Bulk carrier lifetime measurement from transient diffusion photocurrent in semiconductor diodes

Sohd-StateElectromcs Vol 21, pp 1219-1226 © Pergamon Press Ltd, 1978 Pnnted m Great Britain

0038-1101/7811001-121915020010

BULK CARRIER LIFETIME MEASUREMENT FROM TRANSIENT DIFFUSION PHOTOCURRENT IN SEMICONDUCTOR DIODESf DAN1ELLE M. BIELLE-DASPET and GILBERT D. GASSET CESR:[: 9, Avenue du Colonel Roche-31400 Toulouse, France

(Received 16 May 1977, m revtsed[orm 12 April 1978) Abstract--The theoreUcal analysts of the transtent diffuston photocurrent io(t) created m the dtode substrate, followmg weak carrter mjection level by a homogeneous photoexcitation of short duratmn T, shows that the decay to(t) can be used m two ways to obtain the substrate bulk career lifetune ~. Depending both on the decay times t considered and the values of the substrate parameters 7~, D (minority carrier diffusion constant), W (thickness), s (back contact carrier recombination velocity), $ (carrier velocity ratio at the p-n luncUon boundary), then etther (1)~-~may be deduced from the/off) decay tune constant ~-if ¢ is measured at long enough tunes t > tt, or else (2)¢~ ~s given by the to(t) X ~/t product decay time constant 0 if 0 is measured at short enough times t. The numerical dlustratmn of the accuracy and validity conditions of each of the above two ways of exploiting the decay of to(t) IS given In the case of a P type sfltcon substrate with a resistivity of 0.2, 1 or 10 flcm, W from 50 to 500/zm, ~-~from less than 0.1/zs to more than 100 p,s and various pazrs of s (0 or oo) and/3 (0 to co) values. In practice, the use of a transtent photocurrent decay to obtain the dtode substrate carrier lifetime also unpiles a prevtous analysts of factors such as the device response time constant and transient hias modulaUon, and the career pbotoexotation level tn the substrate. Experimental results obtained wtth N+P silicon-cells (W = 460 p,m and 200 #m) are given and discussed as an illustration of the above study.

V junction voltage W substrate thtckness Zk see expressions (10), (11), (13).

NOTATION

A area of the diode transition zone a

o~ = Z L ,

/] carrier veloctty ratto v/vo at the p-n juncUon boundary D minority carrier diffuston constant g(t) excited cartier generatton pulse G magnitude of the rectangular excttaUon pulse to(t) transient diffuston photocurrent J diffusion current density L~.~ bulk diffusion length of the n or p minority careers n, p total density of electron or hole minority carriers of the substrate no, Po equilibrium density q elementary charge s back contact career recombinaUon velocay T photoexcitation pulse duratmn to to=3T t~ time from which only the fundamental mode k = 1 is revolved in the to(t) decay t,. tune when the amphtude to(t,.) is 1/10 of the amplitude io(t = 3T) 0 decay time constant of the (to(t) x ~/t) product Om value of decay Ume constant 0 at t = t~, r effective decay time constant ¢ = Ck= J ~'~, time constant of the harmonic k = i term ~'k Ume constant of harmonics of mode k • v bulk carner lifetime v minority cartier veloctty when they penetrate the depletion zone VD minority career diffusion velocity mside the hulk substrate

tThis work was camed out under contrac~ DGRST 73-7-1361 and ESTEC 20.62173 sponsored by the D61~gation G~n~rale h la Recherche Scienafique et Techmque and the I'Agence Spaaale Europ~enne, respectively. SLaboratoire associ6 au CNRS No. 153.

l. INTRODUCTION

For the case of assymmetrical P ÷ N (or N÷P) diodes, the transient diffusion current of the diode provides an interesting means of measuring the minority carrier lifetime in the homogeneous N (or P ) substrate region. The transient diffusion current is used in various measurement methods employing either the transient reverse current involved in the diode recovery technique [I] or the diode transient short-circuit photocurrent induced by a carrier excitation pulse [2-5]. However, the carrier lifetime measured directly using the above methods [I--4] is effective lifetime r of the substrate carriers, i.e. their lifetime taking into account the bulk carrier lifetime ev of the material itself, as well as the specific parameters of the substrate studied. The following study investigates the relationship between the substrate bulk lifetime ~'~ and the decay of the photocurrent in short-circuit of a diode by considering the case of a diode of planar geometry under a transient carrier excitation pulse lasting T. The purpose is to analyze the conditions under which this transient diffusion photocurrent method leads to the substrate bulk lifetime r~ as in Fig. 1 depending on the duration T of the excitation, and time t of the diffusion current decay io(t) considered, and finally the parameters characterizing the substrate: thickness W, diffusion coefficient D, bulk lifetime ~-~ and limit conditions s (carrier recombination velocity at the rear contact, at x = W) and (ratio between the velocity v of the carriers just when

