Technical Article

What is an Open-Circuited P-N Junction?

June 14, 2021 by Lorenzo Mari

In this “semiconductor basics” series, we’ll learn about the properties of the P-N junction with no external power applied.

A p-n junction is a boundary or interface between two types of semiconductor materials, p-type and n-type, in a semiconductor crystal. Electrons are the majority carriers on one side, and holes are the majority carriers on the other. The p-n junction puts the diode into practice, plays the main character in the operation of the bipolar junction transistor (BJT), and is vital to study the MOSFET functioning.

Diodes. Image courtesy of Pixabay.

Diodes. Image courtesy of Pixabay.


Representation of P-type and N-type Materials

Figure 1 shows two pieces of semiconductor material, like silicon. The p material incorporates a tiny percentage of atoms with a valence of +3, like boron, aluminum, or gallium. The circles with the negative signs are the acceptor atoms; the minus sign is an acceptor ion because it becomes a negative ion after accepting an electron – a bound negative charge. Associated with each acceptor atom is a hole, represented by a positive sign.



An acceptor atom is an atom that substitutes for a regular atom of the material but has one less valence electron.

The positive sign inside a square represents an even smaller percentage of intrinsic atoms with lost electrons due to thermal agitation (thermal ionization) or photoemission. The negative sign inside a square symbolizes the free electrons released.

The n material includes a tiny percentage of atoms with a valence of +5, like phosphorus, arsenic, or antimony. The circles with the positive signs are the donor atoms; the plus sign is a donor ion because it becomes a positive ion after donating an electron – a bound positive charge. The negative symbols represent the free electrons due to the donor atoms.



A donor atom is an atom within a ligand that is bonded to the central atom or ion within a coordination complex.

As in the p material, the intrinsic atoms make some electron-hole pairs. The electrons are the negative sign in a square, and the holes are a positive sign in a square.

Bound charges cannot move through the crystal because the atomic nucleus is tightly bound in the lattice by the covalent bonds.

Both pieces of material, p-type and n-type, are electrically neutral.

Figure 1. p-type and n-type materials.
Figure 1. p-type and n-type materials.


Majority Carriers and Minority Carriers

The holes in the P material and the free electrons in the N material are the majority carriers. The few free electrons produced in the p material and the few holes created in the N material by thermal agitation, photons, and other causes (designated with signs inside squares in figure 1), are the minority carriers.


The P-N junction

Having N-type and P-type crystals at hand, it is possible to make a p-n junction simply by pressing them mechanically. However, such a process will render poor results since it is not suitable for making the tiny junctions used in semiconductor electronics. The best way to get a p–n junction is doping one side of a single semiconductor piece to be n-type and doping the other side to be p-type. It involves introducing acceptor impurities into one side and donor impurities into the other side of a single semiconductor crystal.


The P-N Junction Without an External Voltage

A charge redistribution occurs after connecting the two pieces of semiconductor materials. Figure 2 shows the conditions existing in a P-N junction before the application of any potential. Holes are the dominant carriers on the p-type side – contributed by acceptor atoms – and electrons on the n-type side – contributed by donor atoms.

Bound negative charges associated with acceptor atoms in the crystal lattice neutralize the holes’ positive charge. The P-type side also contains a few free electrons arising from thermal agitation or photoemission.

Similarly, bound positive charges associated with the donor atoms neutralize the electrons’ negative charge in the N-type side. Thermal agitation or photoemission creates a few holes in the N-type side.

Figure 2. The P-N junction with no applied voltage.
Figure 2. The P-N junction with no applied voltage.


The Diffusion Current

Diffusion is a mechanism by which carriers may move within a solid and cross the junction. The diffusion process’s fundamental idea is that particles will flow from heavily concentrated regions to neighboring zones based on their random thermal motion.

Due to the high hole concentration on the P-type side compared to the n-type side, some holes diffuse through the junction into the n-type side. After crossing the junction, the holes find a region populated by free electrons and recombine immediately. Likewise, some of the free electrons in the N-type side diffuse to the p-type side and recombine with the extra holes. It is interesting to note that neither carrier penetrates profoundly into the other’s domain.

The two current components that cross the junction combine to establish the diffusion current (Id). The diffusion current direction is from the P-type side to the N-type side, as shown in Figure 2.


The Space-charge Layer

The carrier’s recombination on both sides of the junction creates a zone with few carriers named the carrier-depletion region. All over the N-type side and P-type side charge carriers neutralize the bound charges related to the ionized impurity atoms. But there are no carriers to neutralize the bound charges in the carrier-depletion region. Then, these bound charges – called uncovered – create a dipole layer of charge at the junction. Another name for the carrier-depletion region is the space-charge layer.

As a result of this process, the P-type side assumes a net negative charge, and the N-type side takes a net positive charge.

Figure 3 shows the general shape of the charge density ρ. The space charge density is zero at the junction, positive to the right and negative to the left.

Figure 3. Charge density ρ.
Figure 3. Charge density ρ.


Outcome of the Dipole Layer

The dipole layer – created by the diffusion process – establishes an electric field from right to left, as indicated in Figure 2. The positively charged N-type side charges attract the electrons and, similarly, the negatively charged P-type side draws the holes, counteracting the diffusion process. Figure 4 shows the negative electric field intensity Ɛ created by the electric lines of flux.

Figure 4. Electric field intensity Ɛ.
Figure 4. Electric field intensity Ɛ.


The field intensity curve is proportional to the integral of the charge density curve shown in Figure 3.


The Junction Contact Potential

The electric field produced by the dipole layer generates a potential difference of V0 across the junction. All electrically dissimilar materials in contact make this potential difference – named contact potential difference or contact potential. This potential difference is a few tenths of a volt at room temperature – typical values for the contact potential across a silicon p-n junction range between 0.6 and 0.9 V.

The potential difference across the junction (V0) does not appear between the external wires connected to the semiconductor because it is impossible to draw energy from the junction. A contact potential exists in both of the external contacts. These contact potentials cancel the contact potential across the junction, and there is no potential difference between the wires.


The Potential Distribution

The electrostatic potential variation is the negative integral of the function Ɛ depicted in Figure 4. Figure 5 shows the electrostatic potential variation for a hole (positive charge), and Figure 6 shows the variation for an electron (negative charge).

Figure 5. Electrostatic potential for a hole.
Figure 5. Electrostatic potential for a hole.

Figure 6. Electrostatic potential for an electron (Potential-energy barrier).
Figure 6. Electrostatic potential for an electron (Potential-energy barrier).

The Potential-energy Barrier

The electric field across the space-charge layer applies forces on the charged particles in a direction to move the holes toward regions of lower potential and the electrons toward regions of higher potentials. These forces oppose the diffusion of holes and electrons.

Those holes and electrons that can cross the space-charge layer against the field force gain potential energy of W=q∙V0. Therefore, only those carriers with kinetic energies higher than W perpendicularly to the junction will cross the space-charge layer. This kinetic energy is the thermal motion energy.

The larger V0, the lesser carriers will have the kinetic energy needed, reducing the diffusion current’s magnitude. This phenomenon is a potential-energy barrier, or a potential hill, in the space-charge layer opposing the carrier’s diffusion across the junction.  That being the case, the diffusion current depends on the barrier’s height, the barrier’s height depends on the space-charge layer’s field strength, and the latter depends on the amount of uncovered bound charge.

Figure 5 shows the potential energy barrier against further diffusion of holes through the junction, and Figure 6 shows the barrier against the electrons flow. The curves are inverted due to the opposite charge polarity of holes and electrons.


The Drift Current

Some of the minority carriers coming from thermal ionization diffuse to the edge of the space-charge layer and find the electric field. This field rushes them across the layer – the holes in the N-type side move into the P-type side and the electrons in the P-type move into the N-type side of the junction. These two current components add up to generate the drift current (Is). The drift current direction is from the N-type side to the P-type side, as shown in Figure 2.

The drift current is independent of the hill’s height, and the minority carriers travel down the hill through the barrier, adding kinetic energy in crossing the junction. The drift current magnitude depends on the minority carriers’ generation rate and increases exponentially with temperature.


The Equilibrium Condition

Since the majority carriers’ diffusion creates the potential hill, the minority carriers swept through the junction reduce the hill’s height. The equilibrium condition occurs when the flow of majority carriers equals the flow of minority carriers and Id=Is. This conclusion is rational because, with the p-n junction terminals open-circuited, the current flowing into the device is zero. Then, the net current across the junction must be zero, which is an equilibrium condition.


Injection Current and Saturation Current

Other names employed are injection current for the current resulting from the diffusion of the majority carriers and saturation current for the current coming from the minority carriers.



The N-type and P-type semiconductor materials are neutral before making the junction.

After making the junction, the N-type side loses electrons and gains holes due to diffusion. As the electrons enter the P-type side, they recombine with the profuse holes. The hole population next to the junction is depleted as many electrons fill the holes. Wherever an acceptor atom exists on the P-type side, the holes are filled, and negative ions arise.

Likewise, holes traveling from the P-type to the N-type side recombine with the free electrons near the junction. Wherever a donor atom exists on the N-type side, the free electrons are depleted, and positive ions arise.

Consequently, the N-type side becomes positive, and the P-type side becomes negative. They create an electric field at the junction strong enough to inhibit the diffusion process of electrons and holes.

The electric field generates a potential difference across the space-charge layer. The flow of current in an external circuit is not possible because the contact difference of potential at the junction and the contact difference of potential at the outer wires add up a total emf of zero in the closed circuit. No external current exists under open-circuit conditions, then Id=Is.

The space-charge layer’s potential difference acts as a barrier. This barrier must be surmounted for holes to diffuse into the N-type side and electrons to diffuse into the P-type side. Therefore, the majority carriers must have enough kinetic energy to climb the potential hill while the minority carriers fall down the hill with no kinetic energy required.

The diffusion current Id depends on the voltage drop V0 across the carrier-depletion region. The value of the drift current depends on temperature and is independent of the voltage V0.