2 Basic Principles of Photovoltaics
2.1 Solar Radiation
2.2 Solar Energy Converters
2.3 Performances of a PV cell
2.4 Work from a PV cell
2.5 Effects of band gap and spectrum

2 Basic Principles of Photovoltaics

As the heading is telling, this section will focus on basic function of photovoltaics. This includes how the solar resource works, types of solar energy converters, the principle of detailed balance, work available from a PV cell and its efficiency.

2.1 Solar Radiation

To a good approximation, the Sun acts as a perfect emitter of radiation at a temperature close to 5800 K, and thus considered as a black body. The Sun emits electromagnetic light in various wavelengths:

  • UV (<400 nm)
  • Visible (400-800 nm)
  • Infrared (>800 nm)
Figure 2.1 shows the solar irradiance outside the earth's atmosphere, denoted by AM0, and at sea level, denoted by AM1.5.

Figure 2.1 The solar spectrum. Hence the temperature for the black body, which is 5523 K in this case.

As the solar radiation passes the atmosphere, a part of the incident energy is removed by absorption or scattering by molecules, clouds and aerosols. Wavelengths less than 300 nm is filtered out by molecules like ozone, nitrogen and oxygen. Dips in the infrared area are caused by water and CO2.

Did you know...

...that Earth receives more energy from the Sun in just one hour than the world uses in a whole year?




If the surface temperature on a black body is the same everywhere, the spectral photon flux normal to the surface is

(2.1)
Fs is a geometrical factor, and is equal to π just at the surface of the black body. Away from the surface, the angular range is reduced and
(2.2)
On the earth Fs is reduced by a factor of 4.6 · 104, to 2.16 · 10-5 π.

The total emitted power density is

(2.3)
where σs is Stefan's constant:

At the sun's surface this power density is 62 MW/m2, and at a point just outside the atmosphere the power density has shrunk to 1353 W/m2 because of the reduced angular range of the sun.

2.2 Solar Energy Converters

There are mainly three kinds of solar energy converters

  • The photovoltaic converter
  • The solar thermal converter
  • The photochemical converter

2.2.1 The Photovoltaic Converter

The photovoltaic converter transforms the photon energy into electrochemical potential energy. To prevent the excited electrons from falling back into their ground state, there is some built-in asymmetry that pulls the excited electrons away before they can relax. The extra energy of the excited electrons generates a potential difference, Δμ, and it is this force that drives the electrons into the external circuit and exerts work. The excited state (conduction band) and ground state (valence band) are separated by an energy gap, also called band gap. The band gap's function is to maintain the excited electrons at the high energy for a long time compared to the thermal relaxation time, so that they can be collected. Note that electrons in each of the different bands relax to form a QTE with a different QFL.

Figure 2.2. A photon (yellow) excites an electron (blue) to a higher energy and is pulled away by some mechanism of charge separation.

For a two band system, the Gibbs free energy represents the increase in electrochemical potential energy:

where N is the number of promoted electrons, and Δμ is the difference in potential energy between excited and ground state population.

In equilibrium, Δμ is zero. Thus, a ground state that is full initially and an excited state that is empty, would give the best outcome in extraction of energy. This is one of many reasons why semiconductors are beneficial among all the selections of materials.

You might think that solar cells cope well with increased temperature since they in fact are solar cells. But the truth is that increased temperature can decrease the efficiency of photovoltaic conversion. The most significant is the temperature dependence of the voltage which decreases with increasing temperature. The temperature variation of the current or the fill factor are less pronounced. The voltage decrease of a silicon cell is typiclly 2.3mV per °C. Thus they are designed to be in good thermal contact with the ambient.

Figure 2.3: This is an illustration on how the voltage will decrease with increasing temperature of the cell.

2.2.2 The solar thermal converter

In a solar thermal converter, radiation absorbed is converted into internal energy and the temperature of the cell is raised. Because of the difference in temperature between the cell and the surroundings, the cell can now act as a heat engine and do work. In order to maximize the working temperature difference, the cell is thermally insulated from the ambient.

2.2.3 Photochemical energy converter

A photochemical energy converter works almost exactly like a photovoltaic energy converter, the only difference is that instead of converting the energy directly into electricity, the energy results in a permanent increase in chemical potential.

2.3 Performances of a PV cell

The principle of detailed balance is utilised when describing the performance of a photovoltaic cell. As the solar energy converter absorbes the radiant energy, it also emits thermal radiation to its surroundings. The ratio between absorbtion and emission must be equal so that in the steady state the concentration of electrons in the cell remains constant.