1219

D M BIELLE-DASPETandGD GASSET

1220

_J2_

?

0 T

(D/Cv)

0

+,

,

W

OEPt .ETED SUBSTRATE ZONE

~

<2)

lo(t) = qAD On'p(x't) ] Ox I • =o

(3)

and by taking mto account the boundary condmons at the limits x = 0 and x = W of the semiconductor neutral region: ff s = 0

'D{t)= ~ 'Dk
[[

J(x, t) = qD On'p(x't) Ox

Ib

On, p(x, t) I =0 OX I~=

(4)

n,p(W,t) = n,p(W,O) =no, Po

(5)

n,p(O,t) =no, poexp (V/UT) = n,p(O,O)

(6)

On, p(x, t) -vlY-J x n,p(O, t) Ox ,=o- D

(7)

ff s =~

Fig 1. Schematic dmgram of the condltmns studied if fl = they penetrate the depletion zone,'t m x = 0, and the carr|er diffusion velocity co inmde the substrate). The study is c a n e d out from the theoretical analysis of transient diffusmn photocurrent under weak carrier rejection conditions (Section 2). Sectmn 3 provides a numerical illustration of this analysis for P type silicon substrates. The main problems encountered m u s m g the transient diffusion photocurrent method and some experimental results are given in Sectmn 4.

for any

with

D

vo=~, 2. ANALYTICAL EXPRESSIONS FOR THE TRANSIENT DIFFUSION PHOTOCURRENT UNDER WEAK CARRIER INJEC'HON c o m m o N s

2.1 General equations Analytical studies of diffusion photocurrent decrease have already been c a n e d out [2, 8]. They are based on the usual assumptions of semiconductor N or P regions (1) unidtmensional (2) homogeneous and with negligible electric field, (3) subjected to a uniform and rather weak carrier injection so as not to alter appreciably the equilibrium majority carrier density and (4) characterized by constant values of the five substrate parameters W, D, To, s andl3 Tada [2] thus studmd, for an infinite/3 and e~ther a null or infinite s, the transient response of solar-cell shortcircuit current when a steady-state carrier excitatmn ~s terminated. Sigridsson and Leman]8] have treated transient currents induced by a rectangular excitation pulse of duration T as a function of the parameters/3 and W, for a null s. The analytical expressions for the diffusion photocurrent io(t) considered in the following are established for the same hypotheses (1)-(4) quoted above and belong to a synthesis of the studies given m Refs. [2] and [8]. T h e s e expressions refer to a short rectangular photoexcitation pulse. They are obtained by solving the continuity and transport equations of the mmority carriers:

On'p(x't)- D O2n'p(x't) Ot Ox 2

D

× On, p

ax ,=~ ~81

where n, p = total denmty of electron or hole minority c a n e r s of the substrate, with an equilibrium denmty no or po, Lt, = bulk diffusion length of the n or p mmority carriers; L~,.p = x/(D..pz~,.p); v = minority c a n e r velocity in the depletion zone; J=diffusion current density; A = area of the diode transition zone, and V = junction voltage and g(t)=excited carrier generation pulse. The solution of the above system of equations leads to analytical expresmons of the transient diffusion current io(t) which depend on the shape of the excitation pulse g(t) and the boundary conditions s and/3. The analytical expressions for the diffusion photocurrent resulting from a rectangular transient exotation pulse, of magnitude G and duratmn T, are written as follows for the times t > T subsequent to the excitation pulse: (a) In the case of/3 = ~ and any s.

lo(t)=qaG2--~-~[~__ r k ( e x p ( T ) - l ) e x p ( - t ) ] (9)

t>T w~th

n ' p ( x ' t ) - n ° ' p ° + g(t) (1)

iTk= ± ]"r,l + z £ ]

