Multijunction Solar Cell Design & Optimization
Budget: $250 – $750 USD
Solve these questions.
(1) The theory of detailed balance. We found that an ideal single junction solar cell has the I-V characteristic of: I = IL-I0 [eqV/kbTc-1], where IL is the light generated current, I0 is the reverse saturation current, q is the charge of an electron, V is the bias voltage, kb is Boltzmann’s constant, and Tc is the temperature of the cell (assumed to be 300 K). (a)If we assume illumination by the sun and treat it as a blackbody of temperature Ts=5760 K, what is the total power per unit area available to the solar cell? How well does this correspond to the actually power per unit area from the sun at the top of the atmosphere, which corresponds to about 1350 W/m2? (b) For a semiconductor with a bandgap of 1.43 eV, like GaAs, what is the numerical value of the light generated current density, JL =IL/A? (c) For a solar cell with a mirror back as described in class, what is the numerical value of I0/A? (d) Plot the I-V curve for this device and determine the max power density output (Pout/A) and the current density and voltage at max power (Im/A and Vm). Also determine the current density (Isc/A) at V=0 and the voltage (Voc) at I=0. (e) What is the efficiency of this device?
(2) All about the angles. In class we found that concentrating the sunlight can be thought of as widening the acceptance angle of the light from the sun. A concentration factor X=1 (i.e. no concentration) corresponds to θx=1=θs=0.267°. (a) Plot the efficiency of the cell from question 1 as a function of the concentration factor X from X=1 to the max value of X. (b) We also saw that one can in theory restrict the emission angle to be less than π/2. For 1 sun illumination (i.e. X=1) plot the efficiency as a function of emission angle. (c) Compare and contrast the results of (a) and (b) describing what you find.
(3) What is the ideal bandgap? Most semiconductors have bandgaps that range from about 0.7 eV to 5 eV. Perform calculations similar to question 1 in order to determine the best bandgap for a solar cell. Plot your results (efficiency vs bandgap). Assume that the sun is a blackbody at 5760 K. Si is the most manufactured solar cell material. Given the detailed balance calculation, does it seem like a good material to use? What about GaAs?
Use the answers to these questions to solve the following: Install a tool called Afors-HET and use it to design the multi – junction solar cell.
Your goal is to design and optimize a two-junction solar cell based on your previous work with the detailed balance theory and our discussions of multijunction solar cells. In the first part above, you studied the I-V characteristics of single junction solar cells using the Shockley-Queisser model of detailed balance and determined the optimum bandgap energy and efficiency under varying amounts of concentration. Now consider the same model, but for a dual junction solar cell. Again, you can treat the sun as a blackbody (Ts=5760 K) and assume that the cell is kept at room temperature and absorbs all above bandgap energy photons. Remember that the spectrum has to be split up between the two junctions, which can either be done via spectral splitting optics or the natural filters of each material in a tandem configuration. Limit your search to bandgap energies between 0.6-2.0 eV and consider a series connection. Treat the two junctions as independent cells limited only by the detailed balance model and the fact that their currents and voltages are tied by the series connection. Again, think of writing the solutions as teaching someone how to solve the problem.
What are the bandgap energies for the optimized two-junction device under 1-sun blackbody illumination? Show an I-V curve along with the efficiency and other relevant parameters. For this optimized cell, increase the illumination (i.e. number of suns) and determine the efficiency. Can you surpass 50% efficiency? Discuss.
Given the bandgap energies you found in part 1, are there any known materials that could work? Describe challenges associated with using these materials for a dual junction solar cell. Then, given the bandgap energies of these known materials, calculated the efficiency as a function of concentration for this cell. Discuss.
The theory of detailed balance considers the absorption AND emission of photons by the cell. In the above analysis we have treated the two junctions as independent. Describe, in words, what would happen if the two junctions were now coupled through detailed balance and not considered independent and isolated.
(1) The theory of detailed balance. We found that an ideal single junction solar cell has the I-V characteristic of: I = IL-I0 [eqV/kbTc-1], where IL is the light generated current, I0 is the reverse saturation current, q is the charge of an electron, V is the bias voltage, kb is Boltzmann’s constant, and Tc is the temperature of the cell (assumed to be 300 K). (a)If we assume illumination by the sun and treat it as a blackbody of temperature Ts=5760 K, what is the total power per unit area available to the solar cell? How well does this correspond to the actually power per unit area from the sun at the top of the atmosphere, which corresponds to about 1350 W/m2? (b) For a semiconductor with a bandgap of 1.43 eV, like GaAs, what is the numerical value of the light generated current density, JL =IL/A? (c) For a solar cell with a mirror back as described in class, what is the numerical value of I0/A? (d) Plot the I-V curve for this device and determine the max power density output (Pout/A) and the current density and voltage at max power (Im/A and Vm). Also determine the current density (Isc/A) at V=0 and the voltage (Voc) at I=0. (e) What is the efficiency of this device?
(2) All about the angles. In class we found that concentrating the sunlight can be thought of as widening the acceptance angle of the light from the sun. A concentration factor X=1 (i.e. no concentration) corresponds to θx=1=θs=0.267°. (a) Plot the efficiency of the cell from question 1 as a function of the concentration factor X from X=1 to the max value of X. (b) We also saw that one can in theory restrict the emission angle to be less than π/2. For 1 sun illumination (i.e. X=1) plot the efficiency as a function of emission angle. (c) Compare and contrast the results of (a) and (b) describing what you find.
(3) What is the ideal bandgap? Most semiconductors have bandgaps that range from about 0.7 eV to 5 eV. Perform calculations similar to question 1 in order to determine the best bandgap for a solar cell. Plot your results (efficiency vs bandgap). Assume that the sun is a blackbody at 5760 K. Si is the most manufactured solar cell material. Given the detailed balance calculation, does it seem like a good material to use? What about GaAs?
Use the answers to these questions to solve the following: Install a tool called Afors-HET and use it to design the multi – junction solar cell.
Your goal is to design and optimize a two-junction solar cell based on your previous work with the detailed balance theory and our discussions of multijunction solar cells. In the first part above, you studied the I-V characteristics of single junction solar cells using the Shockley-Queisser model of detailed balance and determined the optimum bandgap energy and efficiency under varying amounts of concentration. Now consider the same model, but for a dual junction solar cell. Again, you can treat the sun as a blackbody (Ts=5760 K) and assume that the cell is kept at room temperature and absorbs all above bandgap energy photons. Remember that the spectrum has to be split up between the two junctions, which can either be done via spectral splitting optics or the natural filters of each material in a tandem configuration. Limit your search to bandgap energies between 0.6-2.0 eV and consider a series connection. Treat the two junctions as independent cells limited only by the detailed balance model and the fact that their currents and voltages are tied by the series connection. Again, think of writing the solutions as teaching someone how to solve the problem.
What are the bandgap energies for the optimized two-junction device under 1-sun blackbody illumination? Show an I-V curve along with the efficiency and other relevant parameters. For this optimized cell, increase the illumination (i.e. number of suns) and determine the efficiency. Can you surpass 50% efficiency? Discuss.
Given the bandgap energies you found in part 1, are there any known materials that could work? Describe challenges associated with using these materials for a dual junction solar cell. Then, given the bandgap energies of these known materials, calculated the efficiency as a function of concentration for this cell. Discuss.
The theory of detailed balance considers the absorption AND emission of photons by the cell. In the above analysis we have treated the two junctions as independent. Describe, in words, what would happen if the two junctions were now coupled through detailed balance and not considered independent and isolated.