Influence of illumination on the grain boundary recombination velocity in siliconJ. Oualid, C. M. Singal, J. Dugas, J. P. Crest, and H. Amzil Citation: Journal of Applied Physics 55, 1195 (1984); doi: 10.1063/1.333161 View online: http://dx.doi.org/10.1063/1.333161 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/55/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Temperature dependent recombination dynamics in InP/ZnS colloidal nanocrystals Appl. Phys. Lett. 101, 091910 (2012); 10.1063/1.4749276 Simulation of hole phonon-velocity in strained Si/SiGe metal-oxide-semiconductor transistor J. Appl. Phys. 95, 713 (2004); 10.1063/1.1633346 Valley splitting in strained silicon quantum wells Appl. Phys. Lett. 84, 115 (2004); 10.1063/1.1637718 Auger recombination in narrow-gap semiconductor superlattices incorporating antimony J. Appl. Phys. 92, 7311 (2002); 10.1063/1.1521255 Influence of oxygen on band alignment at the organic/aluminum interface Appl. Phys. Lett. 77, 1212 (2000); 10.1063/1.1289497

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26

Influence of illumination on the grain boundary recombination velocity in silicon

J. Oualid Laboratoire des Materiaux et Composants Semi-conducteurs, Ecole Nationale Superieure de Physique de Marseille, F.13397 Marseille Cedex 13, France

C. M. Singal Department of Physics, University of Roorkee, Roorkee 247662, India

J. Dugas, J. P. Crest, and H. Amzil Laboratoire de Photoelectricite, Faculte des Sciences et Techniques de Marseille St. Jerome, F.13397 Marseille Cedex 13, France

(Received 4 March 1983; accepted for publication 10 June 1983)

The variation with illumination of the grain boundary (GB) barrier heightEB and of the effective recombination velocity Seff is calculated by means of a self-consistent procedure which takes into account the bending of the minority carrier quasi-Fermi level in the GB space-charge region and in the GB quasi-neutral region. The GB interface states have been assumed to be uniformly distributed in a half-filled band whose width and position in the band gap can vary. Seff is nearly proportional to exp(EB/kT), only when EB is sufficiently low. For high EB, Seff is limited by the thermal velocity. The influence of the density of interface states and the grain doping concentration has been studied. The experimental results obtained with Silso-Wacker polycrystalline silicon show that the grain boundaries present different behaviors.

PACS numbers: 85.30.De, 84.60.Jt, 73.40.Lq, 61.70.Ng

I. INTRODUCTION

For terrestrial electrical conversion of solar energy the present trend is to utilize a rustic material such as polycrys­talline silicon. 1 This material is different from monocrystal­line silicon essentially due to the presence of grain boundar­ies (GB) which act as recombination centers for excess carriers.2 This GB electronic activity contributes to a marked decrease of solar cell efficiencies.3--6 As for a semi­conductor surface, this activity is well defined by an interfa­cial recombination velocity.

The G B recombination of the excess carriers takes place via the GB interface states which can be due to the dangling bonds, the dislocations, or the impurities segregated or dif­fused into the GB. Their distribution in the band gap is still not very well known although some direct experimental in­vestigations have been done by J-V deconvolution, 7 by deep level transient spectroscopy (DLTS),8 and by photocapaci­tance.9 So, in any calculation of the GB behavior, it is neces­sary to consider different energy distributions of the GB in­terface states.

As the interface states are generally charged, a band bending appears near a GB characterized by a barrier height EB and a space-charge region which lies on each side of the G B. The high electric field in this space-charge region drifts the minority carriers toward the GB and enhances their re­combination. Therefore, from a practical point of view, it is interesting to consider an effective GB recombination veloc­itylO which takes into account the presence of the GB barrier height.

The charge of the GB interface states depends on the level of excitation which, in the case of a solar cell, is related to the intensity of the incident light. The excess carriers due to the light tend to saturate the GB interface states so that

the G B barrier height 11 and consequently the effective re­combination velocity12 decrease as the excitation level in­creases.

Card and Yang lO have given a model which correlates the effective recombination velocity Seff with the true recom­bination velocity S (0) and the barrier height E B. In this mod­el, the quasi-Fermi levels have been assumed to be flat every­where and the majority and minority carrier densities to be equal at the GB in order to maximize the recombination rate. This model has been used also by Fossum and Lindholm. 13 In a previous communication,14 we have adopted the flat quasi-Fermi level approximation. In the present paper, we have taken into account the bending Li1 and Li2 of the minor­ity carrier quasi-Fermi level in the space-charge region and in the quasi-neutral region. As Seager,12 we have verified that these bendings are not negligible especially for large barrier heights. In contrast to the analysis given by Seager based partially on the thermoionic emission model, we have used only the Shockley-Read-Hall (SRH) theory for the self-consistent determination of E Band Seff·

The purpose of this paper is to present a model which enables a determination of the GB effective recombination velocity Seff' for different cases of interface state energy dis­tributions under different excitation levels, and to explore experimentally the variation of Seff with the excitation level in polycrystalline silicon solar cells. In Sec. II, we develop the theoretical procedure which allows the self-consistent variation of E Band Seff with the density of interface states, the grain doping concentration, and the excitation level for different energy distributions of interface states. In Sec. III, we present the method and the results for the experimental investigation of Seff for different grain boundaries in the case of a solar cell made with p-type Silso-Wacker polycrystal­line silicon under different illumination levels up to 2 AMI

1195 J. Appl. Phys. 55 (4), 15 February 1984 0021-8979/84/041195-11$02.40 © 1984 American Institute of Physics 1195

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26

(2 suns). Finally, in Sec. IV, we provide the most important conclusions of the present study.

II. THEORY A. Model

Figure I gives a schematic representation of the vari­ation of the energy bands and the quasi-Fermi levels with the distance x at a GB under illuminated conditions for a p-type semiconductor. In this model, we assume the following hy­potheses:

(a) Under low and medium excitation conditions, the quasi-Fermi level of the majority carriers Epp is flat every­where but the quasi-Fermi level of the minority carriers EPn is allowed to vary in the space-charge region ( - WB < X < WB ) as well as in the quasi-neutral region as proposed by C. H. Seager. 12 The bending of E Pn in the space­charge region and in the quasi-neutral region is indicated by ..::11 and ..::1 2, respectively, as shown in Fig. 1.

