FOR LONGER than five decades since the introduction of

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1 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 59, NO. 9, SEPTEMBER Transient Thermal Resistance Test of Single-Crystal-Silicon Solar Cell Jihong Zhang, Yulin Gao, Yijun Lu, Lihong Zhu, Ziquan Guo, Guolong Chen, and Zhong Chen Abstract This paper reports the measurement of the junction temperature and the determination of the thermal resistance of the single-crystal-silicon solar cell under the dark and illuminating conditions, respectively. Under the dark condition, the solar cell is considered as a conventional p-n junction and is subject to a reverse current in order to measure its junction temperature and determine the thermal resistance. A white LED array is used as the light source to operate the solar cell in order to avoid the heating effect of the infrared light by the solar simulator. Furthermore, we thoroughly calculate the thermal dissipation power. The result demonstrates that the thermal resistance drops from 3.7 to 2.0 K/W with the increase of the irradiance from 89.6 to W/m 2. It is also found that the thermal resistance under the dark condition is much higher than that under the illuminating condition, which is attributed to the light effect on the thermal resistance. Index Terms Solar cell, thermal dissipation power, thermal resistance, white LED array. I. INTRODUCTION FOR LONGER than five decades since the introduction of the first photovoltaic (PV) device [1], solar cells and solar modules have been contributing an increasing sizeable share to the world s demand for clean and renewable electrical energy. Further attention of the solar cell has been attracted to both commercial and scientific research fields. A solar cell is a device that uses p-n diodes to convert light into electric energy directly. In general, the temperature of a solar cell exerts an important influence on the solar cell s output power and energy conversion efficiency. Normally, the system output power or energy conversion efficiency decreases with the increasing temperature of the cell, due to a decrease in the open-circuit voltage as a function of increasing temperature [2], [3]. For this reason, several papers have been already reported on the junction-temperature measurement of solar cell with reasonable accuracy. Chou et al. introduced an effective methodology that integrates an infrared (IR) thermography measurement and a 3-D finite-element model (FEM) for the thermal characterization of the high-concentration PV (HCPV) Manuscript received April 7, 2012; revised May 31, 2012; accepted June 5, Date of publication July 24, 2012; date of current version August 17, This work was supported by the National Science Foundation under Grant , by the Major Science and Technology Project between University Industry Cooperation in Fujian Province under Grant 2011H6025, and by the Key Project of Fujian Province under Grant 2012H0039. The review of this paper was arranged by Editor A. G. Aberle. The authors are with the Department of Electronic Science, Fujian Engineering Research Center for Solid-State Lighting, Xiamen University, Xiamen , China ( yjlu@xmu.edu.cn, chenz@xmu.edu.cn). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TED solar cell [4]. The maximum temperature of the HCPV module taken by the IR thermometer was 41.0 C, and the analytic result of the FEM was 42.0 C. The minimum temperature of the HCPV module taken by the IR thermometer was 36.5 C, and the analytic results of the FEM offered a good agreement with the experimental data. Wang et al. presented the junction-temperature measurement of a HCPV module by an electrical temperature-sensitive parameter (TSP) method and validated the results with the finite-element analysis (FEA) [5]. It is also found that the proposed detailed FEA of the HCPV module is a reliable tool in examining the transient thermal characteristics of an HCPV module. Jang et al. reported the thermal characterization of the junction in a commercial amorphous silicon (a-si) solar cell package [6]. It is shown that the driving of the solar cell package with a sun power of 1 sun (100 mw/cm 2 and 1.5 AM) resulted in a junction temperature of about 113 C. Huang et al. developed a simple nondestructive method to measure the solar cell junction temperature of PV module [7]. It is shown that the maximum error using the average surface temperature as the junction temperature was 4.8 C underestimation, whereas the maximum error using the nondestructive method was 1.3 C underestimation. So far, all of the studies used a solar simulator as