on the collecting contact to ensure ahigh enough value si during the measurements (cf. (10)).The experimental set up consists of a CILAS VNDM 20 laser

(2 T = 70 ns) with a neodymium doped (Â. = 1.06 J.1m, Eomax = 1 J)or ruby (Â. = 0.69 J.1m) rod and a CILAS VD 162 laser with aneodymium doped rod (2 T = 55 ns, Eo.., = 3 J). The latter

may be associated with an electro-optic shaping cell CILAS DL 11,which can reduce the laser pulse duration to T = 2 ns, and to afrequency-doubling crystal (À = 0.53 J.1m). Measurements are per-formed inside a 8 m3 Faraday cage of 50 dB attenuation at 1 GHz,and with a digital transient signal analyzer (Tektronix WP 22 21)including a R 7912 transient digitizer and a PDP 11 calculator with16 k words of core memory. A 1 to 6 mm diameter optical fiberconveys the laser beam to the sample which is in the dark. At thefiber input, calibrated attenuators are used to adjust the light

224

Fig. 2. 2013 Monocrystalline (P-type silicon) samples used for thecomparative studies of the electrical responses of photoconducti-vity (a), and diffusion photocurrent or open circuit photovoltage (b).(1) = aluminium cold-deposition, (2) = boron cold-implantedlayer, (3) = light-mask, (4) = illuminated area, (5) = front illu-

mination, (6) = back illumination.

Fig. 3. - Evolution versus L1 - or pulse intensity Et - of themeasured amplitudes and decay time constants for the photo-responses of P type monocrystalline silicon sample submitted tofront illumination (cf. Fig. 2) by 2 T = 70 ns laser pulses at 1.06 gm(left hand : Fig. 3a, b) and 0.69 gm (* ; right hand : Fig. 3c, d).Sample : 0.8 n. cm, B doped, floating zone,

EPD : 20 to

35 X 103 cm-2. Solid curve in figure 3a is the photoconductivityamplitude as given in figure la when taking into account the mobilityvariations J.ln,p(N = po + 0394). Solid curve in figure 3b assumes ausual Hall-Schockley-Read one-level recombination lifetime.

Fig. 4. - Evolution versus L1 - or pulse intensity E*0 - of themeasured amplitudes, decay-time constants and descriptive timesfor the photoresponses of P type monocrystalline silicon samplesubmitted to front and back illumination (cf. Fig. 2) by 2 T = 70 nslaser pulses at 1.06 pm (left hand : Fig. b, c, d) and 0.69 Ilm (* ; righthand : Fig. 4e, f, g, h). Sample : 9.2 n.cm, AI doped, floatingzone, EPD : 20 to 35 x 103 cm-2. Solid curve in figure 4a is thephotoconductivity amplitude as given in figure la when takinginto account the mobility variations J1.n,p(N = po + 0394). Solidcurve in figure 4c assumes

a usual Hall-Schockley-Read one-levelrecombination lifetime.

exciting pulse intensity Eo on the sample. The laser pulse intensityon the attenuators is monitored by a PIN photodiode CG 530 whoseresponse is calibrated with a CILAS PS 16 calorimeter. The photo-diode response is used to trigger the sample signal measurement.A band-pass optical filter (à = 10 nm) is placed at the opticalfiber input when the 1 ms duration light from the xenon flash oflaser pumping is to be eliminated.

3.1 PHOTORESPONSE COMPARISON (PENETRATINGLIGHT PULSE). - The results obtained with the usualmonocrystalline silicon samples when using the pene-trating 1.06 Jlffi laser beam are illustrated in figure 3a,b and 4a to d.

3 1. 1 For excess carrier density L1 ~ po. - The

amplitude and decay time of the measured photo-responses of conductivity L1 Va(t) and diffusion currentiD(t) agree with the expressions of figure la and (7),(8) and (10), (15), respectively. In particular, themeasured decay time La corresponds to the bulklifetime Lv deduced from iD(t) by using the iD.tproduct decay - cf. 2.2, a), b) comments appliedto a sample with large W and small s. It is to be noticed

225

here that, in practice, some discrepancy may appearbetween the measured values r,,, 03C4v(i) due to theilluminated sample regions involved : e.g., in figure 3b,03C4v(i)(A) and 03C4v(i)(B) slightly different values are obtainedby using sample contacts A and B, respectively.For the lowest d, temporary minority carrier trappingmay induce an increase in the measured lifetime;such an effect is shown in figure 3b which, moreover,illustrates the great sensitivity of the iD(t) responsesfor studying low resistivity samples - cf. 2.2, e)comment. The trapping effect is then eliminatedwhen the sample is submitted to a pseudo-steady-state light pulse (the laser exciting xenon flash in themeasurements of figure 3b ; cf. hyp. (vi)). When Aincreases, the 03C4v(i)(0394) variation in figures 3b, 4c

agree with the variation of a usual Hall-Shockley-Read one-level-recombination lifetime. It can alsobe noted that the increase of the amplitude with A(cf. Fig. 3a, 4a) and the amplitude times tmax of thediffusion photocurrent and photoconductivity signalsagree with comment 2.2, d) ; in particular, the decay0394V03C3(t) obeys (7) as soon as t 2 T in the range4 gg po (cf. Fig. 4d). Hypothesis (iv), (v) and (vii) arethus also satisfied in the studied samples for thetransient carrier injection conditions used. Further-more, for d 10-’ po and thus AJ « 6, the d valuesdeduced from the measured photoconductivity signalamplitudes 0394V03C3max (cf. Fig. la) agree well with thevalues calculated from the intensity Eo of the incident1.06 03BCm light pulse when assuming a 20 % lightreflection at the sample surface, a quantum efficiencyof unity (d oc Eo) and a homogeneous absorptionof the light in the sample thickness W = 1 mm.When L1 values approach po such that

only an average decay time constant ( 03C403C3 ~ is foundto describe the photoconductivity response decay,even when measuring this decay-time towards thebeginning of the decay. This is in agreement withthe decay expression on 0394V03C3(t) in this d range - cf.comment 2.2, g). However, the measured averagedecay time ~ 03C403C3 ~ remains in agreement with thedecay time tv(i) given by the responses ip(t) as shownin figures 3b and 4c.

In contrast to the above observed signals DVQ(t)and iD(t), the photoconductivity signals 0394I03A3(t) measur-ed when using constant voltage condition appear asthe sum of two responses (cf. Fig. 3a) :

Only the amplitude and decay of the slowest compo-nent AI’2(t) then agree with the sample bulk photo-conductivity response (7), i.e. agree with the valuesand variations with L1 of the amplitude and decayof the 0394V03C3(t) responses. In the case of figure 3, theAIzi(t) component shows a decay time constant

03C403A31 # 0.8 ils dEo. This fast component varies with

sample surface treatment and appears as an enhancedvariation of the equilibrium current density in thesample region near the surface. The measured signalsvco(t) may also appear as the sum of two responses(cf. Fig. 4b). However, the signals obtained for afront illumination must be distinguished here fromthose obtained for a back illumination of the sample(Fig. 2b). In particular, only the front illuminationsignals, as shown in figure 4b, c, decay as the sum oftwo responses :

The back illumination signals are reduced to theslowest component above, vco2(t). The fast componentvco1(t) would thus give evidence of a sample surface-contact contribution for collecting excess carriers.Due to the increased lighted area of the sample- cf. figure 2 - the amplitude of the diffusioncurrent iomax and open circuit voltage vco(t) signalsappear higher for the back illumination of the sample(cf. Fig. 4a, b). The value of the results illustratedin figure 4c is to show that the measured decay timeconstant ’t’c2 of the Vco2 front illumination component,and the decay time constant tc = r,,,2 of the backillumination response, may agree with the measured

decay time 03C403C3 = 03C4v(i). The agreement is observed aslong as the amplitude of the photovoltage componentinvolved is small compared with UT (cf. (31), VAo = 0).As shown in figure 4d, the rise time - tcomax of thephotovoltage signals remains small - cf. comment2. 2, c) for the case 03C4c = sp -.