T~

tv m equivalent to a surface recomblnatlon velocity for the minority carriers diffusing towards the surface at x = 0. The parameter g] thus takes into account the effect of the devlatlons from an infimtly sharp boundary between a diffusion and a drift regmn in the depletion zone close of the boundary at x = 0

L

'+=Fo' s = ~

and Zk so that (2k - 1)2II2L~2~ for s = 0 __1=i I+ •k

To

4W 2

}

(10)

Bulk carder lifetime measurement 1+ ( 2 k - 1)2II2Lfl'~

fors=o ° 1=1 z~

¢o

W~

(11)

]"

(b) In the case of any/3 and a nul s, for example:

1221

From relation (16), the expression describing the decay at t > to of a diffusion photocurrent iD(t) induced by a short enough excitation pulse can then be simplified in two ways according to the weight that the terms with ZE [see expressions (10) and (11)] have in the sum Y, exp--

io(t) = qAOLo ~

k--I

tick. 2[exp ((1 + Zk2)Tlr~) - 1] exp ( - (1 + ZkZ)t]r~)

(12)

[ W Z.2, 1) + ~ ] [1 + Zk2] where ZE is the solution of the equation:

The first simplified form is obtained by considering the conditions for which the parameters ZE2 are greater than I. This means a substrate whose thickness W is comparable to, or less than, the bulk diffusion length of the minority carriers. Depending on the s value, these conditions imply:

W/Lv < I I

(13)

if soo

and In general, the above expressions show that any transient diffusion photocurrent iD(t) is a sum of harmonics of mode k. However, in both cases (a) and (b), the expressions (9) and (12) for iD(t) admit some very simple forms when certain conditions are satisfied. 2.2 Simplified expressions for ~ = oo If we consider expression (9) which deals with an abrupt p-n junction (too), this expression admits useful simplified forms for the following two sets of conditions: (a) The times t considered are long enough, t > t,, so that only the fundamental mode k = 1 is involved. At the times t >t~ the diffusion photoeurrent decrease thus obeys the expression: 2D

ira(t) = qAG ~ ¢[(exp T]'r) - 1] exp - tie

(14)

where t > h and ¢ = ~k- ~. The above expression (14) is then valid whatever T, W and s may be. (b) Let the excitation pulse be short in such a way that T is small compared with the time constant ¢~ of the harmonic k = i term involved, i.e. T < l/3~u and the times t considered be above to = 3T. The condition T < 113¢k, makes it possible to write eqn (9) as: io(t)

=

qAG

T

exp

- -rk'

~

+k-,+, ek{[exp(T/¢k)-- l]exp(--t/,~)}}

(15)

where 1

W / ~ < II/2 if s = O. Indeed, we may then consider that the terms ZK2 dominate the argument (1 +ZE 2) in the expression (10) and (11) of ~k. As soon as the ratio WIL~ is less than 1 or I/2 respectively, depending on the s value, the difference between two consecutive Zkz values is so great that the (16) series term rapidly converges. For all t > to = 3T the iD(t) decay then becomes closer to the exponential decay of the fundamental mode k = 1 as the ratio WIL~ is small compared with 1 or 1/2. The diffusion photocurrent decay may then be described by the expression: iD( t ) =

q A G T -2D ~exp-

t/'r

when ~ L ~ l ~ = o < l / 2 o r ~L~[s~3Z

(17)

1

T<~.

The above simplified expression of (16), which corresponds to the simplified form of (14) for the transient condition T ~ ¢, implies that the decay times t are such that ia~=2(t)~ia~-l(t), i.e. t>>-W2/3,r2D or W2/,r2D depending on whether s is close to s=oo or s = 0 respectively. On the contrary, the second simplified expression of iD(t) corresponds to terms with Zk2 such that the different values tZ~2/¢~ remain small compared with unity, in the sum written as: t

!

exp ( - t/¢k) = exp ( - tier) k~l exp ( - tZk2/To). In expression (15) above for iD(t), the contribution of the harmonics above k = i then becomes neglik~i+l

(18) Sum (18) then admits the limited development:

gibles if the t times considered are greater than 3T, i.e.: 1

2D

io(t) = qAG - ~ T ~

'

exp ( - tlzk) ( e x p - tlzv) (tZ~=,l¢~) -112 e x p - t]'rk

(16)

