9.1 Semiconductor materials and properties

Semiconductors are materials whose electrical conductivity falls between that of conductors and insulators. Understanding their properties is essential because nearly every modern electronic device relies on how semiconductors behave at the atomic level.

This guide covers semiconductor composition and crystal structure, energy bands and the band gap, intrinsic vs. extrinsic semiconductors, and how temperature affects conductivity.

Semiconductor Materials

Composition and Structure

Semiconductors don't conduct as well as metals, but they're far more conductive than insulators like ceramics. What makes them special is that you can control their conductivity, which is why they're the backbone of modern electronics.

Silicon is by far the most commonly used semiconductor material. It's abundant, relatively cheap, and forms a stable oxide layer ($SiO_2$) that's useful for fabricating devices. Germanium was used in early semiconductor devices but has been largely replaced by silicon. Germanium does have a smaller band gap and higher electron mobility, which still makes it useful in certain niche applications.

At the atomic level, semiconductor materials form a crystal structure, typically arranged in a diamond cubic lattice. Each atom is covalently bonded to four neighboring atoms, creating a regular, repeating 3D pattern. This orderly arrangement is what gives rise to the energy band structure discussed next.

Energy Bands and Band Gap

Electronic Structure

In an isolated atom, electrons occupy discrete energy levels. When billions of atoms pack together in a crystal, those discrete levels spread out into continuous ranges called energy bands. Two bands matter most:

• Valence band: The highest energy band that's fully occupied at absolute zero. These are the electrons involved in covalent bonding between atoms.
• Conduction band: The lowest energy band that's unoccupied at absolute zero. Electrons that reach this band are free to move through the material and carry current.

The band gap ($E_g$) is the energy difference between the top of the valence band and the bottom of the conduction band. This single value largely determines whether a material behaves as a conductor, semiconductor, or insulator:

• Conductors (metals): Band gap is essentially zero; the valence and conduction bands overlap.
• Semiconductors: Band gap is moderate, typically 0.5 to 3 eV. Silicon's band gap is about 1.12 eV at room temperature.
• Insulators: Band gap is large (greater than ~4 eV), so very few electrons can jump across.

Electron Excitation and Conduction

At absolute zero (0 K), the valence band is completely filled and the conduction band is empty. No free charge carriers exist, so no conduction occurs.

As temperature rises, some electrons gain enough thermal energy to jump across the band gap into the conduction band. Each electron that jumps leaves behind a vacancy in the valence band called a hole. Holes behave as positive charge carriers because neighboring electrons can shift into the vacancy, effectively moving the hole through the lattice.

Both electrons in the conduction band and holes in the valence band contribute to electrical current. The key relationship: a smaller band gap and a higher temperature both mean more electrons get excited, which means higher conductivity.

Semiconductor Types and Properties

Intrinsic Semiconductors

An intrinsic semiconductor is a pure semiconductor with no intentional impurities. Pure silicon and pure germanium are the standard examples.

In an intrinsic semiconductor, the only source of charge carriers is thermal excitation. Every electron that jumps to the conduction band creates exactly one hole, so the electron concentration always equals the hole concentration. This is written as:

$n = p = n_i$

where $n$ is the electron concentration, $p$ is the hole concentration, and $n_i$ is the intrinsic carrier concentration. For silicon at room temperature, $n_i$ is approximately $1.5 \times 10^{10}$ carriers per $cm^3$.

Because the carrier concentration is so low, intrinsic semiconductors have very low conductivity, typically in the range of $10^{-8}$ to $10^{-6}$ S/cm at room temperature. That's not useful for most devices on its own, which is why doping exists.

Extrinsic Semiconductors

Extrinsic semiconductors are created by intentionally adding small amounts of impurity atoms, a process called doping. Doping dramatically increases the number of charge carriers and gives you control over whether those carriers are mostly electrons or mostly holes.

N-type doping uses donor impurities from Group V of the periodic table (like phosphorus or arsenic). These atoms have five valence electrons. Four of them form covalent bonds with neighboring silicon atoms, and the fifth is loosely bound. At room temperature, that extra electron easily breaks free into the conduction band. The result: electrons are the majority carriers, and holes are the minority carriers.

P-type doping uses acceptor impurities from Group III (like boron or gallium). These atoms have only three valence electrons, so one covalent bond is incomplete. This missing electron acts as a hole that can accept an electron from a neighboring bond. The result: holes are the majority carriers, and electrons are the minority carriers.

Doping increases conductivity enormously. Extrinsic semiconductors typically have conductivities in the range of $10^{-3}$ to $10^{3}$ S/cm, depending on the doping concentration. Even a tiny amount of dopant (on the order of 1 impurity atom per million silicon atoms) can increase conductivity by several orders of magnitude.

Temperature Dependence

The electrical conductivity of semiconductors has a strong temperature dependence, and it behaves opposite to metals. In metals, conductivity decreases as temperature rises (because lattice vibrations scatter electrons). In semiconductors, conductivity increases with temperature because more electrons gain enough energy to cross the band gap.

This relationship follows an exponential pattern described by:

$\sigma = \sigma_0 \exp\left(\frac{-E_a}{kT}\right)$

where:

• $\sigma$ is the electrical conductivity
• $\sigma_0$ is a material-dependent constant
• $E_a$ is the activation energy (related to the band gap; for intrinsic semiconductors, $E_a \approx E_g / 2$)
• $k$ is the Boltzmann constant ($8.617 \times 10^{-5}$ eV/K)
• $T$ is the absolute temperature in Kelvin

The exponential term means that even small temperature changes can significantly alter conductivity. This property is exploited in practical devices like thermistors (temperature-sensitive resistors used in sensors) and thermal imaging devices that detect infrared radiation based on temperature-induced conductivity changes.

One thing to watch for: at very high temperatures in extrinsic semiconductors, thermal generation of carriers can overwhelm the doped carrier concentration, and the material starts behaving more like an intrinsic semiconductor. This is called the intrinsic region of operation, and it sets an upper temperature limit for semiconductor devices.