If we except the enhapced near surface contributionsAlIl(t) and Vcol(t), the above results thus show that thephotoconductivity, diffusion-photocurrent and also

open-circuit photovoltage decay methods describedin section 2 lead to the same (bulk) carrier lifetimemeasured values 03C403C3,v(i),c = 03C4v.

3.1.2 In the high excitation range L1 &#x3E; po. - Theinstantaneous photoresponse decay is used to measurethe carrier lifetime. The carrier lifetime values measur-ed at the decay beginning of the signals AVa(t) - res-ponse in the standard carrier lifetime measurementmethod -, AII2(t), and iD(t) by using (15), remain ingood agreement as figures 3b and 4c show. On theother hand, the decay time ïp of the photovoltageresponse decay vco(t) differs increasingly with thepreviously measured carrier lifetime as L1 increases;the difference between the excited carrier density L1

and the carrier level effective in the open circuit

photovoltage, and between the relative values of

vco(t) and UT in the sample studied, could explain themeasured values of 03C4c. As a whole, the above resultsagree with the remarks in section 2.2, g).

It should also be noted that, in this 4 range, thephotocurrent signal amplitude iomax always tends tosaturate at the value isat = vco sat/Ztot where Ztot is thetotal circuit impédance and Vcosat the measured maxi-mum amplitude [13] of the vco(t) collecting zone

226

response. On the other hand, the signal amplitudes0394V03C3max and 0394I03A32 either continue to increase with A

(cf. Fig. 3a) or saturate (cf. Fig. 4a) above themaximum value of the response amplitude such asVe, calculated from the sample equilibrium para-meters J1n,p’ po, V or I (Fig. la). For the case shownin figure 3a, the usual case for 1 Q. cm P-type silicon,the observed increase agrees with the theoreticaldecrease in majority carrier mobility J1p(A ) that wouldbe in accord with a total impurity concentrationN = po + A [14]. A simultaneous decrease of thelifetime values is observed (cf. Fig. 3b) which qualita-tively agrees with the surface recombination velocityvariation s = so(1 + 4 /po) from so to s~ (cf. (8), (9)for example ; so = 200 cm/s in figure 3b). In theresults of figures 4a, b, c, alterations in the averagelevel filling rates (cf. hyp. (iii)) should be involved toexplain both the response amplitudes and the carrierlifetime behavior observed [2]. Moreover, due to

such carrier injection effects, it is to be noted thatthe amplitudes of the observed ilVa(t) and MI2(t)responses usually appear at times tmax large comparedwith 2 T when A is greater than 10-1 p0 (cf. Fig. 4d).

3 . 2 LIGHT ABSORPTION COEFFICIENT EFFECTS. - Theinfluences of the light absorption coefficient value aand of the associated sample thickness where carrierexcitation occurs (cf. hyp. (iii)) are illustrated in twoways in the results in figures 3 and 4. First, as previouslynoted in paragraph 3.1, these results show a goodagreement between the values 03C4v(0394) given by the io(t)and vco(t) responses which are obtained when lightingthe sample with the 1.06 itm pulses either on thesurface near the contact or on the opposite surface ofthe sample (cf. Fig. 4c). For carrier lifetime measure-ments, excitation by 1.06 ym light in ordinary silicon(a = 30-40 cm-1) up to 1 mm thick thus appears to

give a good experimental condition of uniform carrierinjection. The second illustration is given by thecomparison of the sample photoresponses obtainedwith the 1.06 gm pulses, and with the strongly absorb-ed 0.69 ym ones (a # 2.5 x 103 cm-1; cf. figure 3c, d,4e to h). In the latter case, all the measured samplephotoresponses show two components. For any0.69 gm light pulse intensity E3, the observed res-ponses of conductivity 0394V*03C3(t), AI*(t) and diffusioncurent i*D(t) obey the relations below, illustrating theessential role of the two time constants 03C4*1, 03C4*2 :

where the slowest component 03C4*2 03C4*1 is also thesmallest component in all the above responses. Thisslow time constant i2 also appears in the diffusioncurrent responses observed under a 0.69 ym backillumination of the sample ; it is then preceded by afast component whose time constant 03C4*3 is some-what greater or less than 03C4*1 depending on the rangeof E*0. As for the photoresponses 0394V*03C3(t) and AI*(t),it should be noted that they both exhibit the fast

