THE SOLAR CELL LASER SCANNER

Emmett L. Mi l l e r , Shy-Shiun Chern and Alex Shumka

J e t Propulsion Laboratory, Ca l i fo rn ia I n s t i t u t e of Technology

INTRODUCTION

A s p a r t of t h e Low Cost Solar Array Program a t J e t Propulsion Laboratory, f a i l u r e analyses have been performed on over 300 photovol ta ic modules from t h i r t y d i f f e r e n t manufacturers and f i v e coun- t r i e s . Because of t h e volume of work and the var- i e t y of module types encountered, it has been nec- e s sa ry t o develop non-destructive techniques t o r ap id ly l o c a t e the f a i l u r e s i t e s . This paper w i l l p resent design d e t a i l s and r e s u l t s obtained wi th one instrument developed s p e c i f i c a l l y f o r t h i s purpose, t he Solar Ce l l Laser Scanner (SCLS). The e f f e c t s of applying a b i a s cu r ren t t o t h e modules w i l l a l s o be d iscussed, based upon experimental observat ions and computer generated predic t ions .

THE INSTRUMENT

Preliminary r e s u l t s obtained wi th a prototype SCLS were presented e a r l i e r ( 1 ) . The present in- strument is a completely new design, incorpora t ing s i g n i f i c a n t l y improved r e so lu t ion , scanning and d i sp lay c a p a b i l i t i e s . The instrument is shown i n Figure 1, and a block diagram of the p r i n c i p a l components i s shown in Figure 2. It u t i l i z e s a focused, t e n m i l l i w a t t helium-neon l a s e r beam, raster-scanned over t h e s o l a r module by galvanom- eter-driven mirrors. Op t i ca l components a r e mounted on a 3' x 4' o p t i c a l t a b l e (Figure 3 ) , pro- viding a s t a b l e platform wi th ample space f o r addi- t i o n of a u x i l i a r y apparatus. Standard, commercial- l y a v a i l a b l e components were used wherever poss ib l e , t o minimize c o s t s and development time. This ap- proach r e s u l t e d in a system which is n o t a s compact o r po r t ab le a s an in t eg ra t ed design, but which a l - lows grea t f l e x i b i l i t y f o r f u t u r e modifications.

An "inverted1' geometry was chosen t o provide a t a r g e t pos i t i on located a s c l o s e a s poss ib l e t o t h e scanning mi r ro r s (Module Pos i t i on A i n Figure 2) . For scanning an e n t i r e module, a 45' mirror d i r e c t s t h e beam onto module p o s i t i o n B. The o p t i c a l system c o n s i s t s of an ape r tu re an& v a r i a b l e a t t enua to r , a

The research described i n t h i s paper was c a r r i e d out a t t h e J e t Propulsion Laboratory, Ca l i fo rn ia I n s t i - t u t e of Technology, and was sponsored by t h e Depart- ment of Energy through an agreement wi th NASA.

FIGURE 1. The Solar C e l l Laser Scanner.

FIGURE 2. Block Diagram of t h e Solar C e l l Laser Scanner.

Proceedings of the 15th IEEE Photovoltaic Specialists ConferenceOrlando, FL, May 11-15, 1981, pp. 1126-1133

FIGURE 3. P r inc ipa l o p t i c a l components. L = Laser; S = Shut ter and Aperture; A = Variable Attenuator; E = Beam Expander and S p a t i a l F i l t e r ; F = Focusing Lens; M = Galvanometer Driven Mirrors.

bulb-operated s h u t t e r , and a 9X beam expander and s p a t i a l f i l t e r . Focusing is accomplished by posi- t ion ing t h e output l e n s of t h e beam expander, using a separa te rack-and-pinion mount. The approximate diameter of t h e focused spot is determined by focusing dis tance, D, t h e foca l length of the e x i t l ens , F, and the pinhole diameter, d , where F=80mm and d = 25 um:

D - F Spot Diameter = -

F d*

Thus, f o r the two module pos i t ions , t h e predic ted spot s i z e is:

Pos i t ion A D = 210 mm Size = 3.04 mm (1.57 mil )

Pos i t ion B D = 1730 mm Size = 0.52 mm (20.5 mil)

The scanning system c o n s i s t s of two orthogonally mounted galvanometers with pos i t ion sensors, pro- v id ing feedback t o t h e galvanometer c o n t r o l l e r s and pos i t ion s i g n a i s t o t h e d i sp lay system. The gal- vanometers a r e dr iven by standard e l e c t r i c a l func- t i o n generators with a t r i a n g l e waveform. The beam p o s i t i o n i s monitored on an osci l loscope, whfch a l s o serves t o d i sp lay t h e photocurrent s i g n a l am- p l i tude . I n addi t ion, t h e module under t e s t may be observed continuously on a closed c i r c u i t TV sys- t e m , which a i d s i n posi t ioning t h e beam on a par- t i c u l a r area.

* Catalog Data Sheet, Or ie l Corporation

The e a r l i e r r e s u l t s were obtained by d i r e c t imaging of t h e photocurrent on a standard osc i l lo - scope. This has now been replaced by an image s to r - age system, which permits the photocurrent image t o be s tored a t the slow galvanometer scan r a t e and then displayed f o r extended per iods on a high reso- l u t i o n TV monitor. The scan converter/image s to r - age u n i t r ece ives i ts beam pos i t ion s i g n a l s from t h e mirror pos i t ion s igna l s through t h e scan con t ro l u n i t developed in-house. This scan con t ro l u n i t in- corporates a s i n g l e con t ro l which serves t o vary t h e magnification of t h e image by a t tenuat ing the def lec- t i o n s igna l s fed t o t h e galvanometer con t ro l l e r s , and simultaneously amplifying t h e mirror pos i t ion s igna l outputs an equivalent amount. Thus, t h e beam pos i t ion s igna l s fed t o the image s torage u n i t always have the same amplitude, independent of the s i z e of t h e a rea scanned. This scanned a rea can be posit ioned anywhere on a 3' x 4' a rea (Module posi- t i o n B). A sweep s igna l invers ion switch i s pro- vided f o r use wi th t h e 45' mirror t o r e t a i n co r rec t image re la t ionsh ips . The most c r i t i c a l p a r t of t h e d i sp lay system is the s igna l ampl i f ier . This must not only amplify t h e small photocurrent generated by t h e l a s e r , but permit app l i ca t ion of a consider- ab ly l a r g e r dc b i a s cu r ren t through t h e module. The ampl i f i e r developed a t JPL is e s s e n t i a l l y a current- to-voltage converter with v a r i a b l e o f f s e t t o ad jus t f o r the dc vol tage r e s u l t i n g from app l i ca t ion of a dc forward b i a s cu r ren t t o t h e module. A highly s t ab le , ex te rna l dc cu r ren t source i s u t i l i z e d t o supply t h i s b ias . The output ga in ,po la r i ty and o f f s e t a r e con t ro l l ab le , and d i g i t a l panel meters a r e provided f o r se tup and monitoring purposes.

P r a c t i c a l Limitations

Ear l ig r , t h e minimum o p t i c a l path length and re- s u l t a n t spot s i z e were discussed. Actual r e so lu t ion is l imi ted by a number of o ther f a c t o r s including:

1. Sca t t e r ing from'dust i n the atmosphere and on the var ious o p t i c a l surfaces .

2. Imperfections i n t h e o p t i c a l components.

3. The textured g l a s s supers t r a t e used on many modules.

4. Ref lect ions wi thin the modules.

5. Defocusing v s scan angle.

6. *Resolution of t h e image s to rage and d i sp lay system.

