PV Theory

Photovoltaic cells use semiconducting materials to capture the energy of sunlight, which is composed of photons. These photons contain an energy corresponding to their wavelengths in the solar spectrum. When sunlight or photons strike a PV cell, three events occur:

1. Photons pass straight through the cell. This depends on the band gap energy of the material (The band gap energy is discussed in the following section). Photons with energy less than the band gap energy pass through the PV cells.

2. Photons reflect off the surface. This depends on the surface characteristics of the material.

3. Photons are absorbed by the PV cell. Only photons with a certain level of energy are able to free electrons from their atomic bonds. By leaving this position, the electron causes a “hole” to form. The electrons from nearby atoms will move into this hole, and the process will continue until it reaches the external electrical circuit. If the energy of the absorbed photons is higher than the band gap energy, sometimes heat is generated, depending on the band structure. The process is shown in Fig. 2.36.

Although silicon is most widely used for making PV cells, pure silicon is nearly an insulator. The atomic structure of silicon is shown in Figs. 2.37 and 2.38. Silicon has four electrons in its outer shell. The atoms in crystalline solids are held together by covalent bonds. For silicon, four outer shell electrons of each atom are shared by neighboring atoms. As a result, silicon crystals have no free electrons to make it a conducting metal. However, silicon can be made a semi-conductor by doping it with another element (called dopant), such as boron or phosphorous. Depending on the dopant, silicon can become either p-type or я-type semi-conductor. This is discussed in the following section.

Materials of n-type and p-type are best understood by looking at the columns of the periodic table around silicon (Fig. 2.39). Silicon’s atomic structure, since it is in the third row of the periodic table, has two electrons that reside in the 1S shell,

Fig. 2.36 The interaction of photons with a semiconductor material. (a) The atom of the semicon­ductor material, (b) Interaction of the atom with sunlight or photons, (c) The ijection of electron and creation of the hole, (d) Absorption of energy

two electrons that reside in the 2S shell, six electrons that reside in the 2P shell, two electrons that reside in the 3S shell and two electrons that reside in the 3P shell (for a total of 14 electrons shown above). Since the crystalline structure of silicon depends upon covalent bonds (or the sharing of electrons with neighboring atoms), the crystal structure is symmetric due to the bond sharing between silicon atoms. If an impurity atom is substituted in place of a silicon atom, the subtraction or addition of a P shell electron in the crystal matrix changes the nature of the local covalent bond. This leads to the formation of a p-type center when there is an absence of an electron (hole) or an n-type center if there is an addition of an electron (free electron).

Fig. 2.39 Columns III, IV, V, and VI of the period table

The valence electrons come from the paired electrons in covalent bonds where one electron comes from each atom. The valence electrons contain energies in a range known as the valence band. The energy of electrons in this band has various energy levels, one for each valence electron. The valance band is generally filled and no more valence electrons can be added to the lattice. Some elements have extra electrons that are not held via the covalent bond and can move freely through the lattice. These electrons are called conduction electrons and are responsible for electrical conductivity of metals. Their energies are in another band known as the conduction band that has higher energy level than the valence band. Electrons from the valance band must be excited or energized to move them to the conduction band. The difference between the energy at the bottom of the conduction band and the energy at the top of the valence band is called the band-gap energy of the element. This level of energy is specific to a particular element and crystalline structure. Therefore, the band-gap energy is defined as the amount of energy required to dislodge an electron from its covalent bond. These electrons can be harvested to generate electricity by completing an electrical circuit. No electrons can have energies between the highest energy level in the valence band and the lowest energy level in the conduction band: this band is often called a forbidden band of energies. Conducting metal may not have this forbidden band, whereas semiconducting materials, such as silicon, may have few electrons in the conduction band. The characteristics of insulators, semiconductors, and conductors are shown in Fig. 2.40.

Crystalline silicon is mainly used in PV cells. The behavior of the silicon semiconductor when exposed to sunlight is explained in Fig. 2.41. A number of other semiconducting materials have been developed or are under development, however, the basic working principles of all these materials are the same.

Pure silicon crystal cannot be used directly to make PV cells. Pure silicon crystal is first changed to either an n-type or p-type semiconductor. An n-type silicon semiconductor is obtained by doping pure silicon with Group V elements

Semiconductor Conductor

(Hie thermal energy (There is no band gap.

can bridge the band gap The valance band between the valance overlaps the conduction

and conduction bands band)

for a small fraction of electrons).

Fig. 2.40 Energy bands of insulators, semiconductors, and conductors

Conduction band

of the periodic table: phosphorous (P), arsenic (As), or antimony (Sb). Among these elements, phosphorous is most widely used. The purpose of n-type doping is to produce an abundance of mobile or “carrier” electrons in the material. The purpose of p-type doping is to create an abundance of holes. This is done by doping silicon with a group III element of the periodic table, such as boron or aluminum, which is substituted into the crystal lattice. Other important aspects of creating PV cells are the formation of a p-n junction. A p-n junction in silicon is created from a

• •

Fig. 2.42 Structure of doped silicon (a) n-type: doped with phosphorus (b) p-type: doped with boron (Reprinted with permission from Exell RHB [226]) single crystal with different dopant concentrations diffused across it. Creating a semiconductor from two separate pieces of material introduces a grain boundary between them which would severely inhibit its utility by scattering the electrons and holes. The p-n junction of silicon solar cells is made by diffusing an n-type dopant into one side of a p-type wafer (or vice versa). The crystal structures of silicon following doping with phosphorous and boron are shown in Fig. 2.42.

Often, a PV cell needs to be tuned to maximize the capture of photon energy. Special electrical properties of the PV cell—a built-in electric field—provide the voltage needed to drive the current through an external load. There are two main mechanisms for charge carrier separation in a solar cell:

• Drift of carriers, which is driven by an electrostatic field established across the device. In p-n junction solar cells, the main mode of charge carrier separation is by drift.

• Diffusion of carriers, which is due to the concentration gradient of charges between zones of high and low carrier concentration.

The current and voltage generated in a solar cell depend on a host of factors. To calculate the current and voltage from solar cells, an equivalent electrical circuit shown in Fig. 2.43 may be considered.

The output current (I) from a solar cell is given by:

I = Ip — Id — Ish (2.2)

where, IP = photon generated current due to photoelectric effect

ID = diode current ISH = shunt current

The diode current, assuming an ideal diode, can be expressed by the Shockley diode equation as:

Id = lo^e^T – ^ (2.3)

where I0 is the saturation current of the diode, q is the elementary charge (1.6 x 10_19C), к is the Boltzmann constant (1.38 x 10_23J/K), T is the cell temperature in Kelvin, and VD is the measured cell voltage that is either produced (power quadrant) or applied (voltage bias).

The shunt current is given by:

where, Rsh is shunt resistance. The output voltage (V) from the cell is given by

V = Vd – IRs (2.5)

where, VD is voltage across both the diode and the shunt resistor, and Rs is the load shown in Fig. 2.42.

Substitution of Eqs. 2.3-2.5 into Eq.2.2 provides

q(V CIRs) V + IRS

I = Ip – Io [e-^- – 1j – —R s (2.6)

A typical I – V curve represented by Eq. 2.6 for a semiconductor when illuminated is shown in Fig. 2.44.

Many performances related parameters for the cell can be determined from this I – V curve. These are discussed below.

Fig. 2.44 A typical I – V curve for a solar cell. (VOC: open circuit voltage, Isc: short circuit current)

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