# Solar cells | electrical engineering | Arizona State University

1)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 10 19 electron-hole pairs/(cm 3 s), if the minority carrier lifetime is 500 µs, and the surface recombination velocity is 200 cm/s, calculate the following:

(a) Using the charts below, what are the doping concentration and majority-carrier

mobility?

(b) Also using the charts below, what are the minority-carrier mobility, diffusion coefficient, and diffusion length?

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

(d) What is Δn at the surface?

(e) 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.

(f) What is the flux of minority electrons recombining at the surface (per unit surface area, per unit time)?

(g)  What is the flux of minority electrons in the bulk flowing toward the surface at x = 2 L n (per unit surface area, per unit time)?

(h) What is the flux of minority electrons at x = 10 L n ?

(i) What is the flux of minority electrons at x = 100 L n ?

2. An abrupt GaAs n+ p junction has doping levels of N D = 1 × 10 18 cm -3 and N A = 2 × 10 16 cm-3 . In the n-type emitter: µ p =160 cm2 /Vs and τ p = 0.2 ns. In the p-type base: µ n =6000 cm2 /Vs and τ n = 1 ns. At 300K, kT/q = 0.02585 V.

For a constant generation rate G with respect to position in the diode:

(a) Derive the J-V relationship due to minority electrons in the p-type base.

(b)  What is the diode saturation current density due to minority electron recombination in the p-type base?

(c) Derive the J-V relationship for minority holes in the n-type emitter.

(d) What is the diode saturation current density due to minority hole recombination in the n-type emitter?

(e) What is the photogenerated current in the space-charge region of thickness W?

(f) 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) Assuming negligible recombination in the space-charge region, what is the overall diode saturation current density of the solar cell?

(h) What is the built-in voltage V bi of the junction?

(i)  For applied voltage V a = V bi /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) For applied voltage V a = – V bi /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.

(k)At what value of V a 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.

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