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Simulated parametric optimization of the back-lit Si solar cell
Solid State Sciences 12 (2010) 1948e1952
Contents lists available at ScienceDirect
Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie
Simulated parametric optimization of the back-lit Si solar cell Kwang Su Choe* Dept. of Electronic Materials Engineering, College of Engineering, The University of Suwon, Hwaseong-Shi, Gyeonggi-Do 445-743, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 June 2010 Received in revised form 26 July 2010 Accepted 31 July 2010 Available online 13 August 2010
The back-lit design is viable for the Si solar cell because Si is an indirect-gap semiconductor that requires a relatively long absorption depth. In this work, key parameters relating to the operation of the back-lit mono-crystalline Si solar cell are investigated by using the Medici device simulator. On the effect of the photon incident angle on the solar cell power, a reduction of as much as 16% is observed when the incident angle is reduced 3.8 from the vertical incidence. The ideal thickness of the p-type substrate that leads to the maximum cell power is found to be 70 mm or less. In the back-lit design, both the n-type collector contact and the p-type substrate contact are located on the front side. To the extent of the 10 mmwide design investigated, it is found that the larger the n-type collector width, or the smaller the p-type substrate contact, the larger the cell power. In regards to the substrate and collector doping, the optimum doping concentrations leading to a maximum cell power of 2.28 102 W cm2, or 22.8 mW cm2, are found to be 1 1016 cm3 and 1 1017 cm3 for the substrate and the collector, respectively. In terms of the wavelength of the incident light, the cell power is nearly steady up to 0.8 mm, but decreases rapidly above, as the photon energy falls to near or under the energy gap. All considered, the back-lit design, which simplifies fabrication by putting both the cathode and the anode on the front side, is found to produce a cell power as little as 15% less than that of a standard front-lit design. Ó 2010 Elsevier Masson SAS. All rights reserved.
Keywords: Si solar cell Back-lit solar cell Medici Device simulation Solar cell parameters Solar cell efficiency
1. Introduction The rise in the cost of producing fossil fuel and the growing awareness in the dangers, such as global warming and acid rain, stemming from the burning of fossil fuel have generated much interest to renewable and clean energy resources. In this regard, besides expanding the hydroelectric power, efforts are being made to tap geothermal, wind, and solar energies. Of these known renewable clean energies, the solar energy holds the greatest potential as only approximately 1/10000, or an hour worth per year, of the energy received from the sun is needed to power all the human energy needs on earth [1]. Despite the potential and the enormous scientific and engineering progresses over the past decades, the solar energy in the form of converted electricity holds nearly insignificant portion to this day, comprising only 0.03% of the renewable energy and meeting only about 0.0008% of the total worldwide energy use [2]. The solar energy even lags far behind the wind energy. This is because, even at the current energy conversion efficiency or PCE (Photon-to-Current Efficiency) of about 20%, or 20 mW cm2 under AM1.5 [1], the solar energy is still relatively too expensive to produce. At about 50 cents per kWh, the solar energy is at least 5 * Tel.: þ82 10 7212 2175; fax: þ82 31 229 8251. E-mail address: [email protected]. 1293-2558/$ e see front matter Ó 2010 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2010.07.034
times more expensive than the coal, oil, nuclear and even wind energy [2]. The highest PCE reported for the Si solar cell is 24.7% by the PERL (Passivated Emitter, Rear Locally-diffused) method [3]. As the Si-based solar cell has the theoretical limitation of a PCE of less than 30%, works are being reported on the next generation of nonSi-based solar cells. In III-V semiconductor solar cells, the fabrication of monolithic multi-junction solar cells in series on a single substrate is enabled by tunnel junction connections [4]. This can significantly improve the energy conversion efficiency. The overall cost of the solar cell module production, on the other hand, can be drastically reduced by using the light concentrator. Compared to Si which allows light concentration of no more than 20 without losing the conversion efficiency, III-V compound semiconductors permit light concentration up to 500 without compromising the efficiency and up to 1000 with a loss of only 1% in the efficiency [5]. Thus, despite the high material and processing costs, the cost per watt of electric generation is known to be lower for this combined system of III-V solar cell and light concentrator than that of the Si solar cell system [6]. In practice, a multi-junction of GaInP/GaInAs/Ge showed a PCE of 40.7% under AM1.5 and with a 240 concentrator [7]. For the future generation, to harness the full energy of high-energy photons and thereby minimize thermal loss, quantum dots are being considered for multiple excitations of photons in the MEG (Multiple Excitation Generation) solar cells [8,9].
K.S. Choe / Solid State Sciences 12 (2010) 1948e1952
The cost of producing solar energy can be divided into four major parts: solar cells, the module, installation, and maintenance. Of these, the cost of solar cells is minor and generally inversely related to the rest. That is, cheaper solar cells tend to be less efficient and thus require a larger module that is more expensive to produce, install, and maintain. Particularly in densely populated cities, the installation space, including the land, can significantly raise the cost of installation and the overall cost of solar energy. Because highly efficient and durable solar cells made of relatively expensive semiconductor materials could ultimately be more economical, as the cost of module production, installation, and maintenance is driven lower, the cost of material, though important, is not a significant factor in solar cell fabrication. For this reason, semiconductors are preferred over other known photovoltaic materials. Of the semiconductor materials, Si is most widely used because of its wide availability at reasonable cost and technological maturity. Despite the recent advances in the III-V solar cell technologies briefly outlined earlier, presently, Si is still used in over 95% of the global solar cell production [2]. For indirect-gap semiconductors like Si, the back-lit design is viable because the pn junction needs not be located near the surface. That is, in slow-absorbing indirect-gap semiconductors, the photons must penetrate deeper before being completely absorbed. In Si, it is estimated that the distance is about 100 mm for 90% of the incident photons are to be absorbed. If the Si substrate is sufficiently thinned, the back-lit design should, therefore, produce a good number of electron-hole pairs at the pn junction located near the front surface. In terms of device fabrication and operation, the back-lit design has some intrinsic benefits. First, by allowing the formation of the cathode and anode electrodes on the front surface all at once, it simplifies the fabrication. Second, since the backside is free of electrodes, there is no loss of incident photons due to the electrode reflections. As the improvement in the energy conversion efficiency affects directly the per watt production cost of the solar cell electricity, all the available options should be considered prior to actual solar cell fabrication. In this work, the Medici device simulator software is utilized for this purpose. With the emphasis in the back-lit design, the parameters relating to the design and operation of the solar cell are closely examined. The result will suggest the optimum parametric values for a most efficient back-lit solar cell. 2. Experimental The device simulation that the Medici performs consists of four major steps: grid formation, model and parameter selection, simulation, and output extraction. In grid formation, as building a model home using match sticks, the solar cell design is visualized by grids. The grids are two-dimensional and dense near the front and back surfaces and at the pn junction where the electrical activities including the electron-hole pair generation are the greatest and sparse deep in the bulk where the electrical activities are relatively quiescent. As the reference, the back-lit grid structure in the Medici operational manual is used [10]. In this referenced two-dimensional standard structure, the mono-crystalline Si substrate for the solar cell is p-type with an impurity concentration of 1014 cm3 and 10 mm in width and 150 mm in thickness. On the front surface, a 6 mm wide n-type collector diffusion is used to form the pn junction. The n-type collector is doped with an impurity concentration of 1017 cm3. After diffusion, the collector junction depth is 2 mm, and the width is broadened to 7.5 mm. In regards to model and parameter selection, Auger and concentration-dependent Shockley-Read-Hall recombination models and a concentration-dependent mobility model were chosen, the 2-carrier Newtonian iteration is chosen as the mathematical model in the
1949
finite element analysis done by the Medici, and finally except for the parameters that are chosen as experimental variables, default values are used. The photon generation rate, electron-hole-pairs cm3 s1, is an exponential function of distance y from the surface and can be expressed as
Gphoton ¼ FLUX
y exp½Y:CHAR 104 Y:CHAR
(2.1)
where FLUX is defined as the photon flux (photons cm2 s1) and Y.CHAR is defined as the absorption distance (mm) [10]. For a photon flux of 4 1017 cm2 s1 and an absorption distance of 2 mm, for instance, the Eq. (2.1) can be rewritten as y
Gphoton ¼ 2 1021 e2mm cm3 sec1
(2.2)
One should note that the photon absorption is strongly frequency-dependent. That is, higher the frequency, or shorter the wavelength, the stronger the photon absorption and therefore the shorter the absorption distance. The solar cell parameters studied in this work are the photon incident angle, the substrate thickness, the collector, or pn junction, width, and the doping concentrations of the p-type substrate and the n-type collector region. Each parameter is tested one at a time. That is, when a parameter is tested, the rest are kept fixed at a value. Finally, after the simulation, the output is plotted in terms of the photovoltaic equation as expressed in
qV I ¼ Io e kT 1 Isc
(2.3)
From the IeV curve plotted, the open-circuit voltage, Voc, is extracted from where the curve intersects the x-axis, and the shortcircuit current, Isc, is extracted from where the curve intersects the y-axis. The cell power as defined by the maximum power rectangle in the loaded circuit is then extracted.
3. Results and discussion As the absorption distance in Si is dependent on the frequency, or the wavelength, of the incident light wave, the solar cell output power was examined as a function of the wavelength, and Fig. 1 illustrates the result. In it, the cell power is nearly steady for the wavelength from 0.2 to 0.8 mm but falls rapidly above 0.8 mm. This is because, above the wavelength of 1.1 mm, the light energy becomes less than the 1.12 eV bandgap energy of Si. In the AM1.5 spectrum, the light intensity falls rapidly below 0.5 mm [11]. As such, in reality, little light absorption occurs in Si below 0.5 mm as well. For the simulation experiments below, thus, the wavelength of 0.6 mm, which has an absorption distance of 2 mm, is chosen for the incident photons. The photon flux is set at 4 1017 cm2 s1. Due to the reflection on the surface, the incident angle of the photon has direct bearing on the solar cell efficiency. Reflection can be mitigated somewhat by applying the anti-reflection coating on the surface. On the bare Si surface, the effect of the incident angle of the photon on the solar cell output power was investigated, and the result is plotted in Fig. 2. In the figure, the x-axis indicates the x coordinates in microns of where the photon enters and ends up in the 150 mm-thick solar cell. In terms of the incident angle, (10,10) represents q ¼ 90 , the normal incidence, and (0,10) or (10,0) represents q ¼ 86.2 . The y-axis indicates the cell power. As seen in the figure, for the given variance in the incident angle, the output power decreases by as much as 16% from the peak power of 1.76 102 W cm2, or 17.6 mW cm2, which corresponds to the normal incidence, (10,10). Besides the surface reflection, the incident
1950
K.S. Choe / Solid State Sciences 12 (2010) 1948e1952
2
1.85
Cell Power (W-cm-2) X 10-2
Cell Power (W-cm-2) X 10-2
1.8 1.6 1.4 1.2 1 0.8 0.6 0.4
1.8
1.75
1.7
1.65
1.6
0.2
1.55
0 0.2
0.4
0.6
0.8
1.0
10
1.2
30
50
70
90
110
130
150
170
190
Substrate Thickness (µm)
Wavelength (µm) Fig. 1. Cell power vs. wavelength: when the wavelength is 1.1 mm or less, the energy of the incident light is equal or greater than the bandgap energy of Si, 1.12 eV.