(19)

k=l

k=l

if tZk2/'r~ < 1 when t > 3T and T < l/3¢u where ~, is given by (10) or (11) for k = i.

and the expression (16) of iD(t) is reduced to an expres-

1222

D. M. BIELLE-DASPETand G. D GAssEr TItE TRANSIENTP H ~ M~TUO~ CASEOF A e r v ~ SILICONStmST~TE ~ A K

s~on of the form:

3. VALIDrrY CONDmONS OF

i o ( t ) = q A G T 4 ( ~ -D~ ) exp ( - th-~) 1

wltht1>3T, T , ~ a n d

cARRIER IN/ECTION CONDITIONS)

(20)

z

From a practical point of view, and assuming the excitation pulse of duration T to be sufficiently short, the conditions for (20) to be "exploitable" thus correspond either (1) to any times t > 3 T , should the substrate thickness W be large enough compared with L~, i.e. ratio W/L~ large compared with II or If/2 for s close to s = oo or s = 0 respectively, or, on the contrary (2) to substrates of any characteristic parameters W, s, ¢~, D, if we consider only the t>~3T times which remain small compared with WE/II2D or 4W2/II2D, depending on whether s is close to s = oo or s = 0, respectively. 2.3 Simplified expressions .for finite/3 It must be noted that expression (12), relative to a p-n junction for any/3, may also lead to a simplified form of io(t) when/3 is large compared with unity. For example, if the condition W large compared with ~ is satisfied, expression (12) admits the simplified form:

As was shown m the previous section, the possibilities for measuring the carrier lifetime from the transient diffusion photocurrent decay are determined by the validity conditions of expressions (14), (17) or (20). The analysis reported m Section 2 shows that these validity conditions depend at the same time on the parameters W, s, fl, D, ~ which characterise the substrate, on the time "t" m which the photocurrent decay io(t) is considered and on the duration T of the carrier excitation pulse. These expressions, with the conditions for their validity, are listed in Table 1. In this table, the time t validity conditions of the transmnt case T ,~ r = ~'k= ~ are expressed in terms of the bulk lifetime ¢~ and the ratio W/Lo. To illustrate these condRions m the case of a homogeneous diode substrate, we shall assume in what follows that the excitation pulse duration T is chosen at a low enough value so as to remain, in each case, less than the time constant ~'k-~oof the ki = 10 harmonic and that the times t concerned are higher than 3T. The conditions under which expression (16) Is reduced to one of the two simple expressions (17) and (20) can be illustrated by rewritting expression (16) as follows: iD(t) = qAG2-~-~ T exp ( - t/¢o)

to(t) = qAG

~-~ e x p - t/r~ 1 -

(21)

x k~, exp [ - a t]( 2r k -~ , 1)2

(22)

2

where a = .Zk= l so that, w~th

a = (wLd2W) 2 for s = 0 /3>>1, W >>L~.

or

a = HrLdW) 2 for s~ Expression (21) shows that, under the above conditions, only the beginmng of the decay io(t) is altered by the fimte value of /3 when /3 exceeds 1. Again, the remainder of the decay thus derives from the simple expression (20).

Figure 2, which

gives

the

evolution of

exp [ - ct(t/%)(2k - 1)2] vs (at/¢o), shows the ranges of

k=l

(at/'r~) in which the sum term Y in expression (22) above

Table 1 Key expressions of the dtffusloncurrent decay wRh the conditionsfor their vahdlty m the case of ~1= c¢ [see expressions (14), (17) and (20) with z = ek=d

Whatever T, W, and s may be

2D~ [(exp- TT}

tD(t > t 1) : q A O - ~ -

-11

exp - t/'C

t 1 such that ~Dk=l ( t : t l ) >~ ~Dk=2 (t : t l ) , "C:~5k= 1 J ~Dk' ~ k given by (9), (10) or (1|) T<~£

1

~
,

W 2 / 3 = 2 L v 2 ~ =oo or I ~ v 2D i D (t> t l ) = q A G T - ~ exp (-t/'C:

t >t1 =

[~v

, 3T
tI =

l:,v W2/3

~D (t< t 1 ) = q A O l ~ \ ~ -

2 L 2 v

Y=

s :oo

exp (-t/"~ v)

w2/~ 2 Lv2

I

=o

or "~v W 2 / ~ 2 L 2 v

, t >3T

I

s=o

Bulk carrier lifetime measurement 100

t

........