(b) The GB interface state levels E, are located within a band of width 2b, with the mean level situated atEa from the intrinsic Fermi level E;. The interface states are lying in the range E; + Ea - {j to E; + Ea + {j with a density N,/2{j

per unit energy range. When {j is zero, the distribution is monoenergetic with a density N, per unit area and when Ea = 0 and {j = EG/2 the distribution is uniform.

(c) The charge of states is given by the half-filled band model (HFB)15 in which a pair of states is associated with each dangling bond. When this pair is not occupied at all, the charge of the dangling bond is positive. A single or double occupancy of this pair leads to a zero charge or a negative charge respectively. The HFB model is often used in the case of undissociated dislocations 16 and can be applied in the case of a low angle GB which can be considered as a line of dislo­cations.

(d) The occupation probability is given by the usual Fer­mi-Dirac functionfo at equilibrium and by the Shockley­Read-Hall functionf (Ref. 17) under nonequilibrium condi­tions.

G.8. , , , , , , , , ,

~Ec

:: E 2 --------~r-------m~-:+:.-:.-:.-:.-:.-:.-:.-:-:.-:.-:.m---~ - - - - E fn

Il --------t-----':-~----: i III :, ! // ! '------, .

I r : ~ Efp

E8 ----~ >- E,

~----~----------~I r---- x

FIG. I. Band diagram at the vicinity ofa grain boundary in ap-type illumi­nated semiconductor: NA = 10'6 cm -3; Eo = 0; {j = 0; N, = 1013 cm - 2;

..:1 (0) = 0.1 eV; Ln = 50 pm; Dn = 20 cm2/s.

1196 J. Appl. Phys., Vol. 55, No.4, 15 February 1984

(e) The carrier recombination rate Us via a GB interface state E, is determined by the well-known SRH expression. 17

(f) The excitation is uniform in the base of the solar cell which is nearly the case under long wavelength illumination. The excitation level is characterized by the difference of the quasi-Fermi levels, EPn - Epp ' in the neutral region of the grains.

On the basis of these assumptions, a self-consistent pro­cedure for the calculation of the GB barrier height and effec­tive recombination velocity is presented in the following sub­sections. The GB effective recombination velocity is defined 10 in terms of the minority carrier density n( WB ) at the edge of the GB space-charge region by

I Self = 2" US/[n(WB) - no], (1)

where no is the minority carrier density at equilibrium. Equation (1) is the boundary condition of the continuity equation which allows the determination of the minority carrier distribution in the grains. Self can be experimentally accessible by means of the GB photoelectric profile as shown by Zook. 18

B. GB barrier height EB

The GB barrier height EB in a p-type semiconductor with a grain doping concentration NA is easily obtained in the case of the fully depleted space-charge approximation by writing the neutrality condition

(2)

In this case, the interface state distribution is assumed to be monoenergetic with a density N,.

The occupation probability fis given by17

f= n(O)+n,exp[(E,-E,)/kT] (3)

n(O) + p(O) + 2n, cosh [(E, - E, )/kT]

The hole and electron concentrations p(O) and n(O) at the G B are given by

[E;(O) - Ef: ]

p(O) = n; exp kT p (4)

and

[Epn(O) - E;(O)]

n(O) = n; exp . kT

(5)

Assuming that the majority carrier quasi-Fermi level re­mains flat and equal to the equilibrium Fermi level, expres­sions (4) and (5) can be rewritten as

p(O) = NA exp( - :~) (6)

and

n~ [..::1 (O)+EB] n(O) = - exp ----NA kT

(7)

where

..::1 (0) = EPn(O) - Epp .

Oualid et al. 1196

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26

So the GB surface charge is given byll

qN, sinh(EalkT) + exp[.J (0)/2kT]sinhp QB = -- ,

2 cosh(Ea1kT) + exp[.J (0)/2kT]coshP (8)

where

P= In(NA) _ EB _ ..1 (0). nj kT 2kT

If the GB interface states are spread in their energy within the interval E j + Ea - D to E j + Ea + D, the net GB charge density can be obtained by integration over this ener­gy distribution II

QB = In ---.:...~.....:....;....;....--..:....-~:.......:..---~ qNt kT { [ n(O) + p(O) + 2nj cosh [(Ea + D)lkT] ]

~ n(O) + p(O) + 2nj cosh[(Ea - D)/kT]

n(O) - p(O) In[ n(O) + p(O) + 2nj + atl X n(O) + p(O) + 2nj - at2 ]}

a n(O) + p(O) + 2nj - at l n(O) + p(O) + 2nj + at2 (9)

where

a = { [n(O) + plOW - 4nn 112,

and

E -D 12 = tanh _a __ •

kT

Ea +D tl = tanh ---,

kT

In all the cases the surface charge QB depends on E B as the space-charge width WB given by the classical relation

WB = (2EEB/q2NA )112.

So the neutrality condition (2) is an implicit equation for EB which can be obtained numerically for any grain doping con­centration N A , any interface state density Nt with energy distribution parameters Ea and D, and any excitation level defined at the GB plane by ..1 (0). But.J (0) is not experimen­tally accessible. The excitation level can be more clearly de­fined by the difference E Fn - E Fp in the neutral region of the adjacent grains. Consequently, it is necessary to determine the relation between ..1 (0) and E Fn - E Fp'

As

UVth Nt kT 2 Us = [p(O) n(O) - nj ]

~a

(10)

the bendings.J I and.J 2 of the minority carrier quasi-Fermi level must be calculated. This calculation needs in particular the knowledge of the GB effective recombination velocity.

C. GB effective recombination velocity Se"

As shown by the definition given by expression (1), the GB effective recombination velocity can be determined ifthe surface recombination rate Us at the GB and the minority carrier density n( WB ) at the edge of the GB space-charge region are known.