the solar irradiation source. As we know, the IR part of sunlight will also contribute to the heating of the solar cell, and the difficulty of the evaluation of thermal power consumed by solar cell increases the thermal-resistance error. In this paper, a white LED array was used as the light source to stimulate the photoelectric effect of the single-crystal-silicon solar cell in order to avoid the thermal caused by the IR. Moreover, we used a thermal transient method [8] to determine the thermal resistance of the solar cell. We also analyzed the variations of energy conversion efficiency and thermal performance under various illuminating conditions. Aside from that, the changes of the thermal resistance with increasing irradiance have been discussed, and the thermal dissipation power was thoroughly calculated. On the other side, the solar cell is also a p-n junction diode; thus, the thermal resistance can be measured when the solar cell is purely considered as a conventional p-n junction and driven by electric current. The junction temperature rapidly increased because the input power was completely converted into heat under the dark condition. Then, we could attain its thermal resistance by the thermal transient method easily and also analyze the variations of the thermal resistance with increasing current. In this paper, we studied the thermal resistance under two different conditions involving the solar cell driven by electric current [referred to as current driving method (CDM) /$ IEEE

2 2346 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 59, NO. 9, SEPTEMBER 2012 hereafter] and operated by the white LED [referred to as light illuminating method (LIM) hereafter], respectively. We have also analyzed the differences between the two methods. II. THERMAL RESISTANCE Thermal resistance is determined by the temperature difference between the junction and the reference point and is generally used to characterize the thermal performance of electronic devices. It is defined by the following equation: R JX = T J T X P T (1) where R JX is the thermal resistance (in kelvins per watt or degree Celsius per watt), T J is the junction temperature (in degree Celsius), T X is the reference temperature (degree Celsius), usually the heat-sink or case temperature of the device, and P T is the thermal dissipation power (in watts). The key to decide the thermal resistance is the determination of the temperature difference between the junction and the reference point. Generally, we could measure the surface temperature of the solar cell using a thermocouple but cannot attain its junction temperature by this way. The solar cell could be regarded as a p-n junction diode that is an excellent temperature sensor. Its forward-voltage drop is linearly proportional to the increment of the junction temperature, as shown by ΔV = K ΔT (2) where ΔV is the forward-voltage variation, ΔT is the junctiontemperature variation, and K is the coefficient, a constant value known as the TSP. Therefore, this property could be utilized to measure the junction temperature of the solar cell. To measure the junction temperature and the thermal resistance, we should calculate the thermal dissipation power accurately. A. Thermal Power of CDM When the solar cell is driven by an electric current under the dark condition, its photoelectric effect is invalid and is only regarded as a p-n junction diode. Therefore, the thermal power P current is calculated as follows: P current = VI (3) where V is the forward voltage and I is the drive current. B. Thermal Power of LIM When the solar cell is operated under illuminating condition, it works as a current source, and part of the electrical energy produced by the solar cell is consumed on the load, while the rest converts into thermal power. Additionally, the solar cell only utilizes photons with energy equal to the band gap of silicon, and the excess photon energy larger than the band gap of silicon converts into heat that also partly contributes to the rise of the junction temperature. In this case, the thermal power is comprised of two parts. 1) The excess photon energy lost as heat can be given by P T1 = S ( h c λ [(1 ρ(λ)) E(λ)] E g(ev ) ) h c dλ (4) λ where S is the area of the solar cell, ρ(λ) is the spectral reflectivity of the solar cell, E(λ) is the irradiance of the optical source at the wavelength of λ, the wavelength range of irradiance E(λ) for white LED is nm, E g is the band gap of silicon (1.12 ev), c is the light speed, and h is the Planck constant. (hc/λ E g (in electronvolts)) is the photon energy at the wavelength of λ larger than the band gap of silicon. 