7. Scanning speedltime-constant e f f e c t s .

8. E l e c t r i c a l no i se and spurious pickup.

9 . Signal d r i f t when using b i a s current .

Other than per iodic cleaning, l i t t l e can be done about t h e f i r s t four f ac to r s . Defocusing versus scan angle is a l imi t ing f a c t o r when scan- ning a reas g rea te r than about 50mm diameter a t pos i t ion A, o r 60 cm diameter a t pos i t ion B. A t t h e extreme d e f l e c t i o n angle of f12.5' mirror

angle , t h e defocused spot s i z e would be about 2 m , compared wi th t h e center l i n e spot s i z e of 0.05 - 0.5 mrn. When higher r e so lu t ion is required, i t i s necessary t o l i m i t t h e d e f l e c t i o n angle and inc rease t h e image magnification on t h e TV screen. The image s torage/scan converter system and t h e TV mon- i t o r a r e high reso lu t ion u n i t s , each capable of over 1000 l i n e s r e so lu t ion . A t un i ty magnification, t h i s corresponds t o an image r e s o l u t i o n of about 0.25mm. The s tored image can be enlarged wi th the zoom con- t r o l up t o 36X to take advantage of t h i s c a p a b i l i t y . A TV r a t e of 1225 l ines / f rame is u t i l i z e d , r a t h e r than t h e standard 525 l i n e s , t o f u r t h e r improve t h e displayed image.

Scanning speedlt ime constant e f f e c t s a r e q u i t e no t i ceab le on modules from c e r t a i n manufacturers, e s p e c i a l l y those using l a r g e a rea c e l l s with high shunt r e s i s t a n c e . These e f f e c t s can be p a r t i a l l y av@femE $j i gpplging a b i a s cu r ren t t o t h e panel; however, t h e operator may be forced t o use a much slower scan speed than normal. This is more of an operat ing l i m i t a t i o n than a reso lu t ion l i m i t a t i o n , so long a s t h e operator monitors t h e s igna l wave- form and a d j u s t s these parameters t o e l iminate time constant e f f e c t s ( i .e . , overshoot and undershoot when t h e beam crosses me ta l l i za t ion s t r i p s ) .

E l e c t r i c a l no i se pickup has been troublesome, compounded by t h e antenna-like l a r g e su r face a rea of t h e module. Considerable ca re must be paid t o sh ie ld ing and e l iminat ing ground loops. An addi- t i o n a l problem occasional ly encountered is s igna l d r i f t when applying l a r g e r than normal b i a s cur- r e n t s , e spec ia l ly t o modules wi th high shunt r e s i s - tance c e l l s . This is suggestive of a heat ing ef- f e c t , but t h e mechanism has not y e t been conclu- s i v e l y i d e n t i f i e d .

Attempts have been made t o measure t h e a c t u a l r e so lu t ion of t h e instrument by scanning over a sharp edge placed i n f r o n t of a bare photocel l a t var ious working d i s t ances . With t h e instrument i n ILS uurual condlclon, ~ . e . , without taking unusual measures t o optimize i t s performance, t h e approxi- mate beam diameter was about 0.5mm a t pos i t ion B , i n agreement wi th the predic ted c a p a b i l i t y of t h e beam expander. A t p o s i t i o n A, t h e measurement i s more d i f f i c u l t t o perform accurate ly , but t h e ap- parent beam diameter was i n t h e range of 0.05 - 0.1 m, somewhat l a r g e r than predic ted.

RESULTS

A t JPL t h e SCLS has been used rou t ine ly on mod- u l e s submitted f o r f a i l u r e ana lys i s . Many of these modu-les had previously been, subj ec ted t o environ- mental t e s t i n g o r extended f i e l d service , and ex- h ib i t ed s i g n i f i c a n t l o s s e s in power output. Cracked c e l l s , f r ac tu red in terconnect ions , delami- nat ion, and va r ious o the r f a i l u r e modes have been encountered. The most common use of t h e SCLS has been t h e rapid loca t ion of cracked o r shorted c e l l s which have a s i g n i f i c a n t e f f e c t on the module out- put. Rela t ively l i t t l e d e t a i l e d , high reso lu t ion study of individual d e f e c t s has been done a s ye t , al though other author,^ have reported on t h e use- fu lness of t h e technique f o r such inves t iga t ions (2-4).