In the case of a monoenergetic distribution ofGB inter­face states, Us is given by

n(O) p(O) - n; Us = UV,h N, -----:.....:...:~~-..-..:..----

n(O) + p(O) + 2n I cosh [(E, - E,)/ k T ]

(11)

In the case of an uniform distribution of GB interface states over a range E j + Ea - D < E, < Ej + Ea + D, Us can be ob­tained by integration

X~ X , ( n(O) + p(O) + 2nj + at l n(O) + p(O) + 2nj - at2)

n(O) + p(O) + 2n j - atl n(O) + p(O) + 2nj + at2

(12)

where n(O), p(O), a, fl' and t2 have been already defined. To determine n( WB ), we have assumed no recombina­

tion-generation processes in the GB space-charge region due to the presence of the high electric field. So the minority carrier flux F" (x) at any plane x is easily related to the GB recombination rate Us (Ref. 17)

Dn ) a [E ( )] 1 U (13) F,,{x) = - kT nIx ax Fn X = -"2 s'

where nIx) is defined classically by

( ) [EFn(X)- Ej(X)]

nx =nj exp . kT

(14)

1197 J. Appl. Phys., Vol. 55, No.4, 15 February 1984

I The band bending profile under the depletion approxima­tion is given by

Ej(X)=Ej(WB)-EB(I- :Br (15)

So E Fn (x) is obtained by solving the differential equation

a [ EFn(X)] ax exp--;;r

= .l....!:!.:...-exp[Ej(WB)-EB(I-X/WB)2]. (16) 2 Dnn j kT

The resolution of this differential equation is quite easy and

Oualid 6t a/. 1197

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26

allows the determination of n( WB ) defined by expression (14) for x = WB :

n(wB)=n(o)exp(- EB)+ {ii Us WB _1_ erf(71B),(17) kT 4 Dn 7lB

where

_ (EB )112 7lB - kT .

The first term gives the value of n( WB ) in the condition of a flat minority carrier quasi-Fermi level which is consequently realized if the barrier height is not too large. At the contrary, in the case of a sufficiently large barrier height (EB/kT> 1), n(WB ) is given by the simple relation

(18)

In this case, we obtain a limiting value for Self given by

. 2 D (E ) 112 (2 q2 N ) 112 S hm", _ _ n_ -.!!... = _ __ A_ D

eff- n" {ii WB kT 1TE kT

(19)

By introducing the Debye length defined by

LD = ~ kTdq2NA ,S~:; can be expressed by

s~:;=$ ~; '" -fEUlh. (20)

So when the barrier height is large, there is a limiting value of the GB effective recombination velocity which is about the half of the thermal velocity.

In the general case, the GB recombination velocity can be easily determined by Eq. (1) where Us is given by Eqs. (11) or (12) and n(WB) by Eq. (17) if EB is known.

D. Bending of the minority carrier quasi-Fermi level

Once the value of n( WB ) is obtained, it is easy to deter­mine the bendingLl I of the minority carrier quasi-Fermi lev­el in the GB space-charge region.

[n(WB )]

.J 1 = E Fn (W B) - E Fn(O) = E B + k TIn ----;;(0)

=kTIn[1 + {ii Us WB erf(71B) exp(EB )].(21) 4 Dn n(O) 7lB kT

The last expression shows that for large GB barrier heights, Lli can be quite significant and must be taken into account.

To determine the band bending Ll2 in the quasi-neutral region, it is necessary to know the minority carrier distribu­tion which is given, in the case of a grain size much larger than the minority carrier diffusion length L n , by

Self Ln/Dn ] nIx) = n(oo) - [n(oo) - no

1 + Self Ln/Dn

xexp( - X ~nWB). (22)

n( 00 ) is the electron concentration in the neutral region. Sub­stituting x = WB in Eq. (22), n( 00) is defined by

1198 J. Appl. Phys., Vol. 55, No.4, 15 February 1984

(23)

So Ll2 is easily deduced

Ll2 = kTIn(~) n(WB )

= kTIn[1 + Self Ln (1 _ ~)]. Dn n(WB )

(24)

In the case of an excitation sufficiently high [n( WB ) >no] the bending Ll2 of the quasi-Fermi level in the quasi-neutral region is given by

Ll2=kTIn( 1 + Se;~n). (25)

As we have shown that Self is limited near 5 X 106 cm/s, Ll2 is also limited for a given semiconductor.

E. Theoretical results

The GB barrier height EB , the effective recombination velocity Self' and the bending of the minority carrier quasi­Fermi level can be determined by the following self-consis­tent procedure.

(a) A choice is made of the grain doping concentration NA , the interface state energy distribution parameters N, ,Ea , and 8, and the diffusion length Ln of the minority carriers in the bulk of the grains. The minority carrier diffu­sion coefficient Do is allowed to vary with the doping con­centration N A • 19

(b) An excitation level Ll (0) at the grain boundary is se­lected.

(c) The GB barrier height EB and the space-charge re­gion width WB are determined by an iterative solution ofEq. (2) where the GB surface charge is given by Eqs. (8) or (9).

(d) The GB recombination rate Us is calculated from Eqs. (11) or (12) and n(WB ) from Eq. (17). Thus Self can be deduced from definition (1).

(e) The quasi-Fermi level bendings Lli and Ll2 are deter­mined from Eqs. (21) and (24). Thus, the excitation level in the bulk of the grains EFn - EFp corresponding to the value .J (0) is calculated from Eq. (10).

In this way, the variations of Lli andLl 2, EB and Self can be plotted versus the excitation level defined by the differ­ence E Fn - EFP in the bulk of the grains.