2) Heat derived from electrical energy: The solar cell under the illuminating condition can be regarded as a current source, connected in parallel with a diode, a shunt resistance, and a series resistance, as shown in Fig. 1. The relationship of the electric current and the output voltage is given by I = I ph I d I sh [ = I ph I 0 exp q(v +IR ] S) 1 V +IR S (5) nkt R sh where I ph is the photocurrent of the solar cell (in amperes), I 0 is the reverse saturation current (in amperes), n is the ideality factor (1 n 2), k is the Boltzmann constant, T is the absolute temperature of solar cell (in kelvins), q is the electron charge, R s is the series resistance (in ohms), R sh is the shunt resistance (in ohms), I is the output current of the solar cell (in amperes), and V is the output voltage of the solar cell (in volts). We can evaluate an effective series resistance of the solar cell from I V measurements proposed by Wolf and Rauschenbach [9]. Generally, its series resistance is low enough compared with the shunt resistance. Therefore, the following approximation is highly and extensively accepted when the solar cell is operated on a short current at zero output voltage: I ph I sc. (6) Considering that the external load, i.e., resistance R L, is much larger than the series resistance, the thermal power originated from the electric power P T 2 consumed by the solar cell can be calculated by the following: P T2 = V I ph V 2 /R L. (7) III. EXPERIMENTS Both heating methods (CDM and LIM) were used to investigate the thermal behavior of the single-crystal-silicon solar cells by a thermal transient tester (T3ster 2000/100, Mentor Graphics, Ltd.; ±0.2 C). The testing process of the thermal resistance is given as follows,

3 ZHANG et al.: THERMAL RESISTANCE TEST OF SINGLE-CRYSTAL-SILICON SOLAR CELL 2347 TABLE I THERMAL POWER OF THE SOLAR CELL Fig. 1. Principle diagram of the solar cell. Fig. 2. Experimental installation. (a) CDM. (b) LIM. A. CDM Under the Dark Condition Notably, in this case, there was no output power of solar cells under the dark condition. In other words, the photoelectric effect of the sample was restrained without light. The solar cell was mounted on a temperature controlling platform (TCP) with a stable temperature of 30.0 C,asshowninFig.2(a).The process of measuring the junction temperature consisted of two parts. First, we measured the TSP coefficient K by testing the forward voltages of sample versus different operated temperatures. A 3-mA sensing current was used, and the temperature controlling system varied from 30.0 C to 50.0 C, with a temperature increase step of 10.0 C. In the second part, with the TCP of 30.0 C and the applied current varying from 100 to 700 ma, with a 100-mA increment, the sample reached the thermal equilibrium after 30 min. Then, the thermal transient tester was quickly switched to the 3-mA sensing current, and it measured the forward-voltage drop; thus, we could obtain the junction temperature by comparing this voltage drop to the calibration curve that we created beforehand. B. LIM Under the lighting condition, the solar cell converts a portion of available light into electrical energy. The experiment installation used in the measurement consisted of a solar cell and a resistor (10 Ω), as shown in Fig. 2(b). Therefore, the voltage of the solar cell was the same as that of the resistor. Then, the solar cell was put on the TCP with a stable temperature of 30.0 C and was exposed to the visible light generated by a white LED array with the irradiance varying from 89.6 to W/m 2 (as shown in Table I) for 30 min until it reached Fig. 3. Structure functions of the thermal resistances of the solar cell with input currents. Fig. 4. Structure functions of the thermal resistances of the solar cell tested on the TCP and exposed in air, respectively. thermal equilibrium. Its forward-voltage drop was measured under a semidark condition with the irradiance of 22.0 W/m 2, which was so small that the heat generated by the PV effect could be ignored. The surface temperature is an average temperature measured with a thermal couple at several different positions of the surface. The solar cell s area S is cm 2. Therefore, we calculate the thermal dissipation power P T 1 by (4) under different irradiances, and the results are shown in Table I. The series resistances under different irradiances were calculated by the method proposed by Wolf and Rauschenbach [9]. The results are also shown in Table I. Then, we calculate the thermal dissipation power P T 2 by (7) under different irradiances, and the results are also shown together in Table I.