The SCLS images a r e o f t e n q u i t e s t r i k i n g f o r these damaged modules. Figure 4 shows an example where por t ions of c e l l s have been p a r t i a l l y i so- l a t e d from t h e remainder by cracks. The r e s i s t i v e connection ac ross t h e crack a l lows these por t ions t o be imaged a t reduced i n t e n s i t y . Figure 5 shows a l a r g e (2' x 4 ' ) module conta ining 224 ribbon c e l l s , two of which e x h i b i t missing a r e a s because of cracks . Locating cracks on these c e l l s by v i s u a l inspect ion is usua l ly d i f f i c u l t and t ed ious , where- a s the SCLS image c l e a r l y r e v e a l s which c e l l s have s i g n i f i c a n t e l e c t r i c a l degradation. Of course , these modules may have o the r c e l l s wi th l o c a l i z e d d e f e c t s o r cracks which have not a f fec ted t h e i r e l e c t r i c a l c h a r a c t e r i s t i c s appreciably . Such de- f e c t s may.Le revealed a t higher magnif ica t ions . A l l of these module images e x h i b i t s u b s t a n t i a l d i f f e r - ences i n image b r igh tness from c e l l t o c e l l . At zero b i a s cu r ren t , observing t h e s h o r t c i r c u i t cur- r e n t image, t h e r e i s a d i r e c t c o r r e l a t i o n between the b r igh tness of a c e l l and its shunt r e s i s t a n c e . It was noted, however, t h a t t h i s r e l a t i o n s h i p changes wi th a p p l i c a t i o n of forward dc b i a s c u r r e n t . The r e l a t i v e b r igh tness of c e l l s wi th in a module may change t o t h e ex ten t t h a t "dark" c e l l s ( a t zero b ias ) may become b r i g h t , and i n i t i a l l y b r i g h t c e l l s may become da rk under biased condi t ions . A t y p i c a l sequence is shown i n Figure 6. Note t h e complete r e v e r s a l of r e l a t i v e b r igh tness of s e v e r a l c e l l s a s the cu r ren t was increased £om zero t o 48 mA. A t higher b i a s cu r ren t s , t h e ce l l - to -ce l l b r igh tness v a r i a t i o n s tended t o disappear a s t h e o v e r a l l s ig- n a l i n t e n s i t y decreased.

MODULE EFFECTS ON IMAGE BRIGHTNESS

Unlike t h e more common s o l a r module measurements, SCLS generated photocurrent i s obtained from only a

FIGURE 4. SCLS image of a 23" x 23" module containing 42 3" diameter c e l l s . Arrows i n d i c a t e cracked c e l l s .

very small spot i l luminated a t very high i n t e n s i t y , perhaps 10-50 suns. Character izat ion of t h e re- sponse of a cell and a module t o t h i s type of s t i m - u l u s is e s s e n t i a l f o r understanding t h e e f f e c t of c e l l parameters and d e f e c t s on t h e output. The f o l - lowing d i scuss ion considers v a r i a t i o n s of s e r i e s and shunt r e s i s t a n c e and diode s a t u r a t i o n cur ren t , which a r e shown t o have a s i g n i f i c a n t e f f e c t on t h e SCLS image b r igh tness of individual c e l l s i n a mod- ule . E f f e c t s of c e l l shee t r e s i s t a n c e on t h e images of s i n g l e c e l l s have been inves t iga ted by o the rs , and a r e not discussed here ( 2 , 4 ) .

