Applicability of electrical short circuit current decay for solar cell characterization: limits and comparison to other methods

ELSEVIER Solar Energy Materials and Solar Cells 36 (1995) 241-259

~ r n ~ w ~ nna Solu ~als

Applicability of electrical short circuit current decay for solar cell characterization: limits and comparison to other

methods

Klaus Burgard a,*, Wilfried Schmidt a, Wilhelm Warta b

a Deutsche Aerospace AG, Theresienstr. 2, D-74072 Heilbronn, Germany b Fraunhofer-lnstitut fiir Solare Energiesysteme, Oltmannsstr. 5, D-79100 Freiburg, Germany

Received 1 May 1994

Abstract

The electrical short-circuit current decay (ESCCD) method for determination of the bulk diffusion length L and the effective rear surface recombination velocity S is investigated with regard to application in solar cell development. To solve the major experimental problem, the fairly damped oscillations caused by parasitic capacitances and inductances, we introduced a calculation technique that fits the exponential decay plus three damped oscillations to the experimental curve. The measured effective diffusion lengths are compared to the results of an open-circuit voltage decay (OCVD) measurement and an evaluation of the spectral response of the solar cell, showing that only the ESCCD results are exclusively related to the base of the cell. The validity of the method is confirmed by the good agreement of the measured diffusion lengths and surface recombination velocities with those from two comparative measurements - - determination of the bulk diffusion length performed on the unprocessed wafers using photoluminescence profile measurement and determination of L and S by evaluating the asymptotic decay time constants of the short-circuit current and the open-circuit voltage decay after optical excitation. Applying the method to electron-irradiated cells, decreasing diffusion lengths and increasing rear surface recombination velocities with increasing fluences could be observed. A discussion of the errors related to the ESCCD method shows that the accuracy in L and S depends critically on the knowledge of the device parameters.

* Corresponding author. Phone: (+49) 713167-2665, Fax: (+49) 713167-2727.

0927-0248/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0927-0248(94)00176-6

242 K. Burgard et al. / Solar Energy. Materials and Solar Cells" 36 (1995) 241-259

1. Introduction

Modern commercial solar cells are no longer 'thick' cells, where the base thickness greatly exceeds the minority carrier diffusion length. Recombination at the rear surface influences the properties of the base even in low cost solar cells. The two rather simple methods used until now in the solar cell development of the Deutsche Aerospace AG to qualify the base of the solar cells - - determination of the minority carrier lifetime in the base using the OCVD method [1,2] and extraction of the minority carrier diffusion length from spectral response measurement [3] - - provide an effective lifetime and an effective diffusion length, respectively, and do not allow for separating the influence of the volume and the surface. As an inexpensive measurement the ESCCD method introduced by T.-W. Jung et al. [4] and further developed by F.A. Lindholm et al. [5] and A. Zondervan et al. [6] is investigated with regard to application in solar cell development. To facilitate the comparison of the results obtained by different methods, the subject is discussed in terms of diffusion lengths. The measured lifetimes are converted to diffusion lengths using diffusion constants deduced from resistivity measurements.

2. Theory

A steady-state forward current is applied to the p-type base solar cell under study. At time t = 0, the forward current is replaced by a short-circuit. The continuity equation for the excess minority carrier concentration n(x,t) in the quasi-neutral base (QNB) for times t > 0 is given by [4]:

an( x,t ) a2n( x,t ) n( x,t ) - D - - - - , (1)

at ax 2 7"

where D is the diffusion coefficient and r is the carrier-density independent, low-level injection recombination lifetime of the electrons in the base (the emitter is neglected because lifetimes in the emitter are much smaller than those in the base and will influence only the first part of the transient which is not evaluated). If the recombination at the rear surface is described by a carrier-density independent recombination velocity S, the boundary conditions at the two edges of the QNB of thickness W are:

D x=w= -S n (W, t ) (2)

n ( x = 0, t > 0) = 0 (short-circuitcondition). (3)

Solving the differential Eq. (1) under conditions (2) and (3), the transient current can be calculated [6]:

o c

j ( t ) = ~ j i (O)e - ' / " , (4) i - 1

K. Burgard et al. / Solar Energy Materials and Solar Cells 36 (1995) 241-259 243

where

D A i 2qDno z c° tAi WS

Ji(0) = ~ A~A~ O (5)

A 7 2 + WSsin2Ai

is the amplitude and ~'i the time constant of the ith decay mode. q is the elementary charge and A i and A i are given by:

-

h i = , ( 6 ) /~i

and

Ai= W (7)

n o = n ( x = 0, t < 0) is the excess electron density at the interface space-charge region (SCR)-QNB during the steady state forward current and is given by [7]:

n? n o = qv/ T- 1 ) , (8)

(V = voltage at pn-junction). The second equation provided by the solution of (1) under (2) and (3) is the eigenvalue equation

D A i S W tanAi " (9)

The higher decay modes (i > 1) will decay very fast and the first decay mode (i = 1) becomes dominant after a small period of time. Neglecting the part of the curve influenced by higher decay modes the determination of ja(0) and ~'1 is possible by fitting the function

j ( t ) = j l ( O)e - t / ~ (10)

to the measured transient. Elimination of S by substituting (9) in (5) gives

( s i n ( 2 A 1 ) ) -1 J ' (O)W3 A~ 1 - 3,. (11)

2qnoD2~'l 2A 1

The parameter y combines all experimental parameters and is the starting-point for the calculation of S and L. Because of (9) A 1 is restricted to an interval 7r/2 < A 1 < zr, which again restricts 3' to 7rE/4 < 3' < ~r:. The Newton algorithm allows the determination of A r The rear surface recombination velocity S and lifetime of the electrons in the base ~- is then calculated using (6), (7) and (9).

The theory is discussed in detail in [4-5].

244 K. Burgard et aL / Solar Energy Materials and Solar Cells 36 (1995) 241-259

3. Experimental method and procedures

3.1. Experimental set-up

The electrical set-up is shown in Fig. 1. As tong as the signal of the pulse generator (consisting of FAST-series TTL logic 74FXX) is low (U---2 V), the MOS-transistors T1 and T2 (BUZ10) are switched off and a constant current delivered by a voltage-current source (Keithley 228A) is applied to the solar cell mounted on a temperature-controlled brass chuck. At time t = 0 the signal of the pulse generator turns to high (U---6.5 V), the transistors turn on (switching time = 100 ns, on-state resistance ~ 50 mf~) and the solar cell is nearly short-cir- cuited over the resistor R (33.3... 500 ml)). A current flow through the solar cell caused by a small voltage drop over T1 is prevented by the diode D. The transient current is recorded using a digital storage oscilloscope (Tektronix 2430A) and transmitted to an IBM-compatible personal computer.

3.2. Determination o f n o

The excess carrier density for times t < 0 at x = 0 is given by (8), where V is the voltage at the pn-junction. A method to determine V without knowing the series resistance of the solar cell is to measure the open-circuit voltage Voc and short-circuit current Isc under illumination. If the forward current at t < 0 is set equal to Isc then V is equal to Voc [6]. Varying the intensity of the illumination the value of n 0 can easily be controlled.

3.3. Choice o f R and n o

The appropriate choice of resistance R and the excess carrier density n o is an important point in the ESCCD-measurement. In order to obtain the maximum

personal l computer i

I

voltage/current source I-~

t digital I storage oscilloscope

~ - ~ gP~eU InS~rato r

Fig. 1. Electrical set-up.

K. Burgard et aL / Solar Energy Materials and Solar Cells 36 (1995) 241-259 245

i • [ Curnant Current (log. scale) I

I l 04. • e

3 " E 41' ........ ~ 1 intercept jl(O)

i • 0.5 _e

g2 i . s l °pex l

(.~ 1 iiEi eOooooeooOooooooo'~.=••Oo o o ~ 0.1 0.05~.~ "~

° i • 4 0.01

- 1 I ~ , ~ = I L , ~ , I , , J ~ I

0 5 10 15 20 Time (ps)

Fig. 2. PC-1D simulation of the ESCCD curve. The straight line is a fit of the asymptotic decay.

signal, a good signal-to-noise ratio and a minimum of oscillations, R and n o have to be chosen as high as possible. On the other hand, the following conditions must be fulfilled (Re: resistance of the whole short-circuit loop, C: capacitance of the solar cell, A: cell area):

low-level injection: n o << N B,

RC-times negligible: R c C << Zl,

short-circuit condition [6] : V / R c > A j ( t ) .

(12)

(13)

(14)

The injection level can easily be varied to meet low-level injection (see 3.2). With typical values for C ( - 30 n F / c m 2) and Re ( = 500 mf~ for 2 × 2 cm 2 solar cells) the second condition is also fulfilled. The most critical point is the short-circuit condition. I f (14) is violated, the boundary condition (3) is achieved at a time t > 0 and jl(0) is overestimated.

