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The word 'photovoltaic' consists of the two words, photo and Volta. Photo stands for light (Greek phos, photos: light) and Volta (Count Volta, 1745-1827, Italian physicist) is the unit of the electrical voltage. In other words, photovoltaic means the direct conversion of sunlight to electricity. The common abbreviation for photovoltaic is PV.

The history of photovoltaics goes back to the year 1839, when Becquerel discovered the photo effect, but in that century the technology was not available to exploit this discovery. The semiconductor age began about 100 years later. After Shockley had developed a model for the p-n junction, Bell Laboratories produced the first solar cell in 1954. The efficiency of this cell was about 5 per cent. Initially, cost was not a major issue, because the first cells were designed for space applications.

In the following years, solar cell efficiency increased continuously; laboratory silicon solar cells have reached efficiencies of around 25 per cent today. The main material used in the construction of solar cells is still silicon, but other materials have been developed, either for their potential for cost reduction or their potential for high efficiency. Costs have decreased significantly in recent decades; nevertheless, photovoltaic electricity generating costs are still higher than the costs of conventional power plants (see Chapter 6). Due to high growth rates in the photovoltaic sector, cost reduction will continue.

Photovoltaics offer the highest versatility among renewable energy technologies. One advantage is the modularity. All desired generator sizes can be realized, from the milliwatt range for the supply of wristwatches or pocket calculators to the megawatt range for the public electricity supply.

Many photovoltaic applications are built into consumer appliances or relate to leisure activities or off-grid site supply, for example, telecommunications or solar home systems. In several countries, particularly in Japan and Germany, large governmental programmes were initiated, advancing grid-connected installations. Tens of thousands of grid-connected systems that have been installed since the early 1990s have proven the suitability of the technology. The potential for photovoltaic installations is enormous. Theoretically, PV systems could cover the whole electricity demand of most countries in the world.

Figure 4.1 Roof-integrated Photovoltaic System [Georgetown University in Washington (USA), Installed in 1984 with 4464 Photovoltaic Modules and

337 kWp Total Power]

Figure 4.1 Roof-integrated Photovoltaic System [Georgetown University in Washington (USA), Installed in 1984 with 4464 Photovoltaic Modules and

337 kWp Total Power]

Figure 4.1 shows an example of a roof-integrated photovoltaic system, which was installed in the 1980s in the US. Various megawatt roof-integrated PV systems are installed today. One example is the 1-MW photovoltaic system at the Munich exhibition halls, which was finished in 1997. Altogether 7812 photovoltaic modules on a roof area of 38,100 m2 generate about one million kWh of electricity per year. This equals the average consumption of 340 German households.

Worldwide, the installed photovoltaic capacity and the share of electricity generated by PV are still low, despite impressive market growth. The political environment and magnitude of market introduction programmes will determine the future of this technology.

This chapter describes the fundamentals of PV systems such as the operating principles, calculations of the energy yield and systems and their applications. Since the descriptions use many electrical quantities, Table 4.1 gives an overview of them.

Operation of Solar Cells

Bohr's atomic model

This section describes the operating principles of semiconductor solar cells; therefore, an understanding is necessary of what a semiconductor is. The section starts with Bohr's atomic model for single atoms and continues with the energy band model for solids.

Table 4.1 Overview of the Most Important Electrical Quantities







Electrical energy

W, E

W s, J

Specific resistance


Q m

Electrical power



Electrical field strength






Inductivity (inductance)












Electrical charge

Q= fIdt



G = 1/R


Force in electrical field



According to Bohr's atomic model, electrons with rest mass: me = 9.1093897 • 10-31 kg

revolve around the atomic nucleus in an orbit with radius rn and angular frequency mn. This orbital movement results in a centrifugal force:

Electrons, each with the elementary charge of an electron r ^.602.17733 >10" As

are held in obit around the nucleus of an atom (which consists of Z positively charged protons and additional uncharged neutrons) by the attractive Coulomb force:

where cn = S.SS418731762 -10"13

and is called the permittivity or dielectric constant. The Coulomb and the centrifugal force are balanced, keeping the electron in its orbit. According to Planck's theorem, electrons can only remain in orbits where the orbital angular momentum is an integer multiple of:

which is derived from Planck's constant: h = 6.6260755 NT34 J s

The quantization of the orbital angular momentum leads to:

With this expression, the balance of forces FZ = FC can be resolved for the orbital radius, which becomes:

/t1 - h1 4 - it -fu Z t' ~ ■ mr and the angular frequency:

The integer index n describes the orbit number. An electron in orbit n contains the energy:

For instance, the energy of an electron in a hydrogen atom with the proton number Z = 1 at the first orbit (n = 1) is E1Z=1 = 13.59 eV.