I n Figure 7, a standard equivalent c i r c u i t f o r a c e l l is modified t o separa te t h e c e l l i n t o i l lumi- nated and non-illuminated por t ions . This c e l l is connected i n s e r i e s wi th o the rs t o form a module. Becai~se only a small por t ion of t h e c e l l is i l lumi- nated at any time, it may be assumed t h a t t t e shunt r e s i s t a n c e of the non-illuminated region, R s H ~ , is almost equal t o t h a t of the e n t i r e c e l l , RSHX. Also, f o r slow scanning speeds, junction capacitance ef- f e c t s may be neglected. I n Figure 7 , i t i s assumed t h a t t h i s s e r i e s s t r i n g of c e l l s a r e connected t o a current-to-voltage converter having zero input impe- dance, and no ex te rna l cur ren t b i a s is appl ied. Typi- c a l shunt r e s i s t a n c e s a r e i n the range oil-500ohms, and photocurrents from the l a s e r a r e a few m i l l i - amperes o r l e s s . Under these condi t ions , t o a f i r s t approximation, diode e f f e c t s may be neglected and t h e equivalent c i r c u i t becomes a simple resis- tance network. Consequently, t h e output c u r r e n t becomes d i r e c t l y proport ional t o the shunt r e s i s - tance of t h e c e l l being i l luminated.

Bias Current E f f e c t s

The output c h a r a c t e r i s t i c s a r e q u i t e d i f f e r e n t when an e x t e r n a l dc b i a s cur ren t i s appl ied t o t h e module. Referring t o Figure 8 , when a b i a s cur ren t , IB is applied from a constant cur ren t generator , vo l t age source, EB, is adjusted t o o f f s e t the module terminal dc vol tage, VB, r e s u l t i n g f r o m t h e b i a s cur- r en t . Thus, the net dc vol tage a t t h e current-to-

FIGURE 5. SCLS image of a 2 ' x 4 ' module containing 224 ribbon c e l l s . Arrows i n d i c a t e cracked c e l l s .

vo l t age converter inpu t s is zero. Under these con- d i t i o n s , IL = -IB and IS = 0. When a spot is i l l u - minated on a cell, t h e module current , IL, is com- posed of t h e b i a s cur ren t p lus an add i t iona l term, t h e photocurrent, flowing in t h e opposi te d i rec t ion . ~ h u s , IL = IS -IB, o r IS = IL + IB. This is t h e s ig - n a l cu r ren t which is amplified and imaged.

It would be poss ib le t o apply t h e same simplify- ing a s s y p t i o n s made earlier regarding Figure 7, i. e. , R S H ~ ss R s H ~ , and c a l c u l a t e t h e s i g n a l cur ren t of Figure 8 by applying t h e standard equation f o r diode cur ren t a s a funct ion of c e l l voltage. How- ever, s i n c e a computer w i l l be used t o provide numer- i c a l so lu t ions , it is not necessary t o make t h a t approximation. I n Appendix A, t h e following equa- t i o n is derived which r e l a t e s t h e s i g n a l cur ren t t o the parameters of t h e spot being i l luminated, the c e l l on which t h a t spot is located, and t h e remainder of t h e module:

CX is a constant , dependent upon the c h a r a c t e r i s t i c s of t h e spot being i l luminated, i . e . , rSX and rSHX. Fy i s a funct ion of t h e s lopes of t h e I-V curves ( i . e . , the dynamic impedances) of the c e l l being scanned and the remainder of the module a t the se lec ted b i a s cur ren t . ZM i s the e f f e c t i v e dc impedance of t h e remainder of the module a t t h e se lec ted b i a s cur ren t .

Computer Generated Resul ts

An 1108 EXEC 8 computing system was u t i l i z e d t o solve equation (1) f o r se lec ted s o l a r c e l l and module parameters, following an i t e r a t i v e proce- dure. The r e s u l t s presented i n t h i s paper a r e based ,upon the assumptions l i s t e d i n Appendix B. Various curves of Is vs VB were p lo t t ed f o r t h e following cases:

1. The c e l l being scanned contains loca l i zed inhomogeneities, represented by values of r~ and rsHX which d i f f e r from the nominal vafues .