Fig. 3. Cell power vs. substrate thickness: the cell power is nearly constant up to 70 mm and then decreases gradually as the substrate becomes thicker, i.e., as the distance between the back surface and the pn junction becomes longer.
angle also affects the solar cell efficiency as it determines the distance that the photons travel to reach the pn junction. That is, the more slanted the incident angle, the longer the travel distance. This effect, however, was not particularly significant in this case. In this 150 mm-thick sample, the distance from the back surface to the front pn junction which is 2 mm deep is 148 mm for the normal incidence and 148.3 mm for the oblique incidence of q ¼ 86.2 . More on the distance that the photons travel to reach the pn junction, an experiment was performed with the Si substrate thickness, which in effect determines the distance, as the variable. The depth of the front pn junction was fixed at 2 mm, and the substrate thickness was changed from 10 mm to 190 mm. As shown in Fig. 3, the cell power is nearly constant up to 70 mm at about 1.8 102 W cm2, or 18 mW cm2, and then decreases gradually as the substrate becomes thicker, i.e., as the distance between the back surface and the front pn junction becomes longer. This result
suggests that, for the slow photon-absorbing indirect-gap Si, the substrate needs not be thinner than 70 mm to achieve the near maximum cell power in the back-lit design. In the back-lit solar cell, both electrons and holes are extracted through the front surface via ohmic contacts to the n-type collector and the p-type substrate, respectively. In this design, therefore, the front surface is not wholly n-type, but segmented into alternating n-type and p-type areas. The ratio between the two areas is of interest. Fig. 4 illustrates the effect of the width of the n-type collector region, or the pn junction, on the cell power. To the extent of the 10 mm cell width investigated, there is no limit as to how wide the n-type region should be. That is, the wider the n-type region, the wider the area of the pn junction and, as the result, the greater the cell power. So long as physically possible, it was good to extend the width of the collector region. In this case, the width was extended to 8 mm.
1.8
1.8 1.7
1.7
Cell Power (W-cm-2) X 10-2
Cell Power (W-cm-2) X 10-2
1.75
1.65 1.6 1.55 1.5 1.45 1.4
1.6 1.5 1.4 1.3 1.2
1.35
1.1 0,9 0,1 0 10 ,10 10 ,9 10 ,8 10 ,7 10 ,6 10 ,5 10 ,4 10 ,3 10 ,2 10 ,1 10 ,0
0,7 0,8
0,5 0,6
0,3 0,4
0,1 0,2
1.3
Angle of Light Incidence (X.START, X.END)
1 4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Collector Width (µm) Fig. 2. Cell power vs. angle of light incidence: (X.START, X.END) indicates the x coordinates in microns of where the photon enters and ends up in the 150 mmthick solar cell. (10,10) represents q ¼ 90 , the normal incidence, and (0,10) or (10,0) represents q ¼ 86.2 .
Fig. 4. Cell power vs. collector width: the total width of the simulated solar cell is 10 mm. The collector width includes 1.5 mm broadening that occurs during thermal diffusion used to create the 2 mm-deep pn junction.
K.S. Choe / Solid State Sciences 12 (2010) 1948e1952 2.5
1951
2.1 Front-lit Back-lit
1.9
Cell Power (W-cm-2) X 10-2
Cell Power (W-cm-2) X 10-2
2 2
1.5
1
0.5
0 1E10
1E11
1E12
1E13
1E14
1E15
1E16
Substrate Doping Concentration (cm-3)
1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1
Fig. 5. Cell power vs. p-type substrate doping concentration: the n-type collector doping concentration was kept constant at 1 1017 cm3 during the simulation.
1 4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Collector Width (µm) The effect of the doping concentrations in the p-type substrate and the n-type collector region was investigated. Fig. 5 illustrates the p-type substrate doping concentration versus the cell power. The n-type collector doping concentration was kept constant at 1 1017 cm3. In the figure, the output power increases as a function of the p-type substrate doping concentration until 1 1016 cm3, which was the upper limit of the study. At this point, the cell power is 2.28 102 W cm2, or 22.8 mW cm2, which is by far the highest. Fig. 6 illustrates the n-type collector doping concentration versus the cell power. In this case, the p-type substrate doping concentration was kept constant at 1 1014 cm3. In the figure, the cell power is nearly steady in the region of 1 1016 cm3 to 1 1022 cm3 with a peak near 1 1017 cm3. Below 1 1016 cm3, however, the cell power falls rapidly. In the pn junction, the electrons and holes formed in pairs by photon absorption are separated and drifted to the n-type and p-type region, respectively, by the electric field. The electric field is stronger when the barrier potential is larger and the depletion
1.76
Cell Power (W-cm-2) X 10-2
1.75
Fig. 7. Front-lit vs. back-lit: the back-lit design is less efficient than the front-lit design, but the difference is reduced to as little as 15% by increasing the collector width (the back-lit plot is from Fig. 4).
width is smaller. In turn, the barrier potential is larger and the depletion width is smaller when the doping concentration is higher. In this regard, the higher doping concentration in either ntype or p-type region or in both usually lead to higher cell power up to a certain limit, which exists because of the degeneracy in the highly-doped semiconductor. In comparable design, a front-lit Si solar cell yielded a cell power output of 2.05 102 W cm2, or 20.5 mW cm2, as little as 15% higher than that of the back-lit solar cell, as shown in Fig. 7. Despite the lower cell power, the back-lit solar cell design has an advantage in terms of the device processing point of view. That is, instead of using two steps to form the cathode on the front surface and the anode in the back surface as in the front-lit design, both the cathode and the anode can be formed on the front surface in one step in the back-lit design. This processing advantage can be useful so long as it outweighs the power reduction associated with the back-lit design. What that remains as the future work is the actual fabrication of the back-lit Si solar cells.
1.74 1.73
4. Conclusion
1.72
The workhorse of the electric solar energy conversion is Si. Being an indirect-gap semiconductor, Si is a good candidate for back-lit solar cells. In the work, using the Medici semiconductor device simulator, the relationships between the key mono-crystalline Si solar cell parameters and the cell power were investigated. Due to surface reflection, the vertical incidence, q ¼ 90 , of the photon produces the highest cell power. A 4%/degree reduction in the cell power was observed when the photon incident angle was decreased. Being an indirect-gap semiconductor in which the photon absorption is slower, Si substrates 70 mm or less in thickness yielded the highest cell power. On the front surface where both the cathode and the anode are formed, it was observed that the wider the n-type collector region, or the pn junction, the greater the cell power. Generally, the doping concentrations of the p-type substrate and the n-type collector had a positive correlation with the cell
1.71 1.7 1.69 1.68 1.67 1.66 1E15
1E16
1E17
1E18
1E19
1E20
1E21
1E22
Collector Doping Concentration (cm-3) Fig. 6. Cell power vs. n-type collector doping concentration: the p-type substrate doping concentration was kept constant at 1 1014 cm3 during the simulation.
1952
K.S. Choe / Solid State Sciences 12 (2010) 1948e1952
power up to a certain point. Compared to a standard front-lit design, the back-lit solar cells were generally 15% or less in producing the cell power. The cost saving associated with a step reduction in solar cell fabrication by placing both the cathode and the anode on one side merits consideration if it outweighs the loss of the cell power. Summarizing the result, within the limitation of 10 mm wide back-lit solar cell design, the process parameter values that lead to the greatest cell power are as follows: the substrate thickness of 70 mm or less, the n-type collector width of 8 mm after diffusion, the p-type substrate doping of 1 1016 cm3, and the n-type collector doping of 1 1017 cm3.
Acknowledgement The simulation experiments and the rendering of the graphical work were assisted by the undergraduate students, Mr. Seok-Jun Choe, Ms. Eun-Hae Lee, Ms. Eun-Hyeh Lee, Ms. Ji-Young Min, Mr. Seung-Eon Oh, Mr. Jeong-Seop Shin, of the Department of Electronic Materials Engineering of the University of Suwon. The author
wishes to thank them for their diligent work and the good times shared together. References [1] J.H. Kim, M.J. Chu, Y.D. Chung, R.M. Park, H.K. Sung No. 6, Electronics and Telecommunications Trend Analysis (Korean), vol. 23, Electronics and Telecommunications Research Institute (ETRI), Dec. 2008, pp. 2e11. [2] Y.S. Jeon, H.K. Park, H.K. Yun, M.K. Kang, J.D. Kim (Korean), Weekly Technology Trends, vol. 1335, Institute for Information Technology Advancement (IITA), Feb. 2008, pp. 21e28. [3] M.A. Green, K. Emery, D.L. King, Y. Hishikawa, W. Warta, Prog. Photovolt. Res. Appl. 15 (2007) 35e40. [4] L.L. Kazmerski, J. Electron. Spectros. Relat. Phenomena. 150 (2006) 105e135. [5] M. Yamaguchi, T. Takamoto, K. Araki, Sol. Energ. Mater. Sol. Cell. 90 (2006) 3068e3077. [6] R.M. Swanson, Prog. Photovolt. Res. Appl. 8 (2000) 93e111. [7] R.R. King, D.C. Law, K.M. Edmondson, C.M. Fetzer, G.S. Kinsey, H. Yoon, R.A. Sherif, N.H. Karam, Appl. Phys. Lett. 90 (2007) 183516. [8] S. Luque, A. Marti, A.J. Nozik, MRS BULL. vol. 32 (Mar. 2007) 236e241. [9] R.J. Ellingson, M.C. Beard, J.C. Johnson, P. Yu, O.I. Micic, A.J. Nozik, A. Shabaev, A.L. Efros, Nano Lett. 5 (2005) 865e871. [10] Medici Two-Dimensional Device Simulation Program, Ver. 2.2, User’s Manual, vol. 3, Technology Modeling Associates, Inc., Sunnyvale, CA, Jun. 1996, 7.1e7.10. [11] F. Dimorth, S. Kurtz, MRS BULL. vol. 32 (Mar. 2007) 230e235.