3.4. Determination of Jl(O) and T 1

A theoretical transient current calculated using PC-1D [8] is shown in Fig. 2 in a linear and logarithmic scale. The extracted decay time constant for the simulated solar cell (p = 1 Ocm, W = 200 ~m, A = 100 cm 2, L = 300 I~m, S = 100 c m / s ) is 'T 1 = 4.23 ~s. For times t < ~-] the curve is influenced by higher decay modes, for times t > .1" 1 the first mode is dominating and the logarithmic plot is a straight line with slope ~'1 and intercept jl(0). It can be seen that at t = 0 the current changes its sign. In practice, this rapid change in current d j / d t , together with the inductance of the circuit and the capacitance of the cell cause strong oscillations

246 K. Burgard et al. / Solar Energy Materials and Solar Cells 36 (1995) 241-259

15

c

0.5

J 0

C u r r e n t C u r r e n t ( l o g . s c a l e )

I

L ...... L , ~ I , ~ ~ , I , , , L I t , , ~ 0.01

5 10 15 20

Time (ps) F i g . 3 . M e a s u r e d E S C C D c u r v e f o r a t y p i c a l n + p p * - s o l a r c e l l .

1

0.5 ~

v c

0.1 ~

d 0.05

with low damping because of the low resistance (a few hundreds of m i d of the whole circuit. Fig. 3 shows the observed transient current for a n+pp+-solar cell. The exponential decay is superposed by three different damped oscillations. The short oscillations (period--500 ns) are caused by the charge of the gate-source capacitance of transistor T2. Another oscillation (period = 7 ~s) is due to the capacitance of the solar cell. The origin of the third oscillation (period = 2.5 p~s) could not be identified.

Several attempts have been made to remove the oscillations. A critical damping is not generally applicable because this would lead to RC-times in the order of the effective lifetimes. An electronic compensation requires an adjustment to the different cell types and sizes and turned out to be impractical if a variety of cells have to be examined. A fourier analysis failed because of the 8-bit resolution of the oscilloscope.

Without any compensation of the oscillations, an extraction of the parameters of the exponential decay jl(0) and ~-~ is possible by fitting the following function consisting of an exponential decay plus 3 damped oscillations to the experimental data:

s

j ( t ) =Jorr +J1(0) e-'/:~ + ~ . a i e - ' / b ~ s i n t + d i , (15) i = 1 Ci

where joff is a small offset current probably caused by light penetrating the covering and a i, bi, c~ and d, are the amplitude, damping constant, period and phase of the oscillations, respectively. The simplex algorithm [9] is used for the fit. Normally a fit with 15 fit-parameters is ambiguous. In the underlying 15 dimen- sional space of parameters the Simplex algorithm will in general not find the least-squares fit but will stop at some local minimum of the sum of the squared

I~ Burgard et al. / Solar Energy Materials and Solar Cells 36 (1995) 241-259 247

40

'~"~ measurement fit exponential decay I

1 30 ~'

~2oo "~ ~ ~ 10 "" -

- - ~ " ~ , ~ _ _ - ~ - ___~-~ 0

i i i i I i i ~ i I i i i i I i i i

0 10 20 30 Time (ps)

Fig. 4. Least-squares fit of the ESCCD curve. The dotted line is the experimental data, the solid line is the fitted function including 3 damped oscillations, the dashed line is the extracted exponential decay.

residuals. In our case a 15 parameter fit is applicable because most fit parameters are approximately known and must be adjusted only in a small range. In practice, systematic deviations of the fitted function from the experimental curve allowed to distinguish local minima of the squared residual from the absolute minimum (least squares) and to find the least squares fit by setting initial parameters and parameter increments to suitable values. Fig. 4 shows the measured transient current and the fitted function of a typical cell. The deviation of the theoretical curve from the experimental data lie within the resolution of the digital oscilloscope and the noise of the signal.

