# FYS 3028/8028 Solar Energy and Energy Storage. Calculator with empty memory Language dictionaries

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1 Faculty of Science and Technology Exam in: FYS 3028/8028 Solar Energy and Energy Storage Date: Time: 9-13 Place: Åsgårdvegen 9 Approved aids: Type of sheets (sqares/lines): Number of pages incl. cover page: Calculator with empty memory Language dictionaries Lines The exam contains 7 pages included this cover page Observe that your answer has to be written in English. Contact person during the exam: Observe that the questions weigh differently, from 1-12 points. Useful data and formulas can be found in the appendix. Tobias Boström Phone: Cell: PO Box 6050 Langnes, NO-9037 Tromsø / / / uit.no

2 1. You have a pn-junction under illumination. The pn-junction is exposed to three different cases 1) No bias 2) forward bias and 3) reverse bias. For each case, draw the following sketches: a. (3p) Model circuit showing the pn-junction, depletion region with charges and the connection circuit between p and n side b. (3p) Band diagram over the pn-junction, with the conduction and valence band (Fermi level not needed) c. (3p) Illustrate the direction and quantitatively the size (if it is larger, smaller or equal) of the different electron currents present d. (3p) IV-curve and make a X where the working point is 2. (2p) What is conductivity dependent on, and how does temperature affect the conductivity in an intrinsic semiconductor, and what is the conductivity at zero Kelvin? 3. (2p) What is the optimal band gap value for a one band gap solar cell? Also, calculate the equivalent wavelengths the cell can absorb. 4. (2p) What is plasmon resonance and give an example of where it is used in the solar energy field? 5. (4p) Name four major efficiency losses in a crystalline silicon solar cell? Explain them briefly. 6. (2p) In the design of a crystalline silicon solar cell, which are the major material parameters that determine the thickness of the solar cell? 7. (3p) You are designing a solar cell system for the roof on the Realfagsbygget at UiT. The solar cell modules need to be placed in two rows facing south, the modules are fixed at a 40ᵒ angle. The modules are of a standard 60 cell type on 1.0 x 1.5 m 2. What distance should the rows be separated with in order to avoid shading on the second row when the sun is 15ᵒ or higher above the horizon? Should the modules be placed in a portrait or landscape position and why? 8. Draw an IV curve for an ideal diode solar cell in the dark and under illumination. a. (2p) Mark, in your figure, the saturation current and the illumination current for both cases. b. (1p) State the equation each curve is obeying (derived from) 9. (2p) What is the fill factor definition of a solar cell and what is a good fill factor number? 10. (1p) Thin film solar cells often do not have metal front contacts but instead the use transparent conductive oxides. How can TCO s be transparent and still conduct current? 11. (3p) What is a shunt in a solar cell, how can the shunt be created and how can you detect it? 12. A 160-micrometer thick crystalline silicon wafer is doped with acceptors per cubic centimeter. A 1 micrometer thick emitter layer is formed at the surface of this wafer with a uniform concentration of donors per cubic centimeter. Assume that all doping atoms are ionized. The intrinsic carrier concentration in silicon at 27 ᵒC is n i =1.5 x cm -3. The effective density of states at the valence UiT / PO Box 6050 Langnes, NO-9037 Tromsø / / / uit.no 2

3 band N v and at the conduction band N c are respectively 1.0 x cm -3 and 3.0 x cm -3. The wafer is 27 ᵒC and in thermal equilibrium. a. (2p) How large is the electron and hole concentration in the p-type region and n-type region? Which charge carriers are the majority carriers in the p- type region and what is their concentration? b. (3p) What is the position of the Fermi level (in ev) in respect to the conduction band in the p-type and n-type region, respectively? c. (1p) What is the built-in voltage of the p-n junction? 13. (3p) In this question you should show your reasoning skills (there is no correct answer). Max ½ an A4 page is allowed for your answer. What will be the winning (dominating) electric energy storage technology in the year 2025 for; a. electric grid energy storage? b. electric vehicles? 14. (4p) How does V oc and I sc change when varying the band gap of your semiconductor? Explain by using (and modifying) suitable equations from the appendix. UiT / PO Box 6050 Langnes, NO-9037 Tromsø / / / uit.no 3

4 Appendix Useful Equations Reflectance from an interface: Anti-reflection optics: n 1 = n 0 n 2 (2) d 1 = λ (3) 4n 1 n 1 = refractive index of ARC n 2 = refractive index of underlying material n 0 = refractive index of the surrounding medium d 1 = thickness of ARC Ideal diode equation: I = I 0 (e (qv/kt) 1) (4) Current from a solar cell: I = I L I 0 (e qv/kt) 1) (5) Lambert Beers Law: I = I initial e αl (6) Light generated current from a solar cell: I L = qag carrier (L p + W + L n ) (7) W = width of the space charge region L = diffusion length of holes and electrons A = Area G carrier = carrier generation term (1) Saturation current: I 0 = qa Dn i 2 LN D D = minority carrier diffusivity N D = doping concentration (8) Intrinsic carrier concentration: n i 2 = np = N c N v e E g kt (9) n = electron concentration p = hole concentration N v = effective density of states at the valence band N c = effective density of states at the conduction band E g = bandgap energy Minority carrier concentration equals to n i 2 divided on the doping concentration (10) UiT / PO Box 6050 Langnes, NO-9037 Tromsø / / / uit.no 4

5 Width of depletion region: W SCR = 2ε 0ε r ψ 0 q N A = acceptor doping concentration N D = donor doping concentration Built in voltage: ( 1 N A + 1 N D ) (11) ψ 0 = kt q ln (N AN D n i 2 ) (12) Fermi function: Carrier concentration in equilibrium: (13) (14) E F = Fermi level energy E C = Conduction band energy E V = Valence band energy (15) UiT / PO Box 6050 Langnes, NO-9037 Tromsø / / / uit.no 5

6 Energy of a photon: E = hc λ (16) σ = 1 = qµn ρ (17) σ = Conductivity ρ = Resistivity µ = Mobility η = Efficiency V oc = Open Circuit Voltage I sc = Short Circuit Current FF = Fill Factor P rad = incoming radiation on your solar cell (18) Useful info Figure 1. Absorption coefficient (α) of semiconductor materials. UiT / PO Box 6050 Langnes, NO-9037 Tromsø / / / uit.no 6

7 ε r (of silicon at RT) = 11.7 UiT / PO Box 6050 Langnes, NO-9037 Tromsø / / / uit.no 7

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