Contents lists available at ScienceDirect
Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie
Simulated parametric optimization of the back-lit Si solar cell Kwang Su Choe* Dept. of Electronic Materials Engineering, College of Engineering, The University of Suwon, Hwaseong-Shi, Gyeonggi-Do 445-743, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 June 2010 Received in revised form 26 July 2010 Accepted 31 July 2010 Available online 13 August 2010
The back-lit design is viable for the Si solar cell because Si is an indirect-gap semiconductor that requires a relatively long absorption depth. In this work, key parameters relating to the operation of the back-lit mono-crystalline Si solar cell are investigated by using the Medici device simulator. On the effect of the photon incident angle on the solar cell power, a reduction of as much as 16% is observed when the incident angle is reduced 3.8 from the vertical incidence. The ideal thickness of the p-type substrate that leads to the maximum cell power is found to be 70 mm or less. In the back-lit design, both the n-type collector contact and the p-type substrate contact are located on the front side. To the extent of the 10 mmwide design investigated, it is found that the larger the n-type collector width, or the smaller the p-type substrate contact, the larger the cell power. In regards to the substrate and collector doping, the optimum doping concentrations leading to a maximum cell power of 2.28 102 W cm2, or 22.8 mW cm2, are found to be 1 1016 cm3 and 1 1017 cm3 for the substrate and the collector, respectively. In terms of the wavelength of the incident light, the cell power is nearly steady up to 0.8 mm, but decreases rapidly above, as the photon energy falls to near or under the energy gap. All considered, the back-lit design, which simplifies fabrication by putting both the cathode and the anode on the front side, is found to produce a cell power as little as 15% less than that of a standard front-lit design. Ó 2010 Elsevier Masson SAS. All rights reserved.
Keywords: Si solar cell Back-lit solar cell Medici Device simulation Solar cell parameters Solar cell efficiency
1. Introduction The rise in the cost of producing fossil fuel and the growing awareness in the dangers, such as global warming and acid rain, stemming from the burning of fossil fuel have generated much interest to renewable and clean energy resources. In this regard, besides expanding the hydroelectric power, efforts are being made to tap geothermal, wind, and solar energies. Of these known renewable clean energies, the solar energy holds the greatest potential as only approximately 1/10000, or an hour worth per year, of the energy received from the sun is needed to power all the human energy needs on earth [1]. Despite the potential and the enormous scientific and engineering progresses over the past decades, the solar energy in the form of converted electricity holds nearly insignificant portion to this day, comprising only 0.03% of the renewable energy and meeting only about 0.0008% of the total worldwide energy use [2]. The solar energy even lags far behind the wind energy. This is because, even at the current energy conversion efficiency or PCE (Photon-to-Current Efficiency) of about 20%, or 20 mW cm2 under AM1.5 [1], the solar energy is still relatively too expensive to produce. At about 50 cents per kWh, the solar energy is at least 5 * Tel.: þ82 10 7212 2175; fax: þ82 31 229 8251. E-mail address: [email protected]. 1293-2558/$ e see front matter Ó 2010 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2010.07.034
times more expensive than the coal, oil, nuclear and even wind energy [2]. The highest PCE reported for the Si solar cell is 24.7% by the PERL (Passivated Emitter, Rear Locally-diffused) method [3]. As the Si-based solar cell has the theoretical limitation of a PCE of less than 30%, works are being reported on the next generation of nonSi-based solar cells. In III-V semiconductor solar cells, the fabrication of monolithic multi-junction solar cells in series on a single substrate is enabled by tunnel junction connections [4]. This can significantly improve the energy conversion efficiency. The overall cost of the solar cell module production, on the other hand, can be drastically reduced by using the light concentrator. Compared to Si which allows light concentration of no more than 20 without losing the conversion efficiency, III-V compound semiconductors permit light concentration up to 500 without compromising the efficiency and up to 1000 with a loss of only 1% in the efficiency [5]. Thus, despite the high material and processing costs, the cost per watt of electric generation is known to be lower for this combined system of III-V solar cell and light concentrator than that of the Si solar cell system [6]. In practice, a multi-junction of GaInP/GaInAs/Ge showed a PCE of 40.7% under AM1.5 and with a 240 concentrator [7]. For the future generation, to harness the full energy of high-energy photons and thereby minimize thermal loss, quantum dots are being considered for multiple excitations of photons in the MEG (Multiple Excitation Generation) solar cells [8,9].
