Intrinsic and Extrinsic Semiconductors (N and P type)

Intrinsic Semiconductor

A semiconductor is a material whose electrical conductivity is intermediate between that of a conductor and an insulator. The key characteristic of semiconductors is that their conductivity can be significantly altered by factors like temperature, light, or the addition of impurities. An intrinsic semiconductor is a semiconductor material in its purest form, containing no intentionally added impurities.

Properties of Intrinsic Semiconductors

Common examples of intrinsic semiconductors are Germanium (Ge) and Silicon (Si), which are tetravalent elements (having four valence electrons). In a crystal lattice of silicon or germanium, each atom forms four covalent bonds with its four nearest neighbours.

Diagram illustrating covalent bonds in a silicon crystal lattice

Schematic of covalent bonds in a silicon crystal.

In terms of energy bands:

At absolute zero temperature (0 K), all valence electrons are tightly bound in covalent bonds. The valence band is completely filled, and the conduction band is completely empty. There are no free charge carriers, and the intrinsic semiconductor behaves as an ideal insulator.
As temperature increases, thermal energy causes some covalent bonds to break. Electrons gain enough energy to jump from the valence band to the conduction band, leaving behind vacancies called holes in the valence band.
Both the free electrons in the conduction band and the holes in the valence band act as charge carriers. Electrons move randomly in the conduction band, and holes move randomly in the valence band (due to electrons hopping into adjacent holes).
Under the influence of an external electric field, electrons in the conduction band drift in the opposite direction of the field, and holes in the valence band drift in the direction of the field. This constitutes the electric current.
In an intrinsic semiconductor, the number density of free electrons ($n_e$) in the conduction band is always equal to the number density of holes ($n_h$) in the valence band. This is because each electron that moves to the conduction band leaves behind one hole in the valence band.
$ n_e = n_h = n_i $
Where $n_i$ is the intrinsic carrier concentration, which is highly dependent on temperature.
The conductivity of an intrinsic semiconductor is relatively low at room temperature and increases significantly with increasing temperature due to the thermal generation of electron-hole pairs across the band gap.

The conductivity ($\sigma_i$) of an intrinsic semiconductor can be expressed in terms of intrinsic carrier concentration and mobilities:

$ \sigma_i = n_i e (\mu_e + \mu_h) $

Where $e$ is the magnitude of the elementary charge, $\mu_e$ is the electron mobility, and $\mu_h$ is the hole mobility. Electron mobility is typically greater than hole mobility.

While intrinsic semiconductors provide the fundamental material properties, their conductivity is generally too low and not easily controllable for most electronic applications. For practical devices, the conductivity is tailored by adding specific impurities, leading to extrinsic semiconductors.

Extrinsic Semiconductor

An extrinsic semiconductor is a semiconductor material in which a small amount of a suitable impurity element has been intentionally added to the pure intrinsic semiconductor. This process is called doping. Doping dramatically increases the conductivity of the semiconductor by increasing the number of charge carriers (either electrons or holes) in a controlled manner. The impurity atoms (dopants) are chosen such that they substitute for some of the semiconductor atoms in the crystal lattice.

Doping creates two types of extrinsic semiconductors: N-type and P-type, depending on the type of impurity added.

N-Type Semiconductor (Donor Impurity)

An N-type semiconductor is created by doping a pure intrinsic semiconductor (like Si or Ge, which are tetravalent) with a small amount of a pentavalent impurity. Pentavalent elements (having 5 valence electrons) like Phosphorus (P), Arsenic (As), or Antimony (Sb) are commonly used as dopants. These are called donor impurities because they donate an extra electron to the semiconductor lattice.

Diagram illustrating N-type doping in silicon with a pentavalent impurity

N-type doping: A pentavalent impurity atom provides an extra electron.

When a pentavalent impurity atom replaces a silicon atom in the lattice, four of its valence electrons form covalent bonds with the four surrounding silicon atoms. The fifth valence electron is weakly bound to the impurity atom. The energy level of this fifth electron is very close to the conduction band of the semiconductor ($E_D$, the donor energy level).

