comprehensive solar cell mod ling and correlation studies · a - 734a 3 pn_ " 5.2937x 101°...

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m_

COMPREHENSIVE SOLAR CELL MODi=LING ANDCORRELATION STUDIES

RESEARCH TRIANGLE INSTITUTEM

M. L. Lamorter-

I

(a) E

0.604280- 0.49346 E

> ; =_

O g 0.604260- 0.49344 o ;

>_> >_=..,/ >=

¢

0.604240 I' I I 0.49342

AN

'E23.3474- 20,068.,

• C

_ 23.3472- - 20.066 == = _-

(2 :_-, ,_ o_

-? 23.3470 ] 20.064 x

9.904- -- 0.746* (c_

g _'._ 9.902- 0.745 -

- /a: u.

-r

9.900L I [ 0,7440 I 2 3 4

Number of Itelaxions

-.., Fiqure 1. Sola cell terminal char_,',teristics vs. number of iterations:

• ._, (a) open-circuit and mr,ximum power point voltages;.,, (b) short-c.rcu!t ard maximum power pc;nt current

densitie;;_ (c) efficiencyandfillfactor. Twentymesh" _ points, twelve i'mrtion photovoltage s;mulations, and

i twent'/V.l points were used,

r ,_ 349

1986019875-348

https://ntrs.nasa.gov/search.jsp?R=19860019902 2020-05-17T08:34:33+00:00Z

.I

i:HIGH-EFFICIENCY DEVICE RESEARCH

10TM_

4

_---- Estimateof Pnetoinitiate program

ProgramConditions

20 meshpoints

10TM_

I

g1011 --

/ Simulation resultsobtained t

g

10TM

lO9 I I I , , J0 0.32 0.64 0.97 1.29

X, PositionThrough the n+-Emitter X 105 cm

Figure2. Photoexcitedhole concentratio, vs.position i,, the n+-emitter.

350 (_ ,:;",t

-+.--_.. . ,,

1986019875-349

10.0 0.746.-- _..-.

m

• _

"_ 9.8 _ -- 0.745 _

0_ (c) "-

9.6 I l l 0.7440 50 100 15(J 200

Number of Mesh Points

Figure3. Solarcell terminalcharacteristicsvs.numberof meshpoints:(a) open-circuitandmaximumpowerpointvoltages;(b) short-circuitandmaximumpowerpointcurrentdensities;and(c) efficiencyandfUlfactor.Threeiterationspermeshpoint,twelvejunctionphotovoltagesimulations,andtwentyV-I poi,ts wereused.

.i 1

1986019875-350

HIGH-EFFICIENCY DEVICE RESEARCH i'

6 - LEGEND:

_e + 9 mesh points

_ × oQ4' .-"•_ _ 0 27 rn_h points

. qO__ -- _jle _ _Oee _ .81 mesh poines

"_'_-)-" "-i.i×_ g." e., t- _O 0A

• 8_ %°

8 .:_ t_ i(..)0o el

-'r _ __:E2 •

"_6 i t NominalDiililetion "'

A- 245A B- 734A C- 1223_ •

0 ,1 , , ,I , , I, ,"0 181 362 543 724 905 1086 1267 1448

X, Position Through tho Emitter (A)

Figure 4. Photoexcited hole concentration calculated midway between mesh points in the n+mmitter for

3, 9, 27, and 81 mesh points under short-circuit conditions and for three iterations per mesh point. ,

y

(

-,I

t

" 352I

,,__w_.:. i / :..

1986019875-351

I

|

HIGH-EFFICIENCY DEVICE RESEARCH

1.3-LEGEND: •

X 27 me=hpoints ._

• 81 meshpoints1.2(3 and 9 meshpoint cases •not shown,but they coincidewith the 27 end81 point cam) • t" :

1.1- _Je" L

1.0,-- ,

_ .0.9 "_

_," ._._"=

'= o.8 ,,_.'_-6u. }

uJ 0.7-

g.I

0.6- i

}

0.5-

NominalDepletion0.4 - RegionEdge

\0.3 I I I I , I 1 I I I

0 181 362 543 724 905 1086 1267 1448

X, PositionThroughthen+-Emitter(A)

Figure5. Buih-inelectricfieldvs.positioninthen+-emitterof a solarcellusing27 and81 meshpointsundershort.circuitcurrentconditionsandforthreeiterationspermeshpoint.

353 it

• ,; :,.: ,. ..... i ,_j,

1986019875-352

4

t

HIGH-EFFICIENCY DEVICE RESEARCH i

300-J

8

200--

• °

2

/ / Program Conditions100 - f f ,20 meshpoints

_ • 12 photovoltagesimulations ,t = 75 se¢ J • optimum gridseparation :o / • V-I curve (20 biaspoints) ,,

/ • VAX-11/750; Version3,4;: . f floating point hardware

• 95 cell Parameterscalculated; _ per iteration par meshpoint

. / per photovoltage o

/i 0 I I I- I; 0 1 2 3 4

Number of Iterations

Figure6. CPU execution time vs.number of iterations using20 meshpointsand 12 photovolt_ simulations.

1

ii1

354 :_

1986019875-353

y'• HIGH-EFFICIENCY DEVICE RESEAdCH

20--r

: ProgramConditions

' _ • 20 meshpoints_ 15 -- • MAX-11/750; Version3.4;o floating point hardware

, _ "_ .95 cell parameterscalculated ,/4;_ , ,, per iteration per meshpoint

_ per pho

o_:> 10--

S-

' • _O_ y

r 5

! o 1 I I0 I 2 3 4

Number of Iterations: i

, Figure7. CPU computationaltime per photovoltagevs.number of iterations, per meshpoint using20 meshpoints.

/

!!

35_

1986019875-354

v


2000--

1800 -

1400 -- Total

t "G Computetionalv=, 1200--

'_ E.t

e-o,m

8 100o-"" Q

XuJ

Q.¢J

:_ 800 -- Program ConditionsfLu

•, • 3 iterationspermeshpointpot photovoltage

• 12 photovoltege simulations600 -- • Optimum grid separation

" • V-I curve (20 bias points)• VAX-11/750; Version 3.4;

floating point hardware

Y 400 -- ,95 cell parameters calculatedper iteration per mesh point

' per photovo.ltage

200

!J

= 75 -._c0 I I I I0 50 100 150 200

Numberof MeshPoints

Figure 8. CPU execution time vs. number cf mesh points using three iterationsper mesh point and 12 photovoltage simulations,

®/

1986019875-355

.,.! HIGH-EFFICIENCY DEVICE RESEARCH150 -

O

, S"i ; O

100 - Program Conditions

• 3 iterations per mesh pointQ

E • VAX-11/750; Ve_ion 3.4;iT" floating point hardware"_ • 95 ccll parameters calculated.o per iteration per mesh l)ointt.a

per photovoltegeO.E 50--O

U

O.U

, O0

- o I I I i0 50 100 150 200

Number of Mesh Points

. Figure 9. CPU computational time per photo ultage vs.number of meshpoints using three iterations per meshpoint.

• pt,_

r[ 357

1986019875-356

.=j


_ _'-----_ Simulation

MaximumPowerPoint

20-

Experimental

Maximum __

_, PowerPoint

;" _

•-_ JT = 22.41 x 10-3 - 2.7977 x 10-8 (e(Vj-RTJT)/AkT- 1)@

O A = 1.715. RT = 2gi

: --- X Experimental

• Simulation _j/r

- I

o I I I I .. I ,_ :0 0.2 0.4

: Voltage,V

_ Figure10. SimulatedandexperimentallydeterminedV-I curvefor cellNo. 24Cat 300 K, andthe simulateddb.)d(.._quation.

,d

I

"i=J

• _. 358" ft

o

_,_.,. 0 y, ,._..

1986019875-357

q

' HIGH-EFFICIENCY DEVICE RESEARCH

B

<" --_-;'---- "-"-_; -- ----"_-:_" _ M_x_mumPower ,,,/ Point

2O

JT = 22.97 X 10-3 - 1.7780 X 10-7 (e(Vj-RTJT)/AkT- 1) _"

, A = 1.661, RT = 2_ _/" E

E•- _

., _m X Experimental t

o _ • Simulation

. o - I I I I I _r- I_ 0 0.2 0.4 0.6 "

Vohage,V

Figure11. SimulatedandexperimentallydeterminedV-I curvefor cellNo. 2443at 326 K anothediodeequationobtainedfrom the simulationprogram.

.I4=

i

4

'_ 359r,

1986019875-358

' HIGH-EFFICIENCY DEVICE RESEARCH ';

10-4,

10-5

: N

<

10-7

10-8 I I I I _J300 325 350 375 400 425

T, Temperaxure,K

',.,.• Figure 12. Equivalentsaturationcu-mnt densityvs.temperature for cell No. 24C," obtainedfrom simulationresults.

360r'';_

1986019875-359

i '

,,_" HIGH-EFFICIENCY DEVICE RESEARCH Jf

4

1.8

_, 1.7

1.6 -1I

_L:| ,

' I,|

!1.4 ..... I . I , I I I

300 350 400,3

I T, Temperature, K

Figure _3. Diode factor vs. temperaturefor cell No. 24C,obtainedfrom simulationresults.

3,, i®r_" -- -- -': , , in__

1986019875-360

1

HIGH-EFFICIENCY DEVICE RESEARCH 'i

10_-_,_ Legend:__ _ -- -- , X Experimemal

' _ 81 _ _, * Simulation ,_.

'1 4 (a)

• _ Slope- -1.08 x 10.3 (K-1)= o.7I-- __

iz i °_'__--,-.- _-1,14 x 1 '_

; 0.6_ iI (b)

;_ _ 24,mShort-Circuit

! Q I *'

i _E

] MaximumPow.r Point

?

(©)

o.6,j_,..,

.0.2 I. I l I I

300 350 400 (d)

T, Temperature, K

Figure 14. Simulation and exprn-imental bvhavio- of device terminalcharacteristics arG ,reunt_ over the temperature rangeof _00 to a21 K for solar cell No. 24C. Tomlx_aturecoefficients represented by _-iJr._mpondingslop_ are Ilsoshown where the slope i_ t_iquely defined.

362

®:_.. • / ,._"'

1986019875-361

'_ HIGH-EFFICIENCY DEVICE RESEARCH

i

Legend:32 - _" -- -_ Maximum Theoretical

_ .... Simulation, SF = 0' ------ Simulation, SF = 4 x 104cm s-1

Experimental Value = 23,75 mA cm-2

," 30-

_ _: 27.56 mAcm -2

E (R- o.le)_:. _ 26 •

%

- \_ 23.35 mA cm-2

_Z2

- 20- '

v !

,. 18- 1

16-

14 - .I.. t I. _ | I I"_ 0 0,1 0.2 0.3

Air.Oxide Surface Reflectance

Figure 15. Maximum theoretical andsimulationvaluesof short-circuitcurrentdensityvs.air-oxide reflectivity for cell No, 24C where shadowingcc.... tio_ ;snotmade, Maximum theoreticalcurrent is calculatedindependentlyof the

i modeland is basedonly on the absorbedphoton flux and muming 100-_,,._ percentcollectionefficiency.

°!

1986019875-362

t

HIGH-EFFICIENCY DEVICE RESEARCH _r

28-

*- Maximum Theoretical

JSC for R ,, 0.18

26-- '*- - R " 0.18

?_ 24

' i <_ "-Maximum Theoretical

, /j_l JSC for R ,, 0.3_: R - 0.3

i R - 0.18

20

.li _ . / f_-- -- .-0.3 i:I _ 18- f

. i _ Legend:I "_ -- JSC, Simulation " "

16 - J ----- JSCN, Simulation

: J _.m JSC, Manufacturer'sLinearRegressionto the Data

14 I I Ilo lo: lO3 lo4

Ln, BaseElectron Diffusion Length, pm t

Fiuure 16. Simulation of total and baseregion electroncontribution to short-circuitcurrent densityandlinearregressionto experimentaldata at 300 K. Maximum theoreticalcurrent iscalculated

independentlyof the model end is basedonly on the absorbedphoton flux and _-_tzming100 percentcollection efficiency.

q

"1"!

;

r' 364

1986019875-363


OriginalSi SurfacePriorto Oxidation

Oxygen SiAtmosphere

(a)

SiO2 SiO

IA Oxy_n Oxides Si-Rich Oxides I Si

tmospnem of Si I j _

I I- !