Elevating an electron from one orbit to the next highest orbit requires the energy AE = En - En+1. This energy must be provided from outside the atom. All orbits can only hold a limited number of electrons. At the first orbit (n = 1) the maximum number is 2 electrons, at the second 8, then 18, 32, 50 and so on. The electron energy decreases with rising orbit index n. For n = oc it becomes Ek = 0.

The photo effect

Light, with its photon energy, can provide the energy to lift an electron to a higher orbit. The photon energy is given by:

with the wavelength A and the speed of light c = 2.99792458 • 108 m/s. When a photon with an energy of 13.59 eV hits a hydrogen atom electron in the first orbit, this energy is sufficient to lift the electron to orbit E K. In other words, it totally separates the electron from the nucleus. This energy is also called the ionization energy. The total release of an electron from the nucleus by photons is called the external photoelectric effect. The photon in the hydrogen example must have a wavelength lower than A = 90 nm, which places it in the realm of X-rays.

Because photovoltaic cells mainly convert to electricity photons of visible, ultraviolet and infrared light, i.e. photons of lower energy than X-rays, the external photo effect is not applicable to photovoltaic cells. The so-called

Ionization boundary

Single atom

Diatomic Traitomic molecule molecule k atoms (solid)

Figure 4.2 Energy States of Electrons in Atoms, Molecules and Solids internal photo effect determines the effect of light in a solar cell, and is described in the following sections.

Whereas electrons in single atoms take clearly defined energy states, this is not the case in molecules with multiple electrons. Interactions between electrons of molecules with several atoms smear the energy states to narrow neighbouring levels. In a solid with k atoms, these levels are so close to each other that it is no longer possible to separate them. Here the single energy states of the electron orbits become so-called energy bands (see Figure 4.2). However, these energy bands can also carry only a limited number of electrons.

In the energy band model, electrons fill the bands one after another starting with the first, lowest energy band. The highest fully occupied band is called the valence band (VB). The next highest band, which can be partially occupied or totally empty, is called the conduction band (CB). The space between the valence band and conduction band contains forbidden energy states and is therefore called the forbidden band (FB). The energy gap between the bands is called the band gap Eg.

Solids are subdivided into conductors, semiconductors and isolators depending on the arrangement and occupation of the energy bands (see Figure 4.3). Electrons in conductors only fill the conduction band partially. The


Conductor band (CB)



Forbidden band (FB)



Valence band (VB)






Figure 4.3 Energy Bands of Conductors, Semiconductors and Isolators

Photoeffect Solar Cell

Figure 4.4 The Lifting of Electrons from the Valence Band to the Conduction

Band Caused by Light Energy in a Semiconductor (Inner Photo Effect)

Figure 4.4 The Lifting of Electrons from the Valence Band to the Conduction

Band Caused by Light Energy in a Semiconductor (Inner Photo Effect)

conduction band and the valence band can also overlap. Electrons can move within the solid and contribute to the electron conductivity in a partially filled conduction band. The specific electrical resistance of conductors is very low (p < 10-5 Q m). Most conductors are metallic materials.

The specific electrical resistance of isolators is high (p > 107 Q m). The conduction band is totally empty and a relatively large amount of energy is needed to elevate electrons from the valence band to the conduction band due to the high band gap (Eg ^ 5 eV) in isolators.

Semiconductors have the most relevance for photovoltaics. The specific electrical resistance is between 10-5 Q m and 107 Q m. The conduction bands of semiconductors are empty, as in the case of isolators. However, due to the lower band gap (E < 5 eV), electrons can be more easily be lifted to the conduction band (Figure 4.4). The elevation of electrons into the conduction bands by photons is called the inner or internal photo effect.

An incident photon can have several effects: photon energy lower than the band gap will not elevate an electron because it cannot bridge the band gap. Photons with energy larger than the band gap can elevate electrons into the conduction band with a part of its energy. Surplus energy is lost, because the electron falls back to the edge of the conduction band.

Photoresistors, which change their resistance depending on the irradiance, use the internal photo effect. Photovoltaic cells also use the internal photo effect for generating current.

Principle of solar cells

Photovoltaic systems employ semiconductors. They have four electrons in the outer shell, or orbit, on average. These electrons are called valence electrons. Elementary semiconductors are elements of group IV of the periodic table of elements, for instance silicon (Si), germanium (Ge) or tin (Sn). Compounds of two elements containing one element from group III and one from group V (so-called III-V compounds) and II-VI compounds or combinations of various elements also have four valence electrons on average. An example of a III-V semiconductor is gallium arsenide (GaAs) and an example of a II-VI

Table 4.2 Band Gap for Various Semiconductors at 300 K

IV semiconductors

III-V semiconductors

II-VI semiconductors








1.107 eV


1.35 eV


1.44 eV


0.67 eV


0.165 eV


2.58 eV


0.08 eV


1.27 eV


2.26 eV


2.24 eV


0.30 eV

Source: data from Lechner, 1992

Source: data from Lechner, 1992

semiconductor is cadmium telluride (CdTe). Table 4.2 shows the different band gaps of various semiconductors.

Silicon is the material most commonly used in photovoltaics. Silicon is the second most abundant element in the earth's crust after oxygen, but it cannot be found in a chemically pure form. Silicon is an elementary semiconductor of the group IV of the periodic table of elements, i.e. silicon has four valence electrons in the outer shell. In order to obtain the most stable electron configuration, two electrons of neighbouring atoms in the silicon crystal lattice form an electron pair binding. In other words, two atoms jointly use these electrons. Electron pair bindings (covalent bonds) with four neighbours give silicon a stable electron configuration similar to that of the noble gas argon (Ar). In the energy band model, the valence band is now fully occupied and the conduction band is empty. Supplying sufficient energy by incident light or heat can elevate an electron from the valence band into the conduction band. This electron now can move freely through the crystal lattice. A so-called defect electron, or hole, remains in the valence band. Figure 4.5 illustrates this process. The formation of defect electrons is responsible for the so-called intrinsic conduction of semiconductors.

Electrons and holes always arise in pairs, i.e. there are exactly as many electrons as holes. This is described by the following equation using the electron density n and hole density p:

Figure 4.5 Crystal Structure of Silicon (left), Intrinsic Conduction due to Defect Electron in the Crystal Lattice (right)

Figure 4.5 Crystal Structure of Silicon (left), Intrinsic Conduction due to Defect Electron in the Crystal Lattice (right)

The product of electron and hole density is called the intrinsic carrier density n2 and depends on the absolute temperature T and band gap Eg:

where the Boltzmann constant k is given as: k = 1.380658 • 10-23 J/K

The value for silicon is n;o = 4.624015 cm-3 K-3/2. No free electrons and holes exist at a temperature of absolute zero (T = 0 K = -273.15°C). With increasing temperature their number rises rapidly.

If an electrical voltage is applied to the silicon crystal externally, negatively charged electrons will flow to the anode. Electrons neighbouring a hole can move into the hole created by this current. Thus, holes move in the opposite direction to the electrons. The mobility and up of electrons and holes in the semiconductor depends also on the temperature. and u can be calculated for silicon with u0c = 1350 cm2/(V s) and u0p = 480 cm2/(V s) at T0 = 300 K by:

The electrical conductivity

of the semiconductors is given by the sum of the electron and hole currents. The conductivity decreases significantly at very low temperatures. This effect is used for the production of low temperature sensors.

The influence of light also changes the electrical conductivity. This effect is used in light sensible photoresistors. For their application, an electrical voltage must be applied externally. However, this effect is not relevant to the photovoltaic generation of electrical current. Therefore, another effect must be used: the so-called extrinsic or defect conduction (Figure 4.6).

Atoms from group V such as phosphorus (P) and antimony (Sb) have five valence electrons in contrast to silicon's four. If these atoms are embedded into a silicon crystal lattice, the fifth electron cannot participate in electron pair binding. Thus, this electron is bonded very loosely. Little energy is required to separate this electron from the atom and thus create a free electron. The embedding of atoms from group V is called n-doping. The impurity atoms are called donors.

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Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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