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17th European Photovoltaic Solar Energy Conference, Munich, Germany, 22-26 October 2001 GENERALISATION OF THE ILLUMINATION INTENSITY vs. OPEN-CIRCUIT VOLTAGE CHARACTERISTICS OF SOLAR CELLS Mark J. Kerr and Andres Cuevas Centre for Sustainable Energy Systems Department of Engineering, The Australian National University, Canberra ACT 0200, Australia, Email: Mark.Kerr@faceng.anu.edu.au, Phone: (+61) 2 6125 0078, Fax: (+61) 2 6125 0506 ABSTRACT: The current-voltage characteristics of solar cells and photodiodes can be determined by measuring the open-circuit voltage as a function of a slowly varying light intensity. This paper presents a detailed theoretical analysis and interpretation of such quasi-steady-state Voc measurements (QssVoc). The ability of this analysis to accurately obtain the true steady-state device characteristics even in the case of high lifetime, high resistivity silicon devices is demonstrated experimentally. The QssVoc technique can be used to determine the minority carrier lifetime, and the new generalised analysis is required to do this accurately. An important outcome is that solar cell and diode device characteristics can be obtained from measurements of either the photoconductance or the open-circuit voltage, even using transient decay techniques. Keywords: Quasi-steady-state - 1: I-V Characteristics - 2: Lifetime - 3 1. INTRODUCTION widespread. As shown in this paper, even if the light intensity and the electric current are zero, it is still possible The recombination properties of semiconductor devices to obtain the characteristic curves of the device from PCD strongly affect their electrical performance. Experimentally and OCVD measurements. The vertical axis of these plots measuring these recombination properties in a simple and is the rate of change of the carrier density, which represents easy way has been significantly facilitated by the the natural recombination rate in these situations. This introduction of quasi-steady-state (Qss) techniques [1, 2]. generalisation of the device characteristics is conceptually In the QssPC technique, a simple flashlamp is used to very important, and provides a broader understanding of produce a slowly varying illumination and the resulting the different physical mechanisms present in the time dependence of the excess photoconductance (PC) of semiconductor. the sample is measured. Analysis of the data gives the minority carrier effective lifetime as a function of injection level, over a wide range of injection levels. It is possible to 2. GENERALIZATION OF EFFECTIVE analyse the data in a way that accommodates the possible LIFETIME MEASUREMENTS different time dependencies of the light excitation and the excess carrier density in the semiconductor. Such a 2.1 Previous Work generalised analysis has been applied to improve the Three operating regimes for the light excitation can be accuracy of QssPC measurements [3]. identified. The first involves an abrupt cessation of the illumination. This is the traditional transient photo- The Qss approach has also been applied to measure the conductance technique. The second regime is the steady- open-circuit voltage of solar cells as a function of the state illumination, which has also been historically used. In incident light intensity [4]. Again, a monotonically varying the third regime the intensity of the illumination varies illumination from a flashlamp is used to produce a voltage monotonically with time, which is the basis of the quasi- vs. illumination curve. This quasi-steady state open-circuit steady-state method. Proper analysis of all the different voltage method (QssVoc) has important practical possibilities requires use of the continuity equation for the advantages over the classic Isc-Voc technique. Besides an excess minority carriers: almost direct measurement of the I-V characteristics, the ¶D n 1 dJ n QssVoc technique provides an insight into carrier = G b (t , x ) - U b (t , x ) + (1 ) recombination and an alternative path to determine the ¶t q dx minority carrier lifetime. A generalised analysis of QssVoc For regime 1: Gb(t,x) = 0, while for regime 2: measurements is presented in this paper. This corrected ¶Dn/¶t = 0. Further, the transport term reduces to surface analysis is particularly important for solar cells made on recombination terms when equation (1) is integrated over high resistivity, high lifetime silicon, and we have used the sample width. Nagel et al. [3] generalised the analysis such devices to demonstrate the method experimentally. procedure to define an effective minority carrier lifetime regardless of the flashlamp characteristics by combining The extended analysis of time-dependent measurements the bulk and surface recombination rates into an