- Email: [email protected]
Dependence of multi-junction solar cells parameters on concentration and temperature
Solar Energy Materials & Solar Cells 130 (2014) 234–240
Contents lists available at ScienceDirect
Solar Energy Materials & Solar Cells journal homepage: www.elsevier.com/locate/solmat
Dependence of multi-junction solar cells parameters on concentration and temperature Assaf Ben Or, Joseph Appelbaum n Tel Aviv University, School of Electrical Engineering, Tel Aviv 69978, Israel
art ic l e i nf o
a b s t r a c t
Article history: Received 9 May 2014 Received in revised form 5 July 2014 Accepted 7 July 2014
The dependence of InGaP/GaAs/Ge multi- junction solar cell model parameters on concentration and temperature are of interest to solar cell manufacturers. These parameters are related to cell processing and materials. In this work, the cell parameters were estimated by curve fitting of the experimental I–V characteristics to the single diode model equation of the multi-junction cell. The dependence of the cell parameters on light concentration and temperature is shown. Based on the estimated parameters, the performance of multi-junction cells and concentrated photovoltaic arrays under different solar irradiances and temperatures may be predicted. & 2014 Elsevier B.V. All rights reserved.
Keywords: Multi-junction solar cell parameters Parameter estimation Dependence of cell parameters on temperature and concentration
1. Introduction Concentrated photovoltaic (CPV) systems based on high efficiency multi-junction (MJ) solar cells are among the promised technologies for large scale solar electricity production. Modeling the I–V characteristic equation of solar cells is an important tool for the investigation of the performance of solar cells and arrays under different irradiance, temperature and solar spectrum. The I–V characteristic equation is an analytical expression which describes the relation between the electrical parameters of the cell and the current and voltage of the cell terminals. The use of the conventional lump-parameter single-diode model of the solar cell to predict the I–V characteristic equation of MJ cells at different temperatures and irradiances is reported in [1,2]. This model was used also to investigate the dependence of MJ cell performance on spectrum [3,4]. An extended model based on the five parameter model and an additional term which describes the operation of the bypass diode connected to each cell, as in CPV arrays, was shown in [5].The extended model may be used for the analysis of I–V characteristics of CPV dense arrays. The single diode model equation of InGaP/GaAs/Ge MJ solar cell was used, in the present study, to estimate the five parameter values of the solar cell. Newton–Raphson algorithm was applied in the curve fitting procedure where the minimum error between the measured I–V cell characteristic and the theoretical cell equation served as the quality for the estimated parameters [6].
n
Corresponding author. Tel.: þ 972 3 6409014; fax: þ 972 3 640 7052. E-mail address: [email protected] (J. Appelbaum).
http://dx.doi.org/10.1016/j.solmat.2014.07.010 0927-0248/& 2014 Elsevier B.V. All rights reserved.
The measured I–V characteristics pertain to concentration of 350, 555,700 and 900 Sun and temperature of 10 1C, 25 1C, 80 1C and 95 1C. The results of the estimated parameters show a clear and a monotonic dependence of the parameter values on light concentration and on cell temperature. Based on the results, the dependence of the fill factor and the cell efficiency on concentration and temperature is also shown. It should be emphasized that parameter estimation of solar cells based on optimization methods may lead to a local minimum. Different initial parameter values may result in different estimated parameter values. Therefore, there is no confidence in obtaining the global minimum, although the estimated parameters may have physical meanings. Adding to the procedure for estimating the parameters the notion of monotonic behavior of the parameters on different concentrations and temperatures is important to obtain confidence in the results.
2. Parameter estimation of multi-junction solar cells—Single diode model The conventional five parameter model (single diode model) was used to estimate the parameters of the solar cell. The model is described by I ¼ I ph I 0 ðeðV þ IRs Þ=V T n 1Þ
V þ IRs Rsh
ð1Þ
where, I and V are the terminals current and voltage, respectively, Iph is the photo-generated current, I0 is the diode reversed saturated current, n is the ideality factor of the diode, Rs and Rsh
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
are the series and shunt resistances, respectively, and VT is the thermal voltage. A MJ cell consists of several sub-cells (three subcells in triple-junction solar cell). Each sub-cell can be described by a five parameters model, therefore the parameters in Eq. (1) represent equivalent parameters of a MJ cell [7,8].
235
12 I-V Fitted I-V Measured
10
3. Curve fitting procedure The Newton–Raphson algorithm was applied for curve fitting between the measured and the theoretical I–V characteristics at different concentrations and temperatures. The detailed algorithm is described elsewhere [6]. Since the convergence of the algorithm is very sensitive to initial parameter values, these values must be chosen carefully. In this study the initialization of the parameters is performed as described in [5]. Because the measurements contain relatively large errors near the short circuit current and the open circuit voltage, these measurements were excluded in the estimation process.
4. Results Curve fitting was performed on the measured I–V characteristics of MJn solar cells under four light concentrations: 350, 555, 700 and 900 Sun at cell temperatures of 10 1C, 25 1C, 80 1C and 95 1C. A very good fit was achieved for all cell measurements. A comparison between the measured to the fitted I–V characteristic for concentration of 900 Sun at 95 1C is shown in Fig. 1, as an example. The results prove that the single diode model may be used to describe the I–V characteristic of a MJ solar cell at different concentrations and temperatures. Although the model is an analytical expression and does not necessarily describe accurately physical mechanisms inside the cell, some of the equivalent cell parameters may have practical values.