The variations of Lli and Ll2 as a function of the excita­tion level E Fn - E Fp in the bulk of the grains are shown in Fig. 2(a) in the case of a monoenergetic distribution of inter­face states at mid gap (Ea = 0), with a density NT = 10 12

cm-2 and a capture cross section a=2.5XIO- 16 cm- 2. The grains are defined by a doping concentration NA = 1016

cm - 3, a minority carrier diffusion length Ln = 50 pm, and coefficient diffusion Dn = 13.4 cm2/s. The bending of the minority carrier quasi-Fermi level is always much larger in the quasi-neutral region than in the GB space-charge region as obtained also by Seager. 12

At very low or very high excitation, Lli is negligible, but Ll2 is always quite significant. In these cases, the. minority carrier quasi-Fermi level can be assumed to be flat m the GB space-charge region and with a less degree of validity in the

Oualid et al. 1198

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26

0.2 0.2

:;: :;: .!!J ..! I: I: ... ... ..., ..., ~ 0.1 ~ 0.1

§ § >- >--< -< a;: a;: -< -< :> :>

0 0.2 0.4 0.6 0 0.1 0.2 0.3 0.4

(a) Efn-Efp (eV) (b) BARRIER HEIGHT (eV)

FIG. 2. Bendings of the minority carrier quasi-Fermi level in the GB space­charge region (.:1 I) and in the quasi-neutral region of the adjacent grain (.:1 2) vs the excitation level in the bulk of the grains [curves (a)] and vs the GB barrier height. E. = 0; 8 = 0; NA = 10'6 cm- 3

; U= 2.5X 10- 16 cm- 2; Ln

=50Jlm;Dn = 14cm2/s.

grain quasi-neutral region. This approximation is valid at low excitation level due to the small minority carrier flux and at high excitation level due to the decrease of the GB barrier height and the subsequent decrease of the GB effec­tive recombination velocity with the excitation level as shown below . .1 1 and.1 2 are maximum for a critical excita­tion level which depends on the GB interface state distribu­tion and on the doping concentration in the grains. The max­imum value of.1 2 is limited by the value 0.18 e V due to the limiting value of Self'

Figure 2(b) demonstrates that the bending of the minor­ity carrier quasi-Fermi level near a grain boundary in an illuminated semiconductor must be taken into account for large GB barrier heights. The variation of.1 1 and.1 2 with E B

have been calculated in the same case as for Fig. 2(a) with a very low excitation level defined at the grain boundary .1 (0) = 0.001 eV. The GB interface state density varies between 1011 cm- 2 to 1013 cm-2 in order to vary the GB barrier height. We verify that the approximation of flat qua­si-Fermi levels in the depletion region generally holds for E B

< 0.2 eV as indicated by Seager. 12 But the bending.1 2 of the minority carrier quasi-Fermi level in the quasi-neutral re­gion is never negligible.

The influence of the density of GB interface states on the variation of the GB barrier height EB and effective re­combination velocity Self with the excitation level is shown in Figs. 3(a) and 3(b), in the case of a monoenergetic distribu­tion at midgap and with the same parameters as above. For a given excitation, E B and Self increase with Nt. The asympto­tic behavior of Self toward Vth/2 when the barrier height is large is well demonstrated in Fig. 3(b). EB and Self remain constant for low excitation level and strongly decrease for high excitation level. The critical excitation level for which there is a change in the behavior of EB is lower as the GB interface density is larger. When the excitation level is large the variation of E B with E Fn -E Fp is nearly linear as suggest­ed by Fossum and Lindholm. 13 However the slope of the variation of E B decreases with Nt down to - 1 instead of remaining constant and equal to - 0.5. 13

1199 J. Appl. Phys., Vol. 55, No.4, 15 February 1984

0.4 107

5 ~ "-E

.3 106 :; 0.3 4

3 >- 2 >-

>- W 13 c::>

~ 0.2 2

~ 105

:z <>< c::> ..., i >-

~ 104

~ 0.1 m :E c::> W

~ 103

0 0.2 0.4 0.6 0 0.2 0.4 0.6

(a) Efn-Efp (eV) (b) Efn-Efp (eV)

FIG. 3. Variations of the GB barrier height EB (a) and effective recombina­

tion velocity Self (b) with the excitation level in the bulk of the grains for different GB interface state densities. Ea = 0; 8 = 0; U = 2.5 X 10- 16 cm2

;

NA = 10'6 cm- 3; Ln = 50 Jlm; Dn = 14 cm2/s. I: N, = 4X 1011 cm- 2

; 2: N, = 6X 1011 cm- 2

; 3: NI = 8X lO'l cm- 2; 4: N, = 1012 em- 2

; 5: N, = 5X 1012 em- 2•

The influence of the GB interface state distribution on the variation of E B and Self with the excitation level is given in Figs. 4(a) and 4(b). Figure 4(a) shows that for p-type poly­crystalline silicon higher values of Ea lead to larger GB bar­rier height. But, Fig. 4(b) demonstrates that the GB effective recombination velocity is larger when the GB interface traps are concentrated at midgap which is a well-known result deduced from the SRH theory. When the GB interface traps are spread on a width 2/j the GB barrier height decreases with {) as shown by Fig. 4(a). However, when the middle of the GB trap band is above the middle of the band gap, the GB effective recombination velocity increases with {) as shown by Fig. 4(b).

Further, in this case, Self decreases slowly when the ex­citation level is less than the critical level while Self remains constant for the cases Ea < O. This distinguishing feature can be helpful in the interpretation of experimental results. It is clear in Fig. 4(a) that the critical excitation level decreases if

0.5 107

30 ~ 3b "- 20

~ 0.4 E

:> -3e .3 106 2e .!!J >-

>-LJ 30 c::>

LW ~ 105 :J:

2e 10 ~ 0.2 z

2 Ib Q: >-Q:

~ 104 Ie -<

m 0.1

~ m "" c::> LJ

~ 103 0.2 0.4 0.6 0 0.2 0.4 0.6

(a)Efn-Efp (eV) (b) Efn-Efp (eV)

FIG. 4. Variations of the GB barrier height (a) and effective recombination velocity Seff (b) with the excitation level in the bulk of the grains for different distribution of GB interface states. I: Ea = - 0.2 eV; 2: Ea = 0 eV; 3: Ea = + 0.2 eV; a: 8 = 0; b: 8 = 0.1 eV; c: {j = 0.2 eV; N, = 1012 em- 2; NA = 1016 em -3; U = 2.5 X 10- 16 cm2

; Ln = 50 Jlm; Dn = 14 em2/s.