I

........

I

........

I

.......

i

,

direct way of measuring the bulk lifetime. To do this, we calculated the error [¢o- O(tm)l/¢~ made by evaluating 0 at the times t,, when the amplitude iD(tm) is equal to 1/10 the amplitude iD(t = 3T) at time t = 3T when the excitation pulses have ceased. The curves in Fig. 3 represent, for different pairs of values of t] and s, and vs the substrate thickness W, the bulk carrier lifetime ca for which the error I¢~- O(tm)l/r~ is 10%. Each curve thus separates region I, where the conditions ca, D, W, s, are such that 0 provides ~ directly, and region II, where on the contrary the ~o estimate using the time constant 0 of the product iD(t) X x/t becomes inaccurate.

10

a_

,r till

-"

01

~ i

001 0001

001

........

01

I

1223

, ,~,

10

~v

F

Fzg. 2. Comparison vs (atl'r~) of the evolutions of ll~/(at/¢~), exp (-at/'r~,) and 2 exp[-(at/'ro)(2k- 1)2] for z = 10 and t > ~ k=l

where ~'k,IS given by (10) or (11). leads to a decrease in iD(t) which may be described either (1) by the exponential decrease exp ( - a t / ¢ k - O i.e. decrease described by expression (17), or (2) by a decrease in (1/X/t) exp ( - t/¢~) i.e. decrease descr/bed by expression (20). In the specific case of P-type silicon substrates, we have evaluated the conditions under which expressions (17) and (20) can be used in practice by proceeding as follows: for given values of the parameters fl, s, D, W and Ca characterising a substrate, we have calculated the photocurrent &,(t) described by the corresponding full expressions (9) or (12) and simultaneously compared the it,(t)x X/t product decay time constant 0, calculated around different tunes ¢, wRh the ¢~ value put up. These calculations are performed for P type silicon of 10, 1 and 0.2flcm resistivity (that is D, =34,22 and 12cm2s -I respectively), and for different pairs of values of the limit conditions fl and s. The thicknesses W considered range from 50 to 500/~m, and the lifetime ~ from less than 0.1/~s to more than 100 p.s. The numerical values T = 20 ns and 2 ns are used in these calculations and correspond to the pulse durations easily realisable from triggered lasers (see Section 4). It should be observed here and in general that if fl is ®, that is for an abrupt type p-n junction, the 0 time constant is such that the inequality O(t)< ¢~ is always satisfied, and O(t) approaches value ~-~ as the time t considered is shortened. On the contrary, when // decreases, 0 tends to overestimate ~ towards the low times t, and underestimate ~ towards the high times t. The border between these two behaviours is all the nearer towards the high times t as/] is small. This is taken into account in the calculations summafizcd in Fig. 3, the purpose of which is to indicate for what values of the substrate parameters the time constant 0 of the product io(t)x X/t can be used as a SSE Vol 21, No IO---C

;

/,/-/

;

,

!

l

!

50

IS0

250

THICKNESS

350

/,50

W (~Jm)

Fig. 3(a) l

o I

3

~

SI-P, la cm ~eo s=O

®

m :Z.

~r bJ I..I.l.I 1. --i

m

1621 50

I I J J I I ~ I 100 150 200 250 300 350 ~ ~SO 500 THICKNESS

Fig 3(b).

W (.urn)

1224

D M BIELLE-DASPETand G D. GASSET 10L

i

I

m

r

m

i

i

i

f

SI P, lO,n. cm

102

~:o s=0

101

i 1 [ 1 I , | 50 100 150 200 250 300 350 400 450 500 THICKNESS W {l~rn)

Iff2~z

Fig 3(c)

Fig 3 Study of the bulk carrier hfet~me r~ vs the substrate thickness W for which the error Iz~-O(tm)]/T~ is 10% when considering the to(t)x X/t product decay time O(t,.) at the time tm where lrg(t = t~ )= ID(t = 3T)/10