Current [A]
8 6 4 2 0
0
0.5
1
1.5 Voltage [V]
2
2.5
Fig. 1. Measured and fitted I–V characteristic of MJ cell at 900 Sun and 95 1C. n Data provided courtesy by Spectrolab Inc.
limits the cell efficiency [11] and leads to a decrease of the total carrier lifetimes τp/n and, as a result, to an increase of I0. Therefore, the increase of n might be related to the increase in the Auger and radiative recombination mechanisms. The dependence of the Rs and Rsh on the light concentration is shown in Fig. 2d and e. As the light concentration increases, the values of Rs and Rsh decrease. The Rs is strongly dependent on the resistance of the semiconductor layers, on the contact resistance at the semiconductor–metal interface, on the resistance of the metal gridlines, as well as on the tunnel diodes resistivities [12]. The reduction of Rs with the light concentration may be explained by the change in the material resistivity. The resistivity ρ (the inverse of the conductivity σ ) is given by [13] 1
ρ ¼ ¼ 1=qðμn n þ μp pÞ σ
4.1. Dependence of solar cell parameters on light concentration Based on the proposed curve fitting procedure, the dependence of the estimated parameters on the light concentration was studied. Fig. 2a shows a linear dependence of Iph on light concentration, E, as expected [9]: I ph ðEÞ ¼ I ph ðE0 Þ
E E0
ð2Þ
where, E0 ¼ 1 Sun ð1000 W=m2 Þ. The increase of Iph with light concentration is higher for high temperatures due to the reduction of the subcells bandgap resulting in a higher absorption. The saturation corrent, I0 (Fig. 2b) and the ideality factor, n (Fig. 2c) increase with light concentration. The I0 and n of a solar cell are directly related to equivalent recombination processes in the cell (space charge recombination, bulk recombination and surface recombination) [10]. A solar cell with a higher recombination (lower carriers lifetimes) has larger I0 and n. The reverse saturation current, I0, of an ideal p–n diode is given by [10] sffiffiffiffiffiffi ! sffiffiffiffiffiffi Dp n2i Dn n2i þ ð3Þ I0 ¼ q τp N D τn N A where q is elementary charge, A is the cross-sectional area, Dp and Dn are the diffusion coefficients of holes and electrons, respectively, NA and N D are the donor and acceptor concentrations at the n and p sides, respectively, ni is the intrinsic carrier concentration of the semiconductor material, and τp and τn are the carrier lifetimes of holes and electrons, respectively. As the light concentration increases, the recombination processes are enhanced, especially the radiatiave and Auger recombination. This eventually
3
ð4Þ
where n and p are the electron and hole concentration and μn and μp are the electron and hole mobility (material dependent), respectively. As light concentration increases, the charge carriers concentration of electron and holes increases as well and, therefore the material resistivity and hence the series and shunt resistance, decrease. The decrease of the shunt resistanceRsh is a result of higher leakage currents at high light concentration [14]. 4.2. Dependence of solar cell parameters on cell temperature Temperature affects the five parameter model equation in two ways: directly, via the explicit T in the exponential term, and indirectly via the change in the parameters with temperature. The dependence of Iph on temperature is shown in Fig. 3a. The equivalent Iph of the cell is influenced from the light absorption, i. e., charge carrier generation in the cell. As the temperature increases the bandgaps, Eg(T), of all subcells shrink as described by Varshni’s empirical expression [13] Eg ðTÞ ¼ Eg ð0Þ
αT 2 T þβ
ð5Þ
where, Eg(0), α and β are material constants. Therefore, since Eg(T) decreases, more photons have the sufficient energy to create electron–hole pairs and therefore Iph increases. The value of I0 increases exponentially with tempearture (Fig. 3b) mainly due to the increase in the intrinsic carrier concentration, ni [15], as shown in Eq. (3). The intrinsic carrier concentration [15] is given by ni ¼ Ns e ðEg =2kB TÞ
ð6Þ
236
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
Fig. 2. Dependence of cell parameters on light concentration: (a) Iph–photo-generated current, (b) I0—reverse saturation current, (c) n-ideality factor, (d) Rs—series resistance, and (e) Rsh—shunt resistance.
where, Ns p ðT 3=2 Þ is the number per unit volume of the effectively available states. Its value depends on the material (the order of 1019 cm 3 at room temperature) and increases with temperature. In addition, the intrinsic carrier concentration, ni, is strongly
influenced from the reduction in the bandgap energy (see Eqs. (5) and (6)), i.e., with the lowering of bandgaps, the concentration of the intrinsic carrier increases. As for the recombination process in the solar cell, the temperature influences mainly on the
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
237
Fig. 3. Dependence cell parameters on cell temperature: (a) Iph—photo-generated current, (b) I0—reverse saturation current, (c) n-ideality factor, (d) Rs—series resistance, and (e) Rsh—shunt resistance.
