SUNY at Albany Electrical engineering Questions

CHEN E4231 HW4 Due: 5:00 pm on March 26 1. Semiconductor solid state physics: a.) Calculate and plot the position of the fermi level (Ef) with respect to the conduction band minimum (Ec) for a n-Si (Eg=1.12 eV) as function of dopant density (ND) over the range 1×1011 < ND < 1×1022 cm-3. Express the difference (Ec-Ef) in units of electron volts (eV). Additional information: T= 298 K, conduction band density of states (DOS) =NC = 3×1019 cm-3. b.) Report the value of ND for which (Ec-Ef)=0. Semiconductors with doping levels at or above this level are said to be “degenerate”; they possess such a large concentration of free carriers that they exhibit conductivities and other electronic properties that are more similar to metals than semiconductors. c.) Assuming that Ef for Si is located at the “mid gap” of the semiconductor’s band gap, estimate the intrinsic concentration (ni) for undoped Si semiconductor, as well as the electronic DOS for the valence band (NV). 2. Calculating JL and PV thickness requirements: Download the AM1.5G solar spectrum file “AM1pt5G_300-2500nm_10nm_increment.xls” from Canvas (Files-> Resources-> Solar Irradiance Data Sets), which contains the AM1.5G spectral irradiance data in 10 nm increments between 300 nm < λ < 2500 nm. Also download the spreadsheet “OpticalPropertiesOfSilicon.xlsx” containing absorption coefficient α(λ) data for crystalline Si available from the link below [1]. a.) A silicon solar cell has a band gap of Eg=1.12 eV. Calculate the maximum light-generated current density (JL) that could be generated if every photon having energy hv > Eg were absorbed and converted into electrical current (i.e. EQE(λ)=100% for (hc/ λ > Eg). This is equivalent to saying that no reflection, transmittance, or recombination losses occur in this solar cell. b.) Transmittance losses can be avoided by using a very thick Si layer, but this increases the materials cost associated with the Si. Using the optical absorption coefficient α(λ) values for Si[1] use the Beer-Lambert Law to calculate and plot JL as a function of the thickness of Si wafer thickness (tSi) from 5 μm < tSi < 2000 μm for AM 1.5G illumination while still assuming that there are no recombination or reflection losses. What thickness should the Si wafer be such that JL only decreases by 10% compared to a very thick, tSi= 2000 μm wafer? References: [1] Optical Properties of Silicon. PVCDROM. (download spreadsheet in link labeled “Excel Spreadsheet”). Also available for download at “OpticalPropertiesOfSilicon.xlsx” at Courseworks –> Files –>Resources. 3. Using the diode equation to evaluate PV performance: Consider 2 different types of solar cells characterized by the following values of dark saturation current density (Jo), ideality factor (n), and lightgenerated current density (JL) when powered by AM1.5G illumination having a net irradiance of ≈ 1000 W m-2. a.) Plot JV curves (current density vs. voltage) for these two solar cells assuming a temperature of T=300 K. b.) Compute the Voc, fill factor (FF), and photovoltaic efficiencies for both cells. Which cell is more efficient? Cell type (Jo= Io/Ahv ) / A cm-2 n (JL= IL /Ahv ) / mA cm-2 1 1×10-14 1.00 35 -10 2 1×10 1.05 45 Note: Ahv is the illuminated area of the solar cell, assumed to be equal to the junction area. As a basis for this calculation, you may assume Ahv =1 cm2, although you will see that the value of Ahv does not affect the Voc, FF, or efficiency of the solar cell because Ahv is an extrinsic property. Also note that Jo and JL have different units. 4. Finding the optimal semiconductor bandgap- The value of a semiconductor’s band gap (Eg) is one of the most important parameters in determining its maximum achievable PV efficiency (ηPV). As discussed in class, there is a trade-off between the achievable photocurrent (IL) and voltage generated by a solar cell as a function of its bandgap. While narrow Eg semiconductors are capable of generating large IL, their maximum photovoltages are small. Conversely, wide Eg semiconductors are capable of generating large photovoltages per cell, but generate lower IL because they absorb fewer photons with energy > Eg. Since PV power output is the product of current and voltage, this tradeoff results in an optimal Eg that will maximizes ηPV. In this problem, your task is to compute the value of Eg that maximizes the PV efficiency of solar cell that is powered by a “white light” light emitting diode (LED) lamp whose spectral irradiance profile is provided in the file “white_LED_spectrum.xlsx” (Go to Courseworks-> Files-> Resources-> Solar Irradiance Data Sets). LEDs can be very energy efficient light sources, and using them to power solar cells or photocatalysts is of interest for indoor applications (e.g. solar cell powered phones, watches), green house applications, and disinfection applications. For this problem, assume that every photon having energy above the band gap energy (i.e. hν>Eg) is absorbed by the semiconductor and converted into electrical current with EQE=100%, while EQE=0% for those photons with hv< Eg. In order to calculate ηPV, use the following two empirical relationships that correlate Voc and FF of solar cells to the semiconductor Eg for high quality semiconductors: 𝑣 −ln⁡(𝑣𝑜𝑐 +0.72) 𝑉𝑜𝑐 Eqn. (1): 𝑉𝑜𝑐 = 0.6 · 𝐸𝑔 Eqn. (2): 𝐹𝐹 = 𝑜𝑐 𝑣 +1 Eqn. (3): 𝑣𝑜𝑐 = (𝑘𝑇⁡/𝑞) 𝑜𝑐 In Eqn. (1), the units of Eg [=] eV, giving Voc in units of V. Eqn. (2) gives the FF as a function of the normalized Voc, voc, with both FF and voc being unitless. In Eqn. (3), k is the Boltzman constant, T is the temperature, and q is the elementary charge of an electron. a.) Plot the calculated ηPV as a function of Eg, for 1 eV < Eg < 3 eV and T=298 K. b.) From part a.) report the value of the maximum ηPV and the value of the optimal Eg that should be used for this particular LED light source. Comment on how the values of the maximum ηPV and associated optimal Eg compare to the maximum ηPV and optimal value of Eg for solar cells operated under solar AM1.5 illumination, which can be found in reference [1]. In words, explain why the optimal Eg and associated ηPV for the LED light source different than that for the solar AM1.5 spectrum. References [1] PVCDROM, “Limiting solar cell efficiency as a function of semiconductor band gap energy for 1 sun illumination”, in Chapter 4: http://www.pveducation.org/sites/default/files/PVCDROM/Solar-CellOperation/Images/max_efficiency.png

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