PROPERTIES OF SEMICONDUCTORS FOR SOLAR CELLS #
In this section, the properties of semiconductors for solar cells will be introduced. Solar cells are made of semiconductors as the active material. To understand the operation of the solar cells and optimize their characteristics, one has to understand thoroughly their material properties because there is a direct relationship between the cell performance and the material properties.
Semiconductors are a class of materials that have electrical conductivity between the metal and insulators. Accordingly, their electrical characteristics can be controlled by doping and by light. They can be classified according to their chemical structure in elementary form such as Si and Ge, in compound form such as AIII BV and AII BVI, or molecular form such as the organic semiconductors or the perovskites which are hybrid metal organic molecules. All semiconductors have common distinguished properties that govern their performance. The major properties controlling their electrical and optical behavior will be discussed in the next sub-sections. The first property is the atomic structures of the materials. It has a large impact on their performance. There are three distinct atomic arrangements for any material:
- Crystalline, where the atoms are perfectly ordered in a three-dimensional array
- Amorphous, where the atoms of the material have random order compared with their original sites in the single crystal
- Polycrystalline, where the material is composed of crystallographic grains joined together by grain boundaries.
Fig. 1.1 shows an illustration of the three possible structures for a semiconductor material. The solar cells made of crystals give the highest efficiency and those made of amorphous materials give the lowest efficiency. But a much thicker layer of crystalline silicon is required to absorb the light (w300 mm) in comparison with a-Si requiring only w5 mm. Therefore, there is a considerable material saving using a-Si.
THE ENERGY GAP EG AND INTRINSIC CONCENTRATION N #
A semiconductor has an electron-filled valence band and an empty conduction band. The two bands are separated by an energy gap Eg. It ranges from few tenths of electron-Volts to few electron-Volts. Silicon has an energy gap of 1.1 eV and GaAs Eg ¼ 1.45 eV. Elementary semiconductors are characterized by saturated covalent bonds as shown in Fig. 1.2, where each atom is bonded to the neighboring atoms by four covalent bonds.
The valence electrons are shared by the neighboring atoms and are bound by the parent atoms. They are locally fixed and are not capable of conducting electricity. To make such materials conduct electricity we have to free valence electrons. This can be done by doing work sufficient to break the bond. This work can be affected by heating, illuminating the material with a suitable light, and doping the material with suitable impurities.
Any semiconductor material works at room temperature, and hence, it contains heat and bonds will be broken thermally. When a bond is broken, it produces a free hole and a free electron. Both are capable of conducting electricity in the material. The minimum energy required to break a bond and generate an electronehole (eeh) pair is called the energy gap. The energy gap separates the free electrons from the free holes as illustrated in Fig. 1.3.
The electrons are in the conduction band, where they occupy their lowest allowed energy states with an effective overall density of Nc, whereas the holes with positive charges occupy the allowed electronic states in the top of valence band with an effective density of states Nv. This is illustrated in Fig. 1.3. If the material is pure and its temperature is T > 0 K, it contains an electron concentration no = ni and a hole concentration po = ni, where ni is the intrinsic concentration with ni is the thermally generated electron-hole pairs. It is related to Eg and T by n2i = NcNv exp( – Eg=/kBT). kBT is the thermal energy = 25.6 meV at room temperature (T = 300 K). For silicon, ni = 1.5 x 1010 cm-3 at 300 K.
DOPING AND CONDUCTIVITY OF THE MATERIAL #
One of the main properties of the semiconductors is the possibility to alter their electrical characteristics by doping. Doping is intentional addition of specific impurities to the material to produce n-type or p-type conductors and change the electron and hole concentration in the material. To produce n-type Si, we add pentavalent impurity atoms to Si such as P and As, whereas for p-type Si, we add trivalent atoms such as B, Ga, and Al to Si. The charge picture after doping is illustrated in Fig. 1.7.
The product of the concentration po and no of any semiconductor at temperature T are given by the relation nopo ¼ n2i , which is called the mass action law. The conductivity of the semiconductor material can be, generally, expressed by
σ = qμnno + qμpPo
where q is the electron charge; μn is the electron mobility; and μp is the hole mobility. So, the conductivity of the n-type material is
σn ≈ qμnno = qμnND
and that of the p-type material is
σp ≈ qμpPo = qμpNA
ND is the donor concentration and NA, is the acceptor concentration. The conductivity increases by increasing the doping of semiconductor according to Eqs. (1.2a) and (1.2b).
THE SEMICONDUCTOR CURRENTS #
If a voltage V is applied across a semiconductor bar with length L and cross-sectional area A, a current will flow in the bar because of the drift of electrons and holes under the influence of the electric field E developed by the voltage V in the bar as shown in Fig. 1.8.
This current follows the ohm’s law for relatively small electric fields, i.e.,
Jd is the drift current density. The mobility m is the ability of the mobile charges to acquire drift velocities in the presence of the electric field.
Another type of current exists in a semiconductor when concentration differences of mobile changes are present. Such current is termed the diffusion current Jdif. This current can be expressed by
where Dn and Dp are the diffusion coefficients for electrons and holes, respectively, andand are the concentration gradients for electrons and holes, respectively. The diffusion coefficient D is related to the mobility by the Einstein equation