3.5. Calculation of L and S

To calculate the diffusion length L and rear surface recombination velocity S using (6), (7), (8), (9) and (11), the values of n i, NB, V, T, jl(O), W, D, ~1 are needed, whereas the experimentally accessible observables are p, V, T, Vt(t), A, W, R (p: resistivity of the base, Vt(t): transient voltage recorded by the oscilloscope). T is held constant during the measurement (T = 25°C) and A can easily be measured. The statement V= Vo¢ assumes that the I~c-Voc curve equals the series resistance corrected dark I - V characteristic shifted by the illumination current IL, which is true for a good approximation [10]. ni(T) is calculated using the data of Sproul et al. [11] and is accurate within 3%. N a and D are calculated as a function of T and p using the relations of Thurber et al. [12] and Sproul et al. [13], respectively. Jl(0) and ~'1 are extracted from j(t) = Vt(t)/(RA) as described above. The base thickness W is determined either by measuring the thickness of the cell subtracting the thickness of emitter, p+-region and contacts or by measuring the thickness of the unprocessed wafer gravimetrically subtracting the thickness of

248 K. Burgard eta/./Solar Energy Materials and Solar Cells 36 (1995) 241-259

LpL = 200 pm

LpL = 185 pm

LpL = 145 pm

P L O T T E D RANGE

2 n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ! . . . . . . . . . . . . . . i . . . . . . . . . . . . i

05 1 2 £9 26 3 3 4 0

L I F E T I H E [ P s i

T i ~ e R a n g e : 0.4 ms S e n s i t i v i t y : £0 ~ U A v e r a g | n 9 :256 HM F r e q . : 1 0 . 2 5 9 GHz P u l s e M i d t h : 200 T i n e c u r s o r : 1 5 . 8 p s L a s e r P o w e r : 2 5 4

L a s e r M . 1 . : 9 0 4 n .

I [ ~ l ~ l g II1 tradJ R v e r a g R : 2 2 . 6 p s

. a~ i . . . . 4~.4J,~ 5 . s [ ] [ ] [ ] [ ] [ ] [ ] • [ ] [ ] • 4 o ~ D e v i a t i o n : 3 3 . 5 V .

Fig. 5. Lifetime map of a 10x 10 cm 2 CZ wafer. The measurement was carried out on a commercial lifetime scanner Semilab WT-85 based on microwave-detected photoconductance decay. The noted diffusion lengths LpL are the results of the PL profile measurement at the indicated points. On the left, the statistical data of the lifetimes are given.

emitter and p+-region. The second possibility is preferable because it is more accurate and yields a value for the thickness averaged over the whole ceil.

3.6. Sample preparation and material characterization

To get well qualified solar cells, 10 monocrystalline and 10 multicristalline neighbouring wafers were taken. The average thickness of the wafers was measured gravimetrically, a specific resistance mapping was performed on the first and last wafers. The surfaces of the samples were then passivated (dry oxidized at 1000°C for 40 min) and a lifetime mapping was carried out using a commercial lifetime scanner (Semilab WT-85) based on microwave-detected photoconductance decay (/zW-PCD). Another comparative measurement used the photoluminescence (PL) profile while moving the generation locus towards an edge of the sample with high recombination velocity, the other surfaces being passivated, to determine the diffusion length of the bulk material [14].

The /xW-PCD lifetime map of one CZ wafer is shown in Fig. 5. At the three marked points the PL-profile measurement gave diffusion lengths LpL of 145 Ixm, 185 }xm and 200 txm. The relation between these values is in accordance to the relation of the lifetimes obtained from the Semilab equipment (the absolute values cannot be compared because the two measurement techniques work with different injection conditions).

The effective lifetimes vary within the wafer over more than one order of magnitude. These variations are related either to the bulk lifetime or to the quality of the surface passivation. In the former case the integration of the current density

K. Burgard et aL / Solar Energy Materials and Solar Cells 36 (1995) 241-259 249

over the cell area by the ESCCD method should result in deviations from the purely exponential asymptotic decay of the ESCCD curve. This could prevent an application of ESCCD to cells processed on such wafers. The effect was not observed with the small 2 × 2 cm 2 solar ceils investigated, so the latter case is more likely.

The wafers were then processed. The cell design is given in Table 1 (cell type No. t l - t4) . In addition, solar cells from the series production (cell type No. p l - p 3 ) and space production type cells with different rear surfaces (cell type No. s l - s4) were taken.

To make sure that condition (13) and (14) are not violated and to reduce the influence of inhomogeneities in the lifetime and in the base thickness, 2 × 2 cm 2 solar ceils were cut out.

4. Results and discussion

This chapter is divided into four parts. In the first part the influence of carrier density-dependent recombination on the ESCCD measurement is discussed. The second part (Section 4.2) compares the direct results of the measurement, the effective diffusion lengths, to the values obtained by other methods. Section 4.3 presents an uncertainty analysis and in Section 4.4 the separation of the influences of the volume and the rear surface by ESCCD is discussed and compared to other measurements.