4 2348 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 59, NO. 9, SEPTEMBER 2012 Fig. 5. Thermal resistances of the solar cell as a function of the drive current under the dark condition. Fig. 7. Thermal resistances of the solar cell as a function of the irradiance with input white light. Fig. 6. Structure functions of the thermal resistances of the solar cell with input white light. IV. RESULTS AND DISCUSSION A. Results of CDM The structure function is a detailed heat-flow mapping of the package semiconductor [10], from which the thermal-resistance distribution could be clearly identified. Fig. 3 shows the structure functions of the solar cell s thermal resistances by the CDM. The exact thermal resistance of the solar cell is located by comparing the structure functions of the solar cell put on the TCP and exposed to the air (as shown in Fig. 4, the dashed line indicates the separation point of the TCP and the air exposure). Thus, all of the thermal resistances can be attained by this way from Fig. 3. Then, Fig. 5 shows all of the results of the CDM, which shows a monotonous decrease in thermal resistance with increasing heating current. B. Results of LIM Fig. 6 shows the structure functions of its thermal resistances by LIM, and the relationship between thermal resistances of the solar cell and the incident-light irradiances is shown in Fig. 7. The result clearly demonstrates that the thermal resistance drops from 3.7 to 2.0 K/W with the increase in irradiance from 89.6 to W/m 2, and the trend is coincident with that of the CDM, as shown in Fig. 5. The trend could be attributed to the increase in thermal conductivity. As we know, Fig. 8. Efficiency, the junction temperature and the surface temperature of the solar cell as a function of the incident-light irradiance with input visible light. the output power of the solar cell steadily increases with the rising incident-light irradiance. Gaitho et al. reported that, for the single-crystal-silicon cell, the maximum output power of the solar cell steadily increases with the increase in the thermal conductivity of the cell [11]; thus, the thermal conductivity will vary with the rising incident-light irradiance accordingly. Both the junction temperature and the surface temperature of the solar cell show an obvious increase with the increasing irradiance, as shown in Fig. 8. Its efficiency is very sensitive with the junction temperature and is shown to drop from 14.6% to 10.1% when the junction temperature rises from 32.7 C to 35.5 C. This trend possibly stems from a change of the illumination intensity. The higher illumination density causes a higher current density and consequently increased the voltage of the solar cell s series resistance, which causes the decline of the output voltage of the solar cell. Meanwhile, the rising junction temperature causes the weakening of the PV effect of the solar cell. Gottschalg et al. also found that the efficiency can quite appreciably decrease for high irradiance levels but invariably recovers when the irradiance levels fall [12]. There is a noteworthy difference between the results of the two methods. Generally, the thermal resistance of the CDM is much larger than that of the LIM. For example, the thermal resistance is 28.6 K/W when the solar cell is driven by 100-mA current. However, the thermal resistance is only 2.5 K/W when the same 100-mA photocurrent is produced by

5 ZHANG et al.: THERMAL RESISTANCE TEST OF SINGLE-CRYSTAL-SILICON SOLAR CELL 2349 the photoelectric effect under the irradiance of W/m 2, as shown in Table I. The difference is mainly caused by light, which has a major impact on both the thermal conductivity and the thermal power of the solar cell. Gaitho et al. [11] have proved that the thermal conductivity of the solar cell is much lower in the dark condition than that in the light condition. Moreover, under the illuminating condition, the excess photon energy converts into heat that increases the thermal power of the solar cell; thus, the thermal resistance decreases in terms of (1). For actual use, the solar cell is operated under the sunlight; thus, the LIM is more practical than the CDM. Meanwhile, the IR of sunlight also contributes to the junction temperature of the solar cell, and the calculation of the thermal power will be more complex. V. C ONCLUSION In this paper, the thermal resistance of the solar cell has been characterized using the thermal transient method