2. The c e l l being scanned has t o t a l s e r i e s and/ o r shunt r e s i s t a n c e s which d i f f e r from t h e nominal values .

The computer simulation r e s u l t s a r e shown i n Figures 9 and 10. A reference curve f o r a c e l l hav- ing nominal parameters was included on each f igure . It should be r e a l i z e d t h a t these curves represen t a f i r s t order simulation. The computer program- tends t o average the dynamic impedances, ZM and Zy, between t h e i r values with and without i l luminat ion. This is, i n e f f e c t , an assumption of low c a r r i e r

A B C

a) No Bias Current

A B C

-

FIGURE 6. Cell-to-cell br ightness changes with b i a s cur ren t .

i n j e c t i o n l eve l . The r e s u l t a n t curves a r e not in- tended t o represent any p a r t i c u l a r type of d e f e c t , but t o suggest t h e general trend of t h e i r e f f e c t s .

Figure 9 shows t h e e f f e c t s of loca l ized in- homogeneities, i . e . , where t h e parameters of t h e spot being il luminated a r e abnormal, but a l l c e l l s i n the module have t h e same nominal parameters. A s expected, higher s e r i e s r e s i s t a n c e o r diode current r e s u l t i n lower output. However, a region of lower than nominal shunt res i s tance , which would appear dark a t zero o r low b i a s cur ren t , may become br igh te r than surrounding regions a t b i a s cur ren t s over some crossover point , a s shown i n Figure 9b. ,Also, t h e d i f fe rence i n s igna l l e v e l , and there- f o r e t h e image con t ras t between regions of d i f f e r - ing parameters v a r i e s with t h e b i a s cur ren t l e v e l .

Figure 10 shows t h e dramatic e f f e c t of b i a s cur- r e n t on t h e ce l l - to -ce l l br ightness , when t h e c e l l being scanned has lower than nominal shunt r e s i s - tance. In agreement with t h e experimental r e s u l t s shown i n Figure 6, such a c e l l would appear dark a t low b i a s currents , but increase i n br ightness t o a much higher l e v e l a t some higher current l e v e l . Based upon these and other computer simulations, t h e following conclusions can be reached :

Images of c e l l s wi th low shunt r e s i s t a n c e w i l l i nc rease i n b r igh tness with appl ica- t i o n of b ias c u r r e n t , while normal c e l l images decrease i n br ightness . A cross- over point may be reached, such t h a t t h e ce l l - to -ce l l b r igh tness r a t i o s a r e reversed.

Similar bcightness changes could occur on loca l ized inhomogeneities.

Proper s e l e c t i o n of b i a s c u r r e n t l e v e l can improve t h e c o n t r a s t and d e t e c t a b i l i t y of loca l ized inhomogeneities.

CONCLUSIONS

The SCLS has proven t o be an exceedingLy u s e f u l instrument f o r t h e non-destructive evaluat ion and f a i l u r e a n a l y s i s of e n t i r e s o l a r modules, a s we l l a s ind iv idua l c e l l s . It can r a p i d l y d i sc r imina te between d e f e c t s which have an e f f e c t on t h e power output of modules and those which may only be cos- metic. Understanding t h e i n t e r a c t i o n between t h e in tense spot i l luminat ion and t h e module can f u r t h e r increase i ts usefulness , by permit t ing op t i - mum s e l e c t i o n of b i a s conditions.