P type sdlcon substrate with &fferent pau's of values of the/3 and s boundary conditions, and with reslstwlty 0 21-1cm (Fig 3a), 1~cm (Fig 3b) and 101acre (Fig 3c). In the above figures, each curve separates a region I where con&tlons ~, D, W, S,/3 are such that O(t<~tr~) gives ~'~ and a region II where, on the contrary, the z, eshmate using the decay time constant Off <~t~) becomes inaccurate Moreover ~t must be noted that, m Fig. 3 and in the case of any /3, only the absolute value of the errors [~'v-0,,[b'~ relatwe to the times tm Is taken into account. This way of proceeding illustrates the effect of/3, ff the order of magnitude of /3 is known, this enables us to situate the margin of error which 0 can indicate for the value of z~. Furthermore, in such a case, t,, lies around the times where the inequality O(t) > z~ ~s reversed to the inequality O(t) < r~. 4. PRACTICAL CONDITIONS AND EXAMPLES OF USING TRANSIENT DIFFUSION PHOTOCURRENTS FOR MEASURING BULK CARRIER LIFETIME

The practical use of transient diffusion photocurrents for measuring minority carrier lifetime in the substrate of a diode of planar geometry assumes that m addition to the previously discussed validity conditions other problems are taken into account. These problems deal respectively with (a) the real shape of the photoexcitation pulse used [9, 10] 0a) the contribution due to careers created in the neighbouring regions of the diode /The absorption coefficient of hght at l l 7 e V IS about

40 cm-~ in sdicon with resistivity p ~>10-~ f~ cm

(i.e. the depleted transition zone and the surface diffused layer) compared with the contribution of the diffusion photocurrent due to the carriers created in the diode substrate itself [7, 1t] (c) the diode behavlour with regard to the transient disturbance induced by the photoexcitation, i e. the effects of the response time constant of the devtce stu&ed and the transient bias modulation [10, 11] which is mduced at the boundaries of the transmon zone by the rejected carrier inflow (d) the possible influence of temporary minority carrier traps [12] existing in the diode substrate and, finally, (c) the effects of excitation conditions which deviate from the weak level excitation case assumed in the previous sections For this final point the general problem is complex. Within the scope of the studies treated here however it is sufficient to consider the influence of carrier excitation level effects which appear beyond high carrier excitation conditions. In fact, under these final high level conditions, such effects as electrical breakdown and saturation ohmic potential drops, etc. are added to such phenomena [11] as the substrate electric field, conductwity modulations, and the depleted zone modulations in order to disturb the measured device response [10]. Before the very high injection conditions are reached, i e. up to G values around the equilibrium majority carrier density, and assuming a slight reverse bias applied to the diode so that the effects due to the variation in the effective minority carrier distribution near the depletion zone [see (d)] are minimized, the expressions (14), (17) and (20) can again be used to describe the diffusion photocurrents io(t) around a given rime t, provided the variations of the parameters D I l l , 13], ~'~ [14], s [15] and /3 = v~v/(rdD) with G and the time t are taken mto account. Wtthin the scope of Sections 2 and 3, the diagrams for the low injection conditions (see Fig. 3) thus permit us to locate the evolution of the conditions of the io(t)x X/t product method to remain valid when /3, s and z~ are affected by the career excitation level G. Around the times t considered the parameters /3, s, ~'~ are then assumed to be described by thetr instantaneous values at the time t following career excitation. The io X ~/t product method can then be seen as a good way to find the bulk lifetime z~, value vs the effective excess carrier density, particularly as the method is all the more valuable as It applies to the beginning of the photoresponse decay. In order to dlustrate the phenomena discussed in this paper, we gwe two examples of experimental results obtained at room temperature, with the usual n ÷p silicon solar ceils (/3~, s~): wide base solar cells W = 460 ttm (8 lq cm, boron doped, Czochralsky type silicon) designed by Helioteck, and solar cells with a narrow base W = 200ttm, (10 flcm, boron doped, floating zone type sdicon) manufactured by AEG Telefunken. A CILASVD 162 pulsed laser, with a neodymium glass head (140MWatt maximum power), provides a monochromatic pulse of 1.17eV photonsf The pulse duration and intensity monitoring systems, as well as the various measuring apparatus, are placed inside a Faraday cage with a 80 dB attenuation. In the results quoted, the laser pulse (half-width T = 20 ns triangular pulse, or T =

1225

Bulk carrier lifetime measurement

2 ns rectangular pulse) has been superposed on a quasisteady-state excitation light of l ms duration produced by a Xenon lamp and maintained at a low intensity level so that a substrate temporary trap contribution in the measured signal may be avoided. The unirradiated wide-base W = 460/~m solar cell is an example which corresponds to the border of regions I and II as they have been defined in Fig. 3. The signal i(t) observed under very weak carder injection rate G/po-5.10-a is redrawn in Fig. 4(a) (dashed curve). The associated decay time constant 0 of the product iD(t)X %/t evaluated at times t ~
\\

- - - [~, - m ( , l l ~, "\.\.