by the CDM and the LIM, respectively. We have used the white LED array rather than the solar simulator to operate the solar cell in order to study the influence of excess photons that are not absorbed by silicon. Meanwhile, we have thoroughly calculated the thermal dissipation power of the solar cell. The results show that its thermal resistance by the CDM is much higher than that by the LIM. It is mainly influenced by light. Although the solar cell can be considered as a p-n diode, given the influence of light, it is more practical to adopt the LIM to test the thermal resistance of the solar cell other than the CDM. [9] M. Wolf and H. Rauschenbach, Series resistance effects on solar cell measurements, Adv. Energy Convers., vol. 3, no. 2, pp , Apr. Jun [10] V. Szekely, A new evaluation method of thermal transient measurement results, Microelectron. J., vol. 28, no. 3, pp , Mar [11] F. M. Gaitho, F. G. Ndiritu, P. M. Muriithi, R. G. Ngumbu, and J. K. Ngareh, Effect of thermal conductivity on the efficiency of single crystal silicon solar cell coated with an anti-reflective thin film, Solar Energy, vol. 83, no. 8, pp , Aug [12] R. Gottschalg, T. R. Betts, D. G. Infield, and M. J. Kearney, The effect of spectral variations on the performance parameters of single and double junction amorphous silicon solar cells, Solar Energy Mater. Solar Cells, vol. 85, no. 3, pp , Jan Jihong Zhang received the B.S. degree in electron science and technology from China University of Mining and Technology, Xuzhou, China, in She is currently working toward the Ph.D. degree at Xiamen University, Xiamen, China. Yulin Gao received the Ph.D. degree in condensed matter physics from Xiamen University, Xiamen, China, in Since 2011, she has been with the Department of Electronic Science, Xiamen University, where she is currently an Associate Professor. ACKNOWLEDGMENT The authors would like to thank Prof. T. M. Shih of the University of Maryland for his valuable input to this paper. REFERENCES [1] D. M. Chapin, C. S. Fuller, and G. L. Pearson, A new silicon p-n junction photocell for converting solar radiation into electrical power, J. Appl. Phys., vol. 25, no. 5, pp , May [2] D. Meneses-Rodrýguez, P. P. Horley, J. González-Hernández, Y. V. Vorobiev, and P. N. Gorley, Photovoltaic solar cells performance at elevated temperatures, Solar Energy, vol. 78, no. 2, pp , Feb [3] S. Yoon and V. Garboushian, Reduced temperature dependence of highconcentration photovoltaic solar cell open-circuit voltage (Voc) at high concentration levels, in Conf. Rec. IEEE Photovoltaic Energy Convers., Dec. 1994, vol. 2, pp [4] T. L. Chou, Z. H. Shih, H. F. Hong, C. N. Han, and K. N. Chiang, Investigation of the thermal performance of high-concentration photovoltaic solar cell package, in Proc. Int. Electron. Mater. Packag. Conf., Daejeon, Korea, 2007, pp [5] N. Y. Wang, S. Y. Chuang, T. L. Chou, Z. H. Shih, H. F. Hong, and K. N. Chiang, Transient thermal analysis of high-concentration photovoltaic cell module subjected to coupled thermal and power cycling test conditions, in Proc. 12th Int. Thermal Thermodech. Phenom. Electron. Syst. Conf., Las Vegas, NV, 2010, pp [6] S. H. Jang and M. W. Shin, Thermal characterization of junction in solar cell packages, IEEE Electron Device Lett., vol. 31, no. 7, pp , Jul [7] B. J. Huang, P. E. Yang, Y. P. Lin, B. Y. Lin, H. J. Chen, R. C. Lai, and J. S. Cheng, Solar cell junction temperature measurement of PV module, Solar Energy, vol. 85, no. 2, pp , Feb [8] W. J. Hwang, P. Szabo, G. Farkas, and M. W. Shin, Application of structure functions for the transient thermal analysis of GaN-based LEDs with SiC and sapphire substrates, in Proc. 10th Int. Workshops THERMINIC Conf., Valbonne, France, 2004, pp Yijun Lu received the Ph.D. degree in condensed matter physics from Xiamen University, Xiamen, China in Since 2011, he has been with the Department of Electronic Science, Xiamen University, where he is currently an Associate Professor. Lihong Zhu, photograph and biography not available at the time of publication. Ziquan Guo, photograph and biography not available at the time of publication. Guolong Chen, photograph and biography not available at the time of publication. Zhong Chen received the Ph.D. degree from Xiamen University, Xiamen, China in Since 2000, he has been a Full Professor with Xiamen University. His research interests are centered on scientific instrument design and nuclear magnetic resonance.