component il ; the relative contribution of thishowever remains highest in the constant voltageresponses 0394I*03A3(t). Consistent with the analogy notedabove in paragraph 3.1 on the enhanced surfacecontribution appearing in the photoconductance andopen circuit voltage responses compared with thephotoconductivity 0394V03C3(t) and photocurrent iD(t) res-ponses, this enhanced surface contribution may explainwhy a slow component sg appears rarely in the v*co(t)signals observed and obeying the relations :

where 03C4*0 03C4*1 and 03C4*c2 = 03C4*2 in the lowest range of E3 .The values, and/or variations with the 0.69 03BCm

light intensity EÓ, both of the decay time 03C4*2 andamplitude 0394V*03C32, 0394I*03A32 of the slowest componentof the photoconductivity responses correspond to

the values and/or variations with L1 of the decayconstant 03C403C3,v(i),c = ’tv and amplitudes of the samplephotoresponses to the 1.06 03BCm pulses, especially inthe lowest E*0 range. With bulk carrier injection bythe excited carrier diffusion in the sample, with theexception of the open circuit voltage measurements,the above results thus show that strongly absorbedlight pulses also permit bulk carrier lifetime measure-ments in homogeneous samples when using thetransient photoresponse decay methods, especiallyin the low level range of the induced carrier. In such

cases, however, care must be taken when choosingthe portion of the decay signal to be used. The effectiveexcess carrier level L1 * to which the measured lifetimerefers is also difficult to estimate. However, a simpleevaluation of 0394* is given by the low componentA V 2 amplitude of the photoconductivity responses,with L1 * = 0394V*03C32/Ve if 0394V*03C32 V,,Of course, if the sample studied is a n + p structure

such as a solar cell (cf. Fig. lb), only excess carrierscan be induced in the front N+ region when theWN+ region thickness is higher than the effective

light absorption length d = 1/a. In these samples,the iD(t) responses to 1.06 J.U11 and 0.53 pm (T = 2 ns,03B1 ~ 104 cm-1) light, as given by expressions (14)or (15), may be used in carrier lifetime measurementsof the P region substrate and N+ emitter, respecti-vely [1, 6]. The increase and decay of the vco(t) response

227

to 1.06 gm and/or 0.53 gm light usually leads to lessprecise results in such measurements [1].The results described above deal with thick samples

and silicon materials where 1.06 ym light carrierexcitation is produced by a one-photon band-to-bandprocess. The response of thin silicon samples ( W = 50-70 03BCm) to 1.06 ym pulses are illustrated in ref. [4] :the measured conductivity and diffusion current

photoresponses are then described by the expressions(7), (8) and (14) respectively, and also agree with theoverall analysis of section 2. The photoresponsesto 1.06 03BCm light of gallium arsenide samples involvea two-photon band-to-band excitation processd oc E2. Moreover, in these samples, one-photonimpurity ionisation such as di oc Eo can appear as acompetitive carrier excitation process in the lowestEo range. The induced light absorption coefficientand 0394(E0) variations have then to be taken intoaccount when applying the transient photoresponsesto carrier lifetime 1"(A) studies [15].

4. Conclusion. - The analysis of the conditionsunder which the expressions for transient electricalphotoresponses, for low (and intermediate) carrierinjection and for a uniform carrier excitation in ahomogeneous sample, may be reduced to simplerforms makes it possible to determine the conditionsunder which these photoresponses provide carrierlifetime measurements. The study then points outthat the conditions of validity of the associatedmeasurement methods clearly involve (i) the characte-ristics of the sample studied, (ii) the excess carrierdensity A and (iii) light pulse duration T used, as wellas (iv) the times t considered in the response. In

particular, the analysis also gives the conditionswhen the measured lifetimes 1", which may vary withthe photoresponse because of the sample boundaryconditions involved, is the bulk carrier lifetime 03C4v.It also helps in determining the advantages of eachmethod in order to find carrier lifetime in a givensample - e.g. sensitivity, validity or not above theweak carrier injection condition, sample contact

contribution or not in the response. The experimentalresults obtained agree with the above analysis.

