Tut 2 solutions

Tut 2 solutions - rev 07.08.2016 Page 1 of 7 SOLA2540&...

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rev 07.08.2016 Page 1 of 7 SOLA2540 & SOLA9001 Applied Photovoltaics Tutorial 2 Solutions Question 1 The absorption coefficient of silicon decreases from 1.65 × 10 6 cm -1 at 0.3 µ m wavelength to 4,400 cm -1 at 0.6 µ m wavelength to 3.5 cm -1 at 1.1 µ m wavelength. Assuming zero reflection at all wavelengths for the front and rear surfaces, calculate and sketch the generation rate of electron-hole pairs across a silicon cell of 300 µ m thickness, for each wavelength of light, normalized to the surface generation rate in each case. G(x) = α Ne - α x ; G(0) = α N; G(x)/G(0) = e - α x Question 2: A silicon wafer is uniformly doped with 10 16 phosphorus (P) atoms/cm 3 . Assuming that all of these donor impurities are ionised, estimate the density of electrons and holes in this material under thermal equilibrium at 300K. ( ) 3 4 16 2 10 2 2 3 16 cm 10 10 10 1 Since ionised) impurities donor all (assuming cm 10 ~ ion concentrat Electron = × = = = = n n p n pn N n i i Question 3: (a) The resistivity of the p-side material, 1 16 19 Ω cm 49 . 1 420 10 10 6 . 1 1 1 ~ = × × × = h p qp μ ρ and the resistivity of the n-side, 1 17 19 Ω cm 02 . 0 650 10 5 10 6 . 1 1 1 ~ = × × × × = e n qn μ ρ

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rev 07.08.2016 Page 2 of 7 (b) The built in potential is given by: = = 2 1 ln n N N q kT V D A bi (c) The depletion width is given by: ( ) silicon for 7 . 11 ; F/m 10 854 . 8 1 1 ) ( 2 1 1 ) ( 2 12 0 = × = = + = + = r r D A D bi r D A D bi N N q V V N N q V V W ε ε ε ε ε W N N N w W N N N w D A A n D A D p + = + = & (d) The depletion width is given by: = + = D A D bi N N q V V W 1 1 ) ( 2 ε Question 4: (a) Conductivity of an intrinsic semiconductor, = + = + = e h n p qn qp μ μ σ σ σ and the resistivity, = = σ ρ / 1 (b) For a n-type semiconductor, = = = e n e n qn qn μ ρ μ σ σ 1 (c) = = = = A t V I A t R R V I ρ ρ where Question 5 (a) A silicon solar cell (bandgap 1.12 eV) is uniformly illuminated by monochromatic light of wavelength 800 nm and intensity 20 mW/cm 2 . Given that its external quantum efficiency at this wavelength is 0.80, calculate the short-circuit current of the cell given that it’s area is 4 cm 2 . mA A QE QE cm A Area QE cm mW I Intensity nm eV 2 . 41 04118 . 0 I 8 . 0 10 3 10 6.63 40 800 10 1.6 4 10 20 I hc q I.A I hc q (W) Power (A) Current 4 ) ( ; 8 . 0 ; / 20 ) ( ; 800 ; 12 . 1 E SC 8 34 - 9 - 19 - 3 - SC SC 2 2 g = = × × × × × × × = × × = = = = = = = λ λ λ
rev 07.08.2016 Page 3 of 7 (b) For the same quantum efficiency, what would be the value of this current if the cell were made from a semiconductor of bandgap: (i) 0.7 eV; (ii) 2.0 eV.

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