P e r g a m o n

Renewable Energy, Vol.5, Part I, pp. 166-168, 1994 Elsevier Science Ltd

Printed in Great Britain 0960-1481/94 $7.00+0.00

SOLAR CELLS PARAMETERS DETERMINATION BY CONSTANT ILLUMINATION INDUCED TRANSIENT DECAY METHOD

A. Con~a, I. Gaye, B. Ba, L. Ndiaye and G. Sissoko

Laboratoire d' Energie Solaire, d~partement de physique, Facult¢ des Sciences et Techniques Universit6 Cheikh Anta Diop Dakar- S6n6gal

ABSTRACT

Space-charge capacitance discharge and ringing effects (A. Zondervan et al, 1988) are analysed by means of an electrical model of the solar cell under steady illumination. Coupling this network with an external circuit allows a mathematical simulation of the solar cell electrical behaviour during the transient. Analytical results combined with experimental data enable the determination of the solar cell impedence parameters.

KEYWORDS

Solar cell transient voltage - capacitance - shunt and serie resistances - inductance.

Introduction

A new method of impedence parameters determination in solar cells is presented in this paper.The method is based on an analysis of impedence effects which affect the transient measurements (J.E. Mahan et a l . , 1981, S.R. Lederhandler et al. , 1955, R.H. Kingston et al. 1954).Thus, several alternative techniques are used by authors to avoid such interference effects (M.A. Green, 1983, T.W. Jung et al. , 1984 ). In the present work those effects have been rather analysed to determine the solar cell impedence parameters.

Mathematical formulations

Fig.1 shows an electrical model (M.L. Love joy et al., 1992, K. Atallah et al ) equivalent to the solar cell under illumination. Parameters Co, Rs, Rsho represent respectively the space-charge region capacitance including depletion and diffusion capacitance, the series and shunt resistance of the solar device, and LH the self-inductance.

co llR ,ciT IR, Io. ' I T ,ho ' - r ' - .

Fig.1. Equivalent circuit ofthe solar cell and the external circuit Ri/1 Ci

For t < 0, the solar cell is in open-circuit condition with voltage V o for a given illumination intensity. At t = 0 , by means of the switch S, the solar cell is connected to the external circuit. Thus, due to the change of operating point from Vo to Vp, a transient photovoltage can be observed for t > 0. The boundaries conditions are therefore :

U(t = 0 ) = Vo (1)

dU(t)l o -~" it .o- = (2)

The voltage U(t) at the solar cell terminals is then related to the internal photovoltage V(t) by the differential equation below :

p d 2 U(t) . dU(t) + p , U(t) = V(t)

where Pl , P2 and P3 are expressed as following :

(3)

166

167

Let 8 and (3" be given by :

P1 = LHCsh (4)

P2 = ( LH/Rsh)+ RshCsh (5)

P3 = [1 + (R s/Rsh) ] (6)

Csh = Co+Ci (7)

Rsh = Ri/(1 + Ri/Rsho) (8)

-i E =O = [4PIP 3 /p21 (9)

1) Ifl~ >1, the solution of eqn. (3) is given by : -1

U(t )= C exp (-P2 t / 2 Pl ) sin (l~t + ~) + ( P3 ) V(t ) (10) V(t) is given by:

V(t) = (v o -Vp ) exp (- t ,'z c ) + vp (11)

Where the time constant %c is related to the lifetime "[ and back-surface recombination velocity SB of minority charge carriers in the base region of the solar cell.

~ - 2 = [LH/P3(1 -O)I(Co+C i) (12)

while C and (~ are determined by means of eqn.(1) and (2)

For load impedence such that G << 1, then !3 -2 varies linearly with Ci • Extrapolating 13-2(Ci) to 15 = 0 we obtain Co value. The slope (LH/P3) may be used to determine LH and R s with following assumptions : - if R s << Ri << Rsho, then the slope Si can be considered equal to LH. - Once LH is determined, we can then consider Ri values close to that of Rs (usually less than 2I~).

2) If C = 0 , the solution of eqn. (3) is given by : -1

U( t )=(Bi t + B2) exp(-P2 t / 2 P I ) + (P3) V(t) (13)

Impedence parameters determination in such transient decay mode does not seem obvious.

3) If £ < 1, U(t) is then given by: 1

u(t) = A exp(-P 2t/2P 1) sinh [( P 2t/2P 1 ) (I- I~)2- ] + (P3)1 V(t) (14)

When the load resistance Ri value is such that Rsh >>Rs and g <<1, then approximations in expressions (6), (8) and (9) lead to:

U(t) = A exp(- t/RshCsh) + Vo exp(-t / ' tc) + Vp (15)

When "l:c >> RshCsh, the second term at the right-hand side of eqn. (15) vanishes quickly with time and becomes negligible at the

tail of the photovoltage decay curve. So U(t) may be approximated by :

U(t) = A exp (- t / '~z ) + Vp (16)

%z = [(Ri Rsho) / (Ri+Rsho)] (Co + Ci ) (17)

"~z vs. Ci, for fixed Ri, is linear and by extrapolating to 'l:z = 0, we obtain Co value.

When Ri <<Rsho, thus "gz is a linear function of Ri while for Ri >> Rsho, Ri cannot affect significantly 't z value. In such case, "rz

is quite constant. So the "knee of "Cz vs. Ri corresponds to the Ri value equal to Rsho.

Experimental results and discusions

The experimental setup is represented by fig.2 above.

iJ~ co.rant l~ht source

CiJ~.~R i

Oacilloscope computer

Fig.2. Experimental setup

The study was carried out on a complete small ( 2 cm x 2 cm) polycristalline solar cell.(L. Q. Nam et al ). The solar cell is connected to the load charge by means of a MOSFET switch IRF820 drived by a BRMI 85200 square signal generator. Data

168

acquisition is done with a computer via a TEKTRONIX 2212 digital oscilloscope.

The pseudo-sine mode have been obseved for Ri values less than 10 ~ while the aperiodic voltage decay mode corresponds to Ri values from 50 f~ to 20 kfl. Experimental curves are represented by Fig. (3), (4), (5) and (6) here below :

~v ~2°° ~)I00

i

v

0

-100 i i

0 I 0 20 30 t(us)

p~(E-t3;S~l 80

60

40

20

+ 8~

• 7~

S~

4~

• i • l • !

30 60 90 C(nF)

Fig.3 Pseudo-sine response of the solar cell Fig.4 ~-2 versus Ci for ( Ri =3D.; 4E~; 5t); 6f~; 7~; 8f~ )

~II0'

i

~" 6 0 '

10

70

50

30

10 20 40 60 80 ~(pa) 0

• 40aF

• 20xal ~

• OaF

5 I0 15 20Ri(k~)

Fig.5 : aperiodic response Fig.6 : %z versus Ri ; aperiodic mode for ( Ci = 0nF; 20nF; 40 nF )

Table I. Parameters determined in pseudo sine mode (for V o = 400mV ) and in aperiodic mode (for V o = 220 mV) with 10 % of accuracy

Vo = 400 mV Vo = 220 mV

Co(nF/c m2) LH (It H) Co(nF/cm 2) Rsho (k~)

35 32 36 5

Conclusion

~-2(Ci) graph would allow, in principle, the determination of R s. This is unabled by inaccuracy of effective load resistance determination which must include Ri and the MOSFET drain-source resistance. The main interest of our method is that it allows one to determine the solar cell impedence parameters simultaneously by means of interference effects usually avoided. This technique is suitable to any photovoltaic systems or plants control since our experimental conditions are similar to those at which solar cells usually operate i.e. in steady illumination condition.

REFERENCES

A. Zondervan, L.A. Verhoef, F.A. Lindholm (1988). Lifetime and surface Recombination velocity by Electrical Short-circuit Current Decay. IEEE Trans. Elect. Dev.. 85, 85-88. J.E. Mahan and D.L. Barn (1981). Depletion layer effects in OCVD lifetime measurements. Solid-State Electron. vol. 24. 989-994. S.R. Lederhandler and J.J. Giacoletto (1955). Measurement of minority carrier lifetime and surface effects in junction devices. Proc.. I.R.E, 43,447-483. R.H. Kingston (1954). Switching time in junction solar cells and diodes by forward-biased capacitance measurements. !,E,E,E Tr ctronD i ,25,485-490. M.A. Green (1983). Minority carrier lifetime using compensated differential Open-Circuit Voltage Decay. Solid-State Ele¢lrgn, 26,1117-1122. T.W. Jung, F.A. Lindholm and A. Neugroschel (1984). Unifying view of transient response for determining lifetime and surface recombination velocity in silicon diodes and BSF solar cells. Trans. Electron Devices. 31. 588-595. M.L. Lovejoy, M.R. Melloch, R.K. Ahrenkiel and M.S. Lundstrom (1992). Measurement considerations for field time of- flight studies of minority carder diffusion in III-V semiconductors. Solid-State Electronics. 35, 251-259. K. Atallab and H. Martinot (1984). Equivalent circuit and minority carrier lifetime in heterostructure light emitting diodes. Solid- ~ I l lg~dg~m/I~L~, 375-380 Le Quang Nam, M. Rodot, M. Ghannam, J. Coppye, P. de Schepper, J. Nijs, D. Sarti, I. Perichaud, S. Martinuzzi (1992). Solar cells with 15.6 % efficiency on multicrystalline silicon, using impurity gettering, back surface field and emitter passivation, Int. J. Solar Ener(,v, 11,273-279