O..n_f" '''.ZConcentration1 ._\1 I

I- I,-7.,-'t(b)

Figure 17. One-dimensional model representing the thermally grownSi-richoxides:(a) prior to oxidation;and (b) during oxidation.

,;|

365

1986019875-364

,w,": HIGH-EFFICIENCY DEVICE RESEARCH

Air Silicon-Rich Silicon

.. n1 Oxide n3n2

r hvI v

Figure 18. Model of thin film oxide on siliconunder normal incidence.

_°

_°°.

,=e

J 366

-r

]9860]9875-365

HIGH-EFFICIENCY DEVICE RESEARCH3

! 0.2.;

• _o.,'t

0_

q,

0.3 _ _ 200A(b) -.-- 300

'- -_ 51111

-{ eo.,_ ,/k//

4)

ti

0.4'- ,(c)

m

I o., _oA

!. °0.2

0.1

0 I I I I I I ' I I I I0.2 0.4 0.6 0.8 1.0 1.2

;k,Wavelength,pm

Figure 19. Reflectanceundernormal incidenceat the air-oxide interfacevs. wavelengthfor refractiveindicesrepresentingsilicon-rich

.._ oxides:(a) 2.0; (b) 2.5; end (c) 3.0. Oxide thicknessis a parameter.

,

t ,t

'kJ .367

_ ivl

1986019875-366

: HIGH-EFFICIENCY DEVICE RESEARCH

I¥=b4t2. Photoezvlted hole eone_lmtlom_ th_ _ mtd tim pemont dlffemncee In M n +-emitter _ at three points

(A, B, =rodC), for lout mezflt point diztdimUom= (3 9, 27, 81) md_ three Iterations ml each me=It point.

: d__ _ ep_p_dx dx •

d.p._ P_-P,_m) x 10z x 10"Pnzt dx Pn_)

: I, Emitter dxLocation Mesh Points cm"$ cm-4 _ %

A - 2,l,¢,A 3 Pnel " 4.9185x lOt° 7-4_0x 101s +10.1 +47.39 p,_ - 4.6128x 101° 5.,_105x 10Is +3.3 +5.6

4.5050x 101° 5.0746 x 10is +0.9 +0.9: 8127 ondt4)Pn_: 4.4670 x 101° 5.0286 x 10ts -- m

A - 734A 3 Pn_ " 5.2937x 101° -3"8439x I01S +2.8 -36.49 Pnzs" 5'2697x 101° -3"0244x 101s +2.3 -7.3

27 PM(14)" 5.1820x 10t° -2.8725 x 10is +0.6 - 1.981 PM(41)" 5.1504x 101° -2.8181 x 10is -- --

A - 1223A 3 Pne,1" 2"6325x lOt° -6"9382x 101S +18.9 +11.79 Pries" 2.3454x lOtn -7.8405x lOtS +3.0 +0.3

27 Pn=(_ " 2.2880x 101° -7.8819x lOtS +0.5 -0.381 Pne(ee)" 2.2772x lOt° -7.8618x lOtS -- --

368

1986019875-367


Table3. Pammetemused in the simulationwere providedby ordeduced from manufactumm' specificationsfor cell No. 24C.

Cell "lype n+ p

Totalcellthickness 33 x 10-2 cm

Junctiondepth I_ x 10-5 cm

Contactshadowing 4 percent: Frontsurfaceconcentration 4 X 1019cm-3

Frontsurfaceprofile erfci Backsurfaceconcentration 0

i FrontSRV 4 x 104cm S-1: BackSRV 3 x 103

i Baseregionacceptorconcentration 1.2 x 1017cm-3

Baseelectrondiffusionlength(at300 K) 59 x 10-4 cm

n-Typedopant Arsenic ,

Recombinationtraplevelinn-regio,,_(As) 0.049eV ;

p-Typedopant Boron

I Recombinationtraplevel_np-region(B) 0945 eV

i Recombinationconcentrationconstantinp-region 1 x 1014cm-3Recombinationconcentrationconstantinp-region 9.195x 1012cm-3

Thicknessof SiO2 passivationlayer 50 to200A• Air-oxidereflectivity 0 to 034

(notprovidedbymanufacturer)DiodeResistance" 2 £

Temperature* 300 K326 K371K421K

*Measuredby RTI.

r

369

1986019875-368


•rab,.4(-,).

