Semiconductors

The spectrum from insulators to conductors

The electrical behaviour of a material depends on how strongly its valence (outer-shell) electrons are bound to their atomic cores:

Insulators (e.g., diamond): valence electrons are tightly bound in covalent bonds. Applying a voltage causes slight distortion of the crystal lattice, but no charge flows. Conduction does not occur until the electric field is strong enough to cause breakdown.

Conductors (e.g., copper): valence electrons are loosely bound and free to move through the lattice. A voltage causes charge to flow easily. However, the high free-electron density makes it difficult to control the conductivity, which limits the ability to create active electronic devices.

Semiconductors (e.g., silicon): valence electrons occupy an intermediate binding strength. At low temperatures, pure (intrinsic) silicon is a poor conductor since all electrons are tied up in covalent bonds. As temperature rises, thermal vibrations break bonds, creating free electrons and holes. By carefully adding impurities (doping), we can control the density of charge carriers and create a vast range of electronic devices.

Silicon: atomic structure and intrinsic behaviour

Silicon (Si) is a Group IV element with 4 valence electrons. In the crystalline form, each silicon atom forms covalent bonds with four neighbouring silicon atoms. In each bond, two electrons are shared, giving each Si atom an effective 8 valence electrons in a stable configuration. This is the silicon crystal lattice.

At room temperature, pure (intrinsic) silicon is a semiconductor, i.e., a poor conductor but not an insulator. Thermal vibration occasionally breaks a covalent bond: an electron gains enough energy to escape into the conduction band, leaving behind a hole. Both the free electron (negative charge carrier) and the hole (effectively a positive charge carrier) can move through the crystal:

• Free electrons wander through the lattice.
• Holes move when an electron from an adjacent atom fills the hole, shifting the vacancy. This is mathematically equivalent to a positive charge moving in the opposite direction.

In intrinsic silicon, the concentration of free electrons equals the concentration of holes (n = p = n_i, the intrinsic carrier concentration). At room temperature, n_i is about 1.5 × 10^10 cm^⁻3, which is tiny compared to the atomic density of silicon (about 5 × 10^22 atoms/cm^3). This is why intrinsic silicon is a poor conductor.

Doping: controlling conductivity

The key insight of semiconductor physics: we can dramatically increase conductivity by adding tiny amounts of specific impurities, a process called doping. The doping concentration is typically 1 part in 10^6 to 10^8, yet this increases conductivity by orders of magnitude.

n-type doping

Add a pentavalent impurity (Group V: phosphorus P, arsenic As, antimony Sb) to the silicon lattice. The impurity atom has 5 valence electrons. Four form covalent bonds with neighbouring Si atoms; the fifth electron has no bond partner and is only loosely bound to the donor atom. Very little thermal energy (about 0.05 eV) is needed to free it into the conduction band.

The result: each donor atom contributes one free electron while the donor atom itself becomes a fixed positive ion.

In n-type silicon, electrons are the majority carriers. Holes (minority carriers) are present too, but in much smaller numbers. The donor atoms are called donors because they donate electrons.

p-type doping

Add a trivalent impurity (Group III: boron B, aluminium Al, gallium Ga). The impurity atom has only 3 valence electrons. To complete four covalent bonds, it must accept an electron from a neighbouring Si atom, creating a hole in the silicon lattice.

The impurity atom becomes a fixed negative ion (it has accepted an electron). The hole is free to move through the crystal: an adjacent electron can jump into the hole, leaving a new hole at its original position. The net effect is positive charge carrier mobility.

In p-type silicon, holes are the majority carriers. The trivalent impurity atoms are called acceptors because they accept electrons.

Why doping matters for the MOSFET

The MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) that forms the basis of all modern digital logic is built from alternating regions of n-type and p-type silicon. The transistor’s operation hinges on the ability of the gate electrode’s electric field to attract or repel charge carriers, creating or destroying a conductive channel at the semiconductor surface.

In an n-channel MOSFET (see /modules/digital-electronics/12-transistors-and-cmos-logic/01-mosfet-operation/): a p-type substrate has two n-type regions (source and drain). With no gate voltage, no current flows; the two n-type regions are isolated by the p-type substrate (two back-to-back p-n junctions). When the gate voltage exceeds the threshold, electrons are attracted to the surface of the p-type region under the gate, inverting it to n-type and forming a conductive channel between source and drain.

The semiconductor physics is the underlying reason; for the Tripos, you do not need detailed band-diagram analysis. You need the conceptual model: doping creates n-type (electron-rich) and p-type (hole-rich) regions, and the MOSFET gate can create or destroy a channel by attracting or repelling charge carriers.

See also /modules/digital-electronics/11-electronics-fundamentals/05-p-n-junction-and-diodes/ for what happens when p-type and n-type silicon meet.