Moreover, the study points out some practical

aspects which are to be taken into account in thechoice and/or use of these methods. These aspectsdeal particularly with the :

(i) components involved in the experimental res-ponse, especially the fast component due to thecontribution of the sample near-surface region. Thelatter mainly appears in the constant-voltage photo-conductivity AIz(t) and open-circuit photovoltageresponses ;

(ii) interest of back illumination when using dif-fusion-photocurrent or open-circuit photovoltagedecay methods (cf. § 3 . 2) ;and (iii) possibility of using either strongly absorbed

light (i.e. carrier injection involving the diffusion inthe sample of the excited carriers) or light of sub-bandgap photon energy (i.e. carrier injection byinterband multiphoton excitation process) in bulkcarrier lifetime measurements.

From this point of view, the results also illustratethe ease that an experimental set up using the laserpulse excitation technique gives. The followingremarks may aid in choosing a measurement method :

a) in the lowest excitation range, the photocurrentdecay or photovoltage (especially decay) methodsare easier to apply for low resistivity samples ;

b) but photovoltage is to be used carefully to

obtain the carrier lifetime in a given sample neutralregion, and only for measurements under weakcarrier injection conditions;

c) the constant-voltage photoconductivity AIz(t)may be advantageous in the case of high impedancesamples (cf. Fig. la) ;

d) the decay of the constant current photoconducti-vity response à V,(t) remains a valid method for

studying thin samples ;e) at low excess carrier injection, the amplitude

of the constant-current photoconductivity response0394V03C3(t) may be used to calibrate the injected carrierdensity, especially when carrier excitation occurs

near the sample surface (use of DVQ2 for stronglyabsorbed light) or is created in the sample bulk bymultiphoton excitation processes (use of 0394V03C3max).

References

[1] GASSET, G., BENZOHRA, M., JOHAN, A., BIELLE-DASPET, D.,Rev. Phys. Appl.14 (1979) 209.

[2] BIELLE-DASPET, D., JOHAN, A., ESPIOUSSAS, F. and GASSET, G.,Int. Conf. « Recombination in Semiconductors », Solid

State Electron. 21 (1978) 1618.[3] MCKELVEY, J. P. and LONGINI, R. L., J. Appl. Phys. 25 n° 5

(1954).[4] BIELLE-DASPET, D., GASSET, G. and JOHAN, A., Proc. of the

« Photovoltaic Solar Energy Conference » (Luxembourg,sept. 1977) D. Reidel Publ. Co, p. 920-29 (1977).

[5] KUIKEN, H. K. Solid State Electron. 19 (1976) 437.[6] BIELLE-DASPET, D. and GASSET, G., Solid State Electron. 21

(1978) 1219.[7] LINDHOIM, F. A. and TANG SAH, C., J. Appl. Phys. 47 n° 9

(1976) 4203.[8] DHARIWAL, S. R., KOTHARI, L. S. and JAIN, S. C., Solid State

Electron. 20 (1977) 297.

[9] BIELLE-DASPET, D., BENZOHRA, M. and GERVAIS DE LAFOND,Y., Solid State Electron 21 (1978) 909.

[10] BIELLE-DASPET, D., ESPIOUSSAS, F., JOHAN, A., Coll. Soc.

Française de Phys., Toulouse, juin 1979.[11] WERTHEIM, G. K., Phys. Rev. 109 (1958) 1086.[12] BAIKER, J. A., Phys. Rev. 129 n° 3 (1963) 1174.[13] PARROT, J. E., IEEE Trans. Electron Devices, ED 21 (1974) 89.[14] The theoretical decrease 03BCp(0394) is calculated using the pheno-

menological expression given for ohmic mobility as

function of impurity concentration, in : GWYN, C. W.,SCHARFETTER, D. L., WIRTH, J. L., IEEE Trans. Nucl. Sci.NS 14 (1967) 153.

[15] ESPIOUSSAS, F., thèse Doct. Ing., Toulouse, sept. 1979, Mesuresdes propriétés électriques du silicium et de l’arséniure degallium à partir des photoréponses électriques transitoiresà une excitation par laser pulsé.