Photovoltaic Cells.

In space, solar radiation is obviously unaffected by the earth’s atmosphere and has a power density of approximately 1365 watts per square meter. The characteristic spectral power distribution of solar radiation as measured in space is described as the Air Mass 0 distribution. At the earth’s surface, the various gases of which the atmosphere is composed (oxygen, ozone, water vapor, carbon dioxide, etc.) attenuate the solar radiation selectively at different wavelengths. This attenuation increases as the distance, which the sun’s rays have to travel through the atmosphere increases.

When the sun is directly overhead, the distance, which the sun’s rays have to travel through the atmosphere to a PV Cell, is clearly at a minimum. The characteristic spectral power distribution of solar radiation that is observed under these conditions is known as the Air Mass 1 distribution.

When the sun is at a given angle (Q) to a PV Cell at sea level, the Air Mass is defined as the ratio of the path length of the sun’s rays under these conditions to the path length when the sun is directly over a PV Cell. By simple trigonometry, this leads to the definition:

 Air Mass = 1/Cos

 

An Air Mass distribution of 1.5, is the standard test conditions, therefore when the sun is at an angle of 48 degrees that is the ideal test conditions for PV Cells, as:

 Cos48 = 0.67

 1/0.67 = 1.5.  Air Mass = 1.5

IE achieving the standard test conditions for a PV Cell.

Band Gap Theory

According to the quantum theory of matter, the quantity of energy possessed by any given electron in a material will lie within one of several levels or ‘bands’. Those electrons that normally hold the atoms of the material together (by being ‘shared’ between adjoining atoms, are occupying the valence band, some electrons may in certain circumstances acquire higher energy, sufficient to enable them to move around within the material and thus to conduct electricity. They are then described as being in the conduction band.

   There is a so-called energy gap or band gap between these bands, the magnitude of which varies from material to material, and which is measured using a unit known as the electron volt.

Metals, which conduct electricity well, have many electrons in the conduction band. Insulators, which hardly conduct electricity at all, have virtually no electrons in the conduction band. Pure semiconductors have some electrons in the conduction band, but not as many as in a metal. ‘Doping’ pure semiconductors with very small quantities of certain impurities can greatly improve their conductivity, however. If a photon incident on a doped, n-type semiconductor in a PV cell is to succeed in transferring its energy to an electron and ‘exciting’ it from the valence band to the conduction band, it must possess an energy at least equal to the band gap. Photons with energy less than the band gap do not excite valence electrons to enter the conduction band and are wasted. Photons with energies significantly greater than the band gap do succeed in ‘promoting’ an electron into the conduction band, but any excess energy is given off as heat. This wasted energy is one of the reasons why PV cells are not 100% efficient in converting solar radiation into electricity. Another main reason is that some Photons are reflected of the surface of a PV Cell instead of being absorbed.

%efficiency = (power out / power in) x 100

Maximum Power Theory and Open and Short Circuits

One very simple way of envisaging a typical 100 square centimeter silicon PV cell is as a solar powered battery.

This circuit shows a PV cell connected to a variable electrical resistance R, together with an ammeter to measure the current (I) in the circuit and a voltmeter to measure the voltage (V) developed across the cell terminals.

When the resistance is infinite (i.e. when the cell is, in effect, not connected to any resistance, or ‘open circuited’) the current in the circuit is at its minimum (zero) and the voltage across the cell is at its maximum, known as the ‘open circuit voltage’ (Voc). At the other extreme, when the resistance is zero, the cell is in effect ‘short circuited’ and the current in the circuit then reaches its maximum, known as the ‘short circuit current’ (Isc).

   The maximum power is when internal resistance is equal to the resistance of the external load.