SOLAR CELLS INTRODUCTION
Solar cells are in fact large area semiconductor diodes. Due to photovoltaic effect
energy of light (energy of photons) converts into electrical current. At p-n
junction, an electric field is built up which leads to the separation of the charge
carriers (electrons and holes). At incidence of photon stream onto semiconductor
material the electrons are released, if the energy of photons is sufficient.
Contact to a solar cell is realised due to metal contacts. If the circuit is
closed, meaning an electrical load is connected, then direct current flows. The
energy of photons comes in "packages" which are called quants. The energy of each
quantum depends on the wavelength of the visible light or electromagnetic waves.
The electrons are released, however, the electric current flows only if the energy
of each quantum is greater than WL - WV (boundaries of valence and conductive
bands). The relation between frequency and incident photon energy is as follows:
h - Planck constant (6,626·10-34Js), μ - frequency (Hz)
SOLAR CELL FEATURES
Crystalline solar cells
Among all kinds of solar cells we describe silicon solar cells only, for they are
the most widely used. Their efficiency is limited due to several factors. The
energy of photons decreases at higher wavelengths. The highest wavelength when the
energy of photon is still big enough to produce free electrons is 1.15 μm
(valid for silicon only). Radiation with higher wavelength causes only heating up
of solar cell and does not produce any electrical current. Each photon can cause
only production of one electron-hole pair. So even at lower wavelengths many
photons do not produce any electron-hole pairs, yet they effect on increasing
solar cell temperature. The highest efficiency of silicon solar cell is around
23 %, by some other semi-conductor materials up to 30 %, which is
dependent on wavelength and semiconductor material. Self loses are caused by
metal contacts on the upper side of a solar cell, solar cell resistance and due to
solar radiation reflectance on the upper side (glass) of a solar cell.
Crystalline solar cells are usually wafers, about 0.3 mm thick, sawn from
Si ingot with diameter of 10 to 15 cm. They generate approximately 35 mA
of current per cm2 area (together up to 2 A/cell) at voltage of
550 mV at full illumination. Lab solar cells have the efficiency of up to
30 %, and classically produced solar cells up to 20 %.
Wafers and crystalline solar cells
Amorphous solar cells
The efficiency of amorphous solar cells is typically between 6 and 8 %.
The Lifetime of amorphous cells is shorter than the lifetime of crystalline cells.
Amorphous cells have current density of up to 15 mA/cm2, and the
voltage of the cell without connected load of 0.8 V, which is more compared
to crystalline cells. Their spectral response reaches maximum at the wavelengths
of blue light therefore, the ideal light source for amorphous solar cells is
Surface of different solar cells as seen through microscope
(courtesy: Helmholtz-Zentrum Berlin)
SOLAR CELL MODELS
The simplest solar cell model consists of diode and current source connected
parallelly. Current source current is directly proportional to the solar radiation.
Diode represents PN junction of a solar cell. Equation of ideal solar cell, which
represents the ideal solar cell model, is:
IL - light-generated current  (A),
Is - reverse saturation current  (A)
(aproximate range 10-8 A/m2)
V - diode voltage (V),
VT - thermal voltage (see equation below),
VT = 25.7 mV at 25°C
n - diode ideality factor = 1...2 (n = 1 for ideal diode)
Thermal voltage VT (V) can be calculated with the following equation:
k - Boltzmann constant = 1.38·10-23 J/K,
T - temperature (K)
q - charge of electron = 1.6·10-19 As
Ideal solar cell model
Real Solar cell model with serial and parallel resistance 
Rs and Rp,
internal resistance results in voltage drop and parasitic currents
The working point of the solar cell depends on load and solar irradiation. In the
picture, I-V characteristics at short circuit and open circuit conditions can be
seen. Very important point in I-U characteristics is Maximum Power Point, MPP.
In practice we can seldom reach this point, because at higher solar irradition
even the cell temperature increases, and consequently decreasing the output power.
Series and paralell parasitic resistances have influence on I-V curve slope. As a
measure for solar cell quality fill-factor, FF is used.