E

- -

~'",

[~,

"\'x

-

100 80

itself, mainly because it can be applied to the times t < tm where the signal amplitude can be measured most accurately. Similarly, the ~v values of this solar cell can be obtained when the carder excitation rate G/po varies from 5.10-4 to 5.10-1 (Fig. 4b). The ¢~ degradation by proton irradiation (3.10" protons cm -2, 10 MeV) can also be easily measured and the method for determining ~-~ from the iD(t)X ~/t product is well adapted to such a solar-cell degradation study [6]. The 10 fl cm solar cell of W = 200~m thickness (Fig. 5) illustrates a thin diode case. Under weak carder injection level, the pbotocurrent signal shows an exponential decay with the time constant ¢ = 1.1/~s leading to a value of about 15/~s for ¢~. In such a case, the ~'v contribution in ~ is small and the accuracy with which ~v can deduced from measuring ¢ thus depends strongly on the accuracy with which D and W are known. When G mcreases to the order of magnitude of the equilibrium majority carrier density po, the general shape of the i(t) signal observed is maintained and the • measured value varies very little. This slight variation of • complies with the slight variation of the diffusion constant in this injection level range and at the same time indicates that the contribution of "rv(G/po) remains very small. However, following irradiation, as soon as ~ decreases to below one microsecond, the method for measuring ~ by the decay 0 of the iD(t)X X/t product (Fig. 5b) then becomes an accurate tool for studying the base degradation of such a solar-cell [6].

m :]O

o(~V : ,

60

(al

4O

~Xl

A

/

3

<

\/

F

2

"~

1

g0

"'- % ( . ) . . . ~ . , .

~p . . . .

:,/)'~

,~ o,,d ....o,.,.=ol rc,.lsp¢ 50 ~ -.-

{'c, - m( t )l / "A,

::00

",\ 0 1

2

TIME

3

.%

"':\-,..,

(a)

"''-.. I"~" . . . . "i . . . . . . . . 1 2

O

10

TiME m :=L

2

unlrr'~l~ted solar cell

>

-

20

--

k

( F'~)

b

m m

''

t ..... 3

O

I; (~ts)

..... '1 . . . . . . . . I

........ I

......

k) 8 n. crn

L~ :E l-hl LL d

W:460

J D ,..n

÷4 ~2" ..+'~+

+ / 1 0

Mev p~oton~1

bJ -~

16 : 3 x d 1 P / c 2 t

LL "7

/

o.I

1

I(b) ~,m I I

1

-

-0.5

-4

I t IIHIJ I IIHIll[

I Z tIHl~ 0-2

iO

G / Po

Fig. 4. Wide-base N+P silicon solar cells (Helioteck manufacturer, 8 Ctcm base resistivity, s co). (a) Transmnt photocurrent measured under low substtate carder injection G/Po = 5.10-a by a laser beam (T= 20ns) of 1.17eV photons and corresponding (1) calculated iv(t) assuming substrate bulk carder lifetime r~ = 5~,s, (2) errors k~-(~×t)l/~ and I~-O(t)ll'r~ vs time t. ('0) Substrate bulk carrier lifetime vs carrier injectmn level GIPo measured from transient diffusion photocurrent in unirradiated and irradiated samples.

S N}P 1 10 z%. crn i(b) W : 200 prnJ ,~r'odloted solar" cell (2,doIScm "2 I M e v electrons ) bulk hfehme %'vF

re"

Illllld

un.'rodtoted so]or" cell eFFechve hFebme "c

L)

-: 10

I0 2

-I 10

I

10

G/% Fig. 5. Narrow-base N+P solar cell (Telefunken manufacturer, 10[Icm base resistivmty,s ®). Curves have the same meaning as m Fig. 4 except that the unuTadiatedtransient cliffusmnphotocurrent (Fig. 5a, G/Po = ~.10 -3) is calculated here using ¢o = 15/~s.