Shockley–Read–Hall (SRH) and the surface recombination rates [16]. This may explain the decrease in n, which is strongly related to the recombination mechanisms, with temperature as shown in Fig. 3c. The dependence of Rs and Rsh on temperatures is shown in Fig. 3d and e. There are three types of thermal sensitive resistances [17]: conductor type, negative temperature coefficient type and
positive temperature coefficient type. The conductor type follows: RðTÞ ¼ R0 ð1 þ αTÞ
ð7Þ
where α is the conductor temperature coefficient (α 40) and R0 is the resistance at a reference temperature. The negative (Eq. (8)) and the positive (Eq. (9)) temperature coefficient types are
238
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
described by: RðTÞ ¼ R0 expðB=TÞ
ð8Þ
RðTÞ ¼ R0 expðB TÞ
ð9Þ
where B is the semiconductor material coefficient (B4 0). Therefore, Rs which is influenced by the metal conductors and the semiconductor resistivity of the material, behaves according to Eqs. (7) and (8). At lower concentration (350 Sun), the change of the Rs with the temperature is the highest. As mentioned before, at lower light concentration the charge carrier mobility is also low and therefore, as the cell temperature rises, the increase in the resistance is more pronounced. A positive coefficient type (Eq. (9)) behavior of Rs is reported in [17]. Concerning Rsh, (see Fig. 3e) it was found that an increase in temperature leads to a decrease in Rsh (dRsh/dTo 0). Therefore, the shunt resistance behaves according to the Eq. (8). Rsh models conductivity paths through the solar cell or on the cell edges caused by crystal damages or metallization spikes through the p–n junction mainly due to manufacturing defects [18]. As the temperature increases the influence of all these shunt defects increases and the Rsh tends to degrade (decrease) leading to higher shunt currents [2,4]. 4.3. Dependence of fill factor and cell efficiency on light concentration and cell temperature Based on the fitted parameters, the ratio between Vm (the maximum power voltage) and Voc (the open circuit voltage), Vm/Voc, cell fill factor (FF) and the efficiency η were calculated. The dependence of Vm/ Voc on light concentration and cell temperature is shown in Fig. 4. This ratio maybe of interest to the CPV array designer. According to Eq. (1), V oc at E0 (1 Sun) is obtained by I ph ðE0 Þ V oc ðE0 Þ þ1 V oc ðE0 Þ ¼ nðE0 ÞV T ln I ðE Þ R ðE ÞI ðE Þ 0 0 sh 0 0 0 I ph ðE0 Þ ð10Þ nðE0 ÞV T ln I 0 ðE0 Þ With light concentration, Voc increases as follows: I ph ðE0 Þ I ph ðE0 Þ ¼ nðCE0 ÞV T ln þ lnðCÞ V oc ðCE0 Þ ¼ nðCE0 ÞV T ln C I 0 ðCE0 Þ I 0 ðCE0 Þ ð11Þ where C is the concentration ratio and I 0 ðCE0 Þ in the reverse saturation current affected by the concentration. The ratio Vm/Voc
decreases slightly with the light concentration, due to the influence of Rs on Vm. Although Rs decreases with concentration, the voltage drop, ImRs, increases due to higher Im (maximum power current) thus reducing Vm. The decrease in Voc with increasing temperature arises mainly from I0 which increases exponentially with increasing T. The reduction of Vm with the temperature is more significant since it is influenced also from the increase of Rs. Therefore the ratio Vm/Voc decreases eventually with temperature. The Fill Factor (FF) is a measure of the quality of the solar cell. The dependence of FF on the light concentration and cell temperature is shown Fig. 5. FF decreases linearly with the temperature and concentration ratio in a very similar way as the ratio Vm/ Voc since the ratio Im/Isc is very close to unity (as Rsh c 1). Additional information about the FF dependence of MJ solar cells on light concentration and temperature may be found in [19,20]. The ideal fill factor FF' is defined as [21], [Ch.2] FF 0 ¼
V m Im V oc I sc
ð12Þ
where, I sc is the short circuit current. The real fill factor is strongly determined by the series resistance Rs of the solar cell, especially under concentrated light. The efficiency at E0 taking into account the series resistance is given by [21], [Ch.2]
ηðE0 Þ ¼
V oc ðE0 ÞI sc ðE0 ÞFF ' ðE0 Þ Rs ðE0 ÞI 2m ðE0 Þ P in ðE0 Þ
ð13Þ
where P in ðE0 Þis the incident power on the cell at irradiance E0 . The dependence of the cell efficiency on the light concentration and temperature is shown in Fig. 6. This dependency is a function of many parameters:
ηCðE0 Þ ¼ ¼
ðV oc ðE0 Þ þ nðCE0 ÞV T lnCÞCI sc ðE0 ÞFF 0 ðCE0 Þ Rs ðCE0 ÞðCI m ðE0 ÞÞ2 CP in ðE0 Þ V oc ðE0 ÞI sc ðE0 ÞFF 0 ðCE0 Þ Rs ðCE0 ÞCI 2m ðE0 Þ þ nðCE0 ÞV T I sc ðE0 ÞFF 0 ðCE0 ÞlnC P in ðE0 Þ
ð14Þ At high temperatures (80 1C and 95 1C) the efficiency increases slightly with the light concentration. However, at low temperatures (10 1C and 25 1C), the highest efficiency is obtained for concentration ratio of 555 Sun. The change in the cell efficiency with the light concentration is rather small (7 0.5%), therefore, for the analyzed ranged of concentration no clear conclusion can be drawn. As for the
Fig. 4. Dependence of the Vm/Voc on (a) light concentration and on (b) temperature.
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
239
Fig. 5. Dependence of the Fill Factor on (a) light concentration and on (b) temperature.
Fig. 6. Dependence of cell efficiency on (a) light concentration and on (b) cell temperature.
temperature dependence, the cell efficiency decreases linearly with the cell temperature (about 1% per 20 1C), as shown in Fig. 6. The reduction of the cell efficiency with temperature is mainly due to the reduction in the output voltage of the cell (Rs and I 0 increase and ndecreases).