It can be calculated with the following equation:
IMPP - MPP current (A), VMPP - MPP voltage (V)
Isc - short cirquit current (A), Voc - open cirquit voltage (V)
In the case of ideal solar cell fill-factor is a function of open cirquit parameters
and can be calculated as follows:
Where voc is normalised Voc voltage (V) calculated with equation below:
k - Boltzmann constant = 1,38·10-23 J/K,
T - temperature (K)
q - charge of electron = 1,6·10-19 As,
n - diode ideality factor (-)
Voc - open cirquit voltage (V)
For detailed numerical simulations more accurate models, like two diode model, should be used.
For additional explanations and further solar cell models description please see literature below.
SOLAR CELL CHARACTERISTICS
Samples of solar cell I-V and power characteristics are presented on pictures below.
Typical point on solar cell characteristics are open cirquit (when no load is connected),
short cirquit and maximum power point. Presented characteristics were calculated
for solar cell with following data: Voc = 0,595 mV,
Isc = 4,6 A,
IMPP = 4,25 A,
VMPP = 0,51 V,
and PMPP temperature coefficient γ = -0,005 %/K.
Calculation algorithm presented in the book Photovoltaik Engineering (Wagner, see sources) was used.
Solar cell I-V characteristics for different irradiation values
Solar cell power characteristics for different irradiation values
Solar cell I-V characteristics temperature dependency
Solar cell power characteristics temperature dependency
Sometimes term photocurrent IPh is also used.
Sometimes term dark current Io is also used.
For paralell resistanse term shunt resistor Rsh is also used.
Organic Photovoltaics Analysis Platform
- Organic Photovoltaics
Analysis Platform (OPVAP) is a group of software used in the field of solar
cells, which include analyzing experimental data, calculating optimum
architecture based on your materials, and even some research assistant
tools such as PicureProcess.
Website also available in:
- Heliatek was spun-off in 2006 from the Technical University of Dresden (IAPP) and the University of Ulm.
The company’s founding brought together internationally renowned expertise in the fields of organic optoelectronics and organic oligomer synthesis.
Website also available in:
- spherical solar cells technology.
Global Photonic Energy Corp.
- GPEC is harnessing energy of sunlight using small-molecule organic
materials to produce electricity and hydrogen or "Photo Fuel™".
SOURCES AND ADDITIONAL INFORMATION
Luque,A., Hegedus, S.:
Handbook of Photovoltaic
Science and Engineering;
Wiley, 2011, ISBN 978-0470721698.
Wenham, S., Green, M.A., Watt, M., Corkish, R.:
Earthscan, 2011, ISBN 978-1849711425.
Handbuch für Planung, Entwicklung und Anwendung (VDI-Buch);
Springer, 2009, ISBN 978-3642054129.
Green, M. A., Solar cell fill factors: General graph and empirical expressions,
Solid-State Electronics, vol. 24, issue 8, pp. 788 - 789, 1981.
Green, M. A., Accuracy of analytical expressions for solar cell fill factors; Solar Cells, 7,
pp. 337-340, 1982.
Easwarakhanthan, T. Bouhouch, L. Bottin, J. Nguyen, P.H.: Semiempirical expressions for solar cell fill factors;
Electronics Letters, Volume: 21, Issue: 12, 1985, p.529-530, ISSN: 0013-5194.
Grunow, P. et al.:
Weak light performance and annual yields of PV modules and systems as a result of the basic parameter set of industrial solar cells; Proc. of the 19th PVSEC, Paris, 2004, p. 2190.
Grunow, P. et al.: Influence of
micro cracks in multi-crystalline silicon solar cells
on the reliability of PV modules; Proc. of the 20th PVSEC, Barcelona, 2005, 5BV.4.26.
Grunow, P. et al.: The influence of
textured surfaces of solar cells and modules
on the energy rating of PV systems; Proc. of the 20th PVSEC, Barcelona, 2005, 5BV.4.27.