Solar Cells 2

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Name: HW #2 Solar Cells EEE 565, Fall '20 Prof. Richard King Please print out the homework assignment and complete it with pencil or pen. To submit it, please scan it to form an Adobe pdf document, and upload it in the Assignments section of the Canvas website. For consistency, please use the value kT/q = 0.02585 V at 300 K in your calculations. Unless noted otherwise, assume the semiconductor in the problems is silicon, with ni = 1.0 × 1010 cm-3 at 300K. If there is a computer simulation or Excel spreadsheet involved in the homework: Please make 1 or 2 pages that show the key figures, input values, and answers from the simulation or spreadsheet, and please make a pdf copy of those pages. Please join that to the scanned pdf file of the rest of your homework, to form one homework file for upload. Please also upload the computer simulation or Excel spreadsheet that you wrote yourself to solve the problem. A small part of the grade for the problem will based on uploading this file. However, the main part of the grade for the problem will be the pdf pages showing the key figures, input values, and answers that you attach to the rest of your homework. ________________________________________________________________________________ 1. (40 pts total) A thick slab of p-type Si (many times thicker than the diffusion length Ln) with 0.52 Ωcm bulk resistivity is illuminated. For a uniform generation profile in the slab of 1019 electron-hole pairs/(cm3 s), if the minority carrier lifetime is 500 µs, and the surface recombination velocity is 200 cm/s, calculate the following: (a) (4 pts) Using the charts below, what are the doping concentration and majority-carrier mobility? (b) (4 pts) Also using the charts below, what are the minority-carrier mobility, diffusion coefficient, and diffusion length?

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(c) (2 pts) What is the excess minority-carrier concentration Δn far from the surface? (d) (2 pts) What is Δn at the surface?

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(e) (16 pts) Starting from the minority-carrier diffusion equation, derive an expression for the excess minority-carrier concentration Δn as a function of distance from the surface.

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(f) (4 pts) What is the flux of minority electrons recombining at the surface (per unit surface area, per unit time)? (g) (4 pts) What is the flux of minority electrons in the bulk flowing toward the surface at x = 2 Ln (per unit surface area, per unit time)? (h) (2 pts) What is the flux of minority electrons at x = 10 Ln ?

(i) (2 pts) What is the flux of minority electrons at x = 100 Ln ?

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2. (20 pts) Q5., p. 329, in Nelson, The Physics of Solar Cells

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3. (40 pts total) An abrupt GaAs n+p junction has doping levels of ND = 1 × 1018 cm-3 and NA = 2 × 1016 cm-3. In the n-type emitter: µp =160 cm2/Vs and τp = 0.2 ns. In the p-type base: µn =6000 cm2/Vs and τn = 1 ns. At 300K, kT/q = 0.02585 V. For a constant generation rate G with respect to position in the diode: (a) (6 pts) Derive the J-V relationship due to minority electrons in the p-type base.

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(b) (2 pts) What is the diode saturation current density due to minority electron recombination in the p-type base? (c) (6 pts) Derive the J-V relationship for minority holes in the n-type emitter. (d) (2 pts) What is the diode saturation current density due to minority hole recombination in the n-type emitter?

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(e) (2 pts) What is the photogenerated current in the space-charge region of thickness W? (f) (4 pts) What is the overall J-V relationship including all parts of the diode? Please express your answer such that J is positive for a solar cell in forward bias (generation terms positive, recombination terms negative). (g) (2 pts) Assuming negligible recombination in the space-charge region, what is the overall diode saturation current density of the solar cell?

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(h) (4 pts) What is the built-in voltage Vbi of the junction? (i) (4 pts) For applied voltage Va = Vbi /2, calculate the injected minority carrier currents at the edges of the depletion region. What are the injected minority carrier concentrations at 0 µm and 1 µm into the bulk regions? (j) (4 pts) For applied voltage Va = – Vbi /2, calculate the injected (depleted) minority carrier concentrations at the edges of the bulk regions. Calculate the minority carrier currents at the edges of the depletion regions.

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(k) (4 pts) At what value of Va and where in the diode will the assumption of "low-level injection" first be violated, excluding the space-charge region? Use the criterion of the minority carrier reaching 10% of the majority carrier concentration as the threshold for violating the assumption of low-level injection.