Oualidetal. 1199

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26

E a increases and <5 decreases. Atthis point of view the beha v­ior of Self is more complex due to the necessity for Self to be limited. The case Ea = - 0.2 eV corresponds to the hypoth­esis that the GB interface states are due to dangling bonds. 16

In this case the GB barrier height for p-type semiconductor is small. By symmetry the behavior of n-type semiconductor is the same as that of p type with a symmetrical value of Ea' Figure4(a) indicates that in this case the GB barrier height is larger in n type than in p type with all other parameters remaining identical which has been experimentally con­firmed. 20 The influence of the grain doping concentration NA on the variation of E B and Self with the excitation level is shown in Figs. 5(a) and 5(b) in the case of a monoenergetic interface state distribution at midgap with a density Nt = 1012 cm - 2 and with the same other parameters as above. It can be verified that the GB barrier height is maximum for a given value of NA as previously exhibited.4 In this case the maximum of EB is obtained for NA '::::'.5 X 1015 cm -3. It can be observed that the critical excitation level increases with NA. So it is not obvious that an increase of NA near the grain boundaries is always favorable in order to reduce the GB activity under AM 1 excitation.

The behaviors of E B and log Self shown in Figs. 3,4, and 5 appear comparable even if they present some discordances that we have pointed out. It can be noticed that Card and Yang 10 have found that Self varies exponentially with E Band Seagerl2 has limited this type of variation in the case where the minority carrier quasi-Fermi level varies less than kTin the depletion region. This result is confirmed by Fig. 6 which compares the variation of Self with E B obtained by the pres­ent model and the exponential variation in the case Ea = 0 for different values of <5. It is clear that the model of Card and Yang can be applied only for a GB barrier height which must be all the more low as the width ofthe GB trap band is larger.

O. 4 .-'---'---'-'--.--'-,

:;: 0.3 ...'!! >-i3 W 0.2 :z: 0::

~ ~ 0.1 CD

o 0.2 0.4 0.6 0.2 0.4 0.6

(I) Ef n-Ef p (. V) (b) Efn-Efp (eV)

FIG. 5. Variation of the GB barrier height EB (al and effective recombina­tion velocity Seff (bl with the excitation level in the bulk of the grains for different doping concentrations. E

Q = 0; {j = 0; NT = JOI2 cm~2;

U = 2.5X JO~16 cm2 ; L. = 50 JLm; 1: NA = JOI5 cm~3; 2: NA = 3 X JOI5 cm~3; 3: NA = JOI6 cm~3; 4: NA = 3 X JOI6 cm~3; 5: NA = JO" cm~3. D.

varies with the doping concentration. 19

1200 J. Appl. Phys., Vol. 55, No.4, 15 February 1984

107

r. OJ

"-E 0

106 '-"

>-I-...... U a -l

105 w

> z a ...... I-<

104 z

CD :::E: a u w 0::

103

0 o. 1 o. 2 0.3

BARRIER HEIGHT (eV)

FIG. 6. Comparison between the variations of the GB effective recombina­tion velocity Self with the GB barrier height determined from this model and Card and Yang.'" Ea =0; U= 2.5XIO~16cm2; NA = JO'6cm~-'; D.

= 20 cm2/s; L. = 50JLm; 1: {j = 0; 2: {j = 0.2 eV; 3: {j = 0.3 eV.

111. EXPERIMENT A. Method

The GB effective recombination velocity is determined by measuring the light beam induced current (LBIC), for different wavelengths in the vicinity of the GB. This method has been first proposed by ZOOk l8 who has given the photo­current / induced by a small monochromatic light spot of wavelength A at a distance x from a GB:

/(A, S,X) = 1 _ 2.(1 +A)S (YO 7r

("" sinh2t exp( - X cosh t )dt (26)

X Jo cosh t (S + cosh t )(A 2 + sinh2t )

where S = Self L.lDn is the reduced GB recombination ve­locity. X = xlLn is the reduced distance of the light spot to the G B. /00 is the photocurrent measured when the light spot is sufficiently far from the GB so that the GB influence on the photocurrent is negligible. A = a(A)Ln is the reduced absorption coefficient. alA ) is the light absorption coefficient which depends on the wavelength of the light spot and also on the state of stress of the studied sample. The relation alA ) is quite different in the case of stress-relieved silicon and in the case of as-grown silicon.

By means of the above Eq. (26), we have plotted in Fig. 7 the photocurrent profile in the vicinity of a GB, for the half space x> 0, the case A = 0.5 which corresponds to a light penetration depth 1 I a = 100 pm and to a diffusion length of 50 pm. This case corresponds, approximately, to the experi­mental conditions encountered in the study of the GB elec­tronic activity in cast polycrystalline silicon, utilizing long

Oualid et al. 1200

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26

~ 0.8 z w a:: a:: 0.6 :::l u 0 0.4 w u :::l 0 W 0.2 a::

0

A: .5 1 i i 1 1

L-____ ~ ____ ~ ____ ~ ____ ~ ___ ~

0.5 1.5 2 2.5

DISTANCE FROM THE G.B. X=x/L

FIG. 7. Half photoelectric profile of a grain boundary for A = aL. = 0.5

and for different values of the reduced GB effective recombination velocity S=Seff L.lD •. l:S= 0.5;2:S= 1;3:S= 2;4:S= 5; 5:S= 1O;6:S= 00.

wavelength light with A ~ 1 pm. These profiles show that the GB has an electronic influence up to a distance of nearly 2.5 Ln in the adjacent grain. So, the GB detrimental effect on the efficiency of solar cells made with polycrystalline silicon is more marked when the diffusion length in the grain is larger. It is further seen from Fig. 7 that, as expected, the relative attenuation of the local photocurrent at GB is greater when the reduced GB recombination velocity S is higher.

To obtain an accurate experimental GB photocurrent profile it is necessary that the spot size must be smaller than the bulk diffusion length of minority carriers in the adjacent grains. To minimize the influence of the spot size Zook 18 has proposed a method based on the determination of the GB effective width, defined by

w=2 ('" I", -1(A,S,X) dX. Jo I",

This effective width is equal to the area of the surface delim­ited by the GB photocurrent profile, Zookl8 has plotted the variation of the reduced GB effective width W = w/ Ln ver­sus the parameter 1/( 1 + A ) for different values of the re­duced GB recombination velocity S. A comparison of these theoretical curves and the experimental variations of Wwith A or 1/( 1 + A ) allows the determination of S and consequent­ly Self' if the minority carrier diffusion length Ln and diffu­sion coefficient D n in the adjacent grains are known. Though this method has the advantage of being less dependent on the spot size it is very time consuming and cannot be applied when the distribution of intragrain defects is not homogen­eous in the vicinity of the GB. In particular, it seems that the grain boundaries act as sinks for dislocations and impurities. In particular, it is well admitted that phosphorus diffuse preferentially in the GB.21 So, due to the well-known getter­ing effect of phosphorus, the diffusion length may be higher near a GB. Consequently in the case of polycrystalline sili­con with a high density of intragrain defects and with rela­tively low values of diffusion length, it is likely that the diffu­sion length decreases from the GB to the center of the grain. If it is true the GB effective width Wis larger than the value given by Zook's theory based on the experimental value of