2.3.1 In equilibrium

Consider a cell in the dark and in thermal equilibrium with the ambient, which radiates like a black body, then the equivalent current density absorbed from the ambient is

(2.4)
where a(E) is the probability of absorption, the absorptivity, of a photon of energy E, and R(E) is the probability of photon reflection.

Let us take a look at some collectors of area A:

  • If the rear surface of the cell is in contact with air, the total equivalent current is
  • If the rear surface of a cell is in contact with a material of higher refractive index, ns, the total equivalent current is
  • If the rear surface acts as a perfect reflector (capable of reflecting thermal photons), the totalt equivalent current for absorbed thermal photons is
In the last case the device efficiency is greatest.

Emission of thermal photons by spontanious emission is necessary to maintain a steady state. If ε is the emissivity, the equivalent current density for photon emission through the surface of the cell is

(2.5)

Steady state is maintained if (2.4) and (2.5) are balanced: ε(E)=a(E)

2.3.2 Illumination

The equivalent current density for photon absorption under illumination is given by

(2.6)
Under illumination the system develops a chemical potential, Δμ > 0. This results in increased spontanious emission as more excited electrons causes more relaxation events. The photon flux emitted normal to the surface
(2.7)
where
(2.8)
n0 is the refractive index of the ambient. If ε again is the probability of photon emission, the equivalent current density for photon emission is
(2.9)
The net equivalent current density is then
(2.10)

2.4 Work from a PV cell

2.4.1 Photocurrent and dark current

We now have sufficient information to calculate the absolute limiting efficiency of a photovoltaic converter. Assuming perfectly non-reflecing absorbing material, all incident photons of energy E > Eg are absorbed, and perfect charge separation, no radiative recombination, the maximum photocurrent for a given band gap is

(2.11)
Notice that the photocurrent is a function only of the band gap and the incident spectrum. The lower Eg is, the greater Jsc will be.

Current that flows through the photovoltaic device when a bias voltage is applied in the dark is called dark current. The output current J(V) is equal to the difference between the light-generated current Jsc, and the diode current Jdark(V).

As V increases (larger Eg), the emitted flux, which is concentrated on photon energies near Eg, will increase and thus result in a decrease of the net current. Note that, under open circuit, when J(V) = 0, all the light-generated current passes through the diode. Under short circuit (V = 0), all this current passes through the external load. The upper limit on the voltage is V = Eg/q. This means that Voc must always be less than this in order to avoid being a light emitting device.

2.4.2 Limiting efficiency

If it is assumed that no potential is lost through resistance anywhere in the circuit, all collected electrons should have Δμ of electrical potential energy and deliver Δμ of work to the external circuit. Since Δμ = q V, the power conversion, based on P = V J(V) from (1.3) and J(V), is

(2.12)
and with maximum efficiency when
(2.13)

2.5 Effects of band gap and spectrum

Given the earlier assumptions, and with a fixed incident spectrum, η depends only on the band gap. If the band gap is very small, the working value of V would be too small. If it is very large, the photocurrent would be too small. For the standard AM1.5 solar spectrum, the maximum η is around 33% at an Eg about 1.4eV.

Figure 2.4: Limiting efficiency for a single band gap solar cell in AM 1.5

List of band gaps

Material Band gap (eV)
crystalline Si 1.12
amorphous Si ~1.75
CdTe 1.45
GaAs 1.42
CdS 2.4


The spectrum of a 5760 K black body shows a limiting efficiency around 31% at an Eg about 1.3eV outside the Earth's atmosphere (AM0). By reducing the temperature of the radient source (more reddish), the optimal energy gap and efficiency decrease. Similarly, by increasing the temperature of the source, optimal energy gap and efficiency both increases. In the case where Ta (ambient temperature) is zero and the black body temperature is 6000K, the optimum V is Eg/q, which gives a maximum efficiency around 44% at a band gap of 2.2eV.

Another way of improving the effiency through the spectrum is by concentrating the light, so that absorbed flux will increase relative to the emitted flux. For light concentrated by a factor of 1000, a limiting effiency around 37% at Eg about 1.1eV is predicted. And as for a concentration up to 4.6 · 104 (the maximum), η is over 40%. But these estimates ignore the fact that under high concentration the cell will be heated, and emit more strongly.