1226

D M. Btl/LLE-DASPETand G. D. GASSEr

CONCLUSION The method of the diffusion current decay, applied when using a transient uniform carrier photoexcitation such as the one produced by a'pulsed laser beam of penetrating light [5,6], is advantageous in that measurements can be easily performed over a wide range of carrier injection levels, without destroying the sample and without necessarily knowing the precise values of the light absorption coefficient and the carrier diffusion constant in the sample studied. The analysis of the transient diffusion photocurrent io(t) mduced by homogeneous transient photocxcitation enables us to show how these photocurrent measurements may be used to characterise a diode substrate or material. Indeed, the io(t) decay leads to the minority carrier effective lifetime but it primarily allows the bulk lifetime z~ of these carriers to be found directly. Normally, the effective lifetime ~ must be measured towards the end part of the io(t) signal. As 7 depends on the five parameters/3, s, D, W and % which characterise the substrate, deducing r~ from r implies both an accurate measurement of ~"and a knowledge of the precise values of the four parameters /3, s, D and W. In this paper we have also tried to determine, illustrating it in the case of a P type silicon substrate, the conditions required and accuracy attained for a direct measurement of ~'~ deduced from the transient diffusion photocurrents io(t), when using the product io(t) x ~ t decay. Complying with the examples given in Sections 3 and 4, this study brings out four main results: (1) For a given material with given boundary conditions s and/3, the conditions under which the product io(t) x X/t decay can be exploited directly to obtain the bulk carrier lifetime r~ within a 10% accuracy range depends both on the material thickness W and the associated ratio value W/'V/(Dro). The above validity conditions are thus dependent on the minority carrier type and on the material resistivity. (2) In the case of a collecting abrupt junction (too), the

higher the career lifetime rv the more valid the direct exploitation of the product io(t)x V't (permitting ~ to be measured) becomes towards weak W/Lv ratio values. This becomes more noticeable as s decreases. (3) The io(t) × V t product application limits are more affected by the finite value of/3 as the substrate thickness increases (see Fig. 3). (4) When the io(t)x ~/t product method is not valid, the method of studying the io(t) decay itself can give way to even greater rv inaccuracies when z~ and WILy are both great. REFERENCES

1. M. Byczkowska and J. R. Madigan, J Appl. Phys 28, 878 0957). 2 H Y. Tada, J Appl. Phys. 37, 4595 (1966) 3 J L Lindstrom, Solid-St. Electron 14, 827 (1971) 4 H K. Kulken, Solid-St. Electron. 19, 437 (1976). 5 D. Blelle-Daspet and J. Pinel, Proc Int Con]. Composants de haute ~abilit~ Toulouse, March 1972; CNES edn, France, p 89 (1972) 6. D Bielle-Daspet, G. Gasset and L. Castaner-Munoz, ESA Report CR-479 Effet des trradiations combm~.es particulephoton sur les cellules solmres (Mar. 1976). 7 J L. Wirdth and S. C Rogers, IEEE Trans. Nucl. Sct. 2(5), 24 (1964). 8. B Slgfndson and G. Leman, F 04. 4 Report C 4324-29 Some aspects on the theory of transient radiation reduced diffusion currents in semiconductor diodes (Oct. 1967). 9 J. Pmel and F Durbin, Solid-St Electron 19, 265 (1976) I0 D. Blelle-Daspet, J Pinel, M Benzohra and G. Gasset, DGRST contract 73-7-1361, Final Report CESR 75-554 (1975) 11 C. W Gwyn, D L Sharfetterand J L. Wtrdth,IEEE Trans. Nucl. Sc~ 14(6),153 (1967) 12 D. Blelle-Daspet,Sohd-St. Electron. 16, II03 (1973) 13 F Lann, Radiat,ons Effects in Semwonductor Dewces. Wdey, New York (1969). 14 G. K. Wertheun, Phy. Rev. 109, 1086 0958) "15.J. R Hauser and P. M Dunbar, Sol,d-St Electron 18, 715

(1975) 16 D. Bielle-Daspet and G Gasset, Proc. Int. Con/ Electnc~t~ Soiaire. Toulouse March 1976, CNES Edn, France, p. 355 (1976)