5. Conclusions Curve fitting of I–V characteristics was performed to obtain the parameter values of InGaP/GaAs/Ge MJ solar cell under different light concentration (350–900 Sun) and temperatures (10–90 1C). These parameters are related to cell processing and materials and, therefore are of interest to solar cell and CPV system manufacturers. The study shows that, Iph increases; I0 increases; n increases; Rs decreases and Rsh decreases with the increase in concentration. As for the temperature dependence, Iph increases; I0 increases; n decreases; Rs increases and Rsh decreases with the
increase in temperature. The change in the model parameters with the light concentration and temperature is explained by their relations to the physical and material parameters of the solar cell. Based on the estimated parameters, the performance of multijunction cells and CPV arrays as a function of solar irradiance and temperature may be predicted. It should be emphasized that parameter estimation of solar cells based on optimization methods may lead to local minima. Therefore, there is no confidence in obtaining global minima. However, adding the notion of monotonic behavior of the estimated parameters on concentrations and temperatures may be an important indication to obtain confidence in the results.
Acknowledgements The authors wish to acknowledge Spectrolab Inc. for providing solar cell data.
240
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
References [1] G.S. Kinsey, P. Hebert, K.E. Barbour, D.D. Krut, H.L. Cotal, R.A. Sherif, Concentrator multijunction solar cell characteristics under variable intensity and temperature, Prog. Photovoltaics: Res. Appl. 16 (2008) 503–508. [2] K. Nishioka, T. Takamoto, T. Agui, M. Kaneiwa, Y. Uraoka, T. Fuyuki, Annual output estimation of concentrator photovoltaic systems using high-efficiency InGaP/InGaAs/Ge triple-junction solar cells based on experimental solar cell’s characteristics and field-test meteorological data, Sol. Energy Mater. Sol. Cells 90 (2006) 57–67. [3] K. Araki, M. Yamaguchi, Influences of spectrum change to 3-junction concentrator cells, Sol. Energy Mater. Sol. Cells 75 (2003) 707–714. [4] R. Adelhelm, K. Bücher, Performance and parameter analysis of tandem solar cells using measurements at multiple spectral conditions, Sol. Energy Mater. Sol. Cells 50 (1998) 185–195. [5] A. Ben Or, J. Appelbaum, Performance analysis of concentrator photovoltaic dense-arrays under non-uniform irradiance, Sol. Energy Mater. Sol. Cells 117 (2013) 110–119. [6] A. Ben Or, J. Appelbaum, Estimation of multi-junction solar cell parameters, Prog. Photovoltaics: Res. Appl. 21 (2013) 713–723. http://dx.doi.org/10.1002/ pip.2158. [7] G. Timò, A. Minuto, P. Groppelli, L. Oliverio, E. Malsivi, M. Sturm, Modeling and new identification procedures to evaluate concentrating photovoltaic multijunction module equivalent parameters and multijunction cells temperature in operating outdoor conditions, in: Proceedings of the 25th European Photovoltaic Solar Energy Conference, Valencia, Spain, 2010. [8] C.S. Mayberry, K.C. Reinhardt, T.L. Kreifels, Monolithic crystalline multijunction solar cell development and analysis at the US Air Force research laboratory, Renewable Energy 28 (2003) 1729–1740. [9] E. Lorenzo, Solar Electricity: Engineering of Photovoltaic (ISBN:84-86505-550), Progensa, Sevilla, 1994. [10] P. Wuerfel, Physics of Solar Cells: From Basic Principles to Advanced Concepts, Wiley-VCH, Weinhein, ISBN 978-3-527-40857-3, 2003.
[11] A. Vossier, B. Hirsch, J.M. Gordon, Is Auger recombination the ultimate performance limiter in concentrator solar cells? Appl. Phys. Lett. 97 (2010) 193509. http://dx.doi.org/10.1063/1.3510474. [12] H. Cotal, C. Fetzer, J. Boisvert, G. Kinsey, R. King, P. Hebert, H. Yoon, N. Karam, III–V multijunction solar cells for concentrating photovoltaics, Energy Environ. Sci. 2 (2009) 174–192. [13] B. Van Zeghbroeck, Principles of Electronic Devices, University of Colorado, 2011. [14] F. Khan, S.N. Singh, M. Husain, Effect of illumination intensity on cell parameters of a silicon solar cell, Sol. Energy Mater. Sol. Cells 94 (2010) 1473–1476. [15] P.P. Altermatt, A. Schenk, F. Geelhaar, G. Heiser, Reassessment of the intrinsic carrier density in crystalline silicon in view of band-gap narrowing, J. Appl. Phys. 93 (3) (2003) 1598. [16] K. Beyzavi, K. Lee, D.M. Kim, M.I. Nathan, K. Wrenner, S.L. Wright, Temperature dependence of minority-carrier mobility and recombination time in P-type GaAs, Appl. Phys. Lett. 58 (12) (1991) 1268–1270. [17] J. Ding, X. Cheng, T. Fu, Analysis of series resistance and P-T characteristics of the solar cell, Vacuum 77 (2) (2005) 163–167. [18] S. Bensalem, M. Chegaar, Thermal behavior of parasitic resistances of polycrystalline silicon solar cells, Rev. Energies Renouvelabes 16 (1) (2013) 171–176. [19] S. Yoon, V. Garboushian, Reduced temperature dependence of highconcentration photovoltaic solar cell open-circuit voltage (Voc) at high concentration levels, in: Proceedings of 1994 IEEE First World Conference on Photovoltaic Energy Conversion, vol. 2, 1994. 10.1109/WCPEC.1994.520235. [20] H. Cotal, R. Sherif, Temperature dependence of the IV parameters from triple junction GaInP/InGaAs/Ge concentrator solar cells, in: Conference Record of the 2006 IEEE Fourth World Conference on Photovoltaic Energy Conversion, Waikoloa, HI, 2006, pp. 845–848. [21] R.J. Van Overstaeten, R.P. Mertens, Physics, Technology and Use of Photovoltaics, Adam Hilger Ltd., Bristol, England, 1986.