4.1. Carrier density-dependent recombination

During the ESCCD-measurement a big change of the carrier density in the base of the solar cell under study is necessary to obtain a detectable signal. This leads to a deviation from the exponential decay for cells in which carrier density-dependent recombination occurs. To recognize this effect the data is fitted beginning at different times t a. If the curve is not influenced by carrier density dependent recombination, the extracted time constant ~'1 as a function of t a is constant and the curve is evaluable. An example is shown in Fig. 6 where for the monocrystalline back-surface-field(BSF)-cell "/'1 is constant within 3%. Besides this procedure assures that the evaluated part of the curve is not influenced by higher decay modes. For multicrystalline cells and cells with oxide passivated rear surface and point contacts a decreasing ~'1 with increasing time ta could always be observed (see Fig. 6). For the oxide passivated cell this means that the recombination velocity at the rear surface increases with decreasing carrier density. This is a well known property of the Si-SiO 2 interface [15,16]. In case of the multicrystalline cells, the bulk is responsible for this observation [17]. As a consequence the ESCCD method yields only an estimation of the effective diffusion length and does not allow a separation of L and S for multicrystalline solar cells and cells with oxide passivated rear surface.

2 5 0 K. Burgard et al. / Solar Energy Materials and Solar Cells 36 (1995) 241-259

.=.

< ~

<

E

~5 ~

< + +

6 ~ ~5' 6 ~

"-5

,.~ ©

~ -~.

o

E

..,,..

,.z , ,z 8 =


~ '5 .5

5

4.5 0 0

E 4 "0

"6 3.5

U.I 3

3 4 5 6 7 8 9

Begin of evaluation t a (ps)

monocrystalline BSF-cell

multic~stalline BSF-cell

oxide passivated cell e

i i i i I

10 11 12

Fig. 6. Extracted decay time constant as a function of the begin of the fit for three different solar cells.

This reduces the applicability of the method from 11 cell designs taken into consideration (see Table 1) to the 6 types of cells discussed in the following.

4.2. Comparison of effective diffusion lengths

In Table 2 the electrical data and parameters of the cells are summarized and the effective diffusion lengths of the ESCCD-measurement Leff,ESCCD = ~ are compared to values obtained by two comparative measurements. '/'isc is the asymptotic decay time constant of the short-circuit current after optical excitation (see Section 4.5) and Leff,is c = ~ is the related effective diffusion length. Leff,OCVD = DrvTD~ is the result of a simple open-circuit voltage decay (OCVD) measurement using the formula of Gossick [2]:

-1 kT (dV(t) t (16)

"rOCVD=----q - dt ] '

where V(t) is the open-circuit transient voltage after an applied forward voltage. An evaluation of the spectral response (SR) of the solar cells after Stokes and

Chu [3] yields the effective diffusion length L~n,s a (evaluated wavelength range 835-980 nm). These values are expected to be different from the diffusion lengths calculated from measured effective lifetimes. W. Warta showed that L~ff, SR depends strongly on the L/W ratio, the absolute base thickness, the back surface recombination velocity and the front and back surface reflectivity, if multiple reflections occur [18]. As a consequence, the simple evaluation of the spectral response is useful for comparative studies. A more detailed evaluation of internal quantum efficiencies (see e.g. [20]) will not be discussed here.

The Leff, is c values agree very well with the Leff, ESCCD values. The deviation in the measured decay time constants z~ and Tis c lie within 10%, with a tendency


o

o ~E

g ~.o

e ~

[...

"N

~ g

• ~ ~

8 ~

~ - ~ -d d


towards higher values for ~'1- Since the asymptotic time constant should not depend on the type of excitation, these deviations must be related to experimental errors in the determination of the decay time constants. The good agreement confirms the validity of our method to determine the decay parameters.

For cells 2 and 4 (deep emitter), the Laf, ocv D values are in good agreement with the Leff, ESCC D values. For all other cells OCVD yields higher effective diffusion lengths than ESCCD. The overestimation of the effective diffusion length by OCVD increases with the quality of the emitter (see Table 1). The reason is the emitter-base coupling during the OCVD-measurement described theoretically using the quasistatic emitter approximation and confirmed experimentally by S.C. Jain and U,C. Ray [19]. The quality of the emitter is expressed in terms of the emitter saturation current leo. According to [19], only for thick cells (W >> L) and large values of time the voltage decay is solely determined by the minority carrier lifetime in the base r and is independent of leo. For cells with W < L, the voltage decay is linear from the beginning and the decay rate is of the form k T / q ( 1 / z +

1 / t l ) , where t I depends on W, S and leo. This case holds true for all the cells investigated here. To obtain a reliable result using OCVD, the emitter in terms of the emitter saturation current must be taken into consideration.

