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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

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

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

p-n junction diode as solar cell

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

Equivalent circuit of 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.
I-Y characteristics of an ideal (1Ц = 0 and R = oo) solar cell

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

I-Y and P-V characteristics of a 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).

It is evident that the power (P ) obtained by a solar cell depends on the intensity of the light which is known as irradiance (W/m2). As the irradiance increases, the number of photons available to generate hole-electron pairs also increases. This essentially increases the current as a greater number of charge carriers are available. The short circuit current (Isc) has linear relation with the irradiance. This means that, if the intensity is doubled, the short circuit current also doubles. The I-Y and P-V characteristics of a solar cell at various irradiance levels is shown in Figure 7. Figure 8(b) also shows P-V characteristics of a solar cell at different irradiances. The open circuit voltage (Voc) primarily depends on the band gap of the semiconductor material used to make the solar cell. Therefore, open circuit voltage does not have a strong dependence on the in adiance. Marginal increase of the open circuit voltage occurs due to low or moderate increase of in adiance as the photo-generated population of the electrons and holes increase in the conduction and the valence bands, respectively; higher energy levels are now being occupied by these carriers, resulting in an overall increase of their potential energy. In Concentrated Photovoltaic (CPY), where the light intensity is very high (> 100X), this effect is prominent. Significantly more Voc can be obtained at concentrated light as compared to normal (IX) inadiance. The efficiency of CPV is, therefore, higher. As the irradiance is much higher for CPV, the heating of the solar cell becomes a major issue. Additional cooling arrangements should be made to keep the temperature of the solar cell under control.

The temperature effect is very prominent in solar cells. Flowever, in this case, the current is ahnost immune to temperature change. At a fixed inadiance, the ament generated by a solar cell mainly depends on the band gap of the semiconductor material used. The effect of the temperature on the band gap is not significant. In fact, there is a small decrease of the band gap as the temperature increases. Therefore, there is a small increase in the current as temperature increases. The open circuit voltage has strong dependency on the temperature. There is a significant reduction of the open circuit voltage as the temperature increases, see equation (4). This happens due to an increase in the current (ID) through the diode as the Is increases with the temperature. An additional voltage drop occurs in the diode due to this increased current, resulting in an overall voltage drop across the load. The I-V and P-V characteristics at various temperatures are shown in Figure 8. Temperature co-efficient value (T.C. = ДX/ ДТ) of a particular parameter (X) captures the change (ДХ) of that parameter due to a certain change in temperature (ДТ). The temperature co-efficient of voltage ('oc) is denoted as (3. Typical value of p for c-Si technology is -0.36%/°C. The negative sign indicates that the VQC decreases as the temperature increases. The temperature coefficients of ament (Isc) and power (P ) are denoted as a and y, respectively. For c-Si technology, typical values for a and у are +0.05%/°C and -0.4%/°C, respectively. a-Si and CdTe technologies have lower temperature coefficients. CIGS technology, on the other hand, has comparable temperature coefficients to c-Si technology.

As the output of a solar cell varies due to the change of the irradiance and the temperature, it is important to define a Standard Test Condition (STC) for generating specifications. As described earlier,

I-Y and P-V characteristics of a solar cell at different irradiance

Figure 7. I-Y and P-V characteristics of a solar cell at different irradiance.

(a) P-V characteristics of a solar cell at different temperature, (b) P-Y characteristics of a solar cell at different irradiance and (c) I-V characteristics of a solar cell at different temperature

Figure 8. (a) P-V characteristics of a solar cell at different temperature, (b) P-Y characteristics of a solar cell at different irradiance and (c) I-V characteristics of a solar cell at different temperature.

the solar spectrum and the angle of incidence of the incoming light also changes the output. The solar spectrum is somewhat different at AMO, AMI and AMI.5 conditions. The STC for solar cell testing is defined as 1000 W/m2 irradiance in AM 1.5 spectrum falling normal to the cells haring a temperature of 25 °C.

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