Contents lists available at ScienceDirect
Solar Energy Materials & Solar Cells journal homepage: www.elsevier.com/locate/solmat
Dependence of multi-junction solar cells parameters on concentration and temperature Assaf Ben Or, Joseph Appelbaum n Tel Aviv University, School of Electrical Engineering, Tel Aviv 69978, Israel
art ic l e i nf o
a b s t r a c t
Article history: Received 9 May 2014 Received in revised form 5 July 2014 Accepted 7 July 2014
The dependence of InGaP/GaAs/Ge multi- junction solar cell model parameters on concentration and temperature are of interest to solar cell manufacturers. These parameters are related to cell processing and materials. In this work, the cell parameters were estimated by curve fitting of the experimental I–V characteristics to the single diode model equation of the multi-junction cell. The dependence of the cell parameters on light concentration and temperature is shown. Based on the estimated parameters, the performance of multi-junction cells and concentrated photovoltaic arrays under different solar irradiances and temperatures may be predicted. & 2014 Elsevier B.V. All rights reserved.
Keywords: Multi-junction solar cell parameters Parameter estimation Dependence of cell parameters on temperature and concentration
1. Introduction Concentrated photovoltaic (CPV) systems based on high efficiency multi-junction (MJ) solar cells are among the promised technologies for large scale solar electricity production. Modeling the I–V characteristic equation of solar cells is an important tool for the investigation of the performance of solar cells and arrays under different irradiance, temperature and solar spectrum. The I–V characteristic equation is an analytical expression which describes the relation between the electrical parameters of the cell and the current and voltage of the cell terminals. The use of the conventional lump-parameter single-diode model of the solar cell to predict the I–V characteristic equation of MJ cells at different temperatures and irradiances is reported in [1,2]. This model was used also to investigate the dependence of MJ cell performance on spectrum [3,4]. An extended model based on the five parameter model and an additional term which describes the operation of the bypass diode connected to each cell, as in CPV arrays, was shown in [5].The extended model may be used for the analysis of I–V characteristics of CPV dense arrays. The single diode model equation of InGaP/GaAs/Ge MJ solar cell was used, in the present study, to estimate the five parameter values of the solar cell. Newton–Raphson algorithm was applied in the curve fitting procedure where the minimum error between the measured I–V cell characteristic and the theoretical cell equation served as the quality for the estimated parameters [6].
n
Corresponding author. Tel.: þ 972 3 6409014; fax: þ 972 3 640 7052. E-mail address: [email protected] (J. Appelbaum).
http://dx.doi.org/10.1016/j.solmat.2014.07.010 0927-0248/& 2014 Elsevier B.V. All rights reserved.
The measured I–V characteristics pertain to concentration of 350, 555,700 and 900 Sun and temperature of 10 1C, 25 1C, 80 1C and 95 1C. The results of the estimated parameters show a clear and a monotonic dependence of the parameter values on light concentration and on cell temperature. Based on the results, the dependence of the fill factor and the cell efficiency on concentration and temperature is also shown. It should be emphasized that parameter estimation of solar cells based on optimization methods may lead to a local minimum. Different initial parameter values may result in different estimated parameter values. Therefore, there is no confidence in obtaining the global minimum, although the estimated parameters may have physical meanings. Adding to the procedure for estimating the parameters the notion of monotonic behavior of the parameters on different concentrations and temperatures is important to obtain confidence in the results.
2. Parameter estimation of multi-junction solar cells—Single diode model The conventional five parameter model (single diode model) was used to estimate the parameters of the solar cell. The model is described by I ¼ I ph I 0 ðeðV þ IRs Þ=V T n 1Þ
V þ IRs Rsh
ð1Þ
where, I and V are the terminals current and voltage, respectively, Iph is the photo-generated current, I0 is the diode reversed saturated current, n is the ideality factor of the diode, Rs and Rsh
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
are the series and shunt resistances, respectively, and VT is the thermal voltage. A MJ cell consists of several sub-cells (three subcells in triple-junction solar cell). Each sub-cell can be described by a five parameters model, therefore the parameters in Eq. (1) represent equivalent parameters of a MJ cell [7,8].
235
12 I-V Fitted I-V Measured
10
3. Curve fitting procedure The Newton–Raphson algorithm was applied for curve fitting between the measured and the theoretical I–V characteristics at different concentrations and temperatures. The detailed algorithm is described elsewhere [6]. Since the convergence of the algorithm is very sensitive to initial parameter values, these values must be chosen carefully. In this study the initialization of the parameters is performed as described in [5]. Because the measurements contain relatively large errors near the short circuit current and the open circuit voltage, these measurements were excluded in the estimation process.
4. Results Curve fitting was performed on the measured I–V characteristics of MJn solar cells under four light concentrations: 350, 555, 700 and 900 Sun at cell temperatures of 10 1C, 25 1C, 80 1C and 95 1C. A very good fit was achieved for all cell measurements. A comparison between the measured to the fitted I–V characteristic for concentration of 900 Sun at 95 1C is shown in Fig. 1, as an example. The results prove that the single diode model may be used to describe the I–V characteristic of a MJ solar cell at different concentrations and temperatures. Although the model is an analytical expression and does not necessarily describe accurately physical mechanisms inside the cell, some of the equivalent cell parameters may have practical values.
