# An exponential relationship

Now we can define a diode: A diode is a semiconductor component that contains a pn-junction. The p-type material is called the anode, the n-type material is the cathode. The symbol is shown in the figure below. As described earlier, there will be a current flow possible– in the direction of the arrow of the symbol – if the diode is forward biased, so if the voltage at the anode is higher than the voltage at the cathode. For a reverse bias, there will be no current flow. Roughly stated, a diode is a component that allows current flow in one direction, and no current flow in the opposite direction.

The relation between voltage and current can be derived based on the laws of solid matter physics. Using a relatively simple model of a pn-junction, one can derive the following formula for the relationship between the voltage across and the current through a diode:

Legend | |

I_{D} |
current through the diode |

V_{D} |
voltage accross the diode |

I_{S} |
reverse saturation current, in the order of µA to nA |

η |
ideality factor, varies between 1 and 2 |

k |
Boltzmann constant, equals 1.38 x 10^{-23} J/K |

T |
temperature of diode, in Kelvin |

e |
charge of an electron, equals 1.6 x 10^{-19} C |

The most important thing to remember is that the relationship is exponential: The current increases exponentially with voltage. So, from a certain voltage on, currents can be very large. One of the other parameters in the formula is the reverse saturation current that depends on the used materials, the doping levels and the dimensions of the elements. The value kT/e equals approximately 25 mV at room temperature. A graphical representation is given below.

## The graph

If the voltage is zero, the current is zero. This is logical since there is no other external source of energy, like e.g. in a solar cell^{*}. In forward bias, i.e. for positive voltages according to the convention of Figure 2.12, the current is initially very small, but it increases rapidly once the voltage exceeds the so called **knee voltage**. This voltage corresponds to the voltage needed to eliminate the space charge layer around the pn-junction. Typical values for the knee voltage are 0.7V for Silicon diodes, 0.3V for Germanium diodes, and 1.5V to 2.5V for LEDs.

When reverse biased, there will be a small negative current, the **reverse saturation current**. In practice, this current is very small, and can often be ignored when making calculations. If the negative voltage increases in absolute value, the electric field within the diode can be so large, that **breakdown** occurs. In most cases, this is bad news, and your diode might be destroyed. The well-known exception are Zener diodes, that will be discussed later in this chapter.

## Diode power

If diode voltage and diode current are both non-zero, then the diode dissipates power. In regular diodes this power is converted into heat. In order to prevent destruction, the consumed power should be kept low enough. For most diodes, you can find the maximum rating for the power in the diode’s datasheet. The formula that always works for any component is:

_{D}= V

_{D}x I

_{D}

**Common Misconception **A formula that does not work is P = RI^{2} or P = U^{2}/R. This is Joule’s Law that only works for resistive components. A diode has no value for R.

Figure 2.12, I used to think that the cathode is the positive electrode +. Why it isn’t so?

Because it is not so… It’s the convention.

In chemistry the cathode is the electrode that attracts cations (positively charged ions), so it is the negative one.

In electronics, similar story.

It makes sense, thank you!