SOLA3540 & SOLA9001 Applied Photovoltaics 2010
Tutorial 1b
Question 1
The absorption coefficient of silicon decreases from 1.65×106 cm-1 at 0.3 µm wavelength to 4,400
cm-1 at 0.6 µm wavelength to 3.5 cm-1 at 1.1 µm 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 µm thickness, for each wavelength of light, normalized to the surface
generation rate in each case.
Question 2
(a) A silicon solar cell (bandgap 1.12 eV) is uniformly illuminated by monochromatic light of
wavelength 800 nm and intensity 20 mW/cm2. 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 cm2.
(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.
(c) For the silicon cell of part (a) at 300K, calculate the open-circuit voltage, fill factor and energy
conversion efficiency given that its ideality factor is 1.2 and dark saturation current density is
1 pA/cm2.
(d) Estimate the range of values of (i) series resistance; (ii) shunt resistance, which would cause a
relative reduction in the fill factor and energy conversion efficiency of less than 5%.
Question 3
A 4 cm2 solar cell is uniformly illuminated by a monochromatic light source with an intensity of 100
mW/cm2. The wavelength of the light is 500 nm. The solar cell produces a voltage of 400 mV and a
current of 80 mA at its maximum power point and the short circuit current is 85 mA. Calculate:
(a) The conversion efficiency of the solar cell under this light source
(b) The external quantum efficiency (EQE)
Question 4
A solar cell can be represented by the equivalent circuit in the figure below.
(a) Describe the physical processes represented by Rs and Rsh use circuit theory to derive an
expression for I taking these two resistances in account
(b) Sketch an IV curve and label important features of the curve: VOC, ISC, VMPP, IMPP. On the IV
Curve, sketch the effect of increasing Rs and Rsh.
⎛ I SC ⎞
(c) The maximum power of the cell for Rsh=∞ can be approximated by PMPP(Rsh= 0) = PMPP ⎜1− Rs ⎟
⎝ VOC ⎠
A solar cell has ISC = 40mA, VOC = 0.6 V, Rs = 10Ω and no current loss due to shunting.
Calculate the percentage drop in the maximum power with a 10% increase in Rs
Page 1 of 3
(d) Calculate the percentage drop in the maximum power with a 10% increase in Rs for a solar cell
with ISC = 15mA and VOC = 1.1V. What can you conclude from the result?
(e) What is the equivalent ISC if two identical solar cells are connected
(i) in parallel
(ii) in series
Question 5
A crystalline silicon solar cell of area125 mm x 125 mm cell was placed outdoors under illumination
of 1 kW/m2 (AM 1.5) and an ambient temperature of 25ºC for current-voltage (I-V) measurement.
From the outdoor measurement, the cell was found to have the following I-V results: Voc = 635 mV,
Jsc = 35.2 mA/cm2 and FF = 77.3%. The cell was left outside for certain length of time so that the cell
temperature rises to 40ºC, and the I-V measurement was retaken.
(a) Calculate the change in the cell open-circuit voltage (Voc).
(b) Calculate the change in the cell short-circuit current (Isc).
(c) Calculate the change in the cell fill factor (FF).
(d) Calculate the change in the cell maximum power output (Pmax).
Question 6
The band-gap of an InGaAs solar cell is 1.24eV. The device is illuminated by a monochromatic light
of wavelength 827nm and intensity 50mW/cm2. The quantum efficiency of the cell is shown in the
figure.
(a) Calculate the short circuit current of the cell given that its area is 0.5cm2
(b) Calculate the open circuit voltage, the fill factor and energy conversion efficiency, given an
ideality factor of 1.5, T = 300K and I0 = 4 x 10-9A.
(c) The device is now illuminated by a light with a constant intensity of 20mW/cm2. Calculate the
short circuit current of the device if the wavelength of the incoming light is:
(i) λ1 = 300nm
(ii) λ2 = 600nm
(iii) λ3 = 900nm
(iv) λ4 = 1000nm
Page 2 of 3
Question 7
At T = 300 K, a Si solar cell of 100 cm2 area has a Voc = 600 mV and an Isc = 3.3 A under 1 kW/m2 (1-
sun) illumination. Assume the cell is ideal. Calculate:
(a) The dark saturation current density, J0 , of the cell
(b) The Isc of the solar cell if the cell is now under 10-suns illumination
(c) The Voc of the cell under 10x concentration
Short Answer Questions:
Question S1
(a) Briefly describe how a solar cell operates.
(b) Outline the important aspects of solar cell design that affect solar cell efficiency
(c) Briefly discuss features of a silicon solar cell that affect its spectral response
Additional Questions:
Recommended for Postgraduates (can be attempted by Undergraduates).
Question A1
(a) Taking the silicon bandgap as 1.12 eV, and assuming unity quantum efficiency, calculate the
upper limit on the short-circuit current density of a silicon solar cell for the standard
“unnormalized” global AM1.5 spectrum supplied in tabulated form (Appendix B in textbook
Applied Photovoltaics).
(b) Given that, near operating temperatures, the silicon bandgap decreases by 0.273 meV/°C,
calculate the normalized temperature coefficient of this current limit:
⎛ 1 dI sc ⎞
⎜ ⎟
⎝ I sc dT ⎠
Page 3 of 3