1201 J. Appl. Phys., Vol. 55, No.4, 15 February 1984

the bulk diffusion length sufficiently far from the GB. In such a case we propose to directly compare the experimental and theoretical attenuation of the photocurrent at the GB, utilizing a long wavelength light spot so that the light attenu­ation length is comparable to but lower than the thickness of the sample. For this reason we have chosen A = 0.98 pm for LBIC scanning experiments.

Figure 8 gives the variation of the normalized photo­current at the GB with the effective recombination velocity Self for different bulk diffusion lengths and for ,1= 0.98 pm and Dn = 20 cm2/s. We can again see that the normalized photocurrent at the GB decreases as the diffusion length increases for a given GB effective recombination velocity. We can note also that the slope of the curves is maximum near Self ~ 104 cm/s which is near the values found experi­mentally in the case of p-type polycrystalline silicon, as will be seen below. So, in this range of Self' the accuracy of experi­mental determination of Self is fairly good.

Whatever method is used to determine Self it is neces­sary to measure the local minority carrier diffusion length Ln at the nearest point from the GB studied, where the influ­ence of the GB is negligible. This measurement is performed by means of a variant of the well-known surface photovol­tage method. In this method, the inverse of the spectral pho­toresponse Q (A ) is plotted as a function of the inverse of the absorption coefficient a(,1). If the sample thickness Wo is greater than the diffusion length Ln and the light attenuation length 1/a, (i.e., WoILn > 1 and aWo > 1) the graph of Q -I = f(a- I

) vs a-I is a straight line whose intersection with the a-I axis gives the diffusion length Ln.

The samples were cut off from N + Psolar cells prepared by classical phosphorus diffusion22 on Silso-Wacker poly­crystalline silicon either from the center of the cell, charac­terized by a columnar structure, or from the periphery of the cell where the grains present a greater density of dislocations and quite different orientations. Small Mesa diodes (1.5 X 1.5 mm) were etched on these samples in order to localize the investigated part of the sample and to determine, in particu-

1

~ 0.8 z w a:: a:: ::J 0.6 u 0 w 0.4 u ::J 0 W a:: 0.2

0

103

104 IDS 10

6

RECOMBINATION VELOCITY Cem/a)

FIG. 8. Reduced photocurrent at a grain boundary vs GB effective recom­bination velocity for different minority carrier diffusion lengths L •. 1: L. = lO,um; 2:L. = 20Jlm; 3:L. = 30Jlm;4:L. = 4OJlm; 5:L. = 50Jlm; 6:

L. = 75,um; 7: 100 Jlm.

Oualidetal. 1201

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26

lar, the doping density by the usual C -2_V method. A schematic outline of the LBIC apparatus used to in­

vestigate the GB electronic influence is shown in Fig. 9. A monochromator driven by a step motor is employed in order to vary the wavelength of the monochromatic light in the range of 0.40-1.1!-lm. A metallographic microscope with an adjustable aperture is used in order to obtain a light spot of nearly l0!-lm diam on the sample. The sample is mounted on aX- Y stage driven by two step motors. As the intensity of the monochromatic light spot is very weak, the photocurrent is very small. It is necessary, therefore, to use a chopper (fre­quency=l000 Hz), a preamplifier and a lock-in amplifier to make the photocurrent signal large enough so that it can be fed into an on-line microcomputer through an IEEE inter­face. All the step motors and the data acquisitions are con­trolled by this microcomputer which commands also a digi­tal X- Y plotter. A white continuous beam of light can be superimposed on the total surface of the Mesa diode studied. In order to determine the variation of the effective GB re­combination velocity with excitation, the intensity of this light bias can be varied over a large range by means of cali­brated neutral density filters. It has been verified that the continuous short circuit photocurrent of the Mesa diodes is proportional to the white light intensity up to an illumina­tion level corresponding to two AMI suns. The open circuit photovoltage Voc of the Mesa diodes is proportional to the logarithm of the white light intensity. We have assumed that q Voc gives the difference between the quasi Fermi levels EPn - Epp in the bulk of the grains which has been chosen as a parameter in the theoretical study.

B. Results

Figures lO(a) and lO(b) reproduce the LBIC image (at A. = O.98!-lm) of two typical mesa diodes etched at the pe­riphery and at the center, respectively, of a 10 X 10 cm solar cell. The grain boundaries are easily identified on the LBIC images of each diode. The photoresponse in the columnar grains of the center is more uniform than in the transcrystal­line grains of the periphery. Effectively, the periphery pre-

Lasers He Ne ,,----,

FIG. 9. Schema of the experimental setup for the measurements of Self and

Ln'

1202 J. Appl. Phys., Vol. 55, No.4, 15 February 1984

(a)

(b)

FIG. 10. LBIC image (A = 0.98 pm) of two typical mesa diodes (1.5 X 1.5 mm) situated at the periphery (a) or at the center of a same N + P photocell realized on Silso-Wacker polycrystalline silicon. (a) Ise = 21.1 mA/cm2; v,~ = 472 mV(AMl); NA = l.4x 10'6 cm-'. (b) Ise = 29.9 mA/cm'; v,,, = 535 mV(AMl); NA = 1.5 X 10'6 cm- J

sents much more intragrain defects than the center, which explains why the diffusion length and the short circuit pho­tocurrent at one AMI sun are generally higher for the mesa diodes at the center than for those at the periphery, as given in the legends of Figs. lO(a) and lO(b). As a consequence, the local photocurrent at A. = O.98!-lm is generally higher at the center than at the periphery. The sensitivity of the lock-in amplifier used for the scanning given in Fig. lO(a), is two times the sensitivity used for the scanning given in Fig. lO(b).