effective of the excess carrier density under illumination by either recombination rate (Ueff) and not dropping any of the terms conductance or voltage techniques goes beyond pure in equation (1): mathematical accuracy. Applying it to the special case D n av ( t ) where the light excitation is abruptly terminated and the t eff = ¶ D n av ( t ) (2 ) transient decay of the photoconductance or the voltage is G av ( t ) - recorded with time is very important, since the PCD and ¶t OCVD methods have historically been, and still are, 300 To understand the physical meaning underlying this 102 xx Equivalent Steady-State Illumination (Inet -suns) generalised definition of lifetime, it should be realised that uncorrected data - transient decay xx corrected data - transient decay xx xx the recombination rate occurring within an illuminated xx x uncorrected data - 2ms flash xx sample can be affected by both the photogeneration rate at 101 xx xx xx corrected data - 2ms flash xx that instance, as well as the history of the sample (through xx xx xx the time-dependent carrier density - ¶Dn/¶t). What is not 100 x xxx xx x obvious from the generalised lifetime definition of Nagel et xx x xx al. is how to determine other device parameters, like the x xxx x xx x true steady-state open-circuit voltage or the current-voltage 10-1 x xxx x x xx x x x xx characteristics of a solar cell, from QssPC or transient x x xx x xx xx decay measurements. 10-2 x x x xx x xx x x x x x x x x x x x xx x x xx x xx x xx 2.2 Determination of implied Voc vs. illumination from x x x x x x x xx x x x xx lifetime measurements 10-3 xx xx xx x Effectively, the correction of Nagel et al. is equivalent to defining the denominator of equation (2) as a net 0 generation rate (Gnet) that incorporates the actual 0.50 0.55 0.60 0.65 0.70 0.75 0.80 photogeneration (Gav) and the carrier density history: Implied Voc (V) ¶Dnav Gnet = Gav - (3) Figure 1: Corrected and uncorrected implied open-circuit ¶t In the context of characterizing the recombination voltage vs. light intensity curves for a solar cell precursor parameters of solar cells and/or their precursors under real from photoconductance measurements. A flashlamp with a conditions (ie under true steady-state conditions), the decay time of ~2ms has been used as well as the transient concept of net generation can be greatly expanded. The mode where there is no actual illumination of the sample simplest extension of the net generation concept is for during the measurement. The vertical axis is determined obtaining implied open-circuit voltage vs. light intensity from Gav for the uncorrected data and Gnet for the corrected curves from photoconductance based lifetime data using equation (5). measurements [2]. Under the quasi-steady state assumption, the actual illumination level (Ilight - in suns) seen that the uncorrected data is actually quite can be plotted against an implied open-circuit voltage discontinuous, particularly at lower light levels, while the (Voc,imp) using the relationship: corrected data produces a smooth, continuous curve which is physically what would be expected. Further, by qV oc comparing the uncorrected and corrected quasi-steady-state np » D n ( 0 )[ N A + D n ( 0 )] = n i2 exp (4 ) data it can be seen that the correction starts to become kT significant at light intensities below »1 sun for this sample. We know however that the actual illumination level The effect of the correction is to provide a more realistic (Ilight), and therefore the actual photogeneration rate (Gav), determination of the electronic properties of the solar cell does not necessarily account for all the recombination substrate. That is, the uncorrected data over-estimates the events occurring within the sample. The net generation rate quality of the solar cell substrate by over-predicting the (Gnet), as defined in equation (3), needs to be used to Voc. determine the equivalent, steady-state illumination level An interesting, not so obvious consequence of using (Inet) that would need to be used to obtain the same total the net generation concept is that transient recombination rate. This can be expressed in unit of suns photoconductance lifetime measurements can be used to (1sun=1kW/m2) via: determine implied Voc vs. Inet curves even though the actual WG net light intensity is zero. Included in Figure 1 are corrected I net = (5 ) f abs N ph |1 sun and uncorrected implied open-circuit voltage data when the lifetime is measured by the transient method. It can be seen Where W is the sample width, ¦abs is the optical that the two corrected curves agree very well, absorption fraction of the sample to take into account demonstrating the validity of the approach. reflection and absorption losses and Nph½1sun is the density The agreement between PCD and