Energy band diagram for an N-type semiconductor showing the donor energy level near the conduction band

Energy band diagram for an N-type semiconductor. Donor level $E_D$ is below the conduction band $E_C$.

Even at room temperature, this fifth electron easily gains enough thermal energy to break free from the impurity atom and move into the conduction band, becoming a free electron. The impurity atom itself becomes a positively charged ion (fixed in the lattice).

In an N-type semiconductor, the majority charge carriers are electrons (provided by the donor impurity), and the minority charge carriers are holes (generated intrinsically by breaking covalent bonds due to thermal energy). The electron concentration ($n_e$) is much higher than the hole concentration ($n_h$).

$ n_e \gg n_h $

The number of electrons is approximately equal to the concentration of the donor impurity atoms ($N_D$), provided $N_D \gg n_i$.

The conductivity of an N-type semiconductor is much higher than that of an intrinsic semiconductor due to the large number of free electrons. The name "N-type" comes from the fact that the majority carriers are negative electrons.

P-Type Semiconductor (Acceptor Impurity)

A P-type semiconductor is created by doping a pure intrinsic semiconductor (like Si or Ge, which are tetravalent) with a small amount of a trivalent impurity. Trivalent elements (having 3 valence electrons) like Aluminium (Al), Gallium (Ga), or Indium (In) are commonly used as dopants. These are called acceptor impurities because they accept an electron from the semiconductor lattice, creating a hole.

Diagram illustrating P-type doping in silicon with a trivalent impurity

P-type doping: A trivalent impurity atom creates a missing bond (a hole).

When a trivalent impurity atom replaces a silicon atom, its three valence electrons form covalent bonds with three of the surrounding silicon atoms. The fourth covalent bond with the fourth silicon atom is incomplete, as the impurity atom only has three valence electrons. This deficiency of an electron in a covalent bond is equivalent to a hole. The energy level associated with this incomplete bond (the acceptor energy level, $E_A$) is very close to the valence band of the semiconductor.

Energy band diagram for a P-type semiconductor showing the acceptor energy level near the valence band

Energy band diagram for a P-type semiconductor. Acceptor level $E_A$ is above the valence band $E_V$.

Even at room temperature, electrons from the valence band can gain enough thermal energy to jump into these acceptor levels, effectively completing the incomplete bond around the impurity atom. When an electron fills an acceptor level, it leaves behind a hole in the valence band. The impurity atom becomes a negatively charged ion (fixed in the lattice).

In a P-type semiconductor, the majority charge carriers are holes (created by the acceptor impurity), and the minority charge carriers are electrons (generated intrinsically by breaking covalent bonds). The hole concentration ($n_h$) is much higher than the electron concentration ($n_e$).

$ n_h \gg n_e $

The number of holes is approximately equal to the concentration of the acceptor impurity atoms ($N_A$), provided $N_A \gg n_i$.

The conductivity of a P-type semiconductor is much higher than that of an intrinsic semiconductor due to the large number of holes. The name "P-type" comes from the fact that the majority carriers are positive holes.

Carrier Concentrations in Extrinsic Semiconductors

In both N-type and P-type semiconductors, the product of the electron concentration ($n_e$) and the hole concentration ($n_h$) is approximately constant at a given temperature and equal to the square of the intrinsic carrier concentration ($n_i$). This is known as the mass action law:

$ n_e n_h = n_i^2 $

This law holds true for both intrinsic and extrinsic semiconductors in thermal equilibrium.

In an N-type semiconductor ($n_e \approx N_D$), the hole concentration is $n_h = n_i^2 / n_e \approx n_i^2 / N_D$. Since $N_D \gg n_i$, $n_h \ll n_i$.

In a P-type semiconductor ($n_h \approx N_A$), the electron concentration is $n_e = n_i^2 / n_h \approx n_i^2 / N_A$. Since $N_A \gg n_i$, $n_e \ll n_i$.

Extrinsic semiconductors are the building blocks of most semiconductor devices, allowing for the control of charge carrier type and concentration, which is essential for creating rectifying junctions and amplifying transistors.