Semiconductor Theory: Definition & Fundamentals

Band structure helps explain why materials conduct differently. In an undoped semiconductor at 0 K, the valence band is full and the conduction band is empty. Thermal energy or light can excite an electron across the forbidden energy gap into the conduction band. The excited electron and the hole left in the valence band can both carry current.

A wider band gap requires more energy to create mobile electron-hole pairs. Conductors have a partly filled band or overlapping bands, so nearby empty states are available to electrons. Silver, copper and aluminium are familiar examples. Insulators have a much larger gap and very few mobile carriers under ordinary conditions.

Mica and ceramic are common insulators. Their low carrier concentration makes them poor conductors at normal electric fields. Semiconductors have electrical properties that can be controlled through temperature, light, electric fields and deliberately added impurities.

A band gap near 1 eV is a useful introductory rule of thumb, not a definition. At 300 K, representative values include about 0.67 eV for germanium, 1.14 eV for silicon and 1.43 eV for gallium arsenide. Other semiconductor compounds have narrower or wider gaps.

In an intrinsic semiconductor, increasing temperature generates more electron-hole pairs. This carrier increase usually raises conductivity even though carrier mobility can fall as lattice scattering increases. Doped semiconductors show additional temperature regions, including dopant freeze-out and eventual intrinsic behaviour. Silicon and germanium are common elemental semiconductors.

Definition of Semiconductor

A practical definition of semiconductor is a material whose charge-carrier concentration and conductivity can be controlled by factors such as doping, temperature, light or an electric field.

The boxed statement is a useful introductory shortcut, but the 1 eV value is not a strict boundary. Silicon (Si) is the dominant commercial semiconductor, while germanium (Ge) remains important in specialised devices and compound-semiconductor systems. Their band gaps do change with temperature, so device models use temperature-dependent material parameters.

The following expressions approximate the relation between band gap and absolute temperature for Si and Ge over their intended model ranges.

Here, T is absolute temperature in K.
For a nominal room temperature of 300 K, the expressions give the following values.

At room temperature, the resistivity of an undoped semiconductor lies between that of a good conductor and a good insulator. For intrinsic material, thermal generation often makes resistance fall as temperature rises. The behaviour of a doped device can be more complex because carrier concentration and mobility both vary with temperature. Si and Ge are group 14 elements with four valence electrons, and each forms covalent bonds with a neighbouring atom. In the ideal intrinsic model at absolute zero, the valence band is full and the conduction band is empty. Higher temperature excites some electrons into the conduction band and leaves mobile holes behind.

In these energy-band diagrams, CB denotes the conduction band and VB denotes the valence band. At 0 K, VB is full in the ideal intrinsic model.

Intrinsic Semiconductors

In theory of semiconductor, material without intentional dopants is an intrinsic semiconductor. At thermal equilibrium, each excited conduction electron leaves one valence-band hole, so the electron concentration n equals the hole concentration p. We write n = p = n_i, where n_i is the intrinsic carrier concentration. A common approximation for n_i is shown below.
Here, n₀ represents a material-dependent prefactor, T is absolute temperature, V_G is band-gap energy expressed as an equivalent voltage and V_T is thermal voltage.
The thermal voltage follows V_T = kT/q.
Here, k is the Boltzmann constant, approximately 1.381 × 10 ^{− 23} J/K.
In intrinsic semiconductors, both electrons (σ_e) and holes (σ_h) contribute to conductivity.
σ_e = neμ_e and σ_h = peμ_h.
Total conductivity is shown below.
Here, n and p are electron and hole concentrations.
μ_h and μ_e are hole and electron mobilities.
For intrinsic material, N = n = p.
The symbol e denotes the magnitude of carrier charge.

Extrinsic Semiconductors

In theory of semiconductor, a deliberately doped material is an extrinsic semiconductors. An Extrinsic semiconductor contains a controlled concentration of donor or acceptor atoms. The dopant type produces N-type or P-type semiconductors. The required concentration depends on the material, device and target electrical properties; it is not one fixed impurity ratio.

N type Semiconductor

In this material, electrons are the majority carriers and holes are the minority carriers. An N – type semiconductor can be formed by adding a group 15 donor, such as phosphorus (P), arsenic (As) or antimony (Sb), to a silicon crystal.

Four of the donor’s five valence electrons form covalent bonds with neighbouring Si atoms. The remaining electron is weakly bound and can enter the conduction band. The donor therefore raises electron concentration and conductivity. When the hole contribution is negligible, the approximation is
σ ≈ neμ_e

P type Semiconductors

In this material, holes are the majority carriers and electrons are the minority carriers. A p-type semiconductor can be formed by adding a group 13 acceptor with three valence electrons, such as boron (B), aluminium (Al) or gallium (Ga), to silicon.

The acceptor uses its three valence electrons in covalent bonds but leaves one bond incomplete. A neighbouring valence electron can fill that state, leaving a hole elsewhere in the valence band. Repeated electron movement makes the hole behave as a mobile positive carrier. The dopant is called an acceptor because it accepts an electron. When the electron contribution is negligible, the approximation is
σ ≈ peμ_h