QssPC data can be of photons in solar light with an irradiance of 1sun exploited to determine, or verify, the optical properties of (1kW/m2). Alternatively, ¦absNph½1sun can be replaced with the wafer, that is the factor fabs in eq. (5). Further, the an estimated or measured short-circuit current density (Jsc) standard diode analysis and interpretation can be made on under one sun standard illumination. the Ilight-Voc,imp curves, thus relating the injection level An example of an implied open-circuit voltage vs. light dependent effective lifetime of the sample to ideality factor intensity curve both before the correction (Ilight-Voc,imp) and at a given open-circuit voltage. For example, the corrected after the correction (Inet-Voc,imp) is given in Figure 1. The Inet-Voc,imp curve in Figure 1 shows non-ideal diode flashlamp used showed an approximately exponential behaviour at lower voltages (n¹1) due to an injection level reduction in light intensity over time with a decay time of dependent surface recombination velocity and bulk »2ms. The sample being measured is a high lifetime solar lifetime. cell precursor consisting of a phosphorus diffused, high resistivity silicon substrate passivated with high quality TCA based silicon oxide on the front and rear. It can be 301 3. GENERALIZATION OF OPEN-CIRCUIT 102 2(a) VOLTAGE MEASUREMENTS 101 3.1 Introduction Illumination Intensity (suns) x x x xx x The objective of a QssVoc measurement is to obtain the xx x x xxx x diode characteristics of a finished solar cell [4]. These 100 x x xx x xx xx characteristics come about by simply plotting the actual xxx x xx x xxx x open-circuit voltage of the device as a function of the light x x xx xx 10 -1 x xx intensity. We are seeking the dc, or steady-state x xx xx xx xx x xx xx characteristics of the device, that is, the dc value of Voc that xxx x xx xx corresponds to a given value of steady-state light intensity. x xx xx 10 -2 x xx x x x xx xx Analogous to the discussion in section 2.1, the actual x x x x xx xx x x illumination level at the time (and therefore the x x x x xx photogeneration rate) does not necessarily account for all 10-3 xx x x x x x the carriers in the sample. In particular, it does not account for all the carriers at the boundary of the space charge 0 102 Equivalent Steady-State Illumination Intensity (suns) region, which in-turn, determine the open-circuit voltage. 2(b) Again, we need to consider the photogeneration history of the sample by using the net generation rate of equation (3). 101 This can be achieved by solving the quadratic expression of xx xx xx xx equation (4) to determine Dn (only the positive root has a x xx xx xxx xx xx x physical meaning) and its derivative: xx xx xx x 100 xxxx xxx xxxx xxx xx xx xxx xx x qV oc xx xx xx N 2 + 4 n i2 exp - N xx xx A A xx xx xxxx xx xx kT xx Dn = (6 ) and 10-1 xxx xxxx xxx xx xxx xx 2 xxx xx xxx xx xx x xxx x x true steady-state data qV oc qn i2 exp xx xxx 4ms flash ¶Dn ¶ V oc 10-2 x x xx kT (7 ) xx xxx x = xx xxx x 2ms flash xxxx xx xxxx xx x ¶t 2 qV oc ¶t xx xx x x x 0.35ms flash kT N A + 4 n i2 exp transient decay kT 10 -3 Which can be substituted into equation (3) and then into 0.4 0.5 0.6 0.7 0.8 equation (5) to obtain the equivalent, steady-state Open-circuit Voltage (V) illumination level (Inet) that needs to be plotted against the measured Voc. This procedure outlines the generalisation of Figure 2: Uncorrected and corrected open-circuit voltage Voc measurements as a function of light intensity and time. vs. light intensity curves for a high resistivity (90 Wcm), high lifetime (1.6ms) p+nn+ BSF solar cell using four 3.2 Experimental illustration of the correction different illumination conditions. An I-V curve cannot be The open-circuit voltage as a function of light intensity obtained from transient OCVD using conventional was measured for a low recombination solar cell made at analysis. ANU on a 90 Wcm phosphorus-doped silicon wafer. The cell had full area boron and phosphorus diffusions at the the uncorrected curves are quite discontinuous. Most front and rear of the cell respectively, essentially making it importantly, the predicted performance of the device would a 1-dimensional device. The high open-circuit voltage at vary greatly depending on which flashlamp was used and one sun, 677 mV, testifies the quality of the device would be significantly different from the true steady-state (Jsc=32.2mA/cm2, FF=0.781, h=17.1%). It also means that performance. Even for the 4ms flashlamp, there is a the excess carrier density is very high, which adds to the noticeable difference between the true steady-state problem of maintaining steady-state conditions during a measurements and the uncorrected Ilight-Voc data at lower time-dependent measurement. illumination levels. Four different