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# Photovoltaic Materials and Device

The first- and second-generation solar cells, which are primarily based on p-n junction diodes, are made of semiconductor materials. A part of the solar spectrum falling on the semiconductor is absorbed and electron-hole pairs are generated. They are separated due to the in-built potential of p-n junction diode and are then allowed to flow across a load, generating current and voltage. The number of electron hole pairs generated depends on how great a portion of the solar spectrum is absorbed by the semiconductor. There is a cut-off wavelength (.utoff), which is related to the band gap (E = 1.24/k,utoff) of the semiconductor material. The part of the spectrum having X < X off is absorbed by the semiconductor and the rest (X > Anit off) is not absorbed. The current (Isc) produced by a photovoltaic device is directly proportional to

Figure 2. Ideal (theoretical) efficiency of a photovoltaic device as a function of the band gap of the material. Maximum

efficiency is at a band gap of about 1.45 eV.

the number of holes and electrons generated by the incident light. The semiconductor materials having a higher band gap (lower X ff) intercept only a small part of the spectrum, resulting in a smaller current. On the other hand, the voltage (Voc) generated by the photovoltaic devices depends on the potential energy of the carriers generated. The greater the band gap, the greater the potential energy and, thus, the voltage. It may be noted that the higher energy photons (X > Xcutoff) in the solar spectrum generate higher energy electron-hole pairs. However, they ultimately settle to the band gap energy by losing pail of the energy in terms of heat. In the limiting case; E„ —> 0: Isc —> oo, Voc —> 0 and Power (P) —> 0 and E„ —> oo: Isc —> 0, 'ж* ос and Power (P) —> 0. The efficiency (P0ll/Pm) depends on the total power falling on the material (Pm) and the amount of power converted to electrical energy (Pout). The theoretical efficiency, therefore, has strong dependency on the band gap, as shown in Figure 2.

The ideal efficiency of a solar cell occurs at about 1.4 eV (see Figure 2). CdTe has a band gap close to this value and is, therefore, an ideal choice as a solar cell material. Silicon is an elemental semiconductor having a band gap of about 1.1 eV. Although it is not ideal, this material is preferred due to its other advantages. The band gaps of ternary and quaternary compounds, such as CIGS, GalnAS, GaAlInAs, etc., can be tuned by varying the composition of the elements. It is possible to have the band gap adjusted to the ideal value for such materials and to enhance the theoretical efficiency by tandem or Multi Junction (MJ) solar cells. In this, the p-n junctions made with materials with different band gaps are stacked: the highest band gap material being at the top. The majority of the solar spectrum can then be absorbed and the energy loss due to photons having energy greater than the band gap is minimized.

# Electrical Characteristics of Solar Cells

A solar cell is essentially a p-n junction diode (Figure 3). Electron hole pairs are generated due to incident photons. These are separated and travel in the opposite directions aided by in-built potential present in the depletion region and by concentration gradient. They eventually recombine across the load. The flow of charge carriers across the load results in current and associated voltage drop, depending on the load resistance. The equivalent circuit of the solar cell is shown in Figure 4. Photocurrent IL generated due to light partly flows through the diode (ID) and the rest through the load (I), resulting a voltage drop across the load (V). There are some unwanted resistances; series (Rs) and shunt (Rsh). Resistances of the neutral regions of the semiconductor (see Figure 3) and the contact resistances are responsible for Rs, which is small but finite. There is an additional voltage drop across this resistance, therefore, the effective voltage drop across the load is reduced. The shunt resistance appears due to the resistance of the depletion regions (see Figure 3), and even for a perfectly made p-n junction, the resistance is finite due to the presence of minority earners. Imperfection occurring during fabrication of the p-n junction may reduce the shunt

Figure 3. p-n junction diode as solar cell.

Figure 4. Equivalent circuit of solar cell.

resistance further. There is a current across the shunt resistance reducing the effective current across the load. The ideal is infinite. It is clear that the current and the voltage across the load change as the load resistance (RL) varies. In the limiting cases; Rj_ = 0 (short circuit): I = Isc and V = 0 and ^ = 00 (open circuit): 1 = 0 and V = Voc. Isc and Voc are known as short circuit current and open circuit voltage, respectively. In both the extreme cases, the power (P = V x I) is zero. It can be seen that Isc = IL as the entire photo-generated current IL flows across the load in short cncuit condition. The I-Y characteristics of a solar cell at a particular' irradiance can be obtained by varying the load resistance from zero (short circuit) to infinity (open cncuit). This characteristic is shown in Figure 5.

The current appears in the fourth quadrant, positive V and negative I, indicating negative power. This means that the power is extracted from the system. An ideal I-V characteristic (R„ = 0 and R\$h = 00) is shown in Figure 5. For convenience, the I-V characteristic of the solar cells is drawn (Figure 6) in the first quadrant, with an understanding that the current is negative. The P-V characteristic is superimposed in this figure. Various parameters of the solar cells are defined (see Figure 6) as follows:

• a) Voc: Open circuit voltage w'hen the solar cell is not connected to load (RL —> 00) and the solar cell is open circuited. The current across the load is, therefore, zero.
• b) Isc: Short circuit current when there is no load and the solar cell is short circuited (RL —> 0). The voltage drop across the load is zero.
• c) MPP: Maximum Power Point at which the pow'er is maximum (Pm).
• d) Vm: The voltage at MPP. The power extracted from the solar cell is maximum at this voltage.
• e) Im: The current at MPP. This corresponds to current delivered to the load by the solar cell when the voltage across the load is Vm.
• f) Fill factor = (V x Im)/(V0C x I\$c). This signifies the actual power extracted (V x I ) as against the absolute maximum (VQC x Isc).
• g) q: Efficiency defined by (Pou/Pm) = (V x I )/(Irradiance x Area). The irradiance is defined as power per unit area (W/m2), with the area being measured in m2.

Figure 5. I-Y characteristics of an ideal (1Ц = 0 and Rit = oo) solar cell.

Figure 6. I-Y and P-V characteristics of a solar cell.

The governing equations can be derived from the equivalent circuit (Figure 4).

where Is is the reverse saturation current of the diode, к is the Boltzmann constant (8.6 x 1СГ5 eV/K) and T is the temperature in K. In case an ideal solar cell is assumed (Rs = 0 and RSh = oo), the above equation can be simplified as:

The open circuit voltage (Voc) can be obtained by putting 1 = 0 and V = Voc in equation (4)

For IL »Is,

The short circuit current (Isc) can be obtained by putting V = 0 and I = Isc in equation (4).