K.S. Choe / Solid State Sciences 12 (2010) 1948e1952
The cost of producing solar energy can be divided into four major parts: solar cells, the module, installation, and maintenance. Of these, the cost of solar cells is minor and generally inversely related to the rest. That is, cheaper solar cells tend to be less efficient and thus require a larger module that is more expensive to produce, install, and maintain. Particularly in densely populated cities, the installation space, including the land, can significantly raise the cost of installation and the overall cost of solar energy. Because highly efficient and durable solar cells made of relatively expensive semiconductor materials could ultimately be more economical, as the cost of module production, installation, and maintenance is driven lower, the cost of material, though important, is not a significant factor in solar cell fabrication. For this reason, semiconductors are preferred over other known photovoltaic materials. Of the semiconductor materials, Si is most widely used because of its wide availability at reasonable cost and technological maturity. Despite the recent advances in the III-V solar cell technologies briefly outlined earlier, presently, Si is still used in over 95% of the global solar cell production [2]. For indirect-gap semiconductors like Si, the back-lit design is viable because the pn junction needs not be located near the surface. That is, in slow-absorbing indirect-gap semiconductors, the photons must penetrate deeper before being completely absorbed. In Si, it is estimated that the distance is about 100 mm for 90% of the incident photons are to be absorbed. If the Si substrate is sufficiently thinned, the back-lit design should, therefore, produce a good number of electron-hole pairs at the pn junction located near the front surface. In terms of device fabrication and operation, the back-lit design has some intrinsic benefits. First, by allowing the formation of the cathode and anode electrodes on the front surface all at once, it simplifies the fabrication. Second, since the backside is free of electrodes, there is no loss of incident photons due to the electrode reflections. As the improvement in the energy conversion efficiency affects directly the per watt production cost of the solar cell electricity, all the available options should be considered prior to actual solar cell fabrication. In this work, the Medici device simulator software is utilized for this purpose. With the emphasis in the back-lit design, the parameters relating to the design and operation of the solar cell are closely examined. The result will suggest the optimum parametric values for a most efficient back-lit solar cell. 2. Experimental The device simulation that the Medici performs consists of four major steps: grid formation, model and parameter selection, simulation, and output extraction. In grid formation, as building a model home using match sticks, the solar cell design is visualized by grids. The grids are two-dimensional and dense near the front and back surfaces and at the pn junction where the electrical activities including the electron-hole pair generation are the greatest and sparse deep in the bulk where the electrical activities are relatively quiescent. As the reference, the back-lit grid structure in the Medici operational manual is used [10]. In this referenced two-dimensional standard structure, the mono-crystalline Si substrate for the solar cell is p-type with an impurity concentration of 1014 cm3 and 10 mm in width and 150 mm in thickness. On the front surface, a 6 mm wide n-type collector diffusion is used to form the pn junction. The n-type collector is doped with an impurity concentration of 1017 cm3. After diffusion, the collector junction depth is 2 mm, and the width is broadened to 7.5 mm. In regards to model and parameter selection, Auger and concentration-dependent Shockley-Read-Hall recombination models and a concentration-dependent mobility model were chosen, the 2-carrier Newtonian iteration is chosen as the mathematical model in the
1949
finite element analysis done by the Medici, and finally except for the parameters that are chosen as experimental variables, default values are used. The photon generation rate, electron-hole-pairs cm3 s1, is an exponential function of distance y from the surface and can be expressed as
Gphoton ¼ FLUX
y exp½Y:CHAR 104 Y:CHAR
(2.1)
where FLUX is defined as the photon flux (photons cm2 s1) and Y.CHAR is defined as the absorption distance (mm) [10]. For a photon flux of 4 1017 cm2 s1 and an absorption distance of 2 mm, for instance, the Eq. (2.1) can be rewritten as y
Gphoton ¼ 2 1021 e2mm cm3 sec1
(2.2)
One should note that the photon absorption is strongly frequency-dependent. That is, higher the frequency, or shorter the wavelength, the stronger the photon absorption and therefore the shorter the absorption distance. The solar cell parameters studied in this work are the photon incident angle, the substrate thickness, the collector, or pn junction, width, and the doping concentrations of the p-type substrate and the n-type collector region. Each parameter is tested one at a time. That is, when a parameter is tested, the rest are kept fixed at a value. Finally, after the simulation, the output is plotted in terms of the photovoltaic equation as expressed in
qV I ¼ Io e kT 1 Isc
(2.3)
From the IeV curve plotted, the open-circuit voltage, Voc, is extracted from where the curve intersects the x-axis, and the shortcircuit current, Isc, is extracted from where the curve intersects the y-axis. The cell power as defined by the maximum power rectangle in the loaded circuit is then extracted.
3. Results and discussion As the absorption distance in Si is dependent on the frequency, or the wavelength, of the incident light wave, the solar cell output power was examined as a function of the wavelength, and Fig. 1 illustrates the result. In it, the cell power is nearly steady for the wavelength from 0.2 to 0.8 mm but falls rapidly above 0.8 mm. This is because, above the wavelength of 1.1 mm, the light energy becomes less than the 1.12 eV bandgap energy of Si. In the AM1.5 spectrum, the light intensity falls rapidly below 0.5 mm [11]. As such, in reality, little light absorption occurs in Si below 0.5 mm as well. For the simulation experiments below, thus, the wavelength of 0.6 mm, which has an absorption distance of 2 mm, is chosen for the incident photons. The photon flux is set at 4 1017 cm2 s1. Due to the reflection on the surface, the incident angle of the photon has direct bearing on the solar cell efficiency. Reflection can be mitigated somewhat by applying the anti-reflection coating on the surface. On the bare Si surface, the effect of the incident angle of the photon on the solar cell output power was investigated, and the result is plotted in Fig. 2. In the figure, the x-axis indicates the x coordinates in microns of where the photon enters and ends up in the 150 mm-thick solar cell. In terms of the incident angle, (10,10) represents q ¼ 90 , the normal incidence, and (0,10) or (10,0) represents q ¼ 86.2 . The y-axis indicates the cell power. As seen in the figure, for the given variance in the incident angle, the output power decreases by as much as 16% from the peak power of 1.76 102 W cm2, or 17.6 mW cm2, which corresponds to the normal incidence, (10,10). Besides the surface reflection, the incident
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2
1.85
Cell Power (W-cm-2) X 10-2
Cell Power (W-cm-2) X 10-2
1.8 1.6 1.4 1.2 1 0.8 0.6 0.4
1.8
1.75
1.7
1.65
1.6
0.2
1.55
0 0.2
0.4
0.6
0.8
1.0
10
1.2
30
50
70
90
110
130
150
170
190
Substrate Thickness (µm)
Wavelength (µm) Fig. 1. Cell power vs. wavelength: when the wavelength is 1.1 mm or less, the energy of the incident light is equal or greater than the bandgap energy of Si, 1.12 eV.
Fig. 3. Cell power vs. substrate thickness: the cell power is nearly constant up to 70 mm and then decreases gradually as the substrate becomes thicker, i.e., as the distance between the back surface and the pn junction becomes longer.
angle also affects the solar cell efficiency as it determines the distance that the photons travel to reach the pn junction. That is, the more slanted the incident angle, the longer the travel distance. This effect, however, was not particularly significant in this case. In this 150 mm-thick sample, the distance from the back surface to the front pn junction which is 2 mm deep is 148 mm for the normal incidence and 148.3 mm for the oblique incidence of q ¼ 86.2 . More on the distance that the photons travel to reach the pn junction, an experiment was performed with the Si substrate thickness, which in effect determines the distance, as the variable. The depth of the front pn junction was fixed at 2 mm, and the substrate thickness was changed from 10 mm to 190 mm. As shown in Fig. 3, the cell power is nearly constant up to 70 mm at about 1.8 102 W cm2, or 18 mW cm2, and then decreases gradually as the substrate becomes thicker, i.e., as the distance between the back surface and the front pn junction becomes longer. This result
suggests that, for the slow photon-absorbing indirect-gap Si, the substrate needs not be thinner than 70 mm to achieve the near maximum cell power in the back-lit design. In the back-lit solar cell, both electrons and holes are extracted through the front surface via ohmic contacts to the n-type collector and the p-type substrate, respectively. In this design, therefore, the front surface is not wholly n-type, but segmented into alternating n-type and p-type areas. The ratio between the two areas is of interest. Fig. 4 illustrates the effect of the width of the n-type collector region, or the pn junction, on the cell power. To the extent of the 10 mm cell width investigated, there is no limit as to how wide the n-type region should be. That is, the wider the n-type region, the wider the area of the pn junction and, as the result, the greater the cell power. So long as physically possible, it was good to extend the width of the collector region. In this case, the width was extended to 8 mm.
1.8
1.8 1.7
1.7
Cell Power (W-cm-2) X 10-2
Cell Power (W-cm-2) X 10-2
1.75
1.65 1.6 1.55 1.5 1.45 1.4
1.6 1.5 1.4 1.3 1.2
1.35
1.1 0,9 0,1 0 10 ,10 10 ,9 10 ,8 10 ,7 10 ,6 10 ,5 10 ,4 10 ,3 10 ,2 10 ,1 10 ,0
0,7 0,8
0,5 0,6
0,3 0,4
0,1 0,2
1.3
Angle of Light Incidence (X.START, X.END)
1 4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Collector Width (µm) Fig. 2. Cell power vs. angle of light incidence: (X.START, X.END) indicates the x coordinates in microns of where the photon enters and ends up in the 150 mmthick solar cell. (10,10) represents q ¼ 90 , the normal incidence, and (0,10) or (10,0) represents q ¼ 86.2 .
Fig. 4. Cell power vs. collector width: the total width of the simulated solar cell is 10 mm. The collector width includes 1.5 mm broadening that occurs during thermal diffusion used to create the 2 mm-deep pn junction.
K.S. Choe / Solid State Sciences 12 (2010) 1948e1952 2.5
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2.1 Front-lit Back-lit
1.9
Cell Power (W-cm-2) X 10-2
Cell Power (W-cm-2) X 10-2
2 2
1.5
1
0.5
0 1E10
1E11
1E12
1E13
1E14
1E15
1E16
Substrate Doping Concentration (cm-3)
1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1
Fig. 5. Cell power vs. p-type substrate doping concentration: the n-type collector doping concentration was kept constant at 1 1017 cm3 during the simulation.
1 4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Collector Width (µm) The effect of the doping concentrations in the p-type substrate and the n-type collector region was investigated. Fig. 5 illustrates the p-type substrate doping concentration versus the cell power. The n-type collector doping concentration was kept constant at 1 1017 cm3. In the figure, the output power increases as a function of the p-type substrate doping concentration until 1 1016 cm3, which was the upper limit of the study. At this point, the cell power is 2.28 102 W cm2, or 22.8 mW cm2, which is by far the highest. Fig. 6 illustrates the n-type collector doping concentration versus the cell power. In this case, the p-type substrate doping concentration was kept constant at 1 1014 cm3. In the figure, the cell power is nearly steady in the region of 1 1016 cm3 to 1 1022 cm3 with a peak near 1 1017 cm3. Below 1 1016 cm3, however, the cell power falls rapidly. In the pn junction, the electrons and holes formed in pairs by photon absorption are separated and drifted to the n-type and p-type region, respectively, by the electric field. The electric field is stronger when the barrier potential is larger and the depletion
1.76
Cell Power (W-cm-2) X 10-2
1.75
Fig. 7. Front-lit vs. back-lit: the back-lit design is less efficient than the front-lit design, but the difference is reduced to as little as 15% by increasing the collector width (the back-lit plot is from Fig. 4).