flashlamps were used to illustrate the The corrected Inet-Voc curves for the device are plotted method. Along with the transient mode, the decay times of in Figure 2(b). It can be seen that applying the correction the flashlamps were »0.35ms, »2ms and »4ms. The 0.35ms again removes the discontinuities in the curves for all the flashlamp has been included to demonstrate the robustness illumination modes, but most importantly, all the curves of the correction. It would not typically be used for quasi- now overlap with each other and with the true steady-state steady-state measurements. Neutral density filters were measurements. used to vary the intensity of light incident on the solar cell to between 100suns and 0.001suns. 3.3 Determination of the lifetime from Voc Uncorrected Ilight-Voc curves for the device are plotted The correction is more noticeable if the measured in Figure 2(a) along with true steady-state measurements voltage is analysed to determine the effective minority obtained by attenuating the illumination from a solar carrier lifetime. The effective lifetime can be determined simulator with several different neutral density filters and from equation (2) using the minority carrier injection level placing the device subsequently in open and short circuit data derived from equation (6). Alternatively, substituting conditions. Consistent with the discussion in section 2.2, equations (6) and (7) into equation (2) gives the 302 generalised definition of the effective minority carrier 2500 uncorrected data lifetime from the open-circuit voltage: (2ms flash) uncorrected data 2 qV oc N A + 4 n i2 exp - NA 2000 (4ms flash) kT t eff = corrected effective qV oc Effective Lifetime (ms) lifetime qn i2 exp kT ¶ V oc 1500 2 ( G av - ) qV oc ¶t 2 kT N A + 4 n i2 exp kT For the case of low level injection, this can be simplified to 1000 a more familiar form that is easily identifiable with the OCVD lifetime when the generation rate is zero [5]: 500 Dn t eff = (9 ) q D n ¶ V oc G av - kT ¶t 0 The lifetime can thus be easily calculated from the 1012 1013 1014 1015 1016 1017 measured voltage, its time derivative and the actual Minority Carrier Injection Level (cm )-3 illumination level. Figure 3 shows the effective lifetime Figure 3: Minority carrier effective lifetime of a high corresponding to a high efficiency PERL cell fabricated at efficiency 20Wcm n+pp+ PERL cell determined from Fhg-ISE on a 22 Wcm gallium-doped silicon substrate QssVoc data before and after applying the correct (Voc=680mV, Jsc=39.5mA/cm2, FF=0.793, h=21.2%). generalized analysis. The flashlamps used for illumination Minority carrier lifetimes in excess of 1 ms have been the cell had a decay time of ~2ms and ~4ms. independently measured for these wafers by photoconductance techniques. It can be seen from the 5. CONCLUSION corrected data, that the lifetime has a maximum value of »1.1ms at an injection level of 3x1014 cm-3. From the The physical concept of a net photogeneration rate as uncorrected data however, the maximum lifetime depends the sum of the actual photogeneration and the derivative of on the decay time of the flashlamp, with a maximum of the excess carrier density with time has been introduced. »2.2ms and »1.6ms for a 2ms and 4ms decay constant This leads to a generalized analysis procedure for flashlamp respectively. illumination vs. open-circuit voltage characteristic curves of solar cells. In this paper we have shown that the QssVoc 4. DISCUSSION technique can be accurately applied, even to high lifetime devices, for a given time-dependent light source when the In this paper we have demonstrated the generalized generalized analysis is used. It also permits to obtain net analysis procedure using high efficiency and high lifetime illumination vs. voltage curves even for transient decay solar cells. For the majority of industrial solar cells the measurements of the photoconductance or the open-circuit effective lifetime is quite small (10-50ms) and is much less voltage, a feature previously reserved exclusively to steady- than the decay time of the typical flashlamps used. Under state or Qss techniques. these conditions, the effect of the generalised analysis presented here to determine I-V characteristics is small. ACKNOWLEGEMENTS Although the experimental measurements plotted throughout this paper have been focussed on illustrating This work has been funded by the Australian Research the correction to the photogeneration rate, we have Council. Many thanks to S. Glunz and S. Rein of the observed capacitive effects at very low voltages. Junction Fraunhofer Institute for Solar Energy Systems for the use capacitance has traditionally been one of the major of the solar cell used in Figure 3. Many thanks to R. 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