Current [A]
8 6 4 2 0
0
0.5
1
1.5 Voltage [V]
2
2.5
Fig. 1. Measured and fitted I–V characteristic of MJ cell at 900 Sun and 95 1C. n Data provided courtesy by Spectrolab Inc.
limits the cell efficiency [11] and leads to a decrease of the total carrier lifetimes τp/n and, as a result, to an increase of I0. Therefore, the increase of n might be related to the increase in the Auger and radiative recombination mechanisms. The dependence of the Rs and Rsh on the light concentration is shown in Fig. 2d and e. As the light concentration increases, the values of Rs and Rsh decrease. The Rs is strongly dependent on the resistance of the semiconductor layers, on the contact resistance at the semiconductor–metal interface, on the resistance of the metal gridlines, as well as on the tunnel diodes resistivities [12]. The reduction of Rs with the light concentration may be explained by the change in the material resistivity. The resistivity ρ (the inverse of the conductivity σ ) is given by [13] 1
ρ ¼ ¼ 1=qðμn n þ μp pÞ σ
4.1. Dependence of solar cell parameters on light concentration Based on the proposed curve fitting procedure, the dependence of the estimated parameters on the light concentration was studied. Fig. 2a shows a linear dependence of Iph on light concentration, E, as expected [9]: I ph ðEÞ ¼ I ph ðE0 Þ
E E0
ð2Þ
where, E0 ¼ 1 Sun ð1000 W=m2 Þ. The increase of Iph with light concentration is higher for high temperatures due to the reduction of the subcells bandgap resulting in a higher absorption. The saturation corrent, I0 (Fig. 2b) and the ideality factor, n (Fig. 2c) increase with light concentration. The I0 and n of a solar cell are directly related to equivalent recombination processes in the cell (space charge recombination, bulk recombination and surface recombination) [10]. A solar cell with a higher recombination (lower carriers lifetimes) has larger I0 and n. The reverse saturation current, I0, of an ideal p–n diode is given by [10] sffiffiffiffiffiffi ! sffiffiffiffiffiffi Dp n2i Dn n2i þ ð3Þ I0 ¼ q τp N D τn N A where q is elementary charge, A is the cross-sectional area, Dp and Dn are the diffusion coefficients of holes and electrons, respectively, NA and N D are the donor and acceptor concentrations at the n and p sides, respectively, ni is the intrinsic carrier concentration of the semiconductor material, and τp and τn are the carrier lifetimes of holes and electrons, respectively. As the light concentration increases, the recombination processes are enhanced, especially the radiatiave and Auger recombination. This eventually
3
ð4Þ
where n and p are the electron and hole concentration and μn and μp are the electron and hole mobility (material dependent), respectively. As light concentration increases, the charge carriers concentration of electron and holes increases as well and, therefore the material resistivity and hence the series and shunt resistance, decrease. The decrease of the shunt resistanceRsh is a result of higher leakage currents at high light concentration [14]. 4.2. Dependence of solar cell parameters on cell temperature Temperature affects the five parameter model equation in two ways: directly, via the explicit T in the exponential term, and indirectly via the change in the parameters with temperature. The dependence of Iph on temperature is shown in Fig. 3a. The equivalent Iph of the cell is influenced from the light absorption, i. e., charge carrier generation in the cell. As the temperature increases the bandgaps, Eg(T), of all subcells shrink as described by Varshni’s empirical expression [13] Eg ðTÞ ¼ Eg ð0Þ
αT 2 T þβ
ð5Þ
where, Eg(0), α and β are material constants. Therefore, since Eg(T) decreases, more photons have the sufficient energy to create electron–hole pairs and therefore Iph increases. The value of I0 increases exponentially with tempearture (Fig. 3b) mainly due to the increase in the intrinsic carrier concentration, ni [15], as shown in Eq. (3). The intrinsic carrier concentration [15] is given by ni ¼ Ns e ðEg =2kB TÞ
ð6Þ
236
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
Fig. 2. Dependence of cell parameters on light concentration: (a) Iph–photo-generated current, (b) I0—reverse saturation current, (c) n-ideality factor, (d) Rs—series resistance, and (e) Rsh—shunt resistance.
where, Ns p ðT 3=2 Þ is the number per unit volume of the effectively available states. Its value depends on the material (the order of 1019 cm 3 at room temperature) and increases with temperature. In addition, the intrinsic carrier concentration, ni, is strongly
influenced from the reduction in the bandgap energy (see Eqs. (5) and (6)), i.e., with the lowering of bandgaps, the concentration of the intrinsic carrier increases. As for the recombination process in the solar cell, the temperature influences mainly on the
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
237
Fig. 3. Dependence cell parameters on cell temperature: (a) Iph—photo-generated current, (b) I0—reverse saturation current, (c) n-ideality factor, (d) Rs—series resistance, and (e) Rsh—shunt resistance.