FIGURE 8. DC equivalent of a module of N c e l l s with s i n g l e spot i l luminat ion con- nected t o a current-to-voltage converter , C, with a dc o f f s e t vol tage, EB, and a b i a s cur ren t , IB'

The dark equivalent c i r c u i t f o r t h e e n t i r e c e l l .

b- FIGURE 7. DC equivalent of a module of N c e l l s

with s i n g l e spot i l luminat ion, connected t o a current-to-voltage converter with no b i a s cur ren t .

The same il luminated a rea equivalent c i r c u i t a s shown i n Figure 8.

An add i t iona l current generator, IX, i n p a r a l l e l with the above, where IX i s equal t o t h e current which would flow through t h e "il luminated area" a t a c e l l vol tage, VX, i f the l a s e r beam were o f f .

Now, with t h i s subs t i tu t ion , Iy i n Figure 8 becomes t h e t o t a l dark current which would flow through Cel l X a t vol tage VX. This may be calcu- l a ted from t h e standard diode equation. 10, the current flowing from the illuminaSed area, i? now the sum of two currents , IX and IoX, where IoX is t h a t por t ion of t h e generated photocurrents, IoX, which flows out of t h e i l luminated area. Applying t h e standard diode equation, these cur ren t s a re :

where :

I = diode d i f fus ion and recombination D~ and I% cur ren t s

0 = q / k ~ : q = e lec t ron charge; k = Boltzmann1s constant T = temperature, O K

Also :

APPENDIX A

Derivation of Equation (1)

In Figure 8, t h e c e l l being scanned by t h e l a s e r , Ce l l X, is represented by a small i l luminated area , ac t ing a s a cur ren t generator , i n p a r a l l e l with t h e remaining non-illuminated area . The non-illumi- nated remainder a c t s a s a passive diode-res is tor network load. This "load" equivalent c i r c u i t d i f - f e r s from t h a t f o r t h e e n t i r e c e l l only by the ef- f e c t s of t h e "missing" i l luminated area . By adding such an a rea t o t h e non-illuminated c e l l , i t s equiv- a l e n t c i r c u i t may be replaced by t h a t of the e n t i r e c e l l . This added a rea a c t s a s an add i t iona l cur- Define : r e n t load which must be compensated f o r by a paral- l e l current generator , which suppl ies p rec i se ly t h e same amount of cur ren t . Therefore, the representa- t i o n of Ce l l X i n Figure 8 may be replaced by a p a r a l l e l combination of t h r e e elements:

150 I I I I I I I I I

- 1) STANDARD PARAMETERS

MODULE VOLTAGE, V B

a) Effects of High Diode Current (2) and High Series Resistance (3)

01 I 1 1 I I I I 1 0 10 20, 30 40

MODULE VOLTAGE, V B

150.

b) Effects of Low Shunt Resistance

I I I I I I I I

- 1) STANDARD PARAMETERS -

FIGURE 9. IS vs VB for a 40 cell module, showing effects of localized inhomogeneities at spot being illuminated. Iox = 5 mA.

150- 1 I I I I I I I I 1) STANDARD - PARAMETERS -

120 - 2) DIODE CURRENT

4 = 3 (STANDARD) - a (A

- - 90- 5

- OC w 3 - 0

-

60- - - V) P - -

30- - - -

0 I I I I I I I I I 0 8 16 24 32 40

MODULE VOLTAGE, V B

FIGURE 10. IS vs VB for a 40 cell module, showing effects of non-average parameters on the cell being scanned, IOx = 2 mA.

From the above, it may be shown that:

(5) Let ZM be defined as the effective static impedance of the (N-1) non-illuminated cells. The voltage across the cell being scanned, VX, can then be rep- resented as:

ZM is a function of IL which may be approximated by calculations, based upon average cell parameters for the type of cells in the module.