4.3. Uncertainty estimates

The possible sources of uncertainties affecting the evaluation of L and S and an estimate of their influence are listed below.

- - A~" 1, A j1(0): The uncertainty of extracting the decay time r I from the experimental data was about 3%. Because of the exponential shape of the fitted function the uncertainty in the intercept is principally larger than the uncertainty in the slope. The finite switching time and the subsequent uncertainty in the determination of time t = 0 introduces an additional error in jl(0). The uncertainty in j l(0) was typically about 5%.

- - AA, AR: A and R are known with high accuracy in comparison with the other parameters. So AA and AR are neglected.

- - AT, AV: The temperature was constant within 0.2 K; the accuracy in the determination of F was 0.1%.

- - AW: For cells 1 and 3, where the thickness was measured gravimetrically and for the space production type cells (ceils 5 and 6) AW is estimated to be 3 ixm. For the cells taken from series production (cells 2 and 4) the estimated accuracy is 5 ~m.

Remark: In the specification of the wafers as delivered by the manufacturer deviations of the thickness from the mean value within a wafer of + 40 ~m in the case of photovoltaic grade material and + 10 p~m in the case of electronic grade material are allowed. This could introduce further problems in the determination of the mean thickness and, hepce, in the ESCCD measurement. In our case the use of small 4 cm 2 solar cells reduces the problem.


- - Ap: On the unprocessed wafers of cells 1 and 3 a resistivity mapping has been carried out. For all other cells the resistivity values specified in the data of the manufacturer were taken. The related uncertainties were 3% (cells 1, 3.5 and 6) and 5% (cells 2 and 4).

- - A n i, ANB, AD: The models used to calculate n i as a function of T and N B and D as functions of p and T contribute uncertainties of 3% ( n i) [11] and 5% (N B and D) [12,13], respectively. These errors influence all measurements in the same way and do not affect the usefulness of the method for comparative studies. They are not included in the error calculation.

Based on the error estimates listed above, two different error calculations are given in Table 3. The AL and AS values are calculated using the relations deduced in [6]:

L3A,y AL = 2W 2, (17)

and

SAT A S - 2 ( A 2 _ 7 ) . (18)

The approximation d y / d A 1 = 2AI, made to deduce AL and AS, is often violated. A more general way is to calculate the possible range of L and S taking the values of the parameters within their error ranges yielding maximum and minimum values of 7. For the cells with high surface recombination velocity (cells 1 and 2) the resulting maximum 7 is lying outside the allowed range (7 > ar 2) In this case a back ohmic contact (S = 10 6 c m / s ) is assumed and the L range is calculated using (6), (7) and (9).

4.4. E S C C D results a n d d i scuss ion

In this section the ESCCD results are presented and compared to the results of an alternative technique, Photo Current and Voltage Decay (PCVD) [21]: a determination of the asymptotic decay time constants of the short-circuit current (~'isc) and of the open-circuit voltage (~'vo~) after optical excitation by a Nd:YAG laser in cw-mode (wavelength 1064 nm). The method yields upper and lower values for l e o , L and S.

The resolution of the ESCCD method in determining L and S depends on the ratio of basewidth W and diffusion length L. Three cases have to be distinguished:

(a) W>> L: For thick cells (W>> L), nearly all minority carriers recombine in the bulk.

Thus, the transient current is fairly influenced by the rear surface. Consequently, the resolution in the determination of L is high, whereas a determination of S is nearly impossible. Thick cells are no longer common in solar cell production and development and are not investigated.

I~ Burgard et al. / Solar Energy Materials and Solar Cells 36 (1995) 241-259 2 5 5

II

Q

e~

[-, ,..,,

r ~

r ~ ~,~

N =


(b) W << L: Cells 5 and 6 are cells where the diffusion length exceeds the base thickness.