Shockley–Read–Hall (SRH) and the surface recombination rates [16]. This may explain the decrease in n, which is strongly related to the recombination mechanisms, with temperature as shown in Fig. 3c. The dependence of Rs and Rsh on temperatures is shown in Fig. 3d and e. There are three types of thermal sensitive resistances [17]: conductor type, negative temperature coefficient type and
positive temperature coefficient type. The conductor type follows: RðTÞ ¼ R0 ð1 þ αTÞ
ð7Þ
where α is the conductor temperature coefficient (α 40) and R0 is the resistance at a reference temperature. The negative (Eq. (8)) and the positive (Eq. (9)) temperature coefficient types are
238
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
described by: RðTÞ ¼ R0 expðB=TÞ
ð8Þ
RðTÞ ¼ R0 expðB TÞ
ð9Þ
where B is the semiconductor material coefficient (B4 0). Therefore, Rs which is influenced by the metal conductors and the semiconductor resistivity of the material, behaves according to Eqs. (7) and (8). At lower concentration (350 Sun), the change of the Rs with the temperature is the highest. As mentioned before, at lower light concentration the charge carrier mobility is also low and therefore, as the cell temperature rises, the increase in the resistance is more pronounced. A positive coefficient type (Eq. (9)) behavior of Rs is reported in [17]. Concerning Rsh, (see Fig. 3e) it was found that an increase in temperature leads to a decrease in Rsh (dRsh/dTo 0). Therefore, the shunt resistance behaves according to the Eq. (8). Rsh models conductivity paths through the solar cell or on the cell edges caused by crystal damages or metallization spikes through the p–n junction mainly due to manufacturing defects [18]. As the temperature increases the influence of all these shunt defects increases and the Rsh tends to degrade (decrease) leading to higher shunt currents [2,4]. 4.3. Dependence of fill factor and cell efficiency on light concentration and cell temperature Based on the fitted parameters, the ratio between Vm (the maximum power voltage) and Voc (the open circuit voltage), Vm/Voc, cell fill factor (FF) and the efficiency η were calculated. The dependence of Vm/ Voc on light concentration and cell temperature is shown in Fig. 4. This ratio maybe of interest to the CPV array designer. According to Eq. (1), V oc at E0 (1 Sun) is obtained by I ph ðE0 Þ V oc ðE0 Þ þ1 V oc ðE0 Þ ¼ nðE0 ÞV T ln I ðE Þ R ðE ÞI ðE Þ 0 0 sh 0 0 0 I ph ðE0 Þ ð10Þ nðE0 ÞV T ln I 0 ðE0 Þ With light concentration, Voc increases as follows: I ph ðE0 Þ I ph ðE0 Þ ¼ nðCE0 ÞV T ln þ lnðCÞ V oc ðCE0 Þ ¼ nðCE0 ÞV T ln C I 0 ðCE0 Þ I 0 ðCE0 Þ ð11Þ where C is the concentration ratio and I 0 ðCE0 Þ in the reverse saturation current affected by the concentration. The ratio Vm/Voc
decreases slightly with the light concentration, due to the influence of Rs on Vm. Although Rs decreases with concentration, the voltage drop, ImRs, increases due to higher Im (maximum power current) thus reducing Vm. The decrease in Voc with increasing temperature arises mainly from I0 which increases exponentially with increasing T. The reduction of Vm with the temperature is more significant since it is influenced also from the increase of Rs. Therefore the ratio Vm/Voc decreases eventually with temperature. The Fill Factor (FF) is a measure of the quality of the solar cell. The dependence of FF on the light concentration and cell temperature is shown Fig. 5. FF decreases linearly with the temperature and concentration ratio in a very similar way as the ratio Vm/ Voc since the ratio Im/Isc is very close to unity (as Rsh c 1). Additional information about the FF dependence of MJ solar cells on light concentration and temperature may be found in [19,20]. The ideal fill factor FF' is defined as [21], [Ch.2] FF 0 ¼
V m Im V oc I sc
ð12Þ
where, I sc is the short circuit current. The real fill factor is strongly determined by the series resistance Rs of the solar cell, especially under concentrated light. The efficiency at E0 taking into account the series resistance is given by [21], [Ch.2]
ηðE0 Þ ¼
V oc ðE0 ÞI sc ðE0 ÞFF ' ðE0 Þ Rs ðE0 ÞI 2m ðE0 Þ P in ðE0 Þ
ð13Þ
where P in ðE0 Þis the incident power on the cell at irradiance E0 . The dependence of the cell efficiency on the light concentration and temperature is shown in Fig. 6. This dependency is a function of many parameters:
ηCðE0 Þ ¼ ¼
ðV oc ðE0 Þ þ nðCE0 ÞV T lnCÞCI sc ðE0 ÞFF 0 ðCE0 Þ Rs ðCE0 ÞðCI m ðE0 ÞÞ2 CP in ðE0 Þ V oc ðE0 ÞI sc ðE0 ÞFF 0 ðCE0 Þ Rs ðCE0 ÞCI 2m ðE0 Þ þ nðCE0 ÞV T I sc ðE0 ÞFF 0 ðCE0 ÞlnC P in ðE0 Þ
ð14Þ At high temperatures (80 1C and 95 1C) the efficiency increases slightly with the light concentration. However, at low temperatures (10 1C and 25 1C), the highest efficiency is obtained for concentration ratio of 555 Sun. The change in the cell efficiency with the light concentration is rather small (7 0.5%), therefore, for the analyzed ranged of concentration no clear conclusion can be drawn. As for the
Fig. 4. Dependence of the Vm/Voc on (a) light concentration and on (b) temperature.
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
239
Fig. 5. Dependence of the Fill Factor on (a) light concentration and on (b) temperature.
Fig. 6. Dependence of cell efficiency on (a) light concentration and on (b) cell temperature.
temperature dependence, the cell efficiency decreases linearly with the cell temperature (about 1% per 20 1C), as shown in Fig. 6. The reduction of the cell efficiency with temperature is mainly due to the reduction in the output voltage of the cell (Rs and I 0 increase and ndecreases).
5. Conclusions Curve fitting of I–V characteristics was performed to obtain the parameter values of InGaP/GaAs/Ge MJ solar cell under different light concentration (350–900 Sun) and temperatures (10–90 1C). These parameters are related to cell processing and materials and, therefore are of interest to solar cell and CPV system manufacturers. The study shows that, Iph increases; I0 increases; n increases; Rs decreases and Rsh decreases with the increase in concentration. As for the temperature dependence, Iph increases; I0 increases; n decreases; Rs increases and Rsh decreases with the
increase in temperature. The change in the model parameters with the light concentration and temperature is explained by their relations to the physical and material parameters of the solar cell. Based on the estimated parameters, the performance of multijunction cells and CPV arrays as a function of solar irradiance and temperature may be predicted. It should be emphasized that parameter estimation of solar cells based on optimization methods may lead to local minima. Therefore, there is no confidence in obtaining global minima. However, adding the notion of monotonic behavior of the estimated parameters on concentrations and temperatures may be an important indication to obtain confidence in the results.