Also, by inspection of Figure 8:

It should be r e c a l l e d t h a t VB is being held cons tan t because of t h e fixed o f f s e t vo l t age , EB, and t h e low input impedance of the current-to-voltage conver ter . Therefore, when t h e l a s e r i l lumina tes a spo t , IL decreases by an amount IS, r e s u l t i n g i n a drop i n t h e vo l t age a c r o s s t h e (N-1) non-illuminated c e l l s , AV. Iy must inc rease from its i n i t i a l value , IB, by some amount, A I y , such t h a t t h e corresponding in- c r e a s e i n t h e v o l t a g e drop a c r o s s c e l l X, AV, com- pensates f o r t h e reduced voltage-drop ac ross t h e o the r c e l l s of t h e module. Let Zy and ZM be defined a s t h e dynamic impedance of t h e c e l l X, and t h a t of t h e r e s t of t h e s t r i n g , r e spec t ive ly . AIy can then be given by:

Define:

Is Fy = ~g. i . e . , Py = r a t i o of t h e output s i g n a l (9)

c u r r e n t t o t h e photocurrent in jec ted ac ross c e l l X. Applying equat ions (7) and (8), (9) becomes:

Fy can t h e r e f o r e b e ca lcu la ted from t h e character- i s t i c s of c e l l X and t h e remaining non-illuminated c e l l s , by ass ign ing appropr ia t e va lues f o r t h e i r d iode c u r r e n t s , s e r i e s and shunt r e s i s t a n c e s , f o r s e l e c t e d c u r r e n t l e v e l s , IB.

F i n a l l y , t h e d e s i r e d equat ion ( I ) , i s der ived by s u b s t i t u t i n g (6) and (9) i n t o (5).

APPENDIX B

Assumed cond i t ions f o r computer-generated curves of Figures 9 and 10.

1. Module c o n s i s t s of a s e r i e s s t r i n g of f o r t y c e l l s , each having a diameter of 25 mm.

2. Module i s a t room temperature; the re fo re : f? = 39.

3 . Laser generated photocurrent : I = 2 mA and 5 mA. Ox

4. Nominal c e l l parameters assumed f o r a l l 39 non-illuminated c e l l s :

-10 J = 0.7 x 1 0 amperes Px

J?x = 0.54 x amperes

R = 0.09 ohms sx

5. Laser spot s i z e = 1 mm. Therefore, t h e fac- t o r used t o c a l c u l a t e rSX and r S ~ X i s 625,

from t h e r a t i o of t h e spot s i z e t o t h e c e l l a r e a .

REFERENCES

1. E.L. Mi l l e r , A. Shumka, and M. Gauthier, "A Laser Scanner f o r Solar C e l l Evaluation and F a i l u r e Analysis", Proceedings of t h e Advanced Techniques i n F a i l u r e Analysis Symposium (IEEE), pp 16-24, (1978).

2. K. Lehovec and A. Fedotowsky, "Scanning Light Spot Analysis of Faul ty Solar Cells", Sol id S t a t e E lec t ron ics 23, pp 365-576 (1980).

3. D.A. Yates and R.O. Be l l , "Defect Analysis of Ribbon Solar C e l l s Using A Laser Scanner1', Pro- ceedings of t h e 14 th IEEE Photovol ta ic Special- is ts Conference, pp 1402-1403 (1980).

4. D.E. Sawyer, "A Technique f o r Using an Opt ica l Scanner t o Reveal Solar C e l l Defects", Proceed- ings of t h e 13 th IEEE Photovol ta ic S p e c i a l i s t s Conference, pp 1249-1250 (1978).

ACKNOWLEDGEMENTS

The authors would l i k e t o express t h e i r appreci- a t i o n t o Sid Johnson and Tam Nguyen (JPL) f p r pro- v id ing many of t h e SCLS photographs used i n t h i s r e p o r t . They would a l s o l i k e t o thank Bruce Hancock (now a t the Univers i ty of Ca l i fo rn ia a t Santa Barbara) f o r h i s work i n t h e development of t h e s i g n a l ampl i f i e r , and Harold Becker f o r t h e des ign and development of t h e camera used t o photo- graph the TV monitor.