# Ideal Diode Equation Derivation

The ideal diode equation is one of the most basic equations in semiconductors and working through the derivation provides a solid background to the understanding of many semiconductors such as photovoltaic devices. The objective of this section is to take the concepts introduced earlier in this chapter and mathematically derive the current-voltage characteristics seen externally. The operation of actual solar cells is typically treated as a modification to the basic ideal diode equation described here.

The derivation of the ideal diode equation is covered in many textbooks. The treatment here is particularly applicable to photovoltaics and uses the concepts introduced earlier in this chapter. For simplicity we also assume that one-dimensional derivation but the concepts can be extended to two and three-dimensional notation and devices.

The objective is to determine the current as a function of voltage and the basic steps are:

• Solve for properties in depletion region
• Solve for carrier concentrations and currents in quasi-neutral regions
• Find total current

At the end of the section there are worked examples.

Semiconductors are analyzed under three conditions:

• Thermal equilibrium - where the device is in the dark an no voltage is applied to the terminals. This step is important as it describes the basic band diagram.
• Steady state - where a constant voltage or light intensity is applied to the device.
• Transient - where the devices are changing with time and so, for example, parasitic capacitances are considered. As solar cells are steady state devices we generally don't consider transient analysis under normal operation. It is sometimes used during characterization.

The ideal diode model is a one dimensional model. The diode itself is three dimensional but the n-type and p-type regions are assumed to be infinite sheets so the properties are only changing in one dimension. The one dimensional model greatly simplifies the equations.