6.1 Basics of Solar Radiation and Conversion in PV Cells
The solar spectrum outside the earth’s atmosphere has a power density of 1,300 W/m2; this is called the “solar constant”. The energy distribution for the photons (energy per wavelength and area) is shown in Fig 6-1 and resembles the radiation of a black body radiator with a temperature of 6,000 Kelvin – the temperature at the surface of our sun. The visible part of the spectrum from about 400 nm (ultraviolet) up to about 700 nm (red) is only a small part of the complete spectrum. The relationship between energy, frequency and wavelength for a photon is described by
E = h v= h c/ X
with E the energy of the photon, h Planck’s constant, v the frequency, c the light velocity and X the wavelength.
Entering the atmosphere, some absorption of light takes place due to water vapor and other molecules and aerosols in the air. The absorption bands at the various wavelengths of H2O (900, 1,100, 1,400, 1,900 and 2,500nm), O2 (750nm), O3 (250nm), and CO2 (2,050nm) are indicated and result in the decrease of the yellow area down to the red one. This decreases the power of the sunlight which is coming from the outside of the atmosphere. If the sun is in the zenith (perpendicular to the earth surface at noon), that is then the minimum path of the photons through the atmosphere and called “airmass 1” (AM 1, see also Figure 6.1 on the left). All other times, the photons travel a longer distance through the air making a pathway of 1.5 or 2 times the minimum distance (AM 1.5 and AM 2, respectively) which leads to the spectra also shown in Figure 6.1. The integral below the AM 1.5 spectrum which is taken as the standard spectrum for comparison purposes, is about 1,000 W/m2.
The challenge now is converting most of the spectrum into useful electricity through PV solar cells. Typically solar cells consist of a semiconductor, characterized by a so-called band gap (Eg). The energy levels of the ensemble of electrons responsible for forming a crystal out of the individual atoms are characterized by the so-called valence band. If a photon possesses energy just equal to the band gap, this photon can be absorbed by the electron and kicked out of the binding site up into the so-called conduction band, where it can move freely in the semiconductor material. Is the energy of the photon smaller than Eg, this light particle passes through the semiconductor material without absorption. However, if the energy is larger than Eg, the excess energy is transformed into heat (thermalized) and cannot contribute to the electric power generation of the solar cell.
This has an important consequence as shown in Figure 6.2(left) in the case of silicon, with a band gap of 1.1 eV (corresponding to a wavelength of 1,100 nm). All photons with longer wavelengths are lost, because their energy is smaller than the band gap (grey part in picture 6-2 to the right of the red curve). All photons with greater energy than the band gap (grey part in picture 6-2 above the red curve) will lose that part of their energy which is above the band gap, as it is thermalized (lost as heat). Only the red part of the curve can be utilized as useful energy while the remaining grey part is lost when silicon is used as a semiconductor material.
Different semiconductor materials have different band gaps as shown in Figure 6.3. The energy output of a solar cell is given by the product of the
short circuit current Isc (proportional to the number of photons absorbed), the open circuit voltage UOC (a function of the band gap of the semiconductor material) and a so-called fill factor (mostly dependent on losses caused by series and parallel resistances in the real device). If we take a material with a small band gap (small UOC), most of the spectrum is absorbed (high ISC).The other extreme, material with a high band gap (big UOC) will only absorb a small part of the spectrum (low ISC). The obtainable efficiency n (in %) is calculated as the quotient of the energy output of a solar cell (ISC x UOC x FF, where the Fill Factor FF is a device dependent constant) divided by the full solar power (AM 1.5) on the same cell area. The efficiency as function of the band gap is shown in Figure 6.3 where a clear maximum can be seen for semiconductor materials with a band gap of around 1.5 eV.
If we wish to extract more from the solar spectrum than in the silicon case, we have to use two or more materials with different band gaps, as is shown in Figure 6.2 (right) for a three band gap device. One can see that we not only absorb most of the spectrum and increase the open circuit voltage of the device (depending on the number of junctions used, here it is 3), but that there is also much less thermalization, as can be seen by the much smaller remaining grey part above the respective colored areas compared to the silicon case in 6-2 (left).
After the absorption of a photon by a binding electron and the electron being lifted up to the conduction band, there is now a vacancy in the valence band, also called a hole, which acts as a positive charge. If nothing else happens, the electron from the conduction band will fall back into the hole, thereby giving up the energy as heat or radiation. Therefore, we have to create something to separate the two opposite charges, the negative electron and the positive hole. The most appropriate method for this is an asymmetry built into the PV cell by doping the pure semiconductor material on one side positively and negatively on the other by replacing only few silicon atoms with other suitable ones.
Again, we use silicon as a demonstrator. If we replace some of the silicon atoms with boron, which has only three electrons in the outer shell, there are positive holes created in the valence band of the crystal (p-type conducting silicon). If we alternatively exchange some of the silicon atoms with phosphorous, which has five electrons, the result will be excess electrons (n-type conduction) via the conduction band. If we now dope a silicon crystal from both sides differently this results in an asymmetric transport structure: the two differently doped regimes of the crystal act (besides of the photon absorption) like selective transport membranes of the positive and negative charge carriers, respectively. This results in a collection of the photo-generated electrons at the n-doped side of the crystal and the collection of holes at the p-doped side. Thus a voltage is created between the opposite sides of the solar cell. The equilibrium energy of the charge carriers (electrons and holes) in undoped silicon, called Ef (Fermi energy), is located in the middle of the energy gap Eg, while for doped materials the Fermi energy moves nearer to the conduction band (n-doping) or to the valence band (p-doping), respectively (see Figure 6.4). If we bring the two doped semiconductor materials in contact with each other, the Fermi energy under no illumination must have the same level in the two doped materials as seen in the right side of Figure 6.4. It is this asymmetry which causes the separation of the light induced electron-hole pairs. There is – not intended for physicists – a simplified and descriptive picture for the flow of electrons to the contact material on one and holes to the other side of contact material of the solar cell. The flow of electrons can be seen like marbles rolling downwards, pulled by gravity, while the positive holes in contrast – like gas bubbles in water – follow the upwards gradient caused by the asymmetry.
Technology development is now all about finding the most suitable materials, cell architectures and manufacturing processes in order to very effectively fulfill and meet the physical boundary conditions described in a cost effective manner. The first solar cell was developed in 1954 by Chapin, Fuller and Pearson at the Bell Labs in the US [6-1], using silicon wafer and semiconductor know-how. Since then, we have seen a fantastic development from first cell architectures as seen in Figure 6.5 towards more sophisticated high efficiency ones which will be described later.
Figure 6.4 Undoped (left), n – and p-type doped Silicon (2nd and 3rd column) and pn-junction (right) under non illumination with associated band energy diagrams (top).
Contact ~10 pm
The basic cell design in the 70/80s was based on Czochralski wafers. The bulk crystal is normally p-doped with boron. A pn junction was formed in a diffusion furnace. During this process phosphorous accumulates within a thin layer of several hundred nm which then becomes negatively doped (overcompensation of the initial boron doping) and becomes the negative terminal of the solar cell. This thin layer is called emitter while the positive bulk material is called base and the rear side is the positive terminal. Contacts were formed as a grid on the front and as a whole area covering contact on the back. An Anti-reflective coating (AR-coat) was applied with a thickness of about 100nm.