Acknowledgements The authors wish to acknowledge Spectrolab Inc. for providing solar cell data.
240
A. Ben Or, J. Appelbaum / Solar Energy Materials & Solar Cells 130 (2014) 234–240
References [1] G.S. Kinsey, P. Hebert, K.E. Barbour, D.D. Krut, H.L. Cotal, R.A. Sherif, Concentrator multijunction solar cell characteristics under variable intensity and temperature, Prog. Photovoltaics: Res. Appl. 16 (2008) 503–508. [2] K. Nishioka, T. Takamoto, T. Agui, M. Kaneiwa, Y. Uraoka, T. Fuyuki, Annual output estimation of concentrator photovoltaic systems using high-efficiency InGaP/InGaAs/Ge triple-junction solar cells based on experimental solar cell’s characteristics and field-test meteorological data, Sol. Energy Mater. Sol. Cells 90 (2006) 57–67. [3] K. Araki, M. Yamaguchi, Influences of spectrum change to 3-junction concentrator cells, Sol. Energy Mater. Sol. Cells 75 (2003) 707–714. [4] R. Adelhelm, K. Bücher, Performance and parameter analysis of tandem solar cells using measurements at multiple spectral conditions, Sol. Energy Mater. Sol. Cells 50 (1998) 185–195. [5] A. Ben Or, J. Appelbaum, Performance analysis of concentrator photovoltaic dense-arrays under non-uniform irradiance, Sol. Energy Mater. Sol. Cells 117 (2013) 110–119. [6] A. Ben Or, J. Appelbaum, Estimation of multi-junction solar cell parameters, Prog. Photovoltaics: Res. Appl. 21 (2013) 713–723. http://dx.doi.org/10.1002/ pip.2158. [7] G. Timò, A. Minuto, P. Groppelli, L. Oliverio, E. Malsivi, M. Sturm, Modeling and new identification procedures to evaluate concentrating photovoltaic multijunction module equivalent parameters and multijunction cells temperature in operating outdoor conditions, in: Proceedings of the 25th European Photovoltaic Solar Energy Conference, Valencia, Spain, 2010. [8] C.S. Mayberry, K.C. Reinhardt, T.L. Kreifels, Monolithic crystalline multijunction solar cell development and analysis at the US Air Force research laboratory, Renewable Energy 28 (2003) 1729–1740. [9] E. Lorenzo, Solar Electricity: Engineering of Photovoltaic (ISBN:84-86505-550), Progensa, Sevilla, 1994. [10] P. Wuerfel, Physics of Solar Cells: From Basic Principles to Advanced Concepts, Wiley-VCH, Weinhein, ISBN 978-3-527-40857-3, 2003.
[11] A. Vossier, B. Hirsch, J.M. Gordon, Is Auger recombination the ultimate performance limiter in concentrator solar cells? Appl. Phys. Lett. 97 (2010) 193509. http://dx.doi.org/10.1063/1.3510474. [12] H. Cotal, C. Fetzer, J. Boisvert, G. Kinsey, R. King, P. Hebert, H. Yoon, N. Karam, III–V multijunction solar cells for concentrating photovoltaics, Energy Environ. Sci. 2 (2009) 174–192. [13] B. Van Zeghbroeck, Principles of Electronic Devices, University of Colorado, 2011. [14] F. Khan, S.N. Singh, M. Husain, Effect of illumination intensity on cell parameters of a silicon solar cell, Sol. Energy Mater. Sol. Cells 94 (2010) 1473–1476. [15] P.P. Altermatt, A. Schenk, F. Geelhaar, G. Heiser, Reassessment of the intrinsic carrier density in crystalline silicon in view of band-gap narrowing, J. Appl. Phys. 93 (3) (2003) 1598. [16] K. Beyzavi, K. Lee, D.M. Kim, M.I. Nathan, K. Wrenner, S.L. Wright, Temperature dependence of minority-carrier mobility and recombination time in P-type GaAs, Appl. Phys. Lett. 58 (12) (1991) 1268–1270. [17] J. Ding, X. Cheng, T. Fu, Analysis of series resistance and P-T characteristics of the solar cell, Vacuum 77 (2) (2005) 163–167. [18] S. Bensalem, M. Chegaar, Thermal behavior of parasitic resistances of polycrystalline silicon solar cells, Rev. Energies Renouvelabes 16 (1) (2013) 171–176. [19] S. Yoon, V. Garboushian, Reduced temperature dependence of highconcentration photovoltaic solar cell open-circuit voltage (Voc) at high concentration levels, in: Proceedings of 1994 IEEE First World Conference on Photovoltaic Energy Conversion, vol. 2, 1994. 10.1109/WCPEC.1994.520235. [20] H. Cotal, R. Sherif, Temperature dependence of the IV parameters from triple junction GaInP/InGaAs/Ge concentrator solar cells, in: Conference Record of the 2006 IEEE Fourth World Conference on Photovoltaic Energy Conversion, Waikoloa, HI, 2006, pp. 845–848. [21] R.J. Van Overstaeten, R.P. Mertens, Physics, Technology and Use of Photovoltaics, Adam Hilger Ltd., Bristol, England, 1986.