Most minority carriers recombine at the rear surface and a determination of S should be possible, whereas the resolution in L should be fair. In practice the determined back surface recombination velocity depends critically on the experimental parameters. The following example will demonstrate that a sufficiently accurate determination of S requires an almost impossible accuracy in the knowledge of these parameters. The most critical parameters are the basewidth W(y cc W 3) and the specific resistivity of the base p effecting D and N B (see (11)). The consequences for cell 6 are as follows: the measured thickness of the cell without front contact is 240 txm. Subtracting 5 txm for emitter, p+-region and rear contact yields a basewidth of 235 ixm. The other parameters are R = 500 ml~, V = 528 mV, p = 10.3 ~ c m and A = 4 cm 2. The fitted values are ~-1 = 5.3 Ixs and Jr(0) = 20.7 m A / c m 2. The resulting diffusion length is L = 520 Ixm, the rear surface recombination velocity S = 200 cm/s . An under- or overestimation of W by _+ 3 Ixm gives values of L = 400 Ixm, S = 50 c m / s and L = 800 Ixm and S = 350 cm/s , respectively. The effect of a deviation in the resistivity of _+0.3 f~cm on L and S is similar. Considering the errors of all parameters, only the order of magnitude of L and S can consequently be determined. From the PCVD measurement a lower limit for the diffusion length (L > 400 Ixm) and upper limits for the recombination velocity (S < 1.8 108 c m / s for cell 5 and S < 220 c m / s for cell 6) could be determined. The results of the PCVD method depend less critical on the base thickness. For cell 6 a variation of W by _+3 ~m yields variations of the upper limit for the recombination velocity between 170 c m / s and 280 cm/s .

(c) W = L: For cells with W = L both L and S can be determined. The results for the cells

representing this case (cells 1-4) are summarized in Table 3 in comparison with LpcvD and SpcvD determined from the PCVD results and additional knowledge of the cell technology (identical emitter and base material resistivity and quality for cells 1 and 3 and cells 2 and 4). A detailed error calculation for the PCVD method has not been carried out.

With both methods, ESCCD and PCVD, a significant difference in the measured diffusion lengths between the 4 cells could not be observed. This means that neither the high temperature oxidation nor the processing of the p+-region altered the original identical quality of the substrates. Because of the lower determined decay time constants ~'~c the diffusion lengths obtained from PCVD measurement are about 15% lower than the ESCCD values, but lie within the calculated error range. Besides the measured L are consistent with the results of the PL profile measurement. A direct correlation to the PL profile measurement is not possible because the information about the position of the 2 × 2 cm 2 cells within the unprocessed wafers has been lost during the fabrication of the cells. The measured rear surface recombination velocities of both methods agree very well. The resolution in S decreases with increasing S. For high values (cells 1 and 2) only the

If. Burgard et al. / Solar Energy Materials and Solar Cells 36 (1995) 241-259 257

o

e 6 ~

e4~-

= ~


order of magnitude and a lower limit for S can be determined by the ESCCD method.

Another example for the usefulness and the resolution of the ESCCD method is shown in Table 4. Space production type ceils (area 3.78 × 6.19 cm 2, cell type No. s2) irradiated with 1 MeV electrons to different fluences were investigated. It can be seen that the diffusion length decreases and the rear surface recombination velocity increases with increasing fluences. The dependence of the resolution on the L/W ratio discussed above is clearly demonstrated.

An attempt was made to investigate identical cells with a thickness of 75 ~m. The substrates were thinned chemically by etching, resulting in strong deviations from the mean thickness over the wafers (between 70 and 90 ~m). The subsequent high relative error in the determination of W did not allow to separate L and S.

5. Conclusions

The ESCCD method for determination of bulk diffusion length and rear surface recombination velocity in solar cells has been investigated with regard to an application in the solar cell development. To get rid of the major experimental difficulty of the method, the fairly damped oscillations caused by parasitic capacitances and inductances, a calculation technique was introduced that fitted an exponential decay plus three damped oscillations to the experimental curve. The results confirmed the validity and accuracy of this procedure.

The change in carrier concentration over several orders of magnitude during the transient decay prevents an evaluation of solar cells with carrier density dependent recombination. Hence multicrystalline cells and cells with oxide passivated rear surface cannot be investigated.

A comparison of the effective diffusion lengths determined by short-circuit current decay measurements to the values obtained by two currently used methods - - OCVD and spectral response evaluation - - showed that only the short-circuit current decay values are exclusively related to the base of the solar cell. The spectral response evaluation, influenced by the optical properties of the cell, is useful for comparative studies between cells with identical optical properties. To obtain reliable results using OCVD additional knowledge about the emitter is necessary and must be taken into account.

