The pn junction diode characteristics and operation is closely connected to the behaviour of the carriers in the junction formed at the boundary between the ptype and ntype materials. The pn junction is also the basic building block of a variety of other devices, and the basic techniques used for the analysis of the pn junction can be extended to other problems. Here, we study the currentvoltage characteristics of an ideal silicon pn junction diode.

An ideal diode contains several simplifications to the properties and behavior of a more realistic device, but offers the opportunity to compare results with an analytic expression for the currentvoltage relation. The ideal diode is modeled with the following approximations:
•1D formulation,
•ideal ohmic contacts,
•an abrupt metallurgical junction,
•and no recombination.
Based on these approximations, several key properties of the device can be formulated analytically. These values are used to validate the numerical model.
Builtin Voltage
The builtin voltage for a pn junction, assuming perfect ohmic contacts, is independent of the junction profile. Assuming that the distance between the junction and contacts is sufficient to establish local thermal equilibrium in both the ptype and ntype regions, the builtin voltage Vbi can be determined from the following equation,
where k is the Boltzmann constant, NA is the density of acceptors in the ptype region, ND is the density of donors in the ntype region, and ni is the intrinsic carrier concentration.
Junction Width
When an abrupt junction is formed, the width (W) of the spacecharge layer can be predicted using the full depletion approximation. Using the builtin voltage determined previously,
where ε is the dielectric permittivity of the material. Here, several assumptions about the dopants have been applied:
•the dopants fully ionize
•the junction is abrupt
•the carrier density is neglected in the space  charge layer (NA >> p and ND >> n) which is known as the full depletion approximation.
When one side of the junction is doped more heavily than the other, e.g. NA >> ND, the expression simplifies: the majority of the space charge layer is distributed where the lowest dopant concentration exists.
Diode Current
Based on the carrier injection description of current through a pn junction, and the assumption that recombination can be neglected in the spacecharge layer, the diode equation is derived,
where A is the junction area, and V is the applied voltage, The reverse bias saturation current I0 is expressed in terms of the minority hole concentration pn in the ntype region and the minority electron concentration np in the ptype region. Dn,p is the diffusivity, which is related to the mobility of the electrons and holes according to the Einstein relation,
and Ln,p is the diffusion length,
related to the carrier lifetime (due to recombination) τn,p. When a reverse bias voltage (V < 0) is applied where V is more than a few multiples of kT/q, the diode will reach the reverse bias saturation current I0.
Noting that
,
far from the spacecharge layer in the appropriate region (where the subscripts refer to that region – ntype or ptype) and using the equilibrium relation
we then have
A capacitance can be associated with the pn junction due to the charge build up at the depletion layer,
It can be shown that this capacitance for an ideal pn_junction is :
And When NA >> ND , this expression can be simplified: