P–N Junction

A p–n junction is the boundary and associated transition region between p-type and n-type regions of a semiconductor. Redistribution of charge carriers near this boundary creates an internal electric field and a potential barrier. An applied voltage changes the barrier and the flow of carriers, allowing the junction to conduct much more readily in one direction than the other. This behavior underlies semiconductor diodes, while carrier injection and collection at p–n junctions also support the operation of transistors, light-emitting devices, and photovoltaic cells. (ocw.mit.edu)

Semiconductor regions and fabrication

In an n-type semiconductor, electrons are the majority mobile carriers; in a p-type semiconductor, holes are the majority carriers. A hole represents an unoccupied electronic state that behaves as a positively charged carrier. Electrons in p-type material and holes in n-type material are called minority carriers. These carrier populations are commonly established by semiconductor doping: donor impurities supply electrons, whereas acceptor impurities produce holes. The labels “p” and “n” describe the dominant mobile carrier, not an overall positive or negative charge of the bulk material, which is approximately electrically neutral. (ocw.mit.edu)

Practical junctions are generally formed by changing the doping within a semiconductor structure rather than by mechanically pressing two pieces together. In silicon processing, dopants can be introduced by thermal diffusion or ion implantation. Subsequent heat treatment redistributes dopants and establishes the junction depth and concentration profile. Implantation damage and its position relative to the eventual depletion region matter because defects can increase junction leakage. (ocw.mit.edu)

Depletion region and equilibrium

When p-type and n-type regions are brought into electronic contact, differences in carrier concentration drive diffusion: electrons move from the n side toward the p side, and holes move in the opposite direction. Carrier redistribution and recombination leave a region with relatively few mobile carriers near the boundary. This depletion region, also called the space-charge region, contains uncompensated ionized dopants: negatively charged acceptors on the p side and positively charged donors on the n side. (ocw.mit.edu)

The fixed charges generate an electric field directed from the n side toward the p side. The field produces carrier drift opposing diffusion. At thermal equilibrium, drift and diffusion currents cancel for each carrier species, so the net electric current is zero even though carriers continue to move microscopically. Outside the depletion region lie approximately charge-neutral, or quasi-neutral, regions. (left.engr.usu.edu)

In an energy-band diagram, the conduction- and valence-band edges bend through the junction, while the equilibrium Fermi level is spatially constant. For a homojunction with nondegenerate carrier statistics, fully ionized dopants, and quasi-neutral regions dominated by their dopants, the built-in potential is

where $k_{\mathrm B}$ is the Boltzmann constant, $T$ is absolute temperature, $q$ is the positive elementary charge, $N_A$ and $N_D$ are acceptor and donor concentrations, and $n_i$ is the intrinsic carrier concentration. Thus, the built-in potential depends on doping, temperature, and semiconductor material. (ocw.mit.edu)

Applied voltage and rectification

The junction voltage $V$ is conventionally defined as the potential of the p side relative to the n side.

• Forward bias, $V>0$, lowers the barrier. Electrons are injected into the p region and holes into the n region, where they become excess minority carriers.
• Reverse bias, $V<0$, raises the barrier and widens the depletion region. Majority-carrier injection is suppressed, but minority carriers reaching the depletion region can still be collected across it.

The resulting asymmetry in current is called rectification. Reverse bias therefore does not imply an exactly zero current. (openlearninglibrary.mit.edu)

For an ideal junction in steady state, the Shockley diode equation is

Here $I_S$ is the reverse saturation current. In the ideal long-base, low-injection model,

where $A$ is junction area, $D_n$ and $D_p$ are minority-carrier diffusion coefficients, and $L_n$ and $L_p$ are diffusion lengths. Forward current rises exponentially with voltage, whereas reverse current approaches $-I_S$ before breakdown. The equation describes a continuous characteristic, not a sharply defined turn-on threshold. (ocw.mit.edu)

Depletion width and capacitance

The depletion approximation neglects mobile charge within the space-charge region and treats the adjoining regions as neutral. For an abrupt, uniformly doped junction, charge balance requires

where $x_p$ and $x_n$ are the depletion widths on the p and n sides. The depletion region therefore extends farther into the more lightly doped side. If one side is much more heavily doped, the structure is approximately a one-sided junction. (ocw.mit.edu)

Solving Poisson’s equation under these assumptions gives the total width

where $\varepsilon_s$ is the semiconductor permittivity. The expression applies while the depletion approximation remains valid: reverse bias increases $W$, while forward bias reduces it. (openlearninglibrary.mit.edu)

