**1 Introduction to solar cells**

1.1 Voltage and current

1.2 Equivalent circuit of a solar cell

## 1 Introduction to solar cells

The basic idea of a solar cell is to convert light energy into electrical energy. The energy of light is transmitted by
*photons*, small packets or quantums of light. Electrical energy is stored in electromagnetic fields, which in turn
can make a current of electrons flow. Thus a solar cell converts light, a flow of photons, to electric current, a flow of
electrons.

When photons are absorbed by matter in the solar cell, their energy excites electrons higher energy states where the electrons
can move more freely. The perhaps most well-known example of this is the photoelectric effect, where photons give electrons in
a metal enough energy to escape the surface. In an ordinary material, if the electrons are not given enough energy to escape, they
would soon relax back to their ground states. In a solar cell however, the way it is put together prevents this from happening.
The electrons are instead forced to one side of the solar cell, where
the build-up of negative charge makes a current flow through an external circuit. The current ends up at the other side (or *terminal*)
of the solar cell, where the electrons once again enter the ground state, as they have lost energy in the external circuit.

### 1.1 Voltage and current

Two important quantities to characterize a solar cell are

- Open circuit voltage (V
_{oc}): The voltage between the terminals when no current is drawn (infinte load resistance) - Short circuit current (I
_{sc}): The current when the terminals are connected to eachother (zero load resistance)

The short circuit current increases with light intensity, as higher intensity means more photons, which in turn means more electrons.
Since the short circuit current I_{sc} is roughly proportional to the area of the solar cell, the short circuit current density,
J_{sc} = I_{sc}/A, is often used to compare solar cells.

When a load is connected to the solar cell, the current decreases and a voltage develops as charge builds up at the terminals.
The resulting current can be viewed as a superposition of the short circuit current, caused by the absorbtion of photons,
and a *dark current*, which is caused by the potential built up over the load and flows in the opposite direction.
As a solar cell contains a PN-junction (LINK),
just as a diode, it may be treated as a diode. For an ideal diode, the dark current density is given by

(1.1) |

_{0}is a constant, q is the electron charge and V is the voltage between the terminals. The resulting current can be approximated as a superposition of the short circuit current and the dark current:

(1.2) |

To find an expression for the open circuit voltage, V_{oc}, we use (1.2) setting J = 0. This means that the
two currents cancel out so that no current flows, which exactly is the case in an open circuit. The resulting expression is

(1.3) |

#### 1.1.1 Efficiency

In general, the power delivered from a power source is P = IV, i.e. the product of voltage and current. If we instead use the current density J, we get the power density:

(1.4) |

_{oc}(open circuit) at a voltage V

_{m}. The corresponding current density is called J

_{m}, and thus the maximum power density is P

_{d,m}= J

_{m}V

_{m}.

The efficiency of a solar cell is defined as the power (density) output divided by the power (density) output. If the incoming
light has a power density P_{s}, the efficiency will be

(1.5) |

*fill factor*, FF, is another quantity which is used to characterize a solar cell. It is defined as

(1.6) |

(1.7) |

The four quantities J_{sc}, V_{oc}, FF and η are frequently used to characterize the performance of
a solar cell. They are often measured under standard lighting conditions, which implies Air Mass 1.5 spectrum, light flux
of 1000W/m^{2} and temperature of 25°C.

### 1.2 Equivalent circuit of a solar cell

The solar cell can be seen as a current generator which generates the current (density) J_{sc}. The dark current
flows in the opposite direction and is caused by a potential between the + and - terminals. In addition you would have two
resistances; one in series (R_{s}) and one in parallel (R_{p}). The series resistance is caused by the fact
that a solar cell is not a perfect conductor. The parallel resistance is caused by leakage of current from one terminal to
the other due to poor insulation, for example on the edges of the cell.
In an ideal solar cell, you would have R_{s} = 0 and R_{p} = ∞.

When these socalled *parasitic* resistances are included, the current expression (1.3) becomes

(1.8) |