Manu_ RTI/NC A&T4

Plmmltm' SimuhltlOn _ !14Diff Dim I)4Dlff

,h % 10.12 10.1 -0.2 9.8 -3.3

._ FF 0.749 0.74 - 1.2 0.73 - 2.6

Jac,mAcm -2 22.41 22.80 1.7 22.70 1.3

Vo¢,V 0.6029 0.585 - 1.3 0.5856 - 1.2

, Jmp.mA cm -2 20.58 -- 20.00 -2.9

Vmp.V 0.4918 -- 0.4922 0.08

Table 4(b).

Parameter Simulation RTIINC A&T % Difference

n, °/o 9.1 9.3 2.2

FF 0.724 0.723 -0.1

Js¢, mA cm-2 22.97 23.45 2.1

Voc,V 0.5493 0.5458 - 0.6

" Jmp, mAcm -2' 20.79 20.71 -0,4

Vmp,V 0.4394 0.4462 1.5

Table 4(c).

Parameter $1mulMIon RTIINC A&T % Oiffenmcei

_, % . 7.33 7.6 3.6

FF 0,674 0,687 1.9

-_ Jsc, mAcm -2 23.83 24.28 1.8

Voc,V 0.45454 0.45.56 - 0.2

Jmp,mA cm-2 20.85 21.37 2.5Vmp,V 0.3518 0.3561 1.2

Table 4(d).

Parameter Simulation RTIINC A&T *,4 Difference

_, o/o 5.29 5.4 2.04

FF 0.609 0,62 1.77

JJc, mAcm-2 24.63 24.78 0.67

Vo¢,V 0.3525 0.3522 -0.10

Jmp,rnAcm-2 20.41 20.85 2.10

• VmD,V U.2592 0.258 - 0.70

T|ble 4. Results of validation study =_sln_ cell No. 24C, with corresponding parlmeterslimed in Table 3, and where 0,18 i| used for the air-oxide refllctlvlty: e) 300 K;

",,, b) 326 K; c) 371 K; and d) 421 K. Simulation results are obtained using three

.: iterations end 30 mesh points equally separated In the n- end p-regions.

r 370 (_

1986019875-369


Table5. Simuletionand expedmental temperaturecoefficientsand the percent differencefar ceh No. 24C_

_' . Temperature 7 PercentCoefficient Simulation Experimental Dl_rence

dv/IdT,(% K-1) -4.00 x 10-2 -392 x 10-2 -2_4

d(FF)/dT,(K-1) -1.14 x 10-3 -1.08 x 10-3 -5.90

_" dVoc/dT,(VK-1) -2.10 x 10-3 -294 x 10-3 -2.90=

ClVmp/dT,(VK-1) -%g3 x 10-3 -1.94 x 10-3 052I

z

!Table6. Summaryof experimental,calculated, and81muleted

short,,cimuitcurrentdensityfor cell No. 24C at 300 K.

Short-clrcuHMethod currentdensity* Reflectivity Comments

Expedrnental 23.75 x 10-3 _nAcm-2 unknown agreementwithRTIdata I

Calculate0 18..50x 10-3 mAcm-2 unknown usi_,._manufa_urer'sspectral ,(simulationprogram responsecurveandtherevisedwasnotused) AM1.5spectraldata ;

Calculated 22.90 x 10-3 mAcm-2 032 maximumtheoreticalvalue,by(.,=.;mulatedprogram calculatingabsorbedfluxandwasnotu3ed) 2756 x 10-3 mAcm-2 0.18 assuming100%collectionefficiency

,,,, ,,,

Simulat._n 2335 x 10-3 mAcm-2 0.18 RTIsimulationprogramusedResults (resultantcollectionefficiency

is approxima_ely85%)

*Uncorrectedforcontactshadowing.

!,j

371 _

1986019875-370

comprehensive solar cell mod ling and correlation studies · a - 734a 3 pn_ " 5.2937x 101°...

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