Changes in voltage also change the stored space charge, producing a differential junction capacitance. For a planar abrupt junction,

Reverse bias therefore reduces capacitance by increasing the depletion width. Capacitance–voltage measurements can reveal built-in voltage and doping concentration; varying the bias moves the depletion boundary and permits extraction of a doping profile. (left.engr.usu.edu)

Charge storage and switching

Forward injection stores excess minority carriers in the quasi-neutral regions. The voltage dependence of this stored charge gives rise to diffusion capacitance, distinct from depletion capacitance. Diffusion capacitance can dominate under appreciable forward bias, whereas depletion capacitance generally dominates under reverse bias. (archive.nptel.ac.in)

A conducting junction does not necessarily stop conducting immediately when the applied voltage reverses. Stored carriers must first be extracted or recombine, producing a temporary reverse current known as reverse recovery. Recovery depends on minority-carrier lifetime, the preceding forward current, and the external circuit. This dynamic behavior is not contained in the steady-state diode equation. (archive.nptel.ac.in)

Reverse breakdown

At sufficiently strong reverse fields, additional mechanisms produce a large reverse current:

• Zener breakdown involves quantum tunneling through a narrow junction barrier.
• Avalanche breakdown involves impact ionization: accelerated carriers generate additional electron–hole pairs, multiplying the current.

Both mechanisms lie outside the ordinary reverse-saturation behavior of the ideal diode model. (openlearninglibrary.mit.edu)

Junction structures

Junctions differ both in doping profile and in semiconductor composition:

• Abrupt junctions are modeled with a step-like change between p-type and n-type doping.
• Graded junctions have a continuously varying doping profile; their voltage–capacitance relationship differs from that of an abrupt junction.
• Homojunctions use the same semiconductor material on both sides.
• Heterojunctions join different semiconductor materials. Differences in band edges introduce additional barriers and carrier-confinement effects, so the simple homojunction model is insufficient.

Doping-profile design controls depletion and charge storage, while heterojunction design provides additional control over electronic and optical behavior. (archive.nptel.ac.in)

Applications

Rectification and electronic control. A p–n junction with electrical contacts forms a junction diode. In a bipolar junction transistor, coupled junctions allow carriers injected through one junction to be transported through a thin base and collected by the other. Minority-carrier injection is central to this operation. (ocw.mit.edu)

Photodetection and photovoltaics. Absorbed photons can create electron–hole pairs. Carriers generated in the depletion region, or reaching it by diffusion, can be separated and collected by the internal field. This produces photocurrent in a photodiode and enables electrical power generation in a solar cell. Collection competes with recombination, including for carriers generated outside the depletion region. (ocw.mit.edu)

Light emission. In a light-emitting diode, injected electrons and holes can recombine radiatively. The semiconductor band gap and the available recombination processes determine the emitted light and conversion efficiency. Semiconductor lasers also employ junction injection, together with optical feedback and carrier-confinement structures. (ocw.mit.edu)

Historical development

Russell Ohl identified a silicon p–n junction at Bell Telephone Laboratories in 1940. His investigation connected an unusually strong photoelectric response to adjoining silicon regions with different impurity characteristics. The junction provided an important basis for subsequent semiconductor photovoltaic and electronic devices. (ethw.org)

William Shockley conceived the junction transistor in January 1948 and published his theory of p–n junctions and junction transistors in 1949. The theoretical treatment established minority-carrier injection as a central principle of junction-transistor operation and helped turn the p–n junction into a quantitatively understood device structure. (computerhistory.org)

References

1. Lecture 18: The P-N Junction (The Diode)ocw.mit.edu
2. Handout 3: P–N Junctionopenlearninglibrary.mit.edu
3. PN Junctionsleft.engr.usu.edu
4. 012 Microelectronic Devices and Circuits, Lecture 14ocw.mit.edu
5. Diodes in the Darkocw.mit.edu
6. Physics of Microfabrication: Front End Processing, Lecture 8 Transcriptocw.mit.edu
7. Physics of Microfabrication: Front End Processing, Lecture 13 Transcriptocw.mit.edu
8. Module 2: PN Junction (IV), Dynamic Characteristicsarchive.nptel.ac.in
9. Lecture Notes: Compound Semiconductor Devicesocw.mit.edu
10. 007 Lecture 45: Semiconductorsocw.mit.edu
11. Oral-History: Russel S. Ohlethw.org
12. Who Invented the Diode?computerhistory.org