**1. Photovoltaic effect**

A solar cell is a p-n junction diode exposed to light. Light contains photons having energy greater than the energy band gap the inherent semiconductor material can absorb and will generate electron and hole pairs (EHPs). The amount of energy required to move an electron out of the valence band of a silicon atom is called the band gap and is equal to 1.12eV (electron volts). EHPs generated in the neutral layers that is a base on emitter, tend to recombine and lose their energy in other forms. EHPs generated in the depletion zone are also known as the active layer or the absorbed layer will drift in the opposite directions and accumulate in the base and emitter layers under open circuit conditions. Accumulation of these charges result in a potential difference known as photo-voltage and the effect due to potential difference or generation of voltage due to light is known as photovoltaic effect. The voltage measured under open circuit condition is also known as open circuit voltage. Under close circuit condition, electrons move from the point of higher potential energy to the point of lower potential energy from emitter to base and this current due to the flow of electrons is known as the photo-current or the short circuit current [1].

**2. PV cell characteristics and parameters**

**(a) IV curve**

This curve shows that the current is constant for a range of output voltages. The current at which the output voltage is zero is known as the short-circuit current, I_{sc} and the point where current is zero and voltage is maximum denotes the open circuit voltage, V_{oc}.

where

Id is the current flowing through diode,

T is temperature in Kelvins,

k is the Boltzmann constant,

q is the elementary charge in Coulombs,

V is the voltage in volts, and

n is a factor indicating the prevalence of recombination in the depletion layer.

When light is incident, photocurrent, I_{L} is generated and the current flowing out of the loop is given by:

At I_{sc} and V_{oc}, power output is zero. Above the short-circuit point, the PV cell operates with a resistive load and between the short-circuit point and the knee of the IV curve, since current is constant, power output depends only on voltage. Maximum power output occurs at the knee point.

**3. Equivalent circuit**

Under short circuit condition, voltage is zero and photocurrent is the same as the magnitude of the short-circuit current. When light is incident, we apply Kirchoff’s current law (KCL) at node A^{1}. The current, say Iout leaving node A^{1} is given by:

where

A^{1} and B^{1} are the internal terminals for the ideal diode.

K is the device dependent constant and I is the intensity.

A_{n} internal shunt resistance is present due to defects or electron traps which indicate level of losses within the crystals.

Now, we apply Kirchoff’s voltage law (KVL) within the loop A and B.

Apply KCL at node A,

where I_{loss} and I_{RL} are the currents flowing through shunt resistance and load respectively.

Current equation of a solar cell is

**(c) Efficiency and fill factor**

The efficiency of a PV cell is the ratio of the power input to the power output, i.e. the light energy falling on the cell to the light energy that is converted to electrical energy. It is expressed as follows:

where P_{out(max)} is the maximum electrical power output of the cell and is measured when intensity, H = 1 kW/m^{2} (peak rating),

E is the irradiance at the surface of the cell (W/m^{2}) and

A is the surface area of the cell (m^{2}).

The fill factor, FF is the ratio of the cell’s actual maximum power output to its theoretical power output and is expressed as follows:

where V_{MPP} is the maximum power point voltage (V),

I_{MPP} is the maximum power point current (A),

V_{OC} is the open-circuit voltage (V),

I_{SC} is the short circuit current (A).

**(d) Effects of temperature**

Output power of a PV cell depends on temperature. When intensity is constant, the open-circuit voltage decreases as the temperature increases but this does not affect the current significantly. As temperature increases, there is an increase in the intrinsic carrier which increases the generation of charges until the concentration becomes saturated, represented by the saturation current. An increase in temperature causes a reduction of the band gap and energy of electrons is increased in the PV cell. Lower energy is therefore needed to break the bond. V_{OC} is thus the parameter that is most affected as temperature increases. But the most significant effect is due to intrinsic carrier concentration which depends on the band gap energy; with lower band gap, there is a high intrinsic carrier concentration.

**References:**

*[1] “PVEducation.” [Online]. Available: https://www.pveducation.org/pvcdrom.*

*[2] 156x156 mm.” [Online]. Available: https://www.solarinnova.net/en/products/photovoltaic/cells/monocrystalline/156x156mm.*

*[3] “Solar Cell I-V Characteristic | Alternative Energy Tutorials.” [Online]. Available: https://www.alternative-energy-tutorials.com/photovoltaics/solar-cell-i-v-characteristic.html*