The main restrictions for the separation of L and S lie in the resolution and the uncertainties related to the method. In solar cells where the base thickness greatly exceeds the bulk diffusion length (W >> L) the electrical properties are dominated by the bulk and only a determination of L is possible. If L > 2W, the resolution in the determination of L is fair and the extracted value of S depends critically on the base thickness. In this case ESCCD only yields a lower limit for L and an upper limit for S. For ceils with W--- L L and S can be determined. The results for these cells are in good agreement with those obtained by PL-profile and PCVD measurements, showing the principle applicability of ESCCD.


The ESCCD method is a valuable tool in solar cell development if the influence of bulk and rear surface have to be separated. For principle investigations the fabrication of suitable test cells allows a determination of L and S with satisfac- tory resolution and errors. A widespread use or even an in-process control is prevented by the restrictions concerning the L/W-ratio and by the requirement of an accurate knowledge of the cell parameters to obtain acceptable errors.

Acknowledgements

The authors acknowledge contributions of P. Klopp, Institut fiir angewandte Physik, Universt~it Karlsruhe (PL-profile measurement), Dr. K. Graft, TEMIC TELEFUNKEN microelectronic GmbH, Heilbronn (/zW-PCD measurement) and Dr. W. Koch, Bayer AG, Krefeld-Uerdingen (resistivity mapping). The authors also wish to thank the reviewers for their critical comments on the manuscript and in particular K.-J. Finck, Deutsche Aerospace AG, Heilbronn, for his valuable technical support and his interest in the work.

References

[1] S.R. Lederhandler and L.J. Giacoletto. Proc. IRE 43 (1955) 477. [2] B.R. Gossick. J. Appl. Phys. 26(11) (1955) 1356. [3] E.D. Stokes and T.L. Chu. Appl. Phys. Lett. 30(8) (1977) 425. [4] T.-W. Jung, F.A. Lindhoim and A. Neugroschel. IEEE Trans. Electron Dev. ED-31 (1984) 588. [5] F.A. Lindholm, J.J. Liou, A. Neugroschel and T.W. Jung. IEEE Trans. Electron Dev. ED-34

(1987) 277. [6] A. Zondervan, L. Verhoef, F.A. Lindholm and A. Neugroschel. J. Appl. Phys. 63(11) (1988) 5563. [7] S.M. Sze. Physics of Semiconductor Devices, 2nd ed. Wiley, NY, 1981. [8] P.A. Basore. Report No. SAND91-0516.UC-274, Sandia National Laboratories, Albuquerque,

April, 1992. [9] M.S. Caceci and W.P. Cacheris. BYTE Magazine 340 (1984).

[10] A.G. Aberle, S.R, Wenham and M.A. Green. Conf. Rec. 23rd IEEE Photovoitaic Specialists Conf., Louisville, 1993, pp. 133.

[11] A.B. Sproul and M.A. Green. J. Appl. Phys. 70(2) (1991) 846. [12] W.R. Thurber, R.L. Mattis, Y.M. Liu and J.J. Filliben. J. Electrochem. Soc. 127(10) (1980) 2291. [13] A.B. Sproul, M.A. Green and A.W. Stephens. J. Appl. Phys. 72(9) (1992) 4161. [14] E. Daub, P. Klopp, S. Kugler, P. Wiirfel, W. Warta and R. Schindler. Proc. 12th EC Photovoltaic

Solar Energy Conf., Amsterdam, 1994. [15] W.D. Eades and R.M. Swanson. J. Appl. Phys 58(11) (1985) 4267. [16] J. Knobloch, A. Aberle, W. Warta and B. Vog. Proc. 8th EC Photovoltaic Solar Energy Conf.,

Florence, 1988, pp. 1165. [17] J. Metzdorf, H.-C. Holstenberg, T. Wittchen and H. Kaase. Proc. 7th EC Photovoltaic Solar

Energy Conf., Sevilla, 1986, pp. 288 [18] W. Warta. Proc. l l th EC Photovoltaic Solar Energy Conf., Montreux, 1992, pp. 469. [19] S.C. Jain and U.C. Ray. J. Appl. Phys. 54(4) (1983) 2079. [20] P.A. Basore. Conf. Rec. 23rd IEEE Photovoltaic Specialists Conf., Louisville, 1993. [21] W. Warta, R. Bergmann and B. Vo6. Proc. 8th EC Photovoltaic Solar Energy Conf., Florence,

1988, pp. 1416.

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Applicability of electrical short circuit current decay for solar cell characterization: limits and comparison to other methods