width is smaller. In turn, the barrier potential is larger and the depletion width is smaller when the doping concentration is higher. In this regard, the higher doping concentration in either ntype or p-type region or in both usually lead to higher cell power up to a certain limit, which exists because of the degeneracy in the highly-doped semiconductor. In comparable design, a front-lit Si solar cell yielded a cell power output of 2.05 102 W cm2, or 20.5 mW cm2, as little as 15% higher than that of the back-lit solar cell, as shown in Fig. 7. Despite the lower cell power, the back-lit solar cell design has an advantage in terms of the device processing point of view. That is, instead of using two steps to form the cathode on the front surface and the anode in the back surface as in the front-lit design, both the cathode and the anode can be formed on the front surface in one step in the back-lit design. This processing advantage can be useful so long as it outweighs the power reduction associated with the back-lit design. What that remains as the future work is the actual fabrication of the back-lit Si solar cells.
1.74 1.73
4. Conclusion
1.72
The workhorse of the electric solar energy conversion is Si. Being an indirect-gap semiconductor, Si is a good candidate for back-lit solar cells. In the work, using the Medici semiconductor device simulator, the relationships between the key mono-crystalline Si solar cell parameters and the cell power were investigated. Due to surface reflection, the vertical incidence, q ¼ 90 , of the photon produces the highest cell power. A 4%/degree reduction in the cell power was observed when the photon incident angle was decreased. Being an indirect-gap semiconductor in which the photon absorption is slower, Si substrates 70 mm or less in thickness yielded the highest cell power. On the front surface where both the cathode and the anode are formed, it was observed that the wider the n-type collector region, or the pn junction, the greater the cell power. Generally, the doping concentrations of the p-type substrate and the n-type collector had a positive correlation with the cell
1.71 1.7 1.69 1.68 1.67 1.66 1E15
1E16
1E17
1E18
1E19
1E20
1E21
1E22
Collector Doping Concentration (cm-3) Fig. 6. Cell power vs. n-type collector doping concentration: the p-type substrate doping concentration was kept constant at 1 1014 cm3 during the simulation.
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power up to a certain point. Compared to a standard front-lit design, the back-lit solar cells were generally 15% or less in producing the cell power. The cost saving associated with a step reduction in solar cell fabrication by placing both the cathode and the anode on one side merits consideration if it outweighs the loss of the cell power. Summarizing the result, within the limitation of 10 mm wide back-lit solar cell design, the process parameter values that lead to the greatest cell power are as follows: the substrate thickness of 70 mm or less, the n-type collector width of 8 mm after diffusion, the p-type substrate doping of 1 1016 cm3, and the n-type collector doping of 1 1017 cm3.
Acknowledgement The simulation experiments and the rendering of the graphical work were assisted by the undergraduate students, Mr. Seok-Jun Choe, Ms. Eun-Hae Lee, Ms. Eun-Hyeh Lee, Ms. Ji-Young Min, Mr. Seung-Eon Oh, Mr. Jeong-Seop Shin, of the Department of Electronic Materials Engineering of the University of Suwon. The author
wishes to thank them for their diligent work and the good times shared together. References [1] J.H. Kim, M.J. Chu, Y.D. Chung, R.M. Park, H.K. Sung No. 6, Electronics and Telecommunications Trend Analysis (Korean), vol. 23, Electronics and Telecommunications Research Institute (ETRI), Dec. 2008, pp. 2e11. [2] Y.S. Jeon, H.K. Park, H.K. Yun, M.K. Kang, J.D. Kim (Korean), Weekly Technology Trends, vol. 1335, Institute for Information Technology Advancement (IITA), Feb. 2008, pp. 21e28. [3] M.A. Green, K. Emery, D.L. King, Y. Hishikawa, W. Warta, Prog. Photovolt. Res. Appl. 15 (2007) 35e40. [4] L.L. Kazmerski, J. Electron. Spectros. Relat. Phenomena. 150 (2006) 105e135. [5] M. Yamaguchi, T. Takamoto, K. Araki, Sol. Energ. Mater. Sol. Cell. 90 (2006) 3068e3077. [6] R.M. Swanson, Prog. Photovolt. Res. Appl. 8 (2000) 93e111. [7] R.R. King, D.C. Law, K.M. Edmondson, C.M. Fetzer, G.S. Kinsey, H. Yoon, R.A. Sherif, N.H. Karam, Appl. Phys. Lett. 90 (2007) 183516. [8] S. Luque, A. Marti, A.J. Nozik, MRS BULL. vol. 32 (Mar. 2007) 236e241. [9] R.J. Ellingson, M.C. Beard, J.C. Johnson, P. Yu, O.I. Micic, A.J. Nozik, A. Shabaev, A.L. Efros, Nano Lett. 5 (2005) 865e871. [10] Medici Two-Dimensional Device Simulation Program, Ver. 2.2, User’s Manual, vol. 3, Technology Modeling Associates, Inc., Sunnyvale, CA, Jun. 1996, 7.1e7.10. [11] F. Dimorth, S. Kurtz, MRS BULL. vol. 32 (Mar. 2007) 230e235.