Solar Cells

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 (courtesy: SolarWorld)

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 fluorescent lamp.


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 [1] (A), Is - reverse saturation current [2] (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 [3] 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

Notes

[1] Sometimes term photocurrent IPh is also used.
[2] Sometimes term dark current Io is also used.
[3] For paralell resistanse term shunt resistor Rsh is also used.

WEBSITES

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SOURCES AND ADDITIONAL INFORMATION

Books

book

Luque,A., Hegedus, S.: Handbook of Photovoltaic Science and Engineering; Wiley, 2011, ISBN 978-0470721698.

book

Wenham, S., Green, M.A., Watt, M., Corkish, R.: Applied Photovoltaics; Earthscan, 2011, ISBN 978-1849711425.

book

Wagner, A.: Photovoltaik Engineering: Handbuch für Planung, Entwicklung und Anwendung (VDI-Buch); Springer, 2009, ISBN 978-3642054129.

Papers

paper

Green, M. A., Solar cell fill factors: General graph and empirical expressions, Solid-State Electronics, vol. 24, issue 8, pp. 788 - 789, 1981.

paper

Green, M. A., Accuracy of analytical expressions for solar cell fill factors; Solar Cells, 7, pp. 337-340, 1982.

paper

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.

paper

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.

paper

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.

paper

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.

Other information

web

The Basic Physics and Design of III-V Multijunction Solar Cells.

web

Electrical Characterization of Photovoltaic Materials and Solar Cells with the Model 4200-SCS Semiconductor Characterization System; Application Note, Keithley Instruments.

Last modified: 3/7/2013 10:33:52 PM