(Solved): a. (1.5) Light from a source is normally incident on a silicon PV cell with a wavelength of 550n ...

a. (1.5) Light from a source is normally incident on a silicon PV cell with a wavelength of $$550\mathrm{nm}$$ and an irradiance of $$1.5\mathrm{mW}/{\mathrm{cm}}^2$$. Compute the photon flux per $${\mathrm{cm}}^2$$ at the surface of the cell. b. As discussed in class the short circuit current density for a PV cell can be approximated as: $$J_{sc}(?)=q?[1?R(?)]?s?\left[\exp \left[?{?}_n(?)\left(W_n?x_n\right)\right]\right]?b_s(?)$$ Assume that the PV cell material is silicon with a refractive index of $$3.6,s=0.95$$, the area of the PV cell is $$2{\mathrm{cm}}^2$$, an ideality factor of $$1.5$$, and has an absorption coefficient of $$5.5\times 10^2/\mathrm{cm}$$ at $$550\mathrm{nm}$$. If the irradiance at $$550\mathrm{nm}$$ from part a (i.e. $$1.5\mathrm{mW}/{\mathrm{cm}}^2$$ ) illuminates the cell (surrounded by air): i. (1.5) Compute $$I_{sc}$$ for the incident irradiance and wavelength with a cell thickness to the space charge region of $$100?\mathrm{m}$$; ii. (1.5) Compute the corresponding $$V_{oc}$$ when the cell temperature $$\mathrm{T}=25^{?}\mathrm{C}$$ and the reverse saturation current is $$1.5\times 10^{?9}\mathrm{A}$$. iii. (1.5) For the above PV cell and the conditions in i. and ii., compute the current through the load resistance connected across the front and back contacts of the $$\mathrm{PV}$$ cell when the voltage across the load resistance is $$\mathrm{V}=0.5{\mathrm{V}}_{\mathrm{oc}}$$. c. (4) The I-V curve for a PV cell is shown in the figure below when illuminated with $$1000\mathrm{W}/{\mathrm{m}}^2$$ i. (1.5) Use the graphical method to determine the fill factor (FF). ii. (0.5) What are the values for $${\mathrm{V}}_{\mathrm{oc}}$$, Isc, $${\mathrm{V}}_{\mathrm{mp}},{\mathrm{Imp}}_{\mathrm{mp}}$$ and label on the plot. iii. (1.5) What load resistance allows the cell to operate at the maximum power point? iv. (0.5) Draw a new $$\mathrm{I}?\mathrm{V}$$ curve when the same cell is illuminated with $$500\mathrm{W}/{\mathrm{m}}^2$$.