In the case of a high and inhomogeneous intragrain de­fect density, it seems that the effective width W of a GB does not increase with the diffusion length, contrary to Zook's theory. This case is illustrated by Fig. 11 which gives the normalized photocurrent profile of a GB situated at the pe­riphery, for different wavelengths with no light bias [Fig. 11(a)] and with a light bias of 1/3 AMI sun [Fig. 11(b)]. We can observe that the effective half-width is larger than 2.5 times the diffusion length in the grain. Also, we have verified after etching that there are no dislocations in the near vicini­ty of the GB, so that the real diffusion length near the GB (if this notion has always a meaning in this region) can be larger

Oualid eta/. 1202

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26

t-­:z: w a::: a::: => LJ C) t-­C) :r:: CL.

CJ W N

.......J <: ::::E a::: C) :z:

(a)

o

O. 75

O. 1 0.2 O. 3 0.4 0.5

SPOT POSITION (mm)

t-­:z: w a::: a::: => LJ C) t-­C) :r:: CL. O. 50 t---+---t-W-~+--+---j CJ W N

.......J <: ::::E a::: C) :z:

(b)

0.25

o O. 1 0.2 0.3 O. 4 0.5

SPOT POSITION (mm)

FIG. II. Photoelectric profile of a GB situated at the center with no light bias (a) and with a light bias [(b): 1/3 AMI] for different wavelengths: I: .1= 1.05 11m; 2:.1 = 0.98 11m; 3: .1= 0.90 11m; 4: .1= 0.80 11m; 5: .1= 0.70 11m; 6: A = 0.60 11m. The stars give the diffusion lengths normalized by the value of the diffusion length in the left grain L ::,ax. (case a: L ::,ax = 37.3Ilm; case b: L ::,ax = 91.2 11m).

than that measured relatively away from the GB. The inter­granular diffusion of phosphorus must contribute to this in­crease of the diffusion length near the G B as proposed above. In this case, Zook's effective grain boundary width method cannot be applied. The method that we have proposed in the above subsection, directly utilizing the photocurrent attenu­ation at the GB, gives for the effective recombination veloc­ity at this grain boundary the values:

Self = 4.0 X 104 cm/s

for no light bias and

Self = 1.5 X 104 cm/s

for a light bias intensity of 1/3 AMI sun. For a sufficiently high excitation, the intragrain defects

are partially "passivated" as shown by an increase of the diffusion length, L = 37.3 f.lm for zero light bias and L = 92 f.lm for a light bias of 1/3 AM 1 sun, and the improvement of the photocurrent response in the right part of the mesa di­ode. So, in this case, the inhomogeneous distribution of the intragrain defects has a less pronounced effect on the shape

1203 J. Appl. Phys., Vol. 55, No.4, 15 February 1984

of the GB photocurrent profile. Therefore, under a suffi­ciently high level of illumination it is possible to apply Zook's effective grain boundary width method. We have ob­tained by this method, in this case Self = 2.2 X 104 cm/s un­der an illumination level of 1/3 AM 1 sun. This value of Self is slightly higher than the value obtained by our method which can be attributed to the finite size of the light spot used for LBIC scanning. Obviously, our method of determining Self is more sensitive to this last parameter, but the easy and straightforward determination of Self from the photocurrent attenuation at grain boundary justifies the application of this method. It can also be observed from Figs. 11(a) and 11(b) that there is a good correlation between the local variation of the photocurrent, measured at A = 1.02 f.lm, and the local diffusion length.

The "passivation" of the intragrain defects by the light as mentioned above, is well illustrated by Fig. 12. This figure gives the photocurrent scanning at A = 0.98 f.lm of a line which crosses two grain boundaries. The middle grain pre­sents a weak and a very inhomogeneous photocurrent re­sponse at a very low illumination level. As the illumination level increases the response of this grain becomes more ho­mogeneous and comparable to that of the right adjacent grain. A detailed study of this "passivation" effect due to the light on the intragrain defects has been presented in a recent communication.23 The influence of the illumination level on the attenuation of the photocurrent at a G B is also illustrated by Fig. 12. In particular, it can be observed that the detri­mental effect of the left GB is almost completely eliminated as the illumination level is increased from 0 to 1 AMI sun, and that of the right GB is reduced for the same increase of the illumination level.

The variation of the effective recombination velocity with the illumination level has been investigated. Figure 13 gives a comparison of the typical behavior of a GB (9C) situ­ated in the well-oriented part of the wafer (center) and that of a GB (9P) situated in the transition region of the wafer (pe-

t-­:z: w a::: a::: => LJ C) t-­C) :r:: CL.

CJ W N 0.25~~-+-----r----+---~ .......J <: ::::E a::: C) :z: o 0.5 1.5 2

SPOT POSITION (mm)

FIG. 12. Photocurrent scanning (A = 0.98 11m) of a same line for a mesa diode situated at the periphery of a solar cell. I: E"",O; 2: E = AM 1/50; 3: E=AMI/27; 4: E=AMI/13; 5: E=AMI/8; 6: E=AMI/4; 7: E= AMI.

Oualid et al. 1203

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26

,.... 105 Q)

....... E 0

'-'

>-I-........ U

104 CJ -.l W :>

:z: CJ o 9PG + 9CG l- • gpO )( 9CD <: :z: ........

103 a:l ~ 0 100 200 300 400 500 600 CJ u UJ 0:: OPEN CIRCUIT VOLTAGE (mV)

FIG. 13. Influence of the excitation level characterized by the open circuit voltage on the effective recombination velocity of two typical grain boun­daries located at the periphery or at the center of a solar cell.

riphery). The illumination level is characterized in this figure by the open circuit photovoltage Voc generated by each Mesa diode under the given illumination.

GB 9C presents an effective recombination velocity Self

which is identical when measured with respect of the minor­ity carrier flow from the left or the right adjacent grains. Further, Self does not vary appreciably with illumination level, up to 2 AM 1 sun, except for a small variation at very low excitation. This behavior can be explained if we assume that the interface state energy distribution is characterized by Ea = - 0.2 eV, and {j = 0.3 eV with NT = 1012 cm- 2

and a = 2.5 X 10- 16 cm2. The adopted value of a is the same

as that suggested by Seager l2 which has been found to give good agreement with the GB conductance and GB capaci­tance measurements.

The energy distribution of GB interface states is quite wide and located in the lower half of the semiconductor ener­gy bandgap which may be attributed to dangling bonds.

The GB of diode 9P presents a quite different behavior, since Self decreases slowly at low excitation and rapidly at high excitation. This behavior seems to be in agreement with the case Ea > 0 shown in Fig. 4(b). In particular a choice of Ea = 0.3 eV, {j = 0.1 eV, NT = 1012 cm- 2

, and a = 1.5 X 10- 16 cm -2 provides a fairly good fit with this experimental variation of the GB effective recombination velocity with excitation level. The positive value of Ea may be mainly due to some impurity atoms that have segregated or diffused to the GB during the crystallisation process or during the subsequent processing of the cell. It has been found effectively that the intergrain diffusion is particularly important in the transition region of the Wacker-Silso ingots.24

It is sure that the measurement of Self alone cannot give unambiguously the distribution of the GB interface states and their capture cross section. It is necessary to perform direct determinations of the distribution by photocapaci­tance9 or by DLTS8 and of the GB barrier height by J- V deconvolution 7 or by the measurement of the GB capaci­tance. 9

1204 J. Appl. Phys., Vol. 55, No.4, 15 February 1984

IV. CONCLUSIONS

The important results of the present study can be sum­marized as follows.

(a) A self-consistent formulation of the variation of the GB barrier height and the subsequent GB effective recom­bination velocity versus the excitation level is presented, uti­lizing the Shockley-Read-Hall theory of carrier recombina­tion-generation phenomena. This variation depends on the energy distribution of the GB interface states and doping concentration.

(b) The variation of the quasi-Fermi level of the minor­ity carriers, in the grain boundary space-charge layer, as well as in the quasi-neutral region of the adjacent grains has been determined and taken into account.

(c) The effective recombination velocity Self is limited to nearly 1/2 V th as it should be expected for carriers moving in a field free space, i.e., the quasi-neutral region of the grain.

(d) The dependence of Self on EB is nearly exponential only for barrier heights less than 0.2 eV. In this case it has been proved that the quasi-Fermi levels are nearly flat in the GB space-charge region.

(e) The experimental variation of Self with the excitation level seems different either the GB is coherent and decorated or not.

ACKNOWLEDGMENTS

C. M. Singal would like to express his thanks to CNRS (France) for providing a fellowship for this work, which has been partially sponsored by PIRDES (contract no. 1052/ 2005) and by COMES (contract no. 81-11-013-3413) and technically supported by CGE and Photowatt Int. S. A. (France).

'M. Rodot, Adv. So!. Energy 1 (1983) (in press). 2c. H. Seager, D. S. Ginley, and J. D. Zook, App!. Phys. Lett. 36, 831 (1980).

'B. L. Sopori, "Role of Electro-optics in Photovoltaic Energy Conversion," Meeting of the Society of Photooptical Inst. Eng., San Diego, California, edited by S. K. Deb (Washington, 1980), p. 8,248.

4M. Zehaf, H. Amzi1, J. P. Crest, G. Mathian, J. Gervais, S. Martinuzzi, and J. Oualid, Proceedings of the Electrochemical Society, 161 st Meeting, Montreal, May 1982.

'G. Mathian, H. Amzil, M. Zehaf, J. P. Crest, S. Martinuzzi, and J. Oualid, Solid State Electron. 26,131 (1983).

"H. Amzil, M. Zehaf, J. P. Crest, S. Martinuzzi, and J. Oualid, Solar Cells 8, 269 (1983).

7C. H. Seager and G. E. Pike, App!. Phys. Lett. 35, 709 (1979) and 37, 747 (1980).

"C. M. Shyu and L. J. Cheng, Grain Boundaries in Semiconductors, edited by H. J. Leamy, G. E. Pike, and C. H. Seager (North-Holland, New York, 1982), p. 131.

9J. Werner, W. Janisch, and Q. J. Queisser, Solid State Commun. 42, 415 (1982).

IOH. C. Card and E. S. Yang, IEEE Trans. Electron. Devices ED-24, 397 (1977).

"c. M. Singal and B. Prasad, Int. J. Electron. (1982) (in press). 12C. H. Seager, J. App!. Phys. 52, 3960 (1981). 13J. G. Fossum and F. A. Lindholm, IEEE Trans. Electron. Devices ED-27,

692 (1980). 14J. Dugas, J. P. Crest, and J. Oualid, J. Phys. (Paris) 43, CI-83 (1982). 15W. Shockley, Phys. Rev. 91, 228 (1953). lOS. Marklund, Phys. Status Solidi B 85, 673 (1978). 17E. S. Yang, Fundamentals o/Semiconductor Devices (McGraw-Hill, New

York, 1978), p. 38.

Oualid eta/. 1204

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26

ISJ. D. Zook, Appl. Phys. Lett. 37, 223 (1980). 19K B. Adler, A. C. Smith, and R. L. Longini, Introduction to Semiconduc­

tor Physics (Wiley, New York, 1964). 20J. Oualid, M. Bonfils, J. P. Crest, G. Mathian, H. Amzil. J. Dugas. M.

Zehaf, and S. Martinuzzi, Rev. Phys. Appl. 17, 119 (1982). 21H. Baumgart, H. J. Leamy, L. E. Trimble, C. J. Doherty, and G. K. Celler,

Grain Boundaries in Semiconductors, edited by H. J. Leamy, G. E. Pike,

1205 J. Appl. Phys .• Vol. 55, No.4, 15 February 1984

and C. R Seager (North Holland, New York, 1982), p. 31 \. 22The photocells are realized by Photowatt Int. S. A., Caen, france. 23H. Amzil, E. Psaila, M. Zehaf. P. J. Crest, G. Mathian, L. Ammor, S.

Martinuzzi, and J. Oualid, 12th European Solid State Device Research COnference, Munich 11982). p. 67.

24J. L. Liotard, R. Biberian, and J. Cabane, J. Phys. (Paris) 43. CI-213 (1982).

Ouatidetsl. 1205

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.193.164.203 On: Sun, 21 Dec 2014 12:29:26