Solar cells

Solar cells are typically illuminated with sunlight and are intended to convert the solar energy into electrical energy. The solar energy is in the form of electromagnetic radiation, more specifically "black-body" radiation . The sun’s spectrum is consistent with that of a black body at a temperature of 5800 K. The radiation spectrum has a peak at 0.8 eV. A significant part of the spectrum is in the visible range of the spectrum (400 - 700 nm). The power density is approximately 100 mW/cm2.

Only part of the solar spectrum actually makes it to the earth's surface. Scattering and absorption in the earth's atmosphere, and the incident angle affect the incident power density. Therefore, the available power density depends on the time of the day, the season and the latitude of a specific location.

Of the solar light, which does reach a solar cell, only photons with energy larger than the energy bandgap of the semiconductor generate electron-hole pairs. In addition, one finds that the voltage across the solar cell at the point where it delivers its maximum power is less than the bandgap energy in electron volt. The overall power-conversion efficiency of single-crystalline solar cells ranges from 10 to 30 % yielding 10 to 30 mW/cm2.

The calculation of the maximum power of a solar cell is illustrated by Figure1 and Figure 2. The sign convention of the current and voltage is shown as well. It considers a current coming out of the cell to be positive as it leads to electrical power generation. The power generated depends on the solar cell itself and the load connected to it. As an example, a resistive load is shown in the diagram below.

Figure 1 :

Circuit diagram and sign convention of a p-n diode solar cell connected to a resistive load.

The current and the power as function of the forward bias voltage across the diode are shown in Figure 2 for a photocurrent of 1 mA:

Figure 2:

Current-Voltage (I-V) and Power-Voltage (P-V) characteristics of a p-n diode solar cell with Iph= 1 mA and Is = 10-10 A. The crosshatched area indicates the power generated by the solar cell. The markers indicate the voltage and current, Vm and Im, for which the maximum power,Pm is generated.

We identify the open-circuit voltage, Voc, as the voltage across the illuminated cell at zero current. The short-circuit current, Isc, is the current through the illuminated cell if the voltage across the cell is zero. The short-circuit current is close to the photocurrent while the open-circuit voltage is close to the turn-on voltage of the diode as measured on a current scale similar to that of the photocurrent.

The power equals the product of the diode voltage and current and at first increases linearly with the diode voltage but then rapidly goes to zero as the voltage approaches the turn-on voltage of the diode. The maximum power is obtained at a voltage labeled as Vm with Im being the current at that voltage.

The fill factor of the solar cell is defined as the ratio of the maximum power of the cell to the product of theopen-circuit voltage, Voc, and the short-circuit current, Isc, or:

(1)

Example

A 1 cm2 silicon solar cell has a saturation current of 10-12 A and is illuminated with sunlight yielding a short-circuit photocurrent of 25 mA. Calculate the solar cell efficiency and fill factor.

Solution

The maximum power is generated for: where the voltage, Vm, is the voltage corresponding to the maximum power point. This voltage is obtained by solving the following transcendental equation: Using iteration and a starting value of 0.5 V one obtains the following successive values forVm: Vm = 0.5, 0.542, 0.540 V and the efficiency equals: The current, Im, corresponding to the voltage, Vm, was calculated using equation (.1) and the power of the sun was assumed 100 mW/cm2. The fill factor equals: where the open circuit voltage is calculated using equation (